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1808 | 1808.03680_arXiv.txt | The results on ultra-high-energy cosmic rays (UHECR) mass composition obtained with the Telescope Array surface detector are presented. The analysis employs the boosted decision tree (BDT) multivariate analysis built upon 14 observables related to both the properties of the shower front and the lateral distribution function. The multivariate classifier is trained with Monte-Carlo sets of events induced by the primary protons and iron. An average atomic mass of UHECR is presented for energies $10^{18.0}-10^{20.0}\ \mbox{eV}$. The average atomic mass of primary particles shows no significant energy dependence and corresponds to $\langle \ln A \rangle = 2.0 \pm 0.1 (stat.) \pm 0.44 (syst.)$. The result is compared to the mass composition obtained by the Telescope Array with \xmax\ technique along with the results of other experiments. Possible systematic errors of the method are discussed. | \label{sec:intro} The Telescope Array (TA) experiment is the largest ultra-high-energy (UHE) cosmic-ray experiment in the Northern hemisphere, located near Delta, Utah, USA \cite{Tokuno}. TA is designed to register the extensive air showers (EAS) caused by the UHE cosmic rays entering the atmosphere. The experiment operates in hybrid mode and performs simultaneous measurements of the particle density and timing at the ground level with the surface detector array (SD)~\cite{TASD} and the fluorescence light with 38 fluorescence telescopes grouped into three fluorescence detector stations~\cite{Tokuno2}. The SD is an array of 507 plastic scintillator detectors arranged on a square grid with 1.2 km spacing covering an area of approximately 700 ${\mbox{km}}^2$. Each detector is composed of two layers of 1.2 cm thick extruded scintillator of the $3\ {\mbox{m}}^2$ effective area. There is a continuous progress of the experimental techniques, which started since the discovery of the cosmic rays more than a century ago. Recently, the results of three independent experiments confirmed the cut-off in the highest energy part~\cite{HiresGZK,AugerGZK,TAGZK} of the cosmic ray energy spectrum. The latter was predicted in 1966 by Greisen, Zatsepin and Kuzmin~\cite{g,zk}. Still, the origin of the UHE cosmic rays remains unidentified. The mass composition of the UHE cosmic rays at Earth is one of the measurable quantities directly connected to the cosmic-ray acceleration mechanism in the source and source population as well as it is related to the propagation of the UHECR. Moreover, the mass composition is the main source of uncertainty in the expected cosmogenic photon and neutrino fluxes~\cite{Gelmini:2005wu,Aloisio:2015ega}. In the wider scope, one needs the mass composition for precision tests of the Lorentz-invariance~\cite{Saveliev} and to ensure the safety of the future 100~TeV colliders. The latter is based on the constraints on the black hole production derived from the stability of dense astrophysical objects, such as white dwarfs and neutron stars, which interact with the cosmic rays. Black hole production rate depends on the the energy per nucleon and thus on the mass composition of the UHECR~\cite{Sokolov:2016lba}. The most established method for the UHECR composition analysis is based on the measurements of the longitudinal shape of the EAS with the fluorescence telescope. This method uses the depth of the shower maximum \xmax\ as a composition-sensitive observable~\cite{Gaisser:1993ix}. There are UHE composition results available based on \xmax\ measured by the three experiments: HiRes, Pierre Auger Observatory and Telescope Array~\cite{Abbasi2,Aab:2014aea,Hanlon}. The two latter results are compatible within the systematic errors in \xmax\ measurement which are of the order of $10-20~\mbox{g}/\mbox{cm}^2$ in the energy range up to $10^{19}~\mbox{eV}$~\cite{TA_AUGER_Composition_WG}. This Paper is dedicated to an alternative approach to measure the mass composition. The method uses solely the data of the surface detector which has an undoubted advantage of the longer than $95\%$ duty cycle~\cite{TASD}. Still, there is no single observable known that has a comparable to \xmax\ sensitivity to the mass composition, although measurements based on the risetime~\cite{Aab:2016enk,Aab:2017cgk} have come close. In this Paper we use the multivariate boosted decision tree (BDT)~\cite{Breiman,Schapire} technique based on a number of composition-sensitive variables obtained during the reconstruction of the SD events. The BDT method has proved itself reliable with a number of successful applications for the astroparticle physics experiments, see e.g.~\cite{Krause,Aab,Abbasi}. The general scheme of the analysis is the following. The proton-induced and iron-induced Monte-Carlo events are simulated using the real-time calibration of the Telescope Array. The Monte-Carlo events are stored in the same format as the SD data and are split into three parts used in the following stages. First, a BDT classifier is trained using the first part of the proton-induced Monte-Carlo (MC) events as a background and iron-induced events as signal. Second, the distribution of the classifier output $\xi$ for data is compared to the second part of the proton and iron-induced MC events. The comparison results in the average atomic mass $\langle \ln A \rangle$ of the primary particle as a function of energy. Finally, the third part of the MC is used to estimate the bias of the method and to introduce a correction to $\langle \ln A \rangle$ in order to compensate it. The Paper is organized as follows: in the Section~\ref{sec:data} data and Monte-Carlo sets are described. Section~\ref{sec:method} is dedicated to multivariate analysis method and its implementation to mass determination. Finally, results and discussion of the systematic uncertainties are provided in Section~\ref{sec:results}. | \label{sec:results} \subsection{Estimation of the systematic error} \label{subsec:validation} \begin{figure} \includegraphics[width=0.95\columnwidth]{sd_logA_p_Fe_He_N} \caption{$\langle \ln A \rangle$ approximated with a straight line for proton (red), helium (green), nitrogen (purple) and iron (blue) Monte-Carlo sets. Error bars for each $\langle \ln A \rangle$ point represent the statistical uncertainty of the method.} \label{rails} \end{figure} \begin{figure} \includegraphics[width=0.95\columnwidth]{sd_logA_nc_c} \caption{Uncorrected $\langle \ln A \rangle^{(1)}$ in comparison with $\langle \ln A \rangle_{non-linear}$ corrected by non-linear function in each energy bin; statistical error is shown with error bars and systematic error as estimated in Section~\ref{subsec:validation} is shown with brackets of the corresponding color. Numbers represent the number of data events in the corresponding energy bin.} \label{nonlinearcorr} \end{figure} \begin{figure} \includegraphics[width=0.95\columnwidth]{sd_logA_p_c_qgsjet03-04} \caption{$\langle \ln A \rangle$ approximated with a straight line for proton (red) and iron (blue) Monte-Carlo sets created with QGSJETII-03 hadronic interaction set and for proton MC set, created with QGSJETII-04 (orange line). Error bars for each $\langle \ln A \rangle$ point represent the statistical bias of the method.} \label{qgsjet04} \end{figure} \begin{figure} \includegraphics[width=0.95\columnwidth]{delta_lnA_had} \caption{Hadronic model dependency error of the method as a function of energy, based on a comparison with QGSJETII-04 hadronic interaction model.} \label{deltalnAhad} \end{figure} \begin{figure*} \includegraphics[width=0.65\linewidth]{sd_logA_compareTAMD.pdf} \caption{Average atomic mass $\langle \ln A \rangle$ in comparison with the Telescope Array hybrid results \cite{Hanlon}; statistical error is shown with error bars, systematic error is shown with brackets.} \label{Hybrid} \end{figure*} \begin{figure} \includegraphics[width=0.95\columnwidth]{sd_logA_compareAu.pdf} \caption{Average atomic mass $\langle \ln A \rangle$ in comparison with the Pierre Auger Observatory $X^{\mu}_{MAX}$ and risetime asymmetry results \cite{Aab:2016enk,PierreAuger}; statistical error is shown with error bars, systematic error is shown with brackets.} \label{Auger} \end{figure} \begin{figure} \includegraphics[width=0.95\columnwidth]{sd_logA_compareH_Yakutsk.pdf} \caption{Average atomic mass $\langle \ln A \rangle$ in comparison with the HiRes stereo results \cite{Abbasi2} and with the Yakutsk $\rho_{\mu}$ results \cite{Dedenko}; statistical error is shown with error bars, systematic error is shown with brackets.} \label{HiRes} \end{figure} The non-linear correction applied for the method is based on the assumption that the obtained composition is monotype. Thus the main source for the systematic error of the method is the inability to distinguish the mixture of a given elements and the single-type-particle composition. To derive the systematic uncertainty, in each energy bin 100 mixtures of $p$, $He$, $N$ and $Fe$ Monte-Carlo sets were created, among which 50 mixtures are random monotype, 25 are random two-component and 25 are random four-component. Its $\langle \ln A \rangle$ values were estimated with the use of \url{TFractionFitter} template fitting method and non-linear bias corrections applied and compared with the ``true'' values calculated from the known fractions. Mean systematic error is estimated as: \begin{equation}\label{systmixed} \delta \ln A_{syst.} = 0.44 \end{equation} \subsection{Hadronic models dependency} \label{subsec:hadmodels} \todo{add models} Composition results, both derived from surface detectors and in a hybrid mode, have a strong dependence on hadronic models used during Monte-Carlo simulations. Besides the one used in the above analysis, QGSJETII-04~\cite{Ostapchenko:2010vb}, an improvement of QGSJETII-03 model, EPOS-LHC~\cite{Pierog} and SYBILL~\cite{Fletcher} models are also widely used. All of the hadronic interaction models are based on the collider data and extrapolated to the UHECR energies. The analysis by the Pierre Auger Observatory has shown the inconsistency between muon signal predicted by simulations and data~\cite{Aab:2016hkv}. The same conclusions were also made based on the Telescope Array SD data~\cite{Takeishi}. This discrepancy may be the source of additional systematic bias which may affect the observables used for the composition study. We study the systematic error introduced by the limited knowledge of the hadronic interaction models based on the comparison of the two models: QGSJETII-03 and QGSJETII-04~\cite{Ostapchenko:2010vb}. For the latter, an additional proton Monte-Carlo set with the use of QGSJETII-04 model is simulated. The set is subjected to the same multivariate analysis procedure trained with the original QGSJETII-03 Monte-Carlo. The result is shown in the Fig.~\ref{qgsjet04}, while the hadronic model uncertainty as a function of energy is shown in Fig.~\ref{deltalnAhad}. The uncertainty from hadronic interaction models is minimal at $10^{18.5}\ \mbox{eV}$ with $\delta \ln A_{hadr.} = 0.23$ and maximal at $10^{19.75}\ \mbox{eV}$ with $\delta \ln A_{hadr.} = 0.74$. \subsection{Composition} \label{subsec:composition} Mean logarithm of atomic mass as a function of energy without bias corrections and with the linear corrections applied is shown in Fig.~\ref{nonlinearcorr}. Within the errors, the average atomic mass of primary particles shows no significant energy dependence and corresponds to $\langle \ln A \rangle = 2.0 \pm 0.1 (stat.) \pm 0.44 (syst.)$. TA SD composition results in comparison with TA hybrid results are shown in Fig. \ref{Hybrid}. Comparisons with Pierre Auger Observatory SD $X^{\mu}_{MAX}$ based on muon density and muon arrival times and azimuthal risetime asymmetry, HiRes stereo \xmax\ and Yakutsk muon detector results are shown in Fig. \ref{Auger} and \ref{HiRes}, respectively. We mention that while there exist composition results based on the Pierre Auger Observatory hybrid observations~\cite{Aab:2017njo}, we focus only on the comparison with the corresponding surface detector results. The obtained composition is qualitatively consistent with the TA hybrid and the Pierre Auger Observatory results, while all the points lie higher than the pure proton composition observed by HiRes and Yakutsk. | 18 | 8 | 1808.03680 |
1808 | 1808.04775_arXiv.txt | We report on the X-ray spectral analysis and time evolution of GRS 1739$-$278 during its 2014 outburst based on MAXI/GSC and Swift/XRT observations. Over the course of the outburst, a transition from the low/hard state to the high/soft state and then back to the low/hard state was seen. During the high/soft state, the innermost disk temperature mildly decreased, while the innermost radius estimated with the multi-color disk model remained constant at $\sim18\ (\frac{D}{8.5\ \mathrm{kpc}}) \ {(\frac{\cos i}{\cos 30^{\circ}})}^{-1/2}$ km, where $D$ is the source distance and $i$ is the inclination of observation. This small innermost radius of the accretion disk suggests that the central object is more likely to be a Kerr black hole rather than a Schwardzschild black hole. Applying a relativistic disk emission model to the high/soft state spectra, a mass upper limit of $18.3\ \mathrm{M_{\odot}}$ was obtained based on the inclination limit $i<60^{\circ}$ for an assumed distance of 8.5 kpc. Using the empirical relation of the transition luminosity to the Eddington limit, the mass is constrained to $4.0-18.3\ \mathrm{M_{\odot}}$ for the same distance. The mass can be further constrained to be no larger than $9.5\ \mathrm{M_{\odot}}$ by adopting the constraints based on the fits to the NuSTAR spectra with relativistically blurred disk reflection models (Miller et al.\ 2015). | X-ray fluxes of black hole candidates (BHCs) at their outbursts exceed their quiescent levels by many orders of magnitude. Many BHCs exhibit state transitions, associated with changes in their X-ray fluxes during their outbursts. The presence of two different ``states" (low/hard state and high/soft state) in the X-ray emissions of the first BHC, Cyg X-1, was discovered in the early 1970s (Tananbaum et al.\ 1972). Since then, more BHCs (e.g. GX 399$-$4, GS 2000+251; Markert et al. 1973, Tsunemi et al. 1989) have been observed to exhibit one or both of these states. Analyzing state transitions of a BHC can help us learn more about the physics of black hole accretion flows over a wide range of mass accretion rate (Remillard \& McClintock\ 2006). Furthermore, important characteristics about the BHC such as the black hole mass can be extracted assuming that the inner disk radius obtained in high/soft state reaches at the innermost stable orbit (Nakahira et al.\ 2012). In previous studies, light curves, hardness intensity diagrams (HID: a plot of X-ray intensity versus X-ray hardness showing evolutionary track(s); Fender et al.\ 2004), and photon spectra are frequently used to understand the nature of black hole binaries. Moreover, analysis of three interacting spectral components, thermal blackbody-like component, hard power-law component, and reflection component, can provide constraints on the source properties including the spin parameter and geometry. Estimates of the spin parameter were principally obtained by modeling the thermal continuum emission of the accretion disk (e.g. Zhang et al. 1997; McClintock et al. 2014), or relativistically-broadened reflection spectrum (e.g. Fabian et al. 1989; Reynolds 2014). Meanwhile, a reflection spectrum reveals information about the scales of inner disk and corona. (Steiner et al.\ 2016). GRS 1739$-$278 was first discovered in the direction of the Galactic Center with the SIGMA telescope onboard GRANAT (Paul. et al.\ 1996; Vargas et al.\ 1997). Its position close to the Galactic Center at $6-8.5$ was indicated by dust scattering halo in X-ray (Greiner et al.\ 1996). The new source was verified by the detection of a strong radio emission during its 1996 outburst (Hjellming et al.\ 1996). The distance, 8.5 kpc, is preferred according to the study of its candidate optical and infrared counterpart (Marti et al.\ 1997). Later, Borozdin et al.\ (1998) classified GRS 1739$-$278 as a BHC through the spectral analysis of RXTE data, in which a 5-Hz quasi periodic oscillation (QPO) was discovered (Borozdin \& Trodolyubov 2000; Wijnands et al.\ 2001). Following an extended quiescent period, GRS 1739$-$278 was detected in outburst with Swift Burst Alert Telescope in March 2014 (Krimm et al.\ 2014) and by INTEGRAL (Filippova et al.\ 2014). After this event, Miller et al.\ (2015) presented the spectral analysis of the NuSTAR observation, and gave a constraint on the innermost radius, $r_{\mathrm{in}}=5^{+3}_{-4}\ \mathrm{GM/c^2}$ as well as a spin constraint, $a=0.8\pm0.2$ during the raising part of the ``low/hard" state. F\"urst et al.\ (2016) also reported on a spectral analysis of the NuSTAR data at the very faint ``low/hard" state near the end of the outburst. Mereminskiy et al.\ (2017) analyzed the latest outburst of GRS 1739$-$278 in September 2016 using INTEGRAL and Swift/XRT observations and derived a hydrogen column density $N_\mathrm{H}$ as $2.3\times10^{22}\mathrm{\ cm^{-2}}$ from spectral fitting. In this paper we report on the spectral analysis of GRS 1739$-$278 using the Swift/XRT and MAXI/GSC data and describe the time evolution of its X-ray properties during the 2014 outburst. We show a mass constraint of the central object based on the spectral fittings during the high/soft state. We then compare the calculated bolometric luminosities to the Eddington Luminosity at various phases of the outburst. | Based on the Swift/XRT and MAXI/GSC observations, we analysed time evolutions of the intensities and spectra of the BHC, GRS 1739$-$278, during its 2014 outburst. We find that the outburst can be divided into four phases based on spectral analyses: (1) The low/hard state (MJD 56736$-$MJD 56746); (2) The intermediate state during the transition from the low/hard state to the high/soft state (MJD 56746$-$MJD 56870); (3) The high/soft state (MJD 56870$-$MJD 56966); (4) The transition from the high/soft state to the low/hard state (MJD 56966$-$MJD 56994). As commonly seen in most BHCs, the innermost radius of GRS 1739$-$278 remained constant in the high/soft state. Our analysis supports that GRS 1739$-$278 is not likely to be a non-spinning black hole but rather a spinning black hole. Assuming that $a\leq1, i\leq60^{\circ}$, in combination with the previously known constraint on distance of $6-8.5$ kpc and the two conditions on the observational luminosities -- the transition from the hight/soft state to the low/hard occurs at $1\% -4\%$ of $L_{Edd}$, the Eddington luminosity, and the maximum luminosity should not exceed $L_{Edd}$, we constrained the mass of central object to be $2.0-18.3\ \mathrm{M_{\odot}}$ by applying \texttt{kerrbb} model to the spectra in the high/soft state. A narrower constraint was obtained when using the spin parameters and inclinations from NuSTAR's fitting results with the relativistically blurred disk reflection models (Miller et al. 2015). In order to improve our estimate of black hole mass, we need more accurate distance, inclination, and spin parameter that may require independent observations such as imaging superluminal jets, measurement of companion radial velocity as well as better understandings of X-ray spectra. This work is based on the data provided by Swift team and the MAXI team . Authors are grateful for the support obtained. M. S. acknowledges support by the Special Postdoctoral Researchers Program at RIKEN, and by a Great-in-Add for JSPS Young Scientist (B) 16K17672. N. K. acknowledges support by MEXT KAKENHI Grant Number JP 17H06362. | 18 | 8 | 1808.04775 |
1808 | 1808.04296_arXiv.txt | {The occurrence of active galactic nuclei (AGN) is critical to our understanding of galaxy evolution and formation. Radio observations provide a crucial, dust-independent tool to study the role of AGN. However, conventional radio surveys of deep fields ordinarily have arc-second scale resolutions often insufficient to reliably separate radio emission in distant galaxies originating from star-formation and AGN-related activity. Very long baseline interferometry (VLBI) can offer a solution by identifying only the most compact radio emitting regions in galaxies at cosmological distances where the high brightness temperatures (in excess of $10^5$ K) can only be reliably attributed to AGN activity.} % {We present the first in a series of papers exploring the faint compact radio population using a new wide-field VLBI survey of the GOODS-N field. This will expand upon previous surveys, permitting the characterisation of the faint, compact radio source population in the GOODS-N field. The unparalleled sensitivity of the European VLBI Network (EVN) will probe a luminosity range rarely seen in deep wide-field VLBI observations, thus providing insights into the role of AGN to radio luminosities of the order $10^{22}~\mathrm{W\,Hz^{-1}}$ across cosmic time.} {The newest VLBI techniques are used to completely cover an entire 7.\!\arcmin5 radius area to milliarcsecond resolutions, while bright radio sources ($S > 0.1$\,mJy) are targeted up to 25\arcmin~from the pointing centre. Multi-source self-calibration, and a primary beam model for the EVN array are used to correct for residual phase errors and primary beam attenuation respectively.} {This paper presents the largest catalogue of VLBI detected sources in GOODS-N comprising of 31 compact radio sources across a redshift range of 0.11\mbox{-}3.44, almost three times more than previous VLBI surveys in this field. We provide a machine-readable catalogue and introduce the radio properties of the detected sources using complementary data from the e-MERLIN Galaxy Evolution survey (eMERGE).} {} | \label{Sec: Introduction} Radio source counts above mJy flux densities are dominated by radio galaxies and quasars powered by active galactic nuclei (AGN). Below mJy flux densities, there is an observed upturn far in excess of those predicted by extrapolating source counts of high luminosity radio galaxies and quasars. This upturn is found to comprise an increasing fraction of active star forming galaxies and faint ‘non-jetted’ or radio-quiet AGN plus a decreasing fraction of classical radio-loud sources \citep[see][and references therein]{prandoni2001,Huynh2015,Padovani2016}. The majority of extragalactic radio surveys are carried out at arc-second resolutions (corresponding to galactic/$\sim$10's kpc physical scales at $z\geq0.1$) where it can be difficult to distinguish between the sub-kpc scale AGN activity and the kpc star-formation related emission based purely on their radio morphologies. This is particularly important if we are to characterise the properties of radio-quiet AGN whose radio emission in local systems are confined within the host galaxy \citep[see][and references therein]{Orienti:2015sk}. As a result, these surveys rely on multi-wavelength diagnostics, such as radio-excess, SED fitting, X-ray emission etc., in order to identify any AGN activity \citep[e.g.][]{Bonzini2013:cd,Smolcic:2017ef}. These diagnostics are often incomplete with dust masking the signatures of AGN activity. For example, X-rays often do not detect Compton-thick AGN which are estimated to account for over a third of the total AGN population \citep[][]{Mateos:2017fm}. These hidden AGN can be found using high resolution, dust-independent radio observations. Indeed, surveys using e-MERLIN, such as the \textbf{e-MER}lin \textbf{G}alaxy \textbf{E}volution (e-MERGE) survey (Muxlow et al. in prep., \citet{muxlow2005high}), and Very Long Baseline Interferometry (VLBI) \citep[e.g.][]{Middelberg:2011bx,Middelberg:2013hy,Ruiz:2017ur} have shown that deep, sub-arcsecond and sub-kpc observations can effectively isolate AGN activity from compact star-forming related emission in distant galaxies. VLBI observations detect bright, compact objects with brightness temperatures in excess of $10^{5}$\,K. In nearby galaxies, these brightness temperatures can be typically reached by either AGN, supernovae (SNe) and their remnants (SNRs). However, in more distant galaxies ($z > 0.1$), these brightness temperatures can typically only be attained by AGN-related emission processes \citep[e.g.][]{kewley2000compact}, thus making VLBI a unique and invaluable tool to survey distant galaxies for AGN activity. However, until the last decade, there have been many factors preventing VLBI from being used as a survey instrument. Conventional wide-field VLBI observations mapped a significant proportion of the primary beam by using a single correlation pass at a ultra-fine temporal and frequency resolution in order to limit time and bandwidth smearing towards the edge of the primary beam \citep{garrett2001agn}. As a result, the observer would receive a single large and unwieldy (often $\sim$TB size) data set. With the ever increasing number of VLBI-ready telescopes along with widening bandwidths, the bit rates of modern VLBI arrays are rapidly increasing and this method of correlation has become computationally infeasible. Software correlators established the `multiple simultaneous phase centre observing' approach to correlation \citep{deller2011difx,MorganVLBI2011,keimpema2015sfxc} which substantially reduces the computational load. Here, the observer defines a number of sub-fields (also referred to as phase centres) which can be either sources of interest or can be arranged to cover the entire primary beam. When correlated, these data are split and each sub-section is correlated at the ultra high temporal and frequency resolution required to restrain smearing. It is then copied and phase shifted to the various sub-fields of interest and averaged to a small field-of-view (typically 30-60\arcsec). The result is a small ($\sim$GB) dataset per sub-field which is easily manageable and parallelisable when calibrating and imaging. By combining multi-phase centre correlation with advanced calibration techniques such as in-beam phase referencing \citep{garrett2001agn,Garrett:2005fj,LencVLBI2008} and multi-source self-calibration \citep{Middelberg:2013hy,radcliffeMSSC2016}, wide-field VLBI surveys of milliarcsecond scale extragalactic radio sources to $\mu$Jy flux densities have become increasing feasible \citep[e.g.][]{,Middelberg:2011bx,Middelberg:2013hy,chi2013deep,Morgan2013M31,CaoVLBI2014,deller2014mjive,2015MNRAS.452...32R,Ruiz:2017ur}. We here present a new wide-field VLBI survey targeting the well studied Great Observatories Origin Deep survey North (GOODS-N) field using the European VLBI Network (EVN). The GOODS-N field covers 160 arcmin$^2$ with complementary deep multi-wavelength data including \textit{Chandra}, \textit{Spitzer}, \textit{Herschel}, UBVRIJHK photometry and spectroscopy. Previous wide-field VLBI observations targeted the Hubble Deep Field (HDF) and Flanking Fields (HFF) for which the GOODS-N field encompasses. \citet{garrett2001agn} used the EVN to target MERLIN sources within a 3.5\arcmin~ radius from the EVN pointing centre to r.m.s. sensitivities of 33\,$\rm\mu Jy\,beam^{-1}$. This resulted in the detection of 3 sources. These observations were substantially expanded upon by \citet{chi2013deep} who used Global VLBI to target the 92 VLA-MERLIN sources of \citet{muxlow2005high} within a $10\arcmin \times 10\arcmin$ field to r.m.s. sensitivities of 7.3\,$\rm\mu Jy\,beam^{-1}$. This resulted in 12 compact radio source detections (including the 3 detected by \citet{garrett2001agn}) thus beginning the characterisation of the faint compact radio population in GOODS-N. However, these surveys were invariably limited because computational limitations prevented imaging of the entire primary beam at that time. Our survey aims to substantially expand upon this sample, encompassing and surpassing the field-of-view and sensitivities of previous VLBI surveys in GOODS-N by targeting sources within a $30\arcmin\times30\arcmin$ area to $1\sigma$ central sensitivity of $\sim 2\mbox{-}3~{\rm \mu Jy\,beam^{-1}}$ with the completion of this survey. In this paper, we present our initial catalogue of the 31 compact sources detected in the first data release to a $1\sigma$ sensitivity of $\sim 9~{\rm \mu Jy\,beam^{-1}}$ (corresponding to $\sim$ 17.5hr on source) along with derived radio properties of these objects using complementary 1-2\,GHz VLA data. In paper II, we compare our VLBI-selected population to other AGN detection diagnostics used in other wavebands. A future publication, paper III, will describe the final data release which will include an additional 48 hours of observations which comprise of the first wide-field VLBI observations using a combined eMERLIN-EVN array. For this paper, we adopt a spatially-flat 6-parameter $\mathrm{\Lambda CDM}$ cosmology with $H_0 = 67.8\pm0.9~\mathrm{km\,s^{-1}\,Mpc}$, $\Omega_{m} = 0.308\pm0.012$ and $\Omega_{\Lambda} =0.692\pm0.012$ \citep{Planck2016}. We assume $S_\nu \propto \nu^{\alpha}$ throughout, where $S_\nu$ is the radio integrated flux density and $\alpha$ is the intrinsic source spectral index. The paper is organised as follows. Section 2 outlines our observations, source selection strategy, calibration and source detection methodology. Section 3 details the primary beam correction method used for the EVN. Section 4 describes the VLBI catalogue accompanying this paper while a formatted version is presented in Tables 2 and 3. Section 5 presents our results and associated discussion, including redshifts, astrometry, comparisons with other VLBI surveys and the radio properties of the VLBI-selected population. We conclude our findings in Section 6. | \label{Sec:Conclusions} We present a catalogue of 31 faint VLBI detected sources in GOODS-N to \textasciitilde$9~\mu {\rm Jy\,beam^{-1}}$ 1$\sigma$ r.m.s. noise levels and radio luminosities of the order $10^{22}~{\rm W\,Hz^{-1}}$. This has substantially increased the number of VLBI detected sources over previous GOODS-N surveys by \citet{chi2013deep} and \citet{garrett2001agn}, providing a valuable addition to the understanding of the AGN content in this well studied field. We also present a primary beam correction scheme developed for the European VLBI Network. This is publicly available and will be constantly updated. Additional ancillary information about the radio properties of these objects were derived using VLA\,1.5 and 5\,GHz data. The detected objects have radio luminosities of the order $10^{22}\mbox{-}10^{26}~{\rm W\,Hz^{-1}}$ and brightness temperatures in the range $10^6\mbox{-}10^9~{\rm K}$. The high fraction of compact emission (as defined by the VLBI/VLA flux density ratio) may be hinting at the existence of radio-loud but core-dominated systems at high redshift which may be equivalent to the population of FR0 objects in the local universe \citep{Baldi:2015jt,Baldi2018:em}. With previous VLBI surveys effectively characterising the $>$50~$\rm \mu Jy$ radio sky, the scheduled 48 hours of remaining observations will enable us to reach limiting r.m.s. sensitivities of $\sim2~{\rm \mu Jy\,beam^{-1}}$, thus providing the next step in analysing the faint radio-selected AGN population in GOODS-N. The final data release will be able to test whether the increasing fraction of star-forming galaxies at these low flux densities are influenced by AGN activity as postulated in lower resolution surveys. This will be presented in a future publication. In addition, the last 24 hours of these observations will include the first ever wide-field VLBI observations using an integrated EVN-eMERLIN array, providing valuable surface brightness sensitivity improvements with the addition of intermediate length baselines. % \longtab[1]{ \begin{landscape} \begin{longtable}{ccccccccc|cc} \caption{1.6\,GHz VLBI and 1.5\,GHz VLA properties of the VLBI detected sources}\label{Table:Source_catalog} \\ \hline\hline Source ID & $z$ & $z$ type\tablefootmark{c}/ref & R.A. (J2000) & Dec. (J2000) & VLBI $P$ & VLBI $I$ & S/N & Beam & VLA $P$ & VLA $I$ \\ & & & & & [$\rm\mu Jy\,beam^{-1}$] & [$\rm \mu Jy$] & & [mas$\times$mas (deg)] & [$\rm\mu Jy\,beam^{-1}$] & [$\rm\mu Jy$] \\ (1) & (2\mbox{-}4) & (5,6) & (7) & (8) & (9,10) & (11,12) & (13) & (14\mbox{-}16) & (17,18) & (19,20) \\ \hline J123555+620902\tablefootmark{a} & 1.8750 & S\tablefootmark{d} & 12:35:55.1267 & +62:09:01.738 & 100.0$\pm$18.2 & 100.0$\pm$18.2 & 7.4 & 16.0$\times$15.2 (87.1) & 165$\pm$17 & 192$\pm$19 \\ J123607+620951 & 0.6380 & S\tablefootmark{d} & 12:36:06.6120 & +62:09:51.159 & 118.0$\pm$22.8 & 118.0$\pm$21.2 & 6.1 & 5.3$\times$4.6 (3.0) & 169$\pm$17 & 205$\pm$21 \\ J123608+621036\tablefootmark{a} & 0.6790 & S\tablefootmark{d} & 12:36:08.1193 & +62:10:35.906 & 122.0$\pm$16.8 & 140.0$\pm$18.2 & 11.1 & 16.0$\times$15.4 (86.8) & 202$\pm$20 & 236$\pm$24 \\ J123618+621541 & 1.9930 & S\tablefootmark{e} & 12:36:17.5546 & +62:15:40.765 & 177.0$\pm$25.0 & 192.0$\pm$26.0 & 10.1 & 5.4$\times$4.6 (10.6) & 226$\pm$23 & 275$\pm$28 \\ J123620+620844 & 1.0164 & S\tablefootmark{d} & 12:36:20.2620 & +62:08:44.268 & 185.0$\pm$25.8 & 185.0$\pm$24.0 & 10.3 & 5.3$\times$4.6 (3.3) & 141$\pm$14 & 156$\pm$16 \\ J123621+621708\tablefootmark{a} & 1.9920 & S\tablefootmark{f} & 12:36:21.2684 & +62:17:08.459 & 96.5$\pm$14.5 & 135.0$\pm$17.3 & 8.9 & 15.6$\times$15.3 (-8.2) & 138$\pm$14 & 190$\pm$19 \\ J123623+620654\tablefootmark{a} & $1.94\substack{+0.12 \\ -0.12}$ & P\tablefootmark{g} & 12:36:22.5086 & +62:06:53.844 & 114.0$\pm$19.0 & 144.0$\pm$21.4 & 8.2 & 16.1$\times$15.3 (86.3) & 222$\pm$22 & 249$\pm$25 \\ J123624+621643 & 1.9180 & S\tablefootmark{e} & 12:36:23.5437 & +62:16:42.746 & 222.0$\pm$28.2 & 383.0$\pm$42.0 & 12.8 & 5.4$\times$4.5 (10.6) & 384$\pm$39 & 411$\pm$41 \\ J123641+621833 & 1.1456 & S\tablefootmark{d} & 12:36:40.5661 & +62:18:33.081 & 141.0$\pm$26.3 & 141.0$\pm$25.7 & 7.5 & 5.3$\times$4.5 (9.4) & 293$\pm$30 & 302$\pm$30 \\ J123642+621331 & 2.0180 & S\tablefootmark{h} & 12:36:42.0899 & +62:13:31.428 & 97.4$\pm$18.0 & 233.0$\pm$27.9 & 6.5 & 5.4$\times$4.5 (12.6) & 432$\pm$44 & 477$\pm$48 \\ J123644+621133 & 1.0128 & S\tablefootmark{d} & 12:36:44.3860 & +62:11:33.170 & 410.0$\pm$44.8 & 411.0$\pm$44.7 & 25.9 & 5.3$\times$4.5 (11.4) & 737$\pm$74 & 1710$\pm$171 \\ J123646+621405 & 0.9610 & S\tablefootmark{d} & 12:36:46.3307 & +62:14:04.692 & 191.0$\pm$24.9 & 192.0$\pm$24.8 & 12.3 & 5.4$\times$4.5 (12.7) & 260$\pm$26 & 280$\pm$28 \\ J123650+620738\tablefootmark{a} & 1.6095 & S\tablefootmark{d} & 12:36:49.6399 & +62:07:37.844 & 77.3$\pm$17.3 & 98.7$\pm$19.9 & 6.5 & 15.4$\times$14.8 (80.9) & 267$\pm$27 & 301$\pm$30 \\ J123653+621444\tablefootmark{a} & 0.3208 & S\tablefootmark{d} & 12:36:52.8827 & +62:14:44.069 & 109.0$\pm$15.1 & 117.0$\pm$15.6 & 11.0 & 14.8$\times$14.7 (9.6) & 188$\pm$19 & 215$\pm$22 \\ J123659+621833 & $2.17\substack{+0.08 \\ -0.07}$ & P\tablefootmark{g} & 12:36:59.3327 & +62:18:32.566 & 2530.0$\pm$328.9 & 4430.0$\pm$572.7 & 88.2 & 5.3$\times$4.5 (8.5) & 4250$\pm$427 & 4640$\pm$464 \\ J123700+620910 & $2.58\substack{+0.07 \\ -0.06}$ & P\tablefootmark{g} & 12:37:00.2460 & +62:09:09.779 & 153.0$\pm$23.4 & 163.0$\pm$24.1 & 9.4 & 5.3$\times$4.5 (8.0) & 272$\pm$27 & 319$\pm$32 \\ J123709+620838 & 0.9070 & S\tablefootmark{l} & 12:37:09.4300 & +62:08:37.587 & 125.0$\pm$21.4 & 127.0$\pm$21.5 & 7.3 & 5.3$\times$4.5 (6.4) & 155$\pm$16 & 163$\pm$16 \\ J123714+621826 & $3.44\tablefootmark{m}$ & P\tablefootmark{i} & 12:37:13.8694 & +62:18:26.301 & 501.0$\pm$56.8 & 629.0$\pm$69.4 & 25.6 & 5.3$\times$4.6 (6.9) & 575$\pm$58 & 637$\pm$64 \\ J123715+620823 & 0.9335 & S\tablefootmark{j} & 12:37:14.9391 & +62:08:23.223 & 2680.0$\pm$272.9 & 2810.0$\pm$284.0 & 103.0 & 5.3$\times$4.6 (5.4) & 1940$\pm$195 & 2090$\pm$209 \\ J123716+621512 & 0.5605 & S\tablefootmark{d} & 12:37:16.3730 & +62:15:12.343 & 125.0$\pm$20.3 & 125.0$\pm$19.7 & 7.9 & 5.4$\times$4.6 (9.9) & 165$\pm$17 & 178$\pm$18 \\ J123717+621733 & 1.1460 & S\tablefootmark{d} & 12:37:16.6800 & +62:17:33.310 & 150.0$\pm$23.8 & 269.0$\pm$32.7 & 8.2 & 5.4$\times$4.6 (7.5) & 308$\pm$31 & 356$\pm$36 \\ J123720+620741\tablefootmark{a} & $0.91\substack{+0.05 \\ -0.03}$ & P\tablefootmark{k} & 12:37:20.0139 & +62:07:41.410 & 94.8$\pm$14.6 & 112.0$\pm$15.8 & 8.8 & 15.9$\times$15.4 (67.2) & 122$\pm$13 & 132$\pm$13 \\ J123721+621130 & $2.02\substack{+0.06 \\ -0.06}$ & P\tablefootmark{g} & 12:37:21.2517 & +62:11:29.961 & 328.0$\pm$38.3 & 364.0$\pm$41.6 & 20.2 & 5.3$\times$4.5 (8.8) & 338$\pm$34 & 385$\pm$39 \\ J123726+621129\tablefootmark{a} & 0.9430 & S\tablefootmark{j} & 12:37:25.9475 & +62:11:28.699 & 124.0$\pm$16.7 & 142.0$\pm$18.2 & 12.2 & 15.4$\times$15.1 (52.6) & 1190$\pm$120 & 5210$\pm$521 \\ \textit{J123649+620439}\tablefootmark{b} & 0.1130 & S\tablefootmark{d} & 12:36:48.9965 & +62:04:38.850 & $>$92.6 & $>$102.0 & 10.5 & 12.5$\times$11.6 (1.2) & 608$\pm$61 & 834$\pm$83 \\ \textit{J123701+622109}\tablefootmark{b} & 0.8001 & S\tablefootmark{d} & 12:37:01.1023 & +62:21:09.623 & $>$111.0 & $>$154.0 & 11.5 & 12.4$\times$11.0 (3.2) & 285$\pm$29 & 390$\pm$39 \\ \textit{J123739+620505}\tablefootmark{b} & $2.99\substack{+0.81 \\ -1.51}$ & P\tablefootmark{k} & 12:37:39.3204 & +62:05:05.489 & $>$154.0 & $>$194.0 & 11.6 & 12.1$\times$10.9 (5.6) & 223$\pm$23 & 258$\pm$26 \\ \textit{J123751+621919}\tablefootmark{b} & $1.20\substack{+0.11 \\ -0.05}$ & P\tablefootmark{k} & 12:37:51.2327 & +62:19:19.012 & $>$111.0 & $>$181.0 & 8.8 & 11.9$\times$10.5 (0.5) & 136$\pm$14 & 155$\pm$16 \\ \textit{J123523+622248}\tablefootmark{b} & $1.42\substack{+0.10 \\ -0.11}$ & P\tablefootmark{k} & 12:35:22.6144 & +62:22:48.028 & $>$92.5 & $>$144.0 & 7.3 & 12.1$\times$10.6 (7.0) & 1260$\pm$126 & 1690$\pm$169 \\ \textit{J123510+622202}\tablefootmark{b} & $2.33\substack{+0.52 \\ -0.24}$ & P\tablefootmark{k} & 12:35:10.2698 & +62:22:02.067 & $>$88.9 & $>$91.4 & 7.9 & 12.1$\times$10.6 (7.0) & 931$\pm$94 & 1280$\pm$128 \\ \textit{J123656+615659}\tablefootmark{b} & $0.39\substack{+0.05 \\ -0.04}$ & P\tablefootmark{k} & 12:36:55.8230 & +61:56:58.917 & $>$518.0 & $>$528.0 & 12.7 & 9.6$\times$9.0 (39.0) & 3590$\pm$361 & 26700$\pm$2670 \\ \hline \hline\end{longtable} \tablefoot{z: redshift, R.A.: Right Ascension (J2000), Dec.: Declination (J2000), VLBI $P$: VLBI peak brightness ($\mathrm{\mu Jy\,beam^{-1}}$), VLBI $I$: VLBI integrated flux density ($\mathrm{\mu Jy}$), N: noise ($\mathrm{\mu Jy\,beam^{-1}}$), S/N: signal-to-noise, Beam: restoring beam in milliarcseconds and beam angle in degrees (major axis $\times$ minor axis (beam angle)), VLA $P$: VLA 1.5\,GHz peak brightness, VLA $I$: VLA 1.5\,GHz integrated flux densities. Italiscised source IDs correspond to sources with no-primary beam correction applied. The row of numbers below the column titles correspond to the columns in the machine-readable table that accompanies this paper.\\ \tablefoottext{a}{Sources detected using naturally weighted taper (\texttt{UVWTFN=`NA'} in AIPS task \texttt{IMAGR})} \tablefoottext{b}{Not primary beam corrected.} \tablefoottext{c}{S: spectroscopic redshift, P: photometric redshift.} Redshift references: \tablefoottext{d}{\citet{Barger_specz_2008}}, \tablefoottext{e}{\citet{Smail2004:sz}},\tablefoottext{f}{\citet{Chapman:2005wh}},\tablefoottext{g}{\citet{Skelton_HST3D_2014}},\tablefoottext{h}{\citet{Murphy:2017ja}},\tablefoottext{i}{\citet{Cowie2017z}},\tablefoottext{j}{Cowie priv. comm.},\tablefoottext{k}{\citet{Yang_photz_2014}},\tablefoottext{l}{\citet{Cowie2004z}}. \tablefoottext{m}{Unknown photometric error, conservatively set to $\pm0.5$ in calculations of derived properties}} \end{landscape}} \longtab[1]{ \begin{longtable}{cccccc} \caption{Derived VLA \& VLBI radio properties of the 31 GOODS-N AGN.}\label{Table:Derived_properties} \\ \hline\hline Source ID & $\alpha$& $L_\mathrm{{1.5GHz}}$ & $T_b$ & Angular sizes & Linear sizes \\ & & [$\rm W\,Hz^{-1}$] & [$\rm K$] & [mas] & [parsec] \\ (1) & (21) & (22,23) & (24\mbox{-}26) & (27\mbox{-}30) & (31\mbox{-}34) \\ \hline J123555+620902 & - & $(2.7\pm 0.3) \times 10^{{24}}$ & - & - & - \\ J123607+620951 & $-1.02$ & $(3.1\pm 0.3) \times 10^{{23}}$ & - & - & - \\ J123608+621036 & $-0.46$ & $(3.3\pm 0.4) \times 10^{{23}}$ & $ \mathit{1 \times 10^{6}}$ & 11.1$\times$6.3 & 80.8$\times$45.8 \\ J123618+621541 & $-0.62$ & $(4.5\pm 0.4) \times 10^{{24}}$ & $>3 \times 10^{7}$ & 3.7$\times$$<$2.8 & 31.5$\times$$<$23.8 \\ J123620+620844 & $-0.28$ & $(4.9\pm 0.6) \times 10^{{23}}$ & $>2 \times 10^{7}$ & $<$3.2$\times$$<$2.8 & $<$26.3$\times$$<$22.9 \\ J123621+621708 & $-0.78$ & $(3.3\pm 0.3) \times 10^{{24}}$ & - & - & - \\ J123623+620654 & $0.06$ & $(2.0\pm 0.7) \times 10^{{24}}$ & - & - & - \\ J123624+621643 & $-0.52$ & $(6.3\pm 0.7) \times 10^{{24}}$ & $2 \times 10^{7}$ & 5.9$\times$4.0 & 50.8$\times$34.2 \\ J123641+621833 & $-0.94$ & $(2.2\pm 0.2) \times 10^{{24}}$ & $ \mathit{3 \times 10^{6}}$ & $<$12.3$\times$5.0 & 104.4$\times$42.6 \\ J123642+621331 & $-1.05$ & $(1.4\pm 0.1) \times 10^{{25}}$ & $ \mathit{3 \times 10^{6}}$ & 12.1$\times$8.5 & 103.4$\times$73.2 \\ J123644+621133 & $-0.56$ & $(3.1\pm 0.3) \times 10^{{24}}$ & $>1 \times 10^{8}$ & 2.1$\times$$<$1.7 & 17.6$\times$$<$13.9 \\ J123646+621405 & $-0.40$ & $(8.7\pm1.0) \times 10^{{23}}$ & $>2 \times 10^{7}$ & $<$2.9$\times$$<$2.5 & $<$23.9$\times$$<$20.1 \\ J123650+620738 & $-0.56$ & $(3.1\pm 0.3) \times 10^{{24}}$ & - & - & - \\ J123653+621444 & $-0.11$ & $(5.3\pm 0.7) \times 10^{{22}}$ & $ \mathit{2 \times 10^{6}}$ & 9.2$\times$4.8 & 44.1$\times$23.0 \\ J123659+621833 & $-1.19$ & $(2.0\pm 0.1) \times 10^{{26}}$ & $>1 \times 10^{9}$ & 6.2$\times$$<$0.9 & 52.2$\times$$<$7.7 \\ J123700+620910 & $-0.89$ & $(1.3\pm 0.1) \times 10^{{25}}$ & $ \mathit{5 \times 10^{6}}$ & $<$9.5$\times$7.2 & 78.3$\times$59.1 \\ J123709+620838 & $0.15$ & $(3.2\pm 0.5) \times 10^{{23}}$ & $ \mathit{2 \times 10^{6}}$ & 7.8$\times$6.1 & 63.0$\times$49.1 \\ J123714+621826 & $-0.66$ & $(3.9\pm1.2) \times 10^{{25}}$ & $>2 \times 10^{8}$ & 3.8$\times$$<$1.7 & 28.5$\times$$<$12.9 \\ J123715+620823 & $-0.04$ & $(4.8\pm 0.7) \times 10^{{24}}$ & $>3 \times 10^{9}$ & $<$1.0$\times$$<$0.8 & $<$7.9$\times$$<$6.9 \\ J123716+621512 & $-0.19$ & $(1.5\pm 0.2) \times 10^{{23}}$ & $ \mathit{2 \times 10^{6}}$ & 10.4$\times$6.5 & 69.1$\times$43.4 \\ J123717+621733 & $-0.89$ & $(2.2\pm 0.2) \times 10^{{24}}$ & $ \mathit{7 \times 10^{6}}$ & 6.8$\times$5.1 & 57.6$\times$43.2 \\ J123720+620741 & $-0.28$ & $(3.4\pm 0.6) \times 10^{{23}}$ & - & - & - \\ J123721+621130 & $0.01$ & $(3.5\pm 0.8) \times 10^{{24}}$ & $>9 \times 10^{7}$ & 2.8$\times$$<$1.9 & 24.0$\times$$<$16.5 \\ J123726+621129 & $-1.23$ & $(6.6\pm 0.4) \times 10^{{24}}$ & $ \mathit{2 \times 10^{6}}$ & 8.7$\times$6.9 & 71.0$\times$56.1 \\ \textit{J123649+620439} & - & $(2.0\pm 0.4) \times 10^{{22}}$ & - & 8.3$\times$6.0 & 17.7$\times$12.7 \\ \textit{J123701+622109} & - & $(7.0\pm 0.7) \times 10^{{23}}$ & - & 9.4$\times$7.3 & 72.8$\times$56.8 \\ \textit{J123739+620505} & - & $(9.7\pm8.9) \times 10^{{24}}$ & - & 8.6$\times$7.2 & 67.9$\times$56.7 \\ \textit{J123751+621919} & - & $(8.2\pm1.6) \times 10^{{23}}$ & - & - & - \\ \textit{J123523+622248} & - & $(1.1\pm 0.2) \times 10^{{25}}$ & - & - & - \\ \textit{J123510+622202} & - & $(2.4\pm 1.0) \times 10^{{25}}$ & - & - & - \\ \textit{J123656+615659} & - & $(1.7\pm 0.5) \times 10^{{24}}$ & - & 7.3$\times$$<$2.4 & 39.7$\times$$<$13.2 \\ \hline \end{longtable} \tablefoot{$\alpha$: 1.5GHz\mbox{-}5.5\,GHz spectral index, $L_\mathrm{{1.5GHz}}$: monochromatic 1.5\,GHz radio luminosity, $T_b$: brightness temperature (italicised indicates that natural weighting was used to derive $T_b$), Angular size: projected angular size using elliptical Gaussian fitting, Linear size: projected linear size in parsecs. Italiscised source IDs correspond to sources with no-primary beam correction applied. Row of numbers below the column titles correspond to the columns in the machine-readable table that accompanies this paper.} } | 18 | 8 | 1808.04296 |
1808 | 1808.08137_arXiv.txt | We consider cosmological implications of the formation of first stellar size black holes (BHs) in the universe. Such BHs form and grow by accretion in minihaloes of masses $\simeq10^5\hbox{--}10^7\msun$, and emit non-thermal radiation which impact the ionization and thermal state of the IGM. We compute the implications of this process. We show that the influence regions for hydrogen increase to 10kpc (physical length) for non-growing BHs to more than 0.3--1Mpc for accreting BHs, the influence regions are ten times smaller for singly ionized helium. We consider three possible observables from the influence zones around accreting BHs during $8.5<z<25$: HI 21cm line, hyperfine line of $^3$HeII, and HI recombination lines. We show that the 21cm emitting region around a growing BH could produce brightness temperatures $\simeq 15$mK across an evolving structure of 1Mpc in size with hot, ionized gas closer to the BH and much cooler in outer regions. We show that the ongoing and upcoming radio interferometers such as LOFAR and SKA1-LOW might be able to detect these regions. $^3$HeII emission from regions surrounding the growing BH is weak: the corresponding brightness temperatures reaches tens of nano-Kelvin, which is below the range of upcoming SKA1-MED. We show that for growing BHs H$\alpha$ line could be detected by JWST with $S/N=10$ in $10^4$~seconds of integration. In light on the recent EDGES result, we show that with additional cooling of baryons owing to collision with dark matter the HI signal could be enhanced by more than an order of magnitude. | The probes of the epoch of reionization (EoR) and cosmic dawn remain outstanding aims of modern cosmology. While relevant information about the era of cosmic dawn remains elusive, important strides have been made in understanding the EoR since 2000, mainly owing to the detection of Gunn-Peterson effect at $z \simeq 6$ and the CMB temperature and polarization anisotropies by WMAP and Planck \citep{Planck2015,Fanetal}. The discovery of Gunn-Peterson trough indicates that the universe could be making a transition from fully ionized to neutral at $z\simeq 6$. The CMB anisotropy measurements are consistent with the universe being fully ionized at $z \simeq 8.5$. The current best bounds on the redshift of reionization from Planck put strong constraints on the redshift of reionization, $z_{\rm reion} = 8.5 \pm 1$ \citep{Planck2015}. Theoretical estimates {show} that the first { stars} in the universe might have formed at { $z\simeq 65$} { \citep{naoz06}} thereby ending the dark age of the universe. The emission of UV light from these structures carve out ionized regions which might have percolated at $z \simeq 9$ \citep[see e.g. ][and references therein]{Barkana2001}. However, the nature of these first sources that ionize and heat the intergalactic medium is difficult to establish within the framework of current theoretical models. The two mostly likely candidates are star-forming haloes and the precursors of quasars. In the latter case, the emission could be dominated by accretion onto a seed stellar-mass black hole, the case we consider in this paper. One way to probe this phase is through the detection of redshifted hyperfine transition of neutral hydrogen (\ion{H}{1}) from this era. The past one decade has seen major progress on both theoretical and experimental efforts in this direction. Theoretical estimates show that the global \ion{H}{1} signal is observable in both absorption and emission with its strength in the range $-200\hbox{--}20 \, \rm mK$ in a frequency range of $50\hbox{--}150 \, \rm MHz$, which corresponds roughly to a redshift range $25 > z > 8$ \citep[e.g. ][]{1997ApJ...475..429M,2000ApJ...528..597T,2004ApJ...608..611G,Sethi05,pritchard08,cohenfi}. The fluctuating component of the signal is likely to be an order of magnitude smaller on scales in the range $3\hbox{--}100$~Mpc { (comoving)}, which implies angular scales in the range $\simeq 1\hbox{--}30$~arc-minutes \citep[e.g. ][]{Zaldarriaga2004}; \citep[for reviews see e.g. ][]{Zaroubi2013,Furlanettoetal,MoralesWyithe}. Many of the ongoing and upcoming experiments have the the capability to detect this signal in hundreds of hours of integration \citep[e.g. ][]{2015aska.confE...3A,2014MNRAS.439.3262M,parsons12,mcquinn06,morales05,kulkarni16,pen09}. Upper limits on the fluctuating component of the \ion{H}{1} signal have been obtained by many ongoing experiments --- GMRT, MWA, PAPER, and LOFAR \citep{2017ApJ...838...65P,2016ApJ...833..102B,PAPER,GMRT}. In addition to the redshifted hyperfine line of HI, it might be possible to probe cosmic dawn and EoR using other spectral lines of the primordial gas. Therefore, we consider also HI recombination lines and hyperfine line of $^3$HeII. In this paper, we consider the impact of a {growing} black hole (BH)on the thermal and ionization state of the IGM in the redshift range {$8 < z <25$}. {There is copious observational evidences of the existence of supermassive black holes with masses upto $M\sim 10^9~\msun$ at $z\simeq 7$ \citep[see e.g.,][]{mortlock11,banados,shellqs-survey,viking-survey,panstarrs-survey,wu-bhs15}\footnote{http://www.homepages.ucl.ac.uk/~ucapeib/list\_of\_all\_quasars.htm}. The presence of such ``monstrous'' black holes in the young Universe with ages less than 500 Myr seems challenging because of strong radiative and wind feedback \citep[see in][]{bhgrowth-illustris,massiveblack-sim,bhgrowth-eagle,bhgrowth-horizonAGN,negri17,gaspari17,bhgrowth-illustristng,latif16,latif18}. In this paper we address the question of whether the regions around these growing BHs can be observed in 21~cm emission, helium hyperfine line and hydrogen recombination lines. } In the next section, we describe our model of photon emission from a BH that forms in the redshift range $20\hbox{--}25$ and subsequently grows owing to accretion. In section~\ref{sec:obser} we discuss possible observables that can probe the thermal and ionization evolution of the gas influenced by emission from the BH. In section~\ref{sec:resu} we present our main results. In section~\ref{sec:sumcon} we summarize our findings and make concluding remarks. Throughout this paper, we assume the spatially-flat $\Lambda$CDM model with the following parameters: $\Omega_m = 0.254$, $\Omega_B = 0.049$, $h = 0.67$ and $n_s = 0.96$, with the overall normalization corresponding to $\sigma_8 = 0.83$ \citep{Planck2015}. | \label{sec:sumcon} In this paper, we considered the impact of a {growing} black hole on thermal and ionization state of the IGM in the redshift range $8 < z <25$, and discuss possible observables that can probe this influence. We have found that the sizes of {zones of ionized gas} around growing BHs are greater as compared to that for a non-growing BH: for accretion with radiative efficiency $\epsilon=0.1$ they are more than order of magnitude larger at redshift $z=8.5$. The physical size of a zone of influence increases from nearly 10~kpc to 300~kpc during the growth of a BH. The most part of this region contains highly ionized hydrogen upto a reasonable fraction of unity, and temperature exceeding 300~K. Helium ionization region is generally smaller and reaches a maximum of 100~kpc. We consider three observables as probe of growing primordial BHs. We show that the influence region of 21~cm emission around an accreting BH with radiative efficiency $\epsilon\simgt 0.05\hbox{--}0.1$ could be in the range of a few hundred kilo-parsecs to 1 Mpc (Figure~\ref{figh1ya}). The angular scale of this emission and the spatial contrast of the HI signal is accessible to ongoing and upcoming radio telescopes such as SKA1-LOW. We also consider the impact of recent EDGES observation \citep{2018Natur.555...67B} and show that it greatly enhances the expected contrast (Figure~\ref{figh2ya}). We also study the emission of hyperfine line of $^3$HeII ($\lambda = 3.4 \, \rm cm$) from regions surrounding the growing BH. The brightness temperatures in these lines could reach tens of nano-Kelvin. Taking into account the sizes of these regions we anticipate that this emission cannot be detected by upcoming radio telescopes SKA1-MED. We finally consider hydrogen recombination lines (n,n-1) from ionized regions surrounding growing BHs. The H$\alpha$ line provides the best prospect of detection (Figure~\ref{fig-flx}); JWST can detect this line with $S/N=10$ in ten thousand seconds of integration. Expected fluxes from transitions between higher levels (e.g. Figure~\ref{fig-flx} for $n= 30$) are near the thresholds of modern radio telescopes only around very rapidly growing BHs. In sum: we model emission from an accreting primordial BH and study its impact on the ionization and thermal state of surrounding medium. We also consider the prospects of the detection of this dynamical process in the redshift range $8.5 < z < 25$. In conclusion we note that the observability of the features we discuss in the paper would be greatly boosted if the precursors of supermassive black holes could be detected at high redshifts. This possibility has been studied by \citet{valiante18sta,valiante18obs}. Their analysis suggests that future missions such as JWST will be able to detect high-mass BH seeds at $z\sim 16$ directly. \vspace{1cm} We are thankful to the referee for a careful reading of the manuscript and very detailed comments. This work is supported by the joint RFBR-DST project (RFBR 17-52-45063, DST P-276). The work by YS is done under partial support from the joint RFBR-DST project (17-52-45053), and the Program of the Presidium of RAS (project code 28). The code for the thermal evolution has been developed under support by Russian Scientific Foundation (14-50-00043). | 18 | 8 | 1808.08137 |
1808 | 1808.07295_arXiv.txt | Recent results by space borne experiments took cosmic ray data to a precision level. These new results are able to challenge the conventional scenario for cosmic ray acceleration and propagation in the Milky Way. In these contributions, written for the XVII Vulcano Workshop, we will give an overview of the latest results of the cosmic ray fluxes, and some possible interpretations will be discussed. These measurements have a common feature, namely the presence of unexpected and still not yet fully understood spectral features. | We are in a very exciting phase for the field of astroparticle physics: the observation of gravitational waves from the merger of a binary neutron star system~\cite{NS} in coincidence with the electromagnetic radiation detected in a broad range of wavelenghts, in August 2017, marked a milestone for multi-messenger astronomy~\cite{NSmm}, while the IceCube Collaboration announced, in July 2018, the first evidence for a source of high-energy (TeV) cosmic neutrinos~\cite{IC}. The BL Lac object TXS 0506+056 is likely to be the first identified source of high energy neutrinos and, consequently, of cosmic rays~\cite{nucr}. More than 100 years after the discovery of V. Hess, the understanding of the origin, the acceleration and propagation mechanisms of cosmic rays (CRs) in the galaxy and beyond is not yet completely understood and cosmic ray physics is still a lively and fascinating field of research. In the simplified ``conventional scenario''~\cite{rev} to describe the origin and propagation of CRs up to the knee, the primary CRs (e.g. H, He, C) are accelerated in Supernova remnants (SNR) via diffusive shock acceleration up to PeV energies, while their propagation in the interstellar medium (ISM) is described by an homogeneous and energy-dependent diffusion coefficient $K$. Once primary CRs are released from the sources, they propagate in the interstellar medium (ISM), made mainly by protons and helium nuclei, where they are confined by the magnetic fields for times of the order of a few million years~\cite{blasiRev}. When primary particles interact with the ISM they produce secondary CRs, like lithium, beryllium, boron as well as antimatter particles such as positrons and antiprotons. This theoretical framework provides featureless and universal (species independent) single power-law energy spectra, and it was supported by experimental results up to one decade ago. This work aims at providing a concise description of the latest experimental results on direct CR measurements up to the knee, and to provide a quick overview of possible interpretation scenarios. As a further reading, we suggest the reviews by P.~Serpico~\cite{Serpico2015} and L.~Drury~\cite{Drury2017}. | The new observations from recent space borne CR experiments, like PAMELA and AMS-02, revealed subtle and unexpected spectral features that require to re-examine or at least improve the theoretical framework used to describe the CR origin and propagation. In these proceedings I gave a short overview of the recent results of CR proton, helium and heavier nuclei up to oxygen: these measurements have a common feature, namely the presence of unexpected and still not yet fully understood spectral features. The main classes of plausible scenarios to interpret the presented results were outlined: the secondary to primary flux ratio, like the B/C, constitute a solid observable to ascertain the origin of galactic CRs. If the contribution from local sources seems disfavoured by the anisotropies and by the measurement of B/C and other secondary-to-primary flux ratios, the competition between the propagation effect and the re-acceleration in the vicinity of the shockwaves is not yet concluded. A conclusive model that coherently describes the numerous and very precise measurements provided by AMS-02 in the past 7 years is eagerly awaited by the scientific community. | 18 | 8 | 1808.07295 |
1808 | 1808.05773_arXiv.txt | We propose a novel instrument design to greatly expand the current optical and near-infrared SETI search parameter space by monitoring the entire observable sky during all observable time. This instrument is aimed to search for technosignatures by means of detecting nano- to micro-second light pulses that could have been emitted, for instance, for the purpose of interstellar communications or energy transfer. We present an instrument conceptual design based upon an assembly of 198 refracting 0.5-m telescopes tessellating two geodesic domes. This design produces a regular layout of hexagonal collecting apertures that optimizes the instrument footprint, aperture diameter, instrument sensitivity and total field-of-view coverage. We also present the optical performance of some Fresnel lenses envisaged to develop a dedicated panoramic SETI (PANOSETI) observatory that will dramatically increase sky-area searched (pi steradians per dome), wavelength range covered, number of stellar systems observed, interstellar space examined and duration of time monitored with respect to previous optical and near-infrared technosignature finders. | \label{sec:intro} The SETI (Search for ExtraTerrestrial Intelligence) search parameter space has been considerably expanded since the first dedicated observations in 1960 using the 26-m Tatel radio telescope\cite{Drake1961}. Sensitivity, bandwidth, spectral resolution and data handling capacities have increased over the years, but rare efforts have been made to design instruments with wide instantaneous field-of-view (FoV), i.e. the region of the sky that can be examined in a single observation. While the fraction of Sun-like stars hosting Earth-size planets in their habitable zone may be relatively high in our Galaxy ($22\pm 4$\%\cite{Petigura2013}), the fraction of these planets on which life can develop civilizations exposing signs of technology remains totally unknown; technosignatures could be rare and transient. Wide-field instrument designs are hence of crucial importance for surveying large areas of sky. Ultimately, SETI instruments capable of performing all-sky all-time observations with sufficient sensitivity would provide the largest possible angular and temporal coverage, increasing the probability of detecting a transient phenomena coming from an unknown location. Single-aperture wide-field astronomical instruments usually have complex optical designs aimed at minimizing aberrations and maintaining image quality over large fields of view, i.e. a few square degrees. Wide-field large-aperture telescopes made for large surveys such as QUEST\cite{Djorgovski2008}, Pan-STARRS\cite{Chambers2016}, SDSS\cite{Gunn2006}, or the future LSST\cite{Angel2001} have instantaneous FoV of 4, 3, 2.5 and 3.5 degrees respectively\cite{Ackermann2010}. FoV of conventional radio telescopes, limited to the beam area ($\sim\lambda/D$) of a single-dish, can be significantly enlarged if equipped with phased array feed receivers, such as ASKAP\cite{Heywood2016} ( 30 square degrees FoV at 1.4GHz) and WSRT/Apertif \cite{Oosterloo2010} (8 degrees across). Assemblies of single-aperture telescopes capable of observing different parts of the sky are still needed to survey the entire sky quickly and repeatedly. Optical large-aperture telescope arrays have been deployed for this purpose, such as the Fly's Eye Cosmic Ray Detector\cite{Baltrusaitis1985} or the Telescope Array\cite{Tokuno2012}. In radio astronomy, development of low-frequency wide-field telescopes has been made possible with aperture arrays constituted of large assemblies of small, fixed antennas, such as MWA\cite{Tingay2013} (with a FoV of 30 degrees across, at a resolution of several arcminutes), LWA\cite{Ellingson2009} (8 degrees across at a resolution of 8 arcsec) and LOFAR \cite{vanHaarlem2013} (FoV of 2$\pi$ steradians in its low-sensitivity survey mode). Radio interferometer arrays can also be configured for non-interferometric observations, where each dish examines an unique part of the sky, such as the Allen Telescope Array in Fly's Eye mode\cite{Siemion2012} (200 sq.deg at 1.4GHz). Transit observing strategies have been adopted to perform the first optical SETI all-sky surveys\cite{Howard2000, Howard2007} with 0.32 sq.deg of instantaneous FoV covering the sky in 150 clear nights. We propose in this paper a novel instrument designed to greatly expand the current optical and near-infrared SETI phase space by monitoring the entire observable sky during all observable time, in order to search for nano- to micro-second pulsed light signals. We present an instrument conceptual design, based upon an assembly of 198 Fresnel-lens telescopes tessellating two geodesic domes which could be used to search for optical technosignatures. The Pulsed All-sky Near-infrared and Optical SETI instrument project (PANOSETI) is dedicated to the search for technosignatures by means of detecting short ($<$1,000ns) visible and near-infrared pulse emissions with a high sensitivity ($\sim$ 25-50 photons per pulse per aperture). Equipped with fast ($>$200MHz) low-noise visible and near-infrared detector arrays \cite{Wright2018}, each part of the sky will be observed simultaneously from two locations to detect coincident signals and minimize false alarms generated by various sources of noise. With an instantaneous field-of-view covering 20.47\% of the sky (8,445 square degrees), the PANOSETI observatory, further described in Wright et al.\cite{Wright2018} and Cosens et al.\cite{Cosens2018}, is aimed to perform a high-sensitivity panoramic search for technosignatures from the Northern Hemisphere. | \label{sec:conclusion} Presented is a novel preliminary design for a panoramic optical pulsed SETI observatory, for which we propose to use two geodesic assemblies of 198 Fresnel telescopes to search for technosignatures in the visible and near-infrared with low angular resolution ($>$2-4 arcmin) and $\sim 10,000$sq-deg instantaneous FoV. Validation of this design through detailed structural analysis will allow determination of key structural parameters. Refractive Fresnel lenses are ideally suited for low ($>2$arcmin) angular resolution observations, with large pixels ($>$0.3mm) operating as light buckets. Achromatization of the optical system will be investigated for larger bandwidth observations. | 18 | 8 | 1808.05773 |
1808 | 1808.00967_arXiv.txt | We present our statistical analysis of the connection between active galactic nuclei (AGN) variability and physical properties of the central supermassive black hole (SMBH). We constructed optical light curves using data from the QUEST-La Silla AGN variability survey. To model the variability, we used the structure function, among the excess variance and the amplitude from Damp Random Walk (DRW) modeling. For the measurement of SMBH physical properties, we used public spectra from the Sloan Digital Sky Survey (SDSS). Our analysis is based on an original sample of 2345 sources detected in both SDSS and QUEST-La Silla. For 1473 of these sources we could perform a proper measurement of the spectral and variability properties, and 1348 of these sources were classified as variable ($91.5\%$). We found that the amplitude of the variability ($A$) depends solely on the rest frame emission wavelength and the Eddington ratio, where $A$ anti-correlates with both $\lambda_{rest}$ and $L/L_{\text{Edd}}$. This suggests that AGN variability does not evolve over cosmic time, and its amplitude is inversely related to the accretion rate. We found that the logarithmic gradient of the variability ($\gamma$) does not correlate significantly with any SMBH physical parameter, since there is no statistically significant linear regression model with an absolute value of the slope higher than 0.1. Finally, we found that the general distribution of $\gamma$ measured for our sample differs from the distribution of $\gamma$ obtained for light curves simulated from a DRW process. For 20.6\% of the variable sources in our sample, a DRW model is not appropriate to describe the variability, since $\gamma$ differs considerably from the expected value of 0.5. | Active Galactic Nuclei (AGN) show time-variable emission in every waveband in which they have been studied. The characteristic time-scales of the variability range from hours to years, with the shortest time-scales being associated with shorter emission wavelengths. This can be understood in the context of the current AGN structure models, where ultraviolet (UV) and optical emission are originated in an accretion disk around a super-massive black hole (SMBH), and non-thermal X-ray emission is produced in a inner hot plasma component (corona), which is geometrically much smaller and more concentrated than the accretion disk, and therefore able to show more rapid variability. Intensive monitoring of nearby AGN suggests that short term variability from the UV to the near-IR could be driven by the rapid changes in the X-ray flux, which illuminates the accretion disk producing the short term UV/optical variations, since small lags between optical and X-ray bands have been found in reverberation mapping (RM) analyses. However, it has been noticed that at time-scales of months or years, the amplitude of the UV/optical variability is larger than the amplitude of the X-ray variability, which implies that X-ray reprocessing is not the main source of the UV/optical variations, and intrinsic variability from the accretion disk is required \citep{Krolik91,Arevalo08,Lira15,Edelson15}. Even though variability is one of the defining characteristics of AGN we do not completely understand the mechanisms that drive such variations. In particular it is not clear yet how physical properties of the central engine (e.g., luminosity, black hole mass, Eddington ratio, etc) are related to variability properties of the system (e.g., characteristic time-scale, variability amplitude, etc). If we can establish a firm statistical correlation between certain AGN variability features and some SMBH physical properties, we will be able to use the variability as a tool in the future to derive physical properties for huge samples of objects from dedicated synoptic surveys such as the Large Synoptic Survey Telescope (LSST; \citealt{LSST}). Several efforts have been made in the past to assess this issue, some of them restricting the analysis to small numbers of well sampled light curves (e.g. \citealt{Kelly09,Kelly13,Simm16,Smith18}), or studying large samples of sources through ensemble light curve analysis, assuming that sources with similar physical properties would have similar variability features (e.g. \citealt{Wilhite08,Bauer09,MacLeod10,Caplar17}). In order to test whether this assumption is correct, we need to perform an analysis of well sampled individual AGN light curves, with known physical properties. Hence, long and intensive campaigns are crucial. An anti-correlation between the amplitude of the UV-optical variability and luminosity has been consistently observed by previous studies (e.g \citealt{Angione72,Hook94,Cristiani97,VandenBerk04,Wilhite08,Bauer09,Kelly09,MacLeod10,Kelly13,Simm16,Caplar17}). However, the existence of correlation between the amplitude of the variability and the black hole mass or the Eddington ratio is not clear yet. \cite{Wold07} used a sample of $\sim 100$ quasars from the Quasar Equatorial Survey Team, Phase 1 (QUEST1) variability survey \citep{Rengstorf04}. They found a positive correlation between the black hole mass and the amplitude of the variability. \cite{Wilhite08} found a positive correlation between the amplitude of the variability with black hole mass, and proposed that this could be explained by an anti-correlation with the Eddington ratio. \cite{MacLeod10} also found a positive correlation with black hole mass, and propose that the anti-correlation between the amplitude of the variability and the Eddington ratio exists, but an additional dependence on luminosity or black hole mass is required. \cite{Kelly09} found no evidence of correlation between the amplitude of the variability and the black hole mass or the Eddington ratio, and \cite{Kelly13} found a scattered correlation between the amplitude and the black hole mass, and a weak anti-correlation with the Eddington ratio. \cite{Simm16} found no correlation with the black hole mass, and an anti-correlation with Eddington ratio. More recently, \cite{Li18} used a large sample of quasars ($\sim 10^5$) to perform an ensemble variability analysis. They found that the amplitude of the variability correlates positively with redshift, and negatively with bolometric luminosity, rest-frame wavelength and Eddington ratio. They also found that the correlation with black hole mass was uncertain. This uncertainty can be produced by the use of ensemble light curves and also by the large uncertainties that might be present in the black hole mass estimations used in their analysis (taken from \citealt{Kozlowski17a}), since they are calculated by using luminosities derived from broadband extinction-corrected magnitudes obtained from the Sloan Digital Sky Survey (SDSS; \citealt{York00}), and by using the full width at half maximum (FWHM) of the lines obtained by \cite{Paris17a}. It is clear that all these results on the correlation with black hole mass and Eddington ratio are inconsistent, most likely due to the shortcomings on the samples used, as highlighted before. \cite{Rakshit17} used a large sample of narrow-line Seyfert 1 (NLSy1) and broad-line Seyfert 1 (BLSy1) from the Catalina Real Time Transient Survey (CRTS; \citealt{Drake09}). The light curves used in their analysis have a minimum of 50 epochs of data spanning 5 to nine years, thus they could perform a variability analysis for individual light curves. They found a strong anti-correlation between the amplitude of variability and the Eddington ratio, and they proposed that the accretion disk is the main driver of the variability observed in both broad and narrow line Seyfert 1 galaxies. However, since \cite{Rakshit17} used Damp Random Walk (DRW) modelling to measure the variability amplitude, which has several limitations for the analysis of ground-based light curves, since they tend to have gaps and time coverages of a few months or years (see section \ref{var_features}), their results must be confirmed using a different method (e.g. the structure function). Between 2010 and 2015 we carried out an AGN variability survey using the wide-field QUEST camera on the 1m ESO-Schmidt telescope at La Silla Observatory, observing five extragalactic fields: Stripe82, Elais-S1, COSMOS, ECDFS and XMM-LSS. These are some the most intensively observed regions in the sky, with a huge amount of ancillary data ranging from X-rays to radio waves. The aims of our survey are: 1) to test and improve variability selection methods of AGN, and find AGN populations missed by other optical selection techniques \citep{Schmidt10,Butler11,PalanqueDelabrouille11}, which is the subject of a forthcoming paper; 2) to obtain a large number of well--sampled light curves, covering time-scales ranging from days to years; 3) to study the link between the variability properties (e.g., characteristic time-scales and amplitudes of variation) with physical parameters of the system (e.g., black-hole mass, luminosity, and Eddington ratio). \cite{Cartier15} presented the technical description of the survey, the full characterisation of the QUEST camera, and a study of the relation of variability with multi-wavelength properties of X-ray selected AGN in the COSMOS field. In this paper we present our statistical analysis of the connection between AGN variability and physical properties of SMBH. For the variability analysis we used light curves from the QUEST-La Silla AGN variability survey, and derived physical properties from spectra taken from SDSS. We perform the spectral fitting using the procedure of \cite{MejiaRestrepo16} (MR16 hereafter), from which we could derive physical parameters and also line fitting properties such as the FWHM of the emission lines and continuum luminosities. For the variability analysis, we used the same approach as in \cite{Sanchez17} (S17 hereafter). In this work, we used single object light curves, in order to test the claim that sources with similar physical properties have similar variability behaviors (like proposed by \citealt{VandenBerk04,Wilhite08,MacLeod10,Caplar17}, among others). The paper is organized as follows. In section \ref{data} we describe the optical imaging and spectroscopic data used for the analysis. In section \ref{var_analysis} we describe the different variability features used, and we report the results of the variability analysis for our sample. In section \ref{spec_analysis} we explain the procedure followed to obtain the physical properties from the SDSS spectra, and show the distribution of these parameters for our sample. In section \ref{sample} we define the different sub-samples used in our analysis. In section \ref{var_vs_spec} we show the results of our statistical analysis done to connect the variability and physical properties. In section \ref{var_classes} we analyse the differences in the variability parameters of sources classified as Broad Line QSO and normal sources, and sources classified as radio-loud and radio-quiet. Finally, in section \ref{discussion} we discuss the physical implications of our findings and summarize the main results. The photometry reported here is in the AB system. We adopt the cosmological parameters $H_0=70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_m=0.3$ and $\Omega_\Lambda=0.7$. | \label{discussion} In section \ref{var_quest} we showed that there is a correlation between $A$ and $\gamma$, however in section \ref{sim_SF} we demonstrated that such a correlation is produced by the stochastic nature of the light curves together with the light curve sampling. We might need longer light curves to reduce this degeneracy, however, having access to long (decades of coverage) and well sampled light curves for large samples of sources is not possible currently. In section \ref{var_vs_spec} we demonstrated that $A$ anti-correlates with both $\lambda_{rest}$ and $L/L_{\text{Edd}}$, but $\gamma$ does not correlate with any of the physical parameters studied. This confirms our assumption that the correlation between $A$ and $\gamma$ is produced by the light curve properties, and by the stochastic nature of the variability. Nonetheless, the structure function is the best option that we have today to analyse typical ground-based light curves (i.e. with a few years of coverage, a few epochs, and with gaps), since other techniques, like Fourier analyses, requires well sampled light curves (i.e. with several epochs, and without gaps). In sections \ref{spec_prop} and \ref{pca} we reported that our data set presents correlations between the SMBH physical properties. Some of these correlations are produced by selection effects, since our sample is flux limited. For example, the correlations of redshift with luminosity, BH mass, and accretion rate, are produced by the fact that at higher redshifts our sample will naturally contain sources with higher luminosities, higher SMBH masses and higher accretion rates. The results shown in section \ref{var_vs_spec} tell us that the observed amplitude of the variability depends on two variables, $z_{spec}$ and $L/L_{\text{Edd}}$, which means that, at a fixed $z_{spec}$, sources with similar $L/L_{\text{Edd}}$ will have similar variability amplitudes. The positive correlation with redshift can be interpreted as an anti-correlation with the wavelength of rest frame emission. \cite{MacLeod10} analysed \textit{ugriz} light curves of $\sim 9000$ spectroscopically confirmed SDSS S82 quasars. Since they had multiple bands for each quasar, they could separate the dependency of the amplitude of the variability with redshift and $\lambda_{rest}$, finding an anti-correlation with $\lambda_{rest}$ and no correlation with $z_{spec}$. S17 analysed the near infrared variability of X-ray selected AGN. They also found a correlation between the amplitude of the variability and redshift. By comparing the trends between $A$ and $z_{spec}$ for two different bands (Y and J), they showed that the correlation with $z_{spec}$ is explained by an anti-correlation with the wavelength of emission. From this, and other previous results (e.g. \citealt{Kozlowski10}), we conclude that the positive correlation of $A$ with $z_{spec}$ is produced by a dependency on $\lambda_{rest}$, and is not given by evolution over cosmic time. This anti-correlation between $\lambda_{rest}$ and $A$ can be explained considering that the innermost regions of the disk can be the most variable, either intrinsically or by reprocessing. Since at shorter wavelengths a larger fraction of the disc emission is produced by the innermost region, it follows that shorter wavelengths display larger amplitudes of variability \citep{Arevalo08,Lira11,Lira15,Edelson15,Fausnaugh16}. We found an anti-correlation between $A$ and $L/L_{\text{Edd}}$. When we used the standard method to determine black hole masses from single epoch spectra we found a slope of $\beta_{L/L_{\text{Edd}}} = -0.19 \pm 0.02$ for the regression model with $A$ as the dependent variable, and $L/L_{\text{Edd}}$ and $z_{spec}$ as the independent variables, for the not -- C IV sample. When we apply the corrections proposed by \cite{MejiaRestrepo18a}, which intend to account for the effect of the unknown distribution of the gas clouds in the BLR, we found a slope of $\beta_{(L/L_{\text{Edd}})^C} =-0.28 \pm 0.06$. An anti-correlation between $L/L_{\text{Edd}}$ and the amplitude of the variability has also been reported by previous works (e.g. \citealt{Wilhite08,MacLeod10,Simm16,Rakshit17}). \cite{MacLeod10} reported a power-law slope of $-0.23 \pm 0.03$. This value was calculated by binning the parameter space of $M_{\text{BH}}$ and $M_i$ (absolute magnitude), and using ensemble light curves, which can explain the small difference with the value found by us. \cite{MacLeod10} also proposed that an additional dependency with luminosity or black hole mass is needed in order to explain their findings. Here we conclude that such a dependency is not necessary when intrinsic scatter is included in the model. In fact, in Table \ref{tab:reg_A_noCIV} we can see that the value of the intrinsic scatter found with our method is pretty stable, and that including $\text{L}_{5100}$ or $M_{\text{BH}}$ in the regression model with $z_{spec}$ and $L/L_{\text{Edd}}$ produces statistically insignificant slopes for $\text{L}_{5100}$ or $M_{\text{BH}}$. From the results of sections \ref{sim_SF} and \ref{lin_reg_A} we can say that the main contributors to this scatter are the $A-\gamma$ degeneracy (produced by the stochastic nature of the AGN variability), the definition of the SF by itself, the light-curve sampling, and the fact that light curves with coverage of a few years are not a good representation of the whole variability behavior. We could notice in section \ref{lin_reg_A} that when we performed the linear regression model with $z_{spec}$ and $L/_{Edd}$ as independent sources, selecting only those sources from the not--C IV sample whose measured values of $\gamma$ were in the range between 0.43 and 0.63, the measured scatter in the regression was reduced considerably. This confirm our assumption that the $A-\gamma$ degeneracy is one of the main contributors to the measured scatter in the regression models. Possible interpretations of the inverse dependency of the amplitude of the variability with $L/L_\text{Edd}$ are discussed by \cite{Wilhite08}, \cite{MacLeod10}, \cite{Simm16}, and \cite{Rakshit17}. One explanation can be that $L/L_\text{Edd}$ is a proxy of the age of the AGN (e.g. \citealt{Martini03,Haas04,Hopkins05}). Sources with lower $L/L_\text{Edd}$ can suffer from a dwindling of the fuel supply, as they become old, thus, the accretion flow can be more variable, producing larger amplitude in the variability. But, the time-scales of the amplitudes measured in this work are $\sim 1$ year, and therefore, it is unlikely that the variability amplitudes observed are given by variations in the external fuel supply, which requires much longer time-scales to be effective ($10^{5}$ to $10^7$ days). Other possible interpretation is that sources with higher $L/L_{\text{Edd}}$ have hotter accretion disks, as predicted by classical accretion physics \citep{Shakura73}. For typical values of black hole mass and accretion rate, it is expected that the innermost part of the disk emits in the far UV. Because of its smaller size, this region is also the one showing the largest variability amplitude. For lower accretion rates however, the disk becomes cooler, and the innermost, most variable region will shift its emission from the UV to optical wavebands ($r_{\lambda} \propto M_{\text{BH}}^{2/3} (L/L_{\text{Edd}})^{1/3}\lambda^{4/3}$). This would be true regardless of whether the variation of the disk emission is produced by intrinsic processes or by reprocessing of highly variable X-ray emission by the disk surface. \cite{MacLeod10} discarded this assumption because the time-scales ($\tau$) that they measured were not in agreement with this scenario. However, they used DRW modelling to find $\tau$, while it is now clear that DRW models cannot be used to properly describe the time-scales of typical ground-based light curves (see section \ref{var_features}). A third possible explanation for the anti-correlation between $A$ and $L/L_{\text{Edd}}$ can be related with the positive correlation between $L/L_{\text{Edd}}$ and the ratio of the UV/optical-to-X-ray flux $(\alpha_{\text{ox}})$ reported by several studies (e.g. \citealt{Shemmer08,Grupe10,Lusso10,Jin12}). If the UV/optical variability is produced by reflection of the variable X-ray emission, then disks located in systems with higher $\alpha_{\text{ox}}$ values will receive fractionally less X-ray radiation, and therefore the amplitude of the variability detected in the UV/optical range will be small. On the other hand, for sources with lower $\alpha_{\text{ox}}$, the disk will be irradiated with more X-ray light, and therefore we will detect higher UV/optical variability amplitudes. \cite{Kubota18} developed a new spectral model for the SED of AGN that includes a hot corona, an inner warm optically thick Comptonising region and an outer disk. Considering this model, they studied the UV/optical variability resulting from the reprocessing of the rapidly variable X-ray flux. Their model predicts an anti-correlation between the amplitude of the variability and $L/L_{\text{Edd}}$. However their model also predicts a much lower amount of UV/optical variability than what is observed by our analysis and previous studies (e.g. \citealt{MacLeod10}) at time-scales of 1 year or longer. This means that the model needs an extra source of UV/optical variability in order to explain the amplitudes observed at long time-scales, as has been found by previous analyses \citep{Krolik91,Arevalo08,Lira15,Edelson15}. Therefore, the anti-correlation between $A$ and $L/L_{\text{Edd}}$, cannot be solely explain by the correlation between $L/L_{\text{Edd}}$ and $(\alpha_{\text{ox}})$. In this work, we also found that the logarithmic gradient of the variability ($\gamma$) does not correlate significantly with any of the physical parameter studied, and that the general distribution of $\gamma$ measured for our sample differs from the distribution of $\gamma$ obtained for light curves simulated from a DRW process. We showed in sections \ref{var_quest} and \ref{lin_reg_g} that 20,6\% of the light curves have values of $\gamma$ higher than 0.75, for which a DRW model is not appropriate to explain the variability. \cite{Kasliwal15} and \cite{Smith18} used \textit{Kepler} light curves to study whether DRW modelling is sufficient to explain the variability of light curves with high cadence. They concluded that most of the \textit{Kepler} AGN light curves analysed cannot be described by a simple DRW model. \cite{Smith18} also proposed that it is possible that DRW modelling can be correct for ground-based quasar light curves, which in general study different time regimes than \textit{Kepler}. We need larger samples of high cadence light curves, to see whether the results of \cite{Kasliwal15} and \cite{Smith18} are representative for the whole AGN population. | 18 | 8 | 1808.00967 |
1808 | 1808.04668_arXiv.txt | Axions are a potential dark matter candidate, which may condense and form self gravitating compact objects, called axion stars (ASs). In this work, we study for the first time head-on collisions of relativistic ASs with black holes (BHs) and neutron stars (NSs). In the case of BH-AS mergers we find that, in general, the largest scalar clouds are produced by mergers of low compactness ASs and spinning BHs. Although in most of the cases which we study the majority of the mass is absorbed by the BH within a short time after the merger, in favourable cases the remaining cloud surrounding the final BH remnant can be as large as $30\%$ of the initial axion star mass, with a bosonic cloud mass of $\mathcal{O}(10^{-1})M_{\rm BH}$ and peak energy density comparable to that obtained in a superradiant build up. This provides a dynamical mechanism for the formation of long lived scalar hair, which could lead to observable signals in cases where the axion interacts with baryonic matter around the BH, or where it forms the seed of a future superradiant build up in highly spinning cases. Considering NS-AS collisions we find two possible final states (i) a BH surrounded by a (small) scalar cloud, or (ii) a stable NS enveloped in an axion cloud of roughly the same mass as the initial AS. Whilst for low mass ASs the NS is only mildly perturbed by the collision, a larger mass AS gives rise to a massive ejection of baryonic mass from the system, purely due to gravitational effects. Therefore, even in the absence of a direct axion coupling to baryonic matter, NS-AS collisions could give rise to electromagnetic observables in addition to their gravitational wave signatures. | Introduction} In the wake of multiple LIGO detections~\cite{Abbott:2016blz,Abbott:2016nmj,Abbott:2017vtc,Abbott:2017oio,Abbott:2017gyy}, including GW170817~\cite{TheLIGOScientific:2017qsa}, the first combined detection of GWs and electromagnetic signals from the same astrophysical source, there has been renewed interest in the simulation of exotic compact objects (ECOs) which could mimick BH or NS observations, or provide altogether new, and as yet undetected, observational signatures \cite{Giudice:2016zpa}. One of the simplest potential ECOs is a boson star (BS), which is a stable solitonic solution to the coupled Einstein-Klein-Gordon equations for a complex scalar field with gravity. The idea of a self gravitating field configuration dates back to proposals by Wheeler for ``geons"~\cite{Wheeler:1955zz}, but was first shown to work for complex scalar fields in~\cite{Kaup:1968zz, Ruffini:1969qy}. The ideas were extended to real massive scalar fields in~\cite{Seidel:1991zh}, with the (quasi) stable objects later dubbed oscillotons. A non trivial self interaction potential, motivated by, for example, low energy effective theories from string theory or other models, modifies the stability and profile of the solutions, giving rise to new classes of self interacting BSs~\cite{Eby:2015hsq, Colpi:1986ye, Krippendorf:2018tei}. The standard model of particle physics does not contain a bosonic particle that would allow the formation of BSs. Dark matter, on the other hand, may well be composed of bosons, with axion-like particles (ALPs) being a well-motivated class of candidates (see~\cite{Marsh:2015xka} for a thorough review). ALPs are very light, weakly coupled particles that are produced with practically vanishing momenta and extremely high occupation numbers. They are usually treated as classical, real scalar fields, subject to a cosine potential parametrised by the axion decay constant $f_a$ and the axion mass $m_a$. The leading order $\phi^4$ self-interaction for axions is thus attractive, but whilst here we simulate the full cosine potential, we use a large value of $f_a$ such that the the axion is effectively a massive boson and self interactions are negligible. In future work we hope to expand the study to quantify the effect of increasing self interactions. In this work, we focus on ASs with masses comparable to the objects with which they collide since such setups will give rise to strong GW signals. Consequently, the AS masses in the NSAS configurations are $M \sim M_\odot$, whilst in the BHAS case the physical mass of the BH sets the scale of the simulation such that the interpretation as solar mass BHs corresponds to solar mass ASs, and for supermassive BHs similarly the ASs have masses up to $M \sim 10^{10} M_\odot$. With the AS mass fixed, we choose values for the axion mass $m_a$ such that the star is comparatively compact - ie, such that the de Broglie wavelength of the axion is comparable to the radius of the BH or NS. In the solar mass case this corresponds to $m_a \sim 10^{-10}$eV (the lower end of the QCD axion scale), and for supermassive BHs, as low as $m_a \sim 10^{-20}$eV (corresponding to ultra-light ALPs). The original QCD axion emerges as a consequence of the Peccei-Quinn (PQ) symmetry breaking mechanism to solve the strong CP problem \cite{Peccei:1977hh, Weinberg:1977ma}. Its mass is constrained to lie between $m_a = 10^{-12}$ eV and $10^{-2}$ eV, with decay constant $f_a \ll M_{pl}$. If dark matter consists of QCD axions whose PQ symmetry was broken after inflation, high-amplitude density fluctuations on the scale of the cosmological horizon at the time of the QCD phase transition are predicted to exist. They collapse during the radiation era and form so-called axion miniclusters with typical masses of $\sim 10^{-11} M_\odot$ \cite{Hogan:1988mp,Kolb:1993zz}. A fraction of these masses may have formed ASs either directly during the collapse \cite{Schive:2014dra,Veltmaat:2018dfz} or by scalar wave condensation \cite{Levkov:2018kau}. The subsequent evolution of the AS mass function as a result of minicluster mergers or ongoing condensation is largely unknown; although their typical masses at formation are well below those we consider in this work, the existence of a high-mass tail of the distribution cannot be ruled out at present. A population of relativistic ASs could also have been produced by non-standard primordial perturbations with enhanced small-scale power \cite{Widdicombe:2018oeo}. Ultra-light ALPs with masses in the range of $\sim 10^{-22} - 10^{-20}$ eV, motivated from string theory compactifications \cite{Svrcek:2006yi, Arvanitaki:2009fg}, are candidates for ``fuzzy dark matter'' (FDM) with interesting new phenomenology on scales of their de Broglie wavelength in dark matter halos on scales of kpc \cite{Hu:2000ke, Hui:2016ltb}. In particular, cosmological simulations using the nonrelativistic Schrödinger-Poisson equations to describe FDM show the formation of ASs in the form of solitonic halo cores \cite{Schive:2014dra,Veltmaat:2018dfz} with masses of the order of $10^{7} M_\odot$ and above. The evolution of their mass function as a result of halo mergers was studied in \cite{Du:2016aik} and shown to approach the core-halo mass relation found by \cite{Schive:2014dra}. Thus, even if axions make up all the dark matter, relativistic ASs would constitute only a small ($< 1 \%$) fraction of the total mass (also, note that observational constraints from microlensing on compact ASs would be similar to those on primordial BHs). Nevertheless, there could still be a sufficient number density for collisions with known objects such as BHs and NSs to occur, motivating an exploration of their observable signatures. Simulations of ECO mergers more generally have to date focused mainly on complex scalar field BSs, e.g.~\cite{Balakrishna:1999sv,Palenzuela:2006wp, Choptuik:2009ww, Bezares:2017mzk, Lai:2004fw, Palenzuela:2007dm, Cardoso:2016oxy,Dietrich:2018bvi}, but other classes such as real scalar field oscillotons \cite{Helfer:2018vtq}, and just recently, massive, complex vector field Proca stars in \cite{Sanchis-Gual:2018oui,Sanchis-Gual:2017bhw} have been explored. There has, to the best of our knowledge, not yet been a study of the merger of ASs with BHs and NSs, even though these collisions are of interest since the ASs could act as a potential NS or BH mimickers in GW signals. In addition, since some types of axions are expected to couple weakly to baryonic matter, such mergers could result in distinct multi-messenger events, with, for example, phenomena such as Fast Radio Bursts (FRBs). In the case of a NS-AS collision the axions may interact with the neutron star matter either during or after the merger (see for example \cite{Hook:2017psm, Eby:2017xaw, Raby:2016deh, Iwazaki:2014wka, Barranco:2012ur} and the discussion in~\cite{Dietrich:inprep}). Similarly, the case of a BH-AS merger may provide a mechanism by which one can dynamically form long lived (quasibound) scalar clouds, or ``wigs'', around BHs \cite{Barranco:2012qs, Barranco:2017aes, Sanchis-Gual:2016jst, Herdeiro:2015waa, Hod:2012px}. Such clouds could then interact with any baryonic matter present in a potential accretion disc, or, in appropriate cases, provide the seeds for a superradiant instability (see e.g. \cite{Brito:2015oca, Brito:2014wla}) to develop. Several other novel methods for detecting such scalar clouds have also been proposed, see e.g. \cite{Ferreira:2017pth, Hannuksela:2018izj, Degollado:2014vsa}. Consequently, these events have great potential to further constrain the properties of the axion sector. For our simulations, we assume that the axion field is only coupled to baryonic matter via the gravitational interaction, i.e., they interact due to their mutual impact on the metric, and no additional couplings are implemented. As discussed, we also focus on relatively high values for the axion decay constant of $f_a =0.5 M_{pl}$, meaning that self interactions are negligible. These choices are most relevant to the case of ALPs with a negligible coupling to standard model physics. The paper is organised as follows. Sec.~\ref{sec:ICs} summarises the numerical methods used for the work and presents code tests, as well as a preliminary investigation to determine the initial conditions for the simulations shown in the remainder of the paper. In Sec.~\ref{sec:resultsBH} we consider the impact of varying the AS compactness on the remnant clouds left by BH-AS from mergers of ASs with spinning and non-spinning BHs. In Sec.~\ref{sec:resultsNS} we discuss NS-AS collisions, and investigate the remnant of the head-on collision as the NS-AS mass ratio is varied. We summarize our results and future plans in Sec.~\ref{sec:conclusions}.\\ Throughout this paper we employ geometric units, with $G=c=1$ and a mass scale $M$ which in the case of NSs is set to $M_\odot$, but in the case of BHs is a free mass scale by which the results may be scaled for varying BH masses. Consequently code units for lengths, times and masses are multiples of the mass scale $M$\footnote{Note that the scale $\mu$ which appears in the potential function is the quantity $\mu = m_a c / \hbar$, with dimension $[L^{-1}]$ such that a value of $\mu=1$ in code units corresponds to a particle mass of $m =1.3\times 10^{-10} ~ {\rm eV}$ in the NS case (note that $\hbar \neq 1$ in geometric units), we refer to~\cite{Dietrich:2018bvi} for further discussion.}. | Discussion} In this article we have presented what is, to the best of our knowledge, the first study of axion star collisions with black holes and neutron stars using full 3+1D numerical relativity simulations. Such a study seems timely in the gravitational wave astronomy era, in which multiple detections of compact binaries are expected in coming years~\cite{Abbott:2016nhf}. With respect to our black hole-axion star merger simulations, we have investigated the impact of the axion star's compactness, and the BH spin, on the mass of the remnant bosonic cloud surrounding the black hole. Although in most of the considered cases $\sim 98\%$ of the axion star's mass is absorbed by the black hole shortly after the merger, in favourable cases the remaining cloud can be as large as $30\%$ of the initial axion star mass, with a bosonic cloud of mass of $\mathcal{O}(10^{-1})M_{\rm BH}$ and peak energy density of $10^{-4}$, comparable to that obtained in a superradiant build up. We find that the largest scalar clouds are generated for low compactness ASs and spinning black holes. We note that there appear to be particular combinations which are overall more efficient at producing large axion clouds. We speculate that this might be caused by the excitation of particular quasi-bound states of the black hole. The presented results are important since they show (i) that axion star-black holes mergers can provide a dynamical mechanism for the formation of scalar hair around black holes and (ii) that faster spinning (but not yet extremal) black holes allow for relatively large cloud masses. The spinning case is especially interesting as it may provide the seed for a superradiant build up, which could lead to additional observable gravitational wave signatures post merger. However, superradiance requires extremal spins and an appropriate matching of the axion and BH masses, whereas the effects we observe here are in principle more general. It would be worth extending this study to a larger range of mass ratios, spins and spin orientations, to confirm the approximate trends observed in this paper and identify whether the proposal that particular mass ratios and spin combinations are favourable for forming clouds is consistent with a wider set of results. It would also be interesting to consider the effect of larger self interactions of the axion field, other values of $M\mu$ and, in the longer term, interactions with baryonic matter in an accretion disc.\\ For our study of neutron star-axion star collisions, we restricted our investigations to the merger of axion stars of various compactnesses with a ``typical'' neutron star having a gravitational mass of $\sim 1.38M_\odot$ and the SLy equation of state. We found that for the setups studied, there exists a critical mass threshold for the axion star required to form a BH during the collision. In the considered cases, the black hole formation is triggered by the axion star being perturbed within the potential well of the neutron star. Its collapse leads to a black hole within the neutron star, rather than collapse of the neutron star itself. For sub-threshold axion star masses the merger remnant is a perturbed neutron star enveloped in an axion cloud. For super-threshold axion star masses the final remnant is a black hole with a scalar cloud surrounding it. We suggest that the black hole formation threshold may correspond to a type I critical phase transition, as in binary neutron star mergers, and therefore universality and scaling relations could exist near to the critical point. We present a first (although very approximate) estimate of the critical threshold parameter $\phi_c^*$, but further simulations are required for a more stringent constraints on the critical parameters. Interestingly, we found that in the marginally sub critical cases, a large amount of baryonic mass was released from the merger remnant due to the formation of shocks in the NS. These ejecta can give rise to a kilonova-like counterpart, such as ATF201gfo, e.g.~\cite{Monitor:2017mdv,Coulter:2017wya,Cowperthwaite:2017dyu,Smartt:2017fuw,Kasliwal:2017ngb,Kasen:2017sxr}. The potential new type of transient produced by such a near-critical neutron star-axion star collision is discussed in more detail in~\cite{Dietrich:inprep}. In cases where a black hole forms after the merger, the ejection of matter as well as the formation of a baryonic accretion disk or bosonic cloud is suppressed. However, in the most extreme case the final black hole remnant can be embedded in a bosonic cloud of mass $\mathcal{O}(10^{-3})M_\odot$. In future, we plan to perform further numerical simulations in which we add a direct interaction between the axions and the neutron star fluid. Such couplings, which are necessary to correctly model the QCD axion, could also give rise to observable effects in NS-NS collisions that occur in a background of axions. Such an approach would allow us to further constrain the properties of axionic dark matter using observations of the merger of binary neutron stars within dark matter halos. | 18 | 8 | 1808.04668 |
1808 | 1808.04174_arXiv.txt | In this work, we study the short term flaring activity from the high synchrotron peaked blazar Mrk 501 detected by the {\bf FACT} and H.E.S.S. telescopes in the energy range 2-20 TeV during June 23-24, 2014 (MJD 56831.86-56831.94). We revisit this major TeV flare of the source in the context of near simultaneous multi-wavelength observations of $\gamma$--rays in MeV-GeV regime with \emph{Fermi}-LAT, soft X-rays in 0.3-10 keV range with \emph{Swift}-XRT, hard X-rays in 10-20 keV and 15-50 keV bands with MAXI and \emph{Swift}-BAT respectively, UV-Optical with \emph{Swift}-UVOT and 15 GHz radio with OVRO telescope. We have performed a detailed temporal and spectral analysis of the data from \emph{Fermi}-LAT, \emph{Swift}-XRT and \emph{Swift}-UVOT during the period June 15-30, 2014 (MJD 56823-56838). Near simultaneous archival data available from \emph{Swift}-BAT, MAXI and OVRO telescope along with the V-band optical polarization measurements from SPOL observatory are also used in the study of giant TeV flare of Mrk 501 detected by the {\bf FACT} and H.E.S.S. telescopes. No significant change in the multi-wavelength emission from radio to high energy $\gamma$--rays during the TeV flaring activity of Mrk 501 is observed except variation in soft X-rays. The varying soft X-ray emission is found to be correlated with the $\gamma$--ray emission at TeV energies during the flaring activity of the source. The soft X-ray photon spectral index is observed to be anti-correlated with the integral flux {\bf showing harder-when-brighter behavior}. An average value of 4.5$\%$ for V-band optical polarization is obtained during the above period whereas the corresponding electric vector position angle changes significantly.{\bf We have used the minimum variability timescale from the H.E.S.S. observations to estimate the Doppler factor of the emission region which is found to be consistent} with the previous studies of the source. | Blazars are a special class of radio loud active galactic nuclei (AGN) with powerful and highly relativistic jets oriented at small angles ($\le10^\circ$) to the line of sight of the observer on the Earth \citep{Readhead1978, Urry1995}. The jets of blazars are assumed to be powered by rotating supermassive black holes surrounded by accretion disks at the centers of massive elliptical type host galaxies. They are observed to be highly luminous at all wavelengths throughout the electromagnetic spectrum from radio to very high energy (VHE, E$>$100 GeV) $\gamma$--rays. The multi-wavelength emission from blazars is dominated by relativistic effects like Doppler boosting of the observed flux and dilation/compression of timescales due to orientation of the jets. The observed broadband spectral energy distribution (SED) of blazars from radio to $\gamma$--rays is characterized by two broad peaks. The origin of non-thermal SED is attributed to the relativistic charged particles in the blazar jets. The physical process responsible for the low energy peak at UV/optical to soft X-ray is relatively well understood and assumed to be the synchrotron radiation of relativistic electrons in the tangled magnetic field of the jet \citep{Urry1982, Marscher2008}. A significant contribution to the low energy hump has also been observed in the SED of many blazars in the narrow energy range from non-jet components like accretion disk, broad line region (BLR) and dusty torus \citep{Kushwaha2014, Nalewajko2014}. \par The origin of high energy (HE, $>$ 30 MeV) component of the SED peaking at hard X-rays to MeV-GeV $\gamma$--rays is not well understood and two alternative approaches: \emph{leptonic} and \emph{hadronic} have been proposed. In the leptonic approach, the origin of HE component of the SED is attributed to the inverse Comptonization of different circumnuclear low energy seed photons produced within the jet or outside it by relativistic leptons. If seed photons for the inverse Compton upscattering are the synchrotron photons produced by the same population of relativistic leptons within the jet, the process is referred to as synchrotron self Compton (SSC) model \citep{Maraschi1992, Sokolov2004}. On the other hand, if the seed photon field is external to the jet, namely from accretion disk, torus, broad line region or cosmic microwave background radiation, the process is termed as external Comptonization (EC) model \citep{Dermer1992, Sikora1994, Agudo2011}. Alternatively, in the hadronic approach, the emission of high energy component of the blazar SED is attributed to proton synchrotron or secondary emission from p-$\gamma$ interactions \citep{Mannheim1993, Pohl2000, Aharonian2002}. However, the leptonic models are more favored than hadronic processes for modelling the rapid variability observed in $\gamma$--ray emission from blazars \citep{Bottcher2013, Cerruti2015}. \par Blazars are classified into two broad categories: BL Lacertae objects (BL Lacs) and Flat Spectrum Radio Quasars (FSRQs) on the basis of the strength of emission lines in their optical spectra. The optical spectra of BL Lacs are characterized as featureless continuum emission with very weak or no emission lines, whereas FSRQs have prominent and broad emission lines \citep{Urry1995, Stocke1991, Marcha1996}. The position of peak frequency in the low energy component of the SED has also been used to subdivide blazars in three subclasses namely high synchrotron peaked (HSP), intermediate synchrotron peaked (ISP) and low synchrotron peaked (LSP) blazars \citep{Abdo2010}. The location of synchrotron peak frequency for HSPs is observed at UV/X-ray energies whereas FSRQs and ISPs have peak at IR/optical energies. The peak of HE component of the SED lies at GeV-TeV energies for HSPs and at hard X-ray energies for FSRQs and LSPs. BL Lacs and FSRQs have low and high luminosity respectively-forming the so called blazar sequence, but there is no general consensus on this phenomenological feature of blazars \citep{Ghisellini2017}. \par Emissions from most of the blazars have been observed to be variable over the entire electromagnetic spectrum at short timescales during the flaring activities followed by quiescent state. The multi-wavelength emissions from blazars show a high degree of polarization and strong variability on timescales from days to minutes. Rapid flaring activities in blazars on hour and minute timescales are dominant at $\gamma$--ray energies with change in flux up to few magnitudes \citep{Falomo2014, Ackermann2016, Rani2013}. In general, the flaring activity in X-ray and VHE regimes has become one of the most important observational features of the blazars. However, the physical processes involved in the origin of such dramatic behaviour of blazars have not been clearly explained. In this paper, we present the multi-wavelength study of the short term TeV flaring activity from the blazar Mrk 501 detected by the H.E.S.S. and FACT telescopes \citep{Chakraborty2015, Cologna2016} during the night of June 23-24, 2014 (MJD 56831.86-56831.94) . In Section 2, we briefly describe the observational history of the blazar Mrk 501 over the last two decades. The details of multi-wavelength observations and data analysis are given in Section 3. Section 4 provides discussion of the results obtained in this study. Finally, we summarize the important findings of this work in Section 5. We have assumed a flat $\Lambda$CDM cosmology with $\Omega_m = 0.3$, $\Omega_\Lambda = 0.7$ and $H_0 = 70\;km\;s^{-1}\;Mpc^{-1}$ throughout the paper. | \subsection{Multi-wavelength light curve} The multi-wavelength light curves of Mrk 501 from HE $\gamma$--rays to radio for the period June 15-30, 2014 (MJD 56823-56838) covering the period of VHE $\gamma$--ray flare on the night of June 23-24, 2014 (MJD 56831.86-56831.94) are shown in Figure \ref{fig:lc}(a-g). The duration of short term TeV flaring activity detected by the H.E.S.S. telescopes is indicated by two vertical lines in Figure \ref{fig:lc}. The values of average emission in all the energy bands estimated from the constant fit to the light curves and corresponding reduced $\chi^2_r$ (dof: degree of freedom) are given in Table \ref{tab:constant}. We observe that the multi-wavelength emission of the blazar Mrk 501 from HE $\gamma$--rays to radio is consistent with constant emission except for soft X-ray emission detected by \emph{Swift}-XRT during this period. The daily averaged soft X-ray flux in the energy range 0.3-10 keV measured by \emph{Swift}-XRT is shown in Figure \ref{fig:lc}(d). It is evident that near simultaneous X-ray activity of the source in the energy range 0.3-10 keV is consistent with the VHE activity in the energy range 2-20 TeV detected with H.E.S.S. (Figure 1 in \citet{Chakraborty2015}) and above 750 GeV observed with FACT (Figure 1 in \citet{Cologna2016}). In soft X-ray band, the source is observed in the highest activity state on June 21, 2014 (MJD 56829), but no contemporeneous activity is detected in VHE band by the FACT and H.E.S.S. telescopes. In VHE band, the source is observed in extreme activity state on the night of June 23-24 (MJD 56831.86-56831.94) with near simultaneous high state emission in soft X-rays. The variability of the source in VHE band is observed to be very fast with minimum variability timescale of $\sim$ 6 minutes \citep{Chakraborty2015} in the observations of flaring activity with H.E.S.S. but no minute scale variability is obtained in the FACT observations \citet{Cologna2016} due to low sensitivity of the telescope. With this rapid variability of the source, the absence of VHE flare during the highest soft X-ray activity on June 21, 2014 (MJD 56829) can be attributed to the non-simultaneous observations with H.E.S.S., FACT and \emph{Swift}-XRT. However, X-ray emissions in the energy bands 10-20 keV (Figure \ref{fig:lc}(c)) and 15-50 keV (Figure \ref{fig:lc}(b)) detected with MAXI and \emph{Swift}-BAT respectively are consistent with constant emission within statistical uncertainties. \par The HE $\gamma$--ray emission of Mrk 501 observed with \emph{Fermi}-LAT as shown in Figure \ref{fig:lc}(a), also does not show any signature of variability during this period. The flux points with downward arrow in the Figure \ref{fig:lc}(a) represent 2$\sigma$ upper limits on the integral flux above 100 MeV for the observations when source is not significantly detected with \emph{Fermi}-LAT. The constant emissions in UV, optical and radio bands depicted in Figure \ref{fig:lc}(e-g) respectively during the period June 15-30, 2014 (MJD 56823-56838) are consistent with the source behaviour known from the past observations. A positive correlation between VHE $\gamma$--ray emission above 750 GeV observed with FACT and X-rays in the energy range 2-10 keV had been reported by \citet{Cologna2016} for the above observation period. But, the correlation was violated during the TeV flaring activity observed on the night of June 23-24, 2014 \citep{Cologna2016, Cologna2015}. This suggests that the physical parameters involved in the VHE $\gamma$--ray emission during the extreme flaring state may be different from the rest of the emissions observed from Mrk 501 \citet{Cologna2016}. Different values of correlation index between the TeV and X-ray emissions can be derived depending on the assumed evolution scenario in different spectral bands under the frame-work of homogeneous single zone SSC model \citep{Katarzynski2005}. A quadratic or more than quadratic correlation between the TeV and X-ray flux points is expected for simultaneous emission from two independent zones, where one zone emits in X-ray band and other zone dominates at TeV $\gamma$--rays \citep{Katarzynski2010}. However, a quadratic correlation between soft X-ray and TeV $\gamma$--ray flux points during the flaring activity can be explained for a specific choice under the framework of single zone SSC model when the source activity is attributed to the variation in the leptonic particle density \citep{Singh2017, Sahayanathan2018}. In this case, TeV flux due to SSC process varies quadratically with respect to X-ray flux produced by the synchrotron process. Referring to the VHE flare detected by the H.E.S.S. telescopes, the TeV light curve in the energy range 2-20 TeV has been divided into two sub energy bands: 2-4.5 TeV and 4.5-20 TeV (Figure 2 in \citet{Chakraborty2015}). Variations at short timescale are observed in both energy bands. The detailed temporal analysis of the VHE light curve is beyond the scope of the present study. \begin{table} \caption{Constant emission model fit to the multi-wavelength light curves of Mrk 501 during the period June 15-30, 2014 (MJD 56823-56838) as shown in Figure \ref{fig:lc}.} \label{tab:constant} \vspace{0.3cm} \begin{center} \begin{tabular}{lcccc} \hline Energy band &Instrument &Constant flux (erg~$cm^{-2}$~s$^{}$) &$\chi^2_r$/dof\\ \hline 0.1-300 GeV &Fermi/LAT &(2.30$\pm$0.31)$\times10^{-10}$ &0.86/7\\ 15-50 keV &Swift/BAT &(1.17$\pm$0.12)$\times10^{-10}$ &0.66/11\\ 10-20 keV &MAXI &(6.10$\pm$0.68)$\times10^{-10}$ &0.36/5\\ 0.3-10 keV &Swift/XRT &(4.52$\pm$0.26)$\times10^{-10}$ &234/11\\ 203 nm (W2 band)&Swift/UVOT &(3.36$\pm$0.07)$\times10^{-11}$ &9.8/10\\ 223 nm (M2 band)&Swift/UVOT &(2.72$\pm$0.03)$\times10^{-11}$ &2/10\\ 263 nm (W1 band)&Swift/UVOT &(2.54$\pm$0.09)$\times10^{-11}$ &25/11\\ 350 nm (U band) &Swift/UVOT &(3.40$\pm$0.05)$\times10^{-11}$ &0.78/2\\ 432 nm (B band) &Swift/UVOT &(5.25$\pm$0.02)$\times10^{-11}$ &0.49/2\\ 540 nm (V band) &Swift/UVOT &(7.68$\pm$0.04)$\times10^{-11}$ &0.13/2\\ 15 GHz (Radio) &OVRO &(1.76$\pm$0.02)$\times10^{-13}$ &2.34/2\\ \hline \end{tabular} \end{center} \end{table} \begin{figure} \begin{center} \includegraphics[width=1.0\textwidth]{lc.eps} \caption{Daily averaged multi-wavelength light curves of Mrk 501 during the period June 15-30, 2014 (MJD 56823-56838) observed with different instruments from HE $\gamma$--rays to radio. The error bars in XRT, UV and optical flux measurements are very small and their size is comparable to the size of plot points. The time interval between two vertical lines represents the period ($\sim$ 2.1 hours) of TeV flaring activity of the source detected by H.E.S.S. on the night of June 23-24, 2014 (MJD 56831.86-56831.94) \citep{Chakraborty2015}.} \label{fig:lc} \end{center} \end{figure} \subsection{Variability analysis} The variability present in the flux values simultaneously measured in different energy bands would provide useful information regarding the physical processes involved in the emission mechanism at the source. In order to search for the intrinsic variability in the near simultaneous multi-wavelength light curves obtained for the period June 15-30, 2014 during the TeV flaring activity of Mrk 501, we have estimated the fractional variability amplitude (F$_{var}$) parameter. We have used the description proposed in \citep{Vaughan2003} to estimate the fractional variability amplitude in different energy bands from radio to HE $\gamma$--rays. F$_{var}$ is defined as \begin{equation} F_{var}=\frac{\sqrt{S^{2}-\langle \sigma_{err}^{2}\rangle}}{\langle F\rangle} \end{equation} where $\langle F\rangle$ is the average flux, \textit{S} is the standard deviation and $\sigma_{err}^{2}$ is the mean square error of N-flux measurements of a given light curve. Realizing that the variability is not clearly detected (weak intrinsic amplitude or low signal-to-noise ratio) in the multi-wavelength light curves shown in Figure \ref{fig:lc}, the uncertainty in F$_{var}$ can be estimated using the expression \citep{Vaughan2003} \begin{equation} \Delta F_{var}=\frac{1}{F_{var}} \sqrt{\frac{1}{2N}} \frac{\langle \sigma_{err}^{2}\rangle}{{\langle F \rangle}^2} \end{equation} We have estimated the values of F$_{var}$ for all the energy bands from radio to HE $\gamma$--rays during the period June 15-30, 2014 (MJD 56823-56838) of Mrk 501 observations. It is to be noted that for \emph{Fermi}-LAT data, F$_{var}$ has been calculated using only the detected flux points and excluding the upper limits as shown in the light curve. The values of F$_{var}$ are obtained to be negligibly small for OVRO, \emph{Swift}-UVOT, MAXI, \emph{Swift}-BAT and \emph{Fermi}-LAT observations during the above period. However, the soft X-ray emission in the energy range 0.3-10 keV observed with \emph{Swift}-XRT is found to be significantly varying with the value of F$_{var}$ $=$ 0.23$\pm$0.07 during the VHE flaring activity. The value of F$_{var}$ $=$ 0.11$\pm$0.03 has been estimated for VHE $\gamma$--ray emission in the energy range 2--20 TeV during the flaring state of the source observed for $\sim$ 2.1 hours on the night of June 23-24, 2014 (MJD 56831.86-56831.94) by the H.E.S.S. telescopes \citep{Chakraborty2015}. It is observed that the estimated value of F$_{var}$ for the soft X-ray variability is compatible with the VHE variability observed quasi-simultaneously by H.E.S.S. during the flaring activity. However, it can be noted that the estimated value of F$_{var}$ for a given light curve also depends on the size of the time bin. A light curve with smaller time bin can give higher value of F$_{var}$, whereas larger time bins can smooth out the flux variations in the light curve and yield lower value of F$_{var}$. The values of F$_{var}$ estimated for soft X-rays and TeV $\gamma$--rays support the synchrotron and SSC emission models for the blazars like Mrk 501. \begin{figure} \begin{center} \includegraphics[width=0.80\textwidth,angle=-90]{pol.eps} \caption{Optical linear polarization in V-band (bottom) and electric-vector position angle (top) as a function of time measured at Steward Observatory during the period June 15-30, 2014 (MJD 56823-56838). The short term TeV flaring activity of Mrk 501 is detected by the H.E.S.S. telescope on the night of June 23-24, 2014 (MJD 56831.86-56831.94). The maximum synchrotron polarization estimated from \emph{Swift}-XRT observations during the above period are also shown in the lower panel.} \label{fig:pol} \end{center} \end{figure} \subsection{Optical Polarization and TeV flare} Polarization studies of relativistic outflows in extreme astrophysical environments like blazar jets provide important tools to probe the geometry of the magnetic field in the emission region and to identify physical processes for the non-thermal emission. The observables of polarization of electromagnetic radiation emitted from blazars are degree of polarization ($\Pi$) and electric vector position angle (EVPA) or simply polarization angle ($\theta$). The degree of polarization is the fraction of total flux which is polarized, whereas EVPA provides information about the orientation of electric field vector in the sky plane. The optical polarization also directly indicates the ordering of magnetic field in the jet. The time variation of degree of polarization in the optical V-band and associated EVPA measured from Mrk 501 by the \emph{SPOL} telescope during the period June 15-30, 2014 (MJD 56823-56838) is shown in Figure \ref{fig:pol}. The degree of polarization in the V-band optical emission of the blazar Mrk 501 is observed to be constant with an average value of $\sim$ 4.5$\%$, whereas EVPA changes from $\sim$ 133$^\circ$ to a maximum of $\sim$ 141$^\circ$ with a rotation rate of $\sim$ 1$^\circ$ per day during the above period. It is to be noted that the degrees of polarization from \emph{SPOL} measurements shown in Figure \ref{fig:pol} are not corrected for thermal emission from host galaxy. The variation in EVPA is nearly simultaneous with the flaring activity of the source in the soft X-ray and TeV energy bands. The observed possible coincidence of soft X-ray and VHE $\gamma$--ray flares with change in optical polarization angle provides evidence for involvement of the synchrotron and SSC processes in the broad-band emission of the source. \par The measurement of synchrotron polarization is the standard approach to investigate the properties of magnetic field and energy distribution of emitting electrons in the blazar jet \citep{Westfold1959, Itoh2016}. If the underlying energy distribution of leptons (electrons and positrons) emitting synchrotron radiation is described by a power law with spectral index $p$, the maximum degree of linear polarization for a given direction of the magnetic field (ordered) is given by \citep{Westfold1959, Rybicki1986, Marscher2014} \begin{equation} \Pi_{syn}=\frac{p+1}{p+7/3} \end{equation} The spectral distribution of synchrotron photons emitted from the source is also described by a power law with spectral index $\alpha$, which is related to $p$ as \begin{equation} \alpha=\frac{p-1}{2} \end{equation} Equation 3 gives maximum degree of polarization for the synchrotron radiation in an ordered magnetic field. We have estimated the maximum degree of polarization ($\Pi_{syn}$) for synchrotron radiation using the values of photon spectral indices ($\alpha$) obtained from the \emph{Swift}-XRT analysis (Table \ref{tab:xrt}) in equations 3 \& 4. The values of maximum synchrotron polarization calculated from the soft X-ray observations have been compared with the V-band optical polarization measured by \emph{SPOL} at Steward Observatory in Figure \ref{fig:pol} (bottom panel). It is evident from Figure \ref{fig:pol} that the maximum synchrotron polarization ($\Pi_{syn}$) during the period of our study has an average value of more than 80$\%$, which is much higher than the observed V-band optical polarization with an average value of $\sim$ 4.5$\%$. The large difference between observed and estimated maximum polarization values can be attributed to the various physical effects like tangled and inhomogeneous magnetic field \citep{Gruzinov1999}, Faraday rotation and presence of thermal components in the optical emission from the host galaxy \citep{Netzer2013}. {\bf The host galaxies of low redshift blazars like Mrk 501 are huge and luminous with elliptical morphology \citep{Hyvonen2007,Nilsson2007}. The previous optical studies of Mrk 501 indicate that the subtraction of host galaxy contamination is correlated with the observed magnitudes of the source. A reasonable host galaxy subtraction has been found from the optical photometry of the blazar Mrk 501 \citep{Feng2017}. Therefore, the thermal emission from the host galaxy of Mrk 501 has strong impact on the observed polarization of the source}. Also, no clear correlation is observed between the V-band optical flux and degree of polarization during the period of TeV flaring activity detected by the H.E.S.S. telescopes. This can be attributed to the presence of turbulent magnetic field in the jet emission region. Detailed study of the depolarization effects like random magnetic field in the jet emission region and thermal contamination from the host galaxy emission is beyond the scope of this work. \begin{figure} \begin{center} \includegraphics[width=0.80\textwidth,angle=-90]{spec_evol.eps} \caption{Spectral evolution of the soft X-ray emission from Mrk 510 in the energy range 0.3--10 keV measured by \emph{Swift}-XRT during period June 21-24, 2014 (MJD 56829-56832). The arrows indicate time progession of the data points in clock-wise direction during the above period. The data point labelled with TeV flare corresponds to nearest simultaneous XRT observation of the high activity state of Mrk 501 detected by the H.E.S.S. telescopes.} \label{fig:spec_evol} \end{center} \end{figure} \subsection{X-ray Spectral Evolution} The spectral evolution in the blazar emission helps in investigating the acceleration and cooling features in the jet. This is acheived by analysing the hysteresis patterns of the photon spectral index as function of the source integral flux. The spectral evolution of soft X-ray emission observed with \emph{Swift}-XRT in the energy range 0.3-10 keV during the VHE flaring activity of Mrk 501 detected with H.E.S.S. on June 23, 2014 (MJD 56831.86-56831.94) is shown in Figure \ref{fig:spec_evol}. The \emph{Swift}-XRT measurements shown in Figure \ref{fig:spec_evol} correspond to the observation period during June 21-24, 2014 (MJD 56829-56832) including the period of VHE flaring activity. We observe that the soft X-ray photon spectral index is anti-correlated with the integral flux in the energy range 0.3-10 keV and indicates the presence of a possible clockwise hysteresis loop structure in the spectral index versus flux plane {\bf showing harder-when-brighter behavior}. \subsection{Estimation of active region parameter from observables} The source paremeter like Doppler factor ($\delta_D$) can be estimated from the minimum variability timescale observed in the emission of the source. The rapid variability, apparent superluminal motion and high bolometric luminosity observed in blazar emission indicate that the broad band non-thermal emission of blazars is produced in a compact active region, relativistically moving along the jet oriented towards the observer. The flux variability from radio to VHE $\gamma$--rays at timescales from seconds to years is an important observational characteristics of blazars powered by supermassive black holes at the center of elliptical host galaxy. Blandford-Znajek mechanism suggests that the jets in blazars are powered by the extraction of rotational energy from the supermassive black holes at the center \citep{Blandford1977}. For a maximally rotating supermassive black hole of mass $M$, the gravitaional radius is given by \begin{equation} R_g=\frac{GM}{c^2} \end{equation} where $G$ is the universal gravitational constant and $c$ is the speed of light. An observer can see into the hot dense, highly magnetized plasma in the inner parts of the \emph{jet forming region}, whose size will be of the order of $R_g$ \citep{Riordan2016}. Assuming that the emitted radiation is dominated by the turbulent plasma of the \emph{jet forming region} close to the event horizon, the minimum variability timescale in the comoving frame ($t_{var}$) would be comparable to the event horizon light crossing time ($t_{EH}$) which is given by \begin{equation} t_{EH}=\frac{R_g}{c} \end{equation} Relativistic boosting in the blazar emission leads to the shortening of the observed variability timescale ($t_{obs}$) as compared to the variability timescale in the comoving frame ($t_{var}$) given by \begin{equation} t_{obs}=\left(\frac{1+z}{\delta_D}\right)~t_{var} \end{equation} where $z$ is the redshift of the source. With the assumption that $t_{var} \approx t_{EH}$, the observed minimum variability timescale gives \begin{equation} \delta_D=\left(\frac{1+z}{t_{obs}}\right)\frac{GM}{c^3} \end{equation} The host galaxy of blazar Mrk 501 harbours a supermassive black hole of mass $\sim$ 2.2$\times$~10$^9$~$M_\odot$ at its center \citep{Barth2002}. The flare of Mrk 501 detected by H.E.S.S. on the night of June 23-24, 2014 (MJD 56831.86-56831.94) at TeV energies shows fast flux variations on a timescale of $t_{obs}~\sim$ 6 minutes \citep{Chakraborty2015}. Using these observed quantities in equation 8, we have estimated the value of Doppler factor $\delta_D ~\sim$ 31 which is compatible with the value of bulk Lorentz factor for very small jet viewing angle. This implies that the hypothesis that the \emph{jet forming region} in the blazar Mrk 501 is close to the event horizon of the supermassive black hole at the center of its host galaxy. | 18 | 8 | 1808.04174 |
1808 | 1808.03424_arXiv.txt | This paper investigates whether an isotropic zodiacal light from the outer Solar system can account for the detected background excess in near-infrared. Assuming that interplanetary dust particles are distributed in a thin spherical shell at the outer Solar system ($>200$ AU), thermal emission from such cold ($<30$ K) dust in the shell has a peak at far-infrared ($\sim 100$ \micron). By comparing the calculated thermal emission from the dust shell with the observed background emissions at far-infrared, permissible dust amount in the outer Solar system is obtained. Even if the maximum dust amount is assumed, the isotropic zodiacal light as the reflected sunlight from the dust shell at the outer Solar system cannot explain the detected background excess at near-infrared. | The Extragalactic Background Light (EBL) arises from integrated emission from the first star production era to the present day. Thus observation of EBL as the accumulated history of the universe is important to understand the star formation history. Recent observations show that the measured EBL at optical and near-infrared (NIR) has an excess of $\sim 30$ nW/m$^2$/sr over the cumulative light from galaxies \citep{Tsumura, Matsumoto, Sano1, Sano2, Mattila, CIBER}, meaning that there are unknown light sources in the universe. For candidates of light sources for this NIR background excess, intra-halo light \citep{Cooray, Zemcov}, emissions from LIGO-type blackholes \citep{Kashlinsky}, and decaying hypothetical particles \citep{Kohri} are proposed. On the other hand, isolation of the EBL from foreground emissions is difficult due to its diffuse, extended nature. The largest uncertainty comes from the removal of the dominant foreground, the zodiacal light, which is scattered sunlight at optical and NIR, and thermal emission at mid- and far-infrared (FIR) from interplanetary dust (IPD) within the Solar system. In this reason, some authors claimed that the NIR background excess is caused by systematic uncertainty in subtraction of the zodiacal light \citep{Dwek, Kawara}. In the recent EBL observations, the zodiacal light is subtracted using the model based on morphology and time variation measured by DIRBE on {\it COBE} satellite \citep{Kelsall}. If there is an isotropic zodiacal light component showing no time variation, such isotropic component is not included in the zodiacal light model. Thus the isotropic zodiacal light component can be a source of the NIR background excess \citep{Dwek2, Chary}. Such isotropic zodiacal light component, if it exists, is made by IPD around the Earth or around the outer Solar system, because it does not show time variation by the observations from the Earth. \citet{Matsumoto2} compared the zodiacal light model \citep{Kelsall} with the observational data of the zodiacal light during the cruising to Jupiter by {\it Pioneer 10}, and no evidence was found that the isotropic zodiacal light component exists around the Earth. In this reason, the other possibility of the existence of IPD around the outer Solar system is investigated in this paper. The zodiacal light is dominated by the thermal emission from the nearby IPD whose temperature is $\sim$280 K, and the peak of such thermal emission comes at mid-infrared. On the other hand, if the dust exists around the outer Solar system to make the isotropic zodiacal light component, temperature of such IPD is quite low, and thermal emission from such low temperature IPD has a peak at FIR. Thus, as the strategy of this paper, it is investigated whether the NIR background excess is explained by the isotropic zodiacal light from the IPD around the outer Solar system, whose amount is restricted by the FIR background data. This paper is organized as follows. In Section 2, the acceptable upper limit of IPD amount is obtained from the FIR background data. Using this amount of IPD, isotropic zodiacal light component at NIR is calculated, and it is compared with the NIR background excess in Section 3. Then discussion on our results comes in Section 4, and conclusion comes in Section 5. | \subsection{Parameter Dependence of $M_{shell}$} The obtained total mass of the spherical IPD shell $M_{shell}$ in Table \ref{table} depends on the average IPD mass density $\rho$, and $\rho = 2$ g/cm$^3$ is adopted in this paper. Mass density range of IPD particles (5-15 \micron\ size) collected at the stratosphere is 0.3 - 6.0 g/cm$^3$, averaging 2.0 g/cm$^3$ \citep{Love}. \citet{Grun} also state that majority of the IPD have $\rho$ = 2 - 3 g/cm$^3$, whereas 20-40 \% of the IPD has low density ($<1$ g/cm$^3$). Such low density IPD are though to be cometary origin \citep{Joswiak, Wiegert}. In the outer Solar system, contributions of cometary origin IPD may be increased, and thus the average mass density may be smaller than our adopted value of $\rho = 2$ g/cm$^3$. In such a case of smaller mass density, the required total mass of the spherical IPD shell $M_{shell}$ becomes low, thus the upper limit obtained in this paper becomes more conservative. The obtained total IPD mass $M_{shell}$ also depends on the IPD size $a$, because smaller IPD are hotter, thus farther distance $d$ from the Sun is required to be 16-30 K (Figure \ref{temp}), and then more masses is allowed within the FIR background excess. Results in the cases of $a = 1$ \micron\ are also shown in Table \ref{table} for comparison. These results mean that if the IPD in the outer Solar system is dominated by small particles ($a = 1$ \micron), about 100 times more IPD masses than the case of $a = 10$ \micron\ can be acceptable in the outer Solar system within the FIR background excess, resulting that about 10 times more NIR background $\lambda I_{\lambda}^{NIR}$ is obtained. This result is consistent with the result in \citet{Dwek2} of $10^{-3} < M_{shell} / M_{Earth} < 10^{2}$ at $> 700$ AU for $\beta =2$ case. On the other hand, however, the total IPD mass is dominated by large particles ($\sim$100 \micron) from the dust size distribution around the Earth \citep{Kral}. Although this dust size distribution is valid around the Earth, it is difficult to believe that the small IPD particles ($a < 1$ \micron) is dominated in the outer Solar system. Anyway, even in the $a = 1$ \micron\ case with $M_{shell} \sim 10 M_{Earth}$ at $\sim$ 4300 AU (Case A'), the obtained isotropic zodiacal light at NIR $\lambda I_{\lambda}^{NIR}$ is still $< 1/10$ of the NIR background excess. Therefore, the NIR background excess cannot be explained even in the small dust size cases. \subsection{Comparison to Models and Observations} The maximum permissible IPD mass in the outer Solar system obtained in this study is much more than the total IPD mass inside Jupiter's orbit ($10^{-9}$ - $10^{-8}M_{Earth}$) \citep{Fixsen, Nesvorny}. Is it realistic that such amount of IPD exist in the outer Solar system? Outside of the heliosphere ($> 250$ AU), IPD are charged in the interstellar environment and ejected by the interstellar magnetic field. According to \citet{Belyaev}, IPD with $a > 15$ \micron\ at $d > 1000$ AU and $a > 1$ \micron\ at $d > 100$ AU are ejected from the Solar system. \citet{Dwek2} stated that only a cloud consisting of IPD larger than $\sim 1$ cm located between $\sim 5$ and 150 AU would be stable. Therefore, the IPD shell assumed in this study cannot survive unless there is continuous supply of IPD. IPD is believed to be supplied from comets \citep{Nesvorny, Yang} and asteroids \citep{Dermott, Nesvorny2, Tsumura2}, but comets are not active and asteroidal collisions are also less likely to occur in the cold and low density environment in the outer Solar system. Therefore, the large amount of dust assumed in this study cannot be supplied by any of known mechanisms. \citet{Poppe} constructed a dust density model based on the in-situ dust counting by {\it Pioneer 10}, {\it Galileo}, and {\it New Horizons}. According to this model, dust density of 20 \micron\ size is $\sim 5 \times 10^{-4}$ km$^{-3}$ at 70 AU, dominated by dust grains originated from the Edgeworth-Kuiper belt objects and the Oort cloud comets. Even by assuming this dust density is kept up to 1000 AU, the mass of a dust shell at 1000 AU with 10 AU thickness is $<3 \times 10^{-7} M_{Earth}$, which is much less than the required amount to explain the FIR background excess (see Table \ref{table}). In addition, a Solar-type star HD72905 (G1.5V, age $\sim 0.4$ Gyr) has 70 \micron\ excess ($L_{dust}/L_{\star} \sim 10^{-5}$) in its spectrum detected by MIPS/{\it Spitzer}, and this extra emission is produced by cool ($< 100$ K) dust of $<10^{-2} M_{Earth}$ \citep{Bryden}. Because our Solar system has $L_{dust}/L_{\odot} \sim 2 \times 10^{-7}$ \citep{Nesvorny}, the IPD amount in our Solar system should be less than that in HD72905. In these reasons, it is unlikely that a large amount of dust exists in the outer Solar system to explain the FIR background excess, therefore it is even unlikely to explain the NIR background excess by the isotropic zodiacal light. | 18 | 8 | 1808.03424 |
1808 | 1808.05728_arXiv.txt | { Machine learning has increasingly gained more popularity with its incredibly powerful ability to make predictions or calculated suggestions for large amounts of data. We apply the machine learning classification to 85,613,922 objects in the $Gaia$ data release 2, based on the combination of the Pan-STARRS 1 and AllWISE data. The classification results are cross-matched with Simbad database, and the total accuracy is 91.9\%. Our sample is dominated by stars, $\sim$ 98\%, and galaxies makes up 2\%. For the objects with negative parallaxes, about 2.5\% are galaxies and QSOs, while about 99.9\% are stars if the relative parallax uncertainties are smaller than 0.2. Our result implies that using the threshold of 0 $< \sigma_\pi/\pi <$ 0.2 could yield a very clean stellar sample. | The ESA space mission $Gaia$ performs an all-sky astrometric, photometric, and radial velocity survey at optical wavelengths \citep{Gaia16a}. The primary objective of the $Gaia$ mission is to survey more than one billion stars, in order to investigate the origin and subsequent evolution of our Galaxy. Its second data release ($Gaia$ DR2; \citealt{Gaia18}) includes $\sim$ 1.3 billion objects with valid parallaxes. These parallaxes are obtained with a complex iterative procedure, involving various assumptions \citep{Lindegren12}. Such procedure may produce parallaxes for galaxies and QSOs, which should present no significant parallaxes \citep{Liao18}. Besides, $Gaia$ uses two fields of view to observe, and this in principle might lead to a global parallax bias \citep{van05,Butkevich17,Liao17}. Separating galaxies and QSOs from stars allows us to characterize the parallax bias in the $Gaia$ catalog, and to provide a clean and accurate stellar sample for further investigation. Traditionally, the classification of objects involves magnitudes and colors criteria, but the criteria become too complex to be described with functions in a multidimensional parameter space. By contrast, this parameter space can be effectively explored with machine-learning (ML) algorithms, which have helped us to deal with complex problems in modern astrophysics \citep{Huertas08,Huertas09,Manteiga09,Bai18a,Pashchenko18}. ML provides us an alternative option to classify billions of objects that cannot be followed-up spectroscopically. \citet{Bai18a} applied the supervised ML to the star/galaxy/QSO classification based on the combination of SDSS and LAMOST spectral surveys (the SL classifier). Actually, the class labels of the training objects are from spectroscopy, and are regarded as true. Narrow line QSOs are classified as galaxies by both SDSS and LAMOST pipeline because the template of QSO in the pipelines is the theoretical one with broad emission lines. The classifier built with the random forest algorithm showed best performance on time cost and the inner accuracy. Several blind tests were also performed on the objects observed by the RAVE, 6dFGS and UVQS. The accuracies were higher than 99\% for the stars and galaxies, and higher than 94\% for the QSOs. In this paper, we apply the SL classifier to the $Gaia$ DR2 to investigate the potential extragalactic objects. The data and classification are described in Section \ref{data}. Section \ref{res} gives the result and analysis, and a summary is given in Section \ref{sum}. | \label{sum} We apply the SL classifier to 85,613,922 objects in the $Gaia$ DR2, based on the colors built from the PS1 and AllWISE. The classification shows that about 98\% of the sample are stars, and 2\% are galaxies. This result is cross-matched with Simbad database in order to estimate the probability of the possibly wrong classifications, and the total accuracy is 91.9\%. The Galactic plane is dominated by the stars, and the percentages become higher at high latitudes. We find that about 2.5\% of the sample are galaxies for the objects with negative parallaxes, and the threshold of 0 $< \sigma_\pi/\pi <$ 0.2 could yield a very clean stellar sample including about 99.9\% stars. | 18 | 8 | 1808.05728 |
1808 | 1808.09440_arXiv.txt | { We review the advanced version of the KKLT construction and pure $d=4$ de~Sitter supergravity, involving a nilpotent multiplet, with regard to various conjectures that de Sitter state cannot exist in string theory. We explain why we consider these conjectures problematic and not well motivated, and why the recently proposed alternative string theory models of dark energy, ignoring vacuum stabilization, are ruled out by cosmological observations at least at the $3\sigma$ level, i.e. with more than $99.7\%$ confidence.} | \label{sec:intro} \parskip 6pt The observation of late-time cosmic acceleration, almost exactly 20 years ago, is one of the most important cosmological discoveries of all time. As a result of that, we now face two extremely difficult problems at once: we have to explain why the vacuum energy/cosmological constant $\Lambda$ is not exactly zero but is extremely small, about $0.7\times 10^{{-120}}$ in $d=4$ Planck units, and why it is of the same order as the density of normal matter in the universe, but only at the present epoch. This problem was addressed by constructing $d=4$ de Sitter (dS) vacua in the context of KKLT construction in Type IIB superstring theory~\cite{Kachru:2003aw,Kachru:2003sx}. De Sitter vacua in noncritical string theory were studied earlier in~\cite{Silverstein:2001xn,Maloney:2002rr}. The most important part of de Sitter constructions in string theory and its various generalizations is the enormous combinatorial multiplicity of vacuum states in the theory~\cite{Douglas:2003um,Douglas:2006es,Denef:2007pq} and the possibility to tunnel from one of these states to another in the string theory landscape~\cite{Kachru:2003aw,Susskind:2003kw}, just as anticipated in the eternal chaotic inflation scenario~\cite{Linde:1986fd}. The value of the cosmological constant $\Lambda$ originates from an incomplete cancellation between two contributions to energy, a negative one, $V_{\rm AdS}< 0,$ due to the Anti-de Sitter (AdS) minimum used for moduli stabilization, and a positive one, due to an $\overline {D3}$-brane. In different parts (or different quantum states) of the universe, the difference between these two may take arbitrary values, but in the part of the universe where we can live it must be extremely small~\cite{Davies:1980ji,Linde:1984ir,Sakharov:1984ir,Banks:1984cw,Linde:1986fd,Barrow:1988yia,Linde:1986dq,Weinberg:1987dv,Martel:1997vi,Garriga:1999hu,Bousso:2000xa,Susskind:2003kw,Linde:2015edk}, \be \Lambda = V_{\overline {D3}}- V_{\rm AdS} \approx 10^{{-120}} \ . \label{dif}\ee Quantum corrections may affect vacuum energy in each of the dS or AdS minima, but one may argue that if the total number of possible vacua is large enough, there will be many vacua where the cosmological constant belongs to the anthropically allowed range $|\Lambda | \lesssim 10^{{-120}}$, as we have depicted in Fig. \ref{chi}. This makes the anthropic solution of the cosmological constant problem in the context of the string theory landscape rather robust. \begin{figure}[t!] \begin{center} \includegraphics[scale=0.34]{Figs/Landscape3.pdf} \end{center} \hskip 1cm \vskip -0.7cm \caption{\footnotesize There are many vacua before quantum corrections, and many vacua after quantum corrections. The ones on the right in the anthropically allowed range may originate from the ones on the left which were at all possible values of $\Lambda$. In this picture, quantum corrections may be large or small, but there will still be some vacua in the anthropic range, after all possible quantum corrections are made.} \label{chi} \end{figure} Although the basic features of the string landscape theory were formulated long ago, the progress in this direction still continues. Many interesting generalizations of the KKLT scenario have been proposed, some of which are mentioned below. Simultaneously, there have been many attempts to disprove the concept of string theory landscape, to prove that de Sitter vacua in string theory cannot be stable or metastable, and to provide an alternative solution to the cosmological constant problem. However, despite a significant effort during the last 15 years, no compelling alternative solution to the cosmological constant problem has been found as yet. Recently, a new attempt has been made in~\cite{Obied:2018sgi}. The authors conjectured that stable or metastable de Sitter vacua could not exist in string theory, and suggested to return to the development of superstring theory versions of quintessence models, simultaneously imposing a strong (and, in our opinion, not well motivated) constraint on quintessence models, ${| \nabla_\phi V|\over V} \geq c \sim 1$. The list of the currently available models of this type is given in~\cite{Obied:2018sgi}, and their cosmological consequences are studied in~\cite{Agrawal:2018own}, where a confusing conclusion has been drawn. In the abstract of~\cite{Agrawal:2018own} one finds: ``We study constraints imposed by two proposed string Swampland criteria on cosmology \dots~Applying these same criteria to dark energy in the present epoch, we find that specific quintessence models can satisfy these bounds and, at the same time, satisfy current observational constraints.'' However, in Section 5 of the same paper one reads: ``notably there do not exist rigorously proven examples in hand where $c$ is as small as $0.6$, as required to satisfy current observational constraints on dark energy.'' Indeed,~\cite{Agrawal:2018own} has argued that the models with $c > 0.6$ are ruled out at the $3\sigma$ level, even though in the revised version of the paper they say that $c > 0.6$ is ruled out at the $2\sigma$ level. An additional uncertainty has been introduced by Heisenberg et al.~\cite{Heisenberg:2018yae}, who claim that models with $c \leq 1.35$ are consistent with observations. % The first goal of the present paper is to explain that the `no-dS' conjecture of ~\cite{Brennan:2017rbf,Danielsson:2018ztv,Obied:2018sgi} is based, in part, on the no-go theorem~\cite{Maldacena:2000mw}, which has already been addressed in the KKLT construction~\cite{Kachru:2003aw,Kachru:2003sx}. Important developments in the KKLT construction during the last 4 years \cite{Kallosh:2014wsa,Ferrara:2014kva,Bergshoeff:2015jxa,Bergshoeff:2015tra,Hasegawa:2015bza,Kallosh:2015nia,Kallosh:2016aep,Aalsma:2018pll}, including the theory of uplifting from AdS to dS and the discovery of dS supergravity~\cite{Bergshoeff:2015tra,Hasegawa:2015bza} which addressed another no-go theorem~\cite{Pilch:1984aw}, % are not even mentioned in \cite{Brennan:2017rbf,Obied:2018sgi,Agrawal:2018own}, as well as in a recent review on compactification in string theory \cite{Danielsson:2018ztv}. The second goal of our paper is to determine which of the three conclusions of \cite{Agrawal:2018own,Heisenberg:2018yae} on the observational constraints on $c$ is correct. We show that dark energy models with $c > 1$ are ruled out at the $3\sigma$ level, i.e. with $99.7\%$ confidence. All the models discussed in \cite{Obied:2018sgi,Agrawal:2018own}, which may be qualified as derived from string theory in application to the four-dimensional (4d) universe, require $c \geq \sqrt{2} \sim 1.4$, which is ruled out by cosmological observations. If one attempts to extend the conjecture ${| \nabla_\phi V|\over V} \geq 1$ to inflationary models (which would be even less motivated, as discussed in Section \ref{SW}), this conjecture would be in an even stronger contradiction with the cosmological observations. Note that the class of string theory models studied in~\cite{Obied:2018sgi,Agrawal:2018own} includes neither non-perturbative effects, nor the effects related to the KKLT uplifting due to a single $\overline {D3}$-brane, which is described in $d=4$ supergravity by a nilpotent multiplet~\cite{Kallosh:2014wsa,Ferrara:2014kva,Bergshoeff:2015jxa,Bergshoeff:2015tra,Hasegawa:2015bza,Kallosh:2015nia,Kallosh:2016aep,Aalsma:2018pll}. Therefore, the KKLT model, as well as available inflationary models based on string theory, involves elements which do not belong to the class of models studied in \cite{Obied:2018sgi,Agrawal:2018own}. It is therefore not very surprising that all the models of accelerated expansion of the universe studied in~\cite{Obied:2018sgi,Agrawal:2018own} are ruled out by observational data on dark energy and inflation. In Section~\ref{KKLT}, we briefly describe the recent progress in the KKLT construction and dS supergravity. We describe the KKLT scenario in the theory with a nilpotent multiplet, and its generalizations with strong vacuum stabilization which are especially suitable for cosmological applications. In Section~\ref{nogo}, we discuss various no-go theorems which were supposed to support the no-dS conjecture of~\cite{Brennan:2017rbf,Danielsson:2018ztv,Obied:2018sgi}, and reply to the criticism of the KKLT construction in these and other papers. Section~\ref{fullfledged} describes the recent progress towards full-fledged string theory solutions describing dS vacua. Various versions of the no-dS conjecture are described in Section~\ref{SW}. Cosmological constraints on the parameters of quintessence models relevant to the discussions of this paper are obtained in Section~\ref{observations}, where the focus is on models with single-exponential potentials. In Section~\ref{models}, we present a detailed analysis of the string theory based quintessence models proposed in~\cite{Obied:2018sgi}, which, on the one hand, can qualify as derived from string theory compactified to $d=4$, and on the other hand, are used to support the dark energy swampland conjecture $V_{,\phi}/V\geq 1$. This does not include models of quintessence with $d\neq 4$, as well as models for which $V_{,\phi}=0$ is possible. In Section~\ref{problems}, we discuss general conceptual problems with models of quintessence in string theory. Appendix \ref{dSsupergravity} contains a more technical discussion of no-go theorems and of the advanced KKLT construction and dS supergravity. In Appendix \ref{supercritical}, we review quintessence models in supercritical string theory with the total number of dimensions $D\gg 26$~\cite{Dodelson:2013iba}. We compare in Appendix~\ref{sec:priorbounds} the observational bounds on the string theory models of quintessence discussed in Section~\ref{observations} with those provided in \cite{Agrawal:2018own,Heisenberg:2018yae}. Appendix~\ref{sec:doubleexp} and Appendix~\ref{sec:two-field} present a discussion of and observational constraints on double-exponential quintessence potentials, which appear in some of the string theory models of Section~\ref{models}. Finally, in Appendix \ref{pres} we give some examples illustrating the rapidly improving precision of measurements of the cosmological parameters during the last decade. It shows that even a small difference in some of the experimental results can make a huge difference for the development of theoretical cosmology. This is very different from the situation two decades ago, when `order-of-magnitude' theoretical predictions could be good enough. | \label{disc} Dark energy was discovered 20 years ago~\cite{Riess:1998cb,Perlmutter:1998np}. This discovery created a turmoil in theoretical physics, and in string theory in particular. At first, there was a hope that the discovery would go away, but this did not happen. The first attempts to describe dark energy/quintessence in theories based on supersymmetry and supergravity were made in~\cite{Binetruy:1998rz,Brax:1999gp,Kallosh:2002gf}, and in M-theory in~\cite{Kallosh:2002gg,Gutperle:2003kc,Kallosh:2003bq}. The serious conceptual issues with quintessence in M-theory and supergravity were revealed soon, and no consistent string theory models of quintessence % were found in $d = 10$ superstring theory. The situation changed with the invention of the KKLT scenario~\cite{Kachru:2003aw,Kachru:2003sx} and its various generalizations, such as KL~\cite{Kallosh:2004yh} and LVS~\cite{Balasubramanian:2005zx}, which suggested a multitude of possibilities to describe the present value of the cosmological constant in the context of the string theory landscape~\cite{Douglas:2003um,Susskind:2003kw,Douglas:2006es,Denef:2007pq}. This theory is extremely complicated, and is far from being complete, but we have the proof of concept. Due to the extreme multiplicity of the vacua, this scenario is very robust with respect to even very large quantum corrections, as illustrated in Fig.~\ref{chi}. That is, of course, assuming that there are no no-go theorems proving that this whole set of ideas is internally inconsistent, and dS states are simply impossible in string theory. Here we stress that we are discussing no-go theorems, not the arguments in the spirit of the Wilsonian EFT, naturalness, weak or strong versions of the weak gravity conjecture, or the possibility that radiative corrections strongly affect dS vacua and reshuffle them as shown in Fig. \ref{chi}. We are discussing real no-go theorems, which would state that all of the $10^{{500}}$ or more dS vacua in string theory cannot exist. Despite many attempts of many authors to prove such no-go theorems during the last 15 years, no such proofs are available. In this paper, we have explained in detail that all the known no-go theorems of this kind can be evaded. Here in this last section, we first summarize our statements concerning the no-dS conjecture made in \cite{Obied:2018sgi}. Their conjecture that dS vacua in string theory are not possible originates from their use of the original versions of the major no-go theorems. For the case of the Maldacena-Nunez no-go theorem~\cite{Maldacena:2000mw}, they assume nonsingular compactification manifolds. As it is known for two decades, such manifolds fail to describe chiral fermions in $d=4$~\cite{Acharya:2001gy}. Therefore, one should not require using nonsingular compactification manifolds for describing de Sitter geometries. It is known that one can evade the Maldacena-Nunez theorem taking into account higher-order curvature corrections and negative tension O-planes~\cite{Giddings:2001yu,Silverstein:2001xn}, as stressed in~\cite{Kachru:2003aw,Kachru:2003sx}. With regard to the no-go theorem of~\cite{Pilch:1984aw} on dS and supersymmetry, in pure dS supergravity one can evade the theorem by involving a nonlinearly realized supersymmetry, as it follows from the D-brane construction \cite{Aganagic:1996nn,Bergshoeff:2015tra,Hasegawa:2015bza}. It is this construction that was used for the manifestly supersymmetric version of the KKLT construction in~\cite{Kallosh:2014wsa,Ferrara:2014kva,Bergshoeff:2015tra,Hasegawa:2015bza,Bergshoeff:2015jxa,Kallosh:2015nia,Kallosh:2016aep,Aalsma:2018pll}. Moreover, dS supergravity in $d=4$ is now derived in the context of string theory compactification from $d=10$~\cite{Kallosh:2018nrk}. The most recent criticism of the KKLT construction has been presented in~\cite{Sethi:2017phn} and~\cite{Moritz:2017xto,Moritz:2018ani}. A critical discussion of~\cite{Sethi:2017phn} can be found in~\cite{Kachru:2018aqn}. A detailed analysis of~\cite{Moritz:2017xto,Moritz:2018ani} is given in~\cite{Kallosh:2018wme,Cicoli:2018kdo,Kallosh:2018psh}, as well as in Sections \ref{KKLT} and \ref{nogo} of this paper. We believe that the 10d analysis of the KKLT scenario in~\cite{Moritz:2017xto} is unreliable \cite{Kallosh:2018wme,Cicoli:2018kdo}. Meanwhile, the 4d analysis performed in~\cite{Moritz:2017xto} was incorrect. According to~\cite{Kallosh:2018wme,Kallosh:2018psh}, all presently available consistent 4d generalizations of the KKLT construction, in the domain of their validity, confirm the existence of dS vacua in the KKLT scenario. Of course, one can ignore this fact and simply speculate that stable or metastable dS vacua are impossible in a consistent quantum gravity theory, discard all models of dS space in a hope to make string theory great again, and then see what happens \cite{Brennan:2017rbf,Danielsson:2018ztv,Obied:2018sgi}. This no-dS conjecture takes us back to the situation we encountered 20 years ago, when we did not have any consistent description of the observational data in the context of string theory. This does not mean that any success in this direction is impossible, which is why we studied it, despite the fact that the motivation for the no-dS conjecture in \cite{Brennan:2017rbf,Danielsson:2018ztv,Obied:2018sgi} does not seem convincing to us. Returning to the discussion of the swampland, in~\cite{Agrawal:2018own} the analysis of quintessence is mixed with an early universe inflation. Here we stress that the basic no-dS conjecture is satisfied in all slow-roll inflationary models automatically. Indeed, the deviation from dS is the most important feature of all slow-roll inflationary models: the amplitude of inflationary perturbations blows up for $V_{,\phi} > V^{3/2}$. Therefore, there is no obvious reason to impose additional unmotivated constraints of the type of \rf{swamp} on these models. On the other hand, if one insists that the strong form of the no-dS conjecture \rf{swamp} should apply to inflationary models, it will be yet another argument against this conjecture. It is known from the latest Planck data release \cite{Akrami:2018odb} that $r \lesssim 0.064$ during the stage of inflation responsible for structure formation and CMB anisotropy in our part of the universe. This means that \be \epsilon = {1\over 2}\Big( {V_{,\phi}\over V}\Big) ^2 = {1\over 2}c ^2 \lesssim 0.004 \, \implies c \lesssim 0.09\, . \ee An analysis of related issues in~\cite{Agrawal:2018own,Kinney:2018nny} gives similar constraints. Therefore, if we would assume that the constraint \rf{swamp} with $c \sim 1$ applies to inflation, we would conclude that the conjecture \rf{swamp} strongly contradicts the observational data. In the case of dS versus quintessence for the late universe, things are more subtle and may need more attention since during the next decade major new cosmological data on the equation of state $w=p/\rho$ will be available. In this paper, we have asked the question `is the proposal~\rf{swamp}, which is consistent with string theory, compatible with the present data?' We have performed a statistical analysis of the quintessence exponential potential $V_0 e^{\la \phi}$ with regard to the currently available cosmological data on the background expansion of the universe; see Section~\ref{observations}. In view of the controversy about the data in~\cite{Agrawal:2018own,Heisenberg:2018yae} a due diligence was required. Namely, in~\cite{Agrawal:2018own} only a $2\sigma$ bound is proposed in the form $\la=c <0.6$ (in the first version of the paper $c<0.6$ was called a $3\sigma$ bound). In~\cite{Heisenberg:2018yae} it is suggested that their $1\sigma$ bound reproduces the $2\sigma$ bound in \cite{Agrawal:2018own}, while their $3\sigma$ bound is proposed in the form $c<1.35$. This way, the paper by Heisenberg et al.~\cite{Heisenberg:2018yae} has introduced an uncertainty which was necessary to resolve before we study string theory quintessence models. Our results, in the case of an analysis I, where we fixed the parameter $V_0$ to $0.7(3H_0^2)$ and varied the other parameters of the model, i.e. $\lambda$ and $\phi_0$, as well as $\Omega_\text{M}$, provided the one-dimensional, marginalized upper bounds on $c$, \be\label{analysis1} c \lesssim 0.13, \qquad c \lesssim 0.54, \qquad c\lesssim 0.87, \ee for $1\sigma$, $2\sigma$ and $3\sigma$ confidence levels, respectively; see Fig.~\ref{fig:mainConstraints_V0p7}. In an analysis II, we performed a statistical exploration of the parameter space when $V_0$ was allowed to vary as well, in order to take care of some statistical subtleties around $\lambda=0$. In that case, depending on the prior on $\phi_0$, i.e. the range over which $\phi_0$ was allowed to vary, the upper bounds on $c$ varied: the broader the range of $\phi_0$, the lower the upper bounds on $c$. We fixed $\phi_0$ to zero (i.e. we set the $\phi_0$ range to zero) in order to obtain the largest upper bounds on $c$. The marginalized, one-dimensional upper bounds on $c$ in this case are \be\label{analysis2} c\lesssim0.49, \qquad c\lesssim0.80, \qquad c\lesssim1.02, \ee for $1\sigma$, $2\sigma$ and $3\sigma$ confidence levels, respectively; see Fig.~\ref{fig:mainConstraints_phi00}. An additional profile likelihood analysis of the parameter space in a frequentist approach (as opposed to our main Bayesian marginal posterior analysis) provided bounds very close to~(\ref{analysis2}). This demonstrated that (\ref{analysis2}) were indeed the weakest and most prior-independent bounds on $\lambda$ that one could obtain with the cosmological data used in this paper. By including additional information beyond the purely geometrical tests of the background expansion as we have employed in our paper, e.g. by adding the perturbative information from the Planck CMB temperature and polarization data, we expect these bounds to be even tighter. Thus, if we would like to be as tolerant to theoretical cosmological models as possible with regard to the data, we can say that models with $c \lesssim 1.02$ can be looked at more carefully since they are not immediately ruled out by the data. But, one should keep in mind that this is a last resort, as all models with $c \gtrsim 1.02$ should be dismissed without hesitation. On the theoretical side, we went through the list in~\cite{Obied:2018sgi} with an update provided in~\cite{Roupec:2018fsp} to make sure that the models in $d=4$ which we confront with the data were viewed as string constructions, beyond speculations. In particular, we have noticed that all the models with $ c<\sqrt 2 $ suggested in~\cite{Obied:2018sgi} do not really belong to string theory or M-theory constructions. Meanwhile, the data can only tolerate $c\lesssim 1.02$ at most, as we have explained in Section~\ref{observations}, and therefore the models that the authors of~\cite{Obied:2018sgi} are left with, requiring $c\gtrsim1.4$, are all ruled out. The additional quintessence models added in \cite{Agrawal:2018own} are either ruled out by the data, or represent inflationary models with moduli stabilization converted to models of quintessence. All of them contradict the condition \rf{swamp}. But this is not the only problem with the string theory models of quintessence. There are many general conceptual issues discussed in Section~\ref{problems} that must be addressed: decompactification, fifth force, quantum corrections, consistent embedding of dark matter, the problem of initial conditions, etc. On top of that, our analysis brings some surprising news to those who believe in the weak gravity conjecture: The potential $V\sim e^{\lambda\phi}$, or any other similar potential which can be used for describing quintessence in terms of a canonically normalized scalar field $\phi$, is well defined only in the tiny range of values of the potential in the immediate vicinity of the present value of the cosmological constant. This suggests that if a consistent theory of quintessence can be constructed in the context of string theory, it will not replace the string theory landscape scenario, but will rather enhance it, by adding to the many dS minima, which are shown in Fig.~\ref{chi}, a collection of segments of the potential, which should be very flat, with ${| \nabla_\phi V|\over V} < 1$. Note that the last requirement is directly opposite to the strong form of the no-dS conjecture \rf{swamp}. In preparation for potential deviations of the dark energy data from a cosmological constant provided by upcoming or future surveys, we have already constructed quintessential inflation models in string theory motivated versions of supergravity~\cite{Akrami:2017cir}, which might fit such future data. However, a majority of supergravity models compatible with the early universe inflation end up in dS minima and explain dark energy via a cosmological constant taking values in the landscape. Recent cosmological observations have attracted attention to specific ideas/aspects of non-perturbative superstring theory, which are helpful in building models compatible with the data. The $\overline {D3}$-brane is a source of nonlinearly realized supersymmetry and positive contribution to energy, which is a characteristic property of the KKLT uplifting procedure. In phenomenological model building, the corresponding nilpotent multiplet, in addition to providing positive energy, plays the role of a stabilizer superfield, which allows an advanced version of $\alpha$-attractor models \cite{Kallosh:2013yoa}; we called them geometric inflation~\cite{Kallosh:2017wnt,McDonough:2016der}. These models provide a good fit to the Planck 2018 data~\cite{Akrami:2018odb}; see Fig.~\ref{Precision}. Thus, the ideas originating in string theory with dS vacua influenced the construction of phenomenological $d=4$ supergravity models of inflation compatible with the cosmological data. These are the corners of string theory where better understanding and more developments may be useful since they are already in the sweet spot of the data, i.e. in the blue area of the $r-n_s$ plane in Fig.~\ref{Precision}. \ \noindent{\bf {Acknowledgments:}} We are grateful to E. Bergshoeff, S. Ferrara, D. Freedman and A. Van Proeyen for the clarification of the conceptual issues of de Sitter supergravity and of the no-go theorem \cite{Pilch:1984aw}. We are also grateful to the organizers and participants of the conference `Dark Side of the Universe' in Guadeloupe, June 25-29, 2018, especially J. Garcia-Bellido and T. Eifler, for stimulating discussions on the dark energy data. We had very useful discussions of string theory, cosmology and supergravity with S. Kachru, E. McDonough, M. Scalisi, E. Silverstein, R. Wechsler, A. Westphal, T. Wrase, Y. Yamada and M. Zagermann. We also thank O. Contigiani, M. Martinelli and A. A. Sen for helpful discussions on the statistical analysis performed in this paper. Y.A. acknowledges support from the Netherlands Organization for Scientific Research (NWO) and the Dutch Ministry of Education, Culture and Science (OCW), and also from the D-ITP consortium, a program of the NWO that is funded by the OCW. The work of R.K. and A.L. is supported by SITP, by the NSF Grant PHY-1720397, and by the Simons Foundation grant. V.V. is supported by a de Sitter PhD fellowship of NWO. \appendix | 18 | 8 | 1808.09440 |
1808 | 1808.07494_arXiv.txt | The Andromeda galaxy (M31) contains a box/peanut bulge (BPB) entangled with a classical bulge (CB) requiring a triaxial modelling to determine the dynamics, stellar and dark matter mass. We construct made-to-measure models fitting new VIRUS-W IFU bulge stellar kinematic observations, the IRAC-3.6\mum photometry, and the disc's \HI rotation curve. We explore the parameter space for the 3.6\mum mass-to-light ratio $\left(\pml\!\!\right)$, the bar pattern speed ($\pps\!\!$), and the dark matter mass in the composite bulge ($\pdm\!\!$) within $3.2\kpc$. Considering Einasto dark matter profiles, we find the best models for \bml, \bdm and \bps. These models have a dynamical bulge mass of $M_{\rm dyn}^{\rm B}\e4.25^{+0.10}_{-0.29}\times\!10^{10}\sm$ including a stellar mass of $M_{\star}^{\rm B}\e3.09^{+0.10}_{-0.12}\times\!10^{10}\sm$(73\%), of which the CB has $M_{\star}^{\rm CB}\e1.18^{+0.06}_{-0.07}\times\!10^{10}\sm$(28\%) and the BPB $M_{\star}^{\rm BPB}\e1.91\pm0.06\!\times\!10^{10}\sm$(45\%). We also explore models with NFW haloes finding that, while the Einasto models better fit the stellar kinematics, the obtained parameters agree within the errors. The \pdm values agree with adiabatically contracted cosmological NFW haloes with M31's virial mass and radius. The best model has two bulge components with completely different kinematics that only together successfully reproduce the observations ($\mu_{3.6}$, $\upsilon_{\rm los}, \sigma_{\rm los}$, $h3$, $h4$). The modelling includes dust absorption which reproduces the observed kinematic asymmetries. Our results provide new constraints for the early formation of M31 given the lower mass found for the classical bulge and the shallow dark matter profile, as well as the secular evolution of M31 implied by the bar and its resonant interactions with the classical bulge, stellar halo and disc. | \label{sec:intro} The Andromeda galaxy (M31, NGC224) is the closest neighbouring massive spiral galaxy, presenting us a unique opportunity to study in depth the dynamics of disc galaxy substructures, such as classical bulges and bars, the latter found in approximately 70 per cent of the disc galaxies in the local Universe \citep{MenendezDelmestre2007, Erwin2018}. In addition, our external perspective more easily proves a global view of M31 in comparison to the Milky Way, while as a similar mass disk galaxy, it allows us to place our home galaxy in context. Historically, M31's triaxial bulge has been mostly addressed as a classical bulge, while generally the bar component has been only qualitatively considered in the modelling of its stellar dynamics. However, an accurate dynamical estimation of the mass distribution of the stellar and the dark matter in the bulge must take into account the barred nature of M31's central regions \citep{Lindblad1956}. More recent observations better quantify the triaxiality of the bulge which is produced by its box/peanut bulge (\BPB) component \citep{Beaton2007, Opitsch2017}, a situation similar in many aspects to the Milky Way's box/peanut bulge \citep{Shen2010,Wegg2013,Bland-Hawthorn2016}. The M31 \BPB is in addition entangled with a classical bulge (\CB) component \citep{Athanassoula2006}. The \CB is much more concentrated than the \BPB, with the two components contributing with \si1/3 and \si2/3 of the total stellar mass of the bulge respectively, as shown by \citet[hereafter \citetalias{Blana2017}]{Blana2017}. Each substructure in M31 can potentially teach us about the different mechanisms involved in the formation and the evolution of the whole galaxy. In particular, the properties of the \CB component of M31 can give us information about the early formation epoch. Current galaxy formation theories consider classical bulges as remnants of a very early formation process, such as a protogalactic collapse, and/or as remnants of mergers of galaxies that occurred during the first gigayears of violent hierarchical formation \citep{Toomre1977, Naab2003, Bournaud2005}. On the other hand, the massive \BPB of M31 provides us information about the evolution of the disc, as box/peanut bulges are formed later from the disc material. Box/peanut bulges in N-body models are triaxial structures formed through the buckling instability of the bar, which typically lasts for $\lesssim 1\Gyr$, generating a vertically thick structure \citep{Combes1990, Raha1991}. Recent observations of two barred galaxies also show evidence of their bars in the buckling process \citep{Erwin2016}. Box/peanut bulges are frequent being found in 79 per cent of massive barred local galaxies \citep[$M_{\star}\gtrsim 10^{10.4}\sm $,][]{Erwin2017}. Note that box/peanut bulges are sometimes referred as box/peanut pseudobulges, however not to be confused with discy pseudobulges, which are formed by gas accreted into the centres of disc galaxies \citep{Kormendy2013}. Moreover, on even longer time-scales, box/peanut bulges and bars can interact through resonances with the disc and thereby redistribute its material, generating for example surface brightness breaks, as well as ring-like substructures \citep{Buta1991, Debattista2006b, Erwin2008, Buta2017b}. Bars also transfer their angular momentum to the spheroid components, such as classical bulges \citep{Saha2012, Saha2016}, stellar haloes \citep{Perez-Villegas2017a} and dark matter haloes \citep{Athanassoula2002}, changing their dynamical properties. Furthermore, \citet{Erwin2016} show also with observations that classical bulges can coexist with discy pseudobulges and box/peanut bulges building composite bulges, a scenario that has also been reproduced in galaxy formation simulations \citep{Athanassoula2016}. This makes M31 a convenient laboratory to test formation theories of composite bulges and to better understand their dynamics. To understand the formation and the evolution of Andromeda, and to accurately compare it with galaxy formation simulations, it is imperative to first determine the contribution and the properties of each of the substructures, such as their masses and sizes, as well as the dark matter distribution. In the outer disc region the gas kinematics constrain the dark matter distribution \citep{Chemin2009, Corbelli2010}. However, in the centre, the gas may not be in equilibrium due to the triaxial potential generated by the bar. Therefore, we model the stellar kinematics taking into consideration the triaxial structure of the \BPB. \citet[][hereafter \citetalias{Opitsch2016}]{Opitsch2016} and \citet[][hereafter \citetalias{Opitsch2017}]{Opitsch2017} obtained kinematic observations of exquisite detail using the integral field unit (IFU) VIRUS-W \citep{Fabricius2012}, completely covering the classical bulge, the \BPB and most of the projected thin or planar bar. In this paper we use these kinematic observations to fit a series of made-to-measure models that allow us to find constraints for the stellar and dark matter mass within the bulge region, as well as other dynamical parameters such as the pattern speed of the \BPB and the thin bar. This paper is ordered as follows: Section \ref{sec:mod} describes the observational data, its implementation, and the made-to-measure modelling of M31. Section \ref{sec:res} shows the results of the models that are separated in two main parts. In the first, Section \ref{sec:res:param}, we present the main results of the parameter search exploration. In the second part, in Section \ref{sec:res:bm}, we present the properties of the best model and we compare it with the M31 observations. In Section \ref{sec:conc} we conclude with a summary and a discussion of the implications of our findings. | \label{sec:conc} We have presented here dynamical models for M31 built with a classical bulge component (\CB) and a box/peanut bulge component (\BPB). We use the M2M method to measure the main properties of M31's bulge: the IRAC 3.6\mum mass-to-light ratio \pml, the dark matter mass within 3.2\kpc of the bulge \pdm, and the pattern speed of the \BPB and the thin bar \pps. For this we directly fit simultaneously new IFU VIRUS-W bulge stellar kinematic observations \citep{Opitsch2017}, and the 3.6\mum IRAC photometric data \citep{Barmby2006}, with the following main results: \begin{enumerate}[label=\arabic*),leftmargin=*,itemsep=0pt,labelsep=5pt] \item The range of parameters that best reproduce all the observations simultaneously are \bml, \bps and \bdm, using an Einasto dark matter profile. These models have a total dynamical mass within the composite bulge of $M_{\rm dyn}^{\rm B}\e4.25^{+0.10}_{-0.29}\times10^{10}\sm$ with a stellar mass and percentage of $M_{\star}^{\rm B}\e3.09^{+0.10}_{-0.12}\times10^{10}\sm$(73\%). The CB has $M_{\star}^{\rm CB}\e1.18^{+0.06}_{-0.07}\times10^{10}\sm$(28\%) and the \BPB has $M_{\star}^{\rm BPB}\e1.91\pm0.06\times10^{10}\sm$(45\%). We also obtain similar values within the errors for our grid of models with NFW dark matter haloes. The bulge dark matter mass agrees with the expected values for an adiabatically contracted NFW halo with M31's virial mass. However, the best Einasto models fit the bulge stellar kinematics generally better than the models with NFW haloes, favouring a shallow central dark matter halo distribution, similar to that found in the Milky Way \citep{Portail2017a}. This also reveals the importance of kinematic data with high spectral and spatial resolution, and the appropriate modelling to accurately determine the central dark matter mass distribution in galaxies. \item How does the model of \citetalias{Blana2017} compare with the best M2M models? They explored N-body simulations build with \CB components of different masses and sizes, where the \BPB formed from the bar instabilities of the initial disc during the simulations. They find a best model selected from photometric comparisons with M31's bulge. Here we improve the models of B17 by fitting directly the data using the M2M method. The main properties of their \CB are similar to the ones found here. The B17 \BPB luminosity is also similar to the value presented here, however, given their slightly larger mass-to-light ratio their \BPB mass is 15 per cent higher. Their kinematic maps qualitatively match several features observed in M31, however the M2M model highly improves the match quantitatively. For example, the M2M model presented here reproduces now the velocity dispersion in the outer parts of the \BPB due to a more massive dark matter halo. \item Our best model has two bulge components with completely different kinematics that only together successfully reproduce the detailed properties of the kinematic and the photometric maps. Furthermore, our modelling includes dust absorption effects that can approximately reproduce the kinematic asymmetries in the observations. The model, for example, reproduces the higher dispersion of the far side of the galaxy compared to the near side. \item Our results present new constraints on the early formation of M31 given the lower mass found for the \CB component compared to previous estimations in the literature. An implication is on the relation between bulges and central super massive black holes (SMBH). SMBH masses show correlations with classical bulges and not pseudobulges \citep{Hu2008,Kormendy2013a,Saglia2016}. Using the $M_{\bullet}\!-\!M_{\rm bulge}\!-\!\sigma$ relation\footnote{for the sample CorePowerEClassPC} from \citet{Saglia2016} for the \CB component alone with a mass of $M_{\star}^{\rm CB,10\kpc}\e1.71\times10^{10}\sm$ with $\sigma^{\rm CB, max}\si130$ - $150\kms$ predicts a SMBH mass of $M_{\bullet}\e0.4^{+0.4}_{-0.2}\, -\, 0.6^{+0.7}_{-0.3}\times10^8\sm$, where the errors are the instrinsic scatter in the relation. This is somewhat lower than the measured $M_{\bullet}\e1.4^{+0.9}_{-0.3}\times10^8\sm$ \citep{Bender2005}, but lies within the scatter. Using the $M_{\bullet}\!-\!M_{\rm bulge}\,{}^3$ relation predicts a mass of $M_{\bullet}\e0.9^{+1.5}_{-0.5}\times10^8\sm$, that is closer to the measured value in M31. \item The tightly constrained stellar mass-to-light ratio value of \bml is in agreement with the expected values from stellar populations with a Chabrier IMF \citep{Meidt2014}, with the metallicities and ages measured in M31's bulge and bar \citep{Opitsch2016, Saglia2018}. Considering the \CB alone a Chabrier IMF would be consistent with \citet{Cappellari2012} (using $\Upsilon_{\rm r}\si4\ml$ and $\sigma_{\rm CB}\si150\kms$). It is however inconsistent with the Salpeter IMF found for more massive classical bulges measured by \citet[][SWELLS survey]{Dutton2013}. \item Our findings agree with the photometric \citep{Fisher2008} and kinematic \citep{Fabricius2012} bulge classification criteria using the S\'ersic index ($n$) and the central kinematics to distinguish classical bulges ($n>2$) from pseudobulges ($n<2$). As \citet{Fisher2008} mention, and \citet{Erwin2015} investigate further, composite bulges can have an effect on the bulge selection criteria, and they can manifest both bulge type properties. Here we find that M31's composite bulge S\'ersic index is at the boundary with $n_{\rm M31}\si2$ and it shows kinematic properties of both bulge types. Moreover, considering the \CB alone we find $n_{\rm CB}\si4$, a \CB to total mass ratio ${\rm B}/{\rm T}\e0.21$, effective radius $R_{\rm e}^{\CB}\si1\kpc$, and central dispersion $\sigma_{\rm CB}\si150\kms$, which also agree with the criteria for classical bulge types. Here we present two properties of a composite bulge that could improve the selection criteria: i) a composite bulge with $n\!\approx\!2$ can host a classical bulge with a high S\'ersic index, where the composite bulge has a value lowered by the presence of a box/peanut bulge, and ii) the presence of a classical bulge component can increase the total central dispersion by increasing the dispersion of the box/peanut bulge that lives within the classical bulge potential. This suggests that other observed bulges that show low S\'ersic values ($n\lesssim2$), but with high central dispersion and a large dispersion gradient ($\nabla\sigma$) \citep{Neumann2017}, could be hosting a compact classical bulge. \item Our best M31 bar pattern speed value is $\bps$ which results in $\mathcal{R}\e1.6\pm0.2$, placing this bar among the slow bars. This is within the range of recent measurements of $\mathcal{R}$ of barred galaxies, finding $\mathcal{R}\e1.41\pm0.26$ \citep[{\it Spitzer} with gas kinematics][]{Font2017} and $\mathcal{R}\e1.0^{+0.7}_{-0.4}$ \citep[CALIFA survey][]{Aguerri2015}. Furthermore, our pattern speed measurement places the inner Lindblad resonances near the inner gas rings and streams observed within the bulge \citep{Opitsch2017}, and the outer Lindblad resonance near the 10\kpc ring, which could explain its origin and persisting star forming activity \citep{Lewis2015}. \end{enumerate} Finally, the M2M models presented here have many possible uses. They can be applied to investigate further the early formation and the secular evolution of M31. For example, including gas to reproduce the outer 10\kpc ring-like substructure, or the bulge gas distribution. Also, from stellar population and chemodynamical galaxy formation simulations \citep{Kobayashi2011} it is expected that the stars with different chemical elements have different spatial distributions. The M31 bulge metallicity maps \citep{Saglia2018} could be used to dissect the galaxy's orbital structure using a chemodynamical modelling, as similarly done for the MW \citep{Portail2017b}. Other applications of our model involve the interpretation of pixel micro-lensing events in M31's halo for the observational campaigns PAndromeda \citep{Lee2012} and WeCAPP \citep{Lee2015}. For the pixel lensing modelling an important ingredient are accurate dynamical models of the stellar mass distribution to take into account the self-lensing events, and thereby better constrain the lensing events in the halo \citep{Riffeser2006}. The models presented here are the most appropriate as these include the barred nature of the Andromeda galaxy.\\ These models may be available upon request to the authors. | 18 | 8 | 1808.07494 |
1808 | 1808.00757_arXiv.txt | We have analysed archival VLA 8.4-GHz monitoring data of the gravitational lens system JVAS~B1030+074 with the goal of determining the time delay between the two lensed images via the polarization variability. In contrast to the previously published total intensity variations, we detect correlated variability in polarized flux density, percentage polarization and polarization position angle. The latter includes a fast ($<$5~d) 90-degree rotation event. Our best estimate of the time delay is $146\pm6$~d (1~$\sigma$), considerably longer than that predicted by the lens model presented in the discovery paper. Additional model constraints will be needed before this system can be used to measure $H_0$, for example through a detection of the lensed source's VLBI jet in image B. No time delay is visible in total flux density and this is partially due to much greater scatter in the image B measurements. This must be due to a propagation effect as the radio waves pass through the ISM of the lensing galaxies or the Galaxy. | \label{sec:intro} The measurement of gravitational lens time delays offers a single-step determination of the expansion rate of the Universe, $H_0$, at cosmological distances, independent of any intermediate ``distance-ladder'' calibrations \citep{refsdal64}. Given that current determinations of $H_0$ based on observations of relatively local Cepheid-calibrated supernovae \citep{riess16} and the Cosmic Microwave Background \citep{planck16} show signs of inconsistency at the 3-$\sigma$ level, it is perhaps more important than ever that additional methods, such as that offered by lens time delays, be pursued in an effort to try and resolve the potential discrepancy. The lens system B1030+074 \citep[][hereafter X98]{x98} is one of six gravitational lens systems discovered as part of the Jodrell Bank/VLA Astrometric Survey \citep[JVAS --][]{king99}. It consists of two images (A and B) of a $z=1.535$ radio-loud quasar lensed by a spiral galaxy at $z=0.599$ \citep{fassnacht98}. The lensing galaxy is extended westwards of its nucleus and it is unclear if this is substructure in the galaxy or a separate galaxy \citep*{jackson00,lehar00}. The image separation is 1.6~arcsec and lens modelling performed by X98 predicts a time delay of 112~d for $H_0 = 70$~km\,s$^{-1}$\,Mpc$^{-1}$. A number of attempts have been made to determine the time delay, the most useful of which utilised the Very Large Array (VLA) observing at a frequency of 8.4~GHz. A first season of monitoring in 1998 detected moderate changes in the total flux density of image A, but no corresponding features were visible in B \citep{x05}. Further monitoring was carried out in 2000/2001 \citep{rumbaugh15} but the total-flux-density variability again proved insufficient to measure a delay. Ignored by practically all radio campaigns to date has been the potential of monitoring variations in the polarization properties of the source i.e.\ polarized flux density, percentage polarization and polarization position angle (PPA). A notable exception is JVAS~B0218+357 for which polarization monitoring has been an essential part of determining the time delay \citep{corbett96,biggs99,biggs18}. However, B0218+357 is particularly highly polarized (approaching 10~per~cent at high frequencies) and also bright, the total flux density of each image exceeding 100~mJy. In general, radio cores are less polarized than extended emission and few radio lenses are as bright as B0218+357. However, polarization monitoring should be of great interest to time-delay studies as the magnitude of variability tends to be greater than that seen in total intensity and the timescale of variability shorter \citep[e.g.][]{saikia88}. In addition, the PPA is occasionally observed to rapidly rotate \citep{lyutikov17}, an event which should be observable for even a weakly polarized source. We can find no mention in the literature of whether the lensed images of B1030+074 are polarized or not, but our own analysis of archival VLA data revealed polarization at the 1--2~per~cent level. We have therefore reanalysed the VLA 8.4-GHz monitoring data from 1998 and present here the resultant total-intensity and polarization variability curves. We do not include the \citet{rumbaugh15} data as much less time was spent observing the lens during this campaign and the signal-to-noise ratio (SNR) of the polarization measurements is too low to reliably detect image B. | \label{conclusions} Analysis of the polarization variability of the gravitational lens system JVAS~B1030+074 using previously published VLA 8.4-GHz monitoring data has allowed us to measure the time delay between images A and B with an accuracy of 4~per~cent ($146\pm6$~d). We have not attempted to measure a delay in total flux density, partly because image B is subject to additional variability that is presumably caused by passage of the radio waves through the lensing galaxy or galaxies. Additional monitoring at multiple frequencies should be able to distinguish between a microlensing or scintillation origin. Despite the difficulties caused by the external variability, an analysis of total-intensity monitoring from 2000/2001 \citep{rumbaugh15} seems to be consistent with our time delay. In principle, B1030+074 now joins the ranks of those lenses for which $H_0$ can be determined. However, the measured delay is much longer than that predicted by the model published by X98, thus indicating that this is an inaccurate representation of the mass responsible for the lensing. It is not clear which value of the flux density ratio was used as a modelling constraint, but the accurate measurement of this parameter may lead to a more accurate lens model. At the same time, \citet{saha06} use non-parametric modelling to predict a delay that is much closer to our measured value, $153^{+29}_{-57}$~d, albeit with large error bars. To improve future modelling attempts, more constraints would ideally be needed and one route that in our opinion remains promising is VLBI imaging. It has long been known that image A contains a prominent jet, but the large flux ratio renders this difficult to detect in B as its surface area is reduced by this amount relative to A. Almost all imaging to date has been conducted at 1.4~GHz and we recommend new imaging efforts at 5~GHz. This allows an increase of angular resolution by a factor of three and the dramatic increase in sensitivity offered by modern broad-band ($\Delta\nu = 1$~GHz) VLBI arrays will ensure that the detectable length of the jet will be at least as long as in the existing maps, assuming a standard synchrotron spectrum with a spectral index of $-$0.7. Finally, the dramatic variations seen in B1030+074 highlight that gravitational lens monitoring campaigns should always attempt to detect the source polarization, even if this is believed to be weak. The SNR of image B in particular is generally very low, occasionally dropping below 3. However, the higher variability seen in the polarization data more than compensates for this and has led to the measurement of a time delay in a lens system for which this had not seemed possible despite two extensive monitoring campaigns. The enhanced sensitivity of the broad-banded Jansky VLA in particular should allow polarization monitoring of more lens systems. | 18 | 8 | 1808.00757 |
1808 | 1808.04081_arXiv.txt | {} {We focus on early-B type stars with helium overabundance, for which the presence of a magnetic field has not previously been reported.} {The measurements were carried out using high-spectral-resolution spectropolarimetric observations obtained with the High Accuracy Radial velocity Planet Searcher (HARPS) in polarimetric mode, installed at the ESO La Silla 3.6m telescope.} {For five He-rich stars, the longitudinal magnetic field was detected for the first time. For one target, HD\,58260, the presence of a longitudinal magnetic field of the order of 1.8\,kG has already been reported in the literature, but the magnetic field has remained constant over tens of years. Our measurement carried out using the polarimetric spectra obtained in 2015 March indicates a slight decrease of the longitudinal magnetic field strength compared to measurements reported in previous works. A search for periodic modulation in available photometric data allowed us to confidently establish a period of 2.64119$\pm$0.00420\,d in archival ASAS3 data for CPD$-$27\degr 1791. No period could be determined for the other five stars.} {The obtained results support the scenario that all He-rich stars are detectably magnetic and form an extension of the Ap star phenomenon to higher temperatures.} | \label{sec:intro} During the last years an increasing number of massive stars has been investigated for magnetic fields in the framework of the Magnetism in Massive Stars (MiMeS) and B-fields in OB stars (BOB) surveys \citep{mimes, BOB}. Direct magnetic-field measurements are of great importance to properly understand the potential effects of magnetic fields on the evolution of massive stars, including the impact on angular momentum and on stellar wind properties. While the BOB survey mostly concentrated on normal main sequence OB stars, the MiMeS survey consisted of a survey component and a targeted component to characterise a sample of known magnetic stars. Since previously detected magnetic O and early B-type stars on average appeared to have rotation velocities significantly lower than the rest of the population, to enhance the probability of detecting magnetic fields, the majority of the stars targeted by BOB were relatively slowly rotating, with \vsini{} values below 60\,\kms \citep{BOB}. However, according to \citet{Markus2017}, the results of the search for the presence of a magnetic field in these stars did not result in higher yields, with a magnetic field detection rate of 5$\pm$5\%. While these results indicate that the presence of a magnetic field in normal, slowly rotating O and early B-type stars is not common, magnetic early B-type He-rich stars constitute about 10\% of all main sequence early-B type stars. This group contains the most massive chemically peculiar stars with spectral types around B2 and exhibits helium and silicon surface spots \citep[e.g.][]{landstreet, borra, bohlender, Hubrig2017, Castro2017}. The distribution of these spots is non-uniform and non-symmetric with respect to the rotation axis. Also, lines belonging to CNO and iron peak elements frequently show variable line profiles over the rotation periods, but the distribution of these elements is poorly documented in the literature due to the relative weakness of their lines compared to He and Si lines. From previous studies of He-rich stars, we know that inhomogeneous chemical abundance distributions in early-B type stars are only observed on the surface of magnetic chemically peculiar stars with large-scale organised magnetic fields. Among such stars, five stars, \object{CPD$-$27$^{\circ}$1791}, \object{HD\,60344}, \object{HD\,149257}, \object{CPD$-$69$^{\circ}$2698}, and \object{HD\,168785}, have previously been reported to exhibit a surface helium overabundance \citep[e.g.][]{MacConnell1970, Garrison1977}. As no definite magnetic fields were reported in previous studies of these stars, they were included in the BOB target list. Obviously, these He-rich stars are excellent candidates to confirm the positive correlation between the presence of a magnetic field and helium enrichment in the star's atmosphere. The sixth star in our sample, \object{HD\,58260}, was shown to be magnetic by \citet{borra}, but exhibited a surprisingly constant magnetic field over nine years \citep{bohlender1987}. A recent study of this star by \citet{shultz} suggested that its magnetic field shows no variability over a timescale of about 35 years. In the following, we report on our results of the magnetic field measurements in all six stars. | \label{sec:disc} \begin{table*} \centering \caption{ Summary of photometric measurements and \vsini{} estimates. For each star in column~1, we list the interval and number of measurements, for ASAS3 in columns~2 and 3, and for \emph{Hipparcos} in columns~4 and 5. Column~6 presents the \vsini{} values obtained by \citet{Zboril1999} and column~7 has the values measured on our HARPS spectra. } \label{tab:sum} \begin{tabular}{llclccc} \hline \hline Star & ASAS3 & No. & \emph{Hipparcos} & No. & $v\sin i_{\rm{ZN}}$ & $v\sin i^{*}$ \\ & Interval & meas. & Interval & meas. & [\kms] & [\kms] \\ \hline CPD$-$27\degr 1791 & 2000 Nov/2009 Dec & 997 & 1990 Jan/1993 Mar & 178 & 45$\pm$4 & 37$\pm$3 \\ HD\,58260$^{**}$ & 2000 Nov/2009 Dec & 781 & 1989 Nov/1993 Mar & 124 & 45$\pm$6 & 9$\pm$1 \\ HD\,60344 & 2000 Nov/2009 Dec & 617 & 1990 Mar/1993 Mar & 107 & 55$\pm$6 & 10$\pm$1 \\ HD\,149257 & 2001 Jan/2009 Oct & 722 & & & 40$\pm$4 & 48$\pm$2 \\ CPD$-$69\degr 2698 & 2001 Jan/2009 Nov & 653 & 1989 Dec/1993 Feb & 265 & 30$\pm$3 & 26$\pm$2 \\ HD\,168785 & 2001 Feb/2009 Nov & 996 & & & 14$\pm$2 & 14$\pm$1 \\ \hline \end{tabular} \tablefoot{$^{**}$ \citet{shultz} give $v \sin i=3\pm2$\kms.} \tablebib{ZN = \citet{Zboril1999}, $^{*}$ = this work} \end{table*} Our spectropolarimetric observations with HARPSpol allowed us to detect for the first time the presence of relatively strong longitudinal magnetic fields in five He-rich stars. For the sixth He-rich star, HD\,58260, we found an indication of a magnetic field decrease compared to previous measurements. The measurements using different line masks belonging to different elements indicate the presence of chemical spots on the surface of all stars in our sample. Given the presence of clearly detected longitudinal magnetic fields in our targets, the determination of their magnetic periods and magnetic field geometries should be easily feasible and can be carried out in follow-up observations. Periodic magnetic variations in such chemically peculiar stars are related to the rotation periods and are generally described by the oblique rotator model \citep{Stibbs1950} with a magnetic field having an axis of symmetry at an angle to the rotation axis, usually called the obliquity angle $\beta$. Since the rotation periods for our sample stars are unknown, we searched for periodic modulations using photometric data. He-rich stars and chemically peculiar stars in general usually exhibit photometric variability due to surface chemical abundance spots. Therefore, rotational periods can be determined from photometry. We have used archival data from the ASAS3 survey\footnote{http://www.astrouw.edu.pl/asas/} \citep{asas}, covering the time interval from 2000 to 2009 and from the \emph{Hipparcos} survey \citep{Perryman1997,vanLeeuwen2007} covering the time interval from 1989 to 1993. The photometry time intervals and the number of measurements are summarised in Table~\ref{tab:sum} in columns~2--5. After removing some apparent outliers, we carried out a period search using a non-linear least-squares fit to multiple harmonics using the Levenberg--Marquardt method \citep{Press}. To detect the most probable period, we calculated the frequency spectrum, and for each trial frequency we performed a statistical F-test of the null hypothesis for the absence of periodicity \citep{seber}. The resulting F-statistics can be thought of as the total sum, including covariances of the ratio of harmonic amplitudes to their standard deviations, i.e.\ an S/N \citep[e.g.][]{Hubrig2017}. Using ASAS3 observations, a single significant peak has been detected in the frequency spectrum of CPD$-$27\degr 1791 corresponding to $P_{\rm rot}=2.64119\pm0.00420$\,d at a high confidence level with an FAP value of $2.3\times 10^{-9}$. No periodicity was detected in ASAS3 and in \emph{Hipparcos} photometry for the other five stars. In Fig.~\ref{fig:phot} we present in the upper panel the light curve collected by ASAS3 over nine years and in the lower panel the ASAS3 photometry phased with the rotation period of 2.64119\,d. \begin{figure} \centering \includegraphics[width=1.0\columnwidth]{cpd27_photo.eps} \caption{ Rotational period of CPD$-$27\degr 1791. Top: ASAS3 light curve. Bottom: ASAS3 photometry phased with $P_{\rm rot}=2.64119$\,d. } \label{fig:phot} \end{figure} The absence of $\left<B_{\rm z}\right>$ phase curves (i.e.\ the dependence of the magnetic field strength on the rotation phase) for our sample stars does not allow us to conclude on the real field strength, which can be much higher, or the field topology. Since the determination of abundances and \vsini{} values depends on the chemical spot distribution and magnetic line intensification (which is different at different rotational phases), spectropolarimetric time series obtained over the rotation periods are necessary for an in-depth analysis of the atmospheres, that is,\ an exploration of the magnetic field strength and the surface abundance distribution would require Zeeman Doppler Imaging of the chemical abundance pattern. Since HARPS spectra were obtained at an excellent resolving power of 110\,000, we estimated projected rotational velocities for each target by fitting Gaussian profiles with full widths at half-maximum (FWHM) to the unblended \ion{Ne}{i} 6402 line and compared them with literature values. Apart from the values determined for stars HD\,58260 and HD\,60344, our measurements presented in column~7 of Table~\ref{tab:sum} appear to be in good agreement with the determinations of \citet{Zboril1999} presented in column~6, who used lower resolution spectra with $R=30\,000$ obtained with the CES spectrograph at the ESO-CAT telescope on La~Silla in Chile to study CNO abundances in the atmospheres of our sample stars. The obtained results show that magnetic fields can be detected in all He-rich stars and that, in agreement with the suggestion of \citet{Osmer1974}, these stars form an extension of the Ap star phenomenon to higher temperatures. Similar to Ap stars, they are spectrum variables and also show variable photometrical light curves \citep[e.g.][]{Pedersen1977}. However, while the evolution of the magnetic field strength and field geometry, including the evolution of the dipole obliquity angle $\beta$ in Ap and late-B-type stars across the main sequence, has already been the subject of several careful studies using representative stellar samples \citep[e.g.][]{Hubrig2000, Hubrig2007}, no comparable study exists for a representative sample of early B-type He-rich stars with well-defined rotation periods and magnetic field geometries. As we showed in the previous section, the longitudinal magnetic field measurements in He-rich stars are strongly affected by the presence of chemical spots, making the determination of the obliquity angle $\beta$ difficult. Furthermore, the magnetic field geometry in these stars frequently shows contributions from non-dipolar multipoles. In particular, the distribution of the obliquity angle $\beta$ is essential to understand the physical processes taking place in these stars and the origin of their magnetic fields. As discussed by \citet{Moss1986} and later by \citet{Hubrig2007}, randomness in the $\beta$ distribution may be regarded as an argument in favour of the fossil field, since the star-to-star variations in obliquity of the magnetic field axes can plausibly be interpreted as reflecting differences in the intrinsic magnetic conditions at different formation sites. An important issue of the fossil field theory discussed in the past was the survival of the magnetic field over the star's lifetime, as it was difficult to find stable field configurations \citep[e.g.][]{Mestel1984, Moss1986}. However, more recently, \citet{2004Nature} used three-dimensional numerical MHD simulation and showed that stable magnetic field configurations can develop through evolution from arbitrary, random initial magnetic fields. The magnetic field permeating the interstellar medium is amplified during star formation and may naturally relax into a large-scale, mostly poloidal field emerging at the surface. The work of \citet{2004Nature} (see also the work of \citet{Braithwaite2008,Braithwaite2009,Duezetal}) resulted in fundamental revision of our understanding of the behaviour of magnetic fields in stellar radiative zones. On the other hand, the magnetic field excited by a dynamo mechanism is expected to be either symmetric or antisymmetric in regard to the equatorial plane \citep[e.g.][]{Krause1976}. | 18 | 8 | 1808.04081 |
1808 | 1808.06617_arXiv.txt | We present the results of our year-long afterglow monitoring of GW170817, the first binary neutron star (NS) merger detected by advanced LIGO and advanced Virgo. New observations with the Australian Telescope Compact Array (ATCA) and the {\it Chandra X-ray Telescope} were used to constrain its late-time behavior. The broadband emission, from radio to X-rays, is well-described by a simple power-law spectrum with index $\beta$\,$\sim$0.585 at all epochs. After an initial shallow rise $\propto$\,$t^{0.9}$, the afterglow displayed a smooth turn-over, reaching a peak X-ray luminosity of $L_X$$\approx$5$\times$$10^{39}$\,erg\,s$^{-1}$ at 160 d, and has now entered a phase of rapid decline, approximately $\propto$\,$t^{-2}$. The latest temporal trend challenges most models of choked jet/cocoon systems, and is instead consistent with the emergence of a relativistic structured jet seen at an angle of $\approx$22$^{\circ}$ from its axis. Within such model, the properties of the explosion (such as its blastwave energy $E_K\approx2\times10^{50}$\,erg, jet width $\theta_c$\,$\approx$4$^{\circ}$, and ambient density $n$\,$\approx$3$\times$\,$10^{-3}$\,cm$^{-3}$) fit well within the range of properties of cosmological short GRBs. | On August 17$^{\rm th}$, 2017 the Advanced LIGO interferometers detected the first gravitational wave (GW) signal from a binary neutron star (NS) merger, GW170817, followed 1.7 s later by a short duration gamma-ray burst, GRB170817A \citep{LVCGBM}. Located in the elliptical galaxy NGC4993 at a distance of $\sim$40 Mpc, GRB170817A was an atypical sub-luminous explosion. An X-ray afterglow was detected 9 days after the merger \citep{Troja2017}. A second set of observations, performed $\sim$15 days post-merger, revealed that the emission was not fading, as standard GRB afterglows, but was instead rising at a slow rate \citep{Troja2017,Haggard2017}. The radio afterglow, detected at 16 days \citep{Hallinan2017}, continued to rise in brightness \citep{Mooley2018}, as later confirmed by X-ray and optical observations \citep{Troja2018,DAvanzo2018,Lyman2018,Margutti2018}. The delayed afterglow onset and low-luminosity of the $\gamma$-ray { signal} could be explained if the jet was observed at an angle (off-axis) of $\approx$15$^{\circ}$-30$^{\circ}$. Whereas a standard uniform jet viewed off-axis could account for the early afterglow emission, \citet{Troja2017} and \citet{Kasliwal2017} noted that it could not account for the observed gamma-ray signal and proposed two alternative models: a structured jet, i.e. a jet with an {\it angular} profile of Lorentz factors and energy \citep[see also][]{LVCGBM,kathi18}, and a mildly-relativistic isotropic cocoon \citep[see also][]{Lazzati2017b,Kasliwal2017}. In the latter model, the jet may never emerge from the merger ejecta (choked jet). The subsequent rebrightening ruled out both the uniform jet and the simple cocoon models, which predict a sharp afterglow rise. It was instead consistent with an off-axis structured jet \citep{Troja2017} and a cocoon with energy injection \citep{Mooley2018}, characterized by a {\it radial} profile of ejecta velocities. In \cite{Troja2018} we developed semi-analytical models for both the structured jet and the quasi-spherical cocoon with energy injection, and showed that they describe the broadband afterglow evolution during the first six months (from the afterglow onset to its peak) equally well. This is confirmed by numerical simulations of relativistic jets \citep{Lazzati2018,Xie2018} and choked jets \citep{Nakar2018}. Several tests were discussed to distinguish between these two competing models \citep[e.g.][]{GillGranot2018,Nakar2018}. \citet{Corsi2018} used the afterglow polarization to probe the outflow geometry (collimated vs. nearly isotropic), but the results were not constraining. \citet{Ghirlanda2018} and \citet{Mooley2018superluminal} used Very Long Baseline Interferometry (VLBI) to image the radio counterpart, and concluded that the compact source size ($\lesssim$2 mas) and its apparent superluminal motion favor the emergence of a relativistic jet core. A third and independent way to probe the outflow structure is to follow its late-time temporal evolution. In the case of a cocoon-dominated emission, the afterglow had been predicted to follow a shallow decay ($t^{-\alpha}$) with $\alpha$\,$\sim$1.0-1.2 \citep{Troja2018} for a quasi-spherical outflow, and $\alpha$\,$\sim$1.35 for a wide-angled cocoon \citep{LambMandelResmi2018}. A relativistic jet is instead expected to resemble a standard on-axis explosion at late-times, thus displaying a post-jet-break decay of $\alpha \sim 2.5$ \citep{vanEertenMacFadyen2013}. Here, we present the results of our year-long observing campaign of GW170817, carried out with the Australian Telescope Compact Array (ATCA) in the radio, {\it Hubble Space Telescope} (HST) in the optical, the {\it Chandra} X-ray telescope and {\it XMM-Newton} in the X-rays. Our latest observations show no signs of spectral evolution (Sect. \ref{spectral_properties_section}) and a rapid decline of the afterglow emission (Sect. \ref{temporal_properties_section}), systematically faster than cocoon-dominated/choked jet models from the literature (Sect. \ref{decline_results_section}). The rich broadband dataset allows us to tightly constrain the afterglow parameters, and to compare the explosion properties of GW170817 to canonical short GRBs (Sect. \ref{comparison_section}). | The long-term afterglow monitoring of GW170817 supports the earlier suggestions of a relativistic jet emerging from the merger remnant, and challenges the alternative scenarios of a choked jet. Whereas emission at early times ($<$160 d) came from the slower and less energetic lateral wings, the rapid post-peak decline suggests that emission from the narrow jet core has finally entered our line of sight. The overall properties of the explosion, as derived from the afterglow modeling, are consistent with the range of properties observed in short GRBs at cosmological distances, and suggest that we detected its electromagnetic emission thanks to a combination of moderate off-axis angle ($\theta_v$-$\theta_c$\,$\approx$20$^{\circ}$ ) and intrinsic energy of the explosion. | 18 | 8 | 1808.06617 |
1808 | 1808.09921_arXiv.txt | Stellar streams are ubiquitous in the Galactic halo and they can be used to improve our understanding of the formation and evolution of the Milky Way as a whole. The so-called Monoceros Ring might have been the result of satellite accretion. Guglielmo et al. have used $N$-body simulations to search for the progenitor of this structure. Their analysis shows that, if the Ring has a dwarf galaxy progenitor, it might be found in the background of one out of eight specific areas in the sky. Here, we use {\it Gaia} DR2 data to perform a systematic exploration aimed at confirming or rejecting this remarkable prediction. Focusing on the values of the radial velocity to uncover possible multimodal spreads, we identify a bimodal Gaussian distribution towards Galactic coordinates ($l$, $b$) = (271{\degr}, +2{\degr}) in Vela, which is one of the locations of the progenitor proposed by Guglielmo et al. This prominent feature with central values 60$\pm$7~km~s$^{-1}$ and 97$\pm$10~km~s$^{-1}$, may signal the presence of the long sought progenitor of the Monoceros Ring, but the data might also be compatible with the existence of an unrelated, previously unknown, kinematically coherent structure. | Beyond the nominal edge of the Milky Way disc, 15~kpc from the Galactic centre, lies a complex network of coherent stellar structures whose origins are not yet fully understood (see e.g. \citealt{2011PhDT.......171S,2011ApJ...738...79X,Pila15,2016ASSL..420..113S}). Some may be the result of the Milky Way cannibalizing nearby dwarf galaxies \citep{1994Natur.370..194I}, others could be just stellar lumps induced by the combined action of the gravitational potential of the Galaxy and those of passing and/or falling neighbours \citep{2015ApJ...801..105X,2018MNRAS.478.3809S}. The study of these structures can help in understanding how the Milky Way came into existence and how it has evolved progressively to become what we observe now. Among all these structures, the true nature of the so-called Monoceros Ring remains elusive. Originally identified by \citet{2002ApJ...569..245N}, the structure is considered by some as a {\it bona fide} stellar stream (e.g. \citealt{2003MNRAS.340L..21I,2003ApJ...588..824Y,2007MNRAS.376..939C,2008ApJ...689L.117G, 2008ApJ...684..287I,2011MNRAS.414L...1M,2011ApJ...730L...6S,2018MNRAS.473.1218L}), while others put its origin in the (flared thick) disc of the Milky Way (e.g. \citealt{2005ApJ...630L.153C,2006A&A...451..515M,2014ApJ...794...90K,2014A&A...567A.106L,2018ApJ...854...47S, 2018MNRAS.478.3367W}). Alternative scenarios put its provenance in an outer spiral arm such as the one described by \citet{2011ApJ...734L..24D} or in undulations of the disc \citep{2017ApJ...844...74L} like those discussed by \citet{2015ApJ...801..105X}. \citet{2018MNRAS.474.4584G} have recently explored the kinematics, proper motions, and the nature of the putative progenitor of the Monoceros Ring. Although they could not confirm that the Ring has its origin in an accretion episode, their analysis argues that, if the Ring has a dwarf galaxy progenitor, it might be found in the background of one out of eight well-defined areas in the sky. Here, we use {\it Gaia} DR2 data to perform a systematic exploration of these areas aimed at confirming or rejecting their prediction, focusing on the values of the radial velocity to uncover possible multimodal distributions. This Letter is organized as follows. Section~2 presents the input data and tools used in our analysis. The eight radial velocity distributions are explored in Section~3. Section~4 presents the analysis of a bimodal Gaussian distribution found towards Galactic coordinates ($l$, $b$) = (271{\degr}, +2{\degr}) in Vela. In Section~5, we study the statistical significance of our findings. Results are discussed in Section~6 and conclusions are summarized in Section~7. | In this Letter, we have investigated the plausibility of the predictions made by \citet{2018MNRAS.474.4584G} regarding the possible location of the putative progenitor of the Monoceros Ring using data from {\it Gaia} DR2 and focusing on the distribution of radial velocities. A statistically robust feature in the radial velocity distribution of stars in Vela has been identified. Our conclusions are: \begin{enumerate}[(i)] \item Based on the distributions of radial velocities provided by {\it Gaia} DR2, the distant stellar populations located in the regions proposed by \citet{2018MNRAS.474.4584G} appear to be compatible with single populations (i.e. no kinematically heterogenous samples) in all but one case, that of the region towards the constellation of Vela. \item We have identified a statistically significant bimodal Gaussian distribution towards Galactic coordinates ($l$, $b$) = (271{\degr}, +2{\degr}), which is one of the present-day locations of the progenitor of the Monoceros Ring proposed by \citet{2018MNRAS.474.4584G}. This feature has central values of the radial velocity of 60$\pm$7~km~s$^{-1}$ and 97$\pm$10~km~s$^{-1}$. \item The prominent feature found towards Vela may signal the presence of the long sought progenitor of the Monoceros Ring, but the data might also be compatible with the existence of an unrelated, previously unknown, kinematically coherent structure. \item Interstellar extinction may be a major obstacle to disentangle the true nature of the two remote populations that appear to share the patch of sky around ($l$, $b$) = (271{\degr}, +2{\degr}). \end{enumerate} | 18 | 8 | 1808.09921 |
1808 | 1808.05422_arXiv.txt | The mass sensitivity of the vibration-rotation-inversion transitions of H$_3{}^{16}$O$^+$, H$_3{}^{18}$O$^+$, and D$_3{}^{16}$O$^+$ is investigated variationally using the nuclear motion program TROVE~\citep{TROVE:2007}. The calculations utilize new high-level \textit{ab initio} potential energy and dipole moment surfaces. Along with the mass dependence, frequency data and Einstein A coefficients are computed for all transitions probed. Particular attention is paid to the $\Delta|k|=3$ and $\Delta|k-l|=3$ transitions comprising the accidentally coinciding $|J,K\!=\!0,v_2\!=\!0^+\rangle$ and $|J,K\!=\!3,v_2\!=\!0^-\rangle$ rotation-inversion energy levels. The newly computed probes exhibit sensitivities comparable to their ammonia and methanol counterparts, thus demonstrating their potential for testing the cosmological stability of the proton-to-electron mass ratio. The theoretical TROVE results are in close agreement with sensitivities obtained using the nonrigid and rigid inverter approximate models, confirming that the \textit{ab initio} theory used in the present study is adequate. | The hydronium cation (H$_3$O$^+$) is one of the key molecular ions for inferring properties of the interstellar medium, particularly for constraining the cosmic-ray ionization rate of atomic and molecular hydrogen (see \citet{Indriolo:2015} and references therein). Knowledge of such parameters is of astrophysical importance, and as a result, H$_3$O$^+$ is one of the most searched for galactic and extragalactic interstellar molecules~\citep{Hollis:1986,Wootten:1986,Wootten:1991,Phillips:1992,Boreiko:1993,Goi:2001,Tak:2006,Tak:2008,Gerin:2010,Gupta:2010,Aalto:2011,Gonzalez:2013,Lis:2014}. Since H$_3$O$^+$ formation requires presence of H$_2$O, and the chemical relation between H$_3$O$^+$ and H$_2$O is well-understood, H$_3$O$^+$ can serve as an excellent proxy for H$_2$O, which is often hard to observe directly~\citep{Timmermann:1996}. Similar to the ammonia molecule, H$_3$O$^+$ has several far infrared (FIR) and submillimetre transitions that are particularly sensitive to the proton-to-electron mass ratio $\mu$~\citep{Kozlov:2011a,Kozlov:2011b}. The most robust constraint on a variable $\mu$ has recently been determined using methanol absorption spectra observed in the lensing galaxy PKS1830$-$211~\citep{Kanekar:2015}. The three measured lines possessed sensitivities differing by $\Delta T=6.4$, where $T$ is the sensitivity coefficient of a transition. In principle then, hydronium is capable of being used exclusively to constrain a possible variation in the proton-to-electron mass ratio, thus avoiding certain systematic errors which arise when using transitions from different molecular species~\citep{Flambaum:2007,Murphy:2008,Henkel:2009,Kanekar:2011}. A small number of pure inversion and rotation-inversion transitions in the ground vibrational state of H$_3$O$^+$ were originally investigated by \citet{Kozlov:2011a}. However the calculated sensitivity coefficients were overestimated and new values have been computed for H$_3$O$^+$, along with the isotopologues H$_2$DO$^+$, HD$_2$O$^+$, and D$_3$O$^+$~\citep{Kozlov:2011b}. Given the astronomical relevance of H$_3$O$^+$, and a good representative set of accurately measured experimental data~\citep{Uy:1997,Tang:1999,Araki:1999,Furuya:2005,Yu:2009,Yu:2014}, we find it worthwhile to carry out a comprehensive study of hydronium, H$_3{}^{16}$O$^+$ (also referred to as H$_3$O$^+$), and its two symmetric top isotopologues, H$_3{}^{18}$O$^+$ and D$_3{}^{16}$O$^+$. To do this we employ a highly accurate variational approach, which was recently applied to ammonia~\citep{Owens:2015}. Like NH$_3$~\citep{Jansen:2014,Spirko:2014,Owens:2015}, there is a possibility to find transitions with strongly anomalous sensitivities caused by the $\Delta k=\pm 3$ interactions (see \citet{Papousek:1986}), which have not yet been considered. | A robust variational study of the vibration-rotation-inversion transitions of H$_3{}^{16}$O$^+$, H$_3{}^{18}$O$^+$, and D$_3{}^{16}$O$^+$ has been carried out. We hope that by providing theoretical frequency data and Einstein A coefficients, future laboratory and astronomical observations can be tailored to measure transitions which possess sizeable sensitivities. The astrophysical importance of hydronium suggests that this is a realistic prospect. Emphasis should be placed on the `forbidden' combination differences of the $\nu_3$ band, since several of the corresponding transitions have already been experimentally measured~\citep{Uy:1997}. The 7$_{3}^-\leftarrow$7$_{0}^+$ and 9$_{3}^-\leftarrow$9$_{0}^+$ combination differences are separated by $\Delta T=25.934$. This is around four times larger than the $\Delta T$ of the methanol transitions recently used to determine the most reliable constraint on a possible variation in the proton-to-electron mass ratio~\citep{Kanekar:2015}. | 18 | 8 | 1808.05422 |
1808 | 1808.02034_arXiv.txt | { We present state-of-the-art predictions for the ultra-high energy (UHE) neutrino-nucleus cross-sections in charged- and neutral-current scattering. The calculation is performed in the framework of collinear factorisation at NNLO, extended to include the resummation of small-$x$ BFKL effects. Further improvements are made by accounting for the free-nucleon PDF constraints provided by $D$-meson data from LHCb and assessing the impact of nuclear corrections and heavy-quark mass effects. The calculations presented here should play an important role in the interpretation of future data from neutrino telescopes such as IceCube and KM3NET, and highlight the opportunities that astroparticle experiments offer to study the strong interactions. } \begin{document} | 18 | 8 | 1808.02034 |
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1808 | 1808.02491_arXiv.txt | We study the expected spin misalignments of merging binary black holes formed in isolation by combining state-of-the-art population-synthesis models with efficient post-Newtonian evolutions, thus tracking sources from stellar formation to gravitational-wave detection. We present extensive predictions of the properties of sources detectable by both current and future interferometers. We account for the fact that detectors are more sensitive to spinning black-hole binaries with suitable spin orientations and find that this significantly impacts the population of sources detectable by LIGO, while this is not the case for third-generation detectors. We find that three formation pathways, differentiated by the order of core collapse and common-envelope phases, dominate the observed population, and that their relative importance critically depends on the recoils imparted to black holes at birth. Our models suggest that measurements of the ``effective-spin'' parameter $\chi_{\rm eff}$ will allow for powerful constraints. For instance, we find that the role of spin magnitudes and spin directions in $\chi_{\rm eff}$ can be % largely disentangled, and that the symmetry of the effective-spin distribution is a robust indicator of the binary's formation history. Our predictions for individual spin directions and their precessional morphologies confirm and extend early toy models, while exploring substantially more realistic and broader sets of initial conditions. Our main conclusion is that specific subpopulations of black-hole binaries will exhibit distinctive precessional dynamics: these classes include (but are not limited to) sources where stellar tidal interactions act on sufficiently short timescales, and massive binaries produced in pulsational pair-instability supernovae. Measurements of black-hole spin orientations have enormous potential to constrain specific evolutionary processes in the lives of massive binary stars. | Gravitational-wave (GW) observations of merging black-hole (BH) binaries have the potential to unveil the fate of massive stars. As they exhaust all the available fuel, stars with initial masses $M\gtrsim 8 M_\odot$ are expected to undergo gravitational collapse. About $\sim 15\%$ of them are predicted to form BHs \cite{2011ApJ...730...70O}. The detection of stellar-origin BHs in a binary system requires not only the formation of BHs in the first place, but also the occurrence of astrophysical processes that can dissipate enough energy and angular momentum to bring the orbital separation below $r\sim 50 R_\odot$, where GW damping can drive the binary to merger \cite{1964PhRv..136.1224P}. There are two main classes of formation models, depending on whether (i) the two BHs spend their entire lives together as stars, or (ii) they form separately and meet later. In models belonging to class (i), BH binaries are the end product of the life of binaries of massive stars \cite{2014LRR....17....3P}. Each of the two stars undergoes gravitational collapse and, if the binary is not disrupted, a binary BH is left behind. A common-envelope phase -- where the core/remnant of one the two objects sinks into the outer layers of its companion \cite{1976IAUS...73...75P} -- is typically invoked to dissipate enough angular momentum and produce a merging binary. % Models of class (ii) instead require dense stellar environments to facilitate the assembly of multiple BHs and many-body interactions to harden the binary \cite{2013LRR....16....4B}. For a comprehensive review on BH-binary formation channels see, e.g., \cite{2018arXiv180605820M,2016ApJ...818L..22A} and references therein. The most obvious observable to confirm or rule out formation channels is the merger rate, currently constrained to the range $12 - 213\;{\rm Gpc}^{-3} {\rm yr}^{-1}$ \cite{2017PhRvL.118v1101A}. These large uncertainties leave ample room for models in both classes to match the observational constraints which, at present, do not allow us to confirm or rule out any of the preferred scenarios. Measurements of the BH masses also tend to be poorly constraining, partly because of a selection bias: more massive systems are visible farther out. This tends to wash out differences in the intrinsic distributions, such that the observable distributions predicted by various models all tend to overlap. In practice, $\mathcal{O}(100)$ observations could be necessary before strong constraints can be placed using mass measurements \cite{2015ApJ...810...58S,2017ApJ...846...82Z,2017PhRvD..95j3010K,2018MNRAS.477.4685B} (although sharp features like a mass cutoff will be accessible earlier \cite{2017ApJ...851L..25F,2018ApJ...856..173T,2018arXiv180506442W}). Merger redshifts are also weak observables. They are expected to be set by the star formation history \cite{2014ARA&A..52..415M}, which is essentially the same in all star-based BH formation models. Notable exceptions include models where older populations of stars are responsible for present-day BHs \cite{2014MNRAS.442.2963K,2017MNRAS.471.4702B}, as well as predictions which make use of large-scale cosmological simulations \cite{2017MNRAS.472.2422M,2018MNRAS.480.2704L}. BH spin magnitudes can be very powerful observables for constraining the physics of individual massive stars, but provide a less effective way to distinguish between stellar-based compact-binary formation channels. Spin magnitudes are expected to be set by stellar collapse dynamics \cite{2011ApJ...730...70O}, and should therefore be similar for BHs formed either in galactic fields or dynamically. A possible handle could be provided by dependence on the star's metallicity, which is expected to impact processes like angular momentum transport and mass loss. Again, these observables might turn out to be particularly useful to constrain specific mechanisms, such as scenarios where previous mergers, rather than stellar collapse, are responsible for forming the merging BHs \cite{2017PhRvD..95l4046G,2017ApJ...840L..24F,2018PhRvD..97l3003K}. Binary eccentricities may also provide information on some specific models \cite{2012ApJ...757...27A,2018PhRvD..97j3014S}. Eccentricities from the most favored scenarios are expected to be too low in the LIGO/Virgo band to provide stringent constraints \cite{2017CQGra..34j4002A}, {although some scenarios predict events with high eccentricity \cite{2018PhRvD..97j3014S,2018PhRvL.120o1101R}}. To this end, LISA observations at low frequencies (when binaries are not yet fully circularized) may turn out to be crucial \cite{2016PhRvD..94f4020N,2017MNRAS.465.4375N,2016ApJ...830L..18B,2018arXiv180406519S}. The most promising observables to shine light on BH-binary formation are the spin directions. Spins of BHs formed following dynamical encounters are expected to be isotropically distributed {(but see \cite{2017ApJ...846L..11L,2018MNRAS.480L..58A}).} This is because the BH-binary evolution is set by the astrophysical environment, whose coupling to the BH spins is known to be negligible \cite{2017PhRvD..95f4014C}. It is worth pointing out, however, that some angular momentum from the cloud that formed the cluster could be transferred to the stellar spins, thus introducing correlations between their directions \cite{2017NatAs...1E..64C}. Even if present, these correlations are expected to be largely washed out by the many dynamical encounters leading to the formation of the GW sources. % Conversely, the spin directions of BH binaries formed in isolation are greatly influenced by the evolutionary paths of their stellar progenitors. % The two stars will form a binary BH without prominent interactions with other bodies, thus ``carrying memory'' of some of the physical mechanisms occurring during their history. Even in the simplest models where stellar spins are initially aligned to the binary's orbital angular momentum, misalignments are expected to be introduced by recoil velocities imparted to the BHs at birth. These ``supernova kicks'' tilt the orbital plane, thus introducing some misalignment between the orbital angular momentum and the spin directions \cite{2000ApJ...541..319K}. Tidal interactions can also influence the spin directions, generically acting towards realigning spins with the orbital angular momentum \cite{1981A&A....99..126H}. After the BH binary is formed, spin directions are further modified by post-Newtonian (PN) spin-orbit and spin-spin couplings during the long inspiral phase before the binary becomes detectable by LIGO and Virgo \cite{1994PhRvD..49.6274A}. PN effects tend to separate different subpopulations, hence greatly improving model distinguishability \cite{2013PhRvD..87j4028G}. % The effectiveness of BH spin tilts at constraining formation channels was already explored in previous work through astrophysical models \cite{2010CQGra..27k4007M,2013PhRvD..87j4028G,2016ApJ...832L...2R, 2018MNRAS.480L..58A,2017arXiv170607053B}, simulated LIGO/Virgo data \cite{2014PhRvD..89l4025G,2014PhRvL.112y1101V,2016PhRvD..93d4071T,2017MNRAS.471.2801S,2017CQGra..34cLT01V,2017PhRvD..96b3012T} and actual GW observations \cite{2017PhRvL.119a1101O,2017Natur.548..426F,2018PhRvD..97d3014W,2018ApJ...854L...9F,2018arXiv180506442W}. This paper presents a comprehensive study of the expected spin direction distributions of BH binaries formed from isolated pairs of stars. Using the \textsc{StarTrack} \cite{2008ApJS..174..223B} and \textsc{precession} \cite{2016PhRvD..93l4066G} numerical codes, we combine for the first time state-of-the-art evolutions of binary stars to accurate PN spin tracking and coherently model spin evolution from formation to detection (Sec.~\ref{methods}). We present forecasts for both approximate one-spin dynamics through the effective-spin parameter (which is easier to measure; Sec.~\ref{results1}) and genuine two-spin effects (which encode more information; Sec.~\ref{results2}). We then illustrate predictions of our models in terms of the spin morphologies identified in \cite{2015PhRvL.114h1103K,2015PhRvD..92f4016G} (Sec.~\ref{results3}). We conclude with prospects for constraining these mechanisms with current and future GW detectors (Sec.~\ref{conclusions}). Unless otherwise noted, we use geometrical units ($G=c=1$). Our database is publicly available at \href{https://github.com/dgerosa/spops}{github.com/dgerosa/spops} \cite{spops}, where we also provide a convenient python module (called \textsc{spops}) to facilitate its exploration. | \label{conclusions} After the first LIGO detections, it is becoming more widely accepted by the scientific community that BH spin orientations are possibly the cleanest indicators of BH-binary formation channels. In particular, binaries formed in dynamical interactions are predicted to have randomly distributed spins, while conventional wisdom asserts that the spins of binaries formed in isolation are \emph{more or less} aligned. In this paper, we carefully distinguished between spin alignment \emph{at BH-binary formation} and \emph{as observed in GWs}, and we quantified the expected degree of (mis)alignment for the first time. We studied an extensive set of astrophysical models, combining for the first time state-of-the-art stellar population synthesis (\textsc{StarTrack} \cite{2008ApJS..174..223B}) and advanced PN evolution schemes (\textsc{precession} \cite{2016PhRvD..93l4066G}). We quantified the impact of several model parameters --namely the strength of natal kicks, the spin magnitude at formation and the efficiency of tidal alignment-- on the population of spinning BH binaries detectable by current and future ground-based GW interferometers. Within the context of these models, we showed that future measured distributions of effective spins \emph{alone} could break the degeneracy between spin orientation and spin magnitude encoded in the very definition of $\chi_{\rm eff}$. We also confirmed previous claims that binaries formed in isolation cannot produce a symmetric $\chi_{\rm eff}$ distribution \cite{2017Natur.548..426F,2018ApJ...854L...9F}, although individual binaries can have $\chi_{\rm eff}<0$ (in contrast with some previous claims \cite{2016ApJ...832L...2R}). The directions of the individual spins have not been confidently measured so far,\footnote{GW151226 data contains hints of a primary-BH misalignment in the range $25^\circ \lesssim \theta_1\lesssim 80^\circ$ \cite{2016PhRvL.116x1103A,2017PhRvL.119a1101O}.} but louder events, improved waveform models and more sophisticated parameter-estimation techniques may soon allow us to characterize the full (two-spin) dynamics of BH binaries. As shown here, this can have a significant payoff: we may be able to reconstruct the binary's formation history. Our study confirms some of our earlier results \cite{2013PhRvD..87j4028G}, and in particular the observation that the azimuthal precession phase $\Delta\Phi$ encodes clean information on processes that may (or may not) realign stellar spins in between the two core-collapse events forming each BH. We also presented the first prediction of how detectable sources would be distributed in terms of the recently discovered spin morphology \cite{2015PhRvL.114h1103K,2015PhRvD..92f4016G}, a feature of spin precession that does not vary on the precessional timescale. In this paper, rather than focusing on fine model-parameter searches to reproduce current LIGO/Virgo observations, we have preferred to present only predictions from a limited set of astrophysically reasonable simulations. Initial comparisons of our predictions with GW data \cite{2018PhRvD..97d3014W} found that observations from the first LIGO/Virgo observing run constrain $\sigma$ to be $\simeq 200$ ($\simeq 50$) km/s for (in)efficient tides, and marginally prefer small spin magnitudes. Combining the formalism of \cite{2018PhRvD..97d3014W} and the more sophisticated predictions of this paper is an interesting avenue for future work. Furthermore, we plan to explore more advanced model selection techniques (e.g. \cite{2018arXiv180506442W,2018arXiv180608365T}) and to make detailed predictions for the next observing runs of the growing LIGO/Virgo/KAGRA network. Little information will be learned on processes affecting binary BH spins if their magnitudes turn out to be consistently very low. \emph{If} there is something out there to learn, however, the modeling efforts presented in this paper highlight the immense potential of future spin measurements. We are approaching the time when large GW detection catalogs will become available, and GW astronomy will turn into a large-statistics, data-driven field. With the rapid sensitivity improvements of ground-based interferometers, this may well happen sooner rather than later. \pagebreak | 18 | 8 | 1808.02491 |
1808 | 1808.05564_arXiv.txt | We analyze 88 independent high-resolution cosmological zoom-in simulations of disk galaxies in the NIHAO simulations suite to explore the connection between the atomic gas fraction and angular momentum of baryons throughout cosmic time. The study is motivated by the analytical model of \citet{obreschkow16}, which predicts a relation between the atomic gas fraction $f_{\rm atm}$ and the integrated atomic stability parameter $q \equiv j\sigma / (GM)$, where $M$ and $j$ are the mass and specific angular momentum of the galaxy (stars+cold gas) and $\sigma$ is the velocity dispersion of the atomic gas. We show that the simulated galaxies follow this relation from their formation ($z\simeq4$) to present within $\sim 0.5$ dex. To explain this behavior, we explore the evolution of the local Toomre stability and find that $90\%$--$100\%$ of the atomic gas in all simulated galaxies is stable at any time. In other words, throughout the entire epoch of peak star formation until today, the timescale for accretion is longer than the timescale to reach equilibrium, thus resulting in a quasi-static equilibrium of atomic gas at any time. Hence, the evolution of $f_{\rm atm}$ depends on the complex hierarchical growth history primarily via the evolution of $q$. An exception are galaxies subject to strong environmental effects. | \label{sec:intro} A comprehensive theory of galaxy evolution requires understanding the assembly and evolution of the stellar disks and spheroids of galaxies, as well as the co-evolution of these components with the interstellar medium (ISM) and circumgalactic medium (CGM). The accurate modeling of these gaseous components in galaxies is challenging as the gas is subject to non-linear gravitational, hydrodynamic and radiative forces. Several physical processes significantly affect the geometry and thermodynamic phase of the gas, such as cold flow accretion \citep{keres05}, hot mode accretion \citep[e.g.][]{rees77, white78, putman12, werk14}, stellar winds from evolved stars \citep{kalirai08, leitner11} and recycling of the metal-rich gas ejected through stellar winds \citep{oppenheimer10, brook14, ubler14}. Owing to the time-dependent complex geometry of gas flows into and out of galaxies, the detailed evolution of different gas components has yet to be understood. Neutral atomic hydrogen (\hi) dominates the hydrogen budget in local galaxies, except at the highest column densities ($>10 ~\Msun~pc^{-2}$), where this gas normally transitions into the molecular (\hm) phase. \hi is the critical waypoint between the ionized CGM and star formation in the disk \citep{leroy08}. Detailed studies of \hi are therefore invaluable to understanding the formation of galaxies at large. Direct observations in 21cm emission and absorption \citep{ewen51} have revealed a plethora of relationships between the \hi content and other galaxy properties, most notably the star-formation rate \citep{kennicutt89}, stellar mass \citep[e.g.][]{dutton09, obreschkow09, dutton11, catinella13,maddox15}, spin \citep{huang12,obreschkow16} and morphology \citep{catinella10, brown15, brown17}. The atomic gas fraction is defined as: \begin{equation}\label{eq:fatm_def} f_{\rm atm} = \frac{1.35M_{\rm \ion{H}{I}}}{M}, \end{equation} where the total mass $M=M_\star+1.35(M_{\rm HI}+M_{\rm H_2})$, $M_\star$, $M_{\rm HI}$ and $M_{\rm H_2}$ are stellar mass, \hi mass and \hm mass respectively. The factor of $1.35$ accounts for the universal $\sim 26\%$ helium fraction at redshift $z=0$. Computational examinations show that $f_{\rm atm}$ depends sensitively on the numerical resolution, subgrid physics, e.g. feedback from supernovae and active galactic nuclei, \citep[e.g.][]{duffy12, dave13, stinson15, crain17, diemer18} and physical processes related to the cosmological environment, e.g. ram pressure stripping and tidal interactions, \citep{cunnama14, rafieferantsoa15}. It is necessary to identify the key driver(s) that set(s) $f_{\rm atm}$ to first order in some well-defined sense. Several recent empirical and computational works have highlighted that the specific angular momentum of galaxies at fixed stellar mass is strongly correlated to their atomic gas fraction \citep[e.g.][]{dutton10, huang12,obreschkow15b,lagos17, romeo18, stevens18, zoldan18}. \citet{obreschkow16} (hereafter O16) introduced a parameter-free analytical model that predicts $f_{\rm atm}$ as a function of mass and angular momentum in equilibrium disks. This model assumes that galactic disks have an exponential surface density profile and are locally either fully atomic or non-atomic: the disk is atomic where and only where the atomic gas is stable in the sense of \citet{toomre64} at the characteristic dispersion velocity $\sigma$ of the warm neutral medium (about $10~\rm km\,s^{-1}$). In this model $f_{\rm atm}$ only depends on the so-called \emph{integrated atomic stability parameter} \begin{equation}\label{eq:q} q = \frac{j_{\rm gal}\sigma_{\rm gas}}{GM_{\rm gal}}, \end{equation} first introduced by \citet{obreschkow14}, where $M_{\rm gal}$ and $j_{\rm gal}$ are the mass and specific angular momentum (AM) of the galaxy (stellar disk+cold gas) and $G$ is the gravitational constant. O16 predict that $f_{\rm atm}$ depends on $q$, approximately as \begin{equation}\label{eq:fatm} f_{\rm atm} = {\rm min}\{1, 2.5q^{1.12}\} \end{equation} with small ($<10\%$) variations subject to the shape of the rotation curve. To the extent that the assumptions of O16 remain valid across cosmic time, the evolution of $f_{\rm atm}$ should depend on a galaxy's complex assembly and interaction history only (or at least predominantly) via the evolution of $q$. This hypothesis is an interesting test case for cosmological simulations, which provide comprehensive information on the history of the atomic gas in evolving galaxies. The aim of this study is to examine the dependency between $f_{\rm atm}$ and $q$ across the cosmic time in the Numerical Investigation of a Hundred Astrophysical Objects, NIHAO \citep{wang15} project. The NIHAO simulations are a suite of 88 hydrodynamical cosmological zoom-in simulations implementing the tree-smoothed particle hydrodynamics (SPH), \gastwo. The NIHAO runs keep the same stellar physics at the whole mass range. The stellar mass of each halo in the NIHAO sample agrees with the prediction from abundance matching \citep{wang15}. The galaxies in the NIHAO sample reproduce several baryonic properties in observation, such as the star formation main sequence \citep{wang15}, the column density profile of cool \hi \citep{gutcke17}, the Tully-Fisher relation \citep{dutton17} and the local velocity function \citep{maccio16}. Therefore, NIHAO is well suited to study the relation (if any) between $f_{\rm atm}$ and $q$ through cosmic time across six orders of magnitude in stellar mass from $10^5 \Msun$ to $10^{11} ~\Msun$. This paper is structured as follows. The simulation techniques, in particular the modelling of the different hydrogen phases and computation of relevant kinematic parameters, are described in Section~\ref{sec:sim}. The properties of the simulated galaxies and the key results concerning the relation between the atomic gas fraction and $q$ parameter are presented in Section~\ref{sec:revisit}, along with a discussion of the physical mechanisms leading to these results. A summary and outlook are given in Section~\ref{sec:summary}. | \label{sec:summary} In this paper, we used the NIHAO galaxy simulation suite \citep{wang15} to analyze the dependency between the atomic gas fraction $f_{\rm atm}$ and the integrated atomic stability parameter $q$ \citep{obreschkow16} across cosmic time. The $q$ parameter was defined by O16 and used to develop an analytical equilibrium model to predict the atomic gas fraction in disks. NIHAO is a large set of high resolution cosmological zoom-in hydrodynamical galaxy formation simulations in the mass range between dwarf galaxies to Milky-Way mass galaxies. The simulated galaxies have a realistic cosmological environment and realistic dynamical and kinematic properties, making them ideal to test the O16 model in a full cosmological set-up. Our results are: \begin{itemize} \item The atomic gas fractions for all galaxies start at unity and decrease monotonically as the galaxies evolve. The galaxies in the most massive mass bin consume their gas rapidly while galaxies in lower mass bins decrease more mildly. \item Most ($\gtrsim90\%$) atomic gas of most galaxies is stable at any cosmic time. Most of the stable gas is clearly stable (Toomre $Q > 2$). \item The NIHAO sample is qualitatively consistent with the model of O16, which predicts the atomic gas fraction to depend on mass and angular momentum only via the \textit{integrated atomic stability parameter} $q$. The simulation and model agree at almost any time. \end{itemize} The last point is the most important finding. It implies that gravitational equilibrium is the dominant factor regulating $f_{\rm atm}$ at any particular time. The deeper reason for this simple conclusion is that the timescale of \hi accretion is almost always longer than that of the local \hi$\leftrightarrow$~\hm feedback loop. An exception to this rule are galaxies undergoing strong interactions, which can lead to massive instantaneous accretion and/or remove large amounts of \hi, for instance via starbursts, dynamical heating, stripping or fuelling of a central black hole. Some of these additional processes have recently been explored by \citet{stevens18} in a semi-analytic context, but a full physics treatment of these processes remains yet to be presented. | 18 | 8 | 1808.05564 |
1808 | 1808.05746_arXiv.txt | The linear polarization degree (referred to the scattering plane, $P_{\rm r}$) as a function of the solar phase angle, $\alpha$, of solar system objects is a good diagnostic to understand the scattering properties of their surface materials. We report $P_{\rm r}$ of Phaethon over a wide range of $\alpha$ from 19$^\circ$.1 to 114$^\circ$.3 in order to better understanding properties of its surface materials. The derived phase-polarization curve shows that the maximum of $P_{\rm r}$, $P_{\rm max}$, is $>$42.4\% at $\alpha >$114$^\circ$.3, a value significantly larger than those of the moderate albedo asteroids ($P_{\rm max} \sim$9\%). The phase-polarization curve classifies Phaethon as $B$-type in the polarimetric taxonomy, being compatible with the spectral property. We compute the geometric albedo, $p_{\rm v}$, of 0.14 $\pm$ 0.04 independently by using an empirical slope-albedo relation, and the derived $p_{\rm v}$ is consistent with previous results determined from mid-infrared spectra and thermophysical modeling. We could not find a fit to the period in our polarimetric data in the range from 0 up to 7.208 $hr$ (e.g., less than twice the rotational period) and found significant differences between our $P_{\rm r}$ during the 2017 approach to the Earth and that of the 2016. These results imply that Phaethon has a region with different properties for light scattering near its orbital pole. | \label{sec:intro} Asteroid (3200) Phaethon is an Apollo-type near-Earth asteroid with a diameter of 5.1 $\pm$ 0.2 km and a rotational period of 3.603958 $\pm$ 0.000002 $hr$ \citep{Hanus2016}. It has a large orbital inclination (22.2$^\circ$) and small perihelion distance (0.14 au). The surface of Phaethon has a geometric albedo, $p_{\rm v}$, of 0.122 $\pm$ 0.008 using a thermophysical model of its mid-infrared spectra \citep{Hanus2016}. Phaethon is thought to be a collisional family member of asteroid (2) Pallas \citep{Lemaitre_Morbidelli1994}, and they found that the typical $p_{\rm v}$ of the members of the Pallas Collisional Family (PCF) is larger than that of other $B$-type asteroids excluding PCF \citep{Lemaitre_Morbidelli1994}. Phaethon is also likely the parent body of the Geminid meteor shower because of their orbital association \citep{Whipple1983, Williams_Wu1993, deLeon2010}. Recently, the small brightening and comet-like tails of Phaethon observed near perihelion in 2009, 2010, and 2012 were found to be caused by small dust grains produced by thermal fracture and/or desiccation cracking of surface materials and released by the solar radiation pressure \citep{Jewitt_Li2010, Li_Jewitt2013, Jewitt2013}. Because these current mass-loss events are not sufficient to explain the activity of the Geminids \citep{Li_Jewitt2013}, Phaethon probably released a large amount of dust particles in the past, possibly due to comet-like activity driven by water ice sublimation. Because of its small perihelion distance, the surface temperature of Phaethon exceeds 1000 K \citep{Ohtsuka2009, Boice2017} and receives high solar radiation pressure near perihelion. These effects are expected to cause small grains with radius of $<$1 mm to be blown off its surface \citep{Jewitt_Li2010} and thermal metamorphism of surface materials. It is thought that its surface is covered by rocks with coarser grain size and contains hydrated minerals from various observational, experimental, and theoretical studies \citep{Licandro2007, deLeon2010, Hanus2016}. The linear polarization degree referred to the scattering plane, $P_{\rm r}$ \citep{Zellner_Gradie1976}, as a function of the solar phase angle, $\alpha$ (i.e., Sun-object-observer angle) is a good diagnostic to understand the scattering properties of surface materials. Here we call this relation the 'phase-polarization curve'. The $P_{\rm r}$ in the large $\alpha$ region is controlled primarily by the properties of individual particles in the medium \citep{Hapke2012}. Anyway, at the lower phase angle region (at $\alpha < \sim 40^\circ$), the phase-polarization curve has been used for the polarimetric classification for asteroids \citep{Belskaya2017} and estimation of a geometric albedo, $p_{\rm v}$ \citep{Cellino2015}. Recent polarimetric results in the positive polarization branch of Phaethon during the 2016 and 2017 approach to the Earth suggest that Phaethon has an extremely high $P_{\rm r}$ compared to other solar system bodies \citep{Ito2018, Devogele2018}; however, there was no measurement of $P_{\rm r}$ of Phaethon around the inversion angle ($\alpha <30^\circ$). | \label{sec:res} We report the phase-polarization curve of Phaethon over a wide range of $\alpha$ from 19$^\circ$.1 through 114$^\circ$.3 and find that $P_{\rm r}$ grows steadily through $\alpha$ of 114$^\circ$ (Figure \ref{fig:fig1}, Table \ref{tab:results}). The expected maximum linear polarization degree, $P_{\rm max}$, of Phaethon is $>$42.4\% (3$\sigma$ lower limit) and $\alpha_{\rm max}$, $\alpha$ at $P_{\rm max}$, is located at $>$114$^\circ$. This value is consistent with other polarimetric observations of Phaethon \citep{Ito2018, Devogele2018}. The derived $P_{\rm max}$ at $\alpha_{\rm max}$ of Phaethon are more than four times larger than those values for the moderate albedo asteroids (e.g., $P_{\rm max} <\sim$9\%; \citealt{Lupishko2014, Ishiguro2017}, at $\alpha_{\rm max} \sim100^\circ$; \citealt{Geake_Dollfus1986, Lupishko2014}), implying peculiar surface properties of Phaethon. To explain Phaethon's large linear polarization degree, \citet{Ito2018} pointed out the interpretations: lower $p_{\rm v}$ than the current estimations, relatively large grains, and high surface porosity. \begin{deluxetable*}{lcccccc} \tablecaption{Polarimetric results of Phaethon\label{tab:results}} \tablecolumns{15} \tablenum{2} \tablewidth{0pt} \tablehead{ \colhead{UT Time in 2017} & \colhead{JD - 2,458,000} & \colhead{$r_{\rm H}$ (au)} & \colhead{$\Delta$ (au)} & \colhead{$\alpha$ ($^\circ$)} & \colhead{$P_{\rm r}$ (\%)} & \colhead{$\theta_{\rm r}$ ($^\circ$)} } \startdata Dec 9 12:16:13--17:46:49 & 97.011262-- 97.249845 & 1.129--1.126 & 0.154--0.151 & 19.31-- 19.21 & -0.288 $\pm$ 0.002 & 3.8 $\pm$ 0.2 \\ Dec 10 10:58:02--16:57:46 & 97.956968-- 98.206782 & 1.115--1.111 & 0.139--0.135 & 19.12-- 19.19 & -0.217 $\pm$ 0.002 & 177.0 $\pm$ 0.3 \\ Dec 11 10:46:27--16:31:51 & 98.948924-- 99.188785 & 1.100--1.096 & 0.123--0.119 & 19.81-- 20.19 & -0.154 $\pm$ 0.002 & 136.1 $\pm$ 1.0 \\ Dec 12 12:20:02--16:32:54 & 100.013912--100.189514 & 1.083--1.080 & 0.107--0.105 & 22.28-- 22.92 & 0.652 $\pm$ 0.002 & 86.7 $\pm$ 0.1 \\ Dec 13 10:15:17--15:12:28 & 100.927280--101.133657 & 1.068--1.065 & 0.095--0.092 & 26.43-- 27.71 & 2.074 $\pm$ 0.002 & 88.8 $\pm$ 0.1 \\ Dec 14 12:11:57--15:58:44 & 102.008299--102.165787 & 1.051--1.049 & 0.082--0.081 & 34.46-- 35.95 & 4.593 $\pm$ 0.003 & 88.6 $\pm$ 0.1 \\ Dec 15 09:10:53--11:01:58 & 102.882558--102.959699 & 1.037--1.036 & 0.075--0.074 & 43.30-- 44.56 & 8.242 $\pm$ 0.004 & 88.5 $\pm$ 0.1 \\ Dec 16 09:00:58--13:17:53 & 103.875671--104.054086 & 1.021--1.018 & 0.070--0.069 & 56.68-- 59.26 & 15.453 $\pm$ 0.004 & 88.6 $\pm$ 0.1 \\ Dec 17 09:23:30--12:34:53 & 104.891319--105.024225 & 1.004--1.002 & 0.069--0.070 & 71.50-- 73.45 & 23.87 $\pm$ 0.02 & 88.3 $\pm$ 0.1 \\ Dec 18 08:52:14--12:03:59 & 105.869606--106.002766 & 0.987--0.985 & 0.074--0.075 & 85.18-- 86.93 & 31.71 $\pm$ 0.01 & 88.7 $\pm$ 0.1 \\ Dec 19 08:57:50--11:21:10 & 106.873495--106.973032 & 0.970--0.969 & 0.082--0.083 & 97.11-- 98.22 & 37.90 $\pm$ 0.03 & 88.6 $\pm$ 0.1 \\ Dec 20 08:37:34--10:28:23 & 107.859421--107.936377 & 0.953--0.952 & 0.093--0.094 & 106.54--107.19 & 40.76 $\pm$ 0.17 & 89.4 $\pm$ 0.1 \\ Dec 21 08:48:10--09:48:26 & 108.866782--108.908634 & 0.936--0.935 & 0.106--0.107 & 114.03--114.30 & 43.71 $\pm$ 0.44 & 88.4 $\pm$ 0.3 \\ \enddata \tablecomments{ UT date and JD are the mid-time of the start and final sequences. $r_{\rm H}$ and $\Delta$ are the heliocentric and geocentric distances in au and $\alpha$ is the solar phase angle. $P_{\rm r}$ and $\theta_{\rm r}$ are the degree of linear polarization and polarization position angle referred to the scattering plane, respectively. The uncertainty in each value of $P_{\rm r}$ and $\theta_{\rm r}$ includes both random errors (all sequences on each date and standard deviation of polarimetric standard stars during the survey) and the systematic error of PICO.} \end{deluxetable*} \subsection{Polarimetric classification and geometric albedo} To derive an inversion angle, $\alpha_{\rm inv}$ [$^\circ$] at which $P_{\rm r}$ changes its sign, and a polarimetric slope at $\alpha_{\rm inv}$, $h$ [\% deg$^{-1}$], we computed the best-fit of the phase-polarization curve at $\alpha<90^\circ$ using the trigonometrical function \citep{Lumme_Muinonen1993} by $\chi^{2}$ minimization with the Marquardt-Levenberg algorithm \citep{Press1992} (Figure \ref{fig:fig2}). This trigonometrical function is given by $P_{\rm r}(\alpha) = b\sin^{c_{1}}(\alpha) \sin^{c_{2}}(\alpha/2) \sin(\alpha - \alpha_{\rm inv})$, where $b$, $\alpha_{\rm inv}$, $c_{1}$, and $c_{2}$ are free parameters. The trigonometrical function cannot be applied mathematically to polarimetric data when a phase-polarization curve has $\alpha>110^\circ$ \citep{Ishiguro2017}, since there is no solution of $dP(\alpha)/d\alpha$ at $\alpha>110^\circ$ with $c_{2}>0$, which $c_{2}>0$ is the original definition of this function \citep{Lumme_Muinonen1993}. As a result, we applied the trigonometrical function with $c_{2}<0$ and used only limited polarimetric data at $\alpha<90^\circ$. The derived best-fit parameters are $b$ = 21.33 $\pm$ 0.44, $\alpha_{\rm inv}$ = 20$^\circ$.21 $\pm$ 0$^\circ$.07, $c_{1}$ = 0.402 $\pm$ 0.038, and $c_{2}$ = -1.57 $\pm$ 0.07, corresponding to $\alpha_{\rm inv}$ = 20$^\circ$.21 $\pm$ 0$^\circ$.07 and $h$ = 0.174\% $\pm$ 0.053\% deg$^{-1}$. The computed minimum $P_{\rm r}$, $P_{\rm min}$, and $\alpha$ at $P_{\rm min}$, $\alpha_{\rm min}$, have large errors because there are no observations of $P_{\rm r}$ at $<$19$^\circ$ in the polarimetric data set (Figure \ref{fig:fig2} and Table 1). The derived $\alpha_{\rm inv}$ is consistent with that of Phaethon alone (18$^\circ$.8 $\pm$ 1$^\circ$.6; \citealt{Devogele2018}). We note that these fitting results are not complete in the large $\alpha$ region ($\alpha >$90$^\circ$) because of the fitting function. \begin{figure*} \gridline{\fig{./fig2a_Phaethon_1funcs_lower90d_wDevogele2018_Ito2018.eps}{0.45\textwidth}{(a)} \fig{./fig2b_Phaethon_1funcs_lower90d_wDevogele2018_Ito2018_zoom2.eps}{0.45\textwidth}{(b)} } \caption{(a) The best-fit phase-polarization curve of Phaethon in the $R_{\rm C}$-band at $\alpha<90^\circ$. (b) Expanded figure near $\alpha_{\rm inv}$ to show details (green hatch of panel (a)). Axes are identical to Figure \ref{fig:fig1}. Black circles, cross, and plus symbols are the $P_{\rm r}$ of Phaethon in this work, D18 \citep{Devogele2018}, and I18 \citep{Ito2018}, respectively. The dash (orange) lines indicate best-fit phase-polarization curve by the trigonometrical function \citep{Lumme_Muinonen1993}. Note that the fitting result is not complete in the large $\alpha$ region ($\alpha>90^\circ$) because $P_{\rm r}$ at $\alpha>90^\circ$ are not used for these fittings (see Section 3.1). \label{fig:fig2}} \end{figure*} We find that Phaethon is likely to be a $B$-type asteroid as well as $M$- and $K$-type asteroids by comparing our derived $\alpha_{\rm inv}$ and $h$ to the polarimetric taxonomy (Table 3 of \citealt{Belskaya2017}). Phaethon is classified as a $B$-type asteroid by the spectral classification of asteroids \citep{Bus_Binzel2002, DeMeo2009}. We also confirmed that the phase-polarization curve of Phaethon at $\alpha <40^\circ$ shows a similar trend to those of $B$- and $F$-type main-belt asteroids (Figure 4 of \citealt{Gil-Hutton_Garcia-Migani2017}). Regarding the polarimetric taxonomy, a behavior of $P_{\rm r}$ in the high-$\alpha$ region is unknown because mainly main-belt asteroids were used, which are difficult to acquire $P_{\rm r}$ in the high-$\alpha$ region from the ground-based observatories. Moreover, the derived $\alpha_{\rm inv}$ is larger than and derived $h$ is consistent with those of Pallas ($\alpha_{\rm inv}$ = 18$^\circ$.1 $\pm$ 0$^\circ$.1 and $h$ = 0.228\% $\pm$ 0.003\% deg$^{-1}$; \citealt{Masiero2012}). \citet{Belskaya2017} claimed that asteroids with much smaller $\alpha_{\rm inv}$ have larger amount of regolith based on a relation between $P_{\rm min}$ and $\alpha_{\rm inv}$ for asteroids of variable taxonomy types overlapped with lunar bare rocks and fines reported in \citet{Geake_Dollfus1986}. Based on this relation, Phaethon should have smaller grains on its surface compared with Pallas. On the other hand, \citet{Delbo2007} pointed out that much smaller bodies have less regolith or less mature regolith. It is expected that sizes of surface materials of Phaethon are larger than those of Pallas because the diameter of Phaethon ($\sim$5 km; \citealt{Hanus2016}) is much smaller than that of Pallas ($\sim$500 km; \citealt{Carry2010}). This inconsistency implies that $\alpha_{\rm inv}$ of an asteroid reflects scattering properties of grains (e.g., complex refractive index and grain size distribution) rather than a typical size of particles or rocks on the surface. Note that the relation between $P_{\rm min}$ and $\alpha_{\rm inv}$ for asteroids may not be suitable for Phaethon because the $P_{\rm r}$ of the materials that were investigated (e.g., \citealt{Geake_Dollfus1986, Belskaya2017}) is significantly lower than that of Phaethon. We estimate the $p_{\rm v}$ independently by using the empirical slope-albedo relation in the standard $V$-filter given by $\log_{10}p_{\rm v} = C_{1}\log_{10}h + C_{2}$, where $h$ is the polarimetric slope at $\alpha_{\rm inv}$ [\% deg$^{-1}$]. $C_{1}$ and $C_{2}$ are constants ($C_{1}$ = -0.80 $\pm$ 0.04 and $C_{2}$ = -1.47 $\pm$ 0.04 when $p_{\rm v} \geq$ 0.08; \citealt{Cellino2015}). We apply this empirical relation to our polarimetric results in the $R_{\rm C}$-band because no clear difference between $P_{\rm r}$ in the $V$- and $R_{\rm C}$-bands of Phaethon have been reported \citep{Devogele2018}. The derived $p_{\rm v}$ is equal to 0.14 $\pm$ 0.04 using our derived value of $h$ (0.174\% $\pm$ 0.053\% deg$^{-1}$), corresponding to a moderate value among asteroids \citep{Masiero2018}. This value is consistent with a previous measurement of Phaethon determined from mid-infrared spectra and thermophysical modeling ($p_{\rm v}$ = 0.122 $\pm$ 0.008; \citealt{Hanus2016}), and may be high compared with typical cometary values ($\sim$0.04; \citealt{Rickman2017}) claimed in \citet{Devogele2018}. This value is also consistent with $B$-type as well as $M$- and $K$-type asteroids \citep{Belskaya2017}. $P_{\rm r}$ in the low-$\alpha$ region ($\alpha$ $<$15$^\circ$) is required to derive other polarimetric parameters (e.g., $P_{\rm min}$ and $\alpha_{\rm min}$) and classify Phaethon in the polarimetric taxonomy. To understand scattering properties of Phaethon's surface more deeply via reproducing its phase-polarization curve, we require complex refractive index as well as size distribution of dominant surface materials. To derive an absorption coefficient of the complex refractive index, measurement of a circular polarization degree is theoretically useful \citep{Hapke2012}. \citet{Mukai1987} demonstrated the importance of the negative as well as the positive branches of $P_{\rm r}$ to derive a typical complex refractive index of grain materials for comet 1P/Halley. Their result was based on the numerical calculations applying Mie theory and assuming a grain-size distribution obtained by the Vega mission \citep{Mazets1987}. We strongly encourage laboratory experiments to derive phase-polarization curves for various materials expected to exist on the surfaces of asteroids. \subsection{No confirmation of periodic change of $P_{\rm r}$} \begin{figure*} \figurenum{3} \gridline{\fig{./fig3_Phaethon_Pr_time_vari_20171209.eps}{0.49\textwidth}{(a)} \fig{./fig3_Phaethon_Pr_time_vari_20171210.eps}{0.49\textwidth}{(b)} } \gridline{\fig{./fig3_Phaethon_Pr_time_vari_20171211.eps}{0.49\textwidth}{(c)} \fig{./fig3_Phaethon_Pr_time_vari_20171212.eps}{0.49\textwidth}{(d)} } \gridline{\fig{./fig3_Phaethon_Pr_time_vari_20171213.eps}{0.49\textwidth}{(e)} \fig{./fig3_Phaethon_Pr_time_vari_20171214.eps}{0.49\textwidth}{(f)} } \gridline{\fig{./fig3_Phaethon_Pr_time_vari_20171215.eps}{0.49\textwidth}{(g)} \fig{./fig3_Phaethon_Pr_time_vari_20171216.eps}{0.49\textwidth}{(h)} } \caption{(a-m) Time-domain $P_{\rm r}$ of Phaethon from 2017 December 9 to December 21 and (n) the phase dispersion minimization plots for $P_{\rm r}$ of Phaethon from 2017 December 9 to 18. For panels (a) to (m), Black circles indicate $P_{\rm r}$ of Phaethon in each sequence in this work. The uncertainty of each plot includes both random and systematic errors described in Appendix B. The length of the upper horizontal (blue) bars indicate the rotational period of 3.604 $hr$. Orange dashed-lines in the panels of 2017 December 9-18 indicate phase-polarization fits using the trigonometrical function \citep{Lumme_Muinonen1993} in the range of $0^\circ < \alpha < 90^\circ$ (see section 3.1). The values and errors of each plot are listed in Table 3. For panel (n), vertical and horizontal axis are the dispersion of PDM, $\Theta$, and the orbital period in hours, respectively. The horizontal gray dotted-line indicates $\Theta$ = 1.0. We cannot find any best-fit period in the range from 0 up to 7.208 $hr$ (e.g., less than twice the rotational period), since there is no orbital period with small $\Theta$ lower than 1.0. \label{fig:fig3} } \end{figure*} \begin{figure*} \figurenum{3} \gridline{\fig{./fig3_Phaethon_Pr_time_vari_20171217.eps}{0.49\textwidth}{(i)} \fig{./fig3_Phaethon_Pr_time_vari_20171218.eps}{0.49\textwidth}{(j)} } \gridline{\fig{./fig3_Phaethon_Pr_time_vari_20171219.eps}{0.49\textwidth}{(k)} \fig{./fig3_Phaethon_Pr_time_vari_20171220.eps}{0.49\textwidth}{(l)} } \gridline{\fig{./fig3_Phaethon_Pr_time_vari_20171221.eps}{0.49\textwidth}{(m)} \fig{./fig3_pdm_phaethon_vari_20171209-18.eps}{0.49\textwidth}{(n)} } \caption{{\it continued.}\label{fig:fig3} } \end{figure*} \citet{Degewij1979} reported a variation in polarization degree in the $B$-band correlated with the lightcurve for (4) Vesta. The polarization variation was interpreted as albedo inhomogeneities of its surface materials \citep{Degewij1979}. Time-resolved polarimetry is an effective method to investigate albedo heterogeneity on asteroids. Panels (a)-(m) of Figure \ref{fig:fig3} show time-domain $P_{\rm r}$ of Phaethon during our polarimetric survey. We employed the phase dispersion minimization (PDM) method \citep{Stellingwerf1978} to search for periodicity in our polarimetric data, applying the 'cyclocode' software\footnote{\url{http://www.toybox.rgr.jp/mp366/lightcurve/cyclocode/cyclocode.html} developed by \citet{Dermawan2004}}. The best-fit period should have a very small normalized dispersion, $\Theta$, compared with the unphased data, and thus $\Theta \ll$1 indicates that a good fit has been found. To apply PDM fitting, we extract variable components from all $P_{\rm r}$ values until 2017 December 18 at $\alpha <90^\circ$, with the best-fit phase-polarization curve derived by the trigonometrical function (see section 3.1 and Figure \ref{fig:fig3} (a-j)). Panel (n) of Figure \ref{fig:fig3} shows a PDM plot for variable components of $P_{\rm r}$ of Phaethon from 2017 December 9 to 18. We cannot find any good fit to the period in our polarimetric data (e.g., individual or combined dates from 2017 December 9 to 18), although \citet{Borisov2018} found a variation of $P_{\rm r}$ with rotation on 2017 December 15. Note that our polarimetric data on December 15 does not cover a complete period because of weather conditions. Using the pole orientation of ($\lambda_{\rm pole}$, $\beta_{\rm pole}$) = (319$^\circ$, -39$^\circ$) with a 5$^\circ$ uncertainty \citep{Hanus2016}, a surface region as seen from the Earth crossed from edge-on (perpendicular to pole direction) to the near north-pole direction during our survey by considering the positional relation between Earth and Phaethon at the time of these observations. Before 2017 December 18, we observed the edge-on direction (e.g., a different part of the surface at the rotational phase). This result suggests that surface materials on most regions of Phaethon have similar scattering properties (e.g., $p_{\rm v}$). Focusing on Phaethon's polarimetric results in the $R_{\rm C}$-band, Figure \ref{fig:fig1} shows that our phase-polarization curve is significantly different in the high-$\alpha$ region ($\alpha > \sim 60^\circ$) with that during 2016 \citep{Ito2018}, although it is in agreement with that during 2016 in the low-$\alpha$ region \citep{Ito2018} and during 2017 December \citep{Devogele2018}. Polarimetry in 2016 \citep{Ito2018} observed only the edge-on direction (e.g., $\sim$-80$^\circ$ inclination of the north-pole direction seen from the Earth). In this case, materials causing lower polarization in the high-$\alpha$ regions by scattering are distributed near its rotational pole, and most surface regions (except for near the rotational pole region) have similar scattering properties. The difference of scattering properties on Phaethon's surface may reflect formation conditions in the early solar nebula and/or surface alternation after formation by the solar heating near perihelion. It is expected that not only determination of pole orientation but also the variation of scattering properties of materials with location on Phaethon's surface will be elucidated by detailed observations of the close flyby of Phaethon by the DESTINY$^{+}$ mission \citep{Sarli2018}. | 18 | 8 | 1808.05746 |
1808 | 1808.10545_arXiv.txt | We consider disk stability in the quasilinear formulation of MOND (QUMOND), the basis for some $N$-body integrators. We derive the generalisation of the Toomre criterion for the stability of disks to tightly wound, axisymmetric perturbations. We apply this to a family of thin exponential disks with different central surface densities. By numerically calculating their QUMOND rotation curves, we obtain the minimum radial velocity dispersion required for stability against self-gravitating collapse. MOND correctly predicts much higher rotation speeds in low surface brightness galaxies (LSBs) than does Newtonian dynamics without dark matter. Newtonian models thus require putative very massive halos, whose inert nature implies they would strongly stabilize the disk. MOND also increases the stability of galactic disks, but in contradistinction to Newtonian gravity, this extra stability is limited to a factor of 2. MOND is thus rather more conducive to the formation of bars and spiral arms. Therefore, observation of such features in LSBs could be problematic for Newtonian galaxy models. This could constitute a crucial discriminating test. We quantitatively account for these facts in QUMOND. We also compare numerical QUMOND rotation curves of thin exponential disks to those predicted by two algebraic expressions commonly used to calculate MOND rotation curves. For the choice that best approximates QUMOND, we find the circular velocities agree to within 1.5\% beyond $\approx 0.5$ disk scale lengths, regardless of the central surface density. The other expression can underestimate the rotational speed by up to 12.5\% at one scale length, though rather less so at larger radii. | \label{Introduction} MOND \citep{Milgrom_1983} is an alternative to the dark matter (DM) hypothesis in accounting for the observed dynamical discrepancies in galactic systems, especially between their measured rotation curves (RCs) and those predicted by Newtonian gravity \citep[e.g.][]{Rubin_Ford_1970, Rogstad_1972, Roberts_1975}. A discrepancy is also apparent in the `timing argument': in Newtonian gravity, the visible masses of the Galaxy and M31 are insufficient to turn their initial post-Big Bang recession around to the observed extent \citep{Kahn_Woltjer_1959}. MOND posits that these acceleration discrepancies\footnote{sometimes called mass discrepancies, though the reason for the discrepancy may not be missing mass} are not due to the presence of DM but arise from a breakdown of Newtonian dynamics that is reckoned without in analysing the dynamics of these systems. MOND is extensively reviewed in \citet{Famaey_McGaugh_2012} and \citet{Milgrom_2014}. The M31 timing argument in MOND was discussed by \citet{Zhao_2013} and detailed calculations were presented in section 2 of \citet{Banik_Ryan_2018}. MOND introduces $\azero$ as a fundamental acceleration scale of nature. When the gravitational field strength $g \gg \azero$, standard dynamics is restored. However, when $g \ll \azero$, the dynamical equations become scale-invariant \citep{Milgrom_2009_DML}. In this deep-MOND regime, an inevitable consequence of scale invariance is that, asymptotically far outside a distribution of total mass $M$, the rotational speed of a test particle becomes independent of its distance $R$ from the mass. This occurs when $R \gg r_{_M}\equiv \sqrt{GM/\azero}$, where $r_{_M}$ is the MOND radius of the mass $M$. Therefore, in a modified gravity formulation of MOND, $g\propto R^{-1}$ beyond the MOND radius. Applying dimensional arguments to the fact that $\azero$ is the only additional constant in MOND, we must have that \begin{eqnarray} g ~ \propto ~ \frac{\sqrt{GM\azero}}{R} ~~~\text{for } ~ R ~\gg ~ r_{_M}\equiv \sqrt{\frac{GM}{\azero}} \, . \label{Deep_MOND_limit} \end{eqnarray} The normalisation of $\azero$ is taken so that the proportionality here becomes an equality. Empirically, $\azero \approx 1.2 \times {10}^{-10}$ m/s$^2$ to match galaxy RCs \citep[e.g.][]{McGaugh_2011, Li_2018}. It was noticed early on \citep[e.g.][]{Milgrom_1983, Milgrom_1999} that, remarkably, this value is similar to accelerations of cosmological significance. For example, \begin{eqnarray} 2 \mathrm{\pi} \azero ~\approx ~ a_{_H} \left( 0 \right) ~\equiv ~ c H_0 ~\approx ~ a_{_\Lambda} ~\equiv ~ \frac{c^2}{\ell_\Lambda} \, \end{eqnarray} where $H_0$ is the present-day value of the Hubble constant and $\ell_\Lambda = \left( \Lambda/3 \right)^{-1/2}$ is the de Sitter radius corresponding to the observed value of the cosmological constant $\Lambda$ \citep{Riess_1998, Perlmutter_1999}. Stated another way, $\azero$ is similar to the acceleration at which the classical energy density in a gravitational field \citep[][equation 9]{Peters_1981} becomes comparable to the dark energy density $u_{_\Lambda} \equiv \rho_{_\Lambda} c^2$ implied by $\Lambda$. \begin{eqnarray} \frac{g^2}{8\mathrm{\pi}G} ~<~ u_{_\Lambda} ~~\Leftrightarrow~~ g ~\la~ 2\mathrm{\pi}a_{_0} \, . \label{MOND_quantum_link} \end{eqnarray} This association of local MOND with cosmology suggests that MOND may arise from quantum gravity effects \citep[e.g.][]{Milgrom_1999, Pazy_2013, Verlinde_2016, Smolin_2017}. Regardless of its underlying microphysical explanation, MOND correctly predicted the RCs of a wide variety of both spiral and elliptical galaxies across a vast range in mass, surface brightness and gas fraction \citep[e.g.][]{Milgrom_1988, Begeman_1991, Sanders_1996, Sanders_1998, Sanders_2007, Lelli_2017, Li_2018}. Although internal accelerations are harder to measure within ellipticals, this can sometimes be done accurately when they have a surrounding $X$-ray emitting gas envelope in hydrostatic equilibrium \citep{Milgrom_2012} or a thin rotation-supported gas disk \citep[e.g.][]{Serra_2012, Heijer_2015, Serra_2016}. The success of MOND extends down to pressure-supported galaxies as faint as the satellites of M31 \citep{McGaugh_2013} and the Milky Way, though in the latter case one must be careful to exclude galaxies where MOND predicts significant tidal distortion \citep{McGaugh_2010}. For a recent overview of how well MOND works in several different types of galaxy across the Hubble sequence, we refer the reader to \citet{Lelli_2017}. It is worth emphasising that MOND does all this based solely on the distribution of luminous matter. It is clear that these achievements are successful a priori predictions because most of these RCs $-$ and sometimes even the baryon distributions $-$ were measured in the decades after the first MOND field equation was put forth \citep{Bekenstein_Milgrom_1984} and its new fundamental constant $\azero$ was determined \citep{Milgrom_1988, Begeman_1991}. These predictions work due to underlying regularities in galaxy RCs that are difficult to reconcile with the collisionless DM halos of the $\Lambda$CDM paradigm \citep[e.g.][]{Salucci_2017, Desmond_2016, Desmond_2017}. These halos were originally introduced to boost the RCs of disk galaxies. If real, they would also endow their embedded disks with added stability because the halo contribution to the gravitational field responds very little to density perturbations in the disk, making the disk more like a set of test particles. This fact forms the basis of another argument originally adduced for the presence of DM halos around disk galaxies \citep{Ostriker_Peebles_1973} $-$ without such halos, observed galactic disks would be deleteriously unstable \citep{Hohl_1971}. A crucial prediction of MOND was that low surface brightness galaxies (LSBs) would show large acceleration discrepancies at all radii because $g\ll\azero$ everywhere in the galaxy \citep{Milgrom_1983, Milgrom_1983_b}. This prediction was thoroughly vindicated by later observations \citep[e.g.][]{Blok_1997, McGaugh_1998}. In $\Lambda$CDM, such LSBs must be assigned a halo much more massive than the disk. Such a halo would cause the disk to become very stable, stymieing the formation of bars and spiral arms which are believed to result from disk instabilities \citep{Lin_1964}. Since MOND posits that dark halos are absent, the question arises regarding the degree of stability of disks, especially LSB disks in which MOND is predicted to have significant effects. This issue was discussed in some detail by \citet{Milgrom_1989}, who showed that MOND generally does add to the stability of low-acceleration disks with a given mass distribution and velocity dispersion. The reason is that instead of the Newtonian relation $g_d\propto \rho$ between mass density $\rho$ and the acceleration $g_d$ it produces in the disk, the deep-MOND relation is $g_d \propto \sqrt{\rho}$. This means that in Newtonian disks without a DM halo, density perturbations $\delta \rho$ produce acceleration perturbations \begin{eqnarray} \frac{\delta g_d}{g_d} ~\sim ~ \frac{\delta\rho}{\rho} \, . \label{Delta_Ln_g} \end{eqnarray} Adding a non-responsive DM halo with contribution $g_h$, we can write $g_d = g_b+g_h$, where $g_b$ is the Newtonian contribution of the baryonic disk that satisfies Equation \ref{Delta_Ln_g}. Because density perturbations in the disk do not affect $g_h$, we have that \begin{eqnarray} \frac{\delta g_d}{g_d} ~\sim ~ \frac{\delta \rho}{\rho} \left( 1 + \frac{g_h}{g_b} \right)^{-1}. \end{eqnarray} The reduced response of $g_d$ implies increased disk stability. The analogous result in the deep-MOND regime is \begin{eqnarray} \frac{\delta g_d}{g_d} ~\sim ~ \frac{1}{2} \frac{\delta \rho}{\rho} \end{eqnarray} because $g_d \propto \sqrt{\rho}$ and $g_h = 0$. The added degree of stability in deep MOND is thus similar to that endowed by a halo with $g_h \sim g_b$. As MOND effects are strongest in this regime, it is clear that this is the limit to how much MOND enhances the stability of disk galaxies, even those with very low surface densities. However, the massive halos required by $\Lambda$CDM would increase the stability indefinitely as the surface density is reduced. This makes deep-MOND LSBs develop spiral arms and fast-rotating bars more readily than according to $\Lambda$CDM \citep{Tiret_2007, Tiret_2008, Tiret_2016}. Beyond such general semi-qualitative arguments, it is important to study disk stability more quantitatively in specific, action-based MOND theories. This not only gives a more accurate picture, it is also necessary for understanding and avoiding the development of instabilities in numerical codes based on these theories. \citet{Milgrom_1989} studied disk stability analytically in the context of the aquadratic Lagrangian formulation of MOND \citep[AQUAL,][]{Bekenstein_Milgrom_1984}. This was followed by the numerical studies of \citet{Brada_1999}, who solved the AQUAL field equation using an expensive non-linear grid relaxation stage. This is unavoidable in the context of AQUAL and remains an aspect of more recent codes that solve it \citep{Londrillo_2006, Candlish_2015}. Since that time, another non-relativistic, action-based MOND theory has been put forth. This quasilinear formulation of MOND \citep[QUMOND,][]{QUMOND} is much more amenable to numerical simulations because the grid relaxation stage is linear, like in Newtonian gravity. Despite using different field equations to implement MOND consistently, QUMOND and AQUAL give rather similar results, as demonstrated both numerically \citep{Candlish_2016} and analytically \citep{Banik_2015}. QUMOND can be solved numerically using the publicly available $N$-body and hydrodynamics code Phantom of RAMSES \citep{PoR}, an adaptation of the grid-based RAMSES algorithm widely used by astronomers due to its adaptive mesh refinement feature \citep{Teyssier_2002}.\footnote{The similar code RAyMOND can also handle AQUAL \citep{Candlish_2015}. It will eventually be made public.} As a result, QUMOND has become the main workhorse for simulations of galaxy evolution and interactions \citep{Thies_2016, Renaud_2016, Thomas_2017, Thomas_2018, Bilek_2018}. The question of disk stability in QUMOND remains to be addressed analytically despite its importance for understanding the results of such simulations and for establishing their initial conditions. Here, we study some aspects of disk stability in QUMOND. We focus on deriving an analytic expression for the QUMOND generalisation of the Toomre criterion \citep{Toomre_1964}. This gives an estimate of whether part of a disk is vulnerable to self-gravitating collapse. In particular, the Toomre criterion gives a lower limit to the radial velocity dispersion in a thin disk for it to remain stable against short-wavelength axisymmetric perturbations. After outlining the broader context in Section \ref{Introduction}, we explain the steps in our analytic derivation (Section \ref{Section_QUMOND}). Our main result is a generalisation of the Toomre condition to QUMOND (Equation \ref{Min_Q_star_QUMOND}). In Section \ref{Numerical_results}, we apply this to numerically determined RCs of a family of thin exponential disks with different central surface density. Observational constraints on disk stability are discussed in Section \ref{Observations}. We conclude in Section \ref{Conclusions}. | \label{Conclusions} We have generalised the Toomre disk stability condition \citep{Toomre_1964} to the quasilinear formulation of Modified Newtonian Dynamics \citep[QUMOND,][]{QUMOND}. Our main result is Equation \ref{Min_Q_star_QUMOND}. We use this to estimate the minimum radial velocity dispersion $\sigma_r$ required by thin exponential disk galaxies to avoid local self-gravitating collapse. In Newtonian gravity, all such galaxies are identical up to scaling. This is no longer true in MOND as it depends non-linearly on the typical acceleration, which is fully determined by the central surface density. Thus, we set up a one-parameter family of exponential disks and numerically determine their rotation curves (Figure \ref{MOND_rotation_curves}) and minimum $\sigma_r$ profiles (Figure \ref{Min_sigma_r}). We also consider the stability of the analogous galaxies in $\Lambda$CDM, which we assume have a DM halo that causes their RC to match QUMOND predictions based on the baryons alone. Throughout this work, we make use of the WKB approximation, namely that perturbations are much smaller than the galactocentric radius. In Section \ref{Section_WKB}, we test the validity of this approximation. Our results show that it works quite well beyond the central ${\approx 2 r_{_d}}$ of MOND exponential disks. It is expected to work particularly well for LSB disks in $\Lambda$CDM, where the WKB approximation should be very accurate almost everywhere (bottom panel of Figure \ref{L_crit}). The very central regions of galaxies may also be affected by non-axisymmetric instabilities such as bars \citep[e.g.][]{Sellwood_1981}. Moreover, our results pertain only to thin disks and thus cannot be applied to pressure-supported galaxies or regions thereof. In the real Universe, even disk galaxies often have a centrally concentrated bulge. We expect that our analysis applies without modification to the regions outside the bulge, once the RC is calculated appropriately and used to determine $\Omega_r$ in Equation \ref{Min_sigma_r_QUMOND}. The bulge would provide an additional source of stability in the regions outside it by enhancing the RC\footnote{and thus $\Omega_r$} but not the disk surface density. In this sense, a bulge would have a somewhat similar effect to a DM halo, though an important difference is that bulges are often directly observed while DM halos remain speculative \citep{Liu_2017}. Our analytic results provide a stability criterion but shed no light on how exactly instability would develop and whether it could be saturated by non-linear effects. Such questions need to be addressed with numerical simulations. These indicate that rotationally supported self-gravitating disks are unstable in Newtonian gravity \citep{Hohl_1971}. They are generally thought to be stabilised by a massive surrounding DM halo \citep{Ostriker_Peebles_1973}. In principle, this halo can grant an unlimited amount of stability to the disk depending on their relative masses. The situation is very different in MOND, where the modification to gravity can only endow disks with a limited amount of extra stability. This remains true for galaxies with arbitrarily low surface density, even though MOND has a very large effect on the dynamics of such systems. Equation \ref{Perturbation_g_QUMOND} gives a rough understanding of why this is the case. Our numerical calculations allow us to check the closeness of the action-based QUMOND to the often-used algebraic MOND expression $\vg = \nu \vgN$ (Section \ref{Section_ALM}). Our results indicate that beyond the central ${0.5 \, r_d}$, the radial force in the disk mid-plane differs by ${< 3\%}$, even if the galaxy has a very low surface density. However, this is only true if $\nu$ in the ALM expression (Equation \ref{Algebraic_MOND_approximation}) is based on both the radial and vertical components of $\vgN$, with the latter assumed to be $2 \pi G \Sigma$ as appropriate for a point just outside the disk. If this component of $\vgN$ is neglected, then similarly good agreement between the ALM and QUMOND is only attained beyond $\approx 2.5 \, r_d$ (Figure \ref{ALM_error_wrong}). Nonetheless, this form of the ALM (Equation \ref{MDAR}) is correct in some modified inertia interpretations of MOND \citep{Milgrom_1994, Milgrom_2011}. This may provide a way to distinguish whether MOND is best understood as a modification of gravity or of inertia. A recent analysis favoured the former \citep{Frandsen_2018}. Our analytic disk stability condition for QUMOND (Equation \ref{Min_sigma_r_QUMOND}) should prove useful when setting up stable disk galaxies in the efficient $N$-body codes Phantom of RAMSES \citep{PoR} and RAyMOND \citep{Candlish_2015} that implement this theory. We are currently attempting to use the former to simulate a past flyby interaction between the Milky Way and Andromeda galaxies, thus extending our work in \citet{Banik_Ryan_2018} by performing $N$-body simulations similar to those of \citet{Bilek_2018}. We hope to clarify if this flyby scenario can form structures similar to those observed in the Local Group. | 18 | 8 | 1808.10545 |
1808 | 1808.05706.txt | {We investigate the production of neutralino dark matter in a cosmological scenario featuring an early matter dominated era ending at a relatively low reheating temperature. In such scenarios different production mechanisms of weakly interacting massive particles (WIMPs), besides the well--studied thermal production, can be important. This opens up new regions of parameter space where the lightest neutralino, as the best--known supersymmetric (SUSY) WIMP, obtains the required relic abundance. Many of these new sets of parameters are also compatible with current limits from colliders as well as direct and indirect WIMP searches. In particular, in standard cosmology bino--like neutralinos, which emerge naturally as lightest neutralino in many models, can have the desired relic density only in some finetuned regions of parameter space where the effective annihilation cross section is enhanced by co--annihilation or an $s-$channel pole. In contrast, if the energy density of the universe was dominated by long--lived PeV--scale particles (e.g. moduli or Polonyi fields), bino--like neutralinos can obtain the required relic density over wide regions of supersymmetric parameter space. We identify the interesting ranges of mass and decay properties of the heavy long--lived particles, carefully treating the evolution of the temperature of the thermal background.} \begin{document} \def\gsim{\:\raisebox{-0.5ex}{$\stackrel{\textstyle>}{\sim}$}\:} \def\lsim{\:\raisebox{-0.5ex}{$\stackrel{\textstyle<}{\sim}$}\:} | \label{intro} The lightest neutralino as lightest supersymmetric particle (LSP) is one of the oldest and most studied examples of a weakly interacting massive particle (WIMP) candidate for the cosmological Dark Matter (DM); see e.g. \cite{Ellis:1983ew} for an early exploration of parameter space, and \cite{Jungman:1995df,Roszkowski:2017nbc} for reviews. The minimal supersymmetric extension of the Standard Model (MSSM) contains four neutralino current eigenstates: a bino, a wino, and two higgsinos. Given current collider constraints on superparticles, in particular on the masses of charginos and the heavier neutralinos, we now know that over most of parameter space, the mass eigenstates are relatively pure states, with little mixing. Most analyses of WIMP DM worked in the framework of standard cosmology, where the Universe was radiation--dominated starting at the end of inflation and ending at a temperature around $1$ eV. Moreover, it is usually assumed that the post--inflationary reheat temperature was sufficiently high that WIMPs attained full thermal (chemical and kinetic) equilibrium. The WIMP relic density is then basically inversely proportional to its (effective) annihilation cross section \cite{Kolb:1990vq, Gondolo:1990dk}. In that case higgsino--like WIMPs typically need to have a mass near $1$ TeV to have the correct relic density, and a wino--like WIMP should be at least two times heavier. While it has recently been pointed out that these values might be lowered by $30\%$ or so due to co--annihilation effects \cite{Chakraborti:2017dpu}, the required values are still uncomfortably high when compared to estimates of weak--scale finetuning in the MSSM. In particular, while bounds on the masses of scalar tops and gluinos based on simple loop calculations \cite{Papucci:2011wy} are somewhat controversial \cite{Feng:1999mn,Kitano:2006gv,Baer:2014ica}, it is generally agreed that higgsino, and hence LSP, masses above several hundred GeV would lead to percent level (or worse) finetuning; note that in the MSSM the higgsino mass enters the relevant finetuning condition already at tree--level.\footnote{This argument can be evaded \cite{Ross:2016pml} if there is a soft supersymmetry breaking contribution to the higgsino mass; this would not contribute to the Higgs boson masses which in turn determine finetuning. While this is technically possible, it would require a rather complicated supersymmetry breaking scenario.} In standard cosmology, higgsino-- or wino--like WIMPs with masses in the few hundred GeV range would have too small a relic density. In contrast, a bino--like WIMP has too large a relic density in such a scenario, unless its effective annihilation cross section is boosted by co--annihilation \cite{Griest:1990kh, Ellis:1998kh, Boehm:1999bj} or by an $s-$channel pole \cite{Griest:1990kh, Drees:1992am}. A predicted underdensity of WIMP DM can be cured by adding another DM component, e.g. axions \cite{Tegmark:2005dy,Baer:2011hx,Baer:2014eja}; this can be done within the framework of minimal cosmology, and without changing TeV--scale particle physics. On the other hand, a scenario that predicts too large a relic density for a given DM candidate is clearly excluded. This argument thus disfavors bino--like WIMPs, at least within minimal cosmology. At the same time bino--like WIMPs quite easily satisfy the increasingly stringent constraints from direct WIMP searches \cite{pdg,Aprile:2018dbl}; these searches exclude many scenarios where the WIMP is higgsino--like, if the latter contributes most or all of DM. Moreover, indirect searches \cite{pdg,Ahnen:2016qkx} now exclude models where most or all of DM consists of wino--like (higgsino--like) WIMPs with mass below $\sim 0.8$ $(\sim 0.4)$ TeV, but hardly constrain the parameter space if the LSP is bino--like. These null results therefore favor bino--like WIMPs. At the same time bino--like neutralinos often emerge as LSP in simple models where the superparticle spectrum can be described by a small number of free parameters. In particular, if gaugino masses unify at or near the same scale where the gauge couplings meet in the MSSM, the weak--scale bino mass will be about half of the wino mass. Moreover, if stop squarks and Higgs bosons have similar soft breaking masses at this very high energy scale, the weak--scale higgsino mass parameter typically comes out larger than the bino mass. These arguments motivate us to investigate a non--minimal cosmological scenario, in the hope of finding an extended region of parameter space where a bino--like WIMP obtains the required relic density. In particular, we analyse scenarios featuring an early matter--dominated epoch sometime between the end of inflation and Big Bang nucleosynthesis (BBN). This is quite well motivated, since UV--complete theories like supergravity \cite{Polonyi:1977pj} and superstring theory often contain heavy but long--lived scalar particles, nowadays usually called moduli. They are long--lived since their couplings to MSSM fields are suppressed by the inverse of the Planck mass. Nevertheless they can attain large densities if their mass is below the Hubble parameter during inflation \cite{Vilenkin:1982wt,Linde:1982uu,Starobinsky:1982ee, Goncharov:1984qm,Dine:1995uk}. The success of standard BBN implies that the moduli--dominated epoch should end at a final reheat temperature of at least $4$ MeV \cite{Polnarev:1982,Coughlan:1983ci, Kawasaki:2000en,Hannestad:2004px, deSalas:2015glj}. It has been pointed out more than ten years ago that the WIMP relic density in this scenario can be either smaller or larger than in standard cosmology \cite{Gelmini:2006pq,Gelmini:2006pw}. On the one hand, since the moduli decay out of equilibrium, they increase the entropy density of the universe, thereby diluting a pre--existing WIMP density. At the same time new WIMP production mechanisms become possible, including direct moduli to WIMP decays. In addition to the effective WIMP annihilation cross section and mass, the final WIMP relic density now also depends on the mass and lifetime of the modulus as well as on the effective branching ratio for modulus to WIMP decays. The impact of an early matter dominated epoch on WIMP DM has been studied before \cite{Chung:1998rq, Moroi:1999zb, Giudice:2000ex, Pallis:2004yy, Gelmini:2006pq, Gelmini:2006pw, Acharya:2009zt, Arcadi:2011ev, Kane:2015qea,Hamdan:2017psw,Bernal:2018kcw}; specifically supersymmetric WIMPs were considered in this context in \cite{Easther:2013nga,Allahverdi:2013noa, Roszkowski:2014lga, Aparicio:2015sda, Aparicio:2016qqb}. However, as we pointed out recently \cite{Drees:2017iod}, an accurate treatment of the radiation component during the decay of the moduli is very important: even though the entropy is no longer conserved in this scenario, one still has to normalize the WIMP number density to the known radiation density, which is related to the entropy density %normalize the WIMP number density to the %entropy density ; any inaccuracies in the calculation of the latter therefore immediately affect the final prediction of the WIMP relic density. Note also that the temperature of the thermal background during modulus domination can vary over several orders of magnitude. An accurate treatment of the temperature dependence of the effective number of degrees of freedom therefore becomes mandatory if one aims for precise predictions. Here we use the treatment of ref.\cite{Drees:2015exa}, which in turn is based on lattice QCD analyses of the equation of state, which determines the relation between temperature and entropy and energy density in QCD. Moreover, we use the latest results from direct and indirect WIMP searches to further constrain the allowed parameter space. We find that large regions of parameter space with good bino--like WIMP indeed survive, if moduli are not too heavy and have a sufficiently small branching ratio for decays into WIMPs. The remainder of this article is organized as follows. In Sec.~\ref{sec:friedmann-boltzmann} we discuss the set of equations we need to solve in order to compute the WIMP relic density. Then Sec.~\ref{sec:neutralino-thermal} briefly reviews neutralino DM in standard cosmology, including a discussion of current experimental constraints. In Sec.~\ref{sec:neutralino-nonthermal} we return to moduli cosmology, delineating regions in parameter space where various WIMP production mechanisms are important. We then present numerical results from a random scan over the MSSM parameter space. Finally, we summarize our results in Sec. \ref{sec:conclusion}. | \label{sec:conclusion} In this paper we investigated supersymmetric neutralino dark matter in the framework of a non--standard cosmological scenario with an early matter dominated epoch. Building on our earlier work \cite{Drees:2017iod}, which improved the accuracy of the solution of the relevant Boltzmann equations through a careful treatment of the thermal medium, we looked for regions of parameter space where relatively light neutralinos can form all of dark matter; our focus on neutralinos with mass at or below 500 GeV is motivated by naturalness arguments. After setting up the basic framework, in Sec.~3 we reviewed neutralino DM within standard cosmology. In agreement with many earlier studies, we found that a bino--like neutralino typically has too high a relic density, whereas higgsino-- or wino--like neutralinos can obtain the desired relic density only for masses well above the ``natural'' range. Moreover, under the assumption that neutralinos form all of DM, indirect searches exclude wino--like DM for masses below about $0.8$ TeV, which is already well above our naturalness cut--off. For higgsino--like neutralinos the corresponding bound is around 400 GeV, leaving some range of masses where higgsino DM could be (barely) natural if it could get the required relic density. In contrast, if the lightest neutralino is bino--like neither direct nor indirect DM searches are very constraining \footnote{As pointed out in \cite{Erickcek:2015jza} and \cite{Erickcek:2015bda}, indirect bino signals can be boosted if the kinetic decoupling temperature $T_{\rm kd}$ is well above $T_{\rm RH}$. This is because the period of early matter domination will lead to an enhanced growth of structure at very small length scales \cite{Fan:2014zua}. These "microhalos" will be destroyed by free streaming of DM particles if $T_{\rm kd} \lsim T_{\rm RH}$. In case of WIMPs, $T_{\rm kd} \gg T_{\rm RH} > 4$ MeV requires sfermion masses of tens of TeV, well above the range probed in our scan.}. In Sec.~4 we therefore set out to find regions of parameter space where a light bino, or a higgsino with mass near $400$ GeV, can obtain the required relic density. The main new parameters, in addition to those already present in standard cosmology, are the mass $M_\phi$ of the heavy particle $\phi$ that accounts for the early matter--dominated epoch, and its branching ratio $B_\chi$ into the DM candidate. We found three distinct regions, described by eqs.(\ref{range_1}), (\ref{range_2}) and (\ref{range_3}); this is the main result of the present paper. In particular, for relatively small $M_\phi$, below $10^6$ GeV, neutralino annihilation is negligible, and a simple relation for the required $B_\chi$ as a function of $M_\phi$ and $M_\chi$ results, see eq.(\ref{range_1}); this works for both bino-- and higgsino--like states. For higgsino--like neutralinos, annihilation becomes important for $M_\phi > 10^6$ GeV, leading to a second range where $\phi \rightarrow \tilde H$ decays followed by $\tilde H$ annihilation produces the desired relic density; this is still a purely non--thermal mechanism. Finally, for $M_\phi \gsim 5 \cdot 10^6$ GeV a third region opens up, where bino--like neutralinos obtain the desired relic density due to thermal freeze--out during the early matter dominated epoch, see eq.(\ref{range_3}). In this analysis we treated $M_\phi$ and $B_\chi$ as completely free parameters, and assumed that the $\phi$ decay width scales like $M_\phi^3 / M_{\rm Pl}^2$. In particular, in agreement with more general results found in ref.\cite{Drees:2017iod}, we found that bino--like neutralinos can only have the desired relic density even in this non--minimal cosmological scenario if $B_\chi \lsim 10^{-4}$. It would be important to find concrete models possessing a $\phi$ particle with the desired properties. In particular, the upper bound on $B_\chi$ may not be easy to satisfy once higher--order decays into three-- or even four--body final states have been included. We leave this investigation to future work. | 18 | 8 | 1808.05706 |
1808 | 1808.10635_arXiv.txt | The physical processes or trigger mechanisms that lead to the eruption of coronal mass ejections (CMEs), the largest eruptive phenomenon in the heliosphere, are still undetermined. Low-altitude magnetic reconnection associated with flux cancellation appears to play an important role in CME occurrence as it can form an eruptive configuration and reduce the magnetic flux that contributes to the overlying, stabilising field. We conduct the first comprehensive study of 20 small bipolar active regions in order to probe the role of flux cancellation as an eruption trigger mechanism. We categorise eruptions from the bipolar regions into three types related to location and find that the type of eruption produced depends on the evolutionary stage of the active region. In addition we find that active regions that form eruptive structures by flux cancellation (low-altitude reconnection) had, on average, lower flux cancellation rates than the active region sample as a whole. Therefore, while flux cancellation plays a key role, by itself it is insufficient for the production of an eruption. The results support that although flux cancellation in a sheared arcade may be able to build an eruptive configuration, a successful eruption depends upon the removal of sufficient overlying and stabilising field. Convergence of the bipole polarities also appears to be present in regions that produce an eruption. These findings have important implications for understanding the physical processes that occur on our Sun in relation to CMEs and for space weather forecasting. | Coronal mass ejections (CMEs) are the most energetic phemonena in the Solar System, involving around $10^{32}$ ergs of energy in the form of electromagnetic, kinetic, thermal, non-thermal and gravitational potential energy. The energy is ultimately derived from the coronal magnetic field, where it is stored in the form of electric currents \citep{Forbes-2000}. However, the exact evolution of the coronal magnetic field, and the physical processes involved in CMEs, are still subjects of study. CMEs are also of interest because they can drive intense geomagnetic storms \citep{Gosling-1993}. These storms are able to create hazardous space weather conditions at Earth, leading to disruptions of our technological systems, and significant socioeconomic impact \citep[for a review see][]{Eastwood-2017}. Understanding the conditions in which CMEs are created is therefore of importance for a physical understanding of our Sun, as well as for space weather forecasting. The occurrence of CMEs involves an energy storage-and-release process and their formation is often discussed as having two phases; a trigger and a driver. The trigger refers to the physical process(es) that brings the magnetic field to the point of an eruption, whereas the driver is responsible for the sudden expansion and upward acceleration of the erupting volume. The driving mechanism appears to be limited to either magnetic reconnection taking place in a vertical current sheet below the eruptive structure \citep{Moore-2001} or the Lorentz force acting on a flux rope \citep{Forbes-1991,Torok-2005,Kliem-2006,Mackay-2006a,Mackay-2006b,Kliem-2014}. Possible trigger mechanisms, however, appear to be wide-ranging and include, for example, sunspot rotation, flux emergence and photospheric flows. See \cite{Green-2017} for an overview of CME trigger and driver processes. Our efforts to understand (and forecast) CMEs are severely impeded by a lack of knowledge of the relative importance of these trigger mechanisms. In this study we focus on another particular CME trigger known as flux cancellation. In the flux cancellation process small-scale opposite polarity magnetic fragments are seen to converge, collide and disappear along the polarity inversion line (PIL) that separates regions of positive and negative field in the photosphere \citep{Martin-1985}. The disappearance of the two opposite polarity fragments is ultimately the consequence of the fragmentation and dispersion of the magnetic field caused by convective flows and differential rotation. Three scenarios have been proposed to explain the process of flux cancellation (see \cite{Zwaan-1987}): the emergence of a U-loop \citep{vDG-2000,Bernasconi-2002}, the submergence of an $\Omega$-loop below the surface \citep{Harvey-1999,Chae-2004,Yang-2009}, or the result of magnetic reconnection taking place at a low height \citep{vB-1989}. We investigate the third case where flux cancellation due to low-altitude magnetic reconnection is able to gradually transform a sheared arcade field into a flux rope. In this scenario, magnetic reconnection produces two loops: 1) a small loop with a high curvature, which submerges below the photosphere leading to the disappearance of the small bipole; 2) a loop much larger in size-scale that extends into the corona. Ongoing flux cancellation can therefore form a flux rope that is expected to have its underside located in the high plasma-$\beta$ environment of the lower solar atmosphere. During the flux cancellation process an amount of flux equal to that which is cancelled is available to be built into the flux rope. The actual amount of flux that is built into a flux rope depends on the properties of the region, such as the amount of shear and the length of the PIL along which flux cancellation is occurring. The details of this process are discussed in \cite{Green-2011}. The flux cancellation process also has a secondary effect in that it reduces the flux in the region that contributes to the field overlying, and stabilising, the flux rope. If enough flux is transformed from the overlying arcade into the flux rope, a force imbalance can occur leading to a catastrophic loss of equilibrium and a CME \citep{Lin-2000, Bobra-2008}. Or, if the active region evolves to a point where the overlying field decreases rapidly enough with height, the flux rope can become torus unstable \citep{Kliem-2006}. In this way, flux cancellation can be viewed as a CME trigger mechanism, which in itself requires a converging flow, in a sheared field, to bring opposite polarity fragments together. Such a scenario for flux rope formation and eruption due to flux cancellation is well supported by simulations \citep{Amari-2003, Aulanier-2010} and observations \citep{Green-2011, Yardley-2016}. Here we present the first comprehensive study of the eruptive activity in a representative sample of 20 small bipolar active regions (ARs) in order to probe the role of flux cancellation as a CME trigger. We study the evolution of the photospheric magnetic field to quantify the significance of flux cancellation in building an eruptive magnetic field environment. We investigate at what point in an active region's lifetime eruptions occur. | In this study, we investigate the role of flux cancellation as an eruption trigger in a survey of 20 isolated and small bipolar active regions. Nineteen active regions exhibit flux cancellation, the amount of which was quantified from the reduction in the total unsigned magnetic flux with time. This approach is based on the assumption that flux cancellation is the only process by which active region flux is removed from the photosphere on the timescale of a few days. Other mechanisms of removing flux from an active region include the fragmentation and advection of fragments across larger and larger areas by plasma flows. However, these flux fragments are captured in our method of flux measurement. In addition, Ohmic diffusion will cause flux to diffuse through the photosphere, due to the finite electrical resistance of the plasma. This diffusion process occurs on a timescale $t_{D}$, which is given by $t_{D}=L^{2}/\eta$, where L is the length-scale and $\eta$ is the magnetic diffusivity. However, for a sunspot of length-scale 3000~km and using a value of Ohmic diffusion of $\eta=300~$m$^{2}$~s$^{-1}$ gives a large diffusion timescale of the order 1000 years. By definition, flux cancellation as determined by our method can only be calculated during an active region's decay phase, when no new significant flux is emerging into the region and the overall flux value is reducing. We also take into account that even though HMI produces high-quality data products, there are uncertainties and systematic errors present in the line-of-sight magnetic flux measurements. The selection criteria imposed when choosing active regions suitable for the study included that the regions had to emerge between $\pm$60$^{\circ}$. This was to avoid the appearance of symmetric peaks, centred around $\sim$60$^{\circ}$ with respect to central meridian due to the sensitivity of the HMI instrument being dependent upon longitude \citep{Hoeksema-2014, Couvidat-2016}. The increase in flux is caused by the increase in value by a few tens of percent of low to moderate flux densities between 250 and 750~G. However, this effect is still present before the active region reaches 60$^{\circ}$. A recent study by \cite{Falconer-2016} has used a sample of 272 large active regions to reduce the net projection error in parameters measured from deprojected {\it SDO}/HMI vector magnetograms. They remove the average projection error in an active region's total magnetic flux by assuming that the centre-to-limb curve of the average of the absolute values of magnetic flux of a large number of active regions, which is normalised to the value at central meridian for each AR, gives the average fractional projection error at each radial distance from disk centre. In this study we have not followed the method of \cite{Falconer-2016} as we have only analysed flux cancellation that occurs between $\sim \pm$45$^{\circ}$. There are also sinusoidal oscillations with periods of 12 and 24 hours in the evolution of total magnetic flux. This time-varying systematic error is mainly caused by the geosynchronous orbit of the {\textit SDO} spacecraft \citep{Hoeksema-2014}. Since we have selected isolated active regions and studied the flux cancellation that occurred during their decay phase, we are able to probe the characteristics of the active regions that produced eruptions from a low-altitude along their internal PILs and those that did not. Here we single out four active regions that produce internal PIL eruptions (ARs 11437, 11561, 11680 and 12382) and five active regions that produce only high-altitude eruptions (ARs 11446, 11808, 11881, 11886) and analyse their decay phase. In Section~\ref{sec:canc_res} we described that both groups have roughly the same amount of total flux cancelled although the active regions that produce high-altitude eruptions have, on average, a higher flux cancellation rate. These two groups of active region have a similar photospheric field evolution but markedly different outcomes in the evolution of the coronal field. These results lead to two questions. Why do active regions with a higher flux cancellation rate during their decay phase produce no eruptions from their internal PILs as the \cite{vB-1989} flux rope model might suggest? What are the distinguishing features between these two groups of active regions? These questions can be addressed by considering the ratio of cancelled flux that is available to be built into the flux rope, versus the remaining flux in the overlying arcade. When more active region flux is cancelled and built into a flux rope, there is less overlying field remaining in the active region to stabilise the structure. Previous observational flux cancellation studies have found a ratio of flux contained in the rope compared to the flux remaining in the overlying arcade of 1:0.65 \citep{Green-2011} and 1:0.9 \citep{Yardley-2016}. Whereas, studies from a modelling perspective have yielded values between 1:1.5 and 1:1.9 \citep{Bobra-2008, Savcheva-2009, Savcheva-2012}. In this case we found that the ratio of flux cancelled (i.e. the flux available to be built into the rope) compared to that in the overlying field at the time of the internal PIL event is: 1:1.29, 1:1.57, 1:0.03, 1:0.32 for ARs 11437, 11561, 11680 and 12382, respectively. We note that whilst for ARs 11437 and 11561 the ratio is very similar to previous results, for active regions 11680 and 12382 the flux contained in the overlying arcade is very small. This suggests that the assumption that flux cancellation injects an equal amount of flux into the rope as that cancelled may not fully apply here. This is due to the fact that the total flux cancelled is equal to the amount of flux that is {\it available} to be built into the flux rope, and therefore represents an upper limit on the flux that has been built into the rope. However, the actual amount that builds into the rope is dependent upon the shear of the arcade and the length of the active section of the PIL where flux cancellation is taking place \citep{Green-2011}. Both of these parameters can vary during the lifetime of an active region. An increase in the active section of the PIL and the shear of the arcade field can increase the chances of a loop being involved in a flux cancellation event at both of its ends. When this is the case, flux is cancelled without contributing to the amount of flux in the rope. AR 11680 exhibits a strong increase in the length of the active section of the PIL and AR 12382 shows a large increase in shear between the positive and negative polarities meaning that the amount of flux being built into rope may be overestimated. Active regions that produce high-altitude events have a larger proportion of flux remaining in the overlying arcade compared to regions that produce internal PIL events. AR 11881 is an outlier in terms of the ratio for the high-altitude regions as it has a value of 1:0.94, which is within the range that produce internal-PIL eruptions. However, when analysing the AIA data in the time period following the end of our flux cancellation measurement we observe an internal PIL eruption that occurs on 2013 October 31 at around 01:50~UT. This is just over a day after our flux cancellation measurements ceased because the magnetic flux evolution could no longer be followed. There were no internal PIL events observed following the end of the flux cancellation measurement for the remaining active regions that produced high-altitude eruptions. Our results also show that the average shear angle of the active regions that produce internal PIL events is, on average, higher than that of the other event categories. These results suggest that flux cancellation within a sheared arcade may build a potentially eruptive configuration but that a successful eruption depends on the removal of sufficient overlying and stabilising field. In a recent study by \citet{Sterling-2017} the evolution of a series of coronal jets that occurred at the periphery of the leading sunspot of AR 12259 were analysed. They found that seven active region jets occurred during strong flux cancellation calculating an average flux cancellation rate of 1.5 $\times$ 10$^{19}$~Mx~h$^{-1}$ with an average of $\sim$5 $\times$ 10$^{18}$~Mx cancelled prior to each episode. The flux cancellation rates for the active region jets were found to be higher than the active regions in this study. This is not that surprising considering that the photospheric evolution of the jet-productive area is on the same size-scale as the active regions and the area is followed for a period of hours rather than days. On average, the total flux cancelled in the active regions in this study was found to be 2 orders of magnitude larger than for the active region jets. In this study we have focussed on the flux cancellation scenario of \cite{vB-1989} and the role it plays in the productivity of eruptions in small and isolated bipolar ARs. This required an analysis of the relationship between flux cancellation, the evolution of the coronal magnetic field and eruption onset. We conclude that flux cancellation can be considered as a CME trigger if sufficient stabilising field is removed from above the sheared core field. Other studies have investigated which non-potentiality parameters are strong indicators that a CME will occur. For example, \citet{Bobra-2016} used features derived from {\it SDO}/HMI vector magnetograms to deduce whether active regions that produce M1 class flares or above will also produce a CME. They determined which features distinguish flaring active regions that produce CMEs from those that do not. The study found that the highest-performing features, which characterise the non-potentiality of the magnetic field, are the mean horizontal gradient of the magnetic field and the twist parameter. A study by \citet{Tiwari-2015} found that active regions with a larger non-potentiality and total magnetic flux can produce both fast and slow CMEs, whereas smaller active regions with a more potential configuration can only produce slower CMEs. One key factor that plays a key role in CME productivity is the configuration of the overlying field \citep{Torok-2005}. The gradient of the overlying field with height, for the active regions in our study, will be investigated in the future using non-linear force-free modelling. | 18 | 8 | 1808.10635 |
1808 | 1808.04430_arXiv.txt | Identifying the sources of the highest energy cosmic rays requires understanding how they are deflected by the stochastic, spatially intermittent intergalactic magnetic field. Here we report measurements of energetic charged-particle propagation through a laser-produced magnetized plasma with these properties. We characterize the diffusive transport of the particles experimentally. The results show that the transport is diffusive and that, for the regime of interest for the highest-energy cosmic rays, the diffusion coefficient is unaffected by the spatial intermittency of the magnetic field. | \label{sec:intro} The interplay between charged particles and stochastic magnetic fields generated by plasma turbulence is crucial to understanding how cosmic rays propagate through space \citep{Strong2007,Zweibel2013,Schlickeiser2015}. A key parameter for determining the underlying nature of charged-particle diffusion is the ratio of the particle gyroradius $r_g$ to the correlation length $\ell_B$ of the magnetic turbulence. For the vast majority of cosmic rays detected at the Earth, this ratio is small. These are particles that are well confined by the Galactic magnetic field. But for cosmic rays more energetic than about 10 EeV, the ratio is larger than unity. These ultra-high-energy cosmic rays (UHECRs) are not confined to the Milky Way and are presumed to be extragalactic in origin. Identifying their sources requires understanding how they are deflected by the intergalactic magnetic field, which appears to be stochastic and spatially intermittent. Recent data from the Parker Solar Probe mission have also indicated the presence of non-Gaussian magnetic fields near the Sun \citep{Bandyopadhyay2019arXiv}. To study the propagation of cosmic rays, a theoretical framework has been developed based on direct numerical simulations of particle trajectories (e.g., \citet{Sigl2003,Sigl2004}) and statistical techniques (see \citet{ShalchiBook2009} for a review). In particular, it has been shown \citep{Jokipii1966} that random, small-amplitude fluctuations of the magnetic field superimposed on a mean background field lead to diffusive particle propagation. As a result, standard (Markovian) diffusion is widely used in modeling cosmic-ray transport (e.g., \citet{Kotera2008, Globus2008, Globus2017, Globus2019}), although anomalous diffusion has been shown to occur in special cases \citep{Jokipii1969, Reville2008, Lazarian2014}, including resonant scattering of charged particles in spatially intermittent magnetic fields \citep{Shukurov}. Past laboratory experiments have studied particle transport in diffuse plasmas with strong mean magnetic fields \citep{Gustafson2012,Anderson2013,Furno2015,Bovet2015}, but the regime that is relevant to UHECR transport in the intergalactic medium (IGM), i.e., a stochastic, spatially intermittent magnetic field with zero mean ($\langle \bm{B} \rangle = 0$), and under conditions of weak magnetization ($r_g \gg \ell_B$), has not been studied theoretically, numerically, or experimentally. | \label{sec:discussion} Since the charged particle transport is consistent with normal spatial diffusion through a stochastic field, we can compare the experimental results to theoretical predictions from a random walk process. Using characteristic values for the plasma properties corresponding to $t = 38$ ns after the start of the drive, we take the size of the interaction region to be {\color{black}{$\ell_i \simeq 0.08 \, \mathrm{cm}$}}, the typical magnetic field strength {\color{black}{$B_{\rm{rms}} \simeq 100 \, \mathrm{kG}$}}, and the correlation length {\color{black}{$\ell_B \simeq 50 \, \mu \mathrm{m}$}}. For the case of normal diffusion, a random-walk argument gives {$\Delta v_\perp \approx q_e B_{\rm{rms}} \sqrt{\ell_i \ell_B}/m_p \simeq 1.9 \times 10^7 \, {\rm cm}\,{\rm s}^{-1}$} (see Appendix \ref{sec:a.deflections}) where $m_p$ is the mass of a proton. This value is consistent with the measured RMS deflection velocity (Figure~\ref{fig:lineouts}c). Further, since the values of $V$, $B_{\rm{rms}}$, and the power spectrum of the magnetic energy (and therefore the value of $\ell_{B}$) do not change in the experiment after the magnetic-field amplification saturates (see \citet{Tzeferacos2017pop,Tzeferacos2017} and Appendix \ref{sec:a.flash}), the random walk model also predicts a constant {$\kappa/V^3 \sim m_p^2/(q_e B_{\rm{rms}})^2 \ell_B \simeq 1.9\times10^{-16}\,\rm{s}^{2}\,\rm{cm}^{-1}$}, in quantitative agreement with the experimental results (Figure~\ref{fig:lineouts}d). For isotropic statistics and $r_g / \ell_B \gg 1$, the proton mean free path is $\lambda \simeq 10^4\,\rm{cm}$. In this regime, theory~\citep{Dolginov1967} and simulations~\citep{Subedi2017} predict that $\lambda/\ell_B \propto (r_g/\ell_B)^2$. \color{black}{The simulations of \citet{Subedi2017} predict a scaling coefficient of $1.5$ and extend to $r_g/\ell_B \simeq 40$. Extrapolating the results of \citet{Subedi2017} by a factor of $13$ and $28$ to the values $r_g/\ell_B \simeq 520$ for the 3.3 MeV protons and $\simeq 1,100$ for the 15 MeV protons gives $\lambda/\ell_B\simeq 0.6 \times 10^6$ and $\simeq 2\times 10^6$. These values agree within a factor of order unity with the experimental value of $\lambda/\ell_B\simeq 2\times10^6$ that we obtain for the two proton energies. More importantly, our results demonstrate that, for the conditions present in the experiment (i.e., a beam with a diameter $D > \ell_B$ of charged particles in the $r_g \gg \ell_B$ regime that traverses a stochastic and spatially-intermittent magnetic field with a path length $\ell_i > \ell_B$) the diffusion is not affected by the spatial intermittency of the stochastic magnetic fields. This is also demonstrated by the FLASH simulations of the experiment and numerical simulations presented in Appendix \ref{sec:a.intermittency}. The results of our experiments validate the use of standard diffusion theory in modeling the transport of UHECRs in the IGM, e.g., \citet{Kotera2008, Globus2008, Globus2017, Globus2019}, since all three of the above conditions are satisfied. This is useful in view of the increased interest in such modeling motivated by the recent detection by the Pierre Auger Observatory of a significant anisotropy in the arrival directions of cosmic rays of energy above 8 EeV \citep{Aab2017a}. | 18 | 8 | 1808.04430 |
1808 | 1808.03026_arXiv.txt | We have carried out numerical hydrodynamic simulations of radio jets from active galactic nuclei using the PLUTO simulation code, with the aim of investigating the effect of different environments and intermittency of energy injection on the resulting dynamics and observable properties of the jet-inflated lobes. Initially conical jets are simulated in poor group and cluster environments. We show that the environment into which a radio jet is propagating plays a large role in the resulting morphology, dynamics and observable properties of the radio source. The same jet collimates much later in a poor group compared to a cluster, which leads to pronounced differences in radio morphology. The intermittency of the jet also affects the observable properties of the radio source, and multiple hotspots are present for multiple outburst jets in the cluster environment. We quantify the detectability of active and quiescent phases, and find this to be strongly environment-dependent. We conclude that the dynamics and observational properties of jets depend strongly on the details of energy injection and environment. | It is well accepted that outflows from active galactic nuclei play an important role in slowing cooling flows \citep[see reviews by e.g.][]{McNamara2007, Alexander2012, Fabian2012}. The details of how the jet energy couples with the environment is still an open problem, and a detailed prescription is needed for semi-analytic galaxy formation models \citep[e.g.][]{Croton2006,Shabala2009,Raouf2017} and cosmological galaxy formation simulations \citep[e.g.][]{Vogelsberger2014,Schaye2015,Kaviraj2016}. Intermittent jet activity is required in order to maintain the heating/cooling balance of active galactic nuclei and their host galaxies \citep{Heckman2014}, and is supported through observational evidence of double-double radio galaxies \citep[e.g.,][]{Schoenmakers2000a}. The first basic morphology models of FR II \citep{Fanaroff1974} radio sources were introduced by \citet{Scheuer1974} and \citet{Blandford1974}, which both proposed a relativistic outflow from a central region. \citet{Begelman1989} proposed that the cocoons surrounding this relativistic outflow were overpressured with respect to the intergalactic medium, and \citet{Falle1991} showed that these outflows have self-similar expansion. An analytic self-similar expansion model to produce the complete FR II morphology was developed by \citet[][the KA model]{Kaiser1997}, which has radio sources expanding into an environment with a smooth density profile given by a power-law. This was extended by \citet[][the KDA model]{Kaiser1997a} to include energy losses from synchrotron processes due to relativistic electrons in the jet cocoon, allowing the calculation of radio emission from the radio source. An alternative model for the spectral evolution of radio sources was proposed by \citet{Manolakou2002}, which calculates the first-order Fermi acceleration of the electrons at the termination shock as opposed to assuming an electron distribution for the cocoon. The self-similarity assumption used in the KA model does not hold for small ($<1\,\mathrm{kpc}$) scales, and was extended by \citet{Alexander2006a} to better model the uncollimated to collimated transition. The extended model introduces the length-scale $L_1$, which relates the jet density and environment density, and these characteristic length-scales are expanded by \citet[][see Sect 2]{Krause2012}. Recently, semi-analytical models for the evolution of radio sources have been developed \citep{Turner2015,Hardcastle2018} which relax the self-similarity assumptions, and allow arbitrary environments to be specified. Different types of radio sources are found in different environments \citep{Longair1979}: while more powerful, edge-brightened FR II radio sources tend to reside in lower mass halos, the less powerful FR Is (edge-darkened) are more frequent in massive galaxy clusters. There is not a one-to-one mapping, but there is a tendency for FR I hosts to have lower accretion onto their supermassive black holes and less star formation than FR IIs \citep{Buttiglione2009,Hardcastle2013b}, consistent with a dependence on the mass of the dark matter halo. Apart from the basic Fanaroff-Riley morphological classification, one expects the radio morphology and luminosity to be strongly affected by the environment: an FR II jet in a rich cluster will quickly come into sideways pressure equilibrium \citep[see][]{Hardcastle2013}, but the cluster atmosphere will still collimate the jet relatively early, and thus produce a narrow beam. The high cluster density will ensure that the lobes will be bright radio emitters. The gas pressure in a poor group is much lower. Correspondingly, the length scale $L_2$ \citep[see][]{Krause2012}, where the lobes come into pressure equilibrium with the environment is much larger. The lobe pressure can therefore be lower than in the cluster case, while still overpressured with respect to the ambient gas. The latter makes the lobe dynamics different from the cluster case; in groups, jets will be collimated later and hence wider. It is clear from these considerations that it should be much more difficult to observe a jet in a poor group. Yet, the AGN feedback might be crucial just for these halos, as the more massive "green valley" galaxies, that transition from a state of high star formation rate to quiescence, are usually found in such haloes \citep[e.g.][]{Alatalo2014,Alatalo2016}. The advent of a new generation of observing facilities means that their study might become feasible in the near future. The environmental dependence of the radio properties of ambient pressure-collimated jets has been investigated by \citet[][HK13]{Hardcastle2013}. For parameters representing the range from poor groups to rich clusters, it was found that the range in radio luminosity for FR II radio sources that have been evolved for about $10^8$ years spans roughly one order of magnitude for a given jet power. To flesh out the difference in observability, we concentrate here on two environments at the extremes of the parameter range: one with a dark-matter halo mass of $3 \times 10^{12}\,\mathrm{M_\odot}$, and one that is a hundred times more massive, with isothermal IGM/ICM gas in hydrostatic equilibrium with the dark matter halo. We inject jets with FR II parameters, a single jet power and observationally motivated duty cycles, and calculate the luminosity evolution as well as the surface brightness to judge the observability of the simulated sources. | \label{sec:conclusions} We have shown that there is a clear link between the environment into which the jets are propagating, and the resulting morphology of the jet. A large factor in this morphology difference is the collimation distance of the jet, which is larger in the poor group. This results in a wider overall jet beam, and produces different large-scale structures. Clearly, injecting the jet with a finite opening angle is an important factor for the radio morphology. The environment affects the observable properties of the jets, as seen in the P-D tracks and surface brightness maps for jets in both the cluster and poor group environments. Simulated radio observations of the jets show that the jet in the cluster is significantly easier to detect due to its higher surface brightness. Comparing the two surface brightness distributions in \autoref{fig:sb-n4-cluster-group}, detecting emission from the radio lobes in the group environment would be difficult and possibly only the compact core would be visible, whereas the cluster environment has easily detectable extended emission. The detectability of a simulation is quantified in \autoref{fig:observability-1mjy} and \autoref{fig:observability-0.1mjy}, where cluster radio sources are detectable up to $100$ per cent of the time (for a FIRST-like detection threshold) using our adopted parameters, while poor group environments are detectable at most $60$ per cent of the time. Increasing the sensitivity by an order of magnitude allowed both cluster and poor group radio sources to be detectable up to $100$ per cent of the time. This agrees with the findings presented by \citet{Shabala2008,Shabala2018} that massive galaxies (often residing in big haloes) host a larger fraction of extended radio sources. It is expected that next generation radio surveys will detect a greater population of radio sources in poorer environments, due to increased sensitivity. Future simulations for a range of jet powers and environments would allow the P-D diagram to be fully explored and could provide a framework to link observations to the underlying jet properties, aiding in placing radio sources of all sizes, including the ubiquitous compact sources \citep{Sadler2014a,Baldi2015,Shabala2017} on an evolutionary sequence. The intermittency of a jet also plays a role in determining its large-scale morphology and observable properties. Interestingly, the radio sources in subsequent active phases reach a similar radio luminosity to the first outburst, due to efficient entrainment. Intermittency of radio activity is likely responsible for double-double radio sources. Further modelling work, together with high-sensitivity, low-frequency observations \citep{Shimwell2017,Brienza2017} will shed light on the physics of this population. Future work would include simulating a wide range of jet powers, environments, and opening angles, as well as FR I morphologies. Our simulations presented in this paper only focused on producing radio sources with an FR II morphology. Radio sources with an FR I morphology have a different (core-brightened) surface brightness profile, which has direct implications for observed source sizes and integrated luminosities. Similar simulations of lower jet powers typical of FR I jets would provide information on how the observable properties of the FR I jets change due to jet-environment interaction and complement the results presented here. | 18 | 8 | 1808.03026 |
1808 | 1808.03356_arXiv.txt | We present the data reduction pipeline, \texttt{MEAD}, for Arizona Lenslets for Exoplanet Spectroscopy (ALES), the first thermal infrared integral field spectrograph designed for high-contrast imaging. ALES is an upgrade of LMIRCam, the $1-5\,\mu$m imaging camera for the Large Binocular Telescope, capable of observing astronomical objects in the thermal infrared ($3-5\,\mu$m) to produce simultaneous spatial and spectral data cubes. The pipeline is currently designed to perform $L$-band ($2.8-4.2\,\mu$m) data cube reconstruction, relying on methods used extensively by current near-infrared integral field spectrographs. ALES data cube reconstruction on each spectra uses an optimal extraction method. The calibration unit comprises a thermal infrared source, a monochromator and an optical diffuser designed to inject specific wavelengths of light into LBTI to evenly illuminate the pupil plane and ALES lenslet array with monochromatic light. Not only does the calibration unit facilitate wavelength calibration for ALES and LBTI, but it also provides images of monochromatic point spread functions (PSFs). A linear combination of these monochromatic PSFs can be optimized to fit each spectrum in the least-square sense via $\chi^2$ fitting. | \label{sec:intro} Arizona Lenslets for Exoplanet Spectroscopy (ALES \cite{2015SPIE.9605E..1DS}) is a project designed to extend the functionality of the Large Binocular Telescope Interferometer's (LBTI \cite{2008SPIE.7013E..39H, 2008SPIE.7013E..28H, 2012SPIE.8445E..0UH, 2014SPIE.9146E..0TH}) $1-5\,\mu$m imager LMIRCam \cite{2010SPIE.7735E..3HS,2012SPIE.8446E..4FL}. ALES is the first integral field spectrograph (IFS) capable of high-contrast imaging in the thermal infrared. A current scientific goal utilizing ALES on a single aperture of LBT is to deliver low-resolution $LM$-band spectra of young, gas giant exoplanets and substellar companions in order to supplement existing near-infrared $JHK$ spectra for a broader spectroscopic characterization of these bodies. This goal can be accomplished by exploiting the unique properties of IFS data cubes, which comprise photometrically accurate stacks of simultaneous narrowband images spanning multiple wavelength channels. The spatial and spectral information within the IFS cubes enables unambiguous separation of the light from substellar companions and their host star. The success of near-infrared lenslet-based IFSs has been due in large part to the development of robust techniques for automating the construction of wavelength-calibrated spectral data cubes from the thousands of closely-packed spectra in raw frames (e.g. GPI \cite{2008SPIE.7015E..18M, 2014SPIE.9147E..3JP} ; SPHERE \cite{2008SPIE.7014E..3EC, 2008SPIE.7019E..39P} ; Project 1640 \cite{2011PASP..123...74H, 2011PASP..123..746Z} ; CHARIS \cite{2012SPIE.8446E..9CM, 2017JATIS...3d8002B} ; OSIRIS \cite{2006SPIE.6269E..1AL}). These pipelines are critical for the homogenization of data products and the accessibility for other observers. The Methods for Extracting ALES Data (\texttt{MEAD}) package is the Python-language data reduction pipeline for ALES that has leveraged the insights gained during the operations of the near-infrared IFSs in order to orchestrate the construction of ALES data cubes. After a brief overview of the instrument, this paper begins by presenting \texttt{MEAD} in a linear fashion, following a recipe with which most observations will be reduced. Then the paper focuses on the thermal infrared calibration unit for LBTI and how the unit will affect ALES operations. Section \ref{sec:det} summarizes basic processing of raw data frames to remove detector artifacts. Section \ref{sec:fpm} addresses the extent and characterization of flexure in the instrument, as well as the calibration process. Section \ref{sec:cube} briefly states how the cubes are reconstructed. Section \ref{sec:ticu} cover the thermal infrared calibration unit for LBTI. We finish by discussing the immediate future for ALES and \texttt{MEAD} in Section \ref{sec:future}. | 18 | 8 | 1808.03356 |
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1808 | 1808.10365_arXiv.txt | We present the implementation of a spectral kurtosis based Radio-Frequency Interference detection system on the CHIME instrument and its reduced-scale pathfinder. Our implementation extends single-receiver formulations to the case of a compact array, combining samples from multiple receivers to improve the confidence with which RFI is detected. Through comparison between on-sky data and simulations, we show that the statistical properties of the canonical spectral kurtosis estimator are functionally unchanged by cross-array integration. Moreover, by comparison of simultaneous data from CHIME and the Pathfinder, we evaluate our implementation's capacity for interference discrimination for compact arrays of various size. We conclude that a spectral kurtosis based implementation provides a scalable, high cadence RFI discriminator for compact multi-receiver arrays. | The presence of non-astronomical signals in the electromagnetic spectrum (`Radio-Frequency Interference' or RFI) poses a significant hazard to successful radio observations. Sources of such interference include lightning and electrical discharges, inadvertent emissions from terrestrial electronics, radio-frequency telecommunication signals, and communications with satellites and aircraft \citep{1991ASPC...17..213G, 2013MNRAS.435..584O, 2016arXiv161004696S}. The Canadian Hydrogen Intensity Mapping Experiment (CHIME\footnote{\url{http://www.chime-experiment.ca}}) is a newly-constructed radio interferometer with 1024 dual-polarization receivers continuously observing a 400-800\,MHz band. A fully independent reduced-scale prototype, the CHIME Pathfinder (henceforth `the Pathfinder') possesses 128 dual-polarization receivers and an identical observing band \citep{2014SPIE.9145E..22B,2014SPIE.9145E..4VN}. CHIME and the Pathfinder each follow an `FX' correlator architecture, with an FPGA-based Fourier-transform stage \citep{2016JAI.....541005B} followed by a GPU-based outer-product `X-engine' \citep{2015arXiv150306203K,2015arXiv150306189R,2015arXiv150306202D}. The considerable capabilities of the CHIME correlator present an opportunity for powerful, on-the-fly RFI mitigation. CHIME employs a `software' correlator X-engine, and its easily-reconfigurable, general-purpose hardware permits the introduction of additional data processing with minimal development effort. This includes extending the real-time processing system to include the detection and excision of RFI during the correlation process. The architecture of the CHIME X-engine is such that each processing `node' contains data from only a few frequencies, but over the entire array; this constrains the selection of RFI-excision algorithms which may be applied in the GPUs. Our choice of a statistical excision algorithm, based on spectral kurtosis, was informed by both robust performance and modest computational cost. Additionally, as detailed below, the compact layout of CHIME permits multi-receiver RFI detection, lowering the effective threshold for RFI detections while retaining high time resolution. We summarize the theoretical foundations of the spectral kurtosis estimator in \S\ref{sec:theory} and present a multi-receiver formulation of the estimator in \S\ref{ssec:array}. The details of its implementation on CHIME and the Pathfinder are included in \S\ref{ssec:imp} and the results obtained follow in \S\ref{ssec:results}. | We have shown that the excision potential of the $\widetilde{SK}$ estimator may be improved through the combination of signals from multiple receivers within a compact array. Our implementation offers a robust, computationally-efficient method for real-time RFI detection and removal for compact arrays. Data from both CHIME and the Pathfinder agree closely with numerical simulations, confirming that the effects of quantization on the $\widetilde{SK}$ estimator in our correlator system are entirely predictable. Particularly, we find that these effects do not substantially alter the integration-length-dependence of the estimator's statistical moments. We conclude that the multi-receiver formulation of the spectral kurtosis estimator provides high-time-resolution, low-computational-cost RFI excision whose sensitivity improves predictably with the size of the compact array. | 18 | 8 | 1808.10365 |
1808 | 1808.07952_arXiv.txt | The JCMT Gould Belt Survey was one of the first Legacy Surveys with the James Clerk Maxwell Telescope in Hawaii, mapping 47 square degrees of nearby ($< 500$~pc) molecular clouds in both dust continuum emission at 850~\microns\ and 450~\microns, as well as a more-limited area in lines of various CO isotopologues. While molecular clouds and the material that forms stars have structures on many size scales, their larger-scale structures are difficult to observe reliably in the submillimetre regime using ground-based facilities. In this paper, we quantify the extent to which three subsequent data-reduction methods employed by the JCMT GBS accurately recover emission structures of various size scales, in particular, dense cores which are the focus of many GBS science goals. With our current best data-reduction procedure, we expect to recover $100$\% of structures with Gaussian $\sigma$ sizes of $\le $30\arcsec\ and intensity peaks of at least five times the local noise for isolated peaks of emission. The measured sizes and peak fluxes of these compact structures are reliable (within 15\% of the input values), but source recovery and reliability both decrease significantly for larger emission structures and for fainter peaks. Additional factors such as source crowding have not been tested in our analysis. The most recent JCMT GBS data release includes pointing corrections, and we demonstrate that these tend to decrease the sizes and increase the peak intensities of compact sources in our dataset, mostly at a low level (several percent), but occasionally with notable improvement. | The James Clerk Maxwell Telescope (JCMT) Gould Belt Survey \citep[GBS;][]{WardThomp07} is one of the initial set of JCMT Legacy Surveys, and has the goal of mapping and characterizing dense star-forming cores and their environments across all molecular clouds within $\sim$500~pc. The JCMT GBS included extensive maps of the dust continuum emission at 850~\microns\ and 450~\microns\ of all nearby molecular clouds observable from Maunakea using SCUBA-2 \citep[Submillimetre Common User Bolometer Array-2;][]{Holland13}, as well as more-limited spectral-line observations of various CO isotopologues using HARP \citep[Heterodyne Array Receiver Program;][]{Buckle09}. For this paper, we focus on the SCUBA-2 portion of the survey. The SCUBA-2 instrument is an efficient and sensitive mapper of thermal emission from cold and compact dusty structures such as dense cores, the birthplace of future stars. One of the science goals of the JCMT GBS is to identify and characterize these dense cores, which includes estimating their sizes and total fluxes (masses). These are challenging observations to make from the ground, as the Earth's atmosphere is bright and variable at submillimetre wavelengths. As such, all ground-based observations in the submillimetre regime use some form of filtering. Often this filtering is done in the form of `chopping', where fluxes are measured in some differential form \citep[see, e.g.][and references therein]{Haig04}. SCUBA-2, however, combines a fast scanning pattern during observing with an iterative filtering technique during the data reduction process, which has the similar consequence of removing both contributions from the atmosphere and extended source emission \citep[e.g.,][]{Holland13,Chapin13}. Regardless of the method, the largest scales of emission cannot be recovered from ground-based submillimetre observations, as it is not possible to disentangle such signal from that of the atmosphere. Nonetheless, it is desirable for star-formation science to obtain accurate measurements of emission structures on as large a scale as possible. New instrumentation, observing techniques, and data-reduction tools allow for better recovery of larger-scale emission structures than was feasible in the past. As an example, Figure~\ref{fig_scuba_scuba2} shows the emission observed in the NGC~1333 star-forming region in the Perseus molecular cloud as seen with the original SCUBA detector \citep{Sandell01} compared with the same map obtained with SCUBA-2, as part of the GBS survey, and reduced using several different techniques. The SCUBA-2 map was first presented in \citet{Chen16} using the GBS Internal Release 1 reduction method, but is shown in Figure~\ref{fig_scuba_scuba2} using several more recent SCUBA-2 data reduction methods, all of which are discussed further throughout this paper. While bright and compact emission structures appear the same in all panels, the GBS DR3 map clearly recovers the most faint and extended structure, while suffering the least from artificial large-scale features, such as that seen at the centre left of the SCUBA image. In this paper, we focus on the reliability of the GBS SCUBA-2 maps, and do not present any quantitative comparisons with SCUBA data. While not the focus of our present work, we note that space-based submillimetre facilities such as the {\it Herschel Space Telescope} avoid the challenge of observing through the atmosphere, and therefore offer the ability to obtain observations with much less filtering. At the same time, space-based submillimetre facilities have much lower angular resolutions, due to the difficulty in placing large dishes in space. Previous work by JCMT GBS members provide a comparison of star-forming structures observed using {\it Herschel} and SCUBA-2 \citep{Sadavoy13,Pattle15,WardThomp16,Chen16}, although all of these analyses used earlier SCUBA-2 data-reduction methods than the methods analyzed here. The loss of larger-scale emission structures inferred by comparing SCUBA-2 and {\it Herschel} observations will therefore be somewhat less severe when the current data products are used instead. \begin{figure}[htbp] \includegraphics[width=5.9in]{f1.ps} \vspace{-0.75in} \caption{A comparison of emission observed in NGC~1333. The top left panel shows data from SCUBA, published in \citet{Sandell01}, while the remaining three panels show SCUBA-2 observations, converted into Jy~bm$^{-1}$ flux units assuming a 14\farcs6 beam as in \citet{Dempsey13}. The SCUBA-2 reductions shown are the JCMT Legacy Release 1 (LR1; top right), JCMT GBS Data Release 1 (DR1; bottom left) and JCMT GBS Data Release 3 (DR3; bottom right), all discussed further in this paper. In all panels, faint emission is emphasized in the grey scale which ranges from -0.05~Jy~bm$^{-1}$ and 0.1~Jy~bm$^{-1}$. Both the solid blue and dashed orange contours indicate emission at 0.2~Jy~bm$^{-1}$, 1~Jy~bm$^{-1}$, and 3~Jy~bm$^{-1}$. The solid blue contours trace the greyscale image shown in that panel, while the dashed orange contours show the SCUBA-2 DR3 map for reference. } \label{fig_scuba_scuba2} \end{figure} To achieve the various science goals of the GBS, it is important to have a thorough understanding of the completeness and reliability of the sources detected. Uncertainties in source detection and characterization can arise both from the observations and map reconstruction efforts, as well as from the tools used to identify and characterize the emission sources. In the analysis presented here, we aim to investigate thoroughly the first of these issues, i.e., quantifying how well a source of known brightness and size is recovered in a JCMT GBS map, when an idealized source-detection algorithm is used in an ideal (non-crowded) environment. The JCMT GBS has released several versions of ever-improving data products to the survey team for analysis: Internal Release 1 (IR1), Data Release 1 (DR1)\footnote{This is called the `GBS Legacy Release 1' in \citet{Mairs15}.}, Data Release 2 (DR2), and Data Release 3 (DR3), while the JCMT has also released maps of all data 850~$\mu$m data obtained between 2011 February 1 and 2013 August 1 through their `JCMT Legacy Release~1' (LR1; Graves et al, in prep; see also \texttt{http://www.eaobservatory.org/jcmt/science/archive/lr1/}). Table~\ref{tab_published} summarizes all currently published GBS maps. The last three GBS data releases, intended to be made fully public, are the focus of this paper. We also provide an approximate comparison of the GBS data products to the JCMT's LR1 maps, which are qualitatively similar to the intermediate `automask' GBS data products discussed in the text. Within the GBS data releases, DR2 improves on DR1 through the use of improved data-reduction techniques that enhance the ability to recover faithfully large-scale emission structures. Many of these improvements were outlined in \citet{Mairs15}, but it was beyond the scope of that work to replicate fully the data-reduction process used for DR1 and DR2 and quantify how well structure in the maps is recovered. Additionally, several small modifications to the data-reduction procedure were made after the testing performed in \citet{Mairs15}. The majority of this paper focuses on a careful comparison between the recovery of structure using the exact JCMT GBS DR1 and DR2 methodologies. Unlike DR1 and DR2, DR3 does not involve a completely new re-reduction of all JCMT GBS observations with improved recipes. Instead, DR3 focuses on estimating the pointing offset errors present in the observations, and adjusting the final DR2 maps to correct for them. \begin{deluxetable}{clll} \tablecolumns{8} \tablewidth{0pc} \tabletypesize{\scriptsize} \tablecaption{GBS Published Maps\tablenotemark{a}\label{tab_published}} \tablehead{ \colhead{Region} & \colhead{Data Version} & \colhead{Reference} & \colhead{DOI\tablenotemark{b}} } \startdata CrA & DR1 & Bresnahan et al (in prep) & pending \\ Auriga & DR1 & \citet{BroekhovenFiene18} & https://doi.org/10.11570/17.0008 \\ IC5146 & DR1 & \citet{Johnstone17} & https://doi.org/10.11570/17.0001 \\ Lupus & DR1 & \citet{Mowat17} & https://doi.org/10.11570/17.0002 \\ Cepheus & DR1 & \citet{Pattle17} & https://doi.org/10.11570/16.0002 \\ Orion~A & DR1 automask & \citet{Lane16} & https://doi.org/10.11570/16.0008 \\ Taurus~L1495 & IR1 & \citet{WardThomp16} & https://doi.org/10.11570/16.0002 \\ Orion~A\tablenotemark{c} & DR1 & \citet{Mairs16} & https://doi.org/10.11570/16.0007 \\ Perseus & IR1 & \citet{Chen16} & https://doi.org/10.11570/16.0004 \\ Serpens~W40 & DR1 & \citet{Rumble16} & https://doi.org/10.11570/16.0006 \\ Orion~B & DR1 & \citet{Kirk16} & https://doi.org/10.11570/16.0003 \\ Ophiuchus & IR1 & \citet{Pattle15} & https://doi.org/10.11570/15.0001 \\ Serpens~MWC297 & IR1 & \citet{Rumble15} & https://doi.org/10.11570/15.0002 \\ \enddata \tablenotetext{a}{This table includes only published GBS papers where the submillimetre map was publicly released alongside the paper.} \tablenotetext{b}{Digital Object Identifier is a permanent webpage where a static version of the GBS data is stored for public distribution.} \tablenotetext{c}{While analysis was performed only in the southern portion of the map, the entire map is provided at the DOI.} \end{deluxetable} Quantifying the quality and fidelity of our JCMT GBS maps is a crucial step for the over-arching science goals of the survey. For example, one goal is to measure the distribution of core masses and compare this distribution with the initial (stellar) mass function \citep{WardThomp07}. Without detailed knowledge of source recoverability and whether or not there is any bias in real versus observable flux, the obtained core mass function could be misinterpreted. A wide range of artificial Gaussians were used in our testing, ranging from sources that should be difficult to detect (e.g., peak brightnesses similar to the image noise level) to those that should be easy to recover accurately (e.g., compact sources with peaks at 50 times the image noise level). We emphasize that especially for the former case, the recovery results we present here represent an unachievable ideal case for realistic analysis: knowing precisely {\it where} to look for the injected peaks, as well as precisely {\it what} to look for (known peak brightness and width) allows us to recover sources that would never be identifiable in a real observation. A full quantification of completeness would require including non-Gaussian sources (e.g., also filamentary morphologies, and elongated cores with non-Gaussian radial profiles), testing the effects of source crowding, testing several of the commonly used source-finding algorithms and determining the influence of false positive detections, and not tuning the source-finding algorithm to look for emission in known locations. Such an analysis is beyond the scope of this paper, although some aspects have been examined by previous studies \citep[e.g.,][]{Rosolowsky08,Pineda09,Kainulainen09,Kauffmann10,Shetty10,Rosolowsky10,Reid10,Ward12,Menshchikov13}. The paper is structured as follows. In Section~2, we discuss the JCMT GBS observations and the general data-reduction procedure. In Section~3, we describe our method for testing source recoverability and fidelity in source recovery in the DR1 and DR2 maps, and the results are discussed in Section~\ref{sec_completeness_results}. These tests provide essential metrics for future analyses of GBS data where the role of bias and the recoverability of real structure in the observations will need to be understood. In Section~\ref{sec_IR4}, we introduce two independent methods for measuring the telescope-pointing errors in each observation, and demonstrate that the final DR3 maps should have little residual relative pointing error. This analysis provides us with confidence that the properties of emission structures measured in DR3 should not be substantially more blurred out than expected from the native telescope resolution. | \label{sec_conc} In this paper, we present the data-reduction methodology employed by the JCMT Gould Belt Survey, through all three major data releases, DR1 through DR3. All of the DR3 data products, including final mosaics using the external mask reductions, the mask files and CO subtracted 850~$\mu$m maps, are publicly available in conjunction with this paper. [An address for a DOI (permanent webpage) will be made available with the published version of this paper.] In Section~4, we measured the reliability of emission structures recovered in DR1 and DR2. There, we demonstrate that our two-step reduction process allows us to measure true source properties better than prior methods, and that DR2 provides significant improvements over DR1, while both are expected to provide substantially better recovery of extended structures than the JCMT LR1, as already shown in \citet{Mairs15}\footnote{We note that the JCMT LR1 was designed to identify the locations of emission peaks but not recover the total emission present.} GBS science tends to concentrate on the more-compact emission structures (cores and filaments) where source recovery is best. For the DR2 method, in our idealized tests that assume isolated emission and a source detection method tuned to the known source locations, we recover $>95$\% of artificial structures with peaks at 3 times the rms, for sizes of 30\arcsec\ and smaller, and 100\% of the structures with peaks at 5 times the rms. These recovered structures also have reliable properties measured, with typical peak flux and size measurements both lying within 15\% of the true values for sources with peak fluxes at least 3 times the rms, while the total flux measurements lie within 25\% of the true values. In all cases, the observed values can be corrected for the deficit in peak flux, total flux, and size measured to a higher degree of accuracy than the listed percentages. Source recovery statistics and the reliability of measured parameters (peak flux and size) for the full series of artificial Gaussian test inputs are provided for reference in Tables~\ref{tab_complete} and \ref{tab_recov_props}. These numbers should be considered as best-case values if measuring and interpreting source-population properties such as the dense-core mass function. Additional effects, such as the presence of non-Gaussian sources, biases from source detection algorithms, and biases due to source crowding have not been considered here, and are all expected to decrease the fraction of sources recovered and the reliability of their properties. We strongly encourage readers to take care in considering these additional effects for any analyses where our recovery and reliability statistics are being applied. For the final GBS data release (DR3), we estimate the pointing offset present in each observation, by taking advantage of the fact that the survey observed each location on the sky between four and six times. We test two different methods for calculating the offset present between repeated observations of the same field, and find that the KAPPA program \al tends to produce the most-reliable results. The pointing offsets estimated are typically small. About 16\% of the fields have total offsets of at least 3\arcsec, which corresponds to one pixel in the 850~$\mu$m maps and 1.5 pixels in the 450~$\mu$m maps, while 3.3\% have total offsets of at least 5\arcsec. Most mosaics show little discernable difference before and after the pointing offset correction, however, the B1-S field in the PerseusWest mosaic in particular is noticeably improved. The full data-reduction procedure is given in Appendix~A (for DR1 and DR2), and Section~5 (for DR3) to allow other groups to reproduce our methods. We remind the reader that for DR3, we applied positional shifts to observations reduced under the DR2 methodology, so all of the reduction parameters implemented in {\it makemap} are identical to DR2. \appendix | 18 | 8 | 1808.07952 |
1808 | 1808.00575_arXiv.txt | {The Kepler extended mission, also known as \textit{{\it K2}}, has provided the community with a wealth of planetary candidates that orbit stars typically much brighter than the targets of the original mission. These planet candidates are suitable for further spectroscopic follow-up and precise mass determinations, leading ultimately to the construction of empirical mass-radius diagrams. Particularly interesting is to constrain the properties of planets between the Earth and Neptune in size, the most abundant type of planets orbiting Sun-like stars with periods less than a few years.} {Among many other \textit{{\it K2}} candidates, we discovered a multi-planetary system around EPIC~246471491, with four planets ranging in size from twice the size of Earth, to nearly the size of Neptune. We aim here at confirming their planetary nature and characterizing the properties of this system.} {We measure the mass of the planets of the EPIC~246471491 system by means of precise radial velocity measurements using the CARMENES spectrograph and the HARPS-N spectrograph.} {With our data we are able to determine the mass of the two inner planets of the system with a precision better than 15\%, and place upper limits on the masses of the two outer planets.} {We find that EPIC~246471491~b has a mass of $M_\mathrm{b}$\,=\,\mpb\, and a radius of $R_\mathrm{b}$\,=\,\rpb\,, yielding a mean density of $\rho_\mathrm{b}$\,=\,\denpb, while EPIC~246471491~c has a mass of $M_\mathrm{c}$\,=\,\mpc\,, radius of $R_\mathrm{c}$\,=\,\rpc\,, and a mean density of $\rho_\mathrm{c}$\,=\,\denpc. For EPIC~246471491~d ($R_\mathrm{d}$\,=\,\rpd\,) and EPIC~246471491~e ($R_\mathrm{e}$\,=\,\rpe\,) the upper limits for the masses are 6.5\,$M_\oplus$ and 10.7\,$M_\oplus$, respectively. The system is thus composed of a nearly Neptune-twin planet (in mass and radius), two sub-Neptunes with very different densities and presumably bulk composition, and a fourth planet in the outermost orbit that resides right in the middle of the super-Earth/sub-Neptune radius gap. Future comparative planetology studies of this system can provide useful insights into planetary formation, and also a good test of atmospheric escape and evolution theories.} | \label{sec:intro} Space-based transit surveys such as CoRoT \citep{2009A&A...506..411A} and Kepler \citep{2010Sci...327..977B} have revolutionized the field of exoplanetary science. Their high-precision and nearly uninterrupted photometry has opened the doors to explore planet parameter spaces that are not easily accessible from the ground, most notably, the Earth-radius planet domain. However, our knowledge of both super-Earths ($R_{p}$ = 1--2\,$R_\oplus$ and $M_{p}$ = 1--10\,$M_\oplus$) and Neptune planets ($R_{p}$ = 2--6\,$R_\oplus$ and $R_{p}$ = 10--40\,$M_\oplus$) is still limited, due to the small radial velocity (RV) variation induced by such planets and the relative faintness of most of {\it Kepler} host stars ($V>13$\,mag) which make precise mass determinations difficult. Thus, many questions remain unanswered, for example what is the composition and internal structure of small planets? \citet{Fulton17} and \citet{Fulton18} reported a radius gap at $\sim 2\,R_\oplus$ in the exoplanet radius distribution using {\it Kepler} data for Sun-like stars, and \citet{2018AJ....155..127H} indicated that the gap could extend down to the M dwarf domain. This would point to a very different planetary nature for planets on each side of the gap. Is this due to planet migration? Are the larger planets surrounded by a H/He atmospheres while the smaller planet have lost these envelopes? Or, did they already form with very different bulk densities? Answering these questions requires statistically significant samples of well-characterized small planets, especially in terms of orbital parameters, mass, radius and mean density. {\it Kepler}'s extended {\it K2} mission is a unique opportunity to gain knowledge about small close-in planets. Every 3 months, {\it K2} observes a different stellar field located along the ecliptic, targeting up to 15 times brighter stars than the original {\it Kepler} mission. The KESPRINT collaboration\footnote{\href{http://www.iac.es/proyecto/kesprint}{http://www.iac.es/proyecto/kesprint}} is an international effort dedicated to the discovery, confirmation and characterization of planet candidates from the space transit missions {\it K2} and {\it TESS} and, in the future, {\it PLATO}. We have been focusing on determining the masses of small planets around bright stars, especially for planets in or around the radius gap. Here, we present the discovery and characterization of four transiting planets around the star EPIC~246471491. While these planets are observed to have radii between 2 and 3.5 radii of the Earth, our follow-up observations indicate that they have very different bulk compositions. This has significant implications for the physical nature of planets around the radius gap. In this paper we provide ground-based follow-up observations that confirm that EPIC~246471491 is a single object and establish it main stellar properties. We also analyze jointly the {\it K2} data together with high-precision RV data from CARMENES and HARPS-N spectrographs, to retrieve orbital solutions and planetary masses. Finally we discuss the possible bulk compositions of the planets, leading to different densities. | \label{sec:discuss} \begin{figure}% \centering \includegraphics[width=8.3cm,angle=0,clip=true]{plot_mr_3.png} \caption{Mass-radius diagram for all known planets with masses between 0.5--20\,$M_\oplus$ and radius 1--4\,$R_\oplus$, comprising from Earth-like to super-Earth to sub-Neptune regimes. Data are taken from the TEPCat database \citep{2011MNRAS.417.2166S}. Planets belonging to multiple systems are marked in open gray dots while single planets are marked with solid gray dots. The four planets of EPIC~246471491's system are marked in different colors. Theoretical models for the planet's internal composition are taken from \citet{2016ApJ...819..127Z}. } \label{comparativa} \end{figure} We determined masses, radii, and densities for two of the four planets known to transit EPIC~246471491. We find that EPIC~246471491~b has a mass of $M_\mathrm{b}$\,=\,\mpb\, and a radius of $R_\mathrm{b}$\,=\,\rpb, yielding a mean density of $\rho_\mathrm{b}$\,=\,\denpb, while EPIC~246471491~c has a mass of $M_\mathrm{c}$\,=\,\mpc, radius of $R_\mathrm{c}$\,=\,\rpc, and a mean density of $\rho_\mathrm{c}$\,=\,\denpc. For EPIC~246471491~d and EPIC~246471491~e we are able to calculate upper limits for the masses at $6.5\,M_\oplus$ and $10.7\,M_\oplus$, respectively. \citet{Fulton17} and \citet{van2017} reported a bi-modal distribution in the radii of small planets at the boundary between super-Earths and sub-Neptunes. A clear distinction between two different families of planets is reported: on the one hand super-Earths have a radius distribution that peaks at $R_\mathrm{p}$\,$\sim$\,1.5\,$R_\oplus$, and on the other sub-Neptune planets have a radius distribution that peaks at $R_\mathrm{p}$\,$\sim$\,2.5\,$R_\oplus$. These two populations are separated by a gap in the radius distribution. Figure~\ref{comparativa} illustrates the mass-radius diagram of all known planets with precise mass determination, extending the full parameter space encompassing Earth-like, super-Earth and Neptune planets (1--4\,$R_\oplus$, 0.5--20\,$M_\oplus$). The four planets of the EPIC~246471491 system are also plotted. Two of the planets, b and d, fall in the sub-Neptune category, with radius very close to one of the peaks of the bi-modal distribution at 2.5 $R_\oplus$, while planet e belongs to the scarce population of planets located within the radius gap. Planet c is a larger object with only a slightly smaller radius and larger density than Neptune (3.9 vs. 3.5\,$R_\oplus$ and 1.64 vs. 1.95\,$\mathrm{g\,cm^{-3}}$; for Neptune and EPIC~246471491~c, respectively). Using the values in Table~\ref{planetparams}, the estimated transmission signals corresponding to H/He atmospheres (which would be the optimistic case for super-Earth size planets) of the four planets would be of 20, 32, 21 and 8\,ppm for planets b, c, d and e, respectively. For planets d and e the upper mass limit has been used for the calculations, so presumably the true signals would be larger. Still, with such relatively small atmospheric signatures, the planets are not optimal for transmission spectroscopy studies using current instrumentation due to the faintness of the parent star. However, as in the case of the triple transiting system {\it K2}-135 \citep{2017AJ....154..266N, jorge}, the four planets around EPIC~246471491 could provide a great test case to study comparative atmospheric escape and evolution within the same planetary system. From Figure~\ref{comparativa} it is readily seen that the two planets with well determined mass, have very different densities. Planet b has a bulk density close to pure water, while planet c is a much more inflated lower density planet. Assuming that all planets in the system were formed with similar composition, the different bulk densities could be explained by the factor 5 larger insolation flux received by planet b, compared to c, driving atmospheric escape and mass loss. While the masses of the other two planets are only upper limits, planet d (the third in distance from the star) clearly falls in the low density regime, which would be consistent with this hypothesis. For planet e, a larger range in densities is possible, from pure MgSiO$_3$ to extremely low densities. Thus, comparative studies focused on exosphere and atmospheric escape processes, through the detection of H$\alpha$, Ly$\alpha$, or He lines can be conducted for EPIC~246471491 with the next-generation of Extremely Large Telescopes (ELTs). | 18 | 8 | 1808.00575 |
1808 | 1808.09454_arXiv.txt | We extend the work of \protect\citet{Chang:2011aa} to find simple scaling relations between the density response of the gas disk of a spiral galaxy and the pericenter distance and mass ratio of a perturbing satellite. From the analysis of results from a test particle code, we obtained a simple scaling relation for the density response due to a single satellite interacting with a galactic disk, over a wide range of satellite masses and pericenter distances. We have also explored the effects of multiple satellites on the galactic disk, focusing on cases that are commonly found in cosmological simulations. Here, we use orbits for the satellites that are drawn from cosmological simulations. For these cases, we compare our approximate scaling relations to the density response generated by satellites, and find that for two satellite interactions, our scaling relations approximately recover the response of the galactic disk. We have also examined the observed H\,\textsc{i} data in the outskirts of several spiral galaxies from the THINGS sample and compared the observed perturbations to that of cosmological simulations and our own scaling relations. While small perturbations can be excited by satellites drawn from cosmological simulations, we find that large perturbations (such as those that are seen in some THINGS galaxies like M51) are not recovered by satellites drawn from cosmological simulations that are similar to Milky Way galaxies. | Spiral galaxies are surrounded by diffuse neutral hydrogen (H\,\textsc{i}) gas that extends far outside the stellar disk of galaxies \citep[e.g.][]{Walter:2008aa}. This extended H\,\textsc{i} gas disk is susceptible to perturbations from passing substructure due to its kinematically cold and diffuse nature. Furthermore, the location of the H\,\textsc{i} disk, far outside the optical disk, places it where theoretical models expect substructure to be \citep{Springel:2006aa} making it an ideal ``detector'' of substructure. Observations of the Milky Way have shown large perturbations well outside the optical disk of the Galaxy \citep{Levine:2006aa}, the strength and scale of which cannot be explained by differential rotation or propagating density waves induced by the stellar spiral arms \citep{Chakrabarti:2009aa}. In addition, many of the local galaxies observed by The H\,\textsc{i} Nearby Galaxy Survey \citep[THINGS;][]{Walter:2008aa} also display large perturbations in their gas disks. In the current structure formation paradigm of $\Lambda$CDM, large, Milky Way-sized spiral galaxies grow by the merger of smaller galaxies and are thus surrounded by hundreds of subhaloes. Initial surveys of the local dwarf galaxy population showed a large discrepancy between the number of observed and expected dwarf galaxies \citep{Klypin:1999aa,Moore:1999aa}. However, this problem has been alleviated somewhat due to a variety of feedback mechanisms which are thought to inhibit dwarf galaxy growth \citep[e.g.][]{Bullock:2000aa,Kravtsov:2004aa,Wise:2008aa} and by properly accounting for survey bias \citep{Simon:2007aa}. The analysis of perturbations in extended H\,\textsc{i} disks of galaxies may further alleviate this issue and provide constraints on the population of nearly dark subhaloes which reside on the outskirts of galaxies \citet{Chakrabarti:2009aa,Chakrabarti:2011aa}, \citet{Chakrabarti:2011ab}. The work done by \citet{Chakrabarti:2009aa,Chakrabarti:2011aa}, \citet{Chakrabarti:2011ab}, and \citet{Chang:2011aa} has shown that one can constrain the mass, current radial distance, and azimuth of a galactic satellite by finding the best-fit to the low-order Fourier modes of the projected gas surface density of an observed galaxy. By performing and searching a set of hydrodynamical simulations, a best-fit to the observed data can be obtained. This process is called the Tidal Analysis method \citep{Chakrabarti:2009aa, Chakrabarti:2011aa}. In \citet{Chakrabarti:2011ab} this process was applied to M51 and NGC 1512, both of which have known optical companions about $1/3$ and $1/100$ the mass of their hosts, respectively. The masses and relative positions of the satellites in both systems were accurately recovered using this analysis. Moreover, the fits to the data were found to be insensitive to reasonable variations in choice of initial conditions of the primary galaxy or orbital inclination and velocity of the satellite. The advantage of this method is that it can be used to find dark matter dominated satellites, as long as they are at least 0.1 per cent the mass of the primary. There are several methods for detecting the dark matter distribution within galaxies. One method is via gravitational lensing analysis that can constrain substructure within an individual galaxy lens \citep{Vegetti:2012aa}; however, single galaxy strong lenses are very rare systems. The analysis of stellar streams of tidal debris can yield information about past encounters of dwarf galaxies with the host as well as simultaneously provide a tracer of the gravitational potential over a wide range of radii \citep{Johnston:1999aa}; however, it is can only be used on very nearby galaxies where tidal streams can be mapped in three dimensions. Another method involves studying velocity asymmetries in the stellar disk which can provide evidence of past interactions \citep{Widrow:2012aa, Xu:2015aa}. Tidal Analysis has many advantages over these other methods. Firstly, it is not subject to uncertainties in the projected mass distribution like gravitational lensing. Unlike the other methods, Tidal Analysis is not restricted to the stellar disk which has a much smaller cross section for interactions and only the largest interactions can create disturbances. Instead, Tidal Analysis takes advantage of the large surface area covered by the H\,\textsc{i} gas that is easily disturbed by passing substructure. Tidal Analysis also provides an indirect detection method for dark matter dominated objects but it does not make any assumptions about the nature of the dark matter particle like gamma ray \citep{Strigari:2008aa, Hooper:2008aa} or direct detection experiments \citep[e.g.][]{Angle:2008aa, Bernabei:2008aa}. It has been shown that obtaining a H\,\textsc{i} map of a galaxy and searching a set of hydrodynamical simulations can allow observers to constrain substructure. The work of \citet{Chang:2011aa} found that a simple relation exists between the density response of the gas disk (specifically the low-order Fourier amplitudes of the projected surface gas density) and the mass of a perturbing satellite, \begin{equation} a_\text{t,eff}=0.5\left(\frac{m_\text{sat}}{M_\text{host}}\right)^{0.5}, \label{CC11_ateff} \end{equation} \noindent where $a_\text{t,eff}$ is the total effective amplitude of the projected gas surface density response, $m_\text{sat}$ is the mass of a perturbing satellite, and $M_\text{host}$ is the mass of the host galaxy. This type of relation is extremely useful as it gives a way of immediately obtaining useful knowledge of substructure without having to perform time-intensive hydrodynamical simulations. However, the above relation is only valid for interactions that occur when a satellite interacts with a halo at a specific pericenter distance (20 kpc). The purpose of this work is to extend the previous results of \citet{Chang:2011aa} to find simple scaling relations for the density response of the H\,\textsc{i} disk of a galaxy for any interaction that occurs at any pericenter distance. In Section 2 we describe the methods of our study. Here, we simulate satellite interactions with a disk that is initially in equilibrium and vary the pericenter approach distance, the mass ratio of the satellite to the host, and the inclination of approach for an impacting satellite. We then follow the evolution of the disk and record the total effective density response after the interaction has occurred. In Section 3, we present our results of both one satellite and two satellite interactions based on the most significant interactions seen in dark matter simulations. Disturbances in the H\,\textsc{i} gas disk dissipate on the order of a dynamical time or $\sim$1 Gyr \citep{Chakrabarti:2011ab}; however, interactions also occur about every $\lesssim$ 1 Gyr. Therefore, signatures of multiple previous encounters may still be present and it is important to study their effects. In Section 4, we discuss degeneracy in our results and compare our results with observations from THINGS and dark matter simulations. Finally, in Section 5, we conclude. | We have found a scaling relation between the projected gas surface density and mass and pericenter of passing substructure (Eqn. \ref{a_eff_scaling}). We have also examined the effects of multiple perturbers on our results and in particular have studied cases that are common in cosmological simulations which include interactions that occur at the same azimuthal location but are delayed, mirrored interactions, and interactions that occur with a secondary lower mass companion. Since the observed density response in the gas disk from each interaction adds in quadrature, only equal mass satellites make substantial contributions to the total effective response seen (Eqn. \ref{a_eff_scaling_multi}). We applied our scaling relations to galaxies that have already been mapped in H\,\textsc{i} \citep[THINGS,][]{Walter:2008aa} to show the range of satellite masses and pericenter distances that may be expected. We also ranked the cosmological simulations analyzed here in terms of the effective tidal force and compared their Fourier amplitudes with observational data. Interestingly, massive perturbers (as are required for galaxies like M51 that show large disturbances in the outskirts) are not reproduced by sampling satellites from the high resolution cosmological simulations that we studied, although galaxies with low disturbances in the outskirts may be explained by cosmological simulations. Scaling relations are used in many situations in order to gain information of a quantity which is otherwise difficult to obtain or unobservable. In this way, Tidal Analysis allows one to observe the presence of substructure without the necessity of resolving the substructure itself and, in fact, the substructure need not contain baryonic matter since we directly observe its impact on the H\,\textsc{i} disk of the larger galaxy. A direct benefit of the analysis presented here is that one my apply these scaling relations to obtain an initial characterization of the substructure in a galaxy without the need to perform a computationally expensive suite of hydrodynamical simulations. Instead, these relations allow a more directed approach so that only a subset of hydrodynamic simulations are necessary. | 18 | 8 | 1808.09454 |
1808 | 1808.07480_arXiv.txt | We present structural parameters and morphological properties of faint 450-$\mu$m selected submillimeter galaxies (SMGs) from the JCMT Large Program, STUDIES, in the COSMOS-CANDELS region. Their properties are compared to an 850$\mu$m selected and a matched star-forming samples. We investigate stellar structures of 169 faint 450-$\mu$m sources ($S_{\rm 450}=2.8$--29.6~mJy; S/N$>4$) at $z<3$ using \emph{HST} near-infrared observations. Based on our spectral energy distribution fitting, half of such faint SMGs ($L_{\rm IR}=10^{11.65\pm0.98}~{\rm L_\odot}$) lie above the star-formation rate (SFR)/stellar mass plane. The size-mass relation shows that these SMGs are generally similar to less-luminous star-forming galaxies selected by ${\rm NUV}-r$ vs. $r-J$ colors. Because of the intrinsic luminosity of the sample, their rest-frame optical emission is less extended than the 850$\mu$m sources ($S_{\rm 850}>2$~mJy), and more extended than the star-forming galaxies in the same redshift range. For the stellar mass and SFR matched sample at $z\simeq1$ and $z\simeq2$, the size differences are marginal between faint SMGs and the matched galaxies. Moreover, faint SMGs have similar S\'ersic indices and projected axis ratios as star-forming galaxies with the same stellar mass and SFR. Both SMGs and the matched galaxies show high fractions ($\sim$70\%) of disturbed features at $z\simeq2$, and the fractions depend on the SFRs. These suggest that their star formation activity is related to galaxy merging, and the stellar structures of SMGs are similar to those of star-forming galaxies. We show that the depths of submillimeter surveys are approaching the lower luminosity end of star-forming galaxies, allowing us to detect galaxies on the main sequence. | \label{sec1} The population known as ``Submillimeter galaxies'' (SMGs) was first discovered using the Submillimeter Common User Bolometer Array \citep[SCUBA]{1999MNRAS.303..659H} on the James Clerk Maxwell Telescope (JCMT) in the late 1990s in deep 850-$\mu$m images \citep{1997ApJ...490L...5S,1998Natur.394..248B,1998Natur.394..241H}. SMGs are understood to be a population of dusty starburst galaxies undergoing rapid stellar mass growth and thus they play an important role in our understanding of galaxy evolution and formation (see reviews by \citet{2002PhR...369..111B} and \citet{2014PhR...541...45C}). SMGs represents sources of the most luminous galaxies \citep[$L_{\rm IR}\gtrsim10^{12}{\rm L_\odot}$; e.g., ][]{2012A&A...539A.155M,2014MNRAS.438.1267S} at high redshifts \citep[$z\gtrsim2$; e.g., ][]{2005ApJ...622..772C,2014ApJ...788..125S}. Their high luminosities are akin to local ultra-luminous infrared galaxies \citep[ULIRGs, see the review by][]{1996ARA&A..34..749S}, which are almost invariably mergers. All studies of local ULIRGS morphologies converge on a very high merger fraction \citep{1996MNRAS.279..477C,2000ApJ...529..170S,2001MNRAS.326.1333F,2002ApJS..143..315V}, according to their morphology in the optical and near-infrared (NIR). However, theoretical models provide different formation routes for SMGs. They can be major mergers with significant starbursts, similar to local ULIRGs \citep[e.g.,][]{2010MNRAS.401.1613N}; a heterogeneous population of merger-driven starbursts and secularly evolving disk galaxies \citep[e.g.,][]{2011ApJ...743..159H}; or simply represent the most massive star-forming galaxy population at high redshift \citep[e.g., ][]{2005MNRAS.363....2K,2010MNRAS.404.1355D,2015Natur.525..496N}. Moreover, \citet{2016MNRAS.462.3854L} suggested that SMGs are predominately disc-instability triggered starbursts. Additionally, using large-scale simulations, \citet{2015MNRAS.446.1784C} found that SMGs detected in single-dish surveys can be chance superpositions of starbursting galaxies of very different redshifts along the same line of sight \citep[see also ][]{2013MNRAS.434.2572H,2015MNRAS.446.2291M}. Therefore, it is important to investigate structures and morphologies of SMGs in large submillimeter surveys to verify these different possibilities. At high redshift, morphologies of IR-luminous galaxies \citep[e.g.,][]{2009AJ....137.4854M,2010MNRAS.406..230R,2011ApJ...733...21B,2011ApJ...730..125Z,2012ApJ...757...23K,2012MNRAS.424.2232A,2012MNRAS.425.1320I,2013ApJ...768..164A,2016ApJ...827...57O,2017ApJ...844..106F} and massive galaxies \citep[e.g.,][]{2008ApJ...687L..61B} have been investigated. Thanks to the high-resolution imaging available with the Hubble Space Telescope (\emph{HST}), the stellar structure of SMGs has been investigated. \citet{2005MNRAS.358..149P} used \emph{HST}/Advanced Camera for Surveys (ACS) images to find larger sizes and a higher degree of asymmetry for 40 850 $\mu$m selected SMG. \citet{2010MNRAS.405..234S} analyzed the \emph{HST} $F160W$-band images of 25 radio-identified SMGs ($S_{\rm 850}=3$--15 mJy) at $0.7<z<3.4$ from the \citet{2005ApJ...622..772C} survey, and found that the half-light radii of the SMGs and their asymmetries are not statistically distinct from a comparison sample of star-forming galaxies at similar redshifts. However, the intermediate S\'ersic indices ($n\simeq2$) suggest that the stellar structure of SMGs is best described by a spheroid/elliptical galaxy light distribution. \citet{2011MNRAS.413...80C} used $F160W$-band images to study massive galaxies ($M_*>10^{11}{\rm M_\odot}$) at $1.7<z<2.9$, including galaxies detected in the submillimeter, finding that there is a gradual increase in size toward lower redshifts. \citet{2013MNRAS.432.2012T} used the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS, \citealp{2011ApJS..197...35G,2011ApJS..197...36K}) $F160W$-band imaging to study 24 1.1mm and 870$\mu$m sources ($S_{\rm 870\,\mu m}=1.7$--9.1 mJy) at $1<z<3$. They found that almost all the (sub-) millimeter galaxies are well described by either a single exponential disk ($n\simeq1$), or a multiple-component system in which the dominant constituent is disk like. The extended structures are consistent with the sizes of other massive star-forming disks at $z\simeq2$. \citet{2014ApJ...782...68T} showed that $3<z<6$ SMGs are consistent with being the progenitors of $z=2$ quiescent galaxies, based on their size distributions and other properties. More recently, observations with the Atacama Large Millimeter/submillimeter Array (ALMA) help to refine the counterpart identification of single-dish samples. \citet{2015ApJ...799..194C} analyzed \emph{HST} $F160W$-band imaging of 48 ALMA detected SMGs at $1<z<3$. They found that 82\% of them appear to have disturbed morphologies, meaning that they are visually classified as either irregulars or interacting systems. They also found significant differences in the sizes and the S\'ersic indices between $2<z<3$ SMGs and $z\simeq2$ quiescent galaxies, and postulated that the majority of the $2<z<3$ SMGs with $S_{\rm 870}\gtrsim2$ mJy are early/mid-stage major mergers \citep[also see][]{2014ApJ...785..111W}. Despite all the above studies, there does not seem to be a converging picture of whether SMGs are triggered by disc instability or mergers. This might be caused by the differences in sample selections, redshift ranges, or methods of analysis. Furthermore, the previous studies focused on single-dish 850 $\mu$m or 1.1 mm selected SMGs, with typical fluxes of $S_{\rm 850} \gtrsim 2$ mJy, roughly corresponding to $L_{\rm IR}\gtrsim10^{12.3}{\rm L_\odot}$ (dust temperature $T_d\simeq30$K). It is thus still difficult to study the variations as a function of star-formation rates (SFRs) from ULIRGs, luminous infrared galaxies (LIRGs), to normal star-forming galaxies that have $L_{\rm IR}<10^{12}{\rm L_\odot}$. The JCMT SCUBA-2 instrument \citep{2013MNRAS.430.2513H} enables 450-$\mu$m surveys that probe deeper (rms $\simeq$ 0.7 mJy; $L_{\rm IR} \simeq 5 \times 10^{11}{\rm L_\odot}$) than the 850-$\mu$m samples because of the roughly two times higher angular resolution (FWHM $\simeq$ 7$\arcsec$) and therefore lower confusion limit. Observations with SCUBA-2 at 450 $\mu$m can thus provide direct detections of fainter sources, and less ambiguous multi-wavelength counterpart identification. \citet{2013ApJ...762...81C,2013ApJ...776..131C} and \citet{2016ApJ...829...25H} carried out SCUBA-2 450 $\mu$m surveys in various blank fields and lensing cluster fields to detect 450 $\mu$m SMGs sources at $S_{\rm 450}=$1-10 mJy. The SCUBA-2 Cosmology Legacy Survey \citep[S2CLS,][]{2013MNRAS.432...53G,2017MNRAS.465.1789G} and \citet{2013MNRAS.436.1919C} conducted deep 450-$\mu$m imaging in the center of the Cosmic Evolution Survey \citep[COSMOS]{2007ApJS..172....1S} field and various other fields. \citet{2013MNRAS.436..430R} cross-identified 58 450-$\mu$m selected sources from the S2CLS sample \citep[$\sigma_{\rm 450}$= 1.5 mJy,][]{2013MNRAS.432...53G} with \emph{Spitzer} and \emph{HST}/WFC3 data. They showed a correlation between emissivity index $\beta$ and both stellar mass and effective radius. However, the depth was not sufficient to investigate faint SMGs, in the regime of more normal star-forming galaxies. \citet{2018MNRAS.475.5585Z} presented 64 sources ($\sigma_{\rm 450}\simeq$1.9 mJy; $ L_{\rm IR} \simeq 1.5 \times 10^{12} {\rm L_\odot}$ at $z<4$) of the S2CLS sample in the Extended Groth Strip field. They found that the dominant component for most of the galaxies at all redshifts is a disk-like structure (a median S\'ersic index $n\simeq1.4$ and half-light radius ${\rm r}_e\simeq4.8$kpc) by using the \emph{HST} $F160W$-band imaging. They also showed a transition from irregular disks to disks with a spheroidal component at $z\simeq$1.4 and suggested that SMGs are progenitors of massive elliptical galaxies. To further expand the 450 $\mu$m sample and to push to fainter depth ($\sigma_{\rm 450}\simeq$0.7 mJy) and lower luminosity ($L_{\rm IR} \simeq 5 \times 10^{11}{\rm L_\odot}$), our team recently started a new program, the SCUBA-2 Ultra Deep Imaging EAO (East-Asian Observatory) Survey \citep[STUDIES,][]{2017ApJ...850...37W}. STUDIES targets the center of the COSMOS field where there are CANDELS NIR data ideal for a morphological study. We combine all the SCUBA-2 data in the COSMOS-CANDELS region to reach a detection limit of $S_{\rm 450} \simeq 3$ mJy ($\sigma_{\rm 450}\simeq$0.7 mJy). Moreover, the 450 $\mu$m selection does not just enable finding fainter samples. Both the 450 $\mu$m and the parallel deep 850 $\mu$m observations ($\sigma_{\rm 850}\simeq0.12$ mJy) help to constrain the shape of the spectral energy distribution (SED). Our faint SMG sample therefore probes luminosities of approximately $L_{\rm IR} > 2$--$5 \times 10^{11} {\rm L_\odot}$ at $z=1$--2, corresponding to SFRs of $>40$--80 ${\rm {\rm M_\odot}}$ yr$^{-1}$, assuming the standard \citet{1998ApJ...498..541K} relation, overlapping with that of optically selected normal star-forming galaxies. Therefore, we will be able to compare cool dusty galaxies to unobscured starbursts with similar redshifts, SFRs, and stellar masses. The \emph{HST} NIR imaging across the STUDIES region enables us to investigate the stellar structures and morphological properties of these faint 450-$\mu$m sources. In this paper, we present morphological results based on structural analysis and visual classification for faint SMGs (450-$\mu$m sources) detected by STUDIES, as well as for a control sample matched to the STUDIES-SMGs. The structure of this paper is as follows. We describe the data, catalog matching, and SED fitting in Section \ref{sec2}. We analyze the physical and structural properties in Section \ref{sec3}. We discuss the implications in Section \ref{sec4} and summarize in Section \ref{sec5}. We use AB magnitudes thrughout, adopt the cosmological parameters ($\Omega_{\rm M}$,$\Omega_\Lambda$,$h$)=(0.30,0.70,0.70), and assume the stellar initial mass function of \citet{2003PASP..115..763C}. \begin{figure*} \centering \includegraphics[width=0.85\textwidth]{studies_reg.pdf} \caption{STUDIES 450-$\mu$m flux map which provides coverage over $\simeq$700 arcmin$^2$ centered at R.A.$=$10:00:22.26, decl.$=$+02:24:05.06. We show our sample selection of 450-$\mu$m sources (red circles with 10$\arcsec$ in radii, S/N $>$ 4, $S_{\rm 450}>2$mJy) and 850-$\mu$m sources (green circles with 15$\arcsec$ in radii, S/N $>$ 6, $S_{\rm 850}>2$mJy) from the machine-learning method, 850-$\mu$m sources (green box, S/N $>$ 6, $S_{\rm 850}>2$mJy) from the cross-matched method, along with the comparison sample (blue circles with 5$\arcsec$ in radii, $M_*>10^{10} {\rm M_\odot}$, ${\rm NUV}-r$ vs. $r-J$ selection). We consider star-forming galaxies inside the STUDIES coverage as the comparison sample. The yellow region shows the CANDELS footprint.} \label{studies_region} \end{figure*} \begin{figure} \centering \includegraphics[width=0.95\columnwidth]{studies_id} \caption{Offsets of the coordinates between the SMG sources and their counterparts: VLA vs. 450 $\mu$m, 24 $\mu$m vs. 450 $\mu$m, 450 $\mu$m vs. 850 $\mu$m, and VLA vs. 850 $\mu$m. The circles are search radii of $4\arcsec$, $7\arcsec$, and $8\arcsec$. } \label{studies_id} \end{figure} \begin{figure} \centering \includegraphics[width=0.95\columnwidth]{studies_zlir} \caption{Photometric redshift to infrared luminosity plot for 450-$\mu$m sources identified by VLA and 24 $\mu$m position (red circles and blue triangles), as well as VLA and 24 $\mu$m detections (red and blue points, which are not 450-$\mu$m detections). The infrared luminosity is derived by MAGPHYS (see \S~\ref{sec2_4} for more details).} \label{studies_zlir} \end{figure} \begin{figure*} \centering \includegraphics[width=0.9\textwidth]{studies_sed655219} \includegraphics[width=0.9\textwidth]{studies_sed797093} \caption{Two typical SED fitting examples for 450-$\mu$m detected sources. The red points are the photometry and the red arrows are the upper limit of the photometry. The black lines show the best-fitting template. The orange circles label the JCMT detections. The upper example has both 450-$\mu$m and 850-$\mu$m detection, and the lower example has only 450-$\mu$m detection. The residuals and histograms of the physical parameters (stellar mass, SFR, sSFR, and infrared luminosity) are shown in the lower panels. In the histograms, the dashed lines are the median values.} \label{studies_sed} \end{figure*} | \label{sec4} \subsection{How do SMGs compare with normal galaxies in the star-forming sequence?} \label{sec4_1} According to our stellar mass and SFR estimation, most of the SMGs are on or slightly above the star-forming sequence as shown in Figure\,~\ref{studies_ms}. Despite a decade of observational study, the location of the most luminous, 850-$\mu$m selected SMGs relative to the star-forming main sequence remains hotly debated. Indeed, various studies into the properties of luminous SMGs have concluded that these systems either represent starburst galaxies, which lie significantly above the main sequence \citep[e.g.,][]{2015ApJ...806..110D,2017ApJ...840...78D}, or, conversely, that they are simply represent the massive `tip’ of the known main sequence \citep{2016MNRAS.458.4321K,2017MNRAS.469..492M}. The reason for these discrepant results can typically be traced to systematic uncertainties on the measurement of stellar mass, which is strongly affected by different assumptions on the star formation history \citep{2011ApJ...740...96H,2012A&A...541A..85M,2014A&A...571A..75M}. STUDIES allows us to extend such studies to a sample of faint 450-$\mu$m sources. In Table~\ref{tab_1}, the stellar masses and SFRs of the STUDIES 450-$\mu$m sources are lower than those of 850-$\mu$m sources at $z<2.5$. The main reason is that the SED peak of typical z$\sim$2 SMGs is around 200-400 $\mu$m, and 450-$\mu$m observations can detect less luminous SMGs compared to 850-$\mu$m observations. However, 450-$\mu$m detected galaxies still have higher stellar mass and SFRs than normal star-forming galaxies. Can our result that SMGs lie slightly above the star-forming sequence a consequence of overestimated SFRs? \emph{Herschel} observations may overestimate FIR fluxes (and hence SFRs) of dusty galaxies due to source clustering \citep{2010MNRAS.409...75H,2017ApJ...850...37W} within coarse resolution (15-35$\arcsec$ FWHM) of SPIRE imaging at 250-500 $\mu$m. Attempt to correct for this flux bias requires either a complete set of prior positions for deblending \citep[e.g.,][]{2014MNRAS.438.1267S}, or assumptions for the properties of the underlying population \citep[e.g.,][]{2012A&A...542A..58B,2016MNRAS.457.4179H}. To test this, we conducted SED fitting by using only SPIRE (optical+\emph{Spitzer}+PACS+SPIRE) and only SCUBA-2 (optical+\emph{Spitzer}+PACS+SCUBA-2) data in the FIR bands. The resulting mean SFR offset is $4\%$ with a scatter of $9\%$ for SPIRE-detected sources (S/N $>3$ at 250 $\mu$m, 350 $\mu$m, or 500 $\mu$m). The difference is relatively small because MAGPHYS estimates SFRs by considering photometry from UV to FIR wavelengths. The overestimation can be larger if SFRs are derived monochromatically from SPIRE and SCUBA-2 fluxes. In order to avoid such a bias in the SED fitting of our comparison sample, we also considered the upper limits at 450 $\mu$m for them. On the other hand, because \emph{Herschel} fluxes are included in their SED fitting and the SCBUA-2 450 $\mu$m photometry is not deep enough for most of them, it is still possible that their SFRs are overestimated in Figure\,~\ref{studies_ms}. However, this scenario would further strengthen our finding that the SMGs from our deep 450 $\mu$m survey can be on or slightly above the star-forming galaxies on the SFR-$M_*$ plane. We find that 450-$\mu$m selected SMGs ($S_{\rm 450}=2.8$--29.6~mJy; S/N$>4$ at $z<3$) are on or slightly above the star-forming sequence. This result seems robust against potential biases in the estimations of the SFR of our SMG and comparison samples. It is commonly assumed that galaxies above the sequence are undergoing merger-induced starbursts. However, \citet{2017MNRAS.467.1231C} show that dynamically-triggered star formation (e.g. merger/disc-instability) does not necessarily segregate galaxies on the SFR-$M_*$ plane, which may also help to explain the half-on half-off results on the star-forming sequence. Hence even for the SMGs on the star-forming sequence, there may be additional dynamical processes occurring, such as merging. Therefore in the next subsection, we will turn our focus to the stellar structure of SMGs and look for evidence of merging and interaction. We examined the source density and SFR density per comoving volume for $z=1$--3. Above 200 $M_{\odot}$~yr$^{-1}$, the SMG sample dominates over the normal galaxy sample in terms of both source density and SFR density, but the sample sizes are small for both samples. When we go down to $>100 M_{\odot}$~yr$^{-1}$, the normal galaxy sample becomes roughly twice larger than the SMG sample, but their integrated SFR densities are comparable. Below $100 M_{\odot}$~yr$^{-1}$, the normal galaxy sample strongly dominates in both the source density and SFR density. It is now clear that once we probe down to SFR of $\sim100$ $M_{\odot}$~yr$^{-1}$, we see both obscured galaxies (appearing as SMGs) and unobscured galaxies (appearing in the optical sample). Above this limit, SMGs are dominant, and below this, normal galaxies are dominant. Therefore, from the points of view of morphology (the topic of this paper), SED (obscured vs. unobscured star formation as tested with stacking analyses), and comoving SFR density, we see that as we go deeper in the submillimeter, we start to enter the regime where normal galaxies play more important roles, or dusty galaxies become less important. This is also in concordance with our 450 $\mu$m counts \citep{2017ApJ...850...37W}, which suggest that we can fully account for the 450 $\mu$m background once we can detect faint sources of roughly 0.5--0.8 mJy. As we further deepen and widen our 450 $\mu$m map, we will publish better constrained faint-end counts at 450 $\mu$m. We also defer a complete SED analyses of 450 $\mu$m sources versus normal galaxies to a future paper. All these should help to better understand how ultra luminous dusty galaxies are connected to normal star-forming galaxies and their relative contribution to the cosmic star formation history. \subsection{Structures of Dusty Galaxies} \label{sec4_2} The stellar mass to size relation in Figure\,~\ref{studies_mr} shows that the sizes of SMGs are similar to those of star-forming galaxies, rather than passive galaxies. In general, 850-$\mu$m sources are more extended (larger and flatter) than the 450-$\mu$m sources, and 450-$\mu$m sources are more extended than normal star-forming galaxies. The larger spatial extent of the 850-$\mu$m sources can be understood through their higher luminosities and stellar masses. Extended stellar structures were also found in previous SMG studies \citep[e.g.,][]{2000ApJ...528..612S,2010MNRAS.405..234S,2013MNRAS.432.2012T,2015ApJ...799..194C}. The slight difference in size might be explained if the ${\rm NUV}-r$ vs. $r-J$ selections of the star-forming sample are contaminated by passive galaxies. However, such contamination can be removed using the SFR estimated from our SED fitting. After matching the stellar mass and SFR, we still find a small difference in size between our SMGs and the comparison sample at $z\sim2$ as discussed in \S~\ref{sec3_2}. A plausible explanation for the mild size difference is dust extinction. Recent high-resolution ALMA imaging shows that dust continuum emission from SMGs and massive star forming galaxies is quite compact, compared to their NIR stellar continuum emission \citep[e.g.,][]{2015ApJ...810..133I,2015ApJ...807..128S,2016ApJ...829L..10I, 2016ApJ...833..103H,2017ApJ...841L..25T}. Even if SMGs and normal star-forming galaxies are comparable in the sizes of their stellar components, the highly extincted cores caused by the compact dust components could bias the measured effective radii outward. More sophisticated analyses are clearly required to further investigate this possibility, including spatially resolved SED fitting for dust extinction and stellar mass, and high-resolution ALMA imaging for low SFR galaxies, as well as multi-wavelength image simulations. Such studies may explain the lack of obvious difference in S\'ersic index and projected axis ratio between SMGs and the matched sample (as shown in Figure\,~\ref{studies_qn}). Figure\,~\ref{studies_morph} shows that most SMGs (around 70\%) contain irregular/merger features. We find that the irregular/merger fraction is positively correlated with the SFR (Figure\,~\ref{studies_morph_sfr}). Moreover, the comparison sample, which is plausibly less obscured, behaves identically to the submillimeter selected sample. Given the high SFRs of 850-$\mu$m sources (as shown in \S~\ref{sec3_1}), it is thus natural to see them having the highest disturbed feature fraction in Figure\,~\ref{studies_morph}. This is consistent with previous morphological studies of submillimeter samples \citep[e.g.,][]{2003ApJ...596L...5C,2003ApJ...599...92C,2010MNRAS.405..234S,2014ApJ...785..111W, 2015ApJ...799..194C}. The dependence on sSFR is consistent with that of \citet{2013ApJ...778..129H}, who showed that the fraction of interacting merger systems increases with the deviation from star-forming sequence. Moreover, \citet{2011A&A...535A..60H} also demonstrated that galaxy-galaxy interactions and mergers have been strongly affecting SFRs by using \emph{Herschel} data. Unlike the result for the SFR, we see slightly different behaviors of the irregular/merger fractions with sSFR between the SMGs and the matched sample. The disturbed feature fraction of SMGs seems to be higher than a sSFR- matched sample, as shown in the right panels of Figures~\ref{studies_morph} and \ref{studies_morph_sfr}. What this implies is that for galaxies of the same sSFR, those in merging/disturbed systems tend to be more luminous at 450-$\mu$m or 850-$\mu$m, while the undisturbed ones tend to have lower dust obscuration. A naive explanation is that merging systems tend to have more compact star-forming regions in their cores (as revealed in many recent ALMA observations), while undisturbed systems tend to have disk-wide star formation. The small spatial extent of dusty star-forming regions in the merging/disturbed systems then lead to stronger extinction in the UV and thus stronger dust re-radiation in the FIR and submillimeter. This scenario again remains to be tested with more observations and simulations. We also caution that the differences in irregular/merger fractions are far from huge (72$_{-10}^{+7}$\%, 67$_{-7}^{+6}$\%, 57$_{-18}^{+15}$\% for 850-$\mu$m sources, 450-$\mu$m sources, and sSFR matched star-forming galaxies, respectively), and are statistically insignificant, indicating that even if merging events play a role in triggering SMGs among galaxies with the same sSFR, they are probably not the only factor \citep{2011ApJ...743..159H}. As well as having the high SFRs and sSFRs, SMGs also have globally low dust temperature and high attenuation (according to our SED fitting, see also \citealt{2012A&A...539A.155M}). Therefore, we checked dependence of the frequency of merger related features on dust temperature and attenuation. We found that the Pearson correlation coefficients are not high (0.05 for dust temperature and 0.11 for attenuation), as opposed to the value for SFR versus disturbed feature fraction ($>0.96$). Most SMGs do have disturbed features, but the disturbed feature fraction mainly depends on the SFR . This suggests that galaxy merging takes place in bright galaxies with high SFRs and can be related to star formation activity. According to our structural and morphological analyses, dusty galaxies are very similar to star-forming galaxies in the rest-frame optical bands. Recently, several SMGs were imaged at high resolution by ALMA and the results appear to be mixed. Some of them show clumpy and extended structures \citep[i.e., disk-like, e.g.,][]{2016ApJ...829L..10I}, while others show starbursts in compact regions \citep[e.g.,][]{2017ApJ...837..182O,2017ApJ...850...83F} or irregular morphologies \citep[e.g.,][]{2017A&A...606A..17M}. These results show a great variation in the structure of dusty emitting regions in SMGs, and future observations are required to quantify the prevalence of different morphologies in a thorough manner. Moreover, recent findings show that the stellar morphologies of luminous SMGs appear significantly more extended and disturbed than their ALMA dust images at $z\sim2.5$ \citep{2016ApJ...833..103H,2017ApJ...846..108C}. Given these diverse results, it is clear that further investigations of the dust and stellar morphologies of SMGs are necessary. To summarize, we have found that faint SMGs selected with deep 450-$\mu$m observations have stellar structures similar to those of less luminous star-forming galaxies in the optical sample in terms of S\'ersic index, projected axis ratio, and fraction of galaxies with perturbed features. The 450-$\mu$m sources are slightly more extended than normal star-forming galaxies and also lie on or slightly above the star-forming sequence, but these small differences might be a consequence of various selection effects or dust extinction. There is less similarity between the normal star-forming galaxies and the more luminous 850-$\mu$m selected SMGs, in terms of sizes of the stellar distribution. These results show that as our submillimeter surveys approach the lower luminosity end ($<10^{12}{\rm L_\odot}$), we start to detect normal galaxies on the main sequence statistically. | 18 | 8 | 1808.07480 |
1808 | 1808.06023_arXiv.txt | A circumbinary disc around a pair of merging stellar--mass black holes may be shocked and heated during the recoil of the merged hole, causing a near-simultaneous electromagnetic counterpart to the gravitational wave event. The shocks occur around the recoil radius, where the disc orbital velocity is equal to the recoil velocity. The amount of mass present near this radius at the time of the merger is critical in determining how much radiation is released. We explore the evolution of a circumbinary disc in two limits. First, we consider an accretion disc that feels no torque from the binary. The disc does not survive until the merger unless there is a dead zone, a region of low turbulence. Even with the dead zone, the surface density in this case may be small. Second, we consider a disc that feels a strong binary torque that prevents accretion on to the binary. In this case there is significantly more mass in regions of interest at the time of the merger. A dead zone in this disc increases the mass close to the recoil radius. For typical binary-disc parameters we expect accretion to be significantly slowed by the resonant torque from the binary, and for a dead zone to be present. We conclude that provided significant mass orbits the binary after the formation of the black hole binary and that the radiation produced in recoil shocks can escape the flow efficiently, there is likely to be an observable electromagnetic signal from black hole binary mergers. | \label{intro} The direct detection of gravitational waves (GW) from binary black hole mergers has naturally raised the question of whether there could be a corresponding electromagnetic (EM) signal. Recently \cite{deMink2017} suggested that the gravitational effect of a BH + BH merger on a circumbinary disc might lead to an EM signal delayed by the light--travel time from the merging binary to this disc \citep[see also][where this effect is applied to mergers of supermassive black holes]{Rossietal2010}. Given the lack of simultaneity, identifying this latter signal would require spatial coincidence, and so positional information from several GW detectors. This should be available as new detectors become operational. At least two detailed binary evolution scenarios, the classical common--envelope and chemically homogeneous pictures, show how a massive binary can remain bound as it evolves to a BH + BH binary (see the discussion in de Mink \& King 2017, Section 2, and references therein). In both cases the two stars shed large fractions of their original masses. Unless all of this mass is expelled to infinity, or somehow completely re--accreted by the black holes, a residual circumbinary disc must remain, as the only stable configuration for the shed mass. In this paper we consider the evolution of this circumbinary disc around a merging black hole binary. Specifically, we are interested in whether there is sufficient material in the disc at the time of the merger for an electromagnetic signal to be generated by the perturbation from the gravitational wave recoil and the sudden drop in mass of the binary. The circularisation radius of material falling back after a supernova explosion is very small \citep{Perna2014, Perna2016}. This suggests that the angular momentum of the ejected material is small in the frame of the star. Thus the material is ejected with a velocity equal to that of the mass losing star plus a velocity radial from the mass losing star with magnitude $v_{\rm eject}$. For ejection velocities greater than the escape velocity from the binary, $v_{\rm eject} > v_{\rm esc}$, the material is lost. For $v_{\rm eject} \ll v_1$, where $v_1$ is the orbital velocity of the mass--losing star, the material does not escape the Roche-Lobe of the star. For $v_{\rm eject} \sim v_1$ the material has a spread of angular momentum around the angular momentum of the mass--losing star: the material at the back of the star has less, and the material at the front of the star has more. Thus we expect approximately half of the ejected material to have a velocity such that it ends up in a circumbinary configuration with a spread of angular momenta and thus circularisation radii. Whether the material circularises, or passes within the binary and cancels angular momentum with gas on similar but opposed orbits, to circularise at smaller radii, requires more detailed numerical simulations than we attempt here. The angular momentum of the material forming the circumbinary disc may not necessarily be initially aligned to the binary angular momentum. For a circular black hole binary, differential precession driven by the binary torque combined with viscous dissipation causes the disc to move towards alignment or counter--alignment with the binary depending only on the initial inclination \citep[e.g.][]{Kingetal2005,Nixonetal2011b,Foucart2013,Foucart2014}. As the disc angular momentum is usually significantly smaller than the binary angular momentum \citep{Nixon2012}, the alignment or counteralignment condition is straightforward: if the disc begins closer to alignment, it aligns, and if it begins closer to counteralignment it counteraligns. How this alignment proceeds depends upon properties of the disc. \cite{PP1983} showed that the propagation of warps occurs in two distinct ways, the dominant mechanism determined by the relative magnitudes of the disc viscosity and pressure. If the \cite{SS1973} viscosity parameter is less than the disc aspect ratio, $\alpha<H/R$, then the warp propagates through waves, otherwise the warp evolves diffusively \citep[see][for a review of warped disc physics]{Nixon2016}. Since the disc aspect ratio of circumbinary discs around black holes is likely to be small, the inner parts of the disc are likely to be aligned (or counteraligned) while the outer parts of the disc may be strongly warped. The strength of the tidal torque from the binary on the inner parts of the disc depends upon the inclination of the angular momentum of the material, being strongest when it is aligned to the binary angular momentum \citep[e.g.][]{Lubowetal2015,Miranda2015}. For a retrograde circumbinary disc around a circular binary the tidal torque from Lindblad resonances is zero \citep{Nixonetal2011a}. \cite{Nixon2015} showed that resonances do occur in retrograde circumbinary discs around eccentric binaries, but that they are weak enough that they only modulate the accretion flow on to the binary rather than providing a torque of sufficient strength to arrest accretion. The accretion rate from the inner edge of the circumbinary disc on to the components of a binary depends upon the strength of the tidal torque and properties of the disc. This has received significant attention as it impacts a variety of astrophysical systems \citep[e.g.][]{Artymowicz1994, Artymowicz1996,Roedig2012,Shi2012,DOrazio2013,Farris2014}. The gas is subject to two competing torques. The binary transfers angular momentum to the gas, causing the inner disc to move outwards, and viscosity redistributes that angular momentum to larger radii in the disc, allowing the inner disc to shrink. Thus discs subject to a weak torque (or strong viscosity) can move in and accrete on to the binary components. In contrast a strong torque (or weak viscosity) leads to the disc being held out. For the small disc aspect ratio expected in black hole binaries, the accretion rate is significantly suppressed \citep{Ragusa2016}. If the tidal torque is sufficiently strong, accretion on to the binary may be completely halted. Disc solutions in this case correspond to {\it decretion} discs \citep{Pringle1991} rather than traditional {\it accretion} discs in which material flows freely through the inner boundary \citep{Pringle1981}. In Section~\ref{em} we first consider how much material is required in a circumbinary disc for an observable electromagnetic signal to be generated. In the rest of this work, we then estimate how much material is present in an evolving circumbinary disc. Because of the uncertainties in the strength of the tidal torque and the resulting accretion flow on to the binary, we consider two extreme limits. In Section~\ref{full} we consider the disc evolution in the case that the binary provides no torque on the disc and material freely flows inwards and is accreted on to the binary components. The disc is a traditional accretion disc. In Section~\ref{zero} we examine the case where the binary torque is strong enough to prevent all flow on to the binary. We draw our conclusions in Section~\ref{conc}. | \label{conc} We have explored the evolution of a circumbinary disc around a merging black hole system in the two extreme limits of an accretion disc and a decretion disc. The accretion disc feels no torque from the binary. The viscous timescale of such a disc is short and it is unlikely that significant circumbinary material remains at the time of the merger unless there is a dead zone in the disc. The dead zone restricts the accretion flow through the disc and the disc life time is significantly extended. However, the surface density of the disc around the recoil radius is low, unless the dead zone extends into this region. In the opposite limit, where a strong binary torque prevents accretion, the disc behaves as a decretion disc. The surface density at the recoil radius is much larger than in the accretion disc, even without a dead zone. The physical conditions in a disc around a BH--BH binary probably conform to the case of a decretion disc, held out by tidal torques from the binary, and containing dead zones. As we have seen, there is significant mass close to the recoil radius in this case. We conclude that dynamical readjustment of the disc after the BH merger is likely to release significant energy in electromagnetic form. Since all of the disc matter, including its outer skin, is shocked simultaneously, it appears unlikely that this energy is significantly trapped within the shocked disc. The prompt appearance of an electromagnetic counterpart, delayed by the light--travel time to the recoil radius (a few hours) therefore seems promising \citep[cf][]{deMink2017}. | 18 | 8 | 1808.06023 |
1808 | 1808.01435_arXiv.txt | The Large Magellanic Cloud (LMC) has $\sim$60 confirmed supernova remnants (SNRs). Because of the known distance, 50 kpc, the SNRs' angular sizes can be converted to linear sizes, and their X-ray observations can be used to assess X-ray luminosities ($L_X$). We have critically examined the LMC SNRs' sizes reported in the literature to determine the most plausible sizes. These sizes and the $L_X$ determined from \emph{XMM-Newton} observations are used to investigate their relationship in order to explore the environmental and evolutionary effects on the X-ray properties of SNRs. We find: (1) Small LMC SNRs, a few to 10 pc in size, are all of Type Ia with $L_X>10^{36}$ ergs s$^{-1}$. The scarcity of small core-collapse (CC) SNRs is a result of CCSNe exploding in the low-density interiors of interstellar bubbles blown by their massive progenitors during their main sequence phase. (2) Medium-sized (10-30 pc) CC SNRs show bifurcation in $L_X$, with the X-ray-bright SNRs either in an environment associated with molecular clouds or containing pulsars and pulsar wind nebulae and the X-ray-faint SNRs being located in low-density interstellar environments. (3) Large (size$>$30 pc) SNRs show a trend of $L_X$ fading with size, although the scatter is large. The observed relationship between $L_X$ and sizes can help constrain models of SNR evolution. | \label{sec:intro} Most supernova remnants (SNRs), regardless of progenitor types, exhibit some kind of X-ray emission. Thermal emission can arise from shocked interstellar medium (ISM) and/or SN ejecta, while relativisic electrons interacting with amplified magnetic field can produce non-thermal (synchrotron) emission. In the cases of core-collapse (CC) SNRs, there may exist additional X-ray emission from pulsars and pulsar wind nebulae (PWNe). See \citet{vink2012} for a comprehensive review of X-ray emission from SNRs. To make a statistical study of X-ray emission of SNRs, we need a large sample of SNRs with known distances. The Galactic sample of SNRs is quite incomplete because of heavy absorption in the Galactic plane, and the distances to individual SNRs are often very uncertain. The Large Magellanic Cloud (LMC), on the other hand, has small internal and foreground absorption column densities \citep{schlegel1998}, and hosts a large sample of SNRs all at essentially the same known distance 50 kpc\footnote{Note that due to the LMC's inclination of 18-23 degrees in the line of sight, the error in the distance and linear size can be uncertain by up to 10\% \citep{subramanian2010}, and the luminosity can be uncertain by 20\%. These uncertainties, however, do not affect the general conclusions of these paper.} \citep{pietrzynski2013}. At least 59 SNRs have been confirmed and a few additional SNR candidates have been suggested \citep{maggi2016,bozzetto2017}. This large sample of LMC SNRs is ideal for systematic and statistical studies of X-ray emission from SNRs. Recently, \citet{maggi2016} analyzed {\it XMM-Newton} observations of the 59 confirmed SNRs in the LMC, deriving physical properties of the X-ray-emitting plasma from spectral fits. Because of the known distance, it is possible to determine the X-ray luminosity of each SNR. In the meantime, \citet[][hereafter Bo2017]{bozzetto2017} measured the sizes of the 59 LMC SNRs using X-ray, radio and optical images. Intrigued by these results, we have examined the relationship between X-ray luminosity and size of LMC SNRs in order to explore evolutionary effects and environmental impacts on X-ray properties of SNRs. This paper reports our investigation of the relationship between X-ray luminosity and size of SNRs in the LMC. In Section 2, we discuss the physical meaning of SNR sizes measured at optical or X-ray wavelengths, examine the SNR sizes reported in the literature, and assess the most reliable sizes that represent the SNRs' full extent. In Section 3, we plot X-ray luminosities against sizes for LMC SNRs and note intriguing features in the distribution of SNRs in this plot. In Section 4, we discuss the physical reasons behind the distribution of SNRs in the plot of X-ray luminosity versus size. Finally, a summary is given in Section 5. \begin{figure*}[tbh] \centering \includegraphics[scale=0.35]{sizecom4} \includegraphics[scale=0.35]{sizecom5} \caption{The left panels compare the SNR sizes reported by De2010 and Bo2017, with the upper panel plotting De2010 sizes versus Bo2017 sizes and the lower panel plotting the (De2010 size / Bo2017 size) ratios versus Bo2017 sizes. The right panels compare the SNR sizes reported by Ba2010 and Bo2017 in the same way as the left panels. } \end{figure*} | \label{sec:Discussion} We have examined the physical structures and environments of SNRs in the three size ranges in order to understand the physical significance of their distributions in the $L_X$--size plot. The discussion in this section is ordered according to the SNR sizes. \subsection{Small Known LMC SNRs Are Dominated by Type Ia} It is striking that the small LMC SNRs, with sizes a few to 10 pc, are all Type Ia SNRs with $L_X$ of a few $\times$ 10$^{36}$ ergs s$^{-1}$. (Note that SN 1987A is outside the size range under discussion.) For comparison, we show that the Galactic Type Ia SNRs Kepler and Tycho are both located in a similar region as the young LMC Type Ia SNRs. The small range of $L_X$ for small Type Ia SNRs and the scarcity of small CC SNRs can be explained as follows. Type Ia SNe are usually considered to explode in a tenuous and uniform ISM \citep[e.g.,][]{badenes2005}. On the other hand, CC SNe usually explode inside interstellar bubbles blown by the fast stellar winds of their massive progenitors during the main sequence phase \citep{castor1975,weaver1977}. Interstellar bubble interiors have very low densities, and hence CC SNe inside bubbles are called ``cavity explosions''. It is conceivable that the interstellar environments of Type Ia and CC SNe have very different density profiles. Density profiles of ambient medium strongly affect the evolution of an SNR's $L_X$. In a classical model of a SN explosion in a uniform ISM, the resulting SNR goes through free expansion phase, Sedov phase (i.e., adiabatic phase), and radiative phase \citep{woltjer1972}. The Sedov phase starts when the swept-up ISM mass is several times the SN ejecta mass \citep[e.g.,][]{dwarkadas1998}. The $L_X$ of an SNR during the Sedov phase can be calculated \citep[e.g.,][]{hamilton1983}. To illustrate the evolution of $L_X$ for different ambient densities, we plot $L_X$ against age and size in Figure 4. \begin{figure*}[tbh] \centering \includegraphics[scale=0.3]{Lx_evolution_time} \includegraphics[scale=0.3]{Lx_evolution_radius} \caption{Evolution of $L_X$ in the Sedov model. The ambient density $n_0$ in H-atom cm$^{-3}$ is marked for each model. } \end{figure*} For a Type Ia SNR in a partially neutral ISM, only the ionized interstellar gas can be swept up by the shock. Thus, for a uniform density of $\sim$1 H-atom cm$^{-3}$ and a neutral fraction of $\eta$, the Sedov phase will start when the swept-up ionized gas reaches 1.4 $M_\odot$ in mass, corresponding to a radius of 2.4$(1-\eta)^{-1/3}$ pc. This radius is 5.2 pc if $\eta$ = 0.9, and 3 pc if $\eta$ = 0.5. These sizes are comparable to the young Balmer-dominated Type Ia SNRs in the LMC, 0509$-$67.5 and 0519$-$69.0; thus, it is likely that these young Type Ia SNRs are entering the Sedov phase. However, the interstellar density is so much lower than the SN ejecta density that their X-ray emission is still dominated by that produced by the reverse shock into the SN ejecta. This is evidenced in the SN ejecta abundance revealed in the X-ray spectra of these small Balmer-dominated Type Ia SNRs, although the X-ray emission shows a shell morphology \citep{warren2004,kosenko2010}. The larger Type Ia SNRs, such as DEM\,L71 and 0548$-$70.4 with sizes in the 20-30 pc range, must be in the Sedov phase already. Furthermore, their forward shock and reverse shock have traveled farther apart, and their X-ray emission shows the forward shock in an interstellar shell well resolved from the reverse shock in the SN ejecta \citep{hughes2003,hendrick2003}. X-ray emission from reverse shocks is the cause of the high $L_X$ of small Type Ia SNRs. The small scatter of these young bright Type Ia SNRs in the $L_X$ vs size plot reflects their similar ages, the relative uniformity of SNe Ia (in term of nucleosynthesis and explosion energy), and the modest effect the progenitors have on changing their immediate surrounding. The smallest Galactic Type Ia SNR G1.9+0.3 has a low $L_X$ because it is so young ($<$200 yr) that the reverse shock has only gone through very little of the SN ejecta \citep{reynolds2008,borkowski2014}. For CC SNRs whose SNe exploded in cavities of wind-blown bubbles, due to the extremely low density within the bubbles ($\sim 10^{-4}-10^{-2}$ H-atom cm$^{-3}$), the X-ray emission from shocked gas would be too faint to be detected at a young age; only when the SNR's forward shock hits the dense shell/wall of a bubble will the X-ray luminosity jump up several orders of magnitude \citep{dwarkadas2005}. As shown by \citet{naze2001}, main sequence O stars have interstellar bubbles of sizes 15--20 pc. By the time a massive star explodes as a CC SN, its main-sequence bubble has grown larger, and hence the SNR shock goes through the low-density bubble interior without producing detectable X-ray emission until it hits the bubble shell wall at radius of 10 pc or larger. For illustration, considering a spherical interstellar bubble with a radius of 10 pc and assuming a simplistic extreme case (upper limit) of average density of 0.01 H-atom cm$^{-3}$ in the bubble interior, we can calculate the total mass in the bubble interior to be $\lesssim$ 1 $M_\odot$; thus, when the SNR shock reaches the bubble wall, it has swept up only $\sim$1 $M_\odot$, much lower than the CCSN ejecta mass, a few to a few tens $M_\odot$; thus, the Sedov phase has not been reached. The bubble shell consists of swept-up ISM that was originally distributed in the bubble cavity. Assuming the bubble was blown in a diffuse ISM with density of 1 H-atom cm$^{-3}$, the total mass in the bubble shell would be 100 $M_\odot$; therefore, the SNR reaches the Sedov phase when the forward SNR shock traverses the bubble shell. During the free-expansion phase, the SNR shock is not significantly decelerated and it remains fast until it hits the bubble wall. Assuming a constant shock velocity of 10,000 km s$^{-1}$, it only takes 1000 years for the SNR to grow to a radius of 10 pc. Consequently, SNRs inside interstellar bubbles not only emit very faintly in X-rays, but also expand very rapidly to reach the dense shell wall. Such ``cavity explosions'' explain the absence of small CC SNRs in the $L_X$--size plot. Cavity explosions are also responsible for the discrepancies between ionization ages and dynamical ages of LMC SNRs, such as N132D, N63A, and N49B \citep{hughes1998}. We have plotted the young CC SNR Cas A in Figure 3 for comparison. Cas A is small in size and luminous in X-rays. These properties are caused by its interaction with a dense circumstellar medium, i.e., material ejected by the SN progenitor \citep{fesen2001}. Circumstellar bubbles are often observed around Wolf-Rayet stars and luminous blue variables (LBVs), and circumstellar bubbles are smaller than interstellar bubbles \citep{chu2003}. Cas A SN must have exploded in a circumstellar bubble. \subsection{X-ray-Bright and X-ray-Faint Medium-Sized SNRs} The medium-sized LMC SNRs show clear bifurcation in their $L_X$. In the X-ray-bright group with $L_X \ge 10^{36}$ ergs s$^{-1}$, only one is of Type Ia, and the other seven are CC SNRs. Among these X-ray-bright CC SNRs, four are interacting with molecular clouds, as CO emission was detected near the SNRs N23, N49, and N132D \citep{banas1997, park2003} and H$_2$ absorption is detected in \emph{Spitzer} IRS observations towards N63A (Segura-Cox et al.\ 2018, in preparation). None of these four X-ray-bright CC SNRs show sharp H$\alpha$ shell structure enclosing the diffuse X-ray emission, indicating that the forward SNR shocks are still in the low-density interiors of bubbles. In the cases of N23 and N132D, where no prominent shocked cloudlets are seen, the X-ray emission does show limb-brightening, indicating that the ambient medium is dense enough to produce detectable X-ray emission but not optical H$\alpha$ emission, and this ambient medium may correspond to the conduction layer in a bubble interior \citep{weaver1977}. As N23 and N132D are both associated with molecular clouds, their bubble shells and conduction layers must have higher densities, which contribute to the bright X-ray emission. In the cases of N49 \citep{bilikova2007, park2012} and N63A \citep{warren2003}, it is clear that dense cloudlets, possibly associated with the molecular clouds, have been shocked and contribute to the X-ray emission. The other three X-ray-bright CC SNRs possess bright PWNe: 0540$-$69.3 \citep{gotthelf2000}, N157B \citep{wang1998}, and 0453$-$68.5 \citep{gaensler2003}. Pulsars and PWNe are powerful sources of nonthermal X-ray emission and provide additional X-ray emission to boost their SNRs' total $L_X$. Note that the PWN of 0453$-$68.5 is not particularly dominating, but its X-ray image show a limb-brightened sharp shell that indicates that the shock has already reached the bubble shell. While 0453$-$68.5 has a PWN, it is the SNR shock impact on the dense bubble shell giving rise to $L_X$. The X-ray-faint medium-sized SNRs are mostly associated with CC SNe. Among the three X-ray-faint CC SNRs smaller than 20 pc, 0536$-$69.2 and [HP99]483 are not detected in optical, and the Honeycomb SNR shows only a small patch of honeycomb-like nebulosity resulting from SNR shocking a piece of shell wall \citep{chu1995, meaburn2010}. The absence of sharp optical shells enclosing the diffuse X-ray emission indicates a low-density ISM around these SNRs. The Honeycomb SNR has hit a small piece of dense gas and hence it has the highest $L_X$ among these three, but still a couple orders of magnitude fainter than the SNRs interacting with molecular clouds. The X-ray-faint SNRs with sizes 20--30 pc all show optical shell structure enclosing their diffuse X-ray emission, and they have higher $L_X$ than the smaller ones, except J0449$-$6920, whose \emph{XMM-Newton} observation was too shallow to make accurate measurements. These CC SNRs may represent cavity explosions whose SNR shocks have just reached the bubble shell walls. The SNRs N11L and N120 have just reached the bubble shell, but the bubble shell densities are not as high as those of N23 and N132D. \subsection{Fading of X-rays in Large SNRs} Among the large (size $>$30 pc) LMC SNRs, a general trend of decreasing $L_X$ for larger SNRs can be seen, but for any given size, the differences in $L_X$ can be up to one order of magnitude. As an SNR sweeps up more interstellar gas, the shock velocity decreases and when it goes much below $\sim$300 km s$^{-1}$, the post-shock temperature will be below 10$^6$ K, too low to generate X-ray-emitting gas. The hot gas in SNR interior cools, and the X-ray emission diminishes. The scatter in $L_X$ may be caused by the differences in ambient gas densities ($n_0$) and the SN explosion energies ($E$). To evaluate the effects of these two factors, we consider a spherical SNR of radius $R$, whose X-ray emission originates from shocked ISM in a shell. Its $L_X$ is $\propto$ (emitting volume) $\times$ (density)$^2$ $\times$ (emissivity). As (emitting volume) $\times$ (density) is proportional to the total interstellar mass within radius $R$, it is $\propto$ $R^3n_0^2$. The emissivity is a slow function of temperature for photon energies below 2 keV \citep{hamilton1983}. Since the large old SNRs are likely at low X-ray emitting temperatures, a few $\times$10$^6$ K at most, we will treat the emissivity as a constant, and $L_X$ $\propto$ $R^3n_0^{2}$. The total kinetic energy in the SNR shell scales with the explosion energy, so $E \propto R^3n_0 v^2$. The large old SNRs have low expansion velocities of a few $\times 10^2$ km s$^{-1}$, so we will also approximate the expansion velocity as a constant. Thus, $L_X$ $\propto$ $E n_0$ \footnote{ Note that this is in interesting contrast with the radio luminosity, which scales as $L_{radio}$ $\propto$ $E^{1.3} n_0^{0.45}$ or $L_{radio}$ $\propto$ $E^{1.45} n_0^{0.3}$ depending on the magnetic field amplification mechanism by the shock \citep{chomiuk2009}.}. The effects of the ambient density and the SN explosion energy are about equally important. However, the ranges of the ambient gas densities and the SN explosion energies are quite different. The ambient interstellar density can range from 0.01 to a few hundred H-atom cm$^{-3}$, about 4 orders of magnitude, while the SN explosion energies are mostly clustered around 10$^{51}$ ergs with extreme values differing by no more than 3 orders of magnitude \citep[e.g.,][]{woosley1986}. Hence, the large scatter in $L_X$ for SNRs with the same size is more likely caused by the detailed differences in the ambient gas densities, and the SN explosion energy plays a lesser role in raising the scatter in $L_X$. | 18 | 8 | 1808.01435 |
1808 | 1808.01329_arXiv.txt | We have utilized high-resolution optical {\it Hubble Space Telescope} images and deep, ground-based near-infrared images to examine the host-galaxies of 37 active galactic nuclei with reverberation-based black hole masses. Using two-dimensional image decompositions, we have separated the host galaxy from the bright central AGN, allowing a re-examination of the \mlbulge\ and \mlgalaxy\ relationships and the \mmbulge\ and \mmstars\ relationships using V-H color to constrain the stellar mass-to-light ratio. We find clear correlations for all of these scaling relationships, and the best-fit correlations are generally in good agreement with the sample of early-type galaxies with \mbh\ from dynamical modeling and the sample of megamasers. We also find good agreement with the expectations from the Illustris simulations, although the agreement with other simulations is less clear because of the different black hole mass ranges that are probed. \mlbulge\ is found to have the least scatter, and is therefore the best predictor of \mbh\ among the relationships examined here. Large photometric surveys that rely on automated analysis and forego bulge-to-disk decompositions will achieve more accurate \mbh\ predictions if they rely on \mmstars\ rather than \mlgalaxy. Finally, we have examined $M_{\rm BH} / M_{\rm stars}$ and find a clear trend with black hole mass but not galaxy mass. This trend is also exhibited by galaxies with \mbh\ from dynamical modeling and megamaser galaxies, as well as simulated galaxies from Illustris, rising from $~\sim 0.01$\% at $10^6$\,M$_{\odot}$ to $\sim 1.0$\% at $10^{10}$\,M$_{\odot}$. This scaling should be taken into account when comparing galaxy samples that are not matched in \mbh. | The discovery that nearly every massive galaxy hosts a supermassive black hole in its nucleus is one of the lasting legacies of the Hubble Space Telescope (\hst). Direct measurements of the masses of these black holes (\mbh), using luminous tracers inside the gravitational potential of the invisible central massive object, have led to the discovery of scaling relationships between the black holes and other characteristics of their host galaxies. This is true both for the sample of mostly-quiescent galaxies with measurements of \mbh\ from dynamical modeling of stars or gas (e.g., \citealt{kormendy13}) and for the sample of active galaxies that have measurements of \mbh\ from reverberation mapping (e.g., \citealt{bentz15}). Direct black hole mass measurements are time and resource intensive, and they are generally only applicable to galaxies that meet a specific set of criteria. For instance, reverberation mapping is only applicable to broad-lined active galactic nuclei (AGNs), which are rare in the local universe, whereas dynamical modeling is only applicable when the black hole sphere of influence is resolved or nearly so, which is generally only possible out to $\lesssim 100$\,Mpc. The resource-intensive nature of these measurements as well as the limitations on the applicability of each technique mean that, in practical terms, the number of direct \mbh\ measurements that may be accumulated over time is necessarily limited. The scaling relationships derived from these direct \mbh\ measurements, however, provide valuable shortcuts for estimating \mbh\ based on less resource-intensive measurements, such as the bulge stellar velocity dispersion (the \msigma\ relationship; \citealt{ferrarese00,gebhardt00}). As such, direct \mbh\ measurements and the scaling relationships that are based on them provide the foundation for all other \mbh\ determinations, thereby providing avenues to amass large samples for studying black hole and galaxy co-evolution across galaxy types and at different look-back times (e.g., \citealt{lapi14,heckman14,kelly12} and references therein). Scaling relationships between the central black hole and the host galaxy have also become important tools for critical testing of cosmological simulations of dark matter halo mergers (e.g., \citealt{oogi16,degraf11,hopkins10}), numerical investigations of candidate seed black holes (e.g., \citealt{shirakata16,volonteri09,lippai09}), cosmological modeling of galaxy and black hole growth (e.g., \citealt{degraf15,kim11,bonoli09,miller06}), and investigations into black hole feedback mechanisms (e.g., \citealt{steinborn15,kaviraj11,shabala11,ostriker10}). Accurate measurements of the host-galaxy characteristics of black holes with direct \mbh\ measurements are therefore necessary and valuable. Uncorrected biases or unmitigated scatter in the galaxy measurements can adversely affect the accurate and precise calibration of widely-used scaling relationships. In this work, we focus on characterization of the host galaxies of AGNs with reverberation-based \mbh\ measurements. Using high-resolution {\it HST} optical images and deep, ground-based near-infrared images, we characterize the photometric properties of the galaxies through two-dimensional image decompositions. We estimate stellar masses based on photometric colors and widely-used $M/L$ prescriptions. These results then allow us to recalibrate several black hole-galaxy scaling relationships, and to investigate the black hole mass to stellar mass fraction across the sample. Throughout this work, we adopt a standard $\Lambda$CDM cosmology of $H_0=72$\,km\,s$^{-1}$\,Mpc$^{-1}$ with $\Omega_{\Lambda}=0.7$ and $\Omega_{M}=0.3$. | With the measurements of luminosities and masses derived in the previous sections, we examine several black hole scaling relationships here. Linear regressions were carried out with a Bayesian approach using the {\sc linmix\_err} algorithm \citep{kelly07}, which includes measurement errors in both coordinates and a component of intrinsic, random scatter. The values and uncertainties that we report for the slope, intercept, and scatter of each relationship are the median values and $1\sigma$ widths of a large number of draws from the posterior probability distribution for each term. \subsection{Black Hole Mass -- Bulge Luminosity Relationship} The relationship between black hole mass and bulge luminosity, \mlbulge\, was one of the first black hole scaling relationships to be discovered \citep{kormendy95}. However, it was soon eclipsed by the \msigma\ relationship \citep{ferrarese00,gebhardt00}, which was initially reported to have a smaller intrinsic scatter and was therefore viewed as being the more fundamental scaling relationship. However, improvements in the black hole mass measurements, in particular, have led to much tighter \mlbulge\ relationships in recent years where the reported scatter is similar to that of the \msigma\ relationship \citep{marconi03,gultekin09}. These studies have tended to focus on bulge-dominated galaxies while neglecting the late-type galaxies common among local Seyfert hosts. A notable exception, however, is \citet{wandel02}, who drew photometry from the literature to investigate the \mlbulge\ relationship for AGN host galaxies with black hole masses from reverberation mapping. A homogeneous reanalysis of the AGN black hole masses by \citet{peterson04} combined with consistent bulge photometry derived from high quality \hst\ imaging and galaxy photometric decompositions allowed \citet{bentz09a} to update the results of \citet{wandel02}, finding that \mlbulge\ for disk-dominated active galaxies is similar in form and scatter to that of bulge-dominated galaxies with predominantly quiescent black holes and masses derived from dynamical modeling. Here, we are able to improve upon the results of \citet{bentz09a} by extending the sample to lower black hole masses, increasing the number of galaxies included in the fit by 40\%, and by examining the relationship in both the optical and the near-infrared. This last point is an important addition because it allows for the effects of dust and recent star formation on the photometry to be mitigated. For each galaxy, we identified the photometric component most consistent with the expected properties of a bulge. In particular, we looked for a round ($0.7 \lesssim q \lesssim 1.0$) photometric component with \sersic\ index $n>1.0$ and $r < r_{\rm disk}$. In one instance (Mrk\,509), there was no such model component and so we do not include it here in the analysis of galaxy bulges. Mrk\,509 is thus consistent with either a bulgeless disk galaxy or a disk galaxy with a compact bulge that we could not separate from the central AGN. Some of the PG quasars, on the other hand, were modeled by a single spheroidal component which we include as a ``bulge'' here. We do not attempt to discriminate between pseudobulges and classical bulges because we have limited kinematic information regarding the bulges of these galaxies. Numerous studies have shown that pseudobulge identification can be extremely uncertain when it is based solely on photometric information (e.g., \citealt{lasker14a,kormendy04}). In the $V$ band, we find the best-fit relationship between the black hole mass and bulge luminosity to be: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (0.84 \pm 0.10) \log \left(\frac{L_{\rm V,bulge}}{10^{10}L_{\odot}}\right) + (7.71 \pm 0.08) \end{equation} \noindent with a typical scatter of $(0.23 \pm 0.06)$\,dex. This is similar to the slope found by \citet{bentz09a} using a smaller number of galaxies in the reverberation sample and covering a smaller range of black hole masses. The scatter is much decreased, however, from $\sim 0.4$\,dex to $0.23$\,dex. In the $H$ band, we find a best-fit relationship of: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.05 \pm 0.14) \log \left(\frac{L_{\rm H,bulge}}{10^{10}L_{\odot}}\right) + (7.06 \pm 0.11) \end{equation} \noindent with a typical scatter of $(0.25 \pm 0.07)$\,dex. Surprisingly, the scatter in the near-infrared relationship is statistically equivalent to that of the optical relationship, suggesting that dust and/or recent star formation are not strong contributors to the intrinsic scatter in the relationship. As previously mentioned, however, there is still room for improvement in the distances, so it is likely that the scatter in both the optical and near-infrared relationships could be further decreased in the future through efforts to determine distances that do not rely on the galaxy redshift. We display these relationships in Figure~\ref{fig:bulge}. The solid line shows the best fit, while the gray shaded regions show the uncertainties in the fit. We denote broad-line Seyferts 1s (BLS1s) with filled circles and narrow-line Seyferts 1s (NLS1s) with open circles. We follow the original definition of \citet{osterbrock85} and select NLS1s in cases where the broad H$\beta$ emission line has FWHM$<2000$\,km\,s$^{-1}$. While the NLS1s tend to be associated with lower-mass black holes in lower-luminosity bulges, they exhibit the same scatter and general scaling relationship as the BLS1s. Some studies of NLS1s with black hole estimates have shown them to be significantly undermassive relative to BLS1s (e.g., \citealt{mathur12}), but we see no strong tendency for NLS1s to be undermassive relative to the other reverberation-mapped AGNs included here. \begin{figure*} \plotone{f4.eps} \caption{Black hole mass as a function of the total luminosity of the galaxy, as determined from the $V$-band photometry ({\it left}) and the $H$-band photometry ({\it right}). The solid lines show the best fits, while the gray shaded regions show the $1\sigma$ uncertainties on the fits. The scatter for the $H$-band relationship is formally smaller than that for the $V$-band relationship, but they are equivalent within the uncertainties. The black dashed lines show the best fits to the quiescent galaxy sample of \citet{kormendy13}, while the red long-short dashed lines show the best fits to the combined samples, including the $H$-band measurements of megamasers from \citet{lasker16}. The bottom panels show the distributions of measured \mbh\ relative to \mbh\ predicted by the best fit, as a function of $L_{\rm galaxy}$.} \label{fig:galaxy} \end{figure*} \citet{kormendy13} report a near-infrared \mlbulge\ relationship in the 2MASS $K_S$ band for quiescent galaxies that are ellipticals or contain classical bulges, and for which black hole masses have been determined through dynamical modeling. They find a slightly steeper slope of $1.21$ and a scatter of $0.31$\,dex, both of which are consistent within the errors with our finding for the active galaxy sample in $H$. The slightly higher intercept for their sample compared to ours is increased by the color difference between the $H$ and $K$ bands, given that galaxies are typically somewhat brighter in $K$ than $H$. While \citet{kormendy13} do not report a fit to the \mlbulge\ relationship in $V$, they do tabulate bulge absolute magnitudes in $V$. We fit the $V$-band relationship matching their accepted sample and adopted uncertainties and find a slope that agrees with their value reported for the $K_s$ band, which is steeper than the slope that we find in $V$ for the active galaxy sample. The intercept is also somewhat higher, although the fit to their sample agrees with our findings for the active galaxy sample at the low-mass end. The fits to the \citet{kormendy13} sample are shown as black dashed lines in Figure~\ref{fig:bulge}. It is important to note that the active and quiescent samples primarily probe different regions of parameter space in this plot: the active galaxy sample is heavily dominated by galaxies with $M_{\rm BH} < 10^8 M_{\odot}$, while the vast majority of galaxies in the quiescent sample have $M_{\rm BH} > 10^8 M_{\odot}$. \citet{lasker16} report deep $H$-band imaging and surface brightness decompositions for a sample of 9 megamaser galaxies with accurate black hole masses. We find that the megamasers are contained wholly within the scatter of the active galaxy sample presented here in the $H$ band. With the good agreement between the active galaxies, the megamasers, and the quiescent galaxy sample, we therefore refit the \mlbulge\ relationship in $H$ with all three samples combined. Based on the typical galaxy properties in 2MASS reported by \citet{jarrett00b}, we adopt $\langle H-K_s \rangle = 0.3$\,mag for the quiescent sample, which should account for any average color offset between the two filters (although we note that the scatter in $H-K_s$ values is typically $\sim 0.2$\,mag, even for galaxies with a specific morphological type). The best fit is: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.31 \pm 0.09) \log \left(\frac{L_{\rm H,bulge}}{10^{10}L_{\odot}}\right) + (7.27 \pm 0.08) \end{equation} \noindent with a typical scatter of $0.26\pm0.05$\,dex. While \citet{lasker16} do not report $V$-band measurements for the megamaser sample, we can investigate the \mlbulge\ relationship in $V$ for the active and quiescent samples combined. When we do, we find a best fit of: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.13 \pm 0.08) \log \left(\frac{L_{\rm V,bulge}}{10^{10}L_{\odot}}\right) + (8.04 \pm 0.06) \end{equation} \noindent with a typical scatter of $(0.24 \pm 0.05)$\,dex. These fits are displayed as the red long-dashed lines in Figure~\ref{fig:bulge}. In both the $H$ and $V$ bands, the best fit for the combined sample has an almost identical scatter to that found for the active sample alone, even though the combination of the samples more than doubles the number of points being fit and extends the range of \mbh\ by an order of magnitude. This may indicate that the galaxies in all three samples are drawn from the same parent population. \subsection{Black Hole Mass -- Galaxy Luminosity Relationship} We also examined the relationship between black hole mass and total luminosity of the host galaxy. We find a clear correlation between these two measurements, in both the optical and the near-infrared. The best-fit relationships are found to be: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.25 \pm 0.22) \log \left(\frac{L_{\rm V,galaxy}}{10^{11}L_{\odot}}\right) + (8.26 \pm 0.16) \end{equation} \noindent in the $V$ band, with a typical scatter of $(0.34\pm0.09)$\,dex, and \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.56 \pm 0.24) \log \left(\frac{L_{\rm H,galaxy}}{10^{11}L_{\odot}}\right) + (7.75 \pm 0.10) \end{equation} \noindent in the $H$ band, with a typical scatter of $(0.32\pm0.09)$\,dex. While the scatter is somewhat higher than that of the \mlbulge\ relationship, the fact that there is still a relatively tight relationship found when the total galaxy luminosity is used (see Figure~\ref{fig:galaxy}) suggests that bulge/disk decompositions can be avoided when estimating black hole masses from broad-band photometry of disk galaxies, but with a loss of some accuracy. This may be of particular interest for large photometric surveys that are operational or coming online soon (e.g., LSST), where automated measurements will be key to making sense of the large datasets that will be produced. Our best-fit relationships for active galaxies may again be compared to the \citet{kormendy13} sample of quiescent galaxies. The best-fit relationships based on their tabulated measurements in $V$ and $K_s$ have similar slopes and scatter to our findings, but their intercepts are significantly higher. This appears to stem from the differences in morphology among their sample and ours, as well as the different ranges of \mbh\ between the two samples. While the intercepts for the \mlbulge\ relationships traced by the active galaxy sample show good agreement with the quiescent galaxies, 2/3 of the galaxies in the \citet{kormendy13} sample are ellipticals. Thus, the \mlgalaxy\ relationships for their sample are very similar to the \mlbulge\ relationships, because 2/3 of the points between them are exactly the same. On the other hand, the active galaxy sample is dominated by later-type galaxies where the bulge contributes a smaller fraction of the integrated galaxy light, and so the best-fit \mlbulge\ and \mlgalaxy\ relationships that we find for the active galaxies are quite different from each other. We looked at the bulge-to-total ratios for the active galaxy sample and investigated whether splitting the sample into ``early'' (B/T > 0.5) and ``late'' (B/T < 0.5) types uncovered any offsets or separations among the sample that may lead to better agreement with the quiescent galaxy sample. The only obvious difference between these two subsamples is that the ``early'' types have more massive black holes than the ``late'' types, and so a cut in B/T is similar to a cut in \mbh\ and does not improve the agreement. As before, we also investigated the location of the \citet{lasker16} megamasers and find that they are wholly contained within the $H$-band scatter of the active galaxy sample. If we again combine the active, quiescent, and megamaser samples as before, we find best fits of: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.33 \pm 0.17) \log \left(\frac{L_{\rm V,galaxy}}{10^{11}L_{\odot}}\right) + (8.89 \pm 0.13) \end{equation} \noindent in the $V$ band, with a typical scatter of $(0.55\pm0.09)$\,dex, and \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.54 \pm 0.18) \log \left(\frac{L_{\rm H,galaxy}}{10^{11}L_{\odot}}\right) + (8.22 \pm 0.08) \end{equation} \noindent in the $H$ band, with a typical scatter of $(0.52\pm0.08)$\,dex. Thus, while the scatter is significantly increased when galaxies of all morphological types are treated equally, it is likely more representative of the true uncertainty on black hole mass estimates from the total galaxy luminosity. \begin{figure*} \plotone{f5.eps} \caption{Black hole mass as a function of the bulge stellar mass, where stellar mass is calculated based on the $V-H$ color and the $M/L$ prescriptions of \citet{bell01} ({\it left}) and \citet{into13} ({\it right}). The solid lines and gray regions show the best-fit lines and $1\sigma$ uncertainties on the fits. The dashed lines show the best fit for the sample of quiescent galaxies tabulated by \citet{kormendy13}. The blue long-dashed lines show the best fit determined by \citet{sijacki15} for galaxies from the Illustris simulation. The red long-short dashed line is the best fit when the active galaxies, quiescent galaxies, and megamaser samples are combined.} \label{fig:bstmass} \end{figure*} \subsection{Black Hole Mass -- Bulge Stellar Mass Relationship} The relationship between black hole mass and bulge stellar mass is expected to be the physical basis for the \mlbulge\ relationship, where bulge light traces mass. A variety of methods have been used to investigate this relationship in the past, often with the aim of decoupling the \mmbulge\ relationship from any dependence on the \mlbulge\ relationship so they can be studied independently. For example, \citet{magorrian98} carried out axisymmetric dynamical models to constrain the bulge mass and the black hole mass simultaneously. \citet{marconi03} measured effective bulge radii from 2MASS imaging for quiescent galaxies with dynamical black hole masses. The bulge radii were combined with $\sigma_*$ to predict $M_{\rm bulge}$ under the assumption that bulges behave similarly to isothermal spheres. \citet{haring04}, on the other hand, numerically solved the spherical Jeans equation while matching published luminosity and $\sigma_*$ profiles for quiescent galaxies with dynamical black hole masses. We can examine this relationship for active galaxies by estimating the bulge stellar mass from its optical$-$near-infrared color and the $M/L$ prescriptions described above. The best-fit relationship between the black hole mass and the stellar mass of the bulge, based on the \citet{bell01} $M/L$ predictions, is found to be: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.06\pm 0.24) \log \left(\frac{M_{\rm bulge}}{10^{10}M_{\odot}}\right) + (7.02 \pm 0.17) \end{equation} \noindent with a typical scatter of $(0.39 \pm 0.12)$\,dex. If we estimate $M/L$ using the prescriptions of \citet{into13}, we find the best fit to be: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (0.80 \pm 0.30) \log \left(\frac{M_{\rm bulge}}{10^{10}M_{\odot}}\right) + (7.36 \pm 0.15) \end{equation} \noindent with a typical scatter of $(0.55 \pm 0.16)$\,dex. These relationships are displayed in Figure~\ref{fig:bstmass}. \begin{figure*} \plotone{f6.eps} \caption{Black hole mass as a function of the total stellar mass of the galaxy, where stellar mass is calculated based on the $V-H$ color and the $M/L$ prescriptions of \citet{bell01} ({\it left}) and \citet{into13} ({\it right}). The solid lines and gray regions show the best-fit lines and $1\sigma$ uncertainties on the fits. The \citet{bell01} $M/L$ prescriptions lead to a tighter relationship with a somewhat steeper slope. The dashed lines show the best fit for the sample of quiescent galaxies tabulated by \citet{kormendy13}. The dotted line is the predicted ``unbiased'' relationship of \citet{shankar16}, which agrees extremely well with our measurements if we adopt $M/L$ from \citet{bell01} and $f=1$ rather than $f=4.3$ for $M_{\rm BH}$ (as \citealt{shankar16} recommend). The blue long-dashed lines show the relationship found for disk galaxies in the Illustris simulation \citep{mutlupakdil18}, which agrees extremely well with our measurements of \mbh\ and $M_{\rm stars}$ when the $M/L$ prescriptions of \citet{bell01} are adopted. The red long-short dashed line is the best fit when the active galaxies, quiescent galaxies, and megamaser samples are combined.} \label{fig:stmass} \end{figure*} For a direct comparison with the quiescent galaxy sample, we recalculated the bulge masses based on the absolute $V$ magnitudes of the bulges and the $V-K_s$ colors tabulated by \citet{kormendy13} with the $M/L$ prescriptions of both \citet{bell01} and \citet{into13}. Because \citet{kormendy13} only provide an integrated $V-K_s$ color for each galaxy, we note that we would expect there to be a bias in the bulge masses derived for the disk galaxies in their sample because of the different colors of bulges and disks. The best-fit relationships for the quiescent galaxies are shown as the black dashed lines in Figure~\ref{fig:bstmass}. While the active galaxy sample displays a linear relationship between \mbh\ and bulge stellar mass, the quiescent galaxy relationships are quite a bit steeper. The two samples agree better using the $M/L$ prescriptions of \citet{bell01}, although both prescriptions show agreement between the samples at the low mass end. The megamaser sample of \citet{lasker16} reports $M_{\rm bulge}$ based on near-infrared {\it HST} and ground-based imaging and the $M/L$ prescriptions of \citet{bell03}, which allows for a simple comparison with our results. We again find that all 9 megamasers are contained wholly within the scatter of the active galaxy sample, with no apparent offsets in bulge mass or black hole mass. Noting that there is good agreement between the active, quiescent, and megamaser samples, we also fit the \mmbulge\ relationship with all three samples combined. Assuming the \citet{bell01} $M/L$ prescriptions, the best-fit relationship is: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.50 \pm 0.13) \log \left(\frac{M_{\rm bulge}}{10^{10}M_{\odot}}\right) + (7.16 \pm 0.11) \end{equation} \noindent with a scatter of ($0.27 \pm 0.06$)\,dex. The red long-short dashed line in the left panel of Figure~\ref{fig:bstmass} displays this fit. While the slope is quite a bit steeper than that found for the active galaxy sample, they only disagree at the $\sim 1\sigma$ level. Furthermore, there is good agreement with the gray shaded region (which denotes the uncertainty on the fit to the active sample alone) over the range sampled by the active galaxies. This appears to indicate that all three samples may be drawn from the same parent population of galaxies. We also compared our results to those of simulated galaxies. Some caution must be taken when interpreting such comparisons, because cosmological galaxy simulations are generally tuned to match a set of observables. For example, the slope of the \mmbulge\ relationship is not expected to be affected by such tuning, but the intercept is. Furthermore, there is no agreement on the best way to separate the bulges of late-type galaxies from their disks in simulations, where the resolution is often a limiting factor, so the simulated galaxies are either compared to samples of massive early-type galaxies where $M_{\rm bulge} \approx M_{\rm galaxy}$ (e.g., \citealt{steinborn15,schaye15}) or a prescription is applied to estimate the bulge contribution. \citet{sijacki15} used the high-resolution hydrodynamical Illustris simulations to explore the predicted \mmbulge\ relationship for galaxies. The total stellar mass within the stellar half-mass radius was used as a proxy for the bulge mass. This simplification does not take into account different bulge mass fractions of galaxies, nor the fact that some galaxies may not have a bulge at all. Additionally, the Illustris simulations assumed a Chabrier IMF, which can be compared to a ``diet'' Salpeter like that employed by \citet{bell01} by adding 0.093\,dex \citep{gallazzi08}. To compare with a Kroupa IMF like that employed by \citet{into13}, on the other hand, we subtracted 0.057\,dex \citep{bell03,herrmann16}. The best-fit relationship of \citet{sijacki15}, with the IMF scaled appropriately, is displayed as the blue long-dashed lines in Figure~\ref{fig:bstmass}. With a reported slope of $1.21$, it is in good agreement with our findings, especially when we adopt the \citet{bell01} $M/L$ prescriptions. The large-volume Horizon-AGN simulations, which adopt a Salpeter IMF, were analyzed by \citet{volonteri16}. To separate the bulge contribution, they tried various prescriptions, including examining the kinematics and also adopting a double \sersic\ model for each galaxy, where the indices for the two \sersic\ profiles were chosen to be [1.0, 1.0], [1.0, 4.0], or [1.0, 1.0 or 4.0]. The slope of the relationship based on these various prescriptions ranges from $0.75-1.05$, which is in good agreement with our findings for the active galaxies using either the \citet{bell01} or \citet{into13} $M/L$ prescriptions, although it is somewhat in tension with our results for the combined active, quiescent, and megamaser samples. This tension may result from incompleteness in the Horizon-AGN simulation for black holes with $M_{\rm BH} \lesssim 2\times 10^7$\,M$_{\odot}$, which is the region probed by many of the active galaxies. \begin{figure*} \plotone{f7.eps} \caption{Black hole mass fraction as a function of black hole mass ({\it left}) and as a function of galaxy stellar mass ({\it right}). There is no correlation seen between black hole mass fraction and galaxy stellar mass, but there appears to be a strong correlation between black hole mass fraction and black hole mass, with more massive black holes commanding a larger mass fraction.} \label{fig:mbhfrac} \end{figure*} \subsection{Black Hole Mass -- Galaxy Stellar Mass Relationship} In the same way, we can examine the best-fit relationship between the black hole mass and the total stellar mass of the galaxy. When we adopt the \citet{bell01} $M/L$ predictions, we find a best fit of: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.69 \pm 0.46) \log \left(\frac{M_{\rm stars}}{10^{11}M_{\odot}}\right) + (8.05 \pm 0.18) \end{equation} \noindent with a typical scatter of $(0.38 \pm 0.13)$\,dex. If we instead estimate $M/L$ using the prescriptions of \citet{into13}, we find the best fit to be: \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.34 \pm 0.55) \log \left(\frac{M_{\rm stars}}{10^{11}M_{\odot}}\right) + (8.49 \pm 0.41) \end{equation} \noindent with a typical scatter of $(0.49 \pm 0.17)$\,dex. These relationships are displayed in Figure~\ref{fig:stmass}. Interestingly, the \mmstars\ relationship based on the \citet{into13} $M/L$ values is similar to that found by \citet{reines15} for inactive black holes residing in ellipticals and classical bulges. This would seem to contradict their finding that active galaxies lie below the relationship defined by local quiescent galaxies, although a direct comparison is somewhat difficult given that they used $M/L$ prescriptions of \citet{zibetti09}, who employ a different initial mass function than \citet{into13}. We therefore recalculated the \mmstars\ relationship for local quiescent galaxies based on the absolute $V$ magnitudes and the $V-K_s$ colors tabulated by \citet{kormendy13}, using both the \citet{bell01} and \citet{into13} $M/L$ prescriptions for direct comparison with the active galaxies in our sample. The best fits are shown as the dashed lines in Figure~\ref{fig:stmass}. Using the \citet{bell01} prescription, we find a nearly identical slope for the quiescent galaxies compared to the active galaxies, but an intercept that is 0.75\,dex higher, supporting the findings of \citet{reines15} that active galaxies fall below quiescent galaxies in this parameter space. However, using the \citet{into13} prescription instead, we find a slightly steeper slope for the quiescent galaxies which, when coupled with the intercept, show the two samples to be in general agreement at the low-mass end while diverging at the high mass end. If we again combine the active sample with the quiescent galaxies and the megamasers, we find a best-fit relationship of \begin{equation} \log \frac{M_{\rm BH}}{M_{\odot}} = (1.84 \pm 0.25) \log \left(\frac{M_{\rm stars}}{10^{11}M_{\odot}}\right) + (8.40 \pm 0.09) \end{equation} \noindent with a scatter of ($0.44 \pm 0.10$)\,dex. This fit is denoted with the red long-short dashed line in the left panel of Figure~\ref{fig:stmass}. Once again, the consistency with the results derived solely from the active galaxies seems to indicate that all of these subsamples may be drawn from the same parent population. Recently, \citet{shankar16} investigated the potential for selection bias among the quiescent galaxy sample using Monte Carlo simulations and a large sample of galaxies drawn from the Sloan Digital Sky Survey. They concluded that the quiescent galaxy sample is selected from an upper ``ridgeline'' in the distribution of normal galaxy properties, leading to a bias of a factor of $\sim 3$ in the normalization of the \msigma\ relationship. If such a bias exists, that would argue against our choice of scaling factor for reverberation-based masses in the active galaxy sample, and would instead argue for $f \approx 1$. Interestingly, when we adopt $f=1$ for the scaling of reverberation-based \mbh, and examine the \mmstars\ relationship based on the $M/L$ prescriptions of \citet{bell01}, we find that the active galaxy sample closely follows the predicted unbiased relationship in Equation~6 of \citet{shankar16}. The stellar masses predicted by \citet{into13}, however, are undermassive compared to the predicted relationship, even when accounting for the slight differences in assumed IMF. However, it appears that bars will affect the measurements of effective radii \citep{meert15} and possibly velocity dispersion \citep{batiste17} that are adopted for the ``unbiased'' SDSS sample considered by \citet{shankar16}. These effects will be strongest at the low-mass end, where most of the active galaxies in our sample are found, thus complicating the interpretation for reverberation-based masses. Furthermore, forward modeling of velocity-resolved reverberation signals by \citet{pancoast14} and \citet{grier17} has constrained the geometry and kinematics of the broad line region and the black hole mass for 9 AGNs, independent of any $f$ factor. Both studies recover modeling-based black hole masses that agree well with \mbh\ values derived from traditional reverberation analysis and the use of $f\approx4$ (as described in Section 4.5). These findings argue against the use of $f=1$ for the proper scaling of reverberation masses, but do not rule out that there may be biases present in the quiescent galaxy sample. \begin{figure*} \plotone{f8.eps} \caption{{\it Left:} Histogram of black hole masses from the active sample (red), the quiescent sample (black), and the megamaser sample (blue). The majority of the overlap for the active and quiescent samples occurs at $10^7 \leq M_{\rm BH}/M_{\odot} \leq 10^9$, while the megamasers are completely contained within the range of black hole masses probed by the active sample. {\it Right:} Median black hole mass fraction as a function of black hole mass for the active sample (red), the quiescent galaxy sample (black), and the megamaser sample (blue). At least three objects contribute to each of the bins. The error bars on $M_{\rm BH}/M_{\rm stars}$ show the standard deviation for the galaxies in the bin, while the error bars on black hole mass show the bin size. The bins for the quiescent galaxy sample and the megamaser sample have been slightly offset in \mbh\ for clarity.} \label{fig:mbhbin} \end{figure*} Unlike for the \mmbulge\ relationship, comparisons with simulated galaxies are much simpler when the entire galaxy stellar mass is used because the issues with bulge-disk decompositions are avoided, although the caveats related to the tuning of parameters in the simulations remain. \citet{mutlupakdil18} recently examined the relationships between black holes and large-scale galaxy properties for $z=0$ spiral galaxies in the Illustris simulations. Using the same IMF corrections described in the previous section, we compared our best-fit \mmstars\ relationships to theirs (blue long-dashed lines in Figure~\ref{fig:stmass}) and we find excellent agreement, especially when we adopt the \citet{bell01} $M/L$ prescriptions, which may argue against any potential bias in the reverberation-based \mbh\ scaling. \citet{volonteri16} examined the \mmstars\ relationship for galaxies from the Horizon-AGN simulation, and find a slope that is somewhat shallower than we have found, although the low-mass end of their relationship may be biased by incompleteness. \citet{steinborn15} used the Magneticum Pathfinder Simulations to examine the \mmstars\ relationship, excluding simulated galaxies for which $M_{\rm BH} < 5\times 10^7$\,M$_{\rm BH}$. Perhaps unsurprisingly, their reported best-fit relationship (with a slope of 1.09) agrees with the most massive black holes in the active galaxy sample ($M_{\rm BH} \gtrsim 10^8$\,M$_{\odot}$), but diverges at lower black hole masses, predicting a larger $M_{\rm BH}$ at fixed $M_{\rm stars}$, similar to the findings of \citet{volonteri16}. Many large photometric surveys that are currently in operation or are upcoming will collect photometry in multiple filters. When considering that these surveys that may need to be treated in an automated fashion, the stellar mass of the galaxy based on its color appears to be a better predictor of black hole mass than the total galaxy luminosity in a single filter. This can be seen from the decreased scatter in the \mmstars\ relationship for the combined active, quiescent, and megamaser samples ($0.44\pm0.10$\,dex) relative to the \mlgalaxy\ relationship ($\sim0.53\pm0.09$\,dex). \subsection{Black Hole Mass Fraction} Finally, we also investigated the typical fraction of black hole mass to stellar mass for each galaxy. We find a median value of $M_{\rm BH}/M_{\rm stars}= 0.0005 \pm 0.0049$, however we also find a very clear relationship between $M_{\rm BH}/M_{\rm stars}$ and \mbh, while there appears to be no obvious relationship between $M_{\rm BH}/M_{\rm stars}$ and $M_{\rm stars}$ (see Figure~\ref{fig:mbhfrac}). For comparison, we derived the black hole mass fractions for the quiescent galaxy sample of \citet{kormendy13} and find a median value of $M_{\rm BH}/M_{\rm stars}= 0.0058 \pm 0.0077$. At first glance, this would appear to demonstrate that active galaxies host undermassive black holes compared to quiescent galaxies. However, the samples cover different \mbh\ ranges, with the active galaxy sample skewed toward lower \mbh, while the quiescent galaxy sample is skewed to higher \mbh\ (see Figure~\ref{fig:mbhbin}), and $M_{\rm BH}/M_{\rm stars}$ seems to depend strongly on $M_{\rm BH}$. For a better comparison between the two samples, we binned the galaxies in each sample by \mbh\ with bins of width 0.5\,dex. For each bin with three or more objects, we computed the median black hole mass to stellar mass fraction. Figure~\ref{fig:mbhbin} shows the median $M_{\rm BH}/M_{\rm stars}$ as a function of \mbh\ for the two samples, with the active sample in red and the quiescent sample in black. The majority of the overlap between the samples exists within the range $10^7 <M_{\rm BH}/M_{\odot} < 10^9$, with the range extending to lower black hole masses in the active galaxy sample, and extending to higher black hole masses in the quiescent galaxy sample. We have adopted $M_{\rm stars}$ based on the $M/L$ predictions of \citet{bell01} in Figure~\ref{fig:mbhbin}, but while the values slightly change, the overall trend is the same if we adopt $M_{\rm stars}$ based on the \citet{into13} $M/L$ values. The two samples show broad agreement, both in the overall trend -- with more massive black holes comprising larger mass fractions of their galaxies -- and with the typical values for the black hole mass fraction at a fixed value of \mbh. While there seems to be a tendency for the active galaxies to lie slightly below the quiescent galaxies in the expected black hole mass fraction at a fixed black hole mass, the values agree within the standard deviation for each bin, and the small and uneven number of objects in each bin make it difficult to draw firm conclusions about any apparent offset between the two samples. Notably, the trend appears to continue across the full range of black hole masses probed by either sample. We also examined the megamaser sample of \citet{lasker16} for comparison. Adopting the same bins for the megamaser sample as for the above two samples, we show the median $M_{\rm BH}/M_{\rm stars}$ in blue in Figure~\ref{fig:mbhbin}. There is no apparent offset between the megamaser sample and the reverberation sample, nor with the extension of the quiescent sample to lower black hole masses. \citet{lasker16} noted in their study that the megamaser galaxies appeared to probe a lower $M_{\rm BH}$ at fixed galaxy mass than the reverberation sample (as reported by \citealt{bentz09b}), but this discrepancy has been completely erased with the larger sample and extended range of $M_{\rm BH}$ and galaxy properties presented here. The scaling of $M_{\rm BH}/M_{\rm stars}$ as a function of \mbh\ was previously noticed by \citet{trakhtenbrot10}. Using large samples of local non-AGN galaxies and AGN galaxies at $z \approx 0.15, 1, 2$ and scaling relationships to predict $M_{\rm stars}$ and $M_{\rm BH}$, they found that $M_{\rm BH}/M_{\rm stars} \propto (0.7 \pm 0.1)M_{\rm BH}$. A formal fit to the active, quiescent, and maser galaxies examined here finds: \begin{equation} \log \frac{M_{\rm BH}}{M_{\rm stars}} = (0.71 \pm 0.04) \log \left(\frac{M_{\rm BH}}{10^{8}M_{\odot}}\right) - (2.80 \pm 0.04) \end{equation} \noindent with a typical scatter of $(0.04 \pm 0.02)$\,dex, which agrees well with a formal fit to the active galaxies alone, and to the estimated slope reported by \citet{trakhtenbrot10}. Interestingly, we find the same scaling between $M_{\rm BH}/M_{\rm stars}$ and $M_{\rm BH}$ among simulated galaxies from Illustris. \citet{vogelsberger14} provide black hole masses and galaxy stellar masses for two subsamples of representative ``red'' and ``blue'' galaxies from the Illustris simulation. The ``blue'' galaxies preferentially occupy the lower $M_{\rm BH}$ range that is probed here by the active and megamaser samples, and the ``red'' galaxies preferentially occupy the upper $M_{\rm BH}$ range probed by the quiescent galaxies. The scaling in $M_{\rm BH}/M_{\rm stars}$ as a function of $M_{\rm BH}$ in the simulated galaxies matches the observed galaxies extremely well in both slope and offset. It is clear from these studies that the commonly-used assumption of a constant $M_{\rm BH}/M_{\rm stars}$ is incorrect in the local universe and possibly up to $z\approx2$. Attempts to search for cosmic evolution of black holes and host galaxies, or to search for differences in the evolutionary paths of distinct galaxy samples, should be careful to account for this scaling when the samples are not matched in $M_{\rm BH}$. We suggest that the physical meaning of this scaling may be related to differences in feedback efficiency as a function of galaxy mass. High-resolution and zoom-in simulations of individual galaxies show that supernova feedback is extremely effective at prohibiting black hole growth at early times (e.g., \citealt{dubois15,trebitsch18,anglesalcazar17}). Once the host galaxy reaches a critical mass ($M_{\rm stars} \approx 10^9-10^{10} M_{\odot}$; \citealt{dubois15,anglesalcazar17}), supernova feedback can no longer restrict the gas flow to the nucleus and the black hole will undergo a period of rapid growth, effectively ``catching up'' with the galaxy. This period of rapid growth is short-lived, however, because AGN feedback soon becomes important and the black hole then regulates its own growth and the continued growth of the galaxy (e.g., \citealt{dubois15,mcalpine17}). In this scenario, we may currently be witnessing the rapid growth phase for low-mass black holes in the local universe. | 18 | 8 | 1808.01329 |
1808 | 1808.04356_arXiv.txt | With the advent of high power lasers, new opportunities have opened up for simulating astrophysical processes in the laboratory. We show that 2nd-order Fermi acceleration can be directly investigated at the National Ignition Facility, Livermore. This requires measuring the momentum-space diffusion of 3 MeV protons produced within a turbulent plasma generated by a laser. Treating Fermi acceleration as a biased diffusion process, we show analytically that a measurable broadening of the initial proton distribution is then expected for particles exiting the plasma. | Introduction} Turbulent magnetic fields are ubiquitous in the universe and their role in determining energetic particle transport is key to understanding the confinement and acceleration of high-energy cosmic rays \citep{TurbForStochAcc,ImpPlasmaProb,VoidMagnetTurb,TurbAcceleration,gregori2015the}. As particles traverse a turbulent, magnetised plasma, they undergo a random walk in both physical and momentum space. The latter process is referred to as 2nd-order Fermi acceleration, being a generalization of the mechanism proposed by Fermi \citep{FermiAcceleration}. Fermi observed that repeated elastic scattering of fast particles off slow moving `magnetised clouds', when averaged over a random distribution of cloud velocities produce a net gain in energy. The rate of energy gain is slightly higher than the rate of energy loss because head-on collisions are more probable than overtaking ones, the net gain being proportional to $(u/v)^2$ where $u$ is the mean fluid velocity and $v (\gg u)$ the particle velocity. Subsequently the focus has shifted from discrete interactions with magnetised clouds to continuous scattering in magneto-hydrodynamic (MHD) turbulence, but the underlying principle remains the same. Fermi noted shortly afterwards that converging flows such as might exist between Galactic spiral arms result in a faster 1st-order process where the energy gain is proportional to $u/v$ \citep{Fermi54}. Indeed 1st-order Fermi acceleration in the converging fluid flow at astrophysical shock waves is currently the preferred model for the origin of cosmic rays \citep{Bell1,1978ApJ...221L..29B,ParticleAccelerationTheory}. However the 2nd-order mechanism can be more efficient for accelerating non-relativistic thermal background plasma particles and under certain conditions can also preferentially accelerate electrons relative to protons as is required to explain many astrophysical sources \citep{FermiReview}. In reality there may be a hybrid mechanism, e.g. initial 2nd-order acceleration of background plasma particles by turbulence, followed by a second stage of 1st-order acceleration by a shock wave. The 2nd-order Fermi process is quite general, requiring only turbulent magnetised fluid motions and injection of particles with energy above that of the background thermal plasma. Relevant environments are common in the universe and stochastic acceleration is believed to be responsible for phenomena as diverse as e.g. radio emission from young supernova remnants entering the Sedov-Taylor phase \citep{SecOrdFermSolAltern}, the ejection of mass from the Solar corona \citep{1985srph.book..333N}, the acceleration of particles in the jets of active galactic nuclei and in their giant radio lobes \citep{Tramacere07,OSullivan09,Hardcastle09} and $\gamma$-ray emission from the Fermi bubbles \citep{2011PhRvL.107i1101M}. The necessary conditions may be accessible in laboratory experiments \citep{gregori2015the} thus providing a platform to explore particle acceleration in a controlled setting and isolate effects of relevance to astrophysical models. We explore here the possibility of validating the physics of 2nd-order Fermi acceleration using existing experimental set-ups (see supplementary material to Ref.\citep{tzeferacos2018laboratory}. In \S~\ref{sec:level2} we introduce the proposed set-up and place it in the context of previous experiments. The governing equations for the momentum space diffusion process are stated in \S~\ref{sec:level3} and the relevant Fokker-Planck coefficients of the diffusion process are estimated. We discuss the relevant time scales to justify the diffusion approach adopted. An analytic solution for the diffusion equation is investigated in \S~\ref{sec:level4}. Finally in \S~\ref{sec:level5}, laser experiments at the National Ignition Facility (NIF), Livermore, USA~\citep{moses} are discussed. We conclude that the effects of stochastic Fermi acceleration are measurable in the laboratory. | 18 | 8 | 1808.04356 |
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1808 | 1808.03185_arXiv.txt | The search for telluric extrasolar planets with the Radial Velocity (RV) technique is intrinsically limited by the stellar jitter due to the activity of the star, because stellar surface inhomogeneities, including spots, plages and convective granules, induce perturbations hiding or even mimicking the planetary signal. This kind of noise is poorly understood in all the stars, but the Sun, due to their unresolved surfaces. For these reasons, the effects of the surface inhomogeneities on the measurement of the RV are very difficult to characterize. On the other hand, a better knowledge of these phenomena can allow us a step forward in our understanding of solar and stellar RV noise sources. This will allow to develop more tools for an optimal activity correction leading to more precise stellar RVs. Due to the high spatial resolution with which the Sun is observed, this noise is well known for it. Despite this, a link is lacking between the single observed photospheric phenomena and the behavior of the Sun observed as a star. LOCNES (Low Cost NIR Extended Solar Telescope) will allow to gather time series of RVs in order to disentangle the different contributions to the stellar (i.e., sun’s) RV jitter. Since July 2015, a Low Cost Solar Telescope (LCST) has been installed outside the TNG dome to feed solar light to the HARPS-N spectrograph (0.38-0.69 $\mu$m; R=115000). The refurbishment of the Near Infrared (NIR) High Resolution Spectrograph GIANO (now GIANO-B) and the new observing mode GIARPS at TNG (simultaneous observations in visible with HARPS-N and in NIR with GIANO-B) is a unique opportunity to extend the wavelength range up to 2.4 $\mu$m for measuring the RV time series of the Sun as a star. This paper outlines the LOCNES project and its scientific drivers. | \label{sec:intro} % The search for very small extrasolar planets with the Radial Velocity technique is plagued by the stellar jitter due to the activity of the star, because stellar surface inhomogeneities including spots, plages and granules, induce perturbation that hide the planetary signal. This kind of noise is poorly understood in all the stars but the Sun due to their unresolved surfaces. For these reasons the effect of the surface inhomogeneities on the measurement of the Radial velocities are very difficult to characterize. On the other hand, a better understanding of these phenomena can allow us to made a step further in our knowledge of solar and stellar physics. The latter will allow to acquire more skills in the art of developing optimal correction techniques to extract true stellar radial velocities. A viable way to tackle these problems is to observe the Sun as a star getting time series of radial velocities in order to disentangle the several contribution of the stellar (solar) RV jitter\cite{dumusqueetal2015,marchwinskietal2015,haywoodetal2016}. With the aim to obtain long-term observation of the Sun as a star with state-of-the-art sensitivity to RV changes, since July 2015, a Low Cost Solar Telescope (LCST) has been installed\cite{phillipsetal2016} on the outside of the dome at TNG to feed solar light to the HARPS-N spectrograph (0.38-0.69um; R=115000). The main purpose of the LCST is to show that HARPS-N with the Astro Laser Frequency Comb calibrator\cite{philipsetal2012} have enough precision and stability to measure on the spectra of the Sun the Center of Mass (CoM) Radial Velocity (RV; of the order of 9cm/s) due to the gravitational pull of an earth-like planet (Venus for the Sun). While the LCST and HARPS-N continue in an autonomous way to acquire spectra, the interest on the collected data is growing day after day. Thanks to the resolved images of the surface of the Sun produced by the SORCE and SDO satellites (together with magnetograms and doppler maps) it is possible to correlate the observed spectra with surfaces anomalies like spots, plages/flares, granulation etc. In the last decade, new near -- infrared (NIR) spectrograph have been built that are able to measure high precision RVs and thanks to the advent of better technology, specifically in calibration, these spectrographs are able to approach the precision that are routinely obtained in the visible. Among these NIR spectrograph there is the high resolution NIR spectrograph of the Telescopio Nazionale Galileo (TNG) named GIANO--B. The Italian exoplanetary community through the {\it Progetto Premiale WOW} funded the refurbishment of GIANO-A\cite{olivaetal2012} in the framework of the GIARPS project\cite{claudietal2017}. The Near Infrared (NIR) GIANO spectrograph (0.9-2.5um, R=50000) of the TNG underwent a refurbishment improving the throughput and the efficiency. The spectrograph was moved from the Nasmyth A focus of the TNG, where it was fed by optical fibers, to the Nasmyth B focus where it is fed by a preslit optics. The main results are: enhancement of the efficiency of the spectrograph; the elimination of the modal noise due to injection of K band in the Z-Blan fibers and the added advantage of placing GIANO-B close to HARPS--N. The use of a dichroic optical system allows the simultaneous collection of a VIS-NIR spectrum of the observed target. This observing mode, called GIARPS, is a worldwide unique and exclusive facility of the TNG. Taking advantage of the presence of GIARPS we plan to replicate the opto-mechanical configuration of the LCST but extending the wavelength range to the NIR in order to simultaneously feed both HARPS--N and GIANO--B. The VIS part is fundamental in order to be able to observe simultaneously with the LCST and LOCNES Telescope (feeding the 2 fibers of HARPS--N\footnote{The second fiber that will feed HARPS--N is already under discussion with the HARPS--N and LCST utilizer. In any case we consider it as well because it is part of the LOCNES project}) and check that the same spectra are produced on HARPS--N. The NIR part will extend to the full band-width of GIANO-B (0.9 to 2.5um). | \label{sec:conclusion} We outlined the scientific aims and the description of the LOCNES telescope project. LOCNES telescope will begin its duty in Fall 2018, recording, thanks to the two high resolution spectrographs of the TNG, VIS and NIR time series of Sun's radial velocity measurements. The wide wavelength range of LOCNES will help to connect the stellar (solar) activity causes and the different zones and depths of the chromosphere to the resulting RVs allowing the development of more tools for an optimal activity correction. Furthermore, the TNG acquires a low cost simple instrument that makes it the unique astronomical structure in the world with the possibility to gather high resolution spectra of the Sun as a star from the visible up to the K band. | 18 | 8 | 1808.03185 |
1808 | 1808.06769_arXiv.txt | Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay in the barycentric reference frame. As the Earth is orbiting around the Solar system barycentre with the velocity $V$ of 30~km/s, VLBI proves to be a handy tool to detect the subtle effects of the special and general relativity theory with a magnitude of $(V/\textrm{c})^2$. The theoretical correction for the second order terms reaches up to 300~ps, and it is implemented in the geodetic VLBI group delay model. The total contribution of the second order terms splits into two effects - the variation of the Earth scale, and the deflection of the apparent position of the radio source. The Robertson-Mansouri-Sexl (RMS) generalization of the Lorenz transformation is used for many modern tests of the special relativity theory. We develop an alteration of the RMS formalism to probe the Lorenz invariance with the geodetic VLBI data. The kinematic approach implies three parameters (as a function of the moving reference frame velocity) and the standard Einstein synchronisation. A generalised relativistic model of geodetic VLBI data includes all three parameters that could be estimated. Though, since the modern laboratory Michelson-Morley and Kennedy-Thorndike experiments are more accurate than VLBI technique, the presented equations may be used to test the VLBI group delay model itself. | The Very Long Baseline Interferometry (VLBI) technique measures time delay - the difference between times of the signal arrival on two radio telescopes separated by a long baseline. All measurements are referred to the Solar system barycentre, which moves around the Sun with an orbital velocity about 30~km/s. This makes the Earth a natural flying platform and VLBI a very effective tool to detect a tiny effect of special relativity. Each baseline of thousand kilometres length may serve as a ``flying rod", which is traditionally used for theoretical calculation. Precision of each single group delay is about 10~mm and since many observations are collected over a long period of time (20~years or more) the estimate of the time dilation effect will be very accurate. Geodetic VLBI has been used to test general relativity theory either in the frame of the Parameterized Post-Newtonian (PPN) formalism or the Standard-Model Extension (SME) (e.g., \citet{Robertson84}, \citet{Shapiro04}, \citet{Lambert09}, or \citet{LePoncinL16}). However, it has not been considered for testing special relativity in spite of its interferometric nature directly linked to the Michelson-Morley and Kennedy-Thorndike interferometers yet. In this paper we show a possible application of the geodetic VLBI to this experimental work. The conventional group delay $\tau_{g}$ model to approximate the observed VLBI data is given by~\citet[chap.~11]{iers10} as \begin{equation}\label{groupdelay_gcrs} \tau_{g}=\frac{-\frac{(\boldsymbol{b}\cdot\boldsymbol{s})}{\textrm{c}}\Big(1-\frac{2GM}{\textrm{c}^{2} R} -\frac{|\boldsymbol{V}|^{2}}{2\textrm{c}^{2}}-\frac{(\boldsymbol{V}\cdot\boldsymbol{w}_{2})}{\textrm{c}^2}\Big) -\frac{(\boldsymbol{b}\cdot\boldsymbol{V})}{\textrm{c}^{2}}\Big(1+\frac{(\boldsymbol{s}\cdot\boldsymbol{V})}{2\textrm{c}}\Big)} {1+\frac{\boldsymbol{s}\cdot(\boldsymbol{V}+\boldsymbol{w}_{2})}{\textrm{c}}} \end{equation} where $\boldsymbol{b}$ is the vector of baseline $\boldsymbol{b} = \boldsymbol{r_2}-\boldsymbol{r_1}$, $\boldsymbol{s}$ is the barycentric unit vector of radio source, $\boldsymbol{V}$ is the barycentric velocity of the geocentre, $\boldsymbol{w}_{2}$ is the geocentric velocity of the second station, \textrm{c} is the speed of light, \textrm{G} is the gravitational constant, $M$ is the mass of the Sun, and $R$ is the geocentric distance to the Sun.\\ The term $\frac{2GM}{\textrm{c}^{2} R}$ is related to the general relativity effect and we won't focus on it in this note. The impact of $\boldsymbol{w}_{2}$ is small and may be ignored for the sake of simplicity. After these alterations, Equation~(\ref{groupdelay_gcrs}) is given by \begin{equation}\label{groupdelay_gcrs_simple} \tau_{g}=\frac{-\frac{(\boldsymbol{b}\cdot\boldsymbol{s})}{\textrm{c}}\Big(1 -\frac{|\boldsymbol{V}|^{2}}{2\textrm{c}^{2}}\Big) -\frac{1}{\textrm{c}^{2}}(\boldsymbol{b}\cdot\boldsymbol{V}) \Big(1+\frac{(\boldsymbol{s}\cdot\boldsymbol{V})}{2\textrm{c}}\Big)} {1+\frac{1}{\textrm{c}}(\boldsymbol{s}\cdot\boldsymbol{V})} . \end{equation} Using the Taylor series expansion $(1+x)^{-1} = 1-x+x^2$ for $\Big(1+\frac{(\boldsymbol{s}\cdot\boldsymbol{V})}{\textrm{c}}\Big)^{-1}$ and noting the $\frac{|\boldsymbol{V}|^2}{\textrm{c}^2}$ terms only, Equation~(\ref{groupdelay_gcrs_simple}) reduces to \begin{equation}\label{groupdelay_gcrs_simple_v2c3} \begin{aligned} \tau_{g}=&\frac{(\boldsymbol{b}\cdot\boldsymbol{s})}{\textrm{c}} \frac{|\boldsymbol{V}|^{2}}{2\textrm{c}^{2}} - \frac{1}{\textrm{c}^{2}} (\boldsymbol{b}\cdot\boldsymbol{V}) \frac{(\boldsymbol{s}\cdot\boldsymbol{V})}{2\textrm{c}} -\\ &-\frac{(\boldsymbol{b}\cdot\boldsymbol{s})(\boldsymbol{s}\cdot\boldsymbol{V})^2 }{\textrm{c}^3} + \frac{1}{\textrm{c}^{2}} (\boldsymbol{b}\cdot\boldsymbol{V}) \frac{(\boldsymbol{s}\cdot\boldsymbol{V})}{\textrm{c}} =\\ =&\frac{(\boldsymbol{b}\cdot\boldsymbol{s})|\boldsymbol{V}|^{2}}{2\textrm{c}^{3}} - \frac{(\boldsymbol{b}\cdot\boldsymbol{s})(\boldsymbol{s}\cdot\boldsymbol{V})^2}{2\textrm{c}^{3}} \\ &-\frac{(\boldsymbol{b}\cdot\boldsymbol{V})(\boldsymbol{s}\cdot\boldsymbol{V})}{2\textrm{c}^{3}} + \frac{(\boldsymbol{b}\cdot\boldsymbol{V})(\boldsymbol{s}\cdot\boldsymbol{V})}{\textrm{c}^{3}} - \frac{(\boldsymbol{b}\cdot\boldsymbol{s})(\boldsymbol{s}\cdot\boldsymbol{V})^2}{2\textrm{c}^{3}} = \\ =&\frac{(\boldsymbol{b}\cdot\boldsymbol{s})\Big(|\boldsymbol{V}|^{2}-(\boldsymbol{s}\cdot\boldsymbol{V})^2\Big)}{2\textrm{c}^{3}} + \frac{(\boldsymbol{s}\cdot\boldsymbol{V})\Big((\boldsymbol{b}\cdot\boldsymbol{V})-(\boldsymbol{b}\cdot\boldsymbol{s})(\boldsymbol{s}\cdot\boldsymbol{V})\Big)}{2\textrm{c}^{3}} . \end{aligned} \end{equation} In Fig.~\ref{fig_triangle} we introduce the following angles $|\boldsymbol{V}| \cos\theta = (\boldsymbol{s}\cdot\boldsymbol{V})$, $|\boldsymbol{b}| \cos\varphi = (\boldsymbol{b}\cdot\boldsymbol{s})$ and $|\boldsymbol{b}||\boldsymbol{V}| \cos\psi = (\boldsymbol{b}\cdot\boldsymbol{V})$, and from the equation of spherical trigonometry we get $\cos\psi = \cos\theta \cos\varphi + \sin\theta \sin\varphi \cos A$. After applying the substitution \begin{equation}\label{trigfunc1} \begin{aligned} (\boldsymbol{b}\cdot\boldsymbol{s})\Big(|\boldsymbol{V}|^{2}-(\boldsymbol{s}\cdot\boldsymbol{V})^2\Big) = &|\boldsymbol{b}| \cos\varphi \Big(|\boldsymbol{V}|^2-|\boldsymbol{V}|^2 \cos^2\theta\Big) =\\ =&|\boldsymbol{b}| |\boldsymbol{V}|^2 \cos\varphi \sin^2\theta \end{aligned} \end{equation} and \begin{equation}\label{trigfunc2} \begin{aligned} &(\boldsymbol{s}\cdot\boldsymbol{V})\Big((\boldsymbol{b}\cdot\boldsymbol{V})-(\boldsymbol{b}\cdot\boldsymbol{s})(\boldsymbol{s}\cdot\boldsymbol{V})\Big) = \\ &=|\boldsymbol{V}| \cos\theta \Big( |\boldsymbol{b}||\boldsymbol{V}| \cos\psi - (|\boldsymbol{b}| \cos\varphi) (|\boldsymbol{V}| \cos\theta) \Big) = \\ &=|\boldsymbol{b}||\boldsymbol{V}|^2 \cos\theta \Big(\cos\theta \cos\varphi + \sin\theta \sin\varphi \cos A - \cos\theta \cos\varphi\Big) \end{aligned} \end{equation} we get the Equation~(\ref{groupdelay_gcrs_simple_v2c3}) in the following form \begin{equation}\label{groupdelay_sphtrig} \tau_{g}= \frac{|\boldsymbol{b}||\boldsymbol{V}|^{2}}{2\textrm{c}^3} \cos\varphi \sin^2\theta + \frac{|\boldsymbol{b}||\boldsymbol{V}|^{2}}{2\textrm{c}^3} \sin\varphi \sin\theta\cos\theta\cos A . \end{equation} \\ The major term of the geometric delay is \begin{equation}\label{tau_geom} \tau_{g}=-\frac{(\boldsymbol{b}\cdot\boldsymbol{s})}{\textrm{c}} = -\frac{|\boldsymbol{b}|\cos\varphi}{\textrm{c}} . \end{equation} The components of the baseline vector $\boldsymbol{b}$ and the source position vector $\boldsymbol{s}$ can be estimated from a large set of data within an adjustment. The observational delay from a correlator is approximated by the theoretical delay (Equation~(\ref{groupdelay_gcrs})), and the difference between the observational and the theoretical delay is modelled as follows: \begin{equation}\label{dtau} \tau_{obs} - \tau_{calc} = \frac{\partial \tau}{\partial b} \Delta b + \frac{\partial \tau}{\partial s} \Delta s \end{equation} or, by applying Equation~(\ref{tau_geom}) one gets \begin{equation}\label{dtau1} \tau_{obs} - \tau_{calc} = -\Delta b\frac{1}{\textrm{c}} \cos\varphi + \Delta s\frac{|\boldsymbol{b}|}{\textrm{c}}\sin\varphi \end{equation} which means that the corrections to the baseline vector components are calculated with the partials proportional to $\cos\varphi$ and corrections to the source vector components need partials proportional to $\sin\varphi$. Therefore, the first part of Equation~(\ref{groupdelay_sphtrig}) is a variation of the baseline vector (i.e., of the Earth scale) as it is proportional to the factor $(|\boldsymbol{b}|\cos{\varphi})$, and the second part is a variation of the source positions $(|\boldsymbol{b}|\sin{\varphi})$. \begin{figure}[tbp] \includegraphics[trim=0 0 0 0,clip, width=\hsize]{Fig1.png} \caption{Schematic view of the introduced angles with vectors placed in the geocentre.} \label{fig_triangle} \end{figure} | We can conclude that a variety of opportunities is allowed by the geodetic VLBI technique to test the Lorenz invariance in a frame of the kinematic RMS formalism. However, precision of the ground based VLBI measurements is not competitive to the laboratory experiments. While the geodetic VLBI is able to reach an accuracy of the estimation of the $\alpha, \beta$ and $\delta$ parameters at the level of $\sim10^{-2}$ using the barycentric velocity of the Earth in approximation \citep{Smoot77}, the laboratory tests set bounds on the anisotropy of the speed of light to $\sim10^{-12}$ with the Michelson-Morley experiments \citep{Herrmann09} and to $\sim10^{-8}$ with the Kennedy-Thorndike experiments \citep{Tobar10} using the velocity of the Sun with respect to the CMB which is about $\sim 370$~km/s \citep{Smoot77}. Theoretically, space VLBI observations within, e.g., the RadioAstron mission at baselines $\sim50$ times longer than the Earth radius reduced to the CMB reference frame (as proposed by~\citet{Klioner12}) may provide an accuracy of $\sim10^{-6}$ for the $\alpha, \beta$ and $\delta$ parameter combinations. | 18 | 8 | 1808.06769 |
1808 | 1808.04136_arXiv.txt | Several astronomical surveys aimed at the investigation of the extragalactic components were carried out in order to map systematically the universe and its constituents. An excellent level of detail is needed, and it is possible only using space telescopes or with the application of adaptive optics (AO) techniques for ground-based observatories. By simulating $K$-band observations of 6000 high-redshift galaxies in the {\it Chandra Deep Field South} region, we have already shown how an extremely large telescope can carry out photometric surveys successfully using the Global-MCAO, a natural guide stars based technique that allows the development of extragalactic research, otherwise impracticable without using laser guide stars. As the outcome of the analysis represents an impact science case for the new instruments on upcoming ground-based telescopes, here we show how the investigation of other observed deep fields could profit from such a technique. Further to an overview of the surveys suitable for the proposed approach, we show preliminary estimations both on geometrical (FoV and height) and purely AO perspectives (richness and homogeneity of guide stars in the area) for planned giant telescopes. | \label{sec:intro} Understanding the formation and evolution of galaxies is a lively debated topic in astrophysics, because the advent of more powerful telescopes stimulated more detailed theories and numerical simulations to interpret new observations. The main issue concerns the role of the competing scenarios in shaping galaxies: large protogalaxies formed through a dissipational collapse according to the monolithic scenario, whereas galaxies are the result of successive merging between small structures in the hierarchical merging process. Cold or hot-flow accretion, mergers involving gas or not (dissipational or dissipationless), feedback and outflows, and rapid monolithic aggregation are paradigms that live together within theoretical frameworks for understanding the early formation, structural properties, and evolution of galaxies. Observations spanning the full history of the Universe are critical for developing the knowledge of these processes: the early building blocks of galaxies can be studied at {\it z} $>6$, earlier redshift galaxies ($1<z<4$) span the peak of the massive galaxy building era, while, locally, dwarf galaxies can provide a fossil bed of relics from the low-mass end of the galaxy formation spectrum. \begin{table}[!htbp] \caption{Observing parameters for some of the most-studied surveys. Column~1: Name of the survey. Column~2: Right ascension and Column~3: Declination of the central pointing. Column~4: Field of view area. Column~5: Reference. } \label{tab:surveys} \begin{center} \begin{tabular}{|c|c|c|c|c|} % \hline \rule[-1ex]{0pt}{3.5ex} Survey name & RA & DEC & Field of View & Reference \\ \rule[-1ex]{0pt}{3.5ex} & [$^{\circ}$] & [$^{\circ}$] & [square arcmin] & \\ \hline \rule[-1ex]{0pt}{3.5ex} HDF & 189.2042 & 62.2161 & 5 & \citenum{Williams1996} \\ \hline \rule[-1ex]{0pt}{3.5ex} NDWFS-Bootes & 217.500 & 34.5000 & 3.24$10^4$ & \citenum{Jannuzi1999} \\ \hline \rule[-1ex]{0pt}{3.5ex} NDWFS-Cetus & 31.8708 & -4.7356 & 3.31$10^4$ & \citenum{Jannuzi1999} \\ \hline \rule[-1ex]{0pt}{3.5ex} HDF-S & 338.2458 & -60.5508 & 5.3 & \citenum{Williams2000} \\ \hline \rule[-1ex]{0pt}{3.5ex} CDF-S & 53.1167 & -27.8083 & 3.96$10^2$ & \citenum{Giacconi2001} \\ \hline \rule[-1ex]{0pt}{3.5ex} DLS-1 & 13.3542 & 12.5653 & 1.44$10^4$ & \citenum{Wittman2002} \\ \hline \rule[-1ex]{0pt}{3.5ex} DLS-2 & 139.5000 & 30.0000 & 1.44$10^4$ & \citenum{Wittman2002} \\ \hline \rule[-1ex]{0pt}{3.5ex} DLS-3 & 80.0000 & -49.0000 & 1.44$10^4$ & \citenum{Wittman2002} \\ \hline \rule[-1ex]{0pt}{3.5ex} DLS-4 & 163.0000 & -5.0000 & 1.44$10^4$ & \citenum{Wittman2002} \\ \hline \rule[-1ex]{0pt}{3.5ex} DLS-5 & 208.7500 & -10.0000 & 1.44$10^4$ & \citenum{Wittman2002} \\ \hline \rule[-1ex]{0pt}{3.5ex} DLS-6 & 32.5000 & -4.5000 & 1.44$10^4$ & \citenum{Wittman2002} \\ \hline \rule[-1ex]{0pt}{3.5ex} DLS-7 & 218.0000 & 34.2800 & 1.44$10^4$ & \citenum{Wittman2002} \\ \hline \rule[-1ex]{0pt}{3.5ex} EGSS & 214.2500 & 52.5000 & 7.00$10^2$ & \citenum{Davis2003} \\ \hline \rule[-1ex]{0pt}{3.5ex} GEMS & 53.1042 & -27.8139 & 8.00$10^2$ & \citenum{Rix2004} \\ \hline \rule[-1ex]{0pt}{3.5ex} GOODS-N & 189.2292 & 62.2375 & 1.60$10^2$ & \citenum{Giavalisco2004} \\ \hline \rule[-1ex]{0pt}{3.5ex} GOODS-S & 53.1250 & -27.8056 & 1.60$10^2$ & \citenum{Giavalisco2004} \\ \hline \rule[-1ex]{0pt}{3.5ex} SubaruDF & 201.1625 & 27.4906 & 9.18$10^2$ & \citenum{Kashikawa2004} \\ \hline \rule[-1ex]{0pt}{3.5ex} COSMOS & 150.1167 & 2.2058 & 7.200$10^3$ & \citenum{Scoville2004} \\ \hline \rule[-1ex]{0pt}{3.5ex} GSS & 214.4042 & 52.4828 & 1.27$10^2$ & \citenum{Vogt2005} \\ \hline \rule[-1ex]{0pt}{3.5ex} HUDF & 53.1625 & -27.7914 & 11 & \citenum{Beckwith2006} \\ \hline \rule[-1ex]{0pt}{3.5ex} CFHTLS-D1 & 36.4958 & -4.4944 & 3.60$10^3$ & \citenum{Cuillandre2006} \\ \hline \rule[-1ex]{0pt}{3.5ex} CFHTLS-D2 & 150.1167 & 2.2083 & 3.60$10^3$ & \citenum{Cuillandre2006} \\ \hline \rule[-1ex]{0pt}{3.5ex} CFHTLS-D3 & 214.8625 & 52.6822 & 3.60$10^3$ & \citenum{Cuillandre2006} \\ \hline \rule[-1ex]{0pt}{3.5ex} CFHTLS-D4 & 333.8792 & -17.7320 & 3.60$10^3$ & \citenum{Cuillandre2006} \\ \hline \rule[-1ex]{0pt}{3.5ex} AEGIS & 214.2500 & 52.5000 & 7.00$10^2$ & \citenum{Davis2007} \\ \hline \rule[-1ex]{0pt}{3.5ex} UKIDSS-DXS1 & 36.2500 & -4.5000 & 1.26$10^5$ & \citenum{Lawrence2007} \\ \hline \rule[-1ex]{0pt}{3.5ex} UKIDSS-DXS2 & 164.2500 & 57.6667 & 1.26$10^5$ & \citenum{Lawrence2007} \\ \hline \rule[-1ex]{0pt}{3.5ex} UKIDSS-DXS3 & 242.5 & 54.0000 & 1.26$10^5$ & \citenum{Lawrence2007} \\ \hline \rule[-1ex]{0pt}{3.5ex} UKIDSS-DXS4 & 334.2500 & 0.3333 & 1.26$10^5$ & \citenum{Lawrence2007} \\ \hline \rule[-1ex]{0pt}{3.5ex} UKIDSS-UD & 36.2500 & -4.5000 & 2.77$10^3$ & \citenum{Lawrence2007} \\ \hline \rule[-1ex]{0pt}{3.5ex} HUDF9 & 53.1625 & -27.7914 & 4.7 & \citenum{Bouwens2011} \\ \hline \rule[-1ex]{0pt}{3.5ex} C\_GOODS-N & 189.2286 & 62.2385 & 9.18$10^2$ & \citenum{Koekemoer2011} \\ \hline \rule[-1ex]{0pt}{3.5ex} C\_GOODS-S & 53.1228 & -27.8050 & 1.12$10^3$ & \citenum{Koekemoer2011} \\ \hline \rule[-1ex]{0pt}{3.5ex} C\_COSMOS & 150.1163 & 2.2010 & 1.44$10^4$ & \citenum{Koekemoer2011} \\ \hline \rule[-1ex]{0pt}{3.5ex} C\_EGS & 214.8250 & 52.8250 & 7.20$10^3$ & \citenum{Koekemoer2011} \\ \hline \rule[-1ex]{0pt}{3.5ex} C\_UDS & 34.4062 & -5.2000 & 7.20$10^3$ & \citenum{Koekemoer2011} \\ \hline \rule[-1ex]{0pt}{3.5ex} UDF12 & 53.1625 & -27.7914 & 5 & \citenum{Koekemoer2013} \\ \hline \rule[-1ex]{0pt}{3.5ex} XDF & 53.1583 & -27.7833 & 10.9 & \citenum{Illingworth2013} \\ \hline \end{tabular} \end{center} \end{table} Deep field surveys answered to several astrophysical questions, providing a wide database of objects at large and intermediate redshifts. In fact, in about 20 years of observations, a lot of sky regions were mapped and Table~\ref{tab:surveys} shows a list of them that can not be exhaustive. Some of these runs were combined together in order to merge the information in the different bands, making a synergy that is fundamental in order to have a comprehensive view of Universe. In this framework, the NASA's Great Observatories Program can be considered one of the best example of this synergy, being a mission designed to examine specific wavelength/energy regions of the electromagnetic spectrum using different technologies and observatories. A number of future space- and ground-based facilities will definitely contribute to this topic, starting from the next generation of the ELTs, such as the European Extremely Large Telescope \cite{Gilmozzi2007}, the Giant Magellan Telescope \cite{Johns2008} and the Thirty Meter Telescope \cite{Szeto2008}, whose main characteristics are listed in Table~\ref{tab:telescopes}. Moreover, in order to widely progress in this field and to improve the potentialities, two routes can be followed: the sole improvement of the engineering side of the existing instruments, or the attempt to turn into reality novel concepts and new ideas. Being the latter an exciting challenge, [\citenum{Ragazzoni2010}] proposed a new Adaptive Optics technique, called Global-Multi Conjugate Adaptive Optics (GMCAO), in which a wide field of view (labelled technical FoV) can be used to look for natural guide stars and correct the smaller scientific FoV. For a review of the concept and the implementation of an example of such a system, see [\citenum{Viotto2015}]. \begin{table}[!htbp] \caption{Observing capabilities of the ELTs. Column~1: Telescope Name. Column~2: Diameter of the primary mirror. Column~3: Site with coordinates. Column~4: Telescope field of view. Column~5: Resolution. Column~6: Filters.} \label{tab:telescopes} \begin{center} \begin{tabular}{|c|c|c|c|c|c|} % \hline \rule[-1ex]{0pt}{3.5ex} Telescope & Diameter & Site & Field of View & Resolution & Filters\\ \rule[-1ex]{0pt}{3.5ex} & [m] & [$^{\circ}$] & & [mas] & \\ \hline \rule[-1ex]{0pt}{3.5ex} E-ELT (MICADO) & 39 & Cerro Armazones (-70.19,-24.59) & 53\arcsec $\times$ 53\arcsec & 4 & I z Y J H K \\ \rule[-1ex]{0pt}{3.5ex} & & & 16\arcsec $\times$ 16\arcsec & 1.5 & \\ \hline \rule[-1ex]{0pt}{3.5ex} GMT (GMTIFS) & 25.4 & Las Campanas (-70.69,-29.02) & 20.4\arcsec$\times$ 20.4\arcsec & 5 & J H K \\ \hline \rule[-1ex]{0pt}{3.5ex} TMT (IRIS) & 30 & Mauna Kea (-155.47,19.82) & 34\arcsec $\times$ 34\arcsec & 4 & J H K \\ & & La Palma (-17.89,28.89) & & & \\ \hline \end{tabular} \end{center} \end{table} [\citenum{Portaluri2017}] presented a scientific case in the area of applicability of the GMCAO technique, recovering the structural parameters of a sample of 6000 synthetic high-redshift galaxies observed in the {\it Chandra Deep Field South} region with a GMCAO-assisted extremely large telescope (ELT) and performing the source detection and two-dimensional fitting analysis. These studies have shown that the GMCAO approach can produce robust results when studying the photometry of extragalactic fields and can provide a useful frame of reference for a number of science cases. Here, we want to investigate if it is possible to extend the same evaluation to other deep fields, and therefore if GMCAO can be used to map all the regions of the sky. The selection of some representative surveys and their observabilities with the planned ELTs are shown in Section~\ref{sec:obs}, while in Section~\ref{sec:stars} preliminary estimations on AO perspectives are given. | \label{sec:concl} The era of the next generation of giant telescopes requires not only the advent of new technologies but also the development of novel methods, in order to exploit fully the extraordinary potential they are built for. GMCAO pursues this approach, with the goal of achieving good performance over a field of view of a few arcmin and an increase in sky coverage. In this work we have shown that GMCAO is a reliable approach to assist ELT observations of extragalactic interest, especially for the photometric survey strategy. This technique can be applicable to all the sky, as theoretical counts and observational data show, giving a gain in terms of increase of the encircled energy and SRs up to 30\% for the best asterisms. | 18 | 8 | 1808.04136 |
1808 | 1808.04300_arXiv.txt | {} { We aim to characterize the multiwavelength emission from Markarian~501 (Mrk~501), quantify the energy-dependent variability, study the potential multiband correlations and describe the temporal evolution of the broadband emission within leptonic theoretical scenarios. } {A multiwavelength campaign was organized to take place between March and July of 2012. Excellent temporal coverage was obtained with more than 25 instruments, including the MAGIC, FACT and VERITAS Cherenkov telescopes, the instruments on board the \textit{Swift} and \textit{Fermi} spacecraft, and the telescopes operated by the GASP-WEBT collaboration. } { Mrk~501 showed a very high energy (VHE) gamma-ray flux above 0.2 TeV of $\sim$0.5 times the Crab Nebula flux (CU) for most of the campaign. The highest activity occurred on 2012 June 9, when the VHE flux was $\sim$3~CU, and the peak of the high-energy spectral component was found to be at $\sim$2~TeV. Both the X-ray and VHE gamma-ray spectral slopes were measured to be extremely hard, with spectral indices $\textless$ 2 during most of the observing campaign, regardless of the X-ray and VHE flux. This study reports the hardest Mrk~501 VHE spectra measured to date. The fractional variability was found to increase with energy, with the highest variability occurring at VHE. Using the complete data set, we found correlation between the X-ray and VHE bands; however, if the June 9 flare is excluded, the correlation disappears (significance $\textless$ 3$\sigma$) despite the existence of substantial variability in the X-ray and VHE bands throughout the campaign. } { The unprecedentedly hard X-ray and VHE spectra measured imply that their low- and high-energy components peaked above 5~keV and 0.5~TeV, respectively, during a large fraction of the observing campaign, and hence that Mrk~501 behaved like an extreme high-frequency-peaked blazar (EHBL) throughout the 2012 observing season. This suggests that being an EHBL may not be a permanent characteristic of a blazar, but rather a state which may change over time. The data set acquired shows that the broadband spectral energy distribution (SED) of Mrk~501, and its transient evolution, is very complex, requiring, within the framework of synchrotron self-Compton (SSC) models, various emission regions for a satisfactory description. Nevertheless the one-zone SSC scenario can successfully describe the segments of the SED where most energy is emitted, with a significant correlation between the electron energy density and the VHE gamma-ray activity, suggesting that most of the variability may be explained by the injection of high-energy electrons. The one-zone SSC scenario used reproduces the behaviour seen between the measured X-ray and VHE gamma-ray fluxes, and predicts that the correlation becomes stronger with increasing energy of the X-rays. } | 18 | 8 | 1808.04300 |
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1808 | 1808.03716_arXiv.txt | A valuable target for advanced gravitational-wave detectors is the stochastic gravitational-wave background. The stochastic background imparts a weak correlated signal into networks of gravitational-wave detectors, and so standard searches for the gravitational-wave background rely on measuring cross-correlations between pairs of widely-separated detectors. Stochastic searches, however, can be affected by any other correlated effects which may also be present, including correlated frequency combs and magnetic Schumann resonances. As stochastic searches become sensitive to ever-weaker signals, it is increasingly important to develop methods to separate a true astrophysical signal from other spurious and/or terrestrial signals. Here, we describe a novel method to achieve this goal -- gravitational-wave geodesy. Just as radio geodesy allows for the localization of radio telescopes, so too can observations of the gravitational-wave background be used to infer the positions and orientations of gravitational-wave detectors. By demanding that a true observation of the gravitational-wave background yield constraints consistent with the baseline's known geometry, we demonstrate that we can successfully validate true observations of the gravitational-wave background while rejecting spurious signals due to correlated terrestrial effects. \vspace{1cm} | The recent Advanced LIGO-Virgo observations of binary black hole \citep{O1BBH,GW170104,GW170608,GW170814} and binary neutron star \citep{GW170817} mergers suggest that the astrophysical stochastic gravitational-wave background may soon be within reach \citep{Implications150914,Implications170817,IsotropicO1,DirectionalO1}. As the superposition of all gravitational-wave signals too weak to individually detect, the stochastic gravitational-wave background is expected to be dominated by compact binary mergers at cosmological distances \citep{Regimbau2008,Rosado2011,Zhu2011,Wu2012,Zhu2013,Callister2016}. Although the stochastic background is orders of magnitude weaker than instrumental detector noise, it will nevertheless impart a weak \textit{correlated} signal to pairs of gravitational-wave detectors. The stochastic background may therefore be detected in the form of excess correlations between widely-separated gravitational-wave detectors \citep{Christensen1992,Allen1999,Romano2017}. Cross-correlation searches for the stochastic background rely on the assumption that, in the absence of a gravitational-wave signal, the outputs of different gravitational-wave detectors are fundamentally uncorrelated. The LIGO-Hanford and LIGO-Livingston detectors, for instance, are separated by 3000\,km, with a light travel time of $\approx$\,0.01\,s between sites. One might therefore reasonably expect them to be safely uncorrelated at $\sim \mathcal{O}(100\,\mathrm{Hz})$, in the frequency band of interest for ground-based detectors. In reality, however, terrestrial gravitational-wave detectors are \textit{not} truly uncorrelated. Hanford-Livingston coherence spectra consistently show correlated features that, if not properly identified and removed, can severely contaminate searches for the stochastic gravitational-wave background \citep{Covas2018}. Schumann resonances are one expected source of terrestrial correlation \citep{Schumann1,Schumann2}. Global electromagnetic excitations in the cavity formed by the Earth and its ionosphere, Schumann resonances may magnetically couple to Advanced LIGO and Advanced Virgo's test mass suspensions and induce a correlated signal between detectors \citep{Christensen1992,Thrane2013,Thrane2014,Coughlin2016,Coughlin2018}. Another expected source of correlation is the joint synchronization of electronics at each detector to Global Positioning System (GPS) time. In Advanced LIGO's O1 observing run, for instance, a strongly-correlated 1\,Hz comb was traced to blinking LED indicators on timing systems independently synchronized to GPS \citep{Covas2018}. Any undiagnosed terrestrial correlations may yield a false-positive detection of the stochastic gravitational-wave background. While Schumann resonances and frequency combs represent two known classes of correlation, there may exist others. The validation of any apparent observation of the stochastic background will therefore require us to answer the following question: \textit{How likely is an observed correlated signal to be of astrophysical origin, rather than a yet-unidentified source of terrestrial correlation?} We currently lack the tools to quantitatively answer this question. Searches for gravitational-wave transients can address this issue through the use of time-slides: the artificial time-shifting of data from one detector relative to another's. This process eliminates any coherent gravitational-wave signals while preserving all other properties of the data, allowing for accurate estimation of the rate of false positive detections. In cross-correlation searches for the stochastic background, however, time-slides would not only remove a gravitational-wave signal but also any correlated terrestrial contamination as well. Time-slides are therefore of limited use in searches for the gravitational-wave background. Using techniques borrowed from the field of radio geodesy, here we develop a novel method to evaluate the astrophysical significance of an apparent correlated stochastic signal. Just as interferometric observations of the radio sky can serve to precisely localize radio telescopes on the Earth, we demonstrate that measurements of the gravitational-wave background can be similarly reverse-engineered to infer the separations and relative orientations of gravitational-wave detectors. By demanding that a true gravitational-wave background yield results consistent with the \textit{known} geometry of our detectors, we can separate true gravitational-wave signals from spurious terrestrial correlations. First, in Sect. \ref{formalism}, we review search methods for the stochastic gravitational-wave background and introduce gravitational-wave geodesy. In Sect. \ref{modelSelection}, we use geodesy as the basis of a Bayesian test with which to reject non-astrophysical signals, and in Sect. \ref{demonstration}, we demonstrate this procedure using simulated measurements of both a gravitational-wave background and terrestrial sources of correlation. Finally, in Sect. \ref{complications}, we discuss potential complications and outline directions for future work. | As searches for the stochastic gravitational-wave background grow increasingly sensitive, we may be nearing the first detection of the background. This prospect, though, comes with significant risk, namely the high cost of a false-positive detection. To minimize this risk, it will be important to develop methods to validate tentative detections of the gravitational-wave background. Specifically, when assessing any apparent detection, it will be necessary to argue not just that an observed correlation is statistically-significant, but that it it \textit{astrophysical} -- that it is due to gravitational waves and not some other, terrestrial process. While well-developed methods exist to quantify the statistical significance of measured correlations, until now no generic method has existed to gauge whether a statistically significant cross-correlation is indeed astrophysical. In this paper, we explored how gravitational-wave geodesy -- the use of the stochastic gravitational-wave background itself to determine the positions and orientations of gravitational-wave detectors -- can form the basis for a novel consistency check on an apparent detection of the background. If the measured correlation between detectors truly represents a gravitational-wave signal, then the reconstructed detector orientations and positions must be compatible with their true, known values. Correlations due to any terrestrial source, on the other hand, have no reason to prefer the baseline's true geometry over any other possible arrangement. By demanding that gravitational-wave geodesy yield results consistent with the true baseline geometry, we can discriminate between astrophysical and terrestrial sources of correlation. Used in this fashion, gravitational-wave geodesy provides a second independent measure of detection significance besides a standard signal-to-noise ratio. Our analysis has relied on two important assumptions. First, we have adopted a relatively simple model energy-density spectrum (a power law) that was a good description of our simulated stochastic signals. In Appendix \ref{complicationsA}, we investigate how our method performs given more complex models for the stochastic background. Most importantly, we also investigate how are results are affected if we mistakenly assume an \textit{incorrect} form for the background's energy-density spectrum. We find that remains robust, correctly classifying astrophysical signals even given significant mismatch between our model spectrum and the true stochastic signal. Second, we have assumed that the stochastic gravitational-wave background is isotropic, which is unlikely to be strictly true. As discussed further in Appendix \ref{complicationsB}, the expected anisotropies in the stochastic background are small, and therefore are unlikely to affect our analysis. In the case that anisotropy is a significant concern, however, we outline how our analysis should be modified to handle an anisotropic stochastic signal. | 18 | 8 | 1808.03716 |
1808 | 1808.02710_arXiv.txt | {Twenty years ago, GRB 980425/SN~1998bw revealed that long Gamma-Ray Bursts (GRBs) are physically associated with broad-lined type Ic supernovae. Since then more than 1000 long GRBs have been localized to high angular precision, but only in $\sim50$ cases the underlying supernova (SN) component was identified. Using the multi-channel imager GROND (Gamma-Ray Burst Optical Near-Infrared Detector) at ESO/La Silla, during the last ten years we have devoted a substantial amount of observing time to reveal and to study SN components in long-GRB afterglows. Here we report on four more GRB-SNe (associated with GRBs 071112C, 111228A, 120714B, and 130831A) which were discovered and/or followed-up with GROND and whose redshifts lie between $z=0.4$ and 0.8. We study their afterglow light curves, follow the associated SN bumps over several weeks, and characterize their host galaxies. Using SN~1998bw as a template, the derived SN explosion parameters are fully consistent with the corresponding properties of the so-far known GRB-SN ensemble, with no evidence for an evolution of their properties as a function of redshift. In two cases (GRB 120714B/SN~2012eb at $z=0.398$ and GRB 130831A/SN~2013fu at $z=0.479$) additional Very Large Telescope (VLT) spectroscopy of the associated SNe revealed a photospheric expansion velocity at maximum light of about 40\,000 and 20\,000 km s$^{-1}$, respectively. For GRB 120714B, which was an intermediate-luminosity burst, we find additional evidence for a blackbody component in the light of the optical transient at early times, similar to what has been detected in some GRB-SNe at lower redshifts.} | The association of SN~1998bw in the spiral galaxy ESO 184-G82 ($z=0.0085$, \citealt{Tinney1998IAUC}) with the long GRB 980425 (\citealt{Galama1998Natur}) provided the first clue that long-duration GRBs are associated with the deaths of massive stars. Twenty years after SN~1998bw there is mounting observational and theoretical evidence that long GRBs have their origin in a subclass of broad-lined type Ic supernovae (SNe), which spectroscopically reveal high expansion velocities (for reviews see, e.g., \citealt{Cobb2012IAUS,Hjorth2012grbu,Hjorth2013RSPTA, Schulze2014,Olivares2015a,Kann2016,Cano2016}). Since long GRBs signal the explosions of massive stars, they potentially allow for a zoom-in into the high-$z$ universe at times when Population III stars formed and exploded (e.g., \citealt{Mesler2014ApJ...787...91M}). Currently, about 50 GRB-SNe have been discovered photometrically as a late-time bump in GRB afterglows, but only 50\% of these have a spectroscopic confirmation (\citealt{Cano2016}). At least some might be linked to the formation of a magnetar \citep{Mazzali2014MNRAS.443...67,Greiner2015Natur,Kann2016,Wang2017ApJ, Wang2017ApJ...850..148W,Lu2018ApJ}. Supernova bumps have been detected up to a redshift of $z=1.06$ (GRB 000911; \citealt{Masetti2005}) and spectroscopically studied up to $z=1.01$ (GRB 021211/SN~2002lt; \citealt{DellaValle2003IAUC8197,DellaValle2003}). For two decades GRB 980425/SN~1998bw has remained the closest GRB-SN detected. As such it is also the best-studied GRB-SN event and, therefore, used as the standard template for basically all GRB-SN studies in the optical bands \citep{Zeh2004a,Cano2013a}. In the pre-\swift~ (Neil Gehrels \emph{Swift} Observatory) satellite (\citealt{Gehrels2004}) era (1997-2004) the annual discovery rate of long-GRB afterglows with a redshift $z<1$ ($<0.5$), i.e., those potentially suited for GRB-SN detections, was on average about 2--3 (1--2) events per year. In the \swift~ era (2005+) this rate increased to about 6--8 (3--4) per year (no $z<0.5$ burst in 2007, and only 1 burst in 2008 and 2014), while the discovery rate of the accompanying GRB-SNe settled at on average 1 to 2 events per year. For $0.5 < z < 1.0$ visibility constraints and substantial observational efforts for a required photometric long-term follow up might be the main reasons why most GRB-SNe were missed, though in some cases host-galaxy extinction (e.g., \citealt{Soderberg2006ApJ...636..391S}) or an intrinsically faint SN (e.g., \citealt{Niino2012PASJ...64..115N}, but see \citealt{Postigo2018arXiv180704281D}) might have played a role too. One could also speculate that a long-lasting bright optical afterglow could hide a rising SN component (thanks to the referee for pointing this out). Indeed, this was basically the case for GRB 030329; here the $R_C$-band light curve did not show a bump since the transition between afterglow light and SN light was very smooth (see figure 3 in \citealt{Zeh2005NCimC..28..617Z}). Though a detailed investigation of this possibility remains to be done, {\it ad hoc} it appears to be a less likely situation. On the one hand, at least the GROND data archive always includes multi-color data. This might strongly reduce the probability to miss a rising SN component. On the other hand, once a redshift information was known and $z\kr0.5$ found, very likely spectroscopic observations were triggered by the GRB community. At redshifts $z\lesssim0.1$ observational efforts to monitor an expected/accompanying SNe were usually high and led to the discovery of thermal components in early GRB afterglows (e.g., \citealt{Campana2006,Waxman2007,Olivares2012, Starling2012MNRAS.427.2950S,Schulze2014}) and allowed for detailed studies of the SN explosion parameters (for a review see \citealt{Cano2016}, and references therein). Moreover, it led to the discovery of three events where no underlying SN component was found down to deep flux limits (GRB 060505 at $z=0.089$ and GRB 060614 at $z=0.125$: \citealt{DellaValle2006Natur}; \citealt{Fynbo2006Natur}; \citealt{Gal-Yam2006Natur}; \citealt{Xu2009ApJ...696..971X}; \citealt{McBreen2008ApJ...677L..85M}; GRB 111005A at $z=0.01326$, \citealt{Michalowski2016}; \citealt{Tanga2017arXiv170806270T}). This has raised the question whether some long bursts could have their origin in failed supernovae which immediately collapse into a black hole. The low redshift of these well-studied SNe also allowed for detailed studies of their host galaxies (e.g., \citealt{Wiersema2007, Christensen2008A&A...490...45C, Thone2008ApJ...676.1151T, Levesque2011ApJ...739...23L, Levesque2012ApJ...758...92L, Leloudas2011A&A...530A..95L, Fynbo2012grb..book..269F, Michalowski2012ApJ...755...85M, Michalowski2016, Schulze2014, Thone2014MNRAS.441.2034T, Izzo2017MNRAS.472.4480I, Kruhler2017A&A...602A..85K, Tanga2017arXiv170806270T}). Though, even for events at higher redshifts detailed host-galaxy studies have been performed (\citealt{Postigo2018arXiv180704281D}). The relatively small annual discovery rate of GRB-SNe calls for detailed follow-up observations of each event. While spectroscopic observations usually need the biggest telescopes in order to get a reasonable signal-to-noise ratio, photometric studies are less demanding and can be performed using smaller telescopes as well. Here we report on observations of a further set of four GRB-SNe observed with GROND (MPG 2.2m, ESO/La Silla; \citealt{Greiner2007Msngr,Greiner2008}) in the optical/NIR bands in the years between 2007 and 2013. Previous results of follow-up observations of GRB-SNe with GROND were presented in \cite{Olivares2012} (GRB/XRF 100316D/SN~2010bh), \cite{Olivares2015a} (GRBs 081007/SN~2008hw, 091127/SN~2009nz, 101219B/SN~2010ma) as well as \cite{Greiner2015Natur} and \cite{Kann2016} (GRB 111209A/SN~2011kl). Three of the events discussed here are studied for the first time (GRBs 071112C, 111228A, 120714B), while GRB 130831A/SN~2013fu was also explored by \cite{Cano2014a} using an independent data set. Two of the events we study could also be investigated based on spectroscopic follow-up campaigns with the Very Large Telescope (GRB 120714B/SN~2012eb, GRB 130831A/SN~2013fu; \citealt{Klose2012GCN13613,Klose2012a,Klose2013GCN15320,Klose2013b}). The paper is organized as follows. We start with a brief overview concerning the observational details (Sect.~\ref{SecObs}) and then focus on the SN light curves (Sect.~\ref{Photometry}). Thereafter, we report (i) on the results of our early-time VLT/X-shooter spectroscopy of the optical transient that followed GRB 120714B (Sect.~\ref{Shocking}) and (ii) on the results of the VLT/FORS2 (FOcal Reducer and low dispersion Spectrograph) spectroscopy around SN maximum (GRB 120714B/SN~2012eb and GRB 130831A/SN~2013fu; Sect.~\ref{SN.Spectr}). In Sect.~\ref{Discussion} we derive the relevant explosion parameters of the SNe and put the properties of the four GRB-SNe in the context of the present world-sample of well-observed GRB-SNe. In addition, we summarize the properties of the corresponding afterglows and GRB host galaxies. In the following, we use the convention $F_\nu(t)\sim t^{-\alpha}\nu^{-\beta}$ to describe the temporal and spectral evolution of the flux density $F_\nu(t)$ of an afterglow. We use a $\Lambda$CDM cosmology with $H_0=71$~km~s$^{-1}$ Mpc$^{-1}$, $\Omega_M=0.27$, and $\Omega_\Lambda=0.73$ \citep{Spergel2003a}. | 18 | 8 | 1808.02710 |
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1808 | 1808.07629_arXiv.txt | Inelasticity--the fraction of a neutrino's energy transferred to hadrons--is a quantity of interest in the study of astrophysical and atmospheric neutrino interactions at multi-TeV energies with IceCube. In this work, a sample of contained neutrino interactions in IceCube is obtained from 5 years of data and classified as 2650 tracks and 965 cascades. Tracks arise predominantly from charged-current $\nu_{\mu}$ interactions, and we demonstrate that we can reconstruct their energy and inelasticity. The inelasticity distribution is found to be consistent with the calculation of Cooper-Sarkar {\it et al.} across the energy range from $\sim$ 1 TeV to $\sim$ 100 TeV. Along with cascades from neutrinos of all flavors, we also perform a fit over the energy, zenith angle, and inelasticity distribution to characterize the flux of astrophysical and atmospheric neutrinos. The energy spectrum of diffuse astrophysical neutrinos is well-described by a power-law in both track and cascade samples, and a best-fit index $\gamma=2.62\pm0.07$ is found in the energy range from 3.5 TeV to 2.6 PeV. Limits are set on the astrophysical flavor composition that are compatible with a ratio of $\left(\frac{1}{3}:\frac{1}{3}:\frac{1}{3}\right)_{\oplus}$. Exploiting the distinct inelasticity distribution of $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ interactions, the atmospheric $\nu_{\mu}$ to $\bar{\nu}_{\mu}$ flux ratio in the energy range from 770 GeV to 21 TeV is found to be $0.77^{+0.44}_{-0.25}$ times the calculation by Honda {\it et al.} Lastly, the inelasticity distribution is also sensitive to neutrino charged-current charm production. The data are consistent with a leading-order calculation, with zero charm production excluded at $91\%$ confidence level. Future analyses of inelasticity distributions may probe new physics that affects neutrino interactions both in and beyond the Standard Model. | The observation of astrophysical neutrinos \cite{Aartsen:2013jdh,Aartsen:2014gkd} was a landmark in high-energy astrophysics. It introduced a new probe that is directionally sensitive to high-energy hadronic particle accelerators in the universe. Neutrinos provide both good directional information, unaffected by magnetic fields, and extremely long range, allowing us to probe accelerators at cosmologically significant distances. Measurements of the flux and energy spectrum \cite{Aartsen:2015zva,Aartsen:2017mau} and flavor composition \cite{Aartsen:2015ivb,Aartsen:2015knd} are so far fully compatible with conventional acceleration models, but more exotic production mechanisms cannot be ruled out. At the same time, the observation of high-energy astrophysical and atmospheric neutrinos by detectors like IceCube has opened up the study of neutrino interactions at energies orders of magnitude above those accessible at terrestrial accelerators. Already, the 1 km$^3$ IceCube neutrino observatory has used atmospheric and astrophysical neutrinos to measure neutrino absorption in the Earth, and from that determined the neutrino-nucleon cross section at energies from 6.3 TeV to 980 TeV to be in agreeement with the Standard Model prediction \cite{Aartsen:2017kpd}. In this paper, we report on a new study of high-energy charged-current (CC) $\nu_\mu$ interactions contained within IceCube's instrumented volume. These interactions produce a cascade of hadrons and a muon, an event topology known as a starting track. By estimating the hadronic cascade and muon energies separately, we can estimate the inelasticity of each interaction -- the ratio of hadronic cascade energy to total neutrino energy \cite{Dissertation}. The central 90\% of neutrinos have estimated energies in the range from 1.1 TeV to 38 TeV, energies far beyond the reach of terrestrial accelerators. For example, the NuTeV data were used to measure inelasticity distributions at energies up to 250 GeV \cite{Schienbein:2007fs}, while earlier experiments were limited to lower energies \cite{Aubert:1974en}. % The starting track data, together with a similarly obtained set of cascades due to all neutrino flavors are binned by reconstructed energy and zenith angle and (for the tracks) inelasticity. This data is fitted to a neutrino flux model containing both atmospheric and astrophysical neutrinos. From this, we present measurements of neutrino inelasticity and estimate the fraction of neutrino interactions that produce charmed particles. We also compare the track and cascade samples, study whether they have the same astrophysical neutrino flux spectral indices, and constrain the flavor composition of astrophysical neutrinos. Finally, we measure the ratio of neutrinos to antineutrinos in the atmospheric neutrino flux. | We have developed a tool to measure neutrino inelasticity in Gigaton-scale H$_2$O based detectors and presented the first measurements of neutrino inelasticity in very high-energy (above 1 TeV) neutrino interactions, using a sample of starting track events collected by the IceCube Neutrino Observatory. The measured inelasticity distributions are in good agreement with the predictions of a modern NLO calculation. More data is needed to reach anticipated theoretical uncertainties in these calculations. We have made a global fit to these neutrino data, fitting cascades in two dimensions: energy and zenith angle, and starting tracks in three dimensions: energy, zenith angle and inelasticity, to extract information about the astrophysical and atmospheric neutrino fluxes. This fit finds an astrophysical power-law spectral index of $\gamma=2.62\pm 0.07$, in good agreement with previous fits to contained events and cascades, but in tension with previous results based on through-going muons, a sample that is generally higher in energy than the contained event samples. To explore this tension, we performed a fit where we allowed the astrophysical flux to float separately for cascades and starting tracks, with different spectral indices. Unfortunately, this leads to a spectral index for the tracks, $\gamma=2.43^{+0.28}_{-0.30}$, intermediate between the combined result and that for through-going tracks, with an error that is consistent with either. We then relaxed the requirement that the astrophysical neutrino flavor ratio be $\left(\frac{1}{3}:\frac{1}{3}:\frac{1}{3}\right)_{\oplus}$, and calculated the confidence level for other compositions. We found a best fit point consisting of 79\% $\nu_\tau$, 21\% $\nu_\mu$, but with a broad allowed contour that encompasses all of the models that invoke conventional acceleration mechanisms and standard neutrino oscillations. More exotic models may be ruled out. We also set limits on the $\nu_\mu:\bar{\nu}_\mu$ ratio in atmospheric neutrinos and exclude zero production of charm quarks in neutrino interactions at 91\% confidence level. This is only the second study, after measurements of the cross section using neutrinos with energies above 1 TeV. Using the indirect signature in the inelasticity distribution, we observe, at greater than 90\% confidence level, CC charm production in neutrino interactions, at energies between 1.5 and 340 TeV, more than an order of magnitude higher in energy than accelerator measurements. Looking ahead, we expect that IceCube-Gen2 \cite{Aartsen:2017pja} and KM3NeT2.0 \cite{Adrian-Martinez:2016fdl} will collect larger samples of contained events, which can be used to make more precise measurements of inelasticity. These detectors could collect substantial samples of events with energies above 100 TeV. With the increased precision, it will also be possible to study several new topics. Tau neutrinos are one example; $\nu_\tau$ interactions have a distinctive inelasticity distribution which could be used to detect a $\nu_\tau$ signal. Top quark production may also be accessible if enough energetic neutrinos are available. One calculation found that, for 10 PeV neutrinos, top quarks are produced in 5\% of the interactions \cite{Barge:2016uzn}. It may also be possible to study other Standard Model neutrino interactions, such as diffractive production of W bosons in the Coulomb field of oxygen nuclei \cite{Seckel:1997kk,Alikhanov:2014uja}; the cross section for $\nu + O \rightarrow l + W^+ + X$ is about 8\% of the charged-current cross section for 1 PeV neutrinos. Even the first phase of IceCube-Gen2 should enable improved calibrations of the existing data, reducing the systematic uncertainties. With moderately improved calibrations, the precision of the inelasticity measurements should scale as the square root of the effective volume times the live time. With an improved surface veto to reject atmospheric neutrinos, it might also be possible to measure the $\nu:\overline\nu$ ratio of astrophysical neutrinos. If one could use the self-veto and a surface air-shower-array veto to reject atmospheric neutrinos with energies in the 1-10 TeV energy range, the inelasticity distribution could be used to determine the $\nu:\overline\nu$ ratio of astrophysical neutrinos. The data could also be used to search for beyond-standard-model (BSM) physics, such as supersymmetry \cite{Carena1998}, leptoquarks \cite{Anchordoqui2006} or quantum gravity with a relatively low scale \cite{Anchordoqui2007}. These phenomena also produce cross section enhancements which could be visible via increased neutrino absorption in the Earth, but the inelasticity distribution has a higher diagnostic utility than a simple increase in neutrino absorption. The use of inelasticity allows for a more sensitive search than by merely counting cascades and tracks \cite{Becirevic:2018uab}. A combined fit to cross section and inelasticity measurements would provide even better constraints on new physics. For most of these phenomena, the LHC provides better limits compared to IceCube Gen2 and KM3NeT 2.0. However, experiments that aim to record the coherent radio Cherenkov emission from ultra-energetic neutrinos with energies above $10^{17}$ eV can reach supra-LHC energies. The ARA \cite{Allison:2015eky} and ARIANNA \cite{Barwick:2014pca} collaborations both propose to deploy large ($> 100$ km$^3$) arrays that will, unless ultra-high energy cosmic-rays are primarily iron, collect useful (order 100 events) samples of cosmogenic neutrinos. The challenge here is that these experiments are primarily sensitive to cascades, while the energy deposition from tracks is too diffuse to be observable. However, it may be possible to take advantage of the Landau-Pomeranchuk-Migdal (LPM) effect to separate electromagnetic showers, which at energies above $10^{20}$ eV are elongated, from the hadronic showers from the target nucleus, which are less subject to the LPM effect. This leads to a moderately elongated electromagnetic shower following a compact hadronic shower \cite{Gerhardt:2010bj}. With this, it might be possible to measure the inelasticity of charged-current $\nu_e$ interactions \cite{Alvarez1999}. | 18 | 8 | 1808.07629 |
1808 | 1808.00465_arXiv.txt | We present a new method that incorporates the horizontal branch morphology into synthetic colour-magnitude diagram based star formation history determinations. This method, we call {\small MORGOTH}, self-consistently takes into account all the stellar evolution phases up to the early asymptothic giant branch, flexibly modelling red giant branch mass loss. We test {\small MORGOTH} on a range of synthetic populations, and find that the inclusion of the horizontal branch significantly increases the precision of the resulting star formation histories. When the main sequence turn-off is detected, {\small MORGOTH} can fit the star formation history and the red giant branch mass loss at the same time, efficiently breaking this degeneracy. As part of testing {\small MORGOTH}, we also model the observed colour-magnitude diagram of the well studied Sculptor dwarf spheroidal galaxy. We recover a new more detailed star formation history for this galaxy. Both the new star formation history and the red giant branch mass loss we determined for Sculptor with {\small MORGOTH} are in good agreement with previous analyses, thus demonstrating the power of this new approach. | Determining detailed star formation histories (defined as the star formation rate as a function of age and metallicity -- SFHs) for a variety of different types of galaxies is important to the understanding of galaxy formation and evolution. The SFH of galaxies in the local Universe, going back to the earliest times, allows a comparison with predictions, over the same time frame, from cosmological and galaxy evolution models \citep[see, e.g.,][ for models of Local Volume galaxy properties]{Lanfranchi04,Salvadori08,Romano13,Starkenburg13,Garrison-kimmel14,Fattahi16,Sorce16}. In this way we can constrain the conditions in the local Universe when the Milky Way and its satellites were forming. Resolving individual stars, in a stellar population, down to the main sequence turn-off (MSTO), allows a detailed and accurate SFH to be determined. Unfortunately, with current observational capabilities we are only able to resolve a small sample of galaxies, primarily dwarf galaxies in the Local Group \citep[e.g.,][]{Tolstoy09, Weisz11}. Even so, the information that we can extract from these few nearby dwarf galaxies is very valuable and complements what we can learn from the study of unresolved, more distant galaxies \citep[e.g.,][]{Gallazzi08,Boylan-Kolchin16,Goddard17}. Moving beyond the satellites of the Milky Way, detecting the main sequence of the old population becomes challenging, and photometric data is often only able to reach down to the upper red giant branch (RGB) and the horizontal branch (HB) of galaxies \citep[e.g.,][]{Martin16,Martin17}. To determine the SFH of a resolved galaxy, a common approach is to build synthetic colour-magnitude diagrams (CMDs) to compare observed and predicted stellar distributions \citep[e.g.,][]{tosi91,tolstoy96,Aparicio97,Dolphin97,Harris01,Cignoni10}. An important contribution towards quantitative and reliable SFH determinations came with the work of \citet{Dolphin02}, who formalized many of the numerical challenges in SFH recovery, and performed detailed modelling of an homogeneous Hubble Space Telescope (HST) dataset of nearby galaxies. This framework was further developed with a thorough characterization of the typical uncertainties in SFH determinations by \citet{Dolphin12} and \citet{Dolphin13}. The SFH determinations for nearby galaxies, using synthetic techniques, are extensive, thanks especially to the exquisite sensitivity and resolving power provided by the advent of HST \citep[e.g.,][]{Aloisi99,Cole07,Monelli10b,Monelli10a,Weisz11,Weisz14a,Sacchi16}. One of the limitations of current SFH determinations of old stellar populations in the Local Group is that synthetic diagrams are typically only generated up to the tip of the RGB. Therefore, they neglect the later stages of stellar evolution, most importantly the HB phase. The main reason for this has been that RGB mass loss plays a strong role in shaping the morphology of the HB. As the mass loss phenomenon has proven difficult to characterize, this dependence has made predicting the HB of a given stellar population challenging \citep[e.g.,][and references therein]{Gratton10}. Accurately modelling the HB, taking into account the uncertain value of RGB mass loss, is a promising way forward to improve the SFH for nearby and distant galaxies. HB stars are much brighter than their MSTO counterparts, making them less affected by photometric uncertainties. This means that the HB morphology can be accurately characterized out to the edge of the Local Group and beyond. Theoretical calculation shows that the photometric properties of HB stars depend mostly on the metallicity and the stellar mass \citep[e.g.,][]{Iben70}. For a fixed chemical composition, the mass of HB stars is determined by the age of the stellar population and the amount of mass lost during the previous RGB phase. Thus, at fixed mass loss the HB morphology depends only on the SFH of the system. Furthermore, when the MSTO morphology is included, then the modelling of the HB has the potential to dramatically mitigate the age-metallicity degeneracy, as two stellar populations with different age-metallicity combination and the same MSTO luminosity will look quite different on the HB. For these reasons, the information contained in the HB can be used to significantly improve the recovered SFH, provided that we can accurately model the mass loss \citep{savino15}. Previous studies have used the HB to constrain SFHs both in the Milky Way \citep{Preston91,Santucci15} and in external galaxies \citep{Schulte-ladbeck02,Rejkuba11,Grocholski12}. In particular, the analysis of the HB has been crucial to constrain the stellar population properties of galaxies beyond our nearest Galactic companions. However, determining an accurate star formation rate, comparable to measurements from the MSTO, from the HB has been difficult to achieve. This is because these previous analyses necessarily employed theoretical isochrones for the HB modelling. These are built assuming a specific, only loosely constrained, mass loss efficiency. Not allowing this parameter to vary has a big impact on the measured SFH from the HB. In this paper we present a new SFH determination technique that flexibly and consistently takes into account the HB morphology when analysing the CMD of a galaxy, allowing a variation in the RGB mass loss. This approach provides precise SFHs and accurate measurements of the RGB mass loss. The starting point of {\small MORGOTH} (\textbf{M}odelling \textbf{O}f \textbf{R}esolved \textbf{G}alaxies with \textbf{O}ptimized \textbf{T}urn-off and \textbf{H}B synthesis), was the routine {\small TALOS} \citep{deBoer12}, which has been modified to include synthetic HBs, to handle the effect of mass loss and to recover a more detailed SFH, using the information of all the evolutionary phases up to the end of the early asymptotic giant branch. In \S\ref{talos} we give a brief description of how {\small TALOS} works, in \S\ref{morgoth} we describe {\small MORGOTH}, in \S\ref{test} we present several performance tests using mock observations and in \S\ref{Sculptor} we model the stellar population of the Sculptor dwarf spheroidal galaxy (dSph). In \S\ref{conclusion} we summarize our work. | \label{conclusion} We have presented and tested {\small MORGOTH}, to show it is capable of accurately determining the SFH of both simple and complex stellar populations by quantitatively taking into account all the major luminous features of the CMD, including the HB. It takes advantage of the internal structural similarities in evolved low mass stars, to model the helium burning phase of old populations in a flexible and computationally affordable manner. Simple tests with mock stellar populations reveal the benefit of having independent constraints on age and metallicity at the old ages, from the HB, increasing the time resolution of classical SFH determinations. Even with no constraints on the mass loss efficiency, our method is capable of a substantial improvement in the SFH precision, at the same as time measuring the total mass lost by RGB stars. We also tested our method on observations of the Sculptor dSph. The SFH and mass loss estimates obtained are in good agreement with previous analyses \citep{deBoer12,Salaris13}, confirming the reliability of our approach. Our SFH measurements, including the HB, have smaller uncertainties compared with traditional, MSTO only, analysis techniques. Although a statistically consistent modelling of the CMD predicts a relatively simple SFH, enhancing the HB importance in the CMD fit reveals the two stellar subpopulations known to exist in Sculptor. The detailed modelling of the HB of resolved stellar populations in galaxies opens interesting prospects for more distant surveys. Aside from the obvious advantage of having more accurate SFH measurements thanks to the additional age and metallicity indicators, we now also have the means to measure the amount of mass lost by RGB stars in external galaxies. Understanding RGB mass loss has been a stubborn long standing problem. In spite of decades of effort, a reliable characterization of this phenomenon has been difficult, even in apparently simpler systems like the Galactic globular clusters \citep[e.g.,][]{Catelan09}. The origin of this challenge lies in the nature of globular clusters, that are now known to contain a series of chemical peculiarities also reflected in their HB morphology \citep[e.g.,][]{Gratton11}. Dwarf galaxies, on the other hand, seem to be free from these chemical anomalies \citep{Geisler07,Fabrizio15,Salaris13,savino15}, but the intrinsic spreads in the age and metallicity of their stellar populations has made the study of RGB mass loss equally difficult. Developing a method to study this phenomenon in complex stellar populations is, therefore, an important step towards a more complete understanding of both stellar and galactic evolution. Additionally, a deeper knowledge of mass loss will allow us to obtain detailed SFHs, back to the earliest times, for a much larger number of galaxies.With current analysis techniques, accurate SFHs for the earliest stages of galaxy formation can only be measured if the faintest MSTOs are detected. This limits the maximum distance for this kind of study to the edge of the Local Group. If motivated assumptions can be made about the RGB mass loss, our method has the potential to measure the SFH from the HB alone, which is brighter than equivalent age MSTOs. Deep Hubble Space Telescope observations can already resolve the HB in galaxies outside the Local Group \citep[e.g.,][]{Dacosta10,Lianou13}. Next generation facilities, such as the Jame Webb Space Telescope, the European Extremely Large Telescope and the Thirty Meter Telescope, will be able to resolve HB stars for hundreds of galaxies within several Mpc from the Milky Way \citep{Brown08,Greggio12,Fiorentino17}, thus allowing accurate SFHs, back to the earliest times, for a large and diverse sample of resolved stellar systems, covering a range of environments, and over a cosmologically representative volume. | 18 | 8 | 1808.00465 |
1808 | 1808.06978_arXiv.txt | {Macroscopic dark matter (aka {\em macros}) constitutes a broad class of alternatives to particulate dark matter. We calculate the luminosity produced by the passage of a single macro as a function of its physical cross section. A general detection scheme is developed for measuring the fluorescence caused by a passing macro in the atmosphere that is applicable to any ground based or space based Fluorescence Detecting (FD) telescopes. In particular, we employ this scheme to constrain the parameter space ($\sigma_{x} \mbox{ vs} \mbox{ M}_{x}$) of macros than can be probed by the Pierre Auger Observatory and by the Extreme Universe Space Observatory onboard the Japanese Experiment Module (JEM-EUSO). It is of particular significance that both detectors are sensitive to macros of nuclear density, since most candidates that have been explored (excepting primordial black holes) are expected to be of approximately nuclear density.} | If General Relativity is correct, then dark matter constitutes most of the mass density of the Galaxy. While dark matter is widely thought to exist (although see \cite{a}) we have yet to detect it except gravitationally. The most widely considered and searched for candidates are new particles not found in the Standard Model of particle physics, such as the generic class of Weakly Interacting Massive Particles (WIMPs) (especially the Lightest Supersymmetric Particle) and axions. Recently, renewed attention has been paid to primordial black holes and to macroscopic composite objects, aka macros, especially those of approximately nuclear density. The theoretical motivation for this stems originally from the work of Witten \cite{b}, and later, more carefully Lynn, Nelson and Tetradis \cite{c}, Macroscopic objects made of baryons may be stable with sufficient strangeness, and may have formed before nucleosynthesis \cite{b,c}, thus evading the principal constraint on baryonic dark matter. One appeal of such a dark matter candidate is that there would be no need to invoke the existence of new particles to explain the observed discrepancy between gravitational masses and luminous masses in galaxies. Numerous beyond-the-Standard-Model macro candidates have also been suggested (e.g., \cite{d}). Recently one of us (GDS), along with colleagues, presented a comprehensive assessment of limits on such macros as a function of their mass and cross-section \cite{e}, identifying specific windows in that parameter space that were as yet unprobed. (We later refined those \cite{f}.) Taking macros to interact with our detectors with their geometric cross section, the expected number of macro events detected by an observatory/detector with effective area $A_{ef}$ that operates continuously over an observing time $t_{obs}$ is given by \begin{equation} \label{eventrate} \begin{aligned} N_{events}&=\dfrac{\rho_{_{DM}}}{M_{x}}A_{ef} t_{obs} v_{x} \\ &=5.5\left(\frac{kg}{M_{x}}\right) \left(\frac{A_{ef}}{1000\ km^2}\right) \left(\frac{t_{obs}}{yr}\right) \end{aligned} \end{equation} where $\rho_{_{DM}}$ is the local dark matter density $7\times10^{-25}\,$g cm$^{-3}$ \cite{e}, and $M_x$ is the mass of the macro. For the purposes of this paper, we assume macros possess a Maxwellian distribution of speeds given by \begin{equation} f(v_x)_{MB} = \left( \frac{1}{\pi v_{vir}^2}\right)^{\frac{3}{2}}4\pi v_x^2 e^{-\left(\frac{v_x}{v_{vir}}\right)^2}, \label{eq:maxwellian} \end{equation} where $v_{vir} \approx 250\,$km s$^{-1}$. This distribution is slightly modified by the motion of the Earth as described in detail in Section~\ref{sec:fofvx}. The cumulative distribution function is then obtained by integrating the probability distribution function up to the desired value of $v_x$. This allows us to determine the maximum $M_x$ we can probe as a function of $v_x$. With a minimum allowed macro mass of $55\,$g (inferred from mica\cite{e} that has been ``exposed'' to the bombardment of macros for tens of millions of years) the number density, and hence flux, of macros is quite small. Thus, any plan to detect macros on human time scales ({\it e.g.}, years) requires a target of very large area. In this work, we explore the possibility that fluorescence detectors designed to detect ultra-high energy cosmic rays might be simply modified and effectively used to detect the nitrogen fluorescence caused by a macro's passage through the atmosphere. Through elastic scattering, the macro would deposit enough energy to dissociate the molecules and ionize or excite the atoms. This results in the formation of a plasma. Figure~\ref{fig:roughidea} demonstrates the concept of detection of a macro dark matter in the atmosphere by, for example, a modified version of a single Fluorescence Detector (FD) telescope of the Pierre Auger Observatory. In this example, the macro particle penetrates the atmosphere generating a narrow column of ionization within the field of view of the FD. We show below that the size of the macro will determine the size of the resulting plasma. For large enough values of the macro cross-section $\sigma_x$, we find that the plasma becomes optically thick to photons and radiates as a blackbody. We analyze the optically thick and thin mechanisms separately. As heat diffuses out of this region surrounding the macro trajectory, the ions recombine to release photons that can be detected using fluorescence detectors. However, the macro passage through the atmosphere does not create an air shower as when a high energy cosmic ray is detected. \color{black}We find that for the Pierre Auger Observatory (Auger) and the proposed Extreme Universe Space Observatory onboard the Japanese Experiment Module (JEM-EUSO), we can probe masses up to 1.6$\times 10^{4}\,$g and 5.5$\times 10^{6}\,$g respectively for an observation period of 1 year, thus providing significant improvements over the current $55\,$g limit. \begin{figure} \begin{center} \includegraphics[width=6.00in]{tpyr_better.pdf} \caption{Conceptual diagram delineating the plausible detection of a macro dark matter particle by a modified version of a Fluorescence Detector (FD) such as that of the Pierre Auger Observatory. {\bf Left:} Perspective view of the truncated pyramid corresponding to the $30^{\circ} \times 30^{\circ}$ field-of-view of a single camera (`eye') with a fiducial detection volume that ranges from 1~km to 20~km distance from the Auger FD. In this example, the macro particle penetrates the fiducial region at a near-vertical angle generating a perfectly straight ``pencil beam'' of ionized plasma. Note that in contrast to relativistic cosmic rays, a macro particle is moving much slower and will not generate an air shower. {\bf Right:} Example `event display' for a modified Auger FD showing the predicted appearance of a macro signal detected within the field-of-view (the linear path of the macro appears as a slightly bent line due to curvature of the FD camera focal plane). The three-dimensional path of the macro can be fully reconstructed using pixel locations and timing. A macro event is clearly distinguished from cosmic rays and other atmospheric phenomena by it's velocity (about 250~km/s), perfectly straight path, and an ionization signal proportional to the atmospheric density.} \end{center} \label{fig:roughidea} \end{figure} | Macroscopic dark matter is a broad class of alternatives to particulate dark matter that, compellingly, includes plausible Standard Model candidates. The passage of a macro through Earth's atmosphere will cause dissociation and ionization of air molecules, resulting, through recombination, in a signal visible to Fluorescence Detectors such as those used to search for Ultra High Energy Cosmic Rays. As for such UHECR, large effective target areas are necessary to compensate for the low maximum flux of macros. Unlike UHECR, macros would be expected to travel several times faster than typical solar system objects, such as meteoroids, but still very non-relativistically. Existing and planned cosmic ray detectors would therefore need to make software, or possibly hardware, accommodations in order to detect the more slowly traced-out trajectories of macros. If they do, they have significant discovery potential for macroscopic dark matter of nuclear or greater density, including the most compelling non-black-hole candidates, able to probe up to masses of several tonnes, compared to current lower limits of just several tens of grams. | 18 | 8 | 1808.06978 |
1808 | 1808.01243_arXiv.txt | % Within the approach to doubly special relativity (DSR) suggested by Magueijo and Smolin, a new algebraically justified rule of so-called $\kappa$-addition for the energies of identical particles is proposed. This rule permits to introduce the nonlinear $\kappa$-dependent Hamiltonian for one-mode multi-photon (sub)system. On its base, with different modes treated as independent, the thermodynamics of black-body radiation is explored within DSR, and main thermodynamic quantities are obtained. In their derivation, we use both the analytical tools within mean field approximation (MFA) and numerical evaluations based on exact formulas. The entropy of one-mode subsystem turns out to be finite (bounded). Another unusual result is the existence of threshold temperature above which radiation is present. Specific features of the obtained results are explained and illustrated with a number of plots. Comparison with some works of relevance is given. \vskip10pt {\it Keywords:} doubly special relativity; Planck energy; black body radiation; $\kappa$-addition rule; deformed bosons; photons; bounded radiation energy and entropy; modified Planck law; threshold temperature \vskip10pt {PACS:} 03.30.+p; 05.30.-d; 05.30.Jp; 05.70.Ce; 14.70.Bh; 42.50.Ar | Recently, the deformation of the special relativity was accomplished so that it might jointly admit two invariant fundamental scales: one of them being the speed of light, and the other -- an energy scale naturally identifiable with Planck energy \cite{AC02,AC01,LNRT,LNR,MS02}. This deformed theory is usually called a doubly special relativity (DSR) because it has two invariant scales. The DSR is important when one aims to describe the particles' dynamics at very high energies approaching the Planck scale. It is believed that at this scale the spacetime structure can be influenced by effects of quantum gravity. Initially DSR was introduced in an algebraic way, using certain quantum deformations of the Lorentz group \cite{LNRT,LNR}. Later it was also derived by taking as starting point a few physical postulates, including the requirement that it should reduce to special relativity if the low-energy limit is applied~\cite{AC02,AC01}. In the ordinary special relativity, the momentum changes under the Lorentz transformation with the infinitesimal boost generator $J$ as \begin{equation} \delta p_0 = \{ J, p_0 \} =p_1, \qquad \delta p_1 = \{J, p_1\} = p_0, \end{equation} where we consider 1+1 dimensions, and $\{, \}$ denotes the Poisson bracket. The DSR model by Magueijo--Smolin (MS model) \cite{MS02} takes the form \begin{equation}\label{trans2} \delta p_0 = \{ J, p_0 \} = \lb 1 - \frac{p_0}{\kappa}\rb p_1, \qquad \delta p_1 = \{J, p_1\} = p_0 -\frac{p_1^2}{\kappa}, \end{equation} with $\kappa$ the Planck energy. Due to the factor $1-p_0/\kappa$, for $p_0 =\kappa$ we have $\delta p_0 =0$, and thus the invariance of Planck energy. Under the transformation (\ref{trans2}), one has the invariant quantity $p^2/(1-p_0/\kappa)^2,$ where $p^2=p_0^2-p_1^2$. The DSR models imply that the momentum of a particle transforms nonlinearly under the Lorentz group. In this respect, there is a variety of ways to realize nonlinear representations of the Lorentz group obeying the above-mentioned postulates, but, to develop the theory there are two basic routes: working in ordinary spacetime, or to explore a spacetime involving non-commuting coordinates. In the noncommutative case, for defining the Hamiltonian classical dynamics, noncanonical Poisson brackets are used. It is clear that, depending on the choice of initial assumptions, the explored models may lead to differing physical consequences or predictions. In this paper we propose a new, DSR-inspired rule of "$\kappa$-addition" for the energies of particles (Section 2), study its properties, and then introduce the corresponding Hamiltonian for one-mode multi-photon system. On its base, assuming independence of different modes, we explore in Sec.~3 the thermodynamics of black-body radiation in the framework of DSR and derive basic thermodynamic quantities. Our calculations lead to rather unusual results, whose special features are analyzed and illustrated with plots. In the final section, main consequences and conclusions are presented, along with brief comparison with respective aspects in some related works. | In this paper, an original $\kappa$-addition rule inspired by the DSR has been proposed, exhibiting the crucial role played by the Planck energy scale $\kappa$ in all our treatment. That rule has naturally led us to the nonlinear Hamiltonian of self-interacting one-mode systems of photons. The adopted Hamiltonian, possessing essentially nonlinear (rational) dependence on the excitation number operator and combined with the assumption of independence of different modes, was taken as a starting point for the evaluation, within the framework of DSR, of main thermodynamic quantities of black-body radiation. Clearly, the presence of the scale $\kappa$ manifested its importance in our main results on the thermodynamic characteristics and their physical implications. First of all, the energy of one-mode subsystem has the property that it lies entirely in the band of finite width, and the upper bound is determined by $\kappa$. This property influences all the other thermodynamic functions. Next, as follows from Eq.~(48) and is clearly shown in Fig.~4, within our approach a kind of {\it threshold temperature} $T_{\rm th}$ (depending on $z$) appears: it implies that just above these values $T_{\rm th}(z)$ the radiation is present. The disclosed property of the DSR-based black-body radiation may have important consequences and unexpected manifestations. Also it is worth to emphasize the peculiar behavior of the one-mode specific heat and the total one (shown respectively in Fig.~2 and Fig.~5), as well as the unusual dependence on the temperature that was pointed out in the paragraph above Eq.~(42). An interesting equation of state is obtained which essentially differs from what is familiar in the standard physics of black-body radiation. We hope to explore its implications in a separate work. It is worth to comment on some works on black-body physics based on deformed thermodynamics~\cite{Delgado91,Angelo94,Gupta94,Tsallis95,Ch-Ch,Zhang} and compare their conclusions with the well-known handbook results \cite{PB11} and with those presented above. In the mentioned papers, main novelty that appears due to deformation, consisted in some modification of pre-factors in the inferred versions of the Stefan-Boltzmann law. Besides, the Stefan's constant begins to depend on a parameter of deformation. The Wien displacement law is still preserved for the deformed Bose gas, though with certain inclusion of deformation parameter. In \cite{Ch-Ch}, the Planck formula for the deformed Bose gas is really different from the ordinary one: there appear some new terms in Planck's formula, which correspond to the "interactions" among photons. Similar to the case of ideal Bose gas, the total energy of the deformed Bose gas is proportional to the fourth power $T^4$. The peculiar feature is that the Stefan-Boltzmann constant turns out to be effectively reduced by the deformation. In general, most of the results presented in our paper differ from those just mentioned in a principal way, namely what concerns the energy lying within a finite band, the peculiar behavior of specific heat, and the existence of threshold temperature for radiation switching. We hope to develop more specified applications of the obtained results for description of realistic objects in astrophysics and for effective modeling in modern cosmology. \textbf{Acknowledgement.} This work was partly supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2015R1D1A1A01057792) and by Development Fund Foundation, Gyeongsang National University, 2018. Also, the work was partly supported by The National Academy of Sciences of Ukraine (project No. 0117U000237). | 18 | 8 | 1808.01243 |
1808 | 1808.08681_arXiv.txt | This review examines recent theoretical developments in our understanding of turbulence in cold, non-magnetically active, planetesimal forming regions of protoplanetary disks which we refer to throughout as ``Ohmic zones". We give a brief background introduction to the subject of disk turbulence followed by a terse pedagogical review of the phenomenology of hydrodynamic turbulence. The equations governing the dynamics of cold astrophysical disks are given and basic flow states are described. We discuss the Solberg-H{\o}iland conditions required for stability, and the three recently identified turbulence generating mechanisms possibly active in protoplanetary disk Ohmic zones, namely, (i) the Vertical Shear Instability, (ii) The Convective Overstability and (iii) the Zombie Vortex Instability. We summarize the properties of these processes, identify their limitations and discuss where and under what conditions these processes are active in protoplanetary disk Ohmic zones. | \label{sect:introduction} Planet formation is simultaneously one of the oldest and one of the newest concerns of human inquiry. ``How did the Earth come to be?'' is a question that almost invariably appears in the cosmogonies of the ancients. They not always had a clear idea of what ``Earth'' meant, but this is a question that, in one form or another, virtually every society in recorded history has at some point asked itself. Particularly interesting are the ideas of Leucippus (480-420? B.C.E.) who, according to testimonial, is to have said \citep{Diels_Kranz_1961} \begin{quote} {\emph{The worlds come into being as follows: many bodies of all sorts and shapes move from the infinite into a great void; they come together there and produce a single whirl, in which, colliding with one another and revolving in all manner of ways, they begin to separate like to like.}} \par \medskip \noindent Diogenes Laertius IX, 31 \footnote{Scholars of the classical period note that nothing but third person accounts survive of Leucippus' words.} \end{quote} \noindent This vision strikes surprisingly modern, and not without foundation within the modern theory of planet formation. Substitute ``many bodies of all sorts and shapes'' by {\it gas and dust}, then ``single whirl'' by {\it protoplanetary disk} and finally ``revolving in all manner of ways'' by {\it turbulence}, and it could have figured in the introduction of a paper in the latest issue of a major astronomy journal. This attests not to clairvoyance of the ancient Greeks, but to the antiquity of the question. Given the huge sample space, some of the educated guesses of the time are bound to contain some truth. By the 18th century, Newtonian gravity and the orbits of the planets were understood in enough detail to realize that the low inclinations of the orbits implied that the easiest way to attain that configuration was if the planets have formed in a disk that orbited the proto-Sun (Kant 1755). Because Jupiter and Saturn are gas giant planets, this disk must have been a disk of gas. Early mathematical considerations by Laplace (1796) applied Newton's theory of universal gravitation and laws of motion to a slowly rotating spherical cloud, implying that it should collapse under its own weight. Due to conservation of angular momentum, the gas settles into a flat disk orbiting the condensing proto-Sun in the center. In this {\it solar nebula}, planets are taking shape.\par C. F. von Weizs{\"a}cker extended these fundamental notions and pointed out that eddies in the forming solar nebula ought to increase with distance from the Sun prefiguring the role these may have in the formation of planetesimals out of dust \citep{Gamow_Hynek_1945}. Rather presciently, Weizs{\"a}cker also reasoned that many other star systems should harbor similar kinds of nebulae like our own Sun did after its birth. Modern searches have now revealed such disks around young stars \citep{ElsasserStaude78,Rucinski85,Aumann85,SargentBeckwith87,Strom+89, Beckwith+90, O'dellWen94, McCaughreanO'Dell96,Ricci+08}, now called {\it protoplanetary disks} or, in symmetry with the solar nebula, {\it extrasolar nebulae} or {\it exonebulae}. {In general, protoplanetary disks range in radius from 10s to 100s of AU \citep[e.g.][]{Ansdell+18}, in density from $10^{13}$ to $10^{15}$ cm$^{-3}$ {\bf (for mean molecular weight $\mu=2.5$)}, in mass from $10^{-3}$ to $10^{-1} M_\odot$, and from 1000\,K near the star to 10\,K in the outskirts of the disk.} These disks form while the star is being formed, as a consequence of the cloud's gravitational collapse, and here we already find one of the first formidable problems of star and planet formation: as interstellar clouds are huge in size, even the slightest rotation means far too much angular momentum \citep{Mestel65a,Mestel65b}. {Indeed, if a proto-star was to accommodate all the angular momentum in a ring at 1AU containing about 10\% of its mass, it would achieve break-up velocity, a problem that also exists in similar form for the gas giant planets in the Solar System \citep{TakataStevenson96,Bryan+18,Batygin18}. In order to accrete, the gas must somehow find a way to transfer its angular momentum and if a gas parcel does this in nearly circular orbits, it must simultaneously find a way to lose energy in the process. } Because gravity is a radial force, and an axisymmetric disk has no pressure forces in the azimuthal direction, the only process that produces change in angular momentum is viscous stresses. Angular momentum transport is mediated by viscosity; without it, gas will simply orbit the star, not changing its radial position, and star formation will not complete. Although molecular viscosity is much too small to account for the observed mass accretion rate, it was recognized \citep{ShakuraSunyaev73,Lynden-BellPringle74} that the stochastic behavior of turbulence would lead to diffusion of momentum, similarly to viscosity. Moreover, while molecular viscosity acts in the small scales of the flow, turbulence acts all the way up to the integral scale, generating much more powerful stresses. The question of angular momentum transport is thus a question of how the disk becomes turbulent. The 1970s and 1980s saw several possible candidates to generate turbulence and angular momentum transport in disks, such as convection \citep{Cameron78,LinPapaloizou80} or nonlinear instability \citep{Shakura+78}. Yet, it was only with the re-discovery of the magnetorotational instability \cite[MRI;][]{BalbusHawley91} that the question seemed settled. The MRI entails a combination of a weak (subthermal) magnetic field and the shear present in the Keplerian rotation the gas, that de-stabilizes the flow. The instability is powerful, seeming to explain the required accretion rates. The MRI also has a positive effect on planet formation. Starting with micron-sized dust grains, coagulation models \citep{Brauer+07} predict growth to centimeter size by electromagnetic hit-and-stick mechanisms (mostly van der Walls forces). However, growth beyond this size is halted, for two reasons. First, collisions between pebbles lead to destruction rather than growth \citep{Benz00}. Second, because of the balance between pressure, rotation and gravity, the gas orbits the star slightly slower than an independent body at the same distance would. Consequently, pebbles tend to outpace the gas. The resulting headwind drains their angular momentum, leading them into spiral trajectories towards the star, in timescales as short as a hundred years at 1AU \citep{Weidenschilling77a}. A distinct possibility to solve these problems is gravitational instability of the layer of solids \citep{Safronov72,Lyttleton72,GoldreichWard73,YoudinShu02}. When the dust aggregates had grown to centimeter size, the gas drag is reduced and the solids are pushed to the midplane of the disk due to the stellar gravity. Although such bodies do not have enough mass to attract each other individually, the sedimentation increases the solids-to-gas ratio by orders of magnitude when compared to the interstellar value of $10^{-2}$. It was then hypothesized \citep{Safronov72} that due to the high densities of this midplane layer, the solids could collectively achieve critical number density and undergo direct gravitational collapse. Such a scenario has the advantage of occurring on very rapid timescales, thus avoiding the radial drift barrier. This picture was nonetheless shown to be simplistic, in the view that even low levels of turbulence in the disk preclude the midplane layer of solids from achieving densities high enough to trigger the gravitational instability \citep{Weidenschilling80}. Even in the absence of self-sustained turbulence such as the one generated by the MRI, the solids themselves can generate turbulence due to the backreaction of the drag force onto the gas. Such turbulence can be brought about by Kelvin-Helmholtz instabilities due to the vertical shear the dense layer of solids induces on the gas \citep{Weidenschilling80,WeidenschillingCuzzi93,Sekiya98,Johansen+06}, or by streaming instabilities induced by the radial migration of solids particles \citep{YoudinGoodman05,Paardekooper06,YoudinJohansen07,JohansenYoudin07}. In the turbulent motion, the solids are stirred up by the gas, forming a vertically extended layer where the stellar gravity is balanced by turbulent diffusion \citep{Dubrulle+95,GaraudLin04}. But if turbulence precludes direct gravitational collapse through sedimentation, it was also shown that it allows for it in an indirect way. As solid particles concentrate in high pressure regions \citep{HaghighipourBoss03}, the solids-to-gas ratio can be enhanced in the transient turbulent gas pressure maxima, potentially reaching values high enough to trigger gravitational collapse. Numerical calculations by \cite{Johansen+07} show that this is indeed the case, with the particles trapped in the pressure maxima generated by the MRI collapsing into dwarf planets when the gravitational interaction between particles is considered. While the MRI is not strictly necessary, the streaming instability does not seem to operate effectively for solar and subsolar metallicities, requiring more solids than initially present in the Solar Nebula. {However, the conditions for the magnetorotational instability are not met in a huge portion of the disk \citep{BlaesBalbus94}. Being a mechanism that depends on magnetization, it also depends on ionization; as a result, if the ionization fraction is such that resistive effects become important, the MRI may shut down, defining a MRI-dead zone \citep{BlaesBalbus94,Gammie96}. The partially ionized gas can be seen as a three-fluid system, composed of the ion fluid, the electron fluid, and the neutral fluid. In ideal MHD, where density and ionization fraction are sufficiently high, ions and electrons are tied to the magnetic field and they drag the neutrals along with them; deviations from ideal conditions occur when these fluids start to decouple. In the ambipolar diffusion limit the magnetic field is tied to the electrons and ions, and drifts with them through the neutrals \citep{BlaesBalbus94,MacLow+95}. In the Ohmic limit collisions with neutrals are efficient in dragging the ions and electrons, and the magnetic field is not frozen in any fluid. In between these limits lies the domain of Hall MHD, where the electrons are coupled to the magnetic field, but collisions with neutrals decouple the ions \citep{Wardle99,BalbusTerquem01,SalmeronWardle05,PandeyWardle06,Wardle07,PandeyWardle08,WardleSalmeron12}. At constant magnetic field, this is a progression as density increases, that first the neutrals decouple from magnetic effects (ambipolar diffusion), then the ions (Hall MHD), and finally the electrons (Ohmic resistivity). We focus on the Ohmic zone, deep into the resistive regime and any magnetic effect is irrelevant. We could have used ``hydrodynamical'' zone, yet we keep the name Ohmic for juxtaposition to the other non-ideal MHD effects. It is in this non-magnetic regime that the hydrodynamical instabilities we review exist. The physics of the Hall-dominated and ambipolar-dominated zones is not covered in this review, but we point out their importance in providing boundary conditions for the Ohmic zone. The upper atmosphere of the disk will be dominated by ambipolar diffusion, with the emission of a magnetocentrifugal wind \citep{BaiStone11, Gressel+15}. As such, it will provide a ``lid'' to the instabilities here discussed. Until their interaction with the ambipolar zone is defined, we cannot assume that these instabilities are felt in the disk atmosphere; if they are not, they should not be seen in infrared observations. The Hall-dominated zone has a dynamical instability, the Hall shear instability, if the angular momentum vector and the magnetic field are aligned \citep{Kunz08,KunzLesur13,Lesur+14,Bai15}. The reader should keep in mind that our knowledge of the physics is these zones is still taking shape, and it is unclear how the hydrodynamical instabilities we review behave in the ambipolar and Hall zones.} The {Ohmic} zone is extended. In the inner disk, ionization is provided by thermal collisions. Down to $\approx$900K, thermal velocities have enough energy to ionize the alkali metals. {This temperature corresponds to a distance of 0.1\,AU, depending on the underlying disk model, so only inwards of it will the disk be sufficiently ionized for the MRI. Concurrently, outward of $\approx$30\,AU (again depending on the underlying disk model), even though the temperatures are low, the column density is low enough that stellar X-rays can ionize the disk throughout.} Between these limits, a large dead zone exists. This, incidentally, is squarely where we expect planets to form, at least in the Solar System. If we need turbulence to generate accretion and form planets, we have to look beyond the magnetorotational instability. If star formation necessitates turbulent transport through the accretion disk, and if planet formation needs turbulent pressure maxima to trigger the streaming instability in solar metallicity, we need to look beyond the MRI. The past few years have seen a number of processes being proposed for purely hydrodynamical instabilities in disks: {two linear instabilities}, the {\it Vertical Shear Instability} \citep{Nelson+13,Stoll_Kley_2014} and the {\it Convective Overstability} \citep{KlahrHubbard14,Lyra14}, and {a non-linear instability} the {\it Zombie Vortex Instability} \citep{Marcus+15,Marcus+16}. These processes were linked to different regimes of opacities by \cite{Malygin+17}. It is the purpose of this review to frame these disparate processes into a coherent picture of hydrodynamical processes in Ohmic dead zones of accretion disks. This review is organized as follows. In the next section we briefly review the physics of accretion disks. On \sect{sect:turbulence} we give an overview of turbulence, introducing the hydrodynamical instabilities on \sect{sect:instabilities}. A synthesis, the main goal of this review, is given on \sect{sect:synthesis}. Following it, \sect{sect:future} presents our opinion for the directions of the field in the next few years, finally concluding on \sect{sect:conclusions}. \begin{table*} \caption[]{Symbols used in this work.} \label{table:symbols} \begin{center} \begin{tabular}{lll c lll}\hline Symbol & Definition & Description & & Symbol & Definition & Description\\\hline $R$ & & cylindrical radial coordinate&& $N_z$ & \eq{eq:bruntZ} & vertical Brunt-V\"ais\"al\"a frequency \\ $\phi$ & & azimuth && $N_R$ & \eq{eq:bruntR} & radial Brunt-V\"ais\"al\"a frequency \\ $z$ && vertical coordinate&& $\v{F}$ & & body force \\ $r$ && spherical radial coordinate&& $\ell$ & $\approx 2\pi/k$ & vortex eddy length scale \\ $\lambda$ && wavelength&& $u_\ell$ & & typical eddy speed \\ $k$ &$=2\pi/\lambda$& wavenumber&& $t_\ell$ & $\approx \ell/u_\ell$ & eddy overturn time \\ $m$ & & azimuthal wavenumber&& $\ell_0$ & & energy injection scale \\ $t$& & time && $\ell_{\rm diss}$ & & dissipation length scale \\ $\rho$ & & density&& $\varepsilon$ & erg\,s$^{-1}$\,g$^{-1}$& energy dissipation rate per unit mass\\ $\v{u}$ & & velocity&& ${\rm E}_k$ & & energy per mass in eddies between $k$ and $k+\delta k$\\ $T$& & temperature&& ${\cal E}$ &$={\rm E}_k/k$ & energy per mass density\\ $\gamma$ & & adiabatic index&& $\v{\varomega}$&$=\curl{\v{u}}$&vorticity\\ $\cp$ & & specific heat at constant pressure && ${\cal Z}$ &$=\varomega^2$& enstrophy \\ $\cv$ &$=\cp/\gamma$& specific heat at constant volume && $\varPsi$ & $u = \curl{\varPsi\hat{\v{z}}}$ & streamfunction\\ $c_s$ &$=\left[T \ \cp (\gamma-1)\right]^{1/2}$& sound speed&& $\OmegaPV$ & $=\rho^{-1}\v{\varomega}\cdot \del s $ & potential vorticity \\ $p$&$=\cv (\gamma-1) \rho T $ & pressure && $\betaPV$ &$\equiv \pderiv{\OmegaPV}{\rm q}$ & potential vorticity gradient \\ $s$&=$\cv\ln(p/\rho^{\gamma})$ & specific entropy&& $l$ & & latitude\\ $\varPhi$&$=-GM_\star/r$ & gravitational potential&& $\OmegaGPV$ & \eq{eq:general_PV} & generalized potential vorticity \\ $G$& & gravitational constant&& $\overline{u_i' u_j'}$& & spatial correlation of component velocity fluctuations\\ $M_\star$& & stellar mass&& $\sigma_{\rm SB}$ & & Stefan-Boltzmann constant\\ $\mu$& & mean molecular weight&& $\alpha$ & = $\overline{u_r' u_\phi'}\big/c_s^2 $& measure of turbulent intensity\\ ${\rm R}$& & gas constant&& $\nu_t$ & $ = \alpha c_s H$ & effective turbulent viscosity\\ $\v{{\rm T}}$ && viscous stress tensor && $L$ & $=R^2\varOmega$ & angular momentum\\ $\varsigma$& & dynamic shear molecular viscosity&& $K$ & & spring constant\\ $\zeta$& & dynamic bulk molecular viscosity&& $\rm q$ && generalized coordinate\\ $\nu$&$=\varsigma/\rho$ & kinematic viscosity && $\v{\ksi}$ && Lagrangian displacement\\ $\Rey$&$=\mathcal{U}\mathcal{L}/\nu$ & Reynolds number&& $\v{B}$ && magnetic field\\ $\mathcal{U}$& & representative velocity&& $\v{\va}$ & $=\v{B}/\sqrt{4\pi\rho}$ & Alfv\'en velocity\\ $\mathcal{L}$& & representative length&& $\beta$ &$= 2c_s^2/\va^2$ & plasma beta \\ $\mathcal{Q}$& & heat source&& $\eta$ && resistivity\\ $\varOmega$ &$=\sqrt{GM_\star/R^3}$ & Keplerian angular frequency && $\v{J}$&¤t\\ $H$ &$= c_s/\varOmega$ & disk scale height && $c$ && speed of light\\ $h$ &$=H/R$ & disk aspect ratio && ${\rm Re_M}$ &$=\mathcal{U}\mathcal{L}/\eta$ & Magnetic Reynolds number\\ $\varSigma$ & $\propto \rho H$ & column density && $\varLambda$ &$=\va^2/\varOmega\eta$ & Elssaser number\\ $q$ & $=-d\ln \varOmega/d\ln R $ & shear parameter && $Z$&&charge multiplicity\\ $q_\rho$ & $=-d\ln\rho/d\ln R $ & radial density gradient && $\gamma_i$ & $\v{f} \equiv \gamma_i \rho_i \rho (\v{u}_i-\v{u})$ & ion-neutral drag coefficient\\ $q_T$ & $=-d\ln T/d\ln R $ & radial temperature gradient && $\sigma_{\rm coll}$ & & collisional cross section\\ $q_\Sigma$ & $=-d\ln \varSigma/d\ln r $ & column density gradient && $n$ & & number density\\ $\omega$ && complex eigenfrequency&& $x$ & $\equiv n_e/n$ & ionization fraction\\ $\sigma$ & $={\rm Im}(\bar\omega)$ & growth rate && $\kappa_R$ & & Rossland mean opacity\\ ${\rm Ma}$ &$={\cal U}/c_s$& Mach number && $\ell_r$ & $=(\kappa_r\rho)^{-1}$ & photon mean free path\\ $\kappa_{\rm ep}$ & $ = \varOmega\sqrt{2(2-q)}$ & epicyclic frequency && $\tau_r$ & \eq{eq:relaxationtimes} & thermal relaxation time\\ $\mA_k$ & $=c_s \ \partial_k \ln \rho$ &normalized density gradient&& $a_{\rm rad}$ & $=4\sigma_{SB}/c$ & Radiation constant\\ $\mG_k$ & $=\gamma^{-1}c_s\ \partial_k \ln p$ &normalized pressure gradient&& $\chi$ && Coefficient of thermal diffusion\\ $\mS_k$ & $=\mG_k-\mA_k$ & normalized entropy gradient&& ${\rm Ro}$ && Rossby number\\\hline \end{tabular} \end{center} \end{table*} | \label{sect:conclusions} The past decade of disk research have seen the emergency of disk instability mechanisms that provide hydrodynamical turbulence in the Ohmic dead zone. They violate the Rayleigh criterion in different ways. The vertical shear instability (VSI) by having $d\varOmega/dz \neq 0$, the convective overstability (COV) by the presence of entropy gradients with $N_R^2<0$, and the zombie vortex instability (ZVI) with $N_z^2 > 0$. Because of these requirements, they exist in very different regimes of opacity: the ZVI in adiabatic regions, the VSI in isothermal ones, and the COV in between. These can be mapped into different locations, depending on the particular disk model (\fig{fig:butcher} and \fig{fig:butcher2}). The instabilities have different turbulent responses, with $\alpha$ values around $10^{-3}$. Their properties are summarized in \table{table:thermal}. Of the three processes, the most robust seems to be the VSI, as the unstable entropy gradients necessary for the COV are {not necessarily} realized in all disks, and the first perturbation necessary for the ZVI is difficult to maintain over long times. The three instabilities saturate into three-dimensional vortices. The VSI because of RWI and Kelvin-Helmholtz instability of the thin tall sheets. The COV because it builds up the finite difference perturbations that lead to subcritical baroclinic instability. The ZVI also via RWI and Kelvin-Helmholtz instability. All vortices decay due to elliptical instability in the cores \citep{Pierrehumbert86,Bayly86,LesurPapaloizou09}, that leads to a direct enstrophy cascade. { In saturation, vortex strength should be defined by a balance between the saturation mechanism, that feeds the vortices (RWI for VSI/ZVI, SBI for COV), and the rate of decay via elliptic instability \citep{Lyra13}. Weaker vortices (of larger aspect ratio) linger for longer because the growth rates of elliptic instability decrease with vortex aspect ratio.} In this review, we have specifically used the term {\it Ohmic zone} instead of the traditional ``dead'' zone. We could have used ``hydrodynamical'' zone since Ohmic effects, in the sense of magnetic Reynolds numbers close to 1, are not at play. The Ohmic zone is deep into the resistive regime and any magnetic effect is irrelevant. Yet, we keep the name Ohmic for juxtaposition to the other non-ideal MHD effects: the Hall effect and ambipolar diffusion, that may be at play in very low density regions of the disk \citep{Wardle99,Wardle07,Lesur+14}. The Hall effect leads to the Hall shear instability if the magnetic field and the angular momentum vectors are aligned. Ambipolar diffusion leads to magnetocentrifugal winds, evidence for which may have been recently discovered \citep{Simon+16}. The very high up region of the butcher diagram (\fig{fig:butcher}) {are probably prone to ambipolar diffusion, providing a ``lid'' for all instabilities; if the ionization fraction is high enough the MRI can be reactivated. The outer ZVI region may thus be completely quenched, by ambipolar diffusion or the MRI itself. The outer COV region is low density enough for ambipolar diffusion to operate. The VSI region may also operate optimally within the region where the Hall effect is the dominant source of resistivity. It remains to be shown how the instabilities here summarized behave in connection with these non-ideal terms. } The importance of characterizing the shape and quality of turbulence and its influence upon the growth of planetesimals, especially at the smallest scales, is one of the main messages of this review. While we have not delved into how the turbulence mitigates the growth of planetesimals, we have emphasized that the dynamical state of the protoplanetary disk is the fundamental canvas on which the particle growth narrative is etched. With this in mind, we conclude with another quote from the ancients, this time of Hesiod, who writes of the birth of the Earth (``Gaia"), \begin{quote} {\it In the beginning there was Chaos; but then there came to be Gaia, the broad-breasted, the ever-secure seat of all immortals who dwell in the peaks of snowy Olympos.}\par \medskip Hesiod {\emph{Theogony}} 116-118\footnote {Translation by Professor Osman S. Umurhan who notes that ``$\chi\alpha\omicron\sigma$" or ``Chaos" represents not disorder in the modern sense, but a chasm or abyss, whose properties appear to be a dark, gaping space. Later in Hesiod's account this very chasm appears to have the appropriate material ``to catch fire" from Zeus' thunderbolt.} \end{quote} This vision strikes as modern as well: if one substitutes ``chaos" with {\emph{turbulence}} and ``Gaia" with planetesimals, then we have a picture describing elements of today's scientific paradigm of planet formation.\\ | 18 | 8 | 1808.08681 |
1808 | 1808.04716_arXiv.txt | {Recent studies using 21 cm HI line and $^{13}$CO line observations in the inner part of the Galaxy have resulted in new distances for 30 Galactic supernova remnants (SNRs). 15 of those remnants have observed X-ray spectra, for which shocked-gas temperatures and emission measures are measured. Here we apply spherically symmetric SNR evolution models to these 15 remnants to obtain estimates for ages, explosion energies, circum-stellar medium densities and profiles (uniform or wind-type). From the distribution of ages we obtain a supernova birth rate and estimate incompleteness. The energies and densities can be well fit with log-normal distributions. The distribution of explosion energies is very similar to that of SNRs in the Large Magellanic Cloud (LMC), suggesting SN explosions in the LMC and in the Galaxy are very similar. The density distribution has higher mean density for Galactic SNRs than for LMC SNRs, by a factor $\sim$2.5.} | The study of supernova remnants (SNRs) is of great interest in astrophysics (see \cite{2012Vink} and references therein for a recent review). SNRs provide valuable information relevant to stellar evolution, the evolution of the Galaxy and its interstellar medium. SNRs are the dominant source of kinetic energy input into the interstellar medium \citep{2005Cox} and thus measuring SNR energetics is critical to understanding the structure of the interstellar medium. SNRs are observed primarily in X-rays, by emission from hot interior gas with temperature $\sim$1 keV, and in radio, by synchrotron emission from relativistic electrons accelerated by the SNR shockwave. The observational constraints for different SNRs are often different in nature. They depend on the brightness of emissions in different wavebands by a given SNR and by the instruments used to observe that SNR. Only a small fraction of the $\sim$300 observed SNRs in our Galaxy have previously been well enough characterized to determine their evolutionary state, including explosion type, explosion energy and age. A few historical SNR have been observed in great detail and modelled with hydrodynamic simulations. For example, Tycho has been modelled \citep{2006Badenes} and used to test different models for SN Type Ia explosions. However, most SNRs are not observed nearly as well and have not been subject to similar detailed modelling. For these observationally less-constrained SNRs, it is worthwhile to determine their bulk physical characteristics, but with a simpler approach than full hydrodynamic modelling. In order to expedite characterization of SNRs, we have developed a set of analytical SNR models for spherically symmetric SNRs and implemented them in Python \citep{2017LeahyWilliams}. The set of models includes a wide set of models constructed previously by other authors. We carried out the additional step of consistently joining different stages of evolution, which in several cases has not been done before. The resulting models facilitate the process of using different constraints from observations to estimate SNR physical properties of interest. The current work includes the following. First, we extend the models to calculate the X-ray emission from a SNR during the evolutionary phase between the self-similar ejecta dominated phase and the self-similar Sedov-Taylor phase. Then we solve the inverse problem of how to determine the initial parameters of a SNR using its observed properties. Finally, we apply the solution of the inverse problem to a set of SNRs with newly determined distances. The structure of the paper is as follows. Section~\ref{sec:overview} presents an overview of the SNR models and the solution of the inverse problem. Section~\ref{sec:sample} describes the supernova remnant sample and the model fits for individual SNRs. Section~\ref{sec:properties} present our analysis of the properties of the SNR sample and Section~\ref{sec:conclusion} summarizes the results on the distribution of explosion energies and densities. | \label{sec:conclusion} Distances to Galactic SNRs have improved significantly, allowing determination of radii and enabling the application of SNR models. We extended spherically symmetric SNR evolution models to include effects of ejecta mass and emission from shocked ejecta. We applied the models to estimate SNR parameters for our sample of SNRs from the inner Galaxy. Then we examined the distributions of the parameters to determine properties of the Galactic SNR population in the inner Galaxy. The estimated birth rate is consistent with estimates of the overall Galactic SNR birth rate and with estimates of the fraction of SNRs in the Galaxy in our sample. We find that the energies and ISM densities of SNR can be well fit with log-normal distributions. The distribution of explosion energies is very similar to that for SNRs in the Large Magellanic Cloud (LMC), suggesting a surprisingly close similarity in the population of SN explosions in the LMC and in the Galaxy. The ISM density distributions for Galactic and LMC SNRs have similar dispersion but Galactic SNRs have a higher mean density by factor $\sim2.5$. A higher mean density is expected because our sample SNRs are selected from the inner Galaxy. In future, we plan to extend this type of study of SNRs to include all Galactic SNRs with measured distances. The goal is to significantly increase the sample size and better determine the intrinsic properties of SNRs. | 18 | 8 | 1808.04716 |
1808 | 1808.10349_arXiv.txt | We demonstrate how to obtain optimal constraints on a primordial gravitational wave component in lensed Cosmic Microwave Background (CMB) data under ideal conditions. We first derive an estimator of the tensor-to-scalar ratio, $r$, by using an error-controlled close approximation to the exact posterior, under the assumption of Gaussian primordial CMB and lensing deflection potential. This combines fast internal iterative lensing reconstruction with optimal recovery of the unlensed CMB. We evaluate its performance on simulated low-noise polarization data targeted at the recombination peak. We carefully demonstrate our $r$-posterior estimate is unbiased and optimal, making it the most powerful estimator of primordial gravitational waves from the CMB. We compare these constraints to those obtained from $B$-mode band-power likelihood analyses on the same simulated data, before and after map-level quadratic estimator delensing, and iterative delensing. Internally, iteratively delensed band powers are only slightly less powerful on average (by less than 10\%), promising close-to-optimal constraints from a stage IV CMB experiment. | After the completion of the \planck\ Cosmic Microwave Background (CMB) mission\cite{Akrami:2018vks}, the major target of the CMB community has now become precise measurement of the CMB polarization. The magnetic (B) part of the CMB polarization~\cite{Kamionkowski:1996ks, Zaldarriaga:1996xe} on degree scales is a unique signature of the stochastic background of primordial gravitational waves produced during inflation~\cite{Seljak:1996gy, Kamionkowski:2015yta}. Constraints on the tensor-to-scalar power spectrum ratio, $r$, are expected to increase by two orders of magnitude in precision within the next decade: CMB Stage IV (CMB-S4\footnote{\url{https://cmb-s4.org}}) has forecast sensitivity down to $r\sim 5\cdot 10^{-4}$, using delensed $B$-mode band powers after foreground cleaning \cite{Abazajian:2016yjj}. Lensing of the CMB photons by large-scale structures generates $B$ polarization that effectively appears as an approximately white cosmic variance noise~\cite{Zaldarriaga:1998ar, Lewis:2006fu}. In order to reach such tight constraints on the primordial signal, successful delensing of this $5 \mu$K-arcmin noise is mandatory. Currently and for the next few years, the most faithful lensing tracer at the scales relevant for $B$-mode delensing is the Cosmic Infrared Background(CIB) \cite{Sherwin:2015baa}, able to achieve 40\% delensing on 60\% of the sky \cite{Aghanim:2018oex}, and possibly more in areas that are clean from galactic dust. It is also possible to combine the CIB with other large-scale structure tracers \cite{Manzotti:2017oby, Yu:2017djs}, or with the CMB internal reconstruction \cite{Aghanim:2018oex}, in order to increase its fidelity to the CMB lensing field. Lensing estimates for CMB-S4 will be dominated by the internal reconstruction, using polarization quadratic estimators \cite{Okamoto:2003zw} or more powerful iterative estimators, first introduced by Ref.~\cite{Hirata:2003ka}. At the low instrumental noise levels expected for CMB-S4, iterative internal estimation from CMB polarization has been demonstrated on simulated data to give lensing reconstructions that are more than 90\% cross-correlated to the true lensing \cite{Seljak:2003pn,Carron:2017mqf}. One may ask whether it could be possible, at least in principle, to do even better than these forecasts. The lensing deflections introduce non-Gaussianities in the form of higher order statistics in the CMB temperature and polarization \cite{Lewis:2006fu}, which are used to reconstruct the lensing signal \cite{Hanson:2009kr}. Delensing will remove part of the non-Gaussianity, but only imperfectly, and some amount of information must remain beyond the power spectra. Hence, it is plausible that there may be room for alternative statistics that compress more information than delensed $B$-mode band-powers. This paper has two main purposes. The first is to demonstrate how to obtain directly the posterior probability density (PDF) for $r$, from lensed CMB data. The posterior contains all the information on $r$, and constraints based on it are optimal. The second is to compare this optimal method to band-power likelihood analysis. Finding a posterior width in agreement with naive expectations will confirm current forecasting methods and our understanding of how well CMB experiments can constrain primordial gravitational waves. Our approach uses an approximate, analytic marginalization of the large-scale structure lensing to build the statistics of interest, here the tensor-to-scalar ratio, $r$. This analytic marginalization is a fairly natural choice, and has been used already in a different context by Ref.~\cite{Hirata:2003ka}, where the aim was to obtain an optimal estimator of the lensing spectrum. In this paper we provide a rigorous discussion of the accuracy of the approximation and show that corrections are negligible for our purposes and the experimental configurations investigated. We work in the flat-sky approximation. All our simulations use the \planck\ 2015 cosmology~\cite{Ade:2015xua}, with power spectra generated with the \CAMB~\citep{Lewis:1999bs} software. We use square maps of area $645\deg^2$, assuming periodic boundary conditions for simplicity, with pixels of $1.5$ arcmin on a side. Foreground cleaning is a major challenge to the quest for primordial gravitational waves. We do not consider these complications in this paper, assuming throughout we are working with foreground-cleaned maps with white noise power spectra. We always use white Gaussian noise levels of $\sqrt{2} \cdot 1.5 \mu$K-arcmin in polarization, a instrument beam of 3 arcminutes, and consider CMB multipoles below $\ell = 3000$ only. The minimum multipole we probe in our flat-sky implementation of the sky patches is $\ell_{\rm min} = 14$, excluding the reionization peak. We consider 3 different levels of tensor modes, with tensor-to-scalar ratio $r_{\rm in}$ defined at the pivot scale $k = 0.05/\rm{Mpc}$ and a vanishing tensor spectral index. The first has $r_{\rm in} = 0.05$, close to current constraints $r_{0.002} < 0.064$ (95\% c.f.) from \planck\ in combination with BICEP2/KECK array BK14 data~\cite{Akrami:2018odb}. For the configuration just described, the nominal band powers are enough for a strong detection. Second, $r_{\rm in} = 0.01$, in which case the nominal band-powers cannot detect the waves decisively but the delensed band-powers can. Third, a vanishing amplitude $r_{\rm in} = 0.0$ where in all cases only upper limits can be placed from the data. The paper is built as follows. Sec.~\ref{sec:posterior} describes our approximation scheme to the exact posterior density function, and Sec.~\ref{sec:evaluation} gives details on our numerical implementation. In Sec.~\ref{sec:bandpowers}, we discuss our nominal and delensed band powers likelihood and implementation. We present in Sec.~\ref{sec:results} our results and summarise and conclude in Sec.~\ref{sec:summary}. One appendix details a couple of technical points for completeness. | \label{sec:summary} Unless the primordial $B$-mode power produced during inflation is very large, sophisticated analysis techniques such as delensing will be essential to provide best constraints on primordial gravitational waves. We have presented a new estimator, based on a close approximation to the exact posterior of the tensor-mode amplitude. By careful Monte-Carlo investigations of corrections to the approximation, we have demonstrated that it is unbiased and very close to optimal, providing the tightest possible constraints on primordial gravitational waves from CMB data. The estimator uses fast, joint estimation of the best lensing deflection map and of the unlensed CMB. This first investigation used a simplified setting, including periodic sky patches, no analysis mask, and usage of homogeneous noise, facilitating both the iterative lens reconstruction and the unlensed $E$-$B$ recovery from the observed lensed Stoke polarization data. These assumptions did not play a key role in obtaining our results, since the presence of the lensing deflections and data realization dependence break isotropy and prevent the existence of trivial basis to work with. Usage of Monte-Carlo simulations and inversion methods akin to conjugate-gradient seem unavoidable. Lens reconstruction and Wiener-filtering on masked data have already been demonstrated successfully~\cite{Carron:2017mqf} with the same methods, at the cost of a manageable increase in execution time. The posterior reconstruction has dependency on two aspects of the cosmological model used to define the CMB likelihood: the unlensed CMB scalar perturbations spectra and the lensing potential power spectrum. Changes in the lensing spectrum (or lensing deflection map prior) impacts slightly the optimal lens reconstruction, and changes in the scalar spectra the unlensed $E$ and $B$ polarization field reconstruction. Hence, formally, usage of a slightly different fiducial model might lead to a slightly different result. However, all these power spectra are extremely well constrained in practice from observations, including the lensing spectrum, so this is unlikely to bring significant biases. Furthermore, if necessary it is possible to include the uncertainty in the power spectra in the posterior, by obtaining the linear response to the spectra and extending in this way the posterior density, in analogy to the way state-of-art lensing spectrum reconstruction likelihoods are built~\cite{Ade:2015zua, Sherwin:2016tyf}. One can also go a step further and marginalize directly over these using the empirical spectra, as demonstrated by Ref.~\cite{Aghanim:2018oex}. We also restricted our analysis to the extraction of the tensor-to-scalar ratio assuming a fixed template shape of the tensor spectrum. However, this is not a limitation of this approach; using high-quality observations the obvious generalization of this framework will be able to distinguish features as well. We have compared the performance of our estimator to that of more traditionally planned $B$-mode band powers extraction. We found standard, well-demonstrated analytical likelihood models are able to describe meaningfully the delensed band powers, and we have used these likelihoods on nominal, quadratic estimator delensed and iteratively delensed band powers. The performances of these delensed band powers do match naive expectations. For the configuration studied here, targeting the recombination peak of the $B$-mode spectrum with noise levels in line with expectations from a CMB stage-IV experiment, our new estimator does outperform the iteratively delensed band powers by a realization-dependent amount, also depending on the exact value of $r$, reaching $8\%$ on average for small values. Producing the posterior PDF for $r$ as we did is more expensive numerically than producing band powers. Nevertheless, we demonstrated in this paper that the analysis was possible, providing constraints optimal by construction, and improving prospects on detecting a tantalizing component of modern cosmology. | 18 | 8 | 1808.10349 |
1808 | 1808.10455_arXiv.txt | In order to develop and test a methodology to search for UV variability over the entire GALEX database down to the shortest time scales, we analyzed time-domain photometry of $\sim5000$ light curves of $\sim300$ bright $(m_{\rm{FUV}}, m_{\rm{NUV}} \leq 14)$ and blue $(m_{\rm{FUV}} - m_{\rm{NUV}} < 0)$ GALEX sources. Using the \gphoton \ database tool, we discovered and characterized instrumentally-induced variabilities in time-resolved GALEX photometry, which may severely impact automated searches for short-period variations. The most notable artifact is a quasi-sinusoidal variation mimicking light curves typical of pulsators, seen occasionally in either one or both detectors, with amplitudes of up to 0.3 mag and periods corresponding to the periodicity of the spiral dithering pattern used during the observation (P$\sim$120 sec). Therefore, the artifact may arise from small-scale response variations. Other artifacts include visit-long ``sagging'' or ``hump'' in flux, occurring when the dithering pattern is not a spiral, or a one-time change in flux level during the exposure. These instrumentally-caused variations were not reported before, and are not due to known (and flagged) artifacts such as hot spots, which can be easily eliminated. To characterize the frequency and causality of such artifacts, we apply Fourier transform analysis to both light curves and dithering patterns, and examine whether artificial brightness variations correlate with visit or instrumental parameters. Artifacts do not correlate with source position on the detector. We suggest methods to identify artifact variations and to correct them when possible. | The Galaxy Evolution Explorer \citep[{\it GALEX},][]{martin05}, a NASA Small Explorer orbiting observatory, surveyed the sky in the ultraviolet (UV) from 2003 to 2013. Two micro-channel plate (MCP) photon-counting detectors, one in the far-UV (FUV, range 1350 -- 1750 \AA, $\lambda_{\textrm{eff}} = 1516$ \AA ) and one in the near-UV (NUV, range 1750 -- 2750 \AA, $\lambda_{\textrm{eff}} = 2267$ \AA), each with a 1.25 degree field-of-view (FOV), recorded cascades of electrical signals (known as `events') from photons landing on the MCPs with a time resolution of 5 milliseconds. Photon positions and arrival times were recorded and integrated by the mission pipeline over exposure times at each observation or ``visit,'' typically ranging from 150 seconds to 1500 - 1800 seconds (\citealt[(hereafter M07)]{morrissey07}; \citealt{bianchi09, bianchi11a}). A $\sim 1$ arcmin spiral dither pattern with a cycle nearly two minutes long was used in exposures in the Medium Imaging and Deep Imaging Surveys (MIS and DIS, respectively; exposures were typically longer than 1000 sec), but almost never for the All-sky Imaging Survey (AIS; $\sim150$ sec exposures). This dithering was adopted to maximize photometric quality by averaging over pixels with different response and to avoid detector ``fatigue'' from prolonged exposure of some areas to high count rate events. Most earlier studies of variability in the UV with GALEX have used the pipeline-provided photometry integrated over separate observations \citep{welsh06, welsh07, welsh11, wheatley12, gezari13,conti14}. The full potential of the high temporal resolution achievable through {\it GALEX} photometry, however, has been hardly explored to date \citep{robinson05, welsh06, welsh07, welsh11, wheatley08, wheatley12, browne09}, because the full time-resolved photon lists have been not publicly accessible until recently (see e.g., \citet{bianchi14l} for a recent review summary of the GALEX mission). Recently, \citet[][hereafter M16]{million16} released the first database tool enabling time-resolved GALEX photometry, \gphoton. This tool, however, has only been used to examine single objects \citep[e.g.][]{davenport18} or specific stellar populations in varying sample sizes \citep[e.g.][]{boudreaux17, tucker18} and on time scales of 15 - 30 sec. The capabilities of \gphoton \ on shorter timescales are not thoroughly known. This paper presents the first comprehensive analysis of the short-term variability detection capabilities using \gphoton. The analysis revealed a number of instrumentally-induced variations in the source count rate, which were not previously reported and must be taken into account in any study using \gphoton. This paper is organized as follows. In Section \ref{sec:source} we define our sample of sources. Sections \ref{sec:photom} and \ref{sec:analysis} outline our methods to perform time-resolved photometry and search for variability within light curves in our sample, respectively. In Section \ref{sec:artifacts} we describe instrumentally induced variability and examine whether there are correlations with observational parameters. We develop and test a methodology to detect and remove artifacts in Section \ref{sec:detect_char}. In Section \ref{sec:conclusion} we summarize and conclude. We use AB magnitudes throughout this paper. All light curves shown in this study do not include aperture corrections. \begin{figure*} \centering \includegraphics[width=5in]{sample_hist.jpg} \caption{Our analysis sample of 304 sources, comprising 5021 visits. Distribution of (a) total exposure time in FUV and NUV, (b) visit exposure time in each band, (c) apparent magnitude in each band, and (d) FUV-NUV color.} \label{fig:sample} \end{figure*} | \label{sec:conclusion} In this paper we have analyzed 5000 light curves of 304 bright ($m_{\rm{FUV}}, m_{\rm{NUV}} < 14$) and blue ($m_{\rm{FUV}} - m_{\rm{NUV}} < 0$) sources using the database tool \gphoton. We inspected nearly 4000 light curves at least 200 seconds long with a time resolution of 5 seconds, and discovered several previously unreported artificial variations, after removing data points affected by hotspots, short integration times, low response and proximity to the detector edge, which are known causes of potential spurious variations and can be cleaned using the provided flags. Our results can be summarized as follows. \begin{enumerate} \item The most frequent artifacts we find are quasi-sinusoidal variations (``triangle-waves'') with periods $\sim120$ sec and amplitudes $\sim0.2$ mag. These occur in either one or both bands but more often in NUV. They are caused by the spiral dither of the spacecraft pointing, which was used to minimize pixel-to-pixel fluctuations. They can be easily identified by peaks in the light curve Fourier transform matching the dither frequency or its harmonics. We attribute these to spatial inhomogeneities in detector response at the pixel scale. \item Shifts in flux (``jumps'') and gradual changes in brightness (``slopes''), by up to a few tenths of a magnitude, and occur occasionally, the former more often in FUV and the latter more often in NUV. \item Sinusoidal-like variations, with periods equal to the duration of the observation, resembling a ``sagging'' or ``heaving'' of the source flux, with amplitudes $\sim 0.5$ mag, occur more rarely. These are accompanied by a dither motion with the same phase and orbit-long period. Other sources in the field exhibit the same artifact during the same observation, but are not necessarily affected in the same way. \end{enumerate} We developed and tested a methodology to identify the artifacts and remove them from light curves using the Fourier transforms of the light curve and the dither during an observation. A future paper will be devoted to physical variations detected in GALEX time-resolved photometry (see examples in \citealt{bianchi18}) including this sample and to a fainter sample. The current sample is mostly in the non-linear regime although some of the artifacts are also seen at our faintest magnitude of 14. | 18 | 8 | 1808.10455 |
1808 | 1808.07186_arXiv.txt | Massive starforming regions like Giant \hii\ Regions (GHIIR) and \hii\ Galaxies (HIIG) are emission line systems ionized by compact young massive star clusters (YMC) with masses ranging from $10^4 \msun$ to $10^8 \msun$. We model the photometric and dynamical evolution over a Hubble time of the massive gravitationally bound systems that populate the tight relation between absolute blue magnitude and velocity dispersion ($M_{B}-\sigma$) of GHIIR and HIIG and compare the resulting relation with that one of old stellar systems: globular clusters, elliptical galaxies, bulges of spirals. After 12~\gyr\ of evolution their position on the $\sigma$ vs. M$_B$ plane coincides -- depending on the initial mass -- either with the globular clusters for systems with initial mass $M < 10^6 \msun$ or with a continuation of the ellipticals, bulges of spirals and ultracompact dwarfs for YMC with $M >10^6 \msun$. The slope change in the $M_{B}-\sigma$ and $M_B$-size relations at cluster masses around $10^6 \msun$ is due to the larger impact of the dynamical evolution on the lower mass clusters. We interpret our result as an indication that the YMC that ionize GHIIR and HIIG can evolve to form globular clusters and ultra compact dwarf ellipticals in about 12\,\gyr\ so that present day globular clusters and ultra compact dwarf ellipticals may have formed in conditions similar to those observed in today GHIIR and HIIG. | The possible connection between young massive clusters (YMCs) and globular clusters (GCs) has been discussed in the literature mostly in relation with YMC found in the central galaxy of the Perseus cluster [NGC~1275; \citep{SF90, Holtzman92}] in the central regions of interacting galaxies \citep{Portegies2010} and in local group galaxies like the Large and Small Magellanic Clouds. The comparable masses and sizes of YMC and GC lead to the belief that there might be an evolutionary connection between these massive clusters posing the logical question of whether YMC could be young GC. It is important to note that while YMC found in massive interacting galaxies and GC have comparable masses, the former (unlike GC) are metal rich and are formed in high density environments. On the other hand, the YMC that ionize the GHIIR in dwarf irregular galaxies and in the outer regions of late spirals, have a range of masses and $\alpha$-element abundances (oxygen, neon, sulphur, argon) substantially subsolar, similar to those found in GCs. In particular there have been suggestions that 30-Dor, the prototypical GHIIR in the LMC, could be a GC progenitor given its mass, size and metal content \citep[e.g.][]{Meylan1993}. Fe abundance is rarely measured in HII regions, as the ionization correction fractions for Fe can cause uncertainties of factors 2.5 - 3 depending on the degree of ionization of the region (M\'onica Rodr\'\i guez, private communication) and the abundance may also be masked by depletion in dust grains \citep[e.g.][]{Esteban98} . In globular clusters, instead, the stellar abundances of $\alpha$-elements are normally given with respect to Fe ($\alpha$/Fe), and their value relative to H is then deduced from the Fe/H value. The most extreme cases of low metallicity YMC are found in HIIG. These are YMC in dwarf galaxies that completely dominate the luminosity output having metallicities [O/H] down to 1/50th of solar [see e.g. the review by \cite{Kunth2000}]. We have found \citep{Chavez2014, Terlevich2015} that the properties of low- and high-z HIIG are similar in every parameter that we have measured (mass, velocity dispersion, luminosity) thus strongly suggesting that the study of low {\it z} YMC can provide important clues to the formation and evolution of GCs. A particular case is that of ID11 an actively star-forming, extremely compact galaxy and Ly$\alpha$ emitter at $z = 3.1$ that is gravitationally magnified by a factor of $\sim$17 by the cluster of galaxies Hubble Frontier Fields AS1063. The size, luminosity, velocity dispersion and dynamical mass of ID11 resemble those of low luminosity HIIG or GHIIR such as 30 Doradus \citep{Terlevich2016}. HIIG are narrow emission line compact starforming systems selected from spectroscopic surveys as those with the largest emission lines equivalent width (EW), e.g. EW(H$\beta) > $ 50\AA\ (or EW(H$\alpha) > $ 200\AA) in their rest frame. The lower limit in the EW of the recombination hydrogen lines guarantees that a single and very young starburst, less than $\sim 10 $Myr in age, dominates the total luminosity output \citep[cf.][]{Dottori1981, Dottori1981b, Leitherer1999, Melnick2000, Chavez2014}. As a result of this selection, the possible contamination by an underlying older population or older clusters inside the spectrograph aperture as well as the ionizing photon escape are minimised. In brief, HIIG can be considered as ``naked" extremely young starbursts. HIIG thus selected are spectroscopically indistinguishable from young GHIIR in nearby galaxies (e.g.~30 Doradus or NGC~604 in M33). This is underlined by the fact that when first studied in detail, the prototypical\\ HIIGs I~Zw18 and II~Zw40 were dubbed ``Isolated Extragalactic \hii\ regions" \citep{Sargent1970}. It is interesting to note that an important fraction of GHIIR and HIIG are complex systems with one massive cluster -- the youngest -- dominating the luminosity\footnote{These ionizing clusters are much more massive than the typical HII regions in our galaxy, like e.g. Orion.}. The possibility of these systems later merging and forming a single complex cluster is intriguing. From the analysis of the observed distribution of EW of the Balmer lines, \cite{Terlevich2004} concluded that the evolution of HIIG is consistent with a succession of short starbursts separated by quiescent periods and that, while the emission lines trace the properties of the present dominant burst, the underlying stellar continuum traces the whole star-formation history of the galaxy. Thus, observables like the EW of the Balmer lines that combine an emission line flux, i.e. a parameter pertaining to the present dominant burst, with the continuum flux, i.e. a parameter that traces the whole history of star formation, should not be used alone to characterize the present burst. GHIIR have long been applied to the calibration of the extragalactic distance scale \citep{Sandage1974} based on a correlation between region diameter and parent galaxy luminosity. A different approach for using GHIIR as distance indicators was proposed by \citet{Melnick1977, Melnick1978}, who found that their diameters are well correlated with the turbulent widths of the nebular emission lines. Melnick then showed that a tighter correlation than the original one for GHIIR (diameter, parent galaxy luminosity) exists if one uses the mean turbulent velocity of the three largest HIIRs instead of their diameters. It has since been clear that GHIIR can be used as distance indicators provided an adequate high quality calibration sample is obtained. \citet{Terlevich1981} found evidence from a small sample --- the one available at the time --- that scaling relations that apply to gravitationally bound stellar systems like elliptical galaxies, bulges of spirals and galactic globular clusters, apply also -- after taking evolution into account -- to HIIG and GHIIR. These are the relations between H$\beta$ luminosity, absolute blue magnitude, linear size, width of the emission lines and heavy element abundance. The underlying physics of this relation is surprisingly simple: both the luminous and mechanical power of these objects, and the gravitational potential, stem from the same source: a young massive starburst. So the physical parameter at the basis of the correlation is the total mass of the burst component. Since HIIG have a very high luminosity per unit mass, and most of their luminosity is emitted in a few strong and narrow emission lines\footnote{HIIGs can reach $\ha $ luminosities of $10^{43}$ \ergs .}, the spectrum of these objects is easily observable out to large redshifts ($z > 3$) with present day instrumentation. The scatter in the $L(\mathrm{H}\beta)-\sigma$ relation is small enough that it can be used to determine cosmic distances independently of redshift \citep[see][]{Melnick1988,Melnick2000, Fuentes-Masip2000,Bosch2002, Siegel2005,Bordalo2011,Chavez2012,Chavez2014,FernandezArenas2018}. The time is ripe to repeat \citet{Terlevich1981} analysis, using now state-of-the-art data for GC, GHIIR, HIIG and numerical models for the dynamic and stellar evolution of the clusters and such is the purpose of this work. We will assume that these systems are massive virialized star clusters, and evolve them in time. We refer to the massive ionizing stellar clusters as YMC and to the evolved non-ionizing systems as super star clusters (SSC). The paper is organized as follows: \S \ref{dataSa} introduces the data samples used; \S \ref{modellingEvo} presents the method to analyse the cluster evolution divided in photometric evolution, mass loss, two-body relaxation and adiabatic expansion with the consequent changes in the velocity dispersion. \S \ref{evolMBsigma} analyses the evolution of the clusters $M_B-\sigma$ plane. Discussion and conclusions are given in \S \ref{conclu}. | We have calculated the evolution of an individual YMC responsible for the ionization of GHIIR and HIIG as it ages over 12\,\gyr. The almost identical results that we obtained using either a numerical simulation (EMACSS) or the analytical approximation, legitimises the use of the analytical expressions to estimate the evolution of the velocity dispersion from equation \ref{eq:DeltasigmaTotal}. The luminosity evolution was estimated using the results from Section \ref{PhotoEvo}. The position on the $\sigma \, vs. \, M_B$ plot of the YMC of our sample after 12\,\gyr\ of evolution is shown in figure \ref{Ultimate_plot}. Also plotted in the figure and specified in the inset labels, are the data from our compilation as discussed in Section \ref{dataSa}. We have performed fits to the evolved YMC separating the sample in two groups, those with $M<10^6 M\odot$ and those with $M>10^6 M\odot$. The resulting fits are: \begin{equation} \log\sigma=-(0.22M_B +0.85) \, \, M<10^6 M\odot \end{equation} \begin{equation} \log\sigma=-(0.11M_B - 0.04) \, \, M>10^6 M\odot \end{equation}\\ These fittings are shown in Figure \ref{Ultimate_plot} as dot-dashed and dashed lines. \citet{Hasegan2005} investigated the scaling relations for a compilation of galactic, M~31, and NGC~5128 GC, Local Group dSph, Virgo dE,N and their nuclei, Fornax Ultra Compact Dwarfs plus M~32. and elliptical galaxies. Their scaling relations converted to blue magnitudes are: \begin{equation} \log\sigma=-(0.20M_B + 0.64) \, \textrm{ for globular clusters} \end{equation} \begin{equation} \log\sigma=-(0.10M_B - 0.22)\, \textrm{ for elliptical galaxies} \end{equation}\\ The fittings to \citet{Hasegan2005} GC and ellipticals, the latter basically the Faber-Jackson relation, are also shown with solid lines in figure \ref{Ultimate_plot}. It is quite striking that the initial position of the YMC in the $\sigma$ vs. $M_B$ plane in Figure \ref{fig:sigmaMb}, shift after 12\,\gyr\ of evolution to coincide with either the position of the globular clusters for YMC with initial mass $M < 10^6 \msun$ or with a continuation of the ellipticals, bulges of spirals and ultracompact dwarfs for the more massive YMC in figure \ref{Ultimate_plot}. The two branches in the $M_B\, vs.\, \sigma$ plot are related to the break in the mass-sigma and mass-radius relations seen in figure \ref{msigma_plot}-(a) and -(b) at about $10^6 \msun$ which manifest themselves as a change in the slope of the luminosity-sigma relation. This explains the observed different slopes in the L-$\sigma$ relation of elliptical galaxies and globular clusters. This change in slope is clearly seen in the M$_B\, vs.\, \sigma$ plane in figure \ref{Ultimate_plot}, in agreement with \cite{Hasegan2005} findings, also reproduced in the figure. The remarkable result is that not only the position of the evolved YMC in the $\sigma$ vs. M$_B$ plane coincides with the positions of GC and Ultra Compact Dwarfs but also the position of the break in the relation is reproduced and the fits to the evolved YMC are strikingly similar to those of the \cite{Hasegan2005} scaling relations for old spheroidal systems. It is interesting to note that, our sample includes HIIG with redshifts up to 3.0 when the universe was about 2\,\gyr\ old and probably actively forming GCs. This is in line with \cite{Elmegreen2012} suggestion that the low metallicity halo globular clusters seen in spiral galaxies \citep{Brodie2006} could have been formed in dwarf galaxies, in particular Ly$\alpha$ emitters seen as young, metal poor dwarf star-forming galaxies observed at high redshifts that are the building blocks of present day spirals. As mentioned in the introduction, about $60\%$ of our sample of GHIIR and HIIG show evidence of either complex morphology or definite multiplicity with one cluster, the youngest, dominating the luminosity. The possibility of these systems later merging and forming a single complex cluster is consistent with the hierarchical merger scenario for the formation of massive clusters \cite[e.g.][]{Krumholz2007,Offner2008,Sabbi2012,Smilgys2017}. \cite{Terlevich2004} concluded that the evolution of HIIG is consistent with a succession of starbursts separated by short quiescent periods and that, while the emission lines trace the properties of the present dominant burst, the underlying stellar continuum traces the whole star-formation history of the galaxy. \citet{Sabbi2012} in their analysis of the stellar population in the core of the prototypical GHIIR 30~Doradus (NGC~2070) in the Large Magellanic Cloud identified two different stellar populations: the most massive and younger at the centre and a second one $\sim$1 Myr older at about 5pc away. The proximity and morphology of these clusters suggest that an ongoing merger may be occurring within the core of NGC~2070, a finding that is consistent with the predictions of models of hierarchical fragmentation of turbulent giant molecular clouds, according to which star clusters would be the final product of merging smaller sub-structures \citep{Bonnell2003, Bate2009, Federrath2010}. Star formation will not be spread over the whole parent molecular cloud, but will be localized in gravitationally bound pockets of gas \citep{Clark2005, Clark2008}. Additional evidence for this scenario comes from the complexity of the structure of the other well studied GHIIR in the local group, NGC~604 in M~33 \citep{Maiz-Apellaniz2004}. If GC form from mergers of smaller sub-systems, this may be related to the observed abundance anomalies and perhaps also be the reason behind the high fraction of rotating GC. If the HII regions in our sample are indeed the progenitors of the old GCs observed in the nearby Universe, then they could potentially be used to shed light on the multiple population problem of (old) GCs. Globular clusters are characterised by light-element variations, in the form of broadened and/or multiple main sequences, believed to be the result of star-to-star helium variations, and Na-O and Mg-Al anticorrelations \citep[see][for a recent review]{BL18}. The origin of these abundance anomalies is topic of fierce debate, and various `polluters' have been put forward, such as asymptotic giant branch stars \citep[AGB stars, e.g.][]{2001ApJ...550L..65V}, (fast-rotating) massive stars \citep[$\gtrsim20\,{\rm M}_\odot$, e.g.][]{2007A&A...464.1029D, 2009A&A...507L...1D}, and supermassive stars \citep[SMS, M $\gtrsim10^3\,{\rm M}_\odot$, ][]{2014MNRAS.437L..21D, 2018MNRAS.478.2461G}. These multiple populations were once thought to be present only in the old GCs, but N spreads have recently been found in clusters as young as 2 Gyr in the Small and Large Magellanic Clouds \citep[e.g.][]{2018MNRAS.473.2688M}. Measuring these abundance anomalies in the youngest massive clusters ($2\,$Myr) is challenging and upper limits on the Al abundance in several YMCs have been established by \citet{2016MNRAS.460.1869C}. Small spreads in Al have been found in young ($\sim10-40\,$Myr) clusters in the Antennae galaxies \citep{2017MNRAS.468.2482L}. It is therefore not clear, whether YMCs in the Local Universe form in the same way as their older counterparts. In the SMS scenario, the SMS may still be present after most of the gas has been evacuated \citep{2018MNRAS.478.2461G}, hence the HII regions -- especially those at redshift $z \sim 3$ -- could be used to look for strong outflows from a SMS wind, enriched in Al, Na, and He. In conclusion, we interpret our results as a strong indication that both young GHIIR and HIIG can evolve to form globular clusters and ultra compact dwarf ellipticals in about 12\,\gyr. These results make a strong case for the detailed study of the YMC in nearby GHIIR and HIIG given that it can provide important clues to the formation and evolution of GCs. \begin{figure*} \includegraphics[width=15.5cm]{curvefinal_condatos_v6.pdf}. \caption{ The position of evolved YMC is shown in the $\sigma$-M$_B$ plane on top of the observed position of old spheroidal systems, i.e. GC, UCD, bulges of spiral galaxies (BSGs) and elliptical galaxies (EG). The solid line shows the fit to EG and BSGs while the dotted line is the fit to globular clusters given by \protect\cite{Hasegan2005} (equations 12 and 13). Also shown are the fits to the evolved YMC, the dashed line for those with $M>10^6 M\odot$, and the dot-dashed line, for those clusters with $M<10^6 M\odot$ (equations (10), (11)). The upper axis labels represent the mass, estimated using an M/L = 2 taken from \protect\cite{Baumgardt2017}.} \label{Ultimate_plot} \end{figure*} | 18 | 8 | 1808.07186 |
1808 | 1808.00559_arXiv.txt | We present a procedure to optimize the offset angle (usually also known as the \emph{wobble distance}) and the signal integration region for the observations and analysis of extended sources by Imaging Atmospheric Cherenkov Telescopes (IACTs) such as MAGIC, HESS, VERITAS or (in the near future), CTA. Our method takes into account the off-axis instrument performance and the emission profile of the gamma-ray source. We take as case of study indirect dark matter searches (where an a priori knowledge on the expected signal morphology can be assumed) and provide optimal pointing strategies to perform searches of dark matter on a set of dwarf spheroidal galaxies with current and future IACTs. | \label{sec:Introduction} \noindent Imaging Atmospheric Cherenkov Telescopes (IACTs) are ground based instruments capable of detecting gamma rays with energies from $\sim$50~\GeV ~to $\sim$100~\TeV. IACT's typical fields of view (FoVs) are of the order of $\sim$1-10$^{\circ}$. Observations are often performed in the so called \emph{wobble mode}~\citep{Fomin:1994APh}, in which the nominal pointing of the telescope has an offset (by a certain angle $w$, called the \emph{wobble distance}) w.r.t. the position of the source under observation (or, for extended sources, to its center). \emph{Signal} (or ON) region is integrated inside a circular region of angular size $\theta_{\text{c}}$ around the source while \emph{background control} (or OFF) region can be defined equally around a ghost region placed symmetrically w.r.t. the pointing direction (in order to have equal acceptance). Under such wobble observation mode ON and OFF regions are observed simultaneously, what makes an efficient use of the limited duty cycles of IACTs while minimizing possible systematic differences in the acceptance for ON and OFF regions (due e.g. to atmospheric changes in the on-axis observation mode). \newline \noindent Unlike $\theta_{\text{c}}$ that is used in the analysis, $w$ is fixed during data taking (by fixing the pointing direction w.r.t. the center of the source). The value of $w$ can be optimized if one takes into account that for large $w$, ON and OFF regions are defined close to the edge of the FoV, where the performance of the instrument decreases while for low $w$, it may not be possible to define an appropriate signal-free OFF region. These effects become critical for moderately extended sources, as the case for instance of the expected gamma-ray signal coming from Dark Matter (DM) in nearby dwarf spheroidal galaxies (dSphs) or from pulsar wind nebulae from nearby pulsars. \newline \noindent Here we present a procedure to optimize the wobble distance $w$ and signal integration radius $\theta_{\text{c}}$, taking into account the off-axis performance of the instrument and the expected spatial morphology of the source. As a case study, we focus on indirect DM searches and provide optimal pointing configurations for a list of dSphs to be observed for current and future IACTs. We have implemented an open-source tool % so that the procedure can be applied to optimize the pointing strategy of an arbitrary IACT observing an arbitrary circular symmetric moderate extended gamma-ray source. \newline \noindent The rest of this paper is structured as follows: in \autoref{sec:JDInstrument} we introduce the IACT technique and define a set of quantities that allow us to quantify their off-axis performance; in \autoref{sec:JDOptimization} we introduce the quality factor that we use as a figure of merit for the optimization of the pointing strategy; in \autoref{sec:JDDarkMatter} we briefly discuss the DM paradigm and assess its framework, and apply the method for the case of indirect DM searches to provide optimal pointing strategies on a set of dSphs observed with current or future IACTs; finally, in \autoref{sec:Conclusions} we briefly discuss the current status of the software and its applicability. | \label{sec:Conclusions} \noindent In this work, we have proposed a method to optimize the pointing strategy and analysis for extended sources observed by IACTs. The method provides the optimal offset and signal integration distances ($w_{\text{opt}}, \theta_{\text{opt}}$) taking into account: the off-axis performance and the angular resolution of the instrument, and the profile of the source under observation. The method has a potential use in scheduling new observations, but can also be used to optimize the analysis cut $\theta_{\text{c}}$ (typically used by the community as a cut on $\theta^{2}$) for data already taken. We focus on the case of indirect DM searches, and provide optimal pointing strategies for indirect DM searches on a set of dSph to be observed with MAGIC and CTA. \newline \noindent We have implemented the method in a tool that is freely distributed, open source software, accessible from: {\scriptsize \begin{itemize} \item[] \href{https://github.com/IndirectDarkMatterSearchesIFAE/}{\texttt{https://github.com/IndirectDarkMatterSearchesIFAE/}} \end{itemize} } \noindent A released version (\emph{V1.0}), with which the results shown in this paper were computed, can be accessed by:\\ {\scriptsize \begin{itemize} \item[] \texttt{\$~git clone https://github.com/IndirectDarkMatterSearchesIFAE/ObservationOptimization.git} \item[] \texttt{\$~git checkout V1.0} \end{itemize} } \noindent The package is provided with tutorials in order to acquire the basic skills required to reproduce the results shown here. The software is flexible enough so that new sources (not necessary related to DM) or telescopes can be defined easily. This provides an easy, fast, and powerful tool for planning new observations with IACTs. | 18 | 8 | 1808.00559 |
1808 | 1808.02548_arXiv.txt | {Asymptotic Giant Branch (AGB) stars are characterised by complex stellar surface dynamics that affect the measurements and amplify the uncertainties on stellar parameters. As a matter of fact, the uncertainties in observed absolute magnitudes originate mainly from uncertainties in the parallaxes. The resulting motion of the stellar photo-center could have adverse effects on the parallax determination with Gaia.} {We explore the impact of the convection-related surface structure in AGBs on the photocentric variability. We quantify these effects to characterise the observed parallax errors and estimate fundamental stellar parameters and dynamical properties.} {We use 3D radiative-hydrodynamics simulations of convection with CO5BOLD and the post-processing radiative transfer code {{\sc Optim3D}} to compute intensity maps in the Gaia $G$ band [325 -- 1030~nm]. From those maps, we calculate the intensity-weighted mean of all emitting points tiling the visible stellar surface (i.e., the photo-center) and evaluate its motion as a function of time. We extract the parallax error from Gaia DR2 for a sample of semiregular variables in the solar neighbourhood and compare it to the synthetic predictions of photo-center displacements.} {AGB stars show a complex surface morphology characterised by the presence of few large scale long-lived convective cells accompanied by short-lived and small scale structures. As a consequence, the position of the photo-center displays temporal excursions between 0.077 to 0.198~AU ($\approx$5 to $\approx$11$\%$ of the corresponding stellar radius), depending on the simulation considered. We show that the convection-related variability accounts for a substantial part to the Gaia DR2 parallax error of our sample of semiregular variables. Finally, we put in evidence for a correlation between the mean photo-center displacement and the stellar fundamental parameters: surface gravity and pulsation. We denote that parallax variations could be exploited quantitatively using appropriate RHD simulations corresponding to the observed star.} {} | AGBs are low- to intermediate-mass stars that evolve to red giant and asymptotic giant branch increasing the mass-loss during this evolution. They are characterised: (i) by large amplitude variations in radius, brightness and temperature of the star; (ii) and by a strong mass loss rate driven by an interplay between pulsation, dust formation in the extended atmosphere, and radiation pressure on the dust \citep{2018A&ARv..26....1H}. Their complex dynamics affect the measurements and amplify the uncertainties on stellar parameters. Gaia \citep{2016A&A...595A...1G} is an astrometric, photometric and spectroscopic space borne mission. It performs a survey of a large part of the Milky Way. The second data release (Gaia DR2) in April 2018 \citep{2018arXiv180409365G} brought high-precision astrometric parameters (i.e., positions, parallaxes, and proper motions) for over 1 billion sources brighter that $G\approx20$. Among all the objects that have been observed, the complicated atmospheric dynamics of AGB stars affect the photocentric position and, in turn, their parallaxes \citep{2011A&A...528A.120C}. The convection-related variability, in the context of Gaia astrometric measurement, can be considered as "noise" that must be quantified in order to better characterise any resulting error on the parallax determination. However, important information about stellar properties, such as the fundamental stellar parameters, may be hidden behind the Gaia measurement uncertainty. In this work we explore the effect of convection-related surface structures on the photo-center to estimate its impact on the Gaia astrometric measurements. | We used the snapshots from RHD simulations of AGB stars to compute intensity maps in the Gaia $G$ photometric system. The visible fluffy stellar surface is made of shock waves, that are produced in the interior and that are shaped by the top of the convection zone as they travel outward. The surface is characterised by the presence of few large and long-lived convective cells accompanied by short-lived and small scale structures. As a consequence, the position of the photo-center is affected by temporal fluctuations. We calculated the standard deviation of the photo-center excursion for each simulation and found that $\sigma_P$ varies between 0.077 to 0.198~AU ($\approx$5 to $\approx$11$\%$ of the corresponding stellar radius) depending on the simulation. We compared the measure of the mean photo-center noise induced by the stellar dynamics in the simulations ($\sigma_P$) to the measurement uncertainty on the parallax of a sample of AGB stars in the solar neighbourhood cross-matched with the Gaia DR2 data. We found a good agreement with observations probing that convection-related variability accounts for a substantial part to the parallax error. It has to be noted that $\sigma_\varpi$ may still vary in the following data releases because thanks to the increase of Gaia's measurements and further corrections to the parallax solution. Finally, we put in evidence a correlation between the mean photo-center displacement and the stellar fundamental parameters: surface gravity and pulsation. Concerning the latter, we showed that that larger values of $\sigma_P$ correspond to longer pulsation periods. This result, associated with the P-L relation found by \cite{2017A&A...600A.137F} and the good agreement between simulations and observations ($\sigma_P$ versus $\sigma_\varpi$), let us denote that parallax variations from Gaia measurements could be exploited quantitatively using appropriate RHD simulations corresponding to the observed star. | 18 | 8 | 1808.02548 |
1808 | 1808.09977_arXiv.txt | A possible surface type that may form in the environments of M-dwarf planets is sodium chloride dihydrate, or ``hydrohalite" (NaCl $\cdot$ 2H$_2$O), which can precipitate in bare sea ice at low temperatures. Unlike salt-free water ice, hydrohalite is highly reflective in the near-infrared, where M-dwarf stars emit strongly, making the effect of the interaction between hydrohalite and the M-dwarf SED necessary to quantify. We carried out the first exploration of the climatic effect of hydrohalite-induced salt-albedo feedback on extrasolar planets, using a three-dimensional global climate model. Under fixed CO$_2$ conditions, rapidly-rotating habitable-zone M-dwarf planets receiving 65\% or less of the modern solar constant from their host stars exhibit cooler temperatures when an albedo parameterization for hydrohalite is included in climate simulations, compared to simulations without such a parameterization. Differences in global mean surface temperature with and without this parameterization increase as the instellation is lowered, which may increase CO$_2$ build-up requirements for habitable conditions on planets with active carbon cycles. Synchronously-rotating habitable-zone M-dwarf planets appear susceptible to salt-albedo feedback at higher levels of instellation (90\% or less of the modern solar constant) than planets with Earth-like rotation periods, due to their cooler minimum day-side temperatures. These instellation levels where hydrohalite seems most relevant correspond to several recently-discovered potentially habitable M-dwarf planets, including Proxima Centauri b, TRAPPIST-1e, and LHS 1140b, making an albedo parameterization for hydrohalite of immediate importance in future climate simulations. | \label{sec:intro} Planetary climate and habitability are strongly affected by the interaction between the spectral energy distribution (SED) of the planet's host star and the planet's unique surface composition. Surface types exhibit wavelength-dependent radiative properties, making their interactions with different host star SEDs distinct and challenging to model. This complexity is particularly acute for planets orbiting M-dwarf stars, whose near-infrared (near-IR) emission coincides with clear differences in the albedo of specific surface types such as ocean, water ice, and snow at these wavelengths \citep{Joshi2012, Shields2013, Shields2014, Shields2016b}. Here we consider the radiative properties and impact on habitability (the capability of sustaining liquid water on some part of a planet's surface, e.g. \citealp{Seager2013}) of a surface type never before considered in the context of extrasolar planets\textemdash sodium chloride dihydrate, or ``hydrohalite" (NaCl $\cdot$ 2H$_2$O). At low temperatures (T$<$ -23$^\circ$C) on planets with oceans, salt within brine inclusions in bare sea ice can precipitate in crystal form, eventually forming a hydrohalite crust \citep{Light2016, Carns2016}. As shown in Figure 1, hydrohalite is much more reflective than bare sea ice in the near-IR, resulting in higher broadband albedos than even snow. The net impact of the surface salt-albedo feedback mechanism generated by hydrohalite formation on extrasolar planets has not previously been explored. \begin{figure}[!htb] \begin{center} \includegraphics[scale=0.70]{Fig1.pdf} \caption{The spectral distribution of sodium chloride dihydrate, or ``hydrohalite" (NaCl $\cdot$ 2H$_2$O) from Light \emph{et al.} (\citeyear{Light2016}), fine-grained snow (H$_2$O, free of salts, \citealp{Hudson2006}), cold and warm bare ice \citep{Light2016}, and ocean, from Brandt \emph{et al.} (\citeyear{Brandt2005}).} \label{Figure 1.} \end{center} \end{figure} Studies of hydrohalite crusts have been applied to episodes of global-scale glaciation during the Neoproterozoic periods (600-800 million years ago) on the Earth \citep{Light2009, Light2016, Carns2016}, so-called ``Snowball Earth" events \citep{Kirschvink1992}. Low surface temperatures ($< 30^\circ$C) in the tropics during Snowball Earth events \citep{Pierrehumbert2005} may have inhibited melting for long enough for hydrohalite crusts to form over wide areas \citep{Light2009}. In regions of net sublimation in the tropics, where low-latitude ice was present and receiving the majority of the solar insolation, climate would have been far more sensitive to sea ice albedo than in higher-latitude ice-covered regions \citep{Light2009}. The high visible and near-IR albedos of hydrohalite crusts, compared with the salt-free ice albedos previously used in climate modeling of low-latitude glacial episodes, could have significantly altered the surface energy balance of Snowball Earth \citep{Carns2016}. M-dwarf stars are the most common type of stars in the galaxy, and discovering habitable planets around these stars will be the focus of extrasolar planet observational efforts for the foreseeable future, by both large-aperture (30-m class) telescopes on the ground, and space-based observatories such as the Transiting Exoplanet Survey Satellite, (TESS, \citealp{Ricker2014}). Identifying those potentially habitable planets to target for follow-up by the James Webb Space Telescope (JWST, \citealp{Gardner2006}) and the next generation of space missions depends on understanding the impact on habitability of the different interactions between the M-dwarf SED and specific surface types that may be possible on M-dwarf planets, as these interactions defy existing modeling prescriptions. Near the outer edge of the habitable zone, where a number of potentially habitable M-dwarf planets have been discovered \citep{Quintana2014, Dittmann2017, Gillon2017}, surface temperatures on regions of a planet may reach well below -23$^\circ$C (depending on atmospheric greenhouse gas concentrations), where hydrohalite formation may occur, making the climatic effect of this possible surface type on M-dwarf planets particularly important to quantify. In this work we calculate the effect of hydrohalite-induced salt-albedo feedback on the climate of ocean-covered planets orbiting M-dwarf stars, and compare these results to those for similar planets modeled without a parameterization for hydrohalite formation. We identify climate regimes where this surface type could be most relevant and impactful for the surface habitability of M-dwarf planets with Earth-like atmospheres, and discuss differences in the climatic effect of this surface type for planets orbiting brighter, Sun-like stars. In Section 2 we present and explain our methods and models used. In Sections 3 and 4 we present and discuss the results and significance of our simulations. In Section 5 we offer concluding remarks and implications of this work for future studies of the potential climates of recently-discovered potentially habitable exoplanets. | \label{sec:conc} Using a three-dimensional global climate model modified to incorporate an albedo parameterization for sodium chloride dihydrate, or ``hydrohalite" (NaCl $\cdot$ 2H$_2$O)\textemdash a surface type previously unexplored in the context of extrasolar planets\textemdash we have shown that simulations that include the salt-albedo feedback mechanism generated by the crystallization of this surface type in bare sea ice result in lower planetary global mean surface temperatures compared to simulations without this parameterization included, assuming Earth-like levels of CO$_2$. The large differences between the albedo of hydrohalite and water ice in the near-IR are primarily responsible for the difference in global mean surface temperatures on simulated M-dwarf planets with and without the hydrohalite parameterization included. G-dwarf planets, which exhibit greater climate sensitivity to water ice-albedo feedback and are therefore cooler to begin with at a given instellation, exhibit even stronger planetary cooling in simulations incorporating the albedo effects of this surface type. The climatic effect of hydrohalite becomes particularly important on rapidly-rotating habitable-zone M-dwarf planets receiving 65\% instellation from their host stars, with narrow swaths of open water. Habitable-zone M-dwarf planets that are synchronously rotating and receiving less than 90\% instellation from their host stars exhibit increased susceptibility to the climatic effects of this surface type, due to colder minimum surface temperatures reached on the day side of the planet compared with planets with Earth-like rotation periods receiving similar instellation. The effect is even stronger on fully glaciated planets, where net water evaporation exceeds precipitation such that differences in surface albedo are exposed to incoming stellar radiation, rather than masked by falling snow. These planets are therefore likely to be even colder than originally presumed, given the incorporation of an albedo parameterization for hydrohalite formation in climate simulations. The habitable-zone instellation values where the climatic effects of hydrohalite appear most relevant correspond to those of several recently discovered potentially-habitable M-dwarf planets, including LHS 1140b, TRAPPIST-1e, and Proxima Centauri b; therefore, future simulations of the potential climates of these planets would benefit from inclusion of the hydrohalite albedo parameterization we have developed and incorporated here. By depressing global mean surface temperatures, hydrohalite could increase the greenhouse gas concentration required to maintain surface liquid water on planets near the outer edge of their host stars' habitable zones. It may also increase the instellation values necessary to perpetuate free-thaw cycles on planets with non-zero eccentricities or other sources of climate cycling. | 18 | 8 | 1808.09977 |
1808 | 1808.00251_arXiv.txt | {Hydroxylamine (NH$_{2}$OH) and methylamine (CH$_{3}$NH$_{2}$) have both been suggested as precursors to the formation of amino acids and are therefore of interest to prebiotic chemistry. Their presence in interstellar space and formation mechanisms, however, are not well established.} {We aim to detect both amines and their potential precursor molecules NO, N$_{2}$O and CH$_{2}$NH towards the low-mass protostellar binary IRAS 16293--2422, in order to investigate their presence and constrain their interstellar formation mechanisms around a young Sun-like protostar.} {ALMA observations from the unbiased, high angular resolution and sensitivity Protostellar Interferometric Line Survey (PILS) are used. Spectral transitions of the molecules under investigation are searched for with the CASSIS line analysis software.} {CH$_2$NH and N$_{2}$O are detected for the first time towards a low-mass source, the latter molecule through confirmation with the single-dish TIMASSS survey. NO is also detected. CH$_{3}$NH$_{2}$ and NH$_{2}$OH are not detected and stringent upper limit column densities are determined.} {The non-detection of CH$_{3}$NH$_{2}$ and NH$_{2}$OH limits the importance of formation routes to amino acids involving these species. The detection of CH$_{2}$NH makes amino acid formation routes starting from this molecule plausible. The low abundances of CH$_2$NH and CH$_{3}$NH$_{2}$ compared to Sgr B2 indicate that different physical conditions influence their formation in low- and high-mass sources.} | \label{sec.int} The small molecules methylamine (CH$_{3}$NH$_{2}$) and hydroxylamine (NH$_{2}$OH) with an amine (-NH$_{2}$) functional group have both been suggested as precursors to the formation of amino acids \citep{Blagojevic2003,Holtom2005,Snow2007,Bossa2009,Barrientos2012,Garrod2013}. Reactions involving these molecules could explain the presence of the simplest amino acid glycine in comets \citep{Elsila2009,Altwegg2016}. Despite their importance, both CH$_{3}$NH$_{2}$ and NH$_{2}$OH have turned out to be quite elusive molecules in the interstellar medium. CH$_{3}$NH$_{2}$ has exclusively been detected towards Sgr B2 and tentatively towards Orion KL \citep[e.g.][]{Kaifu1974,Pagani2017}. Upper limit abundances of CH$_{3}$NH$_{2}$ towards other high-mass sources are generally found to be consistent with values determined towards Sgr B2 \citep{Ligterink2015}. In the Solar System CH$_{3}$NH$_{2}$ has been detected in comets 81P/Wild 2 and 67P/Churyumov-Gerasimenko \citep[hereafter 67P/C-G][]{Elsila2009,Goesmann2015,Altwegg2017}. NH$_{2}$OH has not been detected thus far, down to upper limit abundances of $\sim$10$^{-11}$ with respect to H$_2$ \citep{Pulliam2012,Mcguire2015}. The lack of detection of these two molecules not only constrains amino acid formation, but also contrasts with model predictions. \citet{Garrod2008} predicted efficient CH$_{3}$NH$_2$ formation from the radical addition reaction CH$_{3}$ + NH$_{2}$ in their models, whereas NH$_{2}$OH is assumed to form from the NH + OH addition followed by hydrogenation and NH$_{2}$ + OH reactions on ice surfaces. Abundances of CH$_{3}$NH$_{2}$ and NH$_{2}$OH are predicted to be on the order of 10$^{-6}$--10$^{-7}$, depending on the model. It is generally found that these models overproduce both molecules compared with observations \citep{Pulliam2012,Ligterink2015}. Therefore, other formation, reaction or destruction mechanisms need to be considered. Several laboratory experiments have investigated the formation of NH$_{2}$OH and CH$_{3}$NH$_2$. \citet{Zheng2010} show the formation of NH$_{2}$OH from electron irradiated H$_{2}$O:NH$_{3}$ ice mixtures, while \citet{He2015} produce the molecule by oxidation of NH$_{3}$ ice. Alternatively, NH$_{2}$OH is seen to efficiently form from the solid-state hydrogenation of nitric oxide \citep[NO;][]{Congiu2012a,Fedoseev2012}. In this scenario, NO is accreted from the gas-phase onto dust grains during cloud collapse \citep{Visser2011}. Nitrous oxide (N$_{2}$O) is found as a by-product of NO hydrogenation reactions. NO has been observed in a variety of sources \citep[e.g.][]{Liszt1978,Yildiz2013,Codella2017}. It is thought to mainly form via the N + OH $\rightarrow$ NO + H neutral-neutral reaction in the gas-phase. Observations suggest that N$_2$O is related to NO \citep{Ziurys1994,Halfen2001}. CH$_{3}$NH$_{2}$ formation has been demonstrated in electron irradiated CH$_{4}$:NH$_{3}$ ice mixtures \citep{Kim2011,Forstel2017}, with the main formation pathways suggested to proceed through CH$_{3}$ + NH$_{2}$ radical reactions. \citet{Theule2011} investigated hydrogenation of solid hydrogen cyanide (HCN) and methanimine (CH$_2$NH), both of which lead to CH$_3$NH$_2$ formation. CH$_{2}$NH is hypothesized to have a larger reaction probability than HCN and reaction pathways to CH$_{3}$NH$_{2}$ may be completely different for reactions starting from either HCN or CH$_{2}$NH. In contrast with CH$_{3}$NH$_{2}$, its potential precursor CH$_{2}$NH has been observed in numerous sources \citep{Dickens1997,Nummelin2000,Belloche2013,Suzuki2016}. \citet{Halfen2013} investigated the relationship between this molecule and CH$_{3}$NH$_{2}$ in Sgr B2 and concluded that the two species have different formation routes, due to observed differences in rotational temperature and distribution. Interestingly, CH$_{2}$NH has also been implied as a precursor to amino acid formation \citep[e.g.][]{Woon2002,Danger2011}. Searches for CH$_{3}$NH$_{2}$ and NH$_{2}$OH have so far mainly focused on high-mass sources. Detections or upper limits of these two molecules and their potential precursors towards a low-mass source would therefore expand our understanding of amine-containing molecules and their formation in the ISM. The low-mass solar-type protostellar binary IRAS 16293--2422 (hereafter IRAS 16293) is an ideal source for such a study. Its physics and chemistry are well studied and it is abundant in complex organic molecules \citep[e.g.][]{jorgensen2016}. Abundance ratios will therefore constrain the chemistry of -NH$_{2}$ molecules as has been done for other nitrogen-bearing species \citep{Coutens2016,Ligterink2017}. In this paper we present the first detection of CH$_{2}$NH and N$_{2}$O towards a low-mass protostar. NO is also detected and analysed. The abundances of NH$_{2}$OH and CH$_{3}$NH$_{2}$ are constrained by upper limits from non-detections. | 18 | 8 | 1808.00251 |
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1808 | 1808.04591.txt | %% and %Several works have focused on investigate impulsive variations of the magnetic helicity change rate associated with eruptive solar flares with the class larger than M5.0. However, it is remain unclear whether the Using the 135-second cadence of the photospheric vector data provided by the Helioseismic and Magnetic Imager telescope on board the {\it Solar Dynamic Observatory}, we examined the time-evolution of magnetic helicity fluxes across the photosphere during 16 flares with the energy class lower than M5.0. During the flare in 4 out of 16 events, we found impulsive changes in the helicity fluxes. This indicates that even the flare with less energy could be associated with anomalistic transportation of the magnetic helicity across the photosphere. Accompanying the impulsive helicity fluxes, the poynting fluxes across the photosphere evolved from positive to negative. As such, the transportations of magnetic energy across the photosphere were toward solar interior during these flares. In each of the 4 events, the impulsive change in the helicity flux was always mainly contributed by abrupt change in horizontal velocity field on a sunspot located near the flaring polarity inversion line. The velocity field on each sunspot shows either an obvious vortex patten or an shearing patten relative to the another magnetic polarity, which tended to relax the magnetic twist or shear in the corona. During these flares, abrupt change in the Lorentz force acting on these sunspots were found. %The resultant force and torque always had the same direction with the rotational motion and shearing motion of these sunspots. The rotational motions and shearing motions of these sunspots always had the same directions with the resultant Lorentz forces. These results support the view that the impulsive helicity transportation during the flare could be driven by the change in the Lorentz force applied on the photosphere. % All of these sunspots were swept by the flare ribbon and connected by the post-flare loops, indicating that motions of the sunspots could be a result of the magnetic reconnection during the flare. % change in the value of $\alpha$ of the coronal field play a role in $$rotational motion of the sunspot may %?????135????HMI??????16???M5???????? ??????????4??????????????????????? ?????????????????????????????????? ?????????????????????????????????? ?????????????????????????????????? ?????????????????????????????????? ?????????????????????????????????? ?????????????????????????? | \label{sec:intro} %The horizonal velocity anomalies would result in the impulsive helicity vsriation. %abrupt and persistent changes in the longitudinal and transverse fields do occur during X- and M-class solar flares, and the rising number of observations suggests that this might be a common phenomenon. %Field changes were significantly stronger for X-class than for M-class flares %But it remain unclear why The rising number of observations supports that abrupt and irreversible changes in the longitudinal magnetic field do occur during some solar flare \citep{Patterson81, Kosovichev99, Kosovichev01, Cameron99, Sudol05, Wang06, Wang11, Johnstone12, Gosain12, Cliver12, Burtseva13, Castellanos18}. %%It has been widely reported that at least one site in the flaring active region field shows the abrupt change in the field during the flare with the class greater than M. Field changes were often significantly stronger for X-class than for M-class flares \citep{Petrie10}. The impulsive field changes were also found in some C-class flare \citep{Wang13,Jing14,Castellanos18}. Based on the vector data, it has been widely reported the flare-induced enhancement in the horizontal magnetic field around the flaring polarity inversion line (PIL) \citep{Wang05, Wang07, Wang10, Li11, Su11, Liu12, Petrie12, Petrie13, Liu13, Song16, Sun17, Xu17, Gomoy17, Wang17}, which is accompanying with the impulsive enhancement in the shear angle of the magnetic field \citep{Wang94,Zhang94}. The increase in magnetic shear seems to contradict with the energy release for energizing flares. The results of NLFFF model show that the magnetic shear and magnetic energy in an area around the flaring PIL increased from the photosphere boundary to an altitude of $\sim$ 10 Mm, but decreased above this space \citep{Jing08,Liu12b,Sun12}. These results suggested that enhancements in the magnetic shear only occurred in a local area. The enhancements in both the horizontal magnetic field and magnetic shear are often regarded as a result of the contraction of the highly sheared field produced by the coronal magnetic reconfiguration in the period of the flare \citep{Hudson00,Ji07,Hudson08}. %% Different from the coronal loop contractions at the periphery of active regions \citep{Liu09,Sun12,Shen12,Simoes13,Kushwaha15,Wang18}, the contraction of the magnetic field around the flaring PIL is discussed in some specific magnetic configurations. \citet{Wang10} proposed that the increase in the horizontal field around PIL may related to the low-lying shorter loop across the PIL, which produced by the the near-surface reconnection between the two sigmoid elbows as suggested by the tether-cutting model for solar eruption \citep{Moore01,Sterling03,Aulanier10,Shibata11,Chen11,Schmieder15,Chen14}. As suggested by \citet{Melrose12}, magnetic reconnection between current-carrying magnetic loops can lead to release of the stored energy, and then a net shortening of the current path, which is consistent with an increase in the horizontal component of the photospheric field during a flare. \citet{Bi16} noted that the changes in the photospheric field covered by the flare ribbon may relate to the difference between the magnetic field before the flare and the newly formed field outlined by the post-flare loop. % \citep{Aulanier16,Ji07,Kosovichev98,Magara03,Pariat05,Su11,Xu18,Zirin81} Magnetic helicity and magnetic energy can be transported between the solar interior and the corona by the motions of magnetic flux on the photosphere \citep{Berger84,Wang96,Demoulin03,Demoulin07}. %% can be result in the transportation of the magnetic helicity between the solar interior and solar corona. The rate of helicity and energy transportation across the photosphere is defined as helicity flux ($\dot{H}$) and energy flux $\dot{E}$, which respectively can be derived as \citep{Kusano02,Liu12} \begin{equation}%\label{4} \dot{H}=\underbrace{2\int_{S}(\mathbf{A}_{p}\cdot \mathbf{B}_{t})V_{\bot n}dS}_{\dot{H}_{e}} -\underbrace{2\int_{S}(\mathbf{A}_{p}\cdot \mathbf{V}_{\bot t})B_{n}dS}_{\dot{H}_{s}} \end{equation} and \begin{equation}%\label{4} \dot{E}=\underbrace{\frac{1}{4\pi}\int_{S}B_{t}^{2}V_{\bot n}dS}_{\dot{E}_{e}} -\underbrace{\frac{1}{4\pi}\int_{S}(\mathbf{B}_{t}\cdot \mathbf{V}_{\bot t})B_{n}dS}_{\dot{E}_{s}} \end{equation} where $\textbf{A}_{p}$ is the vector potential of the potential field, $\mathbf{B}$ and $\mathbf{V}_{\bot}$ denotes the magnetic field and plasma velocity perpendicular to the magnetic field, and the subscript ``t'' and ``n'' refers to the horizontal and vertical component with respect the photosphere, the subscript ``e'' and ``s'' refers to the emerging and shear term, which is contributed from shuffling horizontal motion ($\mathbf{V}_{\bot n}$) of photospheric flux and flux emergency ($\mathbf{V}_{\bot t}$). The shear term is further decomposed into the contributions from the shearing motion between the different flux patches and the spin motion of the isolated flux patch, such as the rotation of a sunspot \citep{Longcope07}. Since the magnetic helicity cannot dissipate in the corona, the helicity injected into the corona will be accumulated in the corona. A mountain of helicity accumulation is found before the flare \citep{Yamamoto05, LaBonte07, Park08, Park10a, Ravindra11, Tziotziou13, Guo13}. \citet{Moon02} reported that the abrupt change in helicity flux during the flare and that the impulsive helicity flux tended to have the sign opposite to that of the active region. \citet{Smyrli10} investigated helicity flux in the 10 active regions and found that the abrupt change in helicity flux present during the 6 flare. On the other hand, some works found the helicity flux changed its sign around the start of the eruption\citep{Zhang08,Park10b,Vemareddy12,Wang14b,Gao18}, and thus the authors suggested that the interaction between the magnetic flux tubes with opposite sign of helicity is fundamental for the eruption to occur \citep{Linton01,Kusano04,Liu04,Liu07,Chandra10,Romano2011a,Romano2011b}. Therefore, the high-cadence magnetogram is essential to study whether the sudden change in the helicity flux is produced by the flare or vice versa. Case studies revealed that the impulsive change in helicity flux was mainly contributed by the abrupt reversal of rotation in a sunspot \citep{Bi16} or the sudden rotational motion of sunspots on both sides of the PIL \citep{Bi17}. The abrupt change in the rotational speed of sunspots during flare was first reported by \citet{Wang14}. \citet{Liu16} noted that the sudden rotation of a sunspot occurred when the flare ribbon propagates towards the sunspot. %sunspot rotation can be one of contributor tothe twist, helicity, and energy of the magnetic field. The rotational motion of a sunspot can play an important role in twisting, energizing, and destabilizing the coronal magnetic field system (\citet{Fan09,Torok13}). It has been widely reported that the continual rotational motions of sunspots were followed by flare activities \citep{Brown03, Romano05, Regnier06, Zang07, Yan07, Li09, Min09, Kazachenko09, Suryanarayana10, Jiang12, Zhu12, Kumar13, Ruan14, Bi15, Suryanarayana15, Li15, Wang16, Vemareddy16, Yan18}. The abrupt overall motion of the sunspot associated with flare \citep{Anwar93,Xu17} could be an alternative mechanism for the impulsive change in the helicity flux. \citet{Wang06} have reported that the sudden motions of the two magnetic polarities during flares had a tendency to reduce the magnetic shear in the corona. The sudden shear-relaxing motion could then generate an impulse helicity flux having the sign opposite with that of the active region as reported by \citet{Moon02}. %``Specifically, some researchers (for example, ref. 13) have reported sudden, shear-relaxing motions in the course of the flares. These motions may be driven by a horizontal Lorentz force that can be deduced from the abrupt changes of the photospheric magnetic field14. We note that such shear-relaxing motions may have a role in the impulsive variations of the helicity transport.'' Using the vector data provided by the Helioseismic and Magnetic Imager \citep[HMI;][]{Schou} telescope on board the {\it Solar Dynamic Observatory (SDO)}, in this article, we surveyed the evolutions in the magnetic helicity across the 16 flaring active region. During 4 out of 16 flares, significant changes in the helicity flux were found, which mainly were contributed by the abrupt motions of the small-sized sunspots nearby the flaring PIL. %The impulsive change in the rotational motion of the sunspots were detected in the course of all of the 4 flares, while the obvious shear-relaxing motions of the sunspot appeared in the periods of 2 flares. % , which were mainly contributed by the impulsive change in the rotational motion of the sunspots located near the PIL on the active region. % Recently, it has been reported that an abrupt change in rotation rate of the sunspot could occur in the period of a major flare. In particular, Wang et al. (2014) noted that two main sunspots in NOAA AR 11158 underwent a sudden acceleration in rotational motion during an X2.2 flare. In contrast, Bi et al. (2016) studied a sunspot that is swept up by a flare ribbon and found that the direction of the sunspot?s rotation is reversed impulsively. | After surveying 16 flares with class lower than M5.0, we found abrupt change in the helicity flux in the 4 events. This indicates that even the flare with less energy could occur with an anomalistic transportation of the magnetic helicity across the photosphere. During each flare of the 4 flares, same similarity as follow: \begin{enumerate} \item The impulsive change in the helicity flux was mainly contributed by either the shear or rotational motion of a sunspot,%the found on the small size sunspot. which was located near the $PIL_{SS}$ and was covered by flare ribbons. % Indicated from the result of DAVE4VM, all of sunspots underwent an abrupt rotation during the flare. \item The helicity flux across the sunspot had the sign opposite with that of the accumulated helicity before the flare. \item The energy flux across the sunspot was negative during the flare while positive before the flare. \item The photospheric magnetic field on the sunspot showed an abrupt and irreversible changes. %\item \deleted{ The change in Lorentz force acted on the sunspot provided a torque on the sunspot, which had the same direction with that of the rotation of the sunspot.} \item The changes in the Lorentz force always tended to rotate these sunspots to decrease the coronal magnetic twist and move these sunspots along the PIL to reduce the magnetic shear in the corona. Consistently, the sudden reversals in the rotations of the sunspots were detected during Flare II, III, and IV, and the impulsive shear-reducing motions were found during Flare I and III. %\item \deleted{The resultant Lorentz force applied on the sunspot tended to drive the sunspot move in such a direction to relax the magnetic shear in the corona.} \item The values of $\bar{\alpha}$ of the NLFFF field connecting the sunspot showed a rapid and irreversible increase. \end{enumerate} % In all of 4 events, the abrupt rotation of the sunspots always occurred after the onset of the flare, indicating that the motion is produced by the flare instead of the trigger of the eruption. %Moreover, The sunspot was located on the endpoints of the post-flare loop. Since all of the sunspots were located on the endpoints of the flaring loop, the sunspots were connected to the reconnected field in the course of the flares. This suggests that the abrupt reversal in the rotation of the sunspot is related to the magnetic reconnection during the flare. This is further supported by the fact that rotation of the sunspot show synchronous changes with 1600 \AA\ emission from the regions of the sunspots that are closest to the PIL. %The rotational motion of a sunspot results in the transportation of the magnetic twist acrosunss the photosphere. Since twisted and sheared fields store the free magnetic energy, the rotational motion of a sunspot relates to the transportation of the magnetic helicity and magnetic energy across the sunspot. % in all of the 4 events, The negative values of the energy flux across the sunspot was found during each flare reported here, indicating that the magnetic energy was impulsively transported toward solar interior. Accordingly, the impulsive changes in helicity flux during these flares are more possible to be a consequence of transpotation from solar atmosphere toward solar interior, instead of the opposite-signed helicity injected from solar interior into the active region during these flares. % with the sign opposite with dominated sign of helicity in the active region Both the rotational motion of a sunspot and the shear motion of sunspots on the two sides of PIL are basically the consequence of the propagation of a shear Alfv$\acute{e}$n wave across the photosphere. Specifically, the rotational motion of a sunspot tends to remove the gradient of the value of $\alpha$ between the solar corona and the solar interior, which produces the Lorentz force that drives sunspot rotation \citep{Parker79,Longcope00,Magara03,Chae03,Fan09,Sturrock15}. If a sunspot rotates in such a direction that the magnetic helicity is transported form the corona into solar interior, the value of $\alpha$ in the corona should be higher than that in the solar interior. Consistently, the results of the NLFFF model show that the value of $\alpha$ aways increased during the flare for all events. Considering that the value of $\alpha$ in the solar interior did not change significantly, we suggest that the flare-induced enhancement in the value of coronal $\alpha$ could change a gradient of value of $\alpha$ form the solar corona to the solar interior. The sunspots on the two sides of PIL would be exerted by the opposite Lorentz force $\mathbf{F}_{x}=-\partial(B^{2}/2)/\partial x+(\mathbf{B} \cdot \nabla)\mathbf{B}_{x}$ \citep{Manchester00,Manchester01,Fan01,Manchester04,Archontis04,Torok14}, where $\hat{\mathbf{x}}$ is parallel to the PIL. Similarly, $\mathbf{F}_x$ would drive a shear motion so as to remove a gradient of $B_{x}$ along a field line. Resulted from the upward expansion of the a twisted flux tube, a decrease in $B_{x}$ in the corona would result in a $F_{x}$ that tends to drive a shear motion to accumulate the magnetic shear in the coronal. In this case, this shearing process produced eruptions that are representative of coronal mass ejections and flares. During flare, a reverse process was reported here. During Flare I and III, the unambiguous shear-relax motions of the sunspots were found to be accompanying with the impulsive increase of the horizontal field along the PIL and the contraction of the field lines as indicated by the NLFFF model. Such an increase in the shear component of the magnetic field is found in the collapsing loop system shown in \citet{Manchester07} % If t he reconnecting magnetic field has the higher value of $\alpha$ than that before the flare, the gradient of the value of $\alpha$ between the solar corona and the solar interior would produce a Lorentz force to rotate the sunspot. Consistently, the results of the NLFFF model always show that the value of $\alpha$ aways increased during the flare for all events. %135s %the size of the sunspot % The impulsive change in the helicity flux are contributed by the motion the the sunspots. % it is worth noting the the size of the sunspots are relatively small. their area ranges from to. The 4 sunspots reported here have the area smaller than 100 $\mu$Hem, which fall into the category of small-sized sunspot as defined by \citet{Mandal16}, who defined the sunspot with the area larger than 200 uHem as the large-sized sunspot. It seems that the flares with the relative low energy have no enough energy to power the motion of the large-sized sunspot, but more surveys is need to clarify how the photospheric motions produced by the flare are related to the flare energy. % We note that only one sunspot, with the area of 40 $\mu$Hem, showed abrupt change in translational motion during the flare \citep{Anwar93}. in the 2 out of 4 events, we can not detect the obvious sudden motion of the sunspot although there was change in the net Lorentz force acted on the sunspot in the period of the flare. Im comparision, all of the sunspots appeared to rotate during flare. It is possible that the rotational motion is more easier to be driven by the imbalance of the Lorentz force during the flare. It could be that Lorentz force torque applied on the sunspot is difficulty to be balanced by the plasma pressure on the photosphere. %rotation is more easy?í % The sunspot was located on the eendpoints of the flaring loop, indicating the the sunspot were connected to the reconnected field. Our result that the reconnected field has higher value of $alpha$ than that before the flare. This indicated the the reconnected field is still twist after the magnetic reconnection. As suggested by, the magnetic field would loss energy during the eruption the then the field must become shorter than that before the eruption. It is possible that the shorten twist field evolves to having higher value of $\alpha$. %helicity and energy and alpha %The time scale of the change in the helicity flux is about 10 minutes. This supports that the abrupt helicity transportations were produced by the magnetic reconfigrure in the corona. Base on the NLFFF model, we found that the value of $\alpha$ aways increased during the flare. It is suggested that the rotation of a sunspot is driven by the Lorentz force that produce by the gradient of the value of $alpha$. The change in the value of $\alpha$ of the coronal field would change the gradian of the $alpha$ from the corona to the solar interior. The impulsive increasing $alpha$ in the corona would work to take the helicity in the corona into the solar interior. This is consistence with the abrupt change in the sign of the helicity flux across the sunspot. This suggest that the corona reconstruction may result in the part of the helicity of the magnetic field taken back into the solar interior. Moreover, the impulsive transportation of the helicity flux may be accompany by the transportation of the magnetic energy from the corona to the solar interior. | 18 | 8 | 1808.04591 |
1808 | 1808.03855_arXiv.txt | We have derived elemental abundances of three field red horizontal branch stars using high-resolution ($R$~$\simeq$ 45,000), high signal-to-noise ratio (S/N $\gtrsim$ 200) $H$ and $K$ band spectra obtained with the Immersion Grating Infrared Spectrograph (IGRINS). We have determined the abundances of 21 elements including $\alpha$ (Mg, Si, Ca, S), odd-Z (Na, Al, P, K), Fe-group (Sc, Ti, Cr, Co, Ni), neutron-capture (Ce, Nd, Yb), and CNO group elements. S, P and K are determined for the first time in these stars. $H$ and $K$ band spectra provide a substantial number of \species{S}{i} lines, which potentially can lead to a more robust exploration of the role of sulfur in the cosmochemical evolution of the Galaxy. We have also derived \carbiso\ ratios from synthetic spectra of the first overtone (2$-$0) and (3$-$1) $^{12}$CO and (2$-$0) $^{13}$CO lines near 23440 \AA\ and $^{13}$CO (3$-$1) lines at about 23730 \AA. Comparison of our results with the ones obtained from the optical region suggests that the IGRINS high-resolution $H$ and $K$ band spectra offer more internally self-consistent atomic lines of the same species for several elements, especially the $\alpha$ elements. This in turn provides more reliable abundances for the elements with analytical difficulties in the optical spectral range. | Low mass core helium burning stars appear in the HR diagram as members of the horizontal branch (HB). These highly evolved objects have effective temperatures that span 4800~K~$\lesssim$~\teff $\lesssim$ 25,000~K and absolute magnitudes with only a small range, 0~$\sim$~$M_V$~$\sim$~+1. HB stars are subdivided into four temperature groups: red clump and red horizontal branch (RC and RHB, $\sim$4800$-$6000~K), the RR~Lyrae instability strip ($\sim$6000$-$7500~K), blue (BHB, $\sim$7500$-$20,000~K), and extreme (EBHB ($\gtrsim$25,000~K). As discussed in \citealt{afsar18a} (hereafter Af{\c s}ar18a), RHB stars are low mass core-helium-burning stars. Af{\c s}ar18a follows the observational RHB definition given by \cite{kaempf05} and defines an RHB range for the stars around solar metallicity with 0.5~$\lesssim$~($B-V$)~$\lesssim$~1.0 and $-$0.5~$\lesssim~M_{\rm V}$~$\lesssim$~1.5. This ``$box$'' also includes so called ``\textit{secondary red clump}'' defined by, e.g., \cite{girardi98} and \cite{girardi99}, in which they investigate secondary clump for different metallicities in synthetic color-magnitude diagrams (e.g. Figure 7 in \citealt{girardi99}). HB astrophysical interests are many, from distance indicators, to stellar population studies, to signposts for interior advanced nucleosynthesis and envelope mixing. HB stars with Galactic disk metallicities ([Fe/H]~$\gtrsim$~$-$1)\footnote{ We adopt the standard spectroscopic notation \citep{wallerstein59} that for elements A and B, [A/B] $\equiv$ log$_{\rm 10}$(N$_{\rm A}$/N$_{\rm B}$)$_{\star}$ $-$ log$_{\rm 10}$(N$_{\rm A}$/N$_{\rm B}$)$_{\odot}$. We use the definition \eps{A} $\equiv$ log$_{\rm 10}$(N$_{\rm A}$/N$_{\rm H}$) + 12.0, and equate metallicity with the stellar [Fe/H] value.}, \eg, metal-rich globular clusters and field thick disk stars, almost always occupy the RHB\footnote{ Metal-rich globular clusters with BHB stars are rare; notable exceptions are the metal-rich globular clusters NGC~6388 and NGC~6441 ([Fe/H]~$\simeq$~$-$0.6) that have both prominent RHB and BHB populations \citep{rich97}.}. In these older populations there is no evolutionary state ambiguity, since subgiant stars in the RHB temperature domain have much lower luminosities, $M_{\rm V}$~$\gtrsim$~+3.5. However in the general Galactic field the low mass thick disk He-burning stars can share the same (\teff, \logg) or ($B-V$, $M_{\rm V}$) domain with higher-mass thin disk subgiants, and also can be confused with the occasional thin-disk He core-burning stars near the high-mass edge of the metal-rich red giant ``clump''. These stellar population confusions, combined with difficulties in determining accurate distances, have hampered the identification of field stars likely to be true RHB stars, thus rendering them under-studied compared to red giants. \cite{kaempf05} conducted a large-scale photometric survey of field stars with Hipparcos parallaxes \citep{vanleeuwen07}, and proposed a ($B-V$, $M_{\rm V}$) area likely to be dominated by RHB stars. Early spectroscopic studies of field RHB chemical compositions were conducted by \cite{tautvaisiene96, tautvaisiene97} and \cite{tautvaisiene01}. Those studies concentrated on thick disk and halo stars. \cite{afsar12} (hereafter ASF12) conducted a small-sample (76 star) survey of bright field stars with temperatures and luminosities consistent with RHB classification, identifying 18 probable true RHB stars, 13 of which appeared to be thin-disk solar metallicity (thus relatively young) objects. Expanding on this unexpected result, we have recently reported an optical high-resolution spectroscopic survey of 340 field RHB candidates Af{\c s}ar18a. This study used equivalent width (EW) measurements to derive model atmosphere parameters, metallicities, and some $\alpha$-group and Fe-group abundance ratios. In Af{\c s}ar18a, kinematics were computed for almost the entire sample from data in the Hipparcos and Gaia DR1 \citep{GAIA16} catalogs. Based only on these data, we estimate that about 150 of the Af{\c s}ar18a sample are true RHB stars, and that there is an admixture of thin and thick-disk members in the sample. In \cite{afsar18b} we will present abundances of elements requiring synthetic spectrum computations: odd-Z, Fe-group, neutron capture ($n$-capture) elements, and the light LiCNO group. We will also be able to refine the stellar evolutionary and Galactic population breakdown of this sample. Optical high-resolution spectra are useful for stellar metallicities and relative abundance ratios of many elements, but they have limitations particularly among the lighter elements. Such deficiencies can be overcome by obtaining data in the infrared ($IR$) spectral domain, $\lambda$~$>$~1~$\mu$m. To this end we have initiated a program to observe a large subset of the Af{\c s}ar18a sample in the photometric $H$ and $K$ bands with the Immersion Grating Infrared Spectrometer (IGRINS). With these spectra we will be able to study light elements either not available or poorly studied in the optical spectral range (P, S, and K), greatly refine the abundances of those with some transitions in both the optical and IR regions ($\alpha$ elements Mg, Si, and Ca; odd-Z elements Na and Al; $n$-capture elements Ce, Nd, Yb), and most importantly improve the abundances of CNO and the carbon isotopic ratios derived from our optical data. In this paper, we present IGRINS observations of three RHB stars from Af{\c s}ar18a (also previously investigated in ASF12): \ffor, \fsev\ and \oneone. We discuss atomic line identifications in the IGRINS data and the transition parameters of the chosen lines. A detailed comparison is made between the resulting abundances and those derived from the optical spectra. A future paper will contain the results from the full IGRINS survey, about 70 stars. In \S\ref{observ} the IGRINS observations and their reductions are described. In \S\ref{model} we present the model atmosphere parameters and abundances of elements derived from the optical spectral region. Abundance determinations from the IGRINS $H$ and $K$ band spectra are described in \S\ref{abund} along with the atomic and molecular data used in abundance determinations. In \S\ref{fei} we investigate the infrared \species{Fe}{i} lines as temperature indicators. Finally, we discuss and summarize our results in \S\ref{disc}. | \label{disc} This paper is the first one of a series of papers that explores stellar atomic and molecular features of Galactic field RHB and red giant stars observed in the near-$IR$ region. IGRINS high-resolution, high S/N $H$ and $K$ band spectra bring valuable new information for this purpose. Several important light elements are poorly studied (\eg, S and K) or not available (\eg, P) in high-resolution optical spectra. IGRINS near-$IR$ spectra provide more robust abundance analysis for many elements. We have conducted, for the first time, the abundance analysis of three RHB stars; \ffor, \fsev\ and \oneone, using high-resolution, high S/N near-$IR$ IGRINS spectra. Detailed abundance analyses were carried out for 21 species of 20 elements including $\alpha$ (Mg, Si, S and Ca); odd-Z (Na, Al, P and K); Fe-group (Sc, Ti, Cr, Co, Fe, and Ni); $n$-capture elements (Ce, Nd, Yb); and CNO group elements. We also used the ground electronic state first overtone ($\Delta$$v$ = 2) R-branch vibration-rotation bands of (2$-$0) and (3$-$1), which are the prominent features in K-band spectra, to determine \carbiso\ ratios from $^{13}$CO (2$-$0) features near 23440 \AA\ and $^{13}$CO (3$-$1) features at about 23730 \AA. To perform the abundance analysis in the $H$ and $K$ band spectra, we adopted the model atmosphere parameters from Af{\c s}ar18a. Using the high-resolution optical spectra of our RHB stars (ASF12), we also determined the abundances of the same elements (except for P) in the optical region. This broad wavelength coverage allowed us too make more comprehensive analyses of our stars. The abundances of $\alpha$ elements obtained from both wavelength regions are generally in good agreement and, on average, they indicate $\alpha$ enhancements of about $\langle$[$\alpha$/Fe]$\rangle$~$\simeq$~0.15 dex. Our IGRINS spectra yield substantial numbers of Mg and S lines with internally self-consistent abundance results (Figure~\ref{alphas}). We have identified 11 \species{Mg}{i} lines in contrast to two optical \species{Mg}{i} lines that come with analytical difficulties due to their large absorption strengths. The $IR$ \species{Mg}{i} lines now give us more robust Mg abundances in these stars. Being located closer to the linear part of the curve-of-growth than the two optical lines, we trust the abundances of Mg obtained from the $IR$ \species{Mg}{i} lines (Figure~\ref{hip54CaSMg}). Sulfur is one of the fundamental building block elements of life in the universe along with C, H, N, O and P. Sulfur and sulfur-containing compounds are common constituents in Solar System material. High amounts of sulfur are produced in supernova nucleosynthesis during explosive oxygen burning (\citealt{truran73}). Sulfur is volatile with its low condensation temperature; it can not be condensed into interstellar dust grains. Therefore, its depletion-free nature makes sulfur a valuable tracer of Galactic nucleosynthesis; understanding of its contribution to Galactic chemical evolution is important. There have been a number of studies that investigate the behavior of S in the Galaxy as one of the $\alpha$ elements. Different investigations claim different results. Some suggest that S behaves like other $\alpha$ elements, showing a [S/Fe] \textit{plateau} at certain metallicities, while others indicate that [S/Fe] has a linear increase with decreasing metallicities (e.g. \citealt{caffau05}, and references therein). There are few well-known \species{S}{i} lines in the optical and shorter wavelengths of near-$IR$: 6743$-$6757 \AA\ optical multiplet, 8694$-$5 \AA, 9212$-$9237 \AA\ $IR$ triplet, and 10455$-$9 \AA\ $IR$ triplet. Most of these lines were investigated by \cite{korotin09} and \cite{takeda16} for their being subjected to nLTE effects. All these S lines appear to need nLTE corrections in different amounts, 6743$-$6757 \AA\ optical multiplet having the smallest (to $-$~0.10 dex) nLTE correction among others. IGRINS provides more \species{S}{i} lines beyond those of the optical and very near-$IR$. We were able to identify 10 useful $H$ and $K$ band \species{S}{i} lines. We also measured the S abundance using the optical triplet centered at 6757.0 \AA. The internal abundance self-consistency of all \species{S}{i} lines is encouraging. The $IR$ S lines are mostly weak and likely to be less affected by nLTE conditions. These lines, studied here for the first time in these stars, promise to provide more robust investigation at a range of metallicities. In the forthcoming paper of this series, we will investigate S in more detail with a larger sample. The abundances of odd-Z elements Na, Al, P and K were computed from both optical (when available) and infrared regions. Optical transitions of these elements are subject to substantial nLTE corrections (e.g. \citealt{takeda02,takeda03,lind11,nord17,mucciarelli17}). Among these, optical \species{Al}{i} lines used in this study are the least affected ones by nLTE, while \species{K}{i} at 7699 \AA\ is the most affected, by up to $-$0.7 dex (\citealt{takeda02,takeda09}). This is also found in our stars (Tables~\ref{tab-54048}$-$\ref{tab-114809}). The Na abundances obtained in both wavelength regions are in good agreement in all three RHB stars but the star-to-star scatter is substantial. Even with nLTE corrections to the optical \species{Na}{i} lines, overabundances observed in both \ffor\ and \oneone\ remain. The good agreement between the optical and $IR$ Na abundances suggests that all of these lines might be affected by nLTE conditions about the same amount. A similar situation is also observed in Al abundances from both regions. \ffor\ and \oneone\ also show slight Al overabundances, reminiscent of the well known [Na/Fe]-[Al/Fe] correlation observed in globular clusters (e.g. \citealt{kraft94} and references therein). Phosphorus is one of the fundamental building blocks of life but its nucleosynthetic origin is still under discussion. Recent studies point to massive star explosions (hypernova, \eg, \citealt{kobayashi06,cescutti12}). There are only two useful \species{P}{i} lines in the $UV$ and two in the $z$ band. The near-$IR$ \species{P}{i} lines located in the $H$ band, 15711.5 and 16482.9 \AA\ (Figure~\ref{PK}) are weak but our high-S/N data yield detections. We estimated P abundances around solar for our RHB stars. K is produced mainly by oxygen burning and its production rate during nucleosynthesis is still under debate. For example, according to \cite{timmes95} [K/Fe] ratios decrease towards lower metallicities, while \cite{samland98} and \cite{goswami00} suggest [K/Fe] decline in the disk and super solar ratios in halo stars. There are observational studies that favor the theoretical predictions of \cite{samland98} and \cite{goswami00}, e.g., \cite{gratton87,chen00,takeda02,zhang06,takeda09,mucciarelli17}. However, the analytical difficulties of the \species{K}{i} resonance lines render them problematical to map the behavior of K in the Galaxy. The $H$ band spectral region provides two more \species{K}{i} lines (Figure~\ref{PK}). Recently, \cite{hawkins16} investigated more than 20 elements using a massive Galactic sample from APOGEE data, including [K/Fe]$-$[Fe/H] relation for $-1.0$~$\lesssim$~[Fe/H]~$<$~0.5 (Figure 16 in \citeauthor{hawkins16}). Their result also supports the predictions of \citeauthor{samland98} and \citeauthor{goswami00}. With higher IGRINS $H$ band resolution, we were able to study 15163.1 and 15168.4 \AA\ \species{K}{i} lines in more detail. The K abundances we derived from these lines are around solar in our stars. Our IGRINS abundance analysis of Fe-group elements Sc, Ti, Cr, Co and Ni has been highlighted by consideration of the substantial isotopic substructure of $IR$ \species{Ti}{i} lines. Accounting for the isotopic effects yields good agreement with observed \species{Ti}{i} line profiles in the Sun, Arcturus, and our three RHB stars. The general agreement between optical and $IR$ abundances for the Fe-peak elements is good with the exception of Sc. Unfortunately, the optical and $IR$ Sc abundances are based on different species of this element and the cause of the small ($\sim$0.15~dex) offset between the Sc abundances in the two wavelength regions cannot be traced easily. The presence of \ncap\ elements in the near-$IR$ were previously discussed by e.g. \cite{hawkins16,hassel16,cunha17}. We determined the abundances of three \ncap\ elements in the near-$IR$, all located in the $H$ band. Among them, Yb is important because its optical counterpart at 3694 \AA\ falls into a very crowded and low-flux spectral region. We derived near-solar abundances for Yb. The Ce and Nd abundances from both wavelength regions show substantial star-to-star scatter, and needs further investigation. We computed the CNO abundances using CO, CN and OH molecular features that are present in the near-$IR$ at considerable amounts. Our mildly metal-poor stars are relatively hot for OH molecular lines to survive; we could only detect five useful ones in our RHB stars. The $IR$ O abundances are in good agreement with their optical counterparts that were obtained from the forbidden [\species{O}{i}] at 6300 and 6363 \AA. The C abundances from $K$ band CO lines agree well with the C abundances derived from the CH and C$_{2}$ molecular lines in the optical. Finally, we used CN molecular lines in the $H$ band to determine N abundances. These results are in good accord with ones obtained from optical CN features. We also measured the C abundances from seven high-excitation potential \species{C}{i} lines: three in the optical, and four in the near-$IR$. As is seen in Table~\ref{tab-cmean}, on average the near-$IR$ high-excitation \species{C}{i} lines yield C abundances in reasonable agreement with the ones obtained from their optical counterparts. The mean C abundance from all species in all stars has small internal scatter, $\sigma$~$\leq$~0.10~dex, and these means are always within 0.02~dex with those obtained just from the CO lines. Since CH, C$_2$, \species{C}{i}, and CO species have different sensitivities to adopted \teff,\ \logg, and O abundance values, their reasonable agreement in our three program stars suggests that the derived mean C abundances are robust. However, this assumption is only based on five stars (including Arcturus and the Sun). Clearly, further investigation is needed with a larger sample to clarify this issue. To the best of our knowledge, this study is the first among others that investigates the C abundances in a more complementary way using four different C features from the optical and near-$IR$ wavelength regions. CNO abundances are the most important indicators of internal nucleosynthesis and envelope mixing in evolved stars. Convective envelope mixing brings up the CN-cycle nuclear processed material to the stellar surface. As a result, C abundance drops, as the N abundance increases (e.g. \citealt{iben64,iben67a,iben67b}). One of the most important indicators of the convective mixing is the carbon isotopic ratio: \carbiso. It decreases from its solar value, $\sim$90, to $\sim$20$-$30 during the giant branch evolution (e.g. \citealt{charbon94,charbon98,gratton00}), sometimes even approaching the CN-cycle equilibrium value of \carbiso = 3$-$4 (e.g. \citealt{caughlan65,sneden86,cottrell86,gratton00}). Determination of the \carbiso\ ratio in the optical is usually possible from the triplet of $^{13}$CN lines near 8004.7 \AA. It is the only reliable feature in the optical region and often really weak. IGRINS $K$ band has two $\Delta$$v$~=~2 transitions of the $^{12}$CO first overtone band heads: (2$-$0) and (3$-$1). The $^{13}$CO (2$-$0) and $^{13}$CO (3$-$1) band heads that accompany $^{12}$CO are located near 23440 and 23730 \AA, respectively. We used both of these regions and re-determined the \carbiso\ ratios for our stars: 12, 8.5 and 15.5 for \ffor, \fsev\ and \oneone, respectively (Table~\ref{tab-carbiso}). The mean C and N abundances from the optical and near-$IR$ for our stars are: [C/Fe] = $-$0.57, [N/Fe] = $+$0.80 for \ffor; [C/Fe] = $-$0.18, [N/Fe] = $+$0.39 for \fsev; and [C/Fe] = $-$0.31, [N/Fe] = $+$0.58 for \oneone. The mean O abundances are within $\pm$~0.1 dex in \ffor\ and \fsev, and slightly above solar, [O/Fe] = 0.13 dex, in \oneone. The C abundance is considerably low while the N abundance is substantially high in \ffor\ compared to other RHB stars. In fact the [C/N] = $-$1.37 of \ffor\ puts its location beyond the [C/N] limits recently studied by, e.g., \cite{lagarde17,lagarde18}, which might imply a very high initial mass for this star. Further investigation is needed for \ffor. The [C/N] values for \fsev\ and \oneone\ are $-$0.57 and $-$0.89, respectively. These values also indicates high initial masses according to \cite{lagarde17} and \cite{lagarde18}. In all three cases a thermohaline mixing process is required in order to explain the low \carbiso\ ratios observed in our stars (Table~\ref{tab-carbiso}). Near-$IR$ IGRINS high-resolution spectra provide an important new opportunity to study stellar chemical compositions in detail. As discussed above, $H$ and $K$ bands often yield more reliable abundance results, while providing new features that come with open questions. Our next paper with about 70 RHB stars will explore the issues that need further investigation with a larger sample and provide more realistic statistical results for many elements in the near-$IR$ spectral range. | 18 | 8 | 1808.03855 |
1808 | 1808.04472_arXiv.txt | \noindent We present thermodynamic material and transport properties for the extreme conditions prevalent in the interiors of massive giant planets and brown dwarfs. They are obtained from extensive \textit{ab initio} simulations of hydrogen-helium mixtures along the isentropes of three representative objects. In particular, we determine the heat capacities, the thermal expansion coefficient, the isothermal compressibility, and the sound velocity. Important transport properties such as the electrical and thermal conductivity, opacity, and shear viscosity are also calculated. Further results for associated quantities including magnetic and thermal diffusivity, kinematic shear viscosity, as well as the static Love number $k_2$ and the equidistance are presented. In comparison to Jupiter-mass planets, the behavior inside massive giant planets and brown dwarfs is stronger dominated by degenerate matter. We discuss the implications on possible dynamics and magnetic fields of those massive objects. The consistent data set compiled here may serve as starting point to obtain material and transport properties for other substellar H-He objects with masses above one Jovian mass and finally may be used as input for dynamo simulations. | \label{sec:Intro} The number of identified exoplanets and brown dwarfs has grown substantially over the past two decades. Even though the observations rarely go beyond characterizing their mass and radius, they have also started to reveal additional information. In particular, the observation of global magnetic fields can offer important constraints on the interior dynamics. While detecting the magnetic fields of exoplanets has proven elusive so far, brown dwarfs show radio emissions clearly indicative of an internal dynamo process \citep{Reiners2010}. Recently, the Zeeman line broadening measurement for a brown dwarf constrained the surface field strength to about $0.5\,$T, a value consistent with the estimates based on the radio emissions \citep{Berdyugina2017}. Dynamo action requires an electrically conducting and convecting region but also depends on the rotation rate and luminosity of an object. Numerical models for the thermal evolution, interior dynamics, or magnetic field generation are indispensable for predicting, interpreting, and understanding the observations. These simulations require an internal model of the studied object that also includes the transport properties. Early approaches to determine the transport properties of degenerate matter were, for example, based on the Kubo theory \citep{Hubbard1966,Hubbard1969}. \cite{Flowers1976} used a variational approach for the solution of the Boltzmann equation and considered all relevant scattering mechanisms. \cite{Stevenson1977a} provided approximate formulae based on the Ziman theory using the static ion-ion structure factor for a hard-sphere system which can be applied for a wide range of densities and temperatures. \cite{Nandkumar1984} relied on the relaxation time approximation and included structure factor effects within the simple one-component plasma model. This approach has been adapted recently by \cite{Harutyunyan2016} to determine the electrical conductivity in the warm crusts of neutron stars. Conductivity models that are valid for the wide ranges of density and temperature in astrophysical and other applications, such as inertial confinement fusion, were proposed by, e.g., \cite{Lee1984} and \cite{Ichimaru1985}. Our work follows a different path to describe the extreme matter in the interior of massive objects governed by strongly correlated ions immersed in a degenerate electron gas. We apply a combination of density functional theory for the electron system and classical molecular simulations for the ions (DFT-MD method) to derive the material properties of H-He mixtures. This approach had been previously applied to Jupiter by \citet{French2012}, whose results were subsequently used for simulations of the planet's interior dynamo processes reproducing the Jovian large scale magnetic field \citep{Gastine2014,Jones2014,Duarte2018}. The work presented here extends the Jupiter study of \cite{French2012}. We select three objects within a mass range of $10-50~\MJ$ from \cite{Becker2014}: the massive exoplanet KOI-889b, and the two brown dwarfs Corot-3b and Gliese-229b. The latter is the most massive object in this set. \cite{Becker2014} predict a pressure of 22000~TPa, a temperature of 1.2$\cdot$10$^6$~K, and a density of 450~g/cm$^3$ at the center of Gliese-229b based on \textit{ab initio} equations of state (EOS). This exceeds the thermodynamic conditions within Jupiter several orders of magnitude. For instance, the core-mantle boundary in Jupiter is predicted at 4~TPa, 20000~K, and 4.3~g/cm$^3$ \citep{Guillot1999,Nettelmann2012}. The thermodynamic conditions typical for the interior of Gliese~229b are already accessible in the laboratory using the world's most powerful laser at the National Ignition Facility (NIF) covering the conditions from substellar objects (giant planets, brown dwarfs) to low-mass stars~\citep{Lindl2004, Moses2011}. It has been demonstrated by~\cite{Hurricane2014} that a deuterium-tritium capsule can be dynamically compressed up to about 400~g/cm$^3$. Hence, the data presented here may also serve as input for the hydrodynamic simulations accompanying these experiments. Our paper is organized as follows. We recapitulate the calculation of interior models for massive giant planets and brown dwarfs according to \cite{Becker2014} in section~\ref{sec:IntBrownie}. The determination of the thermodynamic material properties via \textit{ab initio} simulations is outlined in section~\ref{sec:Tdyn_Props}. The Love number $k_2$ and the equidistance are discussed in section~\ref{sec:k2}. The calculations of the transport properties and corresponding results are described in section~\ref{sec:Lik}. Finally, we discuss the implications of our obtained material properties on planetary and stellar dynamos in section \ref{sec:Implications} and conclude in section \ref{sec:Conclusion}. | \label{sec:Conclusion} We have determined the thermophysical properties of H-He mixtures for conditions inside massive giant planets and brown dwarfs based on \textit{ab initio} simulations. In particular, we discussed thermodynamic material properties, the Love number, the equidistance, as well as transport properties including the closely related opacity. The provided values represent a considerable extension of the dataset calculated for Jupiter by \cite{French2012}. In comparison to Jupiter, the underlying models \citep{Becker2014} start at greater pressures and temperatures where most of the hydrogen is already dissociated. The thermodynamic material properties and transport properties therefore largely lack the features that characterize the properties in Jupiter's outer envelope. For example, the extreme rise in electrical conductivity and the dissociation maximum in the heat capacities \citep{French2012} are absent for the considered massive objects. The properties of degenerate matter play an increasingly important role when the object mass grows. Overall, our dataset, combined with the Jupiter data by \cite{French2012}, increases our knowledge of extreme thermodynamic conditions, covering the broad mass range from Jupiter-sized giant planets up to brown dwarfs. This data will stimulate the development of new models for the interior structure, thermal evolution and internal dynamics of massive exoplanets and brown dwarfs. | 18 | 8 | 1808.04472 |
1808 | 1808.10057_arXiv.txt | We explore the intriguing possibility of employing future ground-based gravitational-wave interferometers to detect the inspiral of binary neutron stars sufficiently early to alert electromagnetic observatories so that a gamma-ray burst (GRB) can be observed in its entirety from its very beginning. We quantify the ability to predict a GRB by computing the time a binary neutron star (BNS) system takes to inspiral from its moment of detection to its final merger. We define the moment of detection to be the instant at which the interferometer network accumulates a signal-to-noise ratio of 15. % For our computations, % we specifically consider BNS systems at luminosity distances of (i) $D\le200\,$Mpc for the three-interferometer Advanced-LIGO-Virgo network of 2020, and (ii) $D \le 1000\,$Mpc for Einstein Telescope's B and C configurations. In the case of Advanced LIGO-Virgo we find that we may at best get a few minutes of warning time, thus we expect no forecast of GRBs in the 2020s. On the other hand, Einstein Telescope will provide us with advance warning times of more than five hours for $D \le 100\,$Mpc. Taking one hour as a benchmark advance warning time, we obtain a corresponding range of roughly 600 Mpc for the Einstein Telescope C configuration. Using current BNS merger event rates within this volume, we show that Einstein C will forecast $\gtrsim \ord(10^2)$ GRBs in the 2030s. % We reapply our warning-time computation to black hole - neutron star inspirals and find that we expect one to three tidal disruption events to be forecast by the same detector. This article is intended as a pedagogical introduction to gravitational-wave astronomy written at a level accessible to Ph.D. students, advanced undergraduates, and colleagues in astronomy and/or astrophysics who wish to learn more about the underlying physics. Though many of our results may be known to the experts, they might nonetheless find this article motivating and exciting. | \label{Sec:Intro} The 6.95\footnote{There have thus far been six detections with $5\sigma$ statistical significance and one additional event, LVT151012 \cite{TheLIGOScientific:2016pea}, with $2\sigma \simeq 95\%$ significance hence 6.95 overall.} \footnote{As of December 2018, the count has been updated to ten including LVT151012 \cite{LIGOScientific:2018mvr}.} gravitational-wave merger events detected by the Advanced LIGO-Virgo network have firmly established gravitational-wave astronomy as an observational science \cite{TheLIGOScientific:2016pea, Abbott:2017gyy, Abbott:2017oio, Abbott:2017vtc, GW170817}. Though the first event of 14 September 2015 (GW150914 \cite{GW150914}) will always be the ``poster-child'' of this field, the icing on the cake was the 17 August 2017 (GW170817 \cite{GW170817}) event involving the inspiral and merger of a binary neutron star system promptly followed, 1.7 seconds later, by a gamma-ray burst (GRB170817A) detected by the Fermi Gamma-ray Burst Monitor \cite{Fermi} and by the International Gamma-Ray Astrophysics Laboratory \cite{Svinkin, Savchenko:2017ffs}. The Advanced-LIGO-Virgo network's initial source localization to within $ 31\,\text{degree}^2$ in the Southern skies enabled astronomers to locate the electromagnetic counterpart in the galaxy NGC 4993, first picked up by the One-Meter, Two Hemisphere team less than 11 hours after the merger \cite{Coulter2017, Coulter:2017wya}. This subsequently launched a massive campaign of multi-messenger astronomy across the entire electromagnetic (EM) spectrum which is still ongoing a year after the initial GRB \cite{GBM:2017lvd}. GW170817 was initially identified by the LIGO-Hanford interferometer (H1) using a template bank of gravitational waveforms computed within the framework of post-Newtonian theory \cite{Buonanno:2009zt, Blanchet_LRR}. The inspiral swept across the Advanced LIGO-Virgo (ALV) network's bandwidth from approximately $ 30\,$Hz to about $ 2\,$kHz in 57 seconds, executing nearly $ 3000$ gravitational wave cycles and accumulating a network signal-to-noise ratio of 32.4 with a false-alarm rate of one per $8.0\times 10^4$ years \cite{GW170817}. The total mass of the system was inferred to be $2.74^{+0.04}_{-0.01} M_\odot$ with component masses in the range $1.17-1.60 M_\odot$, consistent with neutron stars (assuming low spin priors, see Sec.~\ref{sec:idealizations}). Moreover, both the gravitational wave (GW) and EM observations were consistent with a source location in the galaxy in NGC4993 at a luminosity distance of $\sim\! 40\,$Mpc, and supported the hypothesis that GW170817 resulted from the inspiral and merger of two neutron stars, causing the prompt short-hard gamma-ray burst GRB170817A. % This BNS-GRB connection was first proposed in Ref.~\cite{Eichler:1989ve} and the events of 17 August 2017 are the first astrophysical evidence for it. A week after GW170817, the ALV network was taken offline for upgrades for the third observation run (O3) scheduled to start in early 2019 with roughly twice the sensitivity of O2. In addition, the Japanese cryogenic interferometer KAGRA (\cite{KAGRA, KAGRA2}) will start its test runs in 2018-2019 and reach its design sensitivity circa 2021-2022 \cite{Akutsu:2017thy, Aasi:2013wya}. By 2025, LIGO-India detector will join the global interferometer network hence improving both the overall sensitivity and the sky-localization capabilities \cite{Aasi:2013wya}. Around this time, the construction of the first third-generation (3G) ground-based interferometer, Einstein Telescope, should begin in Europe \cite{ET_doc}\footnote{The decision for the funding of Einstein Telescope is expected to be announced in 2019-2020 with the final technical design report to be submitted in 2023-24, and the commissioning to begin in 2030-31 followed by full operations in 2032-33.}. Meanwhile, the US is currently considering a mid-2020s update to LIGO called Voyager \cite{LIGO_Voy} and the construction of an ambitious 40-km long 3G interferometer dubbed Cosmic Explorer \cite{CE}. The science goals of the 3G detectors is very exciting. For example, Einstein Telescope will be able to (i) distinguish between different neutron star equations of state, (ii) conduct high-precision measurements of source parameters to test alternate theories of gravity, (iii) detect binary black hole populations out to redhifts of $\sim 15$ hence (a) measure the Hubble parameter, dark matter and dark energy densities, as well as the dark energy equation-of-state parameter; (b) study the cosmological evolution of the stellar mass black holes (see Sec.~2 of Ref.~\cite{ET_doc} for an excellent summary of the science goals and further details). The prospect of having extremely sensitive 3G GW detectors begs a simple question: can we detect the inspirals of binary neutron star systems early enough to witness gamma-ray bursts and the birth of the subsequent kilonovae as they happen? In other words, can we forecast GRBs using GW detections? The short answer is ``yes''. The long answer is still ``yes'', but depends on many factors such as source distance and sky position, detector sensitivity and orientation. One also needs to account for the fact that GRBs are thought to be collimated emissions with narrow outburst angles \cite{Kumar:2014upa}. As such, most GRBs that occur in the universe are electromagnetically undetectable. Fortunately, this was not the case with GRB170817A, but even for a reasonable GRB jet opening angle of $\sim 10^\circ$, we expect to observe at best $\sim 10\%$ of neutron star mergers as GRBs \cite{Patricelli:2016bkt}. However, it is possible that some of the near-Earth pointing short hard GRBs may be observed as long-duration GRBs or X-ray flashes thus increasing this percentage \cite{Bucciantini:2011kx}. On the other hand, the optical emission from the kilonova should be less collimated, thus much more likely to be detected \cite{Troja:2017nqp}. Given the sensitivities of interferometers to date, efforts have thus far mostly focused on reducing the latency of EM follow-ups, i.e., the lag time between the merger and the alerting of the EM observatories. LIGO-Virgo science runs in 2009-2010 yielded a latency of $\sim\!\! 30$ to $60\,$minutes \cite{Abbott:2011ys} (no detections). In the case of GW170817, the latency was 40\,minutes and $36^{+1.7}\,$seconds \cite{GBM:2017lvd}. It then took an additional $ 10$ hours to locate the optical transient. % Here, we are interested in exploring the predictive power of near-future ground-based GW detectors. More specifically, we wish to find out how much early warning future GW detectors can provide us before the merger/GRB. Ref.~\cite{Cannon:2011vi} approached this from an algorithmic perspective by developing computationally inexpensive methods to detect inspiral signals in GW data to provide early-warning triggers \emph{before} the merger (also see Ref.~\cite{Knowles:2018hqq} for a very recent improvement to what is currently being used in the ALV pipeline). We instead focus on the forecasting capabilities of the ground-based interferometers at their \emph{full design} sensitivity by computing the time interval between the merger and the instant of detection defined in terms of a certain detection criterion which we describe below. To this end, we consider the ALV network of 2020s composed of three L-shaped interferometers operating at their design sensitivities and Einstein Telescope of 2030s made up of V-shaped interferometers. Ref.~\cite{Nissanke:2012dj} investigated the capabilities of three to five-interferometer detector networks of 2020s in terms of their ranges to inspiralling BNSs and their sky-localization of these sources. More recently, Ref.~\cite{Chan:2018csa} added to this results pertaining to the future networks of 2030s both in terms of source localization and advance warning prospects. Our work here is complementary to these articles in the sense that we focus on the details of how to quantify the advance warning. We compute the advance warning times via the following procedure: (${i}$) We start with a GW source presumed to be an inspiralling BNS at a certain luminosity distance. % (${ii}$) We determine the frequency at which the source enters a given interferometer's bandwidth. (${iii}$) We determine the detection time by computing the frequency at which the network's accumulated signal-to-noise ratio for the BNS inspiral equals 15. ($iv$) We define the advance warning time, $T_\text{AW}$, to be the time interval between the instant of detection and the merger. We repeat this procedure for BNSs at luminosity distances varying from 50\,Mpc to 1\,Gpc with the smaller values intended for the ALV network and the larger ones for Einstein Telescope. In order to more faithfully represent an interferometer network such as ALV --- consisting of three separate interferometers which have different orientations and positions --- we employ root-mean-square averages over sky-position and polarization angles, and assign the interferometers angle-averaged sensitivities. Our computation for $T_\text{AW}$ is based on the Newtonian evolution of a binary system composed of two point masses in a quasi-circular Keplerian orbit. The long-term dynamics is governed by the radiation reaction of the GW emission from the system due to the time variance of the quadrupole moment of the binary. Though the Newtonian (leading-order) treatment gives the inspiral time with better than $ 95\%$ accuracy, we nonetheless supplement it with post-Newtonian corrections up to 3.5 post-Newtonian order (3.5PN) \cite{Blanchet_LRR}. However, beyond frequencies of $\sim 100\,$Hz the binary enters the strong-field regime where post-Newtonian approximation become insufficient to provide an accurate depiction of the inspiral. Instead, the strong-field evolution requires fully numerical treatment using general relativistic, magnetohydrodynamic codes with neutrino transport running on large-scale computing clusters and taking up to millions of CPU hours (see Ref.~\cite{Shibata_book, Faber:2012rw} for a review, and Refs.~\cite{Baiotti:2016qnr,Kyutoku:2017voj, Zappa:2017xba, Dietrich:2018upm, Dietrich:2018phi} for the latest developments and references therein). Nonetheless, despite its simple formulation, our quadrupole radiation driven [post]-Newtonian evolution is more than sufficient to provide reliable estimations of advance warning times with an error of $\lesssim 1\,$second. We support this claim in Sec.~\ref{sec:idealizations} with an extensive list of computations which show how much each one of our approximations affects the inspiral time. This article is organized as follows. Sec.~\ref{sec:BNS_inspiral} introduces the formulation for the leading-order evolution of the binary inspiral. Sec.~\ref{sec:IFO_response} details the interferometer response to GWs based on interferometer topology. Sec.~\ref{sec:idealizations} lists the various idealizations we employ to simplify our treatment and supplies justification for each. Sec.~\ref{sec:GW170817} tests our model network and evolution using the parameters of GW170817 and the corresponding observations. Sec.~\ref{sec:results} contains our main results presented as advance warning times in Tables~\ref{table:LIGO2020} and \ref{table:ET}; and as ranges and event rates in Table~\ref{table:horizon}. In Sec.~\ref{sec:BH_NS}, we recompute the advance warning times in the case of binary black hole - neutron star inspirals to see whether or not future detectors can forecast tidal disruption events, for which we summarize our findings in Table~\ref{table:ET_BH_NS}. Throughout the text, $t$ denotes observer/detector time and $f$ denotes the \emph{GW frequency} of the dominant quadrupole mode in observer/detector frame. We employ the $\simeq$ symbol when displaying the numerical values of quantities % which we usually truncate at four significant digits. The $\approx$ symbol is reserved for approximations whereas $\sim$ denotes rough, order-of-magnitude equalities, e.g., $\pi \simeq 3.142$, $\pi \approx 3$, $\pi \sim \ord(1)$. % Overdots denote time derivatives with respect to detector-frame time, e.g., $\dot{E} =dE/dt$, and $\propto$ denotes proportionalities. Unless otherwise noted, we use standard SI units. | \end{figure} | 18 | 8 | 1808.10057 |
1808 | 1808.09620_arXiv.txt | We have computed linear non-adiabatic oscillations of luminous red giants using a non-local and anisotropic time-dependent theory of convection. The results show that low-order radial modes can be self-excited. Their excitation is the result of radiation and the coupling between convection and oscillations. Turbulent pressure has important effects on the excitation of oscillations in red variables. | \label{sec1} In the H-R diagram, there are a lot of pulsating red variables in the low-temperature area to the right of the Cepheid instability strip. They have the largest number among all known types of pulsating variables, and yet we know little about them. In the General Catalogue of Variable Stars \citep{GCVS}, luminous red variables, usually known as long-period variables (LPVs), are divided into three types according to the regularity of their light curves: Miras, semi-regular variables (SRVs) and irregular variables. The study of red variables has made considerable progress in the past two decades with the help of photometric observations from projects like MACHO, OGLE and 2MASS. \citet{Wood1999} and \citet{Wood2000} found 5 ridges (sequences A--E) in the period-luminosity (PL) diagram of luminous red variables in the Large Magellanic Cloud (LMC). OGLE observations showed more complex structures in the PL diagram, and at least 14 ridges could be defined \citep{KB2003, WEP2004, SUK2004, SUK2005, SDU2007}. \citet{SUK2004} found that stars with the primary periods on sequence A rarely had their second and third dominant periods on sequences C and C$'$, and stars with the primary periods on sequence C rarely had their second and third dominant periods on sequence A. This indicates that stars with their primary periods on sequence A are a special type of red variables. They are named OGLE Small Amplitude Red Giants (OSARGs), but their origin is still unclear. At first \citet{Wood1999} thought that variable luminous red giants in MACHO observations were asymptotic-giant-branch (AGB) stars, but later \citet{KB2003} and \citet{ITM2004} found evidence showing that there were luminous red variables on both the AGB and the red-giant branch (RGB). Their PL sequences were parallel with slight offsets. \citet*{TSI2013} compared observed period ratios of luminous red giants with theoretical ones and concluded that OSARGs were radial and non-radial p modes. \citet{Wood2015} reached a similar conclusion, and identified the stars on sequences C and C$'$ as predominantly radial pulsators; the radial pulsation modes associated with A$'$, A, B, C$'$ and C were the fourth, third, second and first overtones and the fundamental modes, respectively. However, \citet{Trabucchi2017} found that both sequences B and C$'$ corresponded to first-overtone pulsation. For a long time, convection has been considered to be a pure damping mechanism of stellar oscillations. The excitation mechanism of pulsating red variables has been a long-standing theoretical problem. There are two different opinions regarding the excitation mechanism of OSARGs. The prevailing opinion is that they are stochastically excited, just like solar-like oscillations \citep{CDKM2001, SDU2007, TSI2013}. However, \citet{XD2013} came to the conclusion that there were no essential differences between the excitation mechanisms of oscillations in OSARGs and Miras. They were both the results of radiation and convective coupling. In this paper, we aim at probing the excitation mechanism for luminous red giants observed by MACHO and OGLE. In section \ref{sec2}, we briefly introduce theoretical stellar models and the scheme of computation. The results of computation of linear non-adiabatic oscillations are given in section 3, and the excitation mechanism of oscillations is discussed in section 4. We summarize our results in section 5. | \label{sec5} We have computed the linear non-adiabatic oscillations of evolutionary models of low-mass red giants. The main results can be summarized as follows. \begin{enumerate} \item Sequences A--C of luminous red variables in LMC of MACHO and OGLE observations are low-order radial modes of low-mass RGB and AGB stars. \item Oscillations in Miras and OSARGs can be self-excited as a result of radiation and the coupling between convection and pulsation. Turbulent pressure has important effects on the excitation of oscillations in low-temperature red variables. \item Our study shows that for low-luminosity red giants, the low-order modes are stable, while the intermediate- and high-order modes are unstable. These stars show characteristics of solar-like oscillations. As the luminosity increases, unstable modes move towards lower orders. In luminous red giants, only a few low-order radial modes are unstable, while all of the intermediate- and high-order modes become stable. These stars show characteristics of Mira-like oscillations. \end{enumerate} | 18 | 8 | 1808.09620 |
1808 | 1808.02704_arXiv.txt | Ly$\alpha$ Emitters (LAEs) may represent an important galaxy population in the low mass regime. We present our deep narrowband imaging surveys in the COSMOS and ECDF-S fields and study the properties of LAEs at $z=2.23\pm0.03$. The narrowband surveys conducted at Magellan II telescope allow us to obtain a sample of 452 LAEs reaching a $5\sigma$ limiting magnitude of $\sim26$ mag. Our Ly$\alpha$ luminosity functions extend to $10^{41.8}$\,erg\,s$^{-1}$ with steep faint-end slope. Using multi-wavelength ancillary data, especially the deep \textit{Spitzer}/IRAC 3.6\,$\mu$m and 4.5\,$\mu$m photometric data, we obtained reliable stellar mass estimates for 130 IRAC-detected LAEs, spanning a range of $8 < {\rm log}(M_\star/M_\odot)< 11.5$. For the remaining IRAC-undetected LAEs, the median-stacked spectral energy distribution yields a stellar mass of ${\rm log}(M_\star/M_\odot)=7.97^{+0.05}_{-0.07}$ and the rest-frame ultraviolet emission indicates a median star formation rate of ${\rm log} (SFR/M_\odot$\,yr$^{-1})=-0.14\pm0.35$. There are six LAEs detected by the \textit{Spitzer}/MIPS 24\,$\mu$m or even \textit{Herschel} far-infrared observations. Taking into account the six MIR/FIR detected LAEs, our LAEs cover a wide range in the star formation rate (${\rm 1<SFR<2000}$\,M$_\odot$\,yr$^{-1}$). Although LAEs as a population are diverse in their stellar properties, they are mostly low-mass star-forming galaxies and follow the star formation main sequence relations or their extrapolations to the low-mass end, implying a normal star-forming nature of LAEs. The clustering analysis indicates that our LAEs reside in dark matter halos with ${\rm <\log(M_{h}/M_{\odot})> =10.8^{+0.56}_{-1.1}}$, suggesting that they are progenitors of local Large Magellanic Cloud-like galaxies. | The epoch at $z\sim2$ is crucial in the history of galaxy evolution when the cosmic star formation rate density (SFRD) reaches its peak \citep[][and references therein]{Madau+2014}. Detailed knowledge of massive ($>10^{10} M_{\odot}$) galaxies at this epoch has been widely investigated \citep[e.g.,][]{Erb+2006,Forster+2009,Steidel+2014,Kriek+2015,Burkert+2016,Wuyts+2016}. On the other hand, low-mass galaxies at $z\sim 2$ pose an unique and important position in studying galaxy evolution because they are building blocks of local mature galaxies. However, our knowledge on low-mass galaxies ($<10^{10} M_{\odot}$) at $z\sim2$ is still limited due to challenges in identifying these faint galaxies. Large samples, on the other hand, are needed for a robust census of such galaxies. The narrowband imaging technique is an effective way of detecting Ly$\alpha$ emitting galaxies (LAEs) at specific redshifts \citep[e.g.,][]{Malhotra+2002,Wang+2005,Finkelstein+2007,Finkelstein+2008,Gawiser+2007, Gronwall+2007, Nilsson+2007,Pirzkal+2007, Lai+2008, Ono+2010a,Ono+2010b,Acquaviva+2011, Zheng+2016}. Other methods such as integral-field spectroscopy \citep[e.g.,][]{vanBreukelen+2005,Drake+2017}, slit spectroscopy \citep[e.g.,][]{Rauch+2008} and medium-band imaging \citep[e.g.,][]{Stiavelli+2001,Taniguchi+2015,Sobral+2018} have also been employed in finding LAEs. LAEs were found to be mostly composed of low-mass star-forming galaxies \citep[e.g.,][]{Gawiser+2006, Finkelstein+2007, Lai+2008, Pirzkal+2007, Nilsson+2011, Guaita+2011, Shimakawa+2017}, red massive star-forming LAEs exist though \citep[e.g.,][]{Stiavelli+2001,Lai+2008,Finkelstein+2008,Finkelstein+2009, Ono+2010b,Acquaviva+2011,Guaita+2011,Nilsson+2011,Oteo+2012,Matthee+2016}. Therefore, LAEs can be used to probe the properties of low-mass galaxies at high redshifts. In the past several years, a number of narrowband imaging surveys and spectroscopic observations have been carried out to search for LAEs at $z\sim2$ \citep[e.g.,][]{Nilsson+2009, Guaita+2010, Nakajima+2012, Blanc+2011, Cassata+2011, Hathi+2016, Matthee+2016, Shimakawa+2017}. These surveys and deep multi-wavelength ancillary data have made it possible to yield measurements of properties of LAEs such as Ly$\alpha$ luminosity function, star formation rate, stellar mass, dark matter halo mass and rest-frame optical spectroscopic properties etc \citep[e.g.,][]{Guaita+2011, Nilsson+2011,Ciardullo+2012, Ciardullo+2014,Guaita+2013, Nakajima+2013, Trainor+2016, Sobral+2017,Kusakabe+2018}. The Ly$\alpha$ luminosity function and its faint-end slope are of special interest since they can serve as probes of galaxy evolution and cosmic re-ionization \citep[e.g.,][]{Rauch+2008, Konno+2016, Zheng+2017}. In order to determine the faint-end slope of the Ly$\alpha$ luminosity function, many surveys have been carried out to detect LAEs with much faint luminosities \citep[e.g.,][]{Blanc+2011, Ciardullo+2012}. Based on a deep spectroscopic survey, \citet{Cassata+2011} put strong constraints on the faint-end slope of the Ly$\alpha$ luminosity functions at $1.95 < z < 3$ and $3 < z < 4.55$. They ruled out a flat slope of $\sim -1$ at 5$\sigma$ and 6.5$\sigma$ levels at these two redshift ranges, and specifically obtained a slope of $-1.6\pm0.12$ for the Ly$\alpha$ luminosity function at $z \sim 2.5$. More recently, a wide-field ($1.43\,{\rm deg^2}$) Subaru Ly$\alpha$ survey with an unprecedented depth obtained a much larger LAE sample of $>$3000 galaxies at $z=2.2$ \citep{Konno+2016}. This sample yields an even steeper slope of $-1.75^{+0.10}_{-0.09}$ at $z\sim2$. Later on, the steep slope was confirmed by another wide-field survey ($1.43\,{\rm deg^2}$) at similar redshifts but with shallower narrowband exposures \citep{Sobral+2017}. All those surveys indicated that there are more galaxies at faint luminosity end, and their volume densities are much higher than those with higher luminosities. Among others, stellar mass is one of the most difficult quantities to be measured due to their faint continuum. Usually it requires the rest-frame long wavelength optical or near-infrared (NIR) photometry to determine a reliable galaxy stellar mass. For an LAE at $z>2$, its rest-frame long wavelength optical and NIR continua move to NIR or mid-IR (MIR) bands. Nonetheless, an LAE appears to be very faint in NIR and MIR. A typical LAE at $z\sim2$ would have a $R$-band magnitude of 25.3--25.5 magnitude \citep{Guaita+2010,Vargas+2014} and a flat Spectral Energy Distribution (SED). Thus its NIR or MIR magnitude will also be 25.5 magnitude or even fainter. There are only $\sim 20\%-30\%$ of luminous LAEs detected at 3.6\,$\mu$m, 4.5\,$\mu$m in the deep Spitzer IRAC surveys \citep{Nilsson+2011}. It requires a large and deep coverage in NIR or MIR to detect faint LAEs and measure their stellar masses. Furthermore, star formation rate (SFR) and stellar mass were found to have a tight correlation for normal star-forming galaxies, called the star formation ``main sequence'' (SFMS) \citep[e.g.,][]{Brinchmann+2004, Elbaz+2007}, which defines a steady star formation mode. Starburst galaxies are located above the SFMS relation \citep[e.g.,][]{Rodighiero+2011}. At high redshifts, the SFMS relation is derived mainly based on galaxies with stellar mass larger than $10^{10} M_{\odot}$ \citep[e.g.,][]{Daddi+2007, Rodighiero+2011, Fang+2012, Shivaei+2015, Shivaei+2017}, and it is often extrapolated to low mass to be compared with LAEs. There is a debate on the locations of LAEs relative to the SFMS relation, i.e. the existing studies found that LAEs lie above \citep{Guaita+2013, Hagen+2014, Hagen+2016, Vargas+2014, Oteo+2015} or on \citep{Shimakawa+2017, Kusakabe+2018} the SFMS. It was suggested that the inconsistent results may be caused by different survey depths or the use of different extinction curves \citep{Shimakawa+2017, Kusakabe+2018}. Different survey depths of both narrowband and broadband observations would result in different sample selection effects and sample properties. Therefore, large and deep coverage in both narrowband and broadband is needed to provide further independent constraints. In this paper series, we will study the properties of LAEs using a deep narrowband-selected LAE sample with deep multi-wavelength data. We specifically designed a customized narrowband filter at 3928\,\AA\ with filter width of 70\,\AA\ (see Figure \ref{transmission.eps}) for detections of LAEs at $z=2.23\pm0.03$. At the same redshift, H$\alpha$ emitters can be selected using the typical NIR narrowband filter at 2.12\,$\mu$m widely available on many telescopes \citep{Geach+2008, Sobral+2013, An+2014}. So this filter design permits a comparison between Ly$\alpha$ and H$\alpha$ selection for galaxy populations at $z=2.23$ \citep[e.g.,][]{Matthee+2016, An+2017, Sobral+2017}. We chose the COSMOS and ECDF-S fields, where deep \textit{HST} imaging data are available including the Galaxy Evolution from Morphologies and SEDs \citep[GEMS;][]{Rix+2004}, the Cosmic Evolution Survey \citep[COSMOS;][]{Scoville+2007}, and the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey \citep[CANDELS;][]{Grogin+2011,Koekemoer+2011}. Both fields were also covered in MIR by the \textit{Spitzer} Extended Deep Survey \citep[SEDS;][]{Ashby+2013}. The deep \textit{Spitzer} and \textit{HST} imaging data allow us to study the stellar masses and SFMS in this paper and UV morphologies in a forth-coming paper (Hao et al. 2018, in preparation) . Our narrowband observations were carried out on Magellan II telescope with excellent seeing condition, making it possible to study morphologies of Ly$\alpha$ emission (Huang et al. 2018, in preparation). This paper is structured as follows. In Section 2, we describe observations and data reduction. Selection of LAEs is presented in Section 3. We have our main results in Section 4 and 5, and conclude in Section 6. We adopt a flat $\Lambda$CDM cosmology with $\Omega_{\rm m}=0.3$, $\Omega_{\rm \Lambda}=0.7$, $H_{\rm 0}=70\,{\rm km \, s^{-1} Mpc^{-1}}$ and $\sigma_8=0.8$ for all calculations, and a Salpeter Initial Mass Function \citep[IMF;][]{Salpeter1955} for stellar population analysis. | We have conducted deep narrowband surveys for the COSMOS and ECDF-S fields to search for Ly$\alpha$ emitters (LAEs) at redshift $z=2.23\pm0.03$ using our customized narrowband filter $N3928$\,\AA\ at Megacam/Magellan II telescope. Our observations reached a 5$\sigma$ limiting magnitudes in a 3\arcsec\ diameter aperture of $\sim26$ mag and a seeing FWHM of 0\farcs6. Using archival broad $U$ and $B$ bands images as a measure of the underlying continuum, we selected 194 (including 4 AGNs) and 258 (including 2 AGNs) LAEs over the 602 arcmin$^2$ and 613 arcmin$^2$ survey areas on the COSMOS and ECDF-S fields, respectively. Our LAEs sample provides reliable measurements of the Ly$\alpha$ luminosity function over the Ly$\alpha$ luminosity range of $10^{41.8}-10^{42.8}$ erg\,s$^{-1}$. Within this luminosity range, the Ly$\alpha$ luminosity functions of the COSMOS and ECDF-S fields are in a good agreement with each other. The overall shapes of our Ly$\alpha$ luminosity functions are consistent with that of \citet{Konno+2016} and \citet{Sobral+2017} based on larger area ($1.43\,{\rm deg^2}$) Ly$\alpha$ surveys at similar redshifts. Thus our Ly$\alpha$ luminosity functions lend further support to the steep faint-end slope. The existing multi-wavelength data from the rest-frame UV to the IR, especially the deep \textit{Spitzer}/IRAC MIR data, allow us to explore the stellar populations and star formation properties of LAEs. The \textit{Spitzer} Extended Deep Survey (SEDS) provides important constraints on the stellar mass estimates. For 29\% of our LAEs that were detected by IRAC at 3.6 \,$\mu$m or 4.5 \,$\mu$m, their stellar masses are in the range of $8 <{\rm log(M_\star/M_\odot)}< 11.5$. On the other hand, the SED fitting to the stacked SED of the IRAC-undetected LAEs indicates a stellar mass of ${\rm log}(M_\star/M_\odot)=7.97^{+0.05}_{-0.07}$ and dust extinction of $A_{\rm v}=0.12^{+0.25}_{-0.08}$ mag. Based on the measurement of the median stellar mass for the IRAC-undetected LAEs, we roughly estimate their mean number density as $\rm {log}(\Phi/{\rm Mpc^{-3} dex^{-1}})=-3.0$ at log($M_\star$/$M_\odot$)=8. Although it is a lower limit and much smaller than the extrapolation of the existing stellar mass functions, it serves as an important observational constraint at such low-mass regime. Rest-frame FUV luminosities calculated from the observed $B$-band flux densities were used to derive SFRs. The dust attenuations were estimated from the UV slope $\beta$, based on public $B$, $V$, $R$ and $I$ bands photometry. The dust-corrected SFRs of our LAEs cover a range of ${\rm 1<SFR<100}$\,M$_\odot$\,yr$^{-1}$, with six \textit{Spitzer}/MIPS 24\,$\mu$m or even \textit{Herschel} FIR detected LAEs having SFRs up to 2000\,M$_\odot$\,yr$^{-1}$. Although LAEs are heterogeneous populations that have stellar mass and SFR covering more than three orders of magnitude, i.e. ${\rm 8 < log(M_\star/M_\odot) < 11.5}$, ${\rm 1<SFR<2000}$\,M$_\odot$\,yr$^{-1}$, they are mostly composed of low-mass galaxies and follow the star formation main sequence relations and their extrapolations to the low mass end. This indicates that the star formation in most LAEs is taking place in a steady mode. The two-point correlation function analysis for our LAEs sample yields a bias factor of $1.31\pm0.34$ and corresponding dark matter halo mass of $\log(M_{h}/M_{\odot}) =10.8^{+0.56}_{-1.1}$, which is consistent with those of \citet{Kusakabe+2018} based on a much larger sample and survey area. | 18 | 8 | 1808.02704 |
1808 | 1808.06311_arXiv.txt | We present extensive spectroscopic observations for one of the closest type Ia supernovae (SNe Ia), SN 2014J discovered in M82, ranging from 10.4 days before to 473.2 days after $B$-band maximum light. The diffuse interstellar band (DIB) features detected in a high-resolution spectrum allow an estimate of line-of-sight extinction as $A_\textrm{v}$ $\sim$1.9$\pm$0.6 mag. Spectroscopically, SN 2014J can be put into the high-velocity (HV) subgroup in Wang's classification with a velocity of Si~{\sc ii} $\lambda$ 6355 at maximum light of $v_0=1.22\pm 0.01 \times 10^4$ km~s$^{-1}$, but has a low velocity gradient (LVG, following Benetti's classification) of $\dot{v}=41\pm2$ km s$^{-1}$ day$^{-1}$, which is inconsistent with the trend that HV SNe Ia generally have larger velocity gradients. We find that the HV SNe Ia with LVGs tend to have relatively stronger Si~{\sc iii} (at $\sim$4400 \AA) absorptions in early spectra, larger ratios of S~{\sc ii}~$\lambda$ 5468 to S~{\sc ii}~$\lambda$ 5640, and weaker Si~{\sc ii} 5972 absorptions compared to their counterparts with similar velocities but high velocity gradients. This shows that the HV+LVG subgroup of SNe Ia may have intrinsically higher photospheric temperature, which indicates that their progenitors may experience more complete burning in the explosions relative to the typical HV SNe Ia. | SN 2014J was discovered in the edge-on starburst galaxy M82 on 2014 January 21.805 (UT dates are used throughout this paper) by Fossey et al. (2014) and it was classified as a type Ia supernova (SN Ia) by Cao et al. (2014). SN 2014J is one of the nearest SNe Ia discovered over the past three decades, with a distance of only $\sim$3.5 Mpc. Extensive followup observations were obtained for this nearby SN Ia soon after its discovery. SN 2014J reached its $B$-band maximum of 11.68$\pm$0.01 mag on MJD 56689.74$\pm$0.13 (Marion et al. 2015), with a post-peak decline rate as $\Delta$ m$_{15}$(B) as 0.96$\pm$0.03 mag (observed value from Srivastav et al. 2016). After correcting for the reddening effect (Phillips et al. 1999) from Milky Way and host galaxy, the true light-curve decline rate $\Delta m_{15}(B)_{true}$ is estimated as 1.08$\pm$0.03 (Srivastav et al. 2016). Based on the early photometric data, the explosion time was estimated to be 2014 Jan. 15.57 UT (MJD = 56672.57, Zheng et al. 2014). With the near-infrared (NIR) and optical spectra from $-9.9$ d to +10.0 d, Marion et al. (2015) identified C~{\sc i} $\lambda$10693. They also found that SN 2014J has a layered structure with little or no mixing, which is consistent with delayed detonation explosion models (H{\"o}flich et al. 2002). Marion et al. (2015) and Srivastav et al. (2016), presenting spectra covering the phases from $-$7.71 d to +351.09 d, suggested that SN 2014J is near the border of the Normal Velocity (NV) group and the High Velocity (HV) group in the classification scheme of Wang et al. (2009a), belongs to the low-velocity gradient (LVG) subgroup in the classification scheme of Benetti et al. (2005), and lies at the border of the Core Normal (CN) and Broad Line (BL) subclasses in the classification scheme of Branch et al. (2009). Galbany et al. (2016) also concluded that SN 2014J is a transitional SN Ia in all the classification schemes. Bright supernovae such as SN 2014J also provide good opportunities to study circumstellar material (CSM) and interstellar material (ISM) along the line of sight, given the relatively high extinction that it suffers. Using high-resolution spectra of SN 2014J in the early phase, Goobar et al. (2014) analyzed the dense intervening material and did not detect any evolution in the resolved absorption features during the rising phase of the light curves. In a series of highest resolution (R$\sim$110,000) spectra of SN 2014J, Graham et al. (2015; hereafter G15) did not detect evolution in any component of Na {\sc i} D and Ca {\sc ii}. However, they established the dissipation/weakening of the two most blueshifted components of K~{\sc i} lines, which was attributed to the photoionization of CSM, favoring a single-degenerate (SD) scenario for SN 2014J. The corresponding velocity components of Na {\sc i} D did not vary with time (which was also noticed by Goobar et al. 2014), but this may be due to its higher ionization energy. Ritchey et al. (2015) and Welty et al. (2014) detected the Na {\sc i}, Ca {\sc ii}, K {\sc i}, Ca {\sc i}, CH$^+$, CH, CN in the high-resolution spectra obtained for SN 2014J between $-$5.6 d and +30.4 d. In particular, the Li {\sc i} detected in the spectrum of SN 2014J is the first report for the detection of interstellar Li beyond the Local Group. The high-resolution spectra of SN 2014J also allow the study of the diffuse interstellar bands (DIBs). It has been a long time since Heger (1922) first reported the DIBs, but the carriers of DIBs are still under debate. The earliest DIB feature detected in the spectra of a supernova was found by Rich (1987) using the spectra of SN 1986G. For SN 2014J, the DIB features have been studied by Welty et al. (2014), Goobar et al. (2014), and G15. Owing to the correlation with dust extinction, the DIB features can help determine the extinction of SN 2014J in its host galaxy M82. In this paper, we present our extensive optical spectroscopic observations for SN 2014J as well as our analysis of the spectral features. We describe the observations and data reduction in \S 2. Analysis of the spectral features is presented in \S 3. We discussed the diversity of spectral features in \S 4, and we summarize our results in \S 5. | In this paper, we present extensive optical spectroscopy (including one very high-resolution spectrum) for SN 2014J, covering the phases from $-$10.4 d to +473.2 d from maximum light. Based on the detected DIBs in our high-resolution spectrum, we derive a total extinction $A_\textrm{v}$ $\sim$1.9$\pm$0.6 mag for SN 2014J. The spectral properties of SN 2014J are overall similar to that of SN 2007co and SN 2007le. It can be classified as a HV SN Ia, but also belongs to the LVG subclass, which is somewhat against the general trend that HV SNe Ia tend to have a larger velocity gradient. Based on the spectral features in the wavelength region 4000-6000 \AA\, we suggest that SN 2014J, SN 2002cd, and SN 2009ig (and perhaps SN 2012fr) share some common properties, and may represent a new HV subtype with a flat velocity evolution (dubbed as HV+LVG subclass). We caution, however, that the classification of SN 2014J as a member of HV+LVG SNe Ia is not as robust as SN 2002cd and SN 2009ig due to that it locates near the boundary of HV and NV subgroups. It is possible that SN 2014J represents a transitional object linking the HV+LVG and NV+LVG subgroups. The HV+LVG objects are found to have higher temperatures, as evidenced by the strong Si {\sc iii} feature at $\sim$4300 \AA\ and the weak Si {\sc ii} $\lambda$5972 absorption seen in their early spectra. Moreover, we find that the ratio of S~{\sc ii} $\lambda$5468 and S~{\sc ii} $\lambda$5640 absorption, $R$(S), measured at $t\sim-$10 days, is inversely correlated with $\Delta m_{15}(B)$. The $R$(S) parameter also shows an inverse correlation with the velocity gradient, but with large scatter at the LVG end. Additional mechanism is needed to account for these anti-correlations of $R$(S), as these two lines of S~{\sc ii} have similar excitation energies. Theoretically, the slow velocity evolution can be formed in a shell-like density structure produced by pulsating delayed detonation scenario, mergers, or interaction of ejecta with circumstellar materials. These scenarios are also consistent with the high photospheric temperatures observed in the HV+LVG subtype of SNe Ia, but a large, well-observed sample of similar properties is needed to test current models. Detailed modeling of W-shaped S~{\sc ii} lines may also help make further distinguish between different scenarios. | 18 | 8 | 1808.06311 |
1808 | 1808.06916_arXiv.txt | GRO J1744--28, commonly known as the `Bursting Pulsar', is a low mass X-ray binary containing a neutron star and an evolved giant star. This system, together with the Rapid Burster (MXB 1730-33), are the only two systems that display the so-called Type II X-ray bursts. These type of bursts, which last for 10s of seconds, are thought to be caused by viscous instabilities in the disk; however the Type II bursts seen in GRO J1744--28 are qualitatively very different from those seen in the archetypal Type II bursting source the Rapid Burster. To understand these differences and to create a framework for future study, we perform a study of all X-ray observations of all 3 known outbursts of the Bursting Pulsar which contained Type II bursts, including a population study of all Type II X-ray bursts seen by \textit{RXTE}. We find that the bursts from this source are best described in four distinct phenomena or `classes' and that the characteristics of the bursts evolve in a predictable way. We compare our results with what is known for the Rapid Burster and put out results in the context of models that try to explain this phenomena. | \par Low Mass X-ray Binaries (hereafter LMXBs) are extremely dynamic astrophysical systems, which exhibit high-amplitude X-ray variability on timescales of milliseconds to years. In these systems a compact object accretes matter from a stellar companion, either via a stellar wind or via Roche-lobe overflow. The donated matter spirals in towards the compact object, forming an accretion disk of matter which heats up by friction to temperatures of $\gtrsim1$\,keV. \par LMXBs are an excellent laboratory in which to explore the behaviour of matter under extreme physical conditions. In addition to extreme temperatures, the inner portion of an accretion disk is a region of extreme gravity, gas pressure and photon pressure. If the primary object in the binary is a neutron star, these systems also contain regions of extreme magnetic fields. \par Many LMXBs containing a neutron star are known to exhibit `bursts'; discrete periods of increased X-ray emission over timescales of seconds. These bursts are generally categorised as either Type I or Type II, depending on the profile of the burst and its spectral evolution \citep{Hoffman_RB,Lewin_Bursts}. Type I bursts are caused by accreted matter on the surface of the neutron star reaching a critical pressure and temperature which triggers runaway thermonuclear burning (see e.g. \citealp{Lewin_Bursts,Strohmayer_TypeI}). They appear in X-ray lightcurves as a sudden increase in intensity, followed by a power-law decay \citep{intZand_Decay}, over a timescale of a few $\sim10$s of seconds. \par Type II bursts are believed to be caused by viscous instabilities in the accretion disk \citep{Lewin_TypeII}. However, the exact details of the mechanism responsible for Type II bursts remain unclear. This type of bursts is more varied in its phenomenological appearance, ranging from near-Gaussian in shape over timescales of $<1$\,s to broad flat-topped lightcurve features which last for $\sim100$\,s (e.g. \citealp{Bagnoli_PopStudy}). \par Type I X-ray bursts are seen in data from over a hundred neutron star LMXBs, while regular Type II bursts have only been unambiguously identified in two sources: the ``Rapid Burster'' MXB 1730-335 \citep{Lewin_TypeII} and the ``Bursting Pulsar'' GRO J1744--28 \citep{Kouveliotou_BP}. Isolated Type II bursts may have also been observed in at least one additional X-ray Binary (SMC X-1, \citealp{Angelini_SMC}), but the identification of these features remains unclear. \par The Type II bursting behaviour in the Rapid Burster has been extensively studied (see e.g. \citealp{Lewin_TypeII,Hoffman_RB}). \citet{Bagnoli_PopStudy} performed a full population study of all Type II bursts observed in this object by the \textit{Rossi X-ray Timing Explorer} (\textit{RXTE}, \citealp{Bradt_RXTE}). Their results suggest that gating of the accretion by a strong magnetic field plays some role in the creation of Type II bursts. To further probe the physics behind Type II X-ray bursts, in this paper we perform a similar population study on bursts from the Bursting Pulsar. \par The Bursting Pulsar \citep{Paciesas_BPDiscovery} is a system containing a neutron star and a G or K class evolved companion star (e.g. \citealp{Sturner_BPNature,Gosling_BPCompanion,Masetti_BPCompanion}). The system lies at a distance of $\sim4$--$8$\,kpc in the direction of the Galactic centre (e.g. \citealp{Kouveliotou_BP,Gosling_BPCompanion,Sanna_BP}), and it is the only known pulsar that regularly displays Type II bursts. The Bursting Pulsar accretes at a high rate: by estimating the accretion rate of the object by measuring how fast the pulsar spins up, \citealp{Sturner_BPNature} found that the Bursting Pulsar accretes at close to the Eddington limit for a neutron star. \par Unlike in the Rapid Burster, unambiguous Type I bursts have never been observed from the Bursting Pulsar (e.g. \citealp{Giles_BP}, however see also \citealp{Lamb_TypeIBP,Doroshenko_NBFlash}). Type II bursts were first identified upon discovery in 1995 by the Burst and Transient Source Experiment (BATSE) aboard the \textit{Compton Gamma Ray Observatory} (\textit{CGRO}, \citealp{Gehrels_CGRO}). Additional outbursts have occurred irregularly; specifically in 1997 and 2014 \citep{Woods_OB2,Kennea_BPOutburst}. An additional outburst may have occurred in 2017 \citep{Sanna_BPOutburst}, but it was significantly less luminous than previous outbursts and the Bursting Pulsar did not transition to the soft state (such events are referred to as `failed outbursts' or `failed state-transition outbursts', see e.g. \citealp{Sturner_Failed}). \par Previous work by \citet{Giles_BP} indicated that Type II bursts in the 1995--1996 outburst of the Bursting Pulsar could be separated into a number of distinct populations based on peak flux. This is a notable difference from the Rapid Burster, in which all Type II bursts have peak fluxes approximately equal to or less than object's Eddington Luminosity \citep{Tan_RBBursts}. In this paper we expand on the work of \citet{Giles_BP} and analyze \textit{RXTE}, \textit{NuSTAR}, \textit{Chandra}, \textit{XMM-Newton}, \textit{Swift} and \textit{INTEGRAL} data to fully quantify the population of Type II bursts in the Bursting Pulsar during all outbursts in which they were observed. We study how the bursting in this object evolves over time throughout each outburst, and we link this behaviour to the long-term evolution of the source. We also perform basic timing, morphology and spectral analysis on bursts, to try and understand the physical processes behind these phenomena. % | \par We analyse all X-ray bursts from the Rapid Burster seen by \textit{RXTE}/PCA during its first and second outbursts, as well as bursts seen by other missions during the third outburst of the source. We conclude that these bursts are best described as belonging to four separate classes of burst: Normal Bursts, Mesobursts, Minibursts and Structured Bursts. We find that the bursting behaviour in these four classes evolves in a similar way throughout the first two outbursts of the Bursting Pulsar. We present a new semi-mathematical model to fit to the Normal Bursts in this object. Using this new framework, we will be able better quantify Bursting-Pulsar-like X-ray bursts when they are observed in other objects in the future. \par We find the bursts in the Rapid Burster and the Bursting Pulsar to be different in burst profile, peak Eddington ratio, and durations. While the fluence of Type II bursts in the Bursting Pulsar depend strongly on the persistent emission at the time, this is not the case in the Rapid Burster. Additionally the waiting time between bursts in the Rapid Burster depend heavily on the fluence of the preceding burst, but we do not find this in the Bursting Pulsar. Therefore, it would be reasonable to conclude that the bursting in these two objects is generated by two different mechanisms. \par However, it is also important to note a number of similarities between the Bursting Pulsar and the Rapid Burster. Bursting behaviour in both objects depends on the global accretion rate of the system and the evolution of its outbursts. For example, the recurrence times of bursts does not depend on persistent emission in either object, and nor does the duration of an individual burst. Notably while Type II bursts in the Rapid Burster only occur at luminosities $L\lesssim0.05L_{Edd}$, we find that Normal bursts in the Bursting Pulsar only occur at $L\gtrsim0.1L_{Edd}$. There is no overlap between the luminosity regimes, in terms of the Eddington Luminosity, at which bursting is observed in the two objects. This leads to the alternative hypothesis that bursts in the two systems may be caused by similar processes, but that these processes take place in very different physical regimes. | 18 | 8 | 1808.06916 |
1808 | 1808.01194_arXiv.txt | As part of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters, we present a detailed investigation of the internal kinematics of NGC 5986. The analysis is based on about 300 individual radial velocities of stars located at various distances from the cluster center, up to $300\arcsec$ (about 4 half-mass radii). Our analysis reveals the presence of a solid-body rotation extending from the cluster center to the outermost regions probed by the data, and a velocity dispersion profile initially declining with the distance from the cluster's center, but flattening and staying constant at $\sim 5$ km s$^{-1}$ for distances larger than about one half-mass radius. This is the first globular cluster for which evidence of the joint presence of solid-body rotation and flattening in the outer velocity dispersion profile is found. The combination of these two kinematical features provides a unique opportunity to shed light on fundamental aspects of globular cluster dynamics and probe the extent to which internal relaxation, star escape, angular momentum transport and loss, and the interaction with the Galaxy tidal field can affect a cluster's dynamical evolution and determine its current kinematical properties. We present the results of a series of N-body simulations illustrating the possible dynamical paths leading to kinematic features like those observed in this cluster and the fundamental dynamical processes that underpin them. | \label{sec_intro} The ESO-VLT Multi-Instrument Kinematic Survey (hereafter the MIKiS survey; \citealp{ferraro+18a}) of Galactic globular clusters (GCs) is a project specifically designed to characterize the kinematical properties along the line-of-sight of an illustrative selection of GCs in the Milky Way. We have measured individual radial velocities (RVs) of hundreds of stars, distributed over the entire radial range of each stellar system. To this end, the survey fully exploits the spectroscopic capabilities of different instruments currently available at the ESO Very Large Telescope (VLT): the adaptive-optics assisted integral-field spectrograph SINFONI, the multi-object integral-field spectrograph KMOS, and the multi-object fiber-fed spectrograph FLAMES. The evolutionary interplay between two-body relaxation-driven processes and the effects of the external tidal environment gives origin to a rich internal kinematics in collisional systems, which is now observationally accessible. Moreover, Milky Way GCs are very old stellar systems (with ages of $\sim 10$ Gyr or more; see e.g. \citealt{forbes+10}) orbiting the Galaxy since the remote epoch of its formation. Hence, signatures of such a long-term interaction could be present in their observational properties. In this context, both the inner and the outer portions of the kinematic profiles provide crucial information on the dynamics of the systems: for instance, a central gradient in the velocity dispersion profile could be used to constrain the presence of an intermediate-mass black hole; the external portion provides information on the possible tidal perturbations due to interaction of the cluster with the Galactic tidal field. A growing set of observational evidence is indeed unveiling an unexpected dynamical complexity in Galactic GCs, demonstrating that the traditional assumptions of sphericity, pressure isotropy and non-rotation are far too simplistic (for references on morphological distortion, velocity anisotropy and rotation observed in Galactic GCs, see the comprehensive list reported in \citealp{ferraro+18a}). In particular, \citet{fabricius+14} detected signals of rotation in all the 11 Milky Way GCs studied in their survey and \citet{kamann+18} found evidence of rotation in $60\%$ of their sample (of 25 objects). In the context of the MIKiS survey, \citet{ferraro+18a} recently found rotation signals at distances of a few half-mass radii from the center in 10 Milky Way GCs (out of 11 investigated) and \citet{lanzoni+18} detected in M5 one of the cleanest and most coherent rotation patterns ever observed in a GC. All these results suggest that, when properly studied, the vast majority of GCs shows signatures of the presence of internal rotation. According to a number of numerical studies (see e.g. \citealt{einsel+99,ernst+07,tiongco+17}), the present-day signatures could be the relic of a stronger internal rotation set at the epoch of the cluster's formation (see e.g., \citealp{vesperini+14, lee+16, mapelli17}) and gradually altered and erased as result of the effects of angular momentum transfer and loss due to internal dynamical processes and star escape. In addition, as shown in the recent study by \citet{tiongco+18}, the interplay between internal dynamics and the interaction with the Galactic tidal field can produce a number of complex kinematical features in rotating clusters, including a radial variation in the orientation of the rotation axis: this would be the manifestation of the transition between the inner regions dominated by the cluster's intrinsic rotation, and the outer regions dominated by the rotation induced by the Galaxy tidal torque. As part of the MIKiS survey, here we present the velocity dispersion and rotation profiles in the intermediate/outer regions of NGC 5986. This is a relatively poorly investigated Galactic GC (see \citealt{alves+01} and reference therein). It is massive (with total $V$-band magnitude $M_V=-8.44$) and of moderate concentration ($c=1.23$), with core and projected half-light (or projected half-mass, at a first approximation) radii $r_c=28.2\arcsec$ and $R_h=58.8\arcsec$, respectively (\citealt{harris96}) and with three-dimensional half-mass radius $r_h\sim 78.16\arcsec$, as obtained from the corresponding \citet{king66} model. Because of various physical properties in common with the group of ``iron-complex'' GCs \citep{dacosta16}, NGC 5986 was suspected to be the remnant of a disrupted dwarf galaxy. However, a recent high-resolution spectroscopic investigation of 25 giant stars \citep{johnson+17} provided accurate measure of the cluster metallicity ([Fe/H]$=-1.54$) and showed that it is homogeneous in iron and with a well defined anti-correlation between the Al and the Mg abundances, in agreement with what expected for genuine GCs. The paper is structured as follows, In Section \ref{sec_obs} we briefly summarize the observations, the adopted data reduction procedures, and the method used to measure the stellar RVs. The main results of our kinematic study are presented in Section \ref{sec_resu}: the cluster has been characterized in terms of its systemic velocity and the radial profiles of its ordered and disordered motions. Section \ref{sec_discuss} discusses the observational results in the context of recent N-body simulations of tidally perturbed clusters, illustrating three possible paths that could lead to the observed features. | \label{sec_discuss} In this paper we presented a novel investigation of the internal kinematics of the Galactic GC NGC 5986, as based on hundred spectra of individual stars. We find one of the most significant rotation patterns hitherto detected in GCs (see also the cases of NGC 4372 in \citealt{kacharov+14}, 47 Tucanae in \citealt{bellini+17}, and M5 in \citealp{lanzoni+18}), the only one so far showing a clear solid-body rotation behavior. For the first time, we also jointly find evidence of a velocity dispersion profile that flattens at distances larger than about one half-mass radius. The physical interpretation of the co-existence of these kinematic features requires particular care, because several dynamical pathways may be envisaged as a possible origin of the observed behaviors. A qualitative discussion of three possible channels, as based on recent theoretical investigations into the kinematic evolution of collisional stellar systems, is provided below. One possibility is that such kinematic properties result from the evolution of the cluster in an external tidal field, with attention to the role played by a population of energetically unbound stars confined within the critical equipotential surface (``potential escapers''; see \citealt{heggie01}). Recent studies based on direct N-body simulations have shown that such a population determines a flattening of the velocity dispersion profile in the outer regions of a stellar system \citep{kuepper+10,claydon+17}. In addition, tidally perturbed clusters, during the course of their dynamical evolution (and irrespectively of their initial conditions), tend to develop a signature of solid-body rotation which depends on their orbital angular velocity partial synchronization (see \citealt{tiongco+16b,claydon+17}) and a degree of anisotropy which depends on their initial filling factor (e.g., see \citealt{giersz+97, tiongco+16a}). As a representative example of such an evolutionary behaviour, we illustrate the rotation curve and velocity dispersion profile of an N-body model originally presented by \citet{tiongco+16b}, depicted a different times (see Figure \ref{fig_models}, first row). Such an N-body simulation starts from initial conditions sampled from a \citet{king66} equilibrium model, which is initially non-rotating, and is evolved on a circular orbit in the tidal field of a Keplerian potential (with an initial ratio of the intrinsic half-mass radius to the Jacobi radius given by $r_h/r_J=0.087$). As apparent from the figure, the system progressively develops a solid-body rotation curve with an angular velocity consistent with $\Omega/2$ (where $\Omega$ denotes the orbital angular velocity; for further details, see model ‘KF075U’ in \citealt{tiongco+16b}). The corresponding velocity dispersion profiles progressively flatten in the outermost regions of the system (see right-hand panels). A second pathway corresponds to the case of a collisional system which is initially characterized by some intrinsic internal rotation and is progressively evolving towards a condition of solid-body rotation (starting from its central to intermediate regions), as a result of the angular momentum transport and loss, induced by two-body relaxation processes. Such a case is exemplified by an N-body model originally presented by \citet{tiongco+16a}, for which we again illustrate the evolution of the rotation curve and velocity dispersion profile at different times (see Figure \ref{fig_models}, second row). The simulation starts from initial conditions sampled from differentially rotating equilibrium models \citep{varri+12} and includes the effect of a mild tidal field (corresponding to an initial ratio of the intrinsic half-mass radius to the Jacobi radius $r_h/r_J=0.093$) associated to a circular orbit in a Keplerian galactic potential (for further details, see model VBrotF04 in \citealt{tiongco+16a}). In this case, the evolution of the central slope value of the rotation curve is not determined by the influence of the tidal environment. In the represented model, only at a very late stage of evolution the rotation curve settles, as in the previous case, into a solid body-like behavior, with an angular velocity determined by the condition of partial synchronization. We wish to note that, in this pathway, the orientation of the axis of the initial intrinsic rotation, in principle, may also be different from the orientation of the orbital rotation axis \citep[see][]{tiongco+18}. As a result, a radial variation of the kinematic position angle may be found \citep[e.g., see][]{bianchini+13,boberg+17}, which is not observed in the range explored in the current kinematic study. An additional possible dynamical path is that of a stellar system experiencing a phase of ``violent relaxation'' in the presence of an external tidal field; in this case the violent relaxation process and the effects of the tidal field leave a distinctive fingerprint on the cluster's internal kinematics from the very early stages of its evolution (see \citealt{vesperini+14}), with a solid-body like behavior of the central portion of the rotation curve. Also in this case, the differential rotation imprinted during the early evolutionary stages progressively evolves towards the condition of partial synchronization described in the two previous cases. This third case is exemplified by a model originally presented by \citet{tiongco+16a} and subsequently studied by \citet[][see model vrQ01F05 for further details]{tiongco+17}. The element of interest in this third case (see Figure \ref{fig_models}, third row) mostly concerns the velocity dispersion profile, which becomes more flattened and extended at earlier times compared to the previous two cases. Such a difference is due to the fact that this model develops the population of energetically unbound stars responsible for the flattening of the velocity dispersion during the early violent relaxation phase. The models shown in Figure \ref{fig_models} serve as a framework for a general interpretation of the observed features, but are not designed to provide a detailed and quantitative fit to the kinematical properties of NGC 5986. In particular we note that the flattening in the velocity dispersion observed in NGC 5986 is more extreme and internal than that found in all our models. As shown in several studies \cite[see][]{casetti+07, allen+08, moreno+14}, NGC 5986 is on an eccentric orbit and specific models for this cluster need to take into account the effects on the velocity dispersion due to the time variation in the strength of the external tidal field \citep[see, e.g.,][]{kuepper+10}. Indeed, a time-variable tidal field, as experienced by a star cluster moving on an elliptic orbit, has direct implications on the properties and time evolution of the population of potential escapers dynamically generated in a collisional stellar system, which, in turn, has an impact on the shape of its outer velocity dispersion profile (see especially Figure 3 in \citealp{kuepper+10}, and also \citealp{drukier+07, claydon+17}). We estimated the orbital parameters of the system in the \citet{johnston+95} Milky Way potential well, adopting $V_{\rm sys} = 100.8$ km s$^{-1}$ as systemic line-of-sight velocity (see Section 3.1) and the proper motions of \citet{casetti+07} for the two components on the plane of the sky. We found that the system has a highly eccentric orbit ($e = 0.80$), practically plunging into the central part of the Milky Way along a path that is confined within the innermost few kpc from the Galactic center, with a pericentric distance $r_p = 0.5$ kpc and the apocenter at $r_a = 5.4$ kpc. These values are in very good agreement with those determined by \citet{casetti+07}, who used only a slightly smaller value of the systemic velocity. The orbital parameters estimated by \citet{helmi+18} from the proper motions presented in the second Gaia data release also suggest that this cluster is on a very eccentric orbit with a very small pericentric distance: depending on the model adopted for the Galactic potential, the eccentricity is equal to 0.7, 0.81 or 0.87, while $r_p$ varies between 0.85, 0.52 and 0.07 kpc, respectively. The orbital parameters derived for NGC 5986 thus suggest quite intense interactions with the central regions of the Galaxy, with an orbital radial period of only $\sim 60$ Myr, corresponding to a few hundreds passages of the cluster close to the Galactic center during its lifetime ($t=12$ Gyr; \citealt{forbes+10}). Thus, the effect of the time variation in the external tidal field is certainly playing an important role in the dynamics of NGC 5986 and must be included in simulations aimed at providing a detailed fit of the observed properties of this cluster. We point out here that, if the solid-body rotation revealed by our observations is the result of the cluster's convergence toward a state of partial synchronization with angular velocity $\Omega/2$, the angular velocity measured for NGC 5986 would correspond to the value of $\Omega/2$ at about 0.46 kpc (simply calculated assuming a circular velocity equal to 220 km/s). To provide a comprehensive dynamical interpretation of this cluster some additional pieces of information are needed. First of all, the line-of-sight kinematics should be assessed also in the outer regions of the cluster, in the proximity (and ideally beyond) the nominal Jacobi radius. Indeed, the shape of the outer rotation curve is crucial to test the applicability of the three pathways described above. We also plan to search for density distortion or streams associated with tidal perturbations. In principle, crucial information will also be added by the stellar proper motions measured by Gaia that, once combined with the line-of-sight kinematics, would allow us to reconstruct the full three-dimensional structure of the velocity space of the system. We have already started to analyze the most recent Gaia data \citep[see, e.g.,][]{helmi+18}, but this study is particularly challenging for NGC 5986 because of its relatively large distance from Earth (10.4 kpc; \citealp{harris96}), the high level of Galactic contamination in the cluster's direction on the sky, and the fact that the cluster proper motion is almost indistinguishable from that of the bulge. From the theoretical point of view, we plan to construct dynamical models and N-body simulations specifically tailored to the case of NGC 5986, exploring, in particular, the effects of an external tidal field in the case of highly eccentric orbits repeatedly crossing the innermost region of the Galaxy. Such a comprehensive investigation is particularly timely, in light of the growing interest for the physical understanding of the morphological and dynamical properties of the peripheries of Galactic GCs, especially regarding the interpretation of the kinematic properties of possible ``extra-tidal'' structures. | 18 | 8 | 1808.01194 |
1808 | 1808.06582_arXiv.txt | The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also a next-to-leading order effect in the phase of gravitational waves emitted by extreme-mass-ratio inspirals (EMRIs), which are expected to become observable by the LISA space mission. Additionally, exploring the Hamiltonian formalism for spinning bodies is important for the construction of the so-called Effective-One-Body waveform models that should eventually cover all mass ratios. The MPD equations require supplementary conditions determining the frame in which the moments of the body are computed. We review various choices of these supplementary spin conditions and their properties. Then, we give Hamiltonians either in proper-time or coordinate-time parametrization for the Tulczyjew-Dixon, Mathisson-Pirani, and Kyrian-Semer{\'a}k conditions. Finally, we also give canonical phase-space coordinates parametrizing the spin tensor. We demonstrate the usefulness of the canonical coordinates for symplectic integration by constructing Poincar{\'e} surfaces of section for spinning bodies moving in the equatorial plane in Schwarzschild space-time. We observe the motion to be essentially regular for EMRI-ranges of the spin, but for larger values the Poincar{\'e} surfaces of section exhibit the typical structure of a weakly chaotic system. A possible future application of the numerical integration method is the inclusion of spin effects in EMRIs at the precision requirements of LISA. | Introduction} The detection of black-hole and neutron-star binary inspirals by the aLIGO and aLIGO-Virgo detectors mark the dawn of gravitational-wave astronomy \citep{gw1,gwkatalog}. The equations of Einstein gravity are put to test not only by the phenomenon and detection of gravitational waves itself, but also by the precise shape of the detected signal \citep{gwtests}. Furthermore, the analysis of the signal from neutron-star binaries provides precious astrophysical information about their composition \citep{gwEOS1,gwEOS2,gwEOS3}, and the observations of the electromagnetic aftermath is key to the explanation of the origin of the energetically unfavorable heavy elements in our Universe \citep{kilonova,r-process}. Upcoming space-based missions such as LISA promise to probe the gravitational-wave spectrum in lower frequencies than terrestrial detectors such as Advanced LIGO and Virgo and, thus, to explore the dynamics of many other types of sources of gravitational radiation \citep{amaro2017}. One such particular class of sources are the so-called extreme-mass-ratio inspirals (EMRIs), during which stellar-mass compact objects spiral into massive black holes, which have masses at least five orders of magnitude above the solar mass \citep{babak2017}. Independent of the mass ratio between the components of the system, neither the primary nor the secondary of the binary can be modeled as point particles in an accurate treatment of the inspiral, and effects of the finite size of the bodies must be taken into account. This is clear in the case of binaries of comparable size and mass, but in the case of EMRIs a more careful argumentation must be given. Let us denote the mass of the primary massive black hole as $M$ and the mass of the secondary stellar-mass object as $\mu$. Then the mass-ratio in EMRIs is $q \equiv \mu/M \sim 10^{-4}-10^{-7}$ and one can describe the gravitational field of the secondary as a perturbation on top of the gravitational field of the primary. As a result, the secondary is usually described as moving on the original background while being subject to a self-force whose relative size with respect to the Christoffel-connection terms is of the order $\mathcal{O}(q)$ \citep[see][for reviews and a complete list of references]{poisson2011,barack2018}. Now consider the effects of the finite size of the secondary. If the secondary is rotating at relativistic speeds, a matter element on its surface will feel a relative acceleration with respect to the center of mass that is proportional to the velocity of the surface $v$, the radius of the object $r$, and the local space-time curvature $R$. Under the assumption of a balance of forces inside the body, this will result in a ``spin force'' $\sim \mu v r R$ acting on the center of mass. Let us further assume that the binary orbital separation is within a few horizon radii of the primary, and that the secondary is either a maximally spinning black hole, a few-millisecond pulsar, or a few-second pulsar. We then get respectively $vrR \sim 1 q/M, 10^{-1} q/M, 10^{-4} q/M$. When we consider that the Christoffel symbols scale as $\sim 1/M$, we see that the relative size of the acceleration caused by the spin force is then $\mathcal{O}(q)$, the same as the gravitational self-force. The effects of the self-force and the spin force on the orbit will thus both scale as $\mathcal{O}(q)$ and would be essentially impossible to distinguish from a geodesic when using observables collected over just a few orbital periods. Nevertheless, the orbit will only decay over $\mathcal{O}(1/q)$ cycles and the small deviations amount to secular effects in the phase of the orbit. The final orbital phase $\phi_\mathrm{f}$ can then be schematically written as a sum of contributions of the form \citep{hinderer2008} \begin{align} \phi_{f} &= \phi^{(1)}_{\mathrm{avg}} && \mathcal{O}(q^{-1}) \\ & + \phi^{(1)}_{\mathrm{osc}} + \phi^{(2)}_{\mathrm{avg}} + \phi^{}_{\mathrm{spin}} && \mathcal{O}(1) \\ & + \phi^{(2)}_{\mathrm{osc}} + \phi^{(3)}_{\mathrm{avg}} + \phi^{}_{\mathrm{quad}} && \mathcal{O}(q) \, \\ & +... && \mathcal{O}(q^2) \,, \end{align} where ``avg'' and ``osc'' stand respectively for contributions from the averaged dissipative, and oscillating dissipative and conservative parts of the self-force computed from the metric perturbations of order $(n)$. Then, at the same order as the first-order conservative piece of the self-force appears the contribution of the spin force. Both the $\mathcal{O}(q^{-1})$ and the $\mathcal{O}(1)$ terms must be eventually included if sub-radian precision is to be achieved in the EMRI wave-form modeling. \revision{Concrete computations of $\phi_\mathrm{spin}$ were carried out by \citet{Warburton2017}, who showed that during the entire length of the inspiral the spin-force can lead to a dephasing as large as 15 cycles as compared to a waveform where the spin-force was neglected.} The $\mathcal{O}(q)$ contributions to the phase then contain the contribution of the next-to-leading effect of the finite size of the secondary, the quadrupolar coupling. In particular, this will include the spin-induced quadrupole that scales as $\sim S^2$ for neutron stars and black holes \citep{hansen1974,laarakkers1999,steinhoff2015}, where $S \sim \mu r v$ is the spin magnitude. Tidal deformation of the body also formally appears in the quadrupole; however, it can be estimated to enter the equations of motion at relative order $\mathcal{O}(q^4)$ \citep{damour2009,binnington2009,steinhoff2012} and it will thus enter the phase only at $\mathcal{O}(q^3)$ for conservative effects and perhaps at $\mathcal{O}(q^2)$ if the dissipative tidal effects contribute to the orbital decay time. In summary, we see that the spin-curvature coupling considered at least to linear order is an indispensable piece of any EMRI model. However, the spin-curvature coupling also plays an important role in the post-Newtonian (weak-field and slow-motion) description of comparable-mass binaries \cite{Blanchet2013, Schafer2018}; the conservative dynamics includes all fourth-order spin-induced effects so far \cite{Levi2016}. But still, a wave-form model that encompasses mass ratios from comparable to extreme is highly desirable. This is one goal of the effective-one-body (EOB) model \cite{Buonanno1998,Bohe2016,Nagar2018,Buonanno2014,Damour2016}, being probably the best candidate to succeed in this endeavor. While incorporating all $\mathcal{O}(1)$ self-force effects is progressing \cite{Akcay2012}, one flavor of EOB models already incorporates the test-spin force on a Kerr background to linear order in the test-spin via a Hamiltonian \cite{barausse2009,Bohe2016}, the central piece encoding the conservative dynamics in any EOB model (but see the progress of the other EOB flavor in Refs. \citep{Damour2014,Harms2016,Kavanagh2017,Bini2018}). In this context, exploring simplified Hamiltonian descriptions of spinning bodies appears to be crucial. In this paper, we study the Hamiltonian formalism for a spinning particle moving in a given space-time metric. \revisiontwo{The so-called Mathisson-Papapetrou-Dixon (MPD) equations, which capture the effects of the spin-force on the orbit, clearly form a conservative system. However, their relation to the Hamiltonian formalism was previously established only partially. The MPD equations require a condition that specifies the referential world-line inside the body, the so-called spin supplementary condition. We complete the previous works \cite{barausse2009,vines2016} by providing Hamiltonians for all commonly used covariant or ``comoving'' supplementary conditions. Additionally, we map the corresponding phase space with canonical coordinates, which allows for efficient numerical integration. An important part of our paper is a discussion of the physical and redundant ``spin-gauge'' degrees of freedom that appear in the equations. In particular, we obtain simple and elegant expressions at the cost of a spin-gauge degree of freedom remaining in our phase space. } In Section \ref{sec:mpd} we review the MPD equations and their properties under various supplementary spin conditions. We then proceed to the Hamiltonian formalism in Section \ref{sec:ham}. We present the Poisson brackets and various sets of variables that can be used during the evolution, and Hamiltonians for all the usual comoving supplementary conditions both in proper-time and coordinate-time parametrizations. Next, in Section \ref{sec:canon}, we also give a set of canonical coordinates covering the spin tensor. Finally, in Section \ref{sec:plan}, we demonstrate the power of the new coordinates and Hamiltonian formalism by numerically studying spinning particles moving in the equatorial plane of a Schwarzschild black hole. The paper also contains a number of Appendices that provide context to the presented results and details of the derivations mentioned in the main text. We use the $G=c=1$ geometrized units and the (-+++) signature of the metric. Our convention for the Riemann tensor $R^{\mu}_{\;\nu\alpha\beta}$ is such that $2 a_{\mu;[\alpha\beta]} = R^{\nu}_{\;\mu\alpha\beta} a_{\nu}$ for a generic $a_\mu$, or explicitly $R^{\mu}_{\;\nu\alpha\beta} = 2 \Gamma^{\mu}_{\;\rho [\alpha} \Gamma^{\rho}_{\;\beta] \nu} -2 \Gamma^{\mu}_{\;\nu [\alpha , \beta]}$. The anti-symmetrization of a tensor is written as $W_{[\alpha\beta]}=\frac{1}{2}\left(W_{\alpha\beta} -W_{\beta\alpha} \right)$, while the symmetrization as $W_{(\alpha\beta)}=\frac{1}{2}\left(W_{\alpha\beta} +W_{\beta\alpha} \right)$. We denote the covariant time derivative by an overdot, $\dot{A}^{\mu \nu...}_{\gamma \delta ...} \equiv \mathrm{D} A^{\mu \nu ...}_{\gamma \delta ...}/ \di \tau \equiv A^{\mu \nu ...}_{\gamma \delta ...;\kappa} \dot{x}^\kappa$. $\eta^{\mu\nu}$ with any indices is the Minkowski tensor, and ${\delta^\mu}_\nu$ denotes the Kronecker delta. | In this paper we have built the Hamiltonian formalism for spinning particles under all commonly used ``comoving'' supplementary conditions, that is, conditions that utilize only the local dynamics of the body and no background vector field. The full set of canonical coordinates that we provide is the minimal set of variables needed to evolve the Mathisson-Pirani and Kyrian-Semer{\'a}k conditions. Hence, our formalism allows to integrate the respective equations at peak efficiency. However, the canonical coordinates contain a redundant degree of freedom for the case of the Tulczyjew-Dixon condition. Nevertheless, a pair of extra variables to be evolved in a numerical routine is a small price to pay for the long-term quality of the evolution such as the one seen in Section \ref{sec:plan}. Of course, it would be interesting to see whether a minimal set of canonical coordinates can be found for the Tulczyjew-Dixon condition. In principle, this can be achieved by constraining the Poisson bracket similarly to \citet{barausse2009}, and by finding the canonical basis thereof. However, the constraint procedure introduces non-zero commutation relations between momenta, space-time coordinates, and spin degrees of freedom. Consequently, the canonical coordinates would in fact be an intricate transformation of all $p_\mu,x^\mu, S^{AB}$. We plan to investigate this possibility in future work. Another less obvious application of the canonical coordinates is the fact that now we are able to formulate a Hamilton-Jacobi equation by making the action $\mathcal{S}$ also a function of the spin angles $\psi,\phi$ with the gradients defining the conjugate momenta $\mathcal{S}_{,\phi} = A,\, \mathcal{S}_{, \psi} = B$. We are currently preparing a manuscript presenting solutions to the Hamilton-Jacobi equation in black hole space-times. Similarly, we believe that the herein presented formalism can be very useful to the various averaging and two-timescale approaches to EMRIs \citep{hinderer2008,pound2008,mino2008,van2018} since we can easily construct action-angle coordinates in the spin sector and thus provide an elegant treatment of the non-dissipative (``fast'') part of the dynamics of the binary. Furthermore, the simplicity of the Hamiltonian under the Kyrian-Semer{\'a}k condition makes it an attractive alternative to the Hamiltonian of \citet{barausse2009} in EOB models \cite{barausse2010}. | 18 | 8 | 1808.06582 |
1808 | 1808.07499_arXiv.txt | {Analysing the kinematics of filamentary molecular clouds is a crucial step towards understanding their role in the star formation process. Therefore, we study the kinematics of 283 filament candidates in the inner Galaxy, that were previously identified in the ATLASGAL dust continuum data. The \ccol and \cool data of the SEDIGISM survey (Structure, Excitation, and Dynamics of the Inner Galactic Inter Stellar Medium) allows us to analyse the kinematics of these targets and to determine their physical properties at a resolution of $30\arcsec$ and $\rm 0.25~km\,s^{-1}$. To do so, we developed an automated algorithm to identify all velocity components along the line-of-sight correlated with the ATLASGAL dust emission, and derive size, mass, and kinematic properties for all velocity components. We find two-third of the filament candidates are coherent structures in position-position-velocity space. The remaining candidates appear to be the result of a superposition of two or three filamentary structures along the line-of-sight. At the resolution of the data, on average the filaments are in agreement with Plummer-like radial density profiles with a power-law exponent of $p \approx 1.5 \pm 0.5$, indicating that they are typically embedded in a molecular cloud and do not have a well-defined outer radius. Also, we find a correlation between the observed mass per unit length and the velocity dispersion of the filament of $m \propto \sigma_\text{v}^2$. We show that this relation can be explained by a virial balance between self-gravity and pressure. Another possible explanation could be radial collapse of the filament, where we can exclude infall motions close to the free-fall velocity.} | Filamentary structures play an important role in the process of star formation. Observations at different wavelengths based on various tracers have revealed that filaments are ubiquitous in the interstellar medium \citep[e.g., ][]{Schneider1979, Molinari2010, Andre2010, Schisano2014, Ragan2014, Li2016b}. Filaments are seen in quiescent and star-forming clouds, in which a significant fraction of pre-stellar cores are located \citep{Andre2010}. Filamentary structures have wide ranges of masses ($\rm \sim 1\text{ -- }10^5 \, M_\odot$) and lengths ($\rm \sim 0.1\text{ -- }100 \, pc$) \citep[e.g., ][]{Bally1987, Jackson2010, Arzoumanian2011, Hernandez2012, Hacar2013, Kirk2013, Palmeirim2013, Li2016b, Kainulainen2013a, Beuther2015, Kainulainen2016, Abreu-Vicente2016, Zucker2017}. The processes of filament formation and filament fragmentation to star-forming cores are not well understood. Because of the wide range of filament size scales and masses these processes might also differ among filaments. High-resolution magnetohydrodynamical simulations of molecular cloud evolution and filament formation show subsonic motions in the inner dense regions of filaments, but the surrounding low density gas is supersonic \citep{Padoan2001,Federrath2016}. Additionally, accretion flows along and radially onto the filament have been seen in observations and simulations \citep{Schneider2010, Peretto2013,Peretto2014a,Henshaw2014,Smith2015}. Therefore, the formation and evolution of filaments is a highly dynamical process and to constrain it is essential to study their kinematics. Studies of filaments have targeted mainly sources in nearby star-forming regions, e.g. Orion, Musca and Taurus \citep{Bally1987,Takahashi2013,Hacar2015,Kainulainen2015,Kainulainen2017}, where high resolution data ($\rm \sim 0.01~pc$, $\rm 0.1~km\,s^{-1}$) reveals sub-structures like fibers \citep{Hacar2013, Hacar2018}, or prominent mid-infrared extinction structures, e.g. ``Nessie'' and infrared dark clouds like G11.11$-$0.12 \citep{Johnstone2003,Pillai2006,Schneider2010,Jackson2010,Kainulainen2013a,Henshaw2014,Mattern2018a}. Detailed studies of these filaments led us to recognize their important role in star formation, and their internal structure, but studies of small samples do not allow to draw general conclusions. In particular the filaments towards the more distant, typically high-mass star forming regions have not yet been systematically studied. Therefore, it is necessary to study a large unbiased sample of filaments. Such studies have recently become feasible because of modern multi-wavelength surveys, which cover the Galactic plane at high resolution and sensitivity. Several catalogues of filamentary structures have been conducted in the last years, which can be divided in two groups. The filaments in the catalogues of \cite{Schisano2014,Koch2015,Li2016b} were identified from continuum data and therefore, miss the kinematic information, and might be affected by line-of-sight projection effects. The catalogues of \cite{Ragan2014,Zucker2015,Abreu-Vicente2016,Wang2015, Wang2016} concentrate on the longest filamentary structures in the Galaxy. While the identification methods and criteria vary in these studies, all filaments are tested for a velocity coherent behaviour. In this study, we target the largest catalogue of filamentary structures published so far \citep{Li2016b}, which is based on the ATLASGAL survey at $\rm 870 \mu m$ \citep{Schuller2009}. As these structures were identified in continuum dust emission data, the scope of this work is to use the SEDIGISM data \citep{Schuller2017} to assess their velocity structure. Because of the large number of targets, it is necessary to perform the analysis in a fully-automated way, which will be also presented in this work. In this paper, we will refer to the structures identified by \cite{Li2016b} as filament candidates. After the analysis of their velocity structure we will refer to the velocity coherent structures in the filament candidates as filaments, where one filament candidate can consist of multiple filaments. Some of these filaments may not meet the definitions of a filament, as they seem to be composed of a chain of dense clumps, or a dense clump with an elongated low column density environment. However, since filaments fragment, these structures could represent a late phase of evolution and should not be ignored. The structure of the paper is as follows: Section \ref{data} introduces the survey data used in this study and the targeted catalogue of filament candidates. The methods used to separate the velocity components of a given filament candidate and to derive its filament parameters are described in Section \ref{methods}. In Section \ref{results} we present the resulting statistics of the velocity separation and the interpretation of the kinematics. We then discuss in Section \ref{discussion} the dependency of the filament mass with increasing radius, and the origin of the correlation found between the line-mass (mass per unit length) and velocity dispersion of the filaments. Finally, we summarize our results in Section \ref{conclusion}. | \label{conclusion} In this study we studied spectral line emission from 283 filament candidates detected with ATLASGAL continuum dust emission from the catalogue of \cite{Li2016b} in the SEDIGISM \cco and \coo survey. As these candidates can be the result of line-of-sight projection of multiple structures, we tested the candidates for coherence in velocity space and derived the mass, size, and a collection of kinematic properties. To do so we developed an automated analysis tool that finds the different velocity components of a candidate, if existing, separates them and checks for correlation with the original ATLASGAL emission. We found 422 velocity-coherent filaments that correlate completely or partially with the original candidate. For these filaments we find the following: \begin{itemize} \item Two-thirds of the filament candidates are single velocity-coherent structures. The other candidates are line-of-sight projections of mainly two and three velocity components, and up to one candidate with seven velocity components. Also, we found a possible indication for a correlation between the maximum intensity within the filament candidate and the number of velocity components for the integrated \cco and ATLASGAL dust emission, but a flat behaviour is within the uncertainties. \item Comparing the kinematics of the filaments seen in \cco and \coo, we could show that both isotopologues trace the same gas. Differences found in the comparison could be identified as biases arising from low signal-to-noise \coo data. \item The filament profiles are on average in agreement with a Plummer-like density distribution with an exponent of $p \approx 1.5 \pm 0.5$. The inner radius cannot be constrained exactly because of the limited resolution of the data. This low exponent indicates that filaments are typically located within larger molecular clouds, and therefore, the outer radius of a filament cannot be well defined. For the mass estimates we chose a radius which includes the gas that can take part in star formation within the next $\rm 2~Myr$. \item The observed line-mass of the filaments is in agreement with the critical non-thermal line-mass and significantly higher than the critical thermal line-mass. However, we do not know the source of the observed velocity dispersion. Comparing the relation we find between velocity dispersion and line-mass with the theoretical infall velocity profile based on \cite{Heitsch2013} generally does not reveal evidence for free-fall collapse. However, radial infall of the gas onto the skeleton can possibly explain the relation. \end{itemize} In this study we analysed the kinematics of 283 filament candidates, finding 180 reliable velocity coherent filaments, 151 with distance estimates between $\rm 1~kpc$ and $\rm 13~kpc$, and 242 other velocity coherent filamentary structures in the line-of-sight of the candidates, leading to the largest statistics of filament parameters so far. However, due to the spatial resolution of $30\arcsec$ and velocity resolution of $\rm 0.25~km\,s^{-1}$, the derived parameters generally only describe global behaviour of the filaments. As the evolution and fragmentation of filaments is a hierarchical process it will be necessary to also study the smaller scales. High resolution observations to recover the small scales ($\rm < 0.1~pc$) are essential, and this study can be the starting point for the selection of a representative sample for such higher resolution follow-ups. | 18 | 8 | 1808.07499 |
1808 | 1808.02872_arXiv.txt | Active galactic nuclei (AGN) release a huge amount of energy into the intracluster medium (ICM) with the consequence of offsetting cooling and star formation (AGN feedback) in the centers of cool core clusters. The Phoenix cluster is among the most massive clusters of galaxies known in the Universe. It hosts a powerful starburst of several hundreds of Solar masses per year and a large amount of molecular gas in the center. In this work we use the high-resolution Reflection Grating Spectrometer (RGS) on board XMM-\textit{Newton} to study the X-ray emitting cool gas in the Phoenix cluster and heating-cooling balance. We detect for the first time evidence of {O\,\scriptsize{VIII}} and {Fe\,\scriptsize{XXI-XXII}} emission lines, {the latter} demonstrating the presence of gas below 2 keV. We find a cooling rate of $350\pm_{200}^{250}\,M_{\odot}\,{\rm yr}^{-1}$ below 2\,keV (at the 90\% confidence level), which is consistent with the star formation rate in this object. This cooling rate is high enough to produce the molecular gas found in the filaments via instabilities during the buoyant rising time. The line broadening indicates that the turbulence ($\sim300$\,km\,s$^{-1}$ or less) is below the level required to produce and propagate the heat throughout the cool core. This provides a natural explanation for the coexistence of large amounts of cool gas, star formation and a powerful AGN in the core. The AGN activity may be either at a young stage or in a different feedback mode, due to a high accretion rate. | \label{sec:intro} Clusters of galaxies are extraordinary laboratories where highly energetic astrophysical phenomena are in action. The study of the intracluster medium (ICM) embedded in their deep gravitational well allow us to understand the role of the strong energetic throughput from the active galactic nuclei (AGN) present in the individual galaxies into their surroundings over large scales up to a hundred kpc or more. A substantial fraction of galaxy clusters show a highly peaked density profile which implies that the central cooling time can be of an order of magnitude lower than the current age of the Universe (cool core clusters, e.g. \citealt{Hudson2010}). In the absence of heating, this would imply the cooling of hundreds of Solar masses of gas per year below $10^{6}$\,K \citep{Fabian1994} for the massive clusters, with a consequent star formation rate of a similar order of magnitude. The best UV and X-ray indicators of cool gas are O\,{\scriptsize VI} emission lines (peaking at $T\sim3\times10^{5}$\,K), O\,{\scriptsize VII} ($T\sim2\times10^{6}$\,K) and Fe\,{\scriptsize XVII} ($T\sim6\times10^{6}$\,K). High-resolution UV and X-ray spectra of ICM were therefore expected to show bright lines, which instead turned out to be much weaker at levels of about $30\,M_{\odot}$\,yr$^{-1}$ or lower (see e.g. \citealt{Bregman2005,Bregman2006}, \citealt{Peterson2003} and \citealt{Pinto2014}). There is a wealth of highly energetic phenomena occurring in the cores and in the outskirts of clusters of galaxies. Galactic mergers and gas sloshing within the gravitational potential may release large amounts of energy in the outskirts via shocks and turbulence injection (see e.g. \citealt{Ascasibar2006}; \citealt{Lau2009}). However, there is a growing consensus that AGN are the most relevant sources of heating in cluster cores, particularly through their powerful relativistic jets (AGN kinetic / radio mode feedback, see e.g. \citealt{Churazov2000} and \citealt{Fabian2012}). For instance, the work done by AGN to inflate bubbles in the surrounding ICM gas proves to be equal if not stronger than the cooling rates \cite{McNamara2007}. There are several mechanisms through which the energy can be released into the ICM. Two elegant solutions involve dissipation of turbulence \citep[see e.g.][]{Zhuravleva2014} or sound waves (see e.g. \citealt{Fabian2003_waves, Fabian2017sw}). There seems to be evidence that the extreme radio mode of AGN feedback has been operating in a steady way for the past 5 Gyr (see, e.g., \citealt{Hlavacek-Larrondo2012} and \citealt{McDonald2013}), but this research field is still rather young and in development. Measurements of AGN-induced turbulence are therefore key to test whether some scenarios of AGN feedback and cooling-heating balance are feasible. This is crucial to understand if there is enough energy in the ICM to propagate the heat throughout the cool core. It is possible to place constraints on turbulence by measuring the velocity broadening of the X-ray emission lines produced by the hot ICM. The Reflection Grating Spectrometers (RGS, \citealt{denherder2001}) on board XMM-\textit{Newton} are currently the only X-ray instruments which have enough collecting area and spectral resolution to enable this measurement. However, this is not very straightforward because the spectrometers do not possess an appropriate slit and therefore instrumental broadening has to be accounted for. \citet{Sanders2010} made the first measurement of cluster velocity broadening using the luminous cluster A\,1835 at redshift 0.25. Due to the limited spatial extent of its bright core, instrumental broadening was minimal and an upper limit of 274\,km\,s$^{-1}$ was obtained. \citet{Sanders2011} constrained turbulent velocities for a large sample of 62 clusters, groups, and elliptical galaxies observed with XMM-\textit{Newton}/RGS. Half of them show velocity broadening below 700\,km\,s$^{-1}$. Recently, \citet{Sanders2013} used continuum-subtracted emission line surface brightness profiles to account for the spatial broadening. \citet{Pinto2015} focused on nearby objects using a catalog of 44 sources, the CHEERS sample, consisting of bright clusters, groups of galaxies, elliptical galaxies with a $\gtrsim5\sigma$ detection of the O\,{\scriptsize VIII} 1s--2p line at 19\,{\AA} and with a well-represented variety of strong and weak cool-core objects. They confirmed the results obtained by \citet{Sanders2013} in more distant objects despite the more severe instrumental broadening due to the short distances ($z<0.1$). \citet{Pinto2015} also showed that the upper limits on the Mach numbers are typically larger than the values required to balance cooling, suggesting that dissipation of turbulence may be high enough to heat the gas and to prevent cooling. Turbulence in giant elliptical galaxies has also been constrained with an alternative method which uses the ratio of the Fe\,{\scriptsize{XVII}} emission lines detected in the RGS spectra (see, e.g., \citealt{Werner2009}, \citealt{dePlaa2012}, \citealt{Pinto2016mnras}, \citealt{Ogorzalek2017}). When the velocity broadening is low, the gas is optically thick in the 15\,{\AA} line due to resonant scattering, while the 17\,{\AA} lines remain optically thin. Comparison between the observed line ratios with simulations for different Mach numbers constrains the level of turbulence. This method is very efficient for cool ($kT<0.9$\,keV) giant elliptical galaxies rich in Fe\,{\scriptsize{XVII}} emission lines, but it is significantly limited by the systematic uncertainty ($\sim$20\%) in the line ratio for an optically thin plasma. Currently, there are no facilities that allow the use of this technique on clusters of galaxies since the optical depth of the higher ionisation lines, typical of clusters, are smaller than those of the Fe\,{\scriptsize{XVII}} lines or they are out of the RGS energy band. Another alternative method to constrain turbulence interprets the surface brightness fluctuations commonly seen in X-ray atmospheres of clusters as turbulent fluctuations (see, e.g., \citealt{SandersFabian2012}, \citealt{Zhuravleva2014}, \citealt{Walker2015} and \citealt{Eckert2017}). The measurements imply motions of one to a few hundred km\,s$^{-1}$. As of today, and likely for the next years until the launch of missions like \textit{XRISM} (a.k.a. XARM) and \textit{ATHENA} (for a review see, e.g., \citealt{Nandra2013} and \citealt{Guainazzi2018}), the most accurate measurement of line broadening and, therefore, constraint on turbulence, has been obtained by the {\textit{Hitomi}} observations of the Perseus cluster of galaxies \citep{Hitomi2016nat}. The soft X-ray microcalorimeter (SXS) onboard {\textit{Hitomi}}, the first successfully operative in space, measured an average line broadening of $164\pm10$\,km\,s$^{-1}$ in a region between 30 and 60 kpc from the central AGN, thanks to an astonishing and unprecedented high spectral resolution of 4.9\,eV in the Fe K energy band. Further work accounting for PSF effects showed that in several regions of the cluster core the turbulence could be lower than 100 km\,s$^{-1}$ \citep{Hitomi2017atm}. These motions may not be able to propagate throughout the cluster rapidly enough to offset radiative losses at each radius of the cluster \citep{Fabian2017sw}. In parallel work (Pinto et al. in prep) we have made a large catalog using all the XMM-\textit{Newton} observations of clusters and groups of galaxies and ellipticals. The main goal is to constrain turbulence and other physical characteristics of a statistical sample of 150 galaxy clusters up to redshift 0.6 using high-resolution RGS spectra. This catalog includes and significantly extends what was previously done in \cite{Sanders2013} and \citet{Pinto2015}. We also use a new technique to account for instrumental broadening that has been introduced in a very recent paper \citep{Bambic2018}. It was tested on three clusters at different redshifts with an observation quality among the best in our sample (A\,1835, A\,2204, and MACS\,J2229.7-2755). Upper limits of 200--250\,km\,s$^{-1}$ were obtained on turbulence, confirming that it might be not high enough to propagate the heat throughout the cool core. In this work we study the Phoenix cluster (SPT-CLJ2344-4243), the most distant object in our XMM-\textit{Newton}/RGS catalog ($z=0.596$), the most luminous X-ray cluster known and one of the most massive clusters ($\sim 2\times10^{15}\,M_{\odot}$, see \citealt{Williamson2011} and \citealt{McDonald2012}). It also exhibits a starburst of $500-800\,M_{\odot}\,{\rm yr}^{-1}$ (see, e.g., \citealt{McDonald2015} and \citealt{Mittal2017}), which is among the largest found in the local Universe ($z<1$). \citet{McDonald2015} found large amounts of mildly-ionized gas, such as {\heii}, {\oiii} and {\ovi}, which is not consistent with cooling but rather suggests that an ionized wind is driven by the AGN and/or the starburst. ALMA observations of the CO(3-2) line emission have shown a huge amount of molecular gas around $2\times10^{10}\,M_{\odot}$ (\citealt{Russell2017}). The molecular gas might have been uplifted directly by the radio bubbles or formed via instabilities in low entropy gas lifted by the jet. \citet{Tozzi2015} observed the Phoenix cluster for 250 ks with XMM-\textit{Newton} and found a cooling rate between 100--1000\,$M_{\odot} {\rm yr}^{-1}$ with the large uncertainties mainly driven by the calibration between the CCD cameras on board the satellite combined with their low spectral resolution. They also used the RGS gratings and claimed to have not found any lines from ionization states below {Fe\,\scriptsize{XXIII}} with an upper limit on the cooling rate of about $500\,M_{\odot}\,{\rm yr}^{-1}$ below 3\,keV. The presence of a high star formation, a high cooling rate and a powerful AGN in the Phoenix cluster casts doubts on the efficiency of AGN feedback to balance cooling. Therefore, we perform an in-depth study of the XMM-\textit{Newton} observations of the Phoenix cluster with particular focus on the high-resolution spectrometers in order to obtain more accurate measurements of the cooling rate and the turbulent broadening. We find that $350\pm_{120}^{150} (68\%) \pm_{200}^{250} (90\%)\,M_{\odot}\,{\rm yr}^{-1}$ are cooling below 2\,keV in the cluster core and that the turbulence level is likely not adequate to fully propagate AGN heating throughout the cool core. The cooling rate is instead high enough to produce the large amount of molecular gas found in the form of filaments if we assume that the gas cools during the bubble rising time. We present the data in Sect.\,\ref{sec:data} and the spectral modeling in Sect.\,\ref{sec:spectral_modeling}. We discuss the results in Sect.\,\ref{sec:discussion} and give our conclusions in Sect.\,\ref{sec:conclusion}. \begin{table} \caption{XMM-\textit{Newton} and \textit{Chandra} log of observations.} \label{table:log} % \renewcommand{\arraystretch}{1.1} \small\addtolength{\tabcolsep}{-4pt} \centering \scalebox{1}{% \begin{tabular}{cccc|ccc} \hline OBS\_ID & t$_{\rm RGS}$\,$^{(a)}$ & c$_{\rm RGS}$\,$^{(c)}$ & t$_{\rm MOS}$\,$^{(b)}$ & & OBS\_ID & t$_{\rm ACIS}$\,$^{(d)}$ \\ (XMM) & (ks) & (counts) & (ks) & & \textit{Chandra} & (ks) \\ \hline 0693661801 & 16.5 & 1.8k & 16.1 & & 13401 & 11.9 \\ 0722700101 & 130.6 & 14.1k & 128.0 & & 16135 & 57.3 \\ 0722700201 & 93.0 & 10.1k & 92.0 & & 16545 & 59.1 \\ \hline \end{tabular}} $^{(a)}$ RGS1, RGS2 and $^{(b)}$ MOS1 net exposure time. \\ $^{(c)}$ RGS total counts and $^{(d)}$ ACIS-I net exposure time. \end{table} \section[]{The data} \label{sec:data} The observations used in this paper are listed in Table~\ref{table:log}. The XMM-\textit{Newton} satellite is provided with two main X-ray instruments: RGS (Reflection Grating Spectrometer) and EPIC (European Photon Imaging Camera). We use RGS for the spectral analysis and EPIC (MOS\,1 detector, which is aligned with RGS) for imaging. The EPIC/MOS\,1 surface brightness profiles are necessary to account for line instrumental broadening due to the slitless nature of the RGS spectrometers. This is done following the procedures used in \citet{Pinto2015} with important updates shown in \citet{Bambic2018}. We perform the data reduction with the XMM-\textit{Newton} Science Analysis System ({\scriptsize{SAS}}) v16, CalDB as of January 2018. We process the RGS data with the SAS task \textit{rgsproc} and the MOS\,1 data with \textit{emproc} to produce event files, spectra, and response matrices for RGS (both 1 and 2) and images for MOS\,1. Following the standard procedures, we filter the MOS event list for bad pixels, bad columns, cosmic-ray events outside the field of view (FOV), photons in the gaps (FLAG = 0), and apply standard grade selection, corresponding to PATTERN $\leq12$. We correct for contamination from soft-proton flares through the SAS task \textit{evselect} by extracting light curves for MOS\,1 in the 10--12 keV energy band, while we use the data from the CCD number 9 for RGS, where hardly any emission from the source is expected. The light curves are grouped in 100\,s intervals and all the time bins with a count rate above 0.35 c/s and 0.15 c/s are rejected for MOS and RGS, respectively. We build the good time interval (GTI) files with the accepted time events for the MOS and RGS data through the SAS task \textit{tabgtigen} and reprocess the data again with \textit{rgsproc} and \textit{emproc}. For RGS 1 and 2 we join the GTI and obtain the same exposure times. The RGS\,1-2 and MOS\,1 total clean exposure times are quoted in Table\,\ref{table:log}. \subsection[]{RGS spectra} \label{sec:data_spectra} The RGS 1 and 2 spectra are extracted using as centroid $(\alpha, \delta)=(23:44:43.9,-42:43:13.7)$ and a width of 50 arcsec by adopting the mask \textit{xpsfincl} $=90$ in the \textit{rgsproc} ($\sim\pm170$\,kpc for a standard $\Lambda$CDM cosmology with $H_{\rm 0} = 70\,$km\,s$^{-1}$ Mpc$^{-1}$, $\Omega_{\rm M} = 0.27$ and $\Omega_{\rm \Lambda} = 0.73$). In order to subtract the background we test both the standard background spectrum which is extracted beyond the 98\% of the RGS point spread function (PSF, \textit{xpsfexcl} $=98$ in the \textit{rgsproc}) and the model background spectrum, which is a template background file based on the count rate in CCD\,9. Normally one would use the model background for an extended source, but due to the large distance we can safely use the observation background since it is extracted beyond $\pm1.4'$. The background spectra are indeed comparable, provide consistent results and about 26,000 net source counts in the RGS 6--33\,{\AA} wavelength band. {More detail on the background is provided in Appendix\,\ref{sec:appendix}.} \begin{figure} \includegraphics[width=1\columnwidth, angle=0]{Fig_Phoenix_RGS_spectrum_black.pdf} \caption{RGS spectrum of the Phoenix cluster with overlaid an isothermal model of gas in collisional equilibrium (red) and a two-temperature model (black). Emission lines commonly detected in RGS spectra of cool core clusters are labelled at the observed wavelengths {with the blue dashed ones referring to lines from cool gas. Bottom plots show the residuals to each model. Note how the second component improves the fit near the {Fe\,\scriptsize{XVII}} and {Fe\,\scriptsize{XXI-XXII}} main transitions.}} \label{Fig:Phoenix_RGS_spectrum} \end{figure} The spectra are converted to the {\scriptsize SPEX}\,\footnote{www.sron.nl/spex} format through the {\scriptsize SPEX} task \textit{trafo}. During the spectral conversion, we choose the option of \textit{sectors} in the task \textit{trafo} to create as many sectors as there are different exposures. This permits us to simultaneously fit the multiple RGS spectra by choosing which parameters to either couple or unbind in the spectral models of different observations. We focus on the first-order spectra because the second-order spectra have too poor statistics. We also combine source and background spectra, and responses from all observations and from both RGS instruments using the SAS task \textit{rgscombine} for plotting purposes only. The stacked spectrum is shown in Fig.\,\ref{Fig:Phoenix_RGS_spectrum} labelling the rest-frame wavelengths of the strongest emission lines commonly found in deep RGS spectra of clusters and groups of galaxies. \subsection[]{MOS images} We produce MOS\,1 images in the $6-35$\,{\AA} wavelength band (see Fig.\,\ref{Fig:Phoenix_MOS_image}), which is the same range used for the RGS spectroscopy, and extract surface brightness profiles to model the RGS line spatial broadening with the standard dispersion equation: \begin{equation} \label{Eq:disp} \Delta\lambda = 0.138 \, \Delta\theta \, {\mbox{\AA}} / m, \end{equation} where $\Delta\lambda$ is the wavelength broadening, $\Delta\theta$ is the source extent in arcseconds and $m$ is the spectral order (see the XMM-\textit{Newton} Users Handbook). The surface brightness is extracted using a region of $50''$ width and a length of $10'$ with the {\scriptsize SPEX} task \textit{rgsvprof} (see, e.g., \citealt{Pinto2015}). The RGS instrumental line broadening as measured through the MOS\,1 surface brightness profile of the Phoenix cluster is shown in Fig.\,\ref{Fig:Phoenix_MOS_profile} (black solid line). We also fit the broadening profile with 3 different models using {\scriptsize QDP/PLT\footnote{https://wwwastro.msfc.nasa.gov/qdp/}}: a single Gaussian, two Gaussian and three Gaussian lines. The single Gaussian line and the narrowest Gaussian of the multi component models are also shown in Fig.\,\ref{Fig:Phoenix_MOS_profile}, but renormalized for plotting purposes. \begin{figure} \centering \includegraphics[width=0.9\columnwidth, angle=0]{Fig_Phoenix_ds9_image.pdf} \caption{EPIC/MOS\,1 image of the Phoenix cluster with the RGS extraction region of width of 50 arcsec.} \label{Fig:Phoenix_MOS_image} \end{figure} \begin{figure} \centering \includegraphics[width=0.95\columnwidth, angle=0]{Fig_IDL_spatial_profiles.pdf} \caption{RGS line spatial broadening as computed through the MOS\,1 surface brightness profile and Eq.\,\ref{Eq:disp}. The lines show the narrowest Gaussian obtained by fitting three different models with either one or two or three Gaussian lines.} \label{Fig:Phoenix_MOS_profile} \end{figure} | \label{sec:conclusion} The Phoenix cluster (SPT-CLJ2344-4243) is the most luminous X-ray cluster known and the most distant cluster observed with high-resolution X-ray spectrometers. It exhibits an outstanding starburst of $500-800\,M_{\odot}\,{\rm yr}^{-1}$, which is among the largest found in the local Universe ($z<1$), and an AGN inflating bubbles via powerful radio jets. The presence of high star formation and cooling rates in combination with a powerful AGN is puzzling if compared to the low rates shown by nearby cooling core clusters. In this work, we perform an in-depth study of the XMM-\textit{Newton} observations of the Phoenix cluster with particular focus on the high-resolution spectrometers in order to obtain accurate measurements of the cooling rate and turbulent broadening. We find that about $220-480\,M_{\odot}\,{\rm yr}^{-1}$ are cooling below 2\,keV in the cluster core, in broad agreement with the estimates of star formation rate, and that the turbulence level is likely not adequate to fully propagate AGN heating throughout the cool core. This provides a natural explanation for the coexistence of a large amounts of cool gas, star formation and a powerful AGN in the Phoenix cluster. However, the comparison with nearby, more quiescent, cool core clusters suggests that the discrepancy is likely due to either to the younger age of the Phoenix cluster, and therefore of the BCG AGN feedback activity, or the accretion rate on the supermassive black hole and the feedback mode. Future missions such as \textit{ATHENA} and \textit{XRISM} will boost the accuracy in measuring crucial parameters in X-ray spectra of clusters of galaxies. In particular, we show that for Phoenix-like clusters it is possible to obtain excellent results - such as a 5\,$\sigma$ detection of turbulence - with short snapshots of about 10ks exposure. | 18 | 8 | 1808.02872 |
1808 | 1808.06726_arXiv.txt | text{ In this paper we introduce a software package, the Very Long Baseline Interferometry Network SIMulator (VNSIM), which provides an integrated platform assisting radio astronomers to design the Very Long Baseline Interferometry (VLBI) experiments and evaluate the network performance with a user-friendly interface. Though VNSIM is motivated to be designed for the East Asia VLBI Network, it can also be expandable to other VLBI networks and generic interferometers. The software package not only integrates the functionality of plotting $(u,v)$ coverage, scheduling the observation, and displaying the dirty and CLEAN images, but also further extends to add new features such as the sensitivity calculation of a certain network and multiple-satellite space VLBI simulations which are useful for future space VLBI mission. In addition, VNSIM provides flexible interactions on both command line and graphical user interface and offers friendly support for log report and database management. VNSIM also supports multiprocessing accelerations, enabling to handle large survey data. To facilitate the future development and update, each simulation function is encapsulated in different Python module allowing for independently invoking and testing. In order to verify the performance of VNSIM, we have carried out various simulations and compared the results with other simulation tools. All tests show good consistency. } \begin{document} \jkashead % | East Asia Very Long Baseline Interferometry (VLBI) Network \citep[EAVN,][]{bgEavn}, consisting of 21 radio telescopes from China, Japan and South Korea, has been astronomically operational since mid -2018. The diverse sub-array configurations and frequency setups of the EAVN make it cover a wide range of research areas including astronomical masers (e.g. hydroxyl, methanol, water and SiO masers in Galactic objects and extragalactic megamasers as well), jets of active galactic nuclei, pulsars and transients (e.g. supernovae, gamma-ray bursts), space exploration and tracking, astrometry and geodesy. The EAVN is expected to promote the regional collaborations in East Asia. Such academic collaborations will offer great opportunities to expand the discovery fields in astronomy and space science, and form a successful model of international academic collaborations with a sustainable operation scheme. Along with the formal operation of the EAVN, a set of user assistance software, having functions of evaluating the network performance, would be helpful for users to prepare proposals and necessary for expanding the user community. The diversity and versatility of the EAVN configurations demand such a tool to be sufficiently flexible and expandable. Currently, there are a number of auxiliary tools used in the VLBI community for different simulation purposes. SCHED\footnote{http://www.aoc.nrao.edu/software/sched/} designed by the National Radio Astronomy Observatory (NRAO) of the US, is commonly used for scheduling VLBI observations. It supports plotting the $(u, v)$ coverage of a given array and time range, the corresponding dirty beam, and displaying the telescope elevation angle change with time which assists scientists to choose proper telescopes. SCHED can also show multiple source scans in time sequence, which facilitates the arrangement of time blocks to optimize the $(u, v)$ coverage within the allocated time period. Since SCHED is configured through importing a pre-defined 'key' file, any parameter change or setup adjustment requires restarting the program. Difmap \citep{softDifmap} is largely used to analyze VLBI data, as a part of the Caltech VLBI Analysis Programs \citep{bgVLBI1, bgVLBI2}. It is characteristic of interactive operations with editing, hybrid imaging, self-calibration and automated pipeline capacities. Difmap provides both scripting language and commands for operations. Although these software packages have been and are still widely used in VLBI community, the architecture and algorithms of SCHED and Difmap are slightly outdated. The aperture synthesis simulator (APSYNSIM) \citep{softApsynsim} is a Python-based software package, providing an interactive tool to visualize the aperture synthesis and perform educational level simulations which are very useful for non-radio astronomers. Besides these auxiliary tools for ground-based VLBI networks, some other software packages were developed with additional functions specially to adapt to space VLBI. These include: the Space VLBI Assistance Software (SPAS) developed by the Satellite Geodetic Observatory of the Institute of Geodesy \citep{softSpas} and {\it Fakesat} \citep{bgfakesat} for VLBI Space Observatory Programme \citep{bgVsop} proposal preparation; Astronomical Radio Interferometer Simulator (ARIS) developed by the Japan Aerospace Exploration Agency \citep{softAris1, softAris2} for Japan's second-generation space VLBI project VSOP2, which adds some new functions to assess the impacts of a variety of error sources on the image quality; the FakeRat software package developed by Astro Space Center of the Lebedev Physical Institute \citep{softFaset} and used for the Russia RadioAstron \citep{bgRadio} space VLBI mission. Since these works are dedicate for specific space missions, thus their general versatility is relatively limited. Shanghai Astronomical Observatory of China once proposed the space millimeter-wavelength VLBI array (SMVA) programme which for the first time involves two space satellites onboard 10-m radio telescopes operated at the highest frequency of 43GHz \citep{bgHong}. In order to support this SMVA, a simulation software \citep{softShaouv} was designed to provide fundamental space-ground and space-space VLBI $(u,v)$ coverage simulations. The major functions of these existing software packages which are adapted for specific applications have been discussed and compared in \citet{softShaouv}. For these tools to work for a new VLBI network such as the EAVN, major modifications have to be made. Moreover, a module-independent, highly scalable, flexible, and user-friendly solution, combining the advantages of each individual software and data-modifying flexibility, is highly desirable. For this purpose, we developed a new software package, VLBI Network SIMulator (VNSIM), which integrates most commonly-used simulation programs and offers assistance for radio astronomers. It is a cross-platform Python-based software package with high scalability and reusability. Each function has been separately designed and independently implemented for the sake of future extension. In addition to common simulation functions, VNSIM also augments some extended functions such as displaying all-year-round $(u,v)$ plots to track the space VLBI $(u,v)$ coverage changes due to the satellite orbit precession and presenting $(u,v)$ plots of multiple sources along with their dirty maps so as to evaluate the imaging performance. The data of stations and sources are dynamically managed by the SQLite database, and the parameter configuration can either be saved and loaded directly or be set up through the interactive graphical interfaces. The data processing with multiple processing accelerations is also adopted, significantly enhancing the execution performance of large survey data. The simulations of EAVN are performed in a straightforward way. Although VNSIM is initially designed for EAVN, it is naturally adapted to other VLBI networks or other generic interferometers. The remaining part of this paper is organized as follows. Section 2 describes the overall designing concept of VNSIM. Details of the main functions are presented in Section 3. In Section 4, we demonstrate some examples of the major functionality of VNSIM and also compare the experimental results with other tools. A summary is given in Section 5. | In this paper, we have introduced an auxiliary tool aiding VLBI network simulations, named as VNSIM. The motivation is to provide an integrated software package to help radio astronomers to make observation schedule and to gain a preliminary evaluation of the interferometer performance. Compared with the existing simulation tools, VNSIM not only integrates commonly used functions but also supplements new features supporting large surveys containing multiple sources. Another new feature is the space VLBI simulation which supplies valuable guidance to future space VLBI missions. Details of the space VLBI $(u,v)$ coverage simulation will be presented in a forthcoming paper. By design, VNSIM is not limited to VLBI networks, but is in general applicable to connected-element interferometers, such as VLA. Considering the usability for non-VLBI astronomers without much interferometric knowledge, VNSIM has been designed to be more friendly in user interfaces and more convenient in database management. All kinds of parameters can also be user specified to investigate more simulation scenarios. The comparison of the simulation results from VNSIM with other tools verified the consistency between them. The current version of VNSIM provides functionality matching the astronomers' basic requirements for scheduling and evaluating ground-based interferometric observations. More sophisticated functions are under development. In the future version, we aim to provide more precise space VLBI simulation with realistic constraints and complete scheduling plans. | 18 | 8 | 1808.06726 |
1808 | 1808.05796_arXiv.txt | {} % {We use parallax data from the \it Gaia \rm second data release (GDR2), combined with parallax data based on \it Hipparcos \rm and \it HST \rm data, to derive the period -- luminosity -- metallicity ($PLZ$) relation for Galactic classical cepheids (CCs) in the $V$, $K$, and Wesenheit $WVK$ bands. } {An initial sample of 452 CCs are extracted from the literature with spectroscopically derived iron abundances. Reddening values, classifications, pulsation periods, and mean $V$- and $K$-band magnitudes are taken from the literature. Based on nine CCs with a goodness-of-fit (GOF) statistic smaller than 8 and with an accurate non-\it Gaia \rm parallax ($\spi$ comparable to that in GDR2), a parallax zero-point offset of $-0.049 \pm 0.018$ mas is derived. Selecting a GOF statistic smaller than 8 removes about 40\% of the sample most likely related due to binarity. Excluding first overtone and multi-mode cepheids and applying some other criteria reduces the sample to about 200 stars. } { The derived $PL(Z)$ relations depend strongly on the parallax zero-point offset. The slope of the $PL$ relation is found to be different from the relations in the LMC at the $3\sigma$ level. Fixing the slope to the value found in the LMC leads to a distance modulus (DM) to the LMC of order 18.7 mag, larger than the canonical distance. The canonical DM of around 18.5 mag would require a parallax zero-point offset of order $-0.1$ mas. Given the strong correlation between zero point, period and metallicity dependence of the $PL$ relation, and the parallax zero-point offset there is no evidence for a metallicity term in the $PLZ$ relation. } {The GDR2 release does not allow us to improve on the current distance scale based on CCs. The value of and the uncertainty on the parallax zero-point offset leads to uncertainties of order 0.15 mag on the distance scale. The parallax zero-point offset will need to be known at a level of 3~$\mu$as or better to have a 0.01 mag or smaller effect on the zero point of the $PL$ relation and the DM to the LMC. } | Classical Cepheids (CCs) are considered important standard candles because they are bright and thus the link between the distance scale in the nearby universe and that further out via those galaxies that contain both Cepheids and SNIa (e.g. \citealt{Riess16} for a recent overview on how to get the Hubble constant to 2.4\% precision). Distances to local CCs may be obtained in several ways, for example through direct determination of the parallax (see below) or main-sequence fitting for Cepheids in clusters (e.g. \citealt{Feast1999, Turner10} for overviews). In addition, distances to CCs can be obtained from the Baade--Wesselink (BW) method. This method relies on the availability of surface-brightness (SB) relations to link variations in colour to variations in angular diameters and an understanding of the projection ($p$-) factor, which links radial velocity to pulsational velocity variations. This method is interesting for more distant cepheids where an accurate direct parallax determination is not possible. The most recent works for 70--120 Galactic and about 40 Magellanic Cloud cepheids are by \cite{Storm11a,Storm11b} and \cite{Gr2013}. These papers also investigated the possible metallicity dependence of the period--luminosity ($PL$) relation, which is one of the remaining possible sources of systematic uncertainties in the application of the $PL$ relation to the distance scale. Although the effect is deemed to be subdominant (0.5\% on a total uncertainty of 2.4\% in the determination of the Hubble constant, as stated by \citealt{Riess16}), estimates in the literature for its actual value and error estimate vary considerably and seem to depend on wavelength (see \citealt{Storm11b} and \citealt{Gr2013} for references) and a closer investigation is certainly in order in the general framework of `precision cosmology' and a 1\% accurate Hubble constant. As accurate direct distances to a sizeable number of Galactic Cepheids were unavalaible pre-\G\ the BW method was the only way to investigate this. Both papers agree that the metallicity dependence in the $K$ band is statistically insignificant with the data they had. Storm et al. found a 2$\sigma$ effect in the classical Wesenheit relation based on $V, I$ [$W(VI)= V - 2.55\;(V-I)$)], while Groenewegen found a 2$\sigma$ effect in the $V$ band. These types of questions can be addressed directly when accurate parallaxes are available for a significant sample of Galactic CCs. The Gaia second data release (GDR2, \citealt{GDR2Sum}) extends GDR1 \citep{GC2016a,GC2016b}. The Gaia parallaxes on CCs extend earlier work based on \Hp\ parallaxes \citep{ESA1997,vanL07,vanL07NR,vanL08}, and parallel work using the {\it Fine Guidance Sensor} \citep{Benedict07} and the {\it Wide Field Camera 3} \citep{Riess14,Casertano16,Riess18} on board the {\it Hubble Space Telescope} (HST) for about 20 CCs. In this paper we aim to investigate the $PL$ relation and its possible metallicity dependence based on a sample of Galactic cepheids available in the {\it Gaia} DR2. The paper is structured as follows. In Section~\ref{S-PRE} the collection of photometric, reddening, metallicity, and other data from the sample is described. Section~\ref{S-GDR2} describes the data taken from GDR2, and compares periods and classifications from the literature with those provided in GDR2. The method used in the analysis in described in Section~\ref{S-Ana}, and tested with simulations in Section~\ref{S-Sim}. Section~\ref{S-Res} presents the results which are summarised and discussed in Section~\ref{S-Dis}. | \label{S-Dis} From an initial sample of 452 Galactic Cepheids with accurate [Fe/H] abundances, period-luminosity and period-luminosity-metallicity relations have been derived based on parallax data from \G\ DR2, supplemented with accurate non-\G\ parallax data when available, for a final sample of about 200 FU mode Cepheids with good astrometric solutions. The influence of a parallax zero-point offset on the derived $PL(Z)$ relation is large, which means that the current GDR2 results do not allow us to improve on the existing calibration of the relation or on the distance to the LMC. The zero point, the slope of the period dependence, and any metallicity dependence of the $PL(Z)$ relations are correlated with any assumed parallax zero-point offset. Based on a comparison for nine CCs with the best non-\G\ parallaxes (mostly from {\it HST} data) a parallax zero-point offset of $-0.049 \pm 0.018$ mas, consistent with other values that appeared in the literature after the release of GDR2, is derived from RGB stars using {\it Kepler} and {\it APOGEE} data (about $-0.053$ mas, \citealt{Zinn18}), eclipsing binaries ($-0.082 \pm 0.033$ mas, \citealt{Stassun18}), a sample of 50 CCs ($-0.046 \pm 0.013$ mas, \citealt{RiessGDR2}), and RR Lyrae stars ($\sim -0.056$ mas, \citealt{Muraveva18}). For a parallax zero-point offset of $-0.049$ mas a final list of calculations, investigating the influence of some other parameters is given Table~\ref{Tab:plzfitsfinal}. The slope of the period dependence has been fixed (solutions 160--190), and the resulting DM to the LMC is listed in the last column. Variations in the assumed dispersion in the photometry, reddening, or period cuts have a relatively small impact on the results (especially in $K$ and $WVK$). These models address some concerns that might arise when combining many sources of photometry, reddening, and iron abundances from the literature. Increasing the error in the mean $V$ and $K$ magnitude, or not applying a transformation of the different NIR magnitude systems at all has very little impact. The most noticeable effect is when the parallax errors in GDR2 are underestimated as this changes the weight of the GDR2 sample with respect to the stars with a non-\G\ parallax. \citet{Lindegren18} in their Appendix~A hint at the fact that the errors in the five astrometric parameters may still be underestimated even after correcting for the DOF bug. This issue will likely be resolved in future releases. The next most important effect is the iron abundance. A smaller error in its determination would help, but equally important is a homogeneous metallicity scale (see \citealt{Proxauf18} for new efforts in this direction). Solutions 200--202 give the current best estimate of the $PL$ relation (for the assumed parallax zero-point offset), without a metallicity dependence as the current data and analysis does not allow us to prove or disprove a dependence. Figure~\ref{Fig:PL} shows these relations in the three bands considered. No additional sigma-clipping in magnitude space has been applied (as is common in deriving $PL$ relations in the LMC). Only stars that were systematic outliers in $\sigma$-space have been removed, as explained in Sect. \ref{S-Res}. As noted before, the slopes of the galactic $PL$ relation are shallower than those derived in the LMC by $\sim 3\sigma$ (for the assumed parallax zero-point offset). If the slope is fixed to values that have been derived for LMC Cepheids, the derived parallax zero-point offset suggests a LMC DM that is larger than commonly adopted. Conversely, a LMC DM of around 18.50 requires a zero-point offset closer to $-0.1$~mas. The results in this paper show that the parallax zero-point offset should be known to a level of $\less3~\mu$as to have a $\less$0.01 mag effect on zero point of the $PL$ relation and the DM to the LMC. It will remain important to have accurate non-\G\ based parallaxes as a control sample, like the ongoing programme using {\it HST} \citep{Riess14,Casertano16,Riess18}. \begin{figure} \centering \begin{minipage}{0.44\textwidth} \resizebox{\hsize}{!}{\includegraphics{MlogP_V.ps}} \end{minipage} \begin{minipage}{0.44\textwidth} \resizebox{\hsize}{!}{\includegraphics{par_parpred_V.ps}} \end{minipage} \begin{minipage}{0.44\textwidth} \resizebox{\hsize}{!}{\includegraphics{MlogP_K.ps}} \end{minipage} \begin{minipage}{0.44\textwidth} \resizebox{\hsize}{!}{\includegraphics{par_parpred_K.ps}} \end{minipage} \begin{minipage}{0.44\textwidth} \resizebox{\hsize}{!}{\includegraphics{MlogP_WVK.ps}} \end{minipage} \begin{minipage}{0.44\textwidth} \resizebox{\hsize}{!}{\includegraphics{par_parpred_WVK.ps}} \end{minipage} \caption{$PL$ relations in the $V$, $K$, and $WVK$ bands (solutions 200--202 from Table~\ref{Tab:plzfitsfinal}). For each filter the second panel gives the deviation between observed and predicted parallax (limited to $\pm5~\sigma$). } \label{Fig:PL} \end{figure} | 18 | 8 | 1808.05796 |
1808 | 1808.07877_arXiv.txt | X-ray reverberation in AGN, believed to be the result of the reprocessing of corona photons by the underlying accretion disk, has allowed us to probe the properties of the inner-most regions of the accretion flow and the central black hole. This process is modeled via raytracing in the Kerr metric, with the disk thickness almost ubiquitously assumed to be negligible (razor-thin) and the corona commonly approximated as a point source located along the polar axis (a lamppost). In this work, we use the new raytracing suite, {\tt Fenrir}, to explore the effect that accretion disk geometry has on reverberation signatures, assuming a lamppost configuration but allowing for a finite disk scale height. We characterize the signatures of finite disk thickness in the reverberation transfer-function and calculate how they might manifest in observed lag-frequency spectra. We also show that a disk-hugging corona (approximated by off-axis point-like flares) exhibits characteristics that are qualitatively different from observation, thus providing further evidence for a flaring corona that is separated from the underlying disk material. | \label{sec:intro} The study of X-ray variability in active galactic nuclei (AGN) probes the structure of and the physical processes that occur in the inner-most regions of the accretion flow. Reverberation is one such phenomenon seen in Seyfert galaxies, where the bands associated with the reflection spectrum will lag behind those dominated by the high-energy power law. The power-law is believed to be produced when a corona containing hot electrons ($\sim\,100$ keV) upscatters the thermal UV photons from the accretion disk ($\sim\,10$ keV) into the X-ray regime. While many of these photons will escape the system and produce the observed continuum, others will be reprocessed by the disk, creating the reflection spectrum and resulting in a natural path difference between direct and reprocessed photons \citep{Fabian+1989, Uttley+2014}. The associated lag allows one to probe the properties of the corona and the underlying disk, with most of the X-rays coming from a very compact region $< \, 10 \, r_{\rm g}$ from the central black hole \citep{Fabian+2015}. Fabian et al. (1989) first proposed reflection as a possible explanation to the broad emission line observed in the stellar mass black hole binary (BHB) Cyg X-1 by \cite{Barr+1985}, arguing that the feature was consistent with that of fluorescent Fe K$\alpha$ due to reprocessing of continuum radiation, the line broadened and skewed due to Doppler and relativistic effects \citep{Cunningham1975}. \cite{Fabian+1989} noted that the reflection process would naturally produce a lag between the continuum and the reprocessed radiation, and that the wings of profile would respond prior to the centroid. The first confirmed detection of reverberation lag was in the AGN 1H 0707-495, with the soft excess at 0.3 -1.0 keV lagging behind the 1-4 keV band by $\sim \, 30$ s at $> 6\times10^{-4}$ Hz, consistent with a compact continuum source within a few gravitational radii of the event horizon \citep{Fabian+2009}. Similar lags were later observed in the broad Fe K$\alpha$ \citep{Zoghbi+2012} and the Compton hump \citep{Zoghbi+2014}, and have now been shown to be fairly common phenomena in Seyfert galaxies (\citealt{Kara+2016} and references therein). While reverberation is the leading hypothesis for high frequency X-ray variability in AGN, at lower Fourier frequencies (e.g $\nu$ $<$ $2\times10^{-4}$ Hz in ARK 564, \citealt{Kara+2016}) the relationship changes, with continuum dominated bands lagging behind those associated with the reflection spectrum, the lag magnitude increasing with photon energy. This low-frequency hard lag was first discovered in BHB Cyg X-1 \citep{Page1985, Miyamoto+Kitamoto1989} and then later in the AGN NGC 7469 \citep{Papadakis+2001}, with linear rms-flux relationships \citep{Uttley+McHardy2001} and lognormal flux distributions \citep{Gaskell2004, Uttley+2005} seen in both system classes. The leading hypothesis to explain this phenomenon is via accretion fluctuations that propagate inwards through a disk corona, the harder lags coming from the inner-most regions of the flow \citep{Kotov+2001, Arevalo+Uttley2006}. The rms-flux relation and flux distribution have been reproduced via recent MHD simulations, being shown to be related to the dynamo. \citep{Hogg+Reynolds2016}. Reverberation is modeled through relativistic raytracing, where one solves the equations of motion for photons in the curved spacetime around the central compact object, tracing their paths from the X-ray emitting corona to the disk, and then from the disk to the observer. The first such calculations were performed by \cite{Stella1990} and \cite{Matt+Perola1992}, and a more rigorous exploration in a Kerr geometry was performed later by \cite{Reynolds+1999}. Raytracing produces both timing and spectral information, allowing one to predict the reverberation lag behavior as a function of Fourier frequency and photon energy \citep{Nowak+1999, Uttley+2014}. There have been a few common simplifying assumptions made in these calculations, with the disk almost ubiquitously assumed to have negligible vertical structure (i.e. "razor thin") and the corona most often being approximated as a point source situated along the rotation axis (a lamppost) \citep{Martocchia+Matt1996, Reynolds+Begelman1997, Miniutti+Fabian2004}. The lamppost corona model is commonly visualized as being a hot electron population near the base of a jet \citep{Biretta+2002, Ghisellini+2004} or in the black hole magnetosphere \citep{Hirotani+Okamoto1998}, and while consistent with estimations of coronal compactness in Seyfert galaxies \citep{Reis+Miller2013, Fabian+2015}, it must be emphasized to be a fiducial model chosen due to a lack of true understanding of coronal geometry. While these calculations have been able to reproduce much of the high-frequency variability and the time-averaged spectral characteristics observed in BHB and AGN \citep{Cackett+2014, Emm+2014, Chainakun+Young2015}, these simplified models still do not account for all aspects of the observed behavior, such as the low-frequency hard lag and the dip in the lag-energy spectrum at $\sim 3$ keV observed in many active galaxies (e.g. 1H 0707-495, \citealt{Wilkins+2016}). Recent work by \cite{Wilkins+2016} and \cite{Chainakun+Young2017} expands upon the lamppost model, allowing for extended coronal geometries and for coherent fluctuations through the corona, thus unifying the modeling of high-frequency and low-frequency variability; these models have shown promise, being successfully fit to XMM observations of I Zw 1 \citep{Wilkins+2017}. While there had been early exploration of the effects accretion disk geometry may have on the time-averaged reflection spectrum (e.g. disk self-eclipsing, \citealt{Pariev+Bromley1998, Wu+Wang2007}), these unified reverberation models still rely on the assumption of a razor-thin disk. Internal pressures within the accretion disk would naturally result in non-zero scale heights, which may not be negligible compared to the other physical scales relevant to the problem (e.g. the height of the lamppost), especially in super-Eddington flows where the radiative efficiency is believed to be small in some models (see \citealt{Jiang+2017} and references therein). In \cite{Taylor+Reynolds2018}, we introduced a new raytracing suite ({\tt Fenrir}) that allows for more complex accretion disk geometries, thus further expanding upon the simple reflection model. Assuming the disk to have finite thickness consistent with a classic optically thick, geometrically thin, radiation pressure dominated \cite{Shakura+Sunyaev1973} accretion disk, and using the lamppost as a fiducial model, we explored the effects that disk thickness may have on the predicted time-averaged spectrum. Focusing on mass accretion rates roughly consistent with moderately bright Seyfert galaxies [$\dot{M}/\dot{M}_{\rm Edd}\,\in\,\{0.1, 0.2, 0.3\}$], we compared the spectra from {\tt Fenrir} to that which is predicted from the razor-thin approximation ({\tt RELXILL}, \citealt{Garcia+2014, Dauser+2014}). We found that, at the razor-thin limit, {\tt Fenrir} is consistent with other contemporary models, but the spectral models start to diverge significantly when $\dot{M} \, > \, 0.1 \, \dot{M}_{\rm Edd}$. Predominantly, these changes could be attributed to "self-shielding", where the inner edges of the disk (that are gravitationally redshifted) act to shield the outer regions, resulting in a suppression of the blue peak and an overall shifting of the line towards lower energies. With these results, we concluded that accretion disk geometry should not be neglected in the detailed modeling of moderate-to-high luminosity AGN reflection spectra, and thus it is reasonable to explore consequences of finite disk thickness in reverberation. In this work, we follow-up the results of \cite{Taylor+Reynolds2018} by exploring the effects that a finite thickness has on reverberation signatures, using {\tt Fenrir} to calculate lag as a function of Fourier frequency and photon energy. We present the transfer functions, lag-frequency spectra, and lag-energy spectra using the lamppost approximation and the previous disk model, as well as the case where the corona has been positioned off-axis, rotating with the disk and situated at some small height above the disk surface (a rough approximation to a magnetic reconnection event close to the surface). We explore the lag signatures associated with this "disk-hugging" corona, and ask if it would be possible for such a corona to mimic a lamppost once disk thickness is taken into account. In Section 2, we give a brief summary of the {\tt Fenrir} raytracing suite, make explicit our simplifying assumptions, and explain the cross spectrum formalism upon which our analysis is based. In Section 3, we present the results for the lamppost approximation, followed by an exploration of the "disk-hugging" corona. In Section 4, we discuss possible consequences that disk thickness may have on the estimation of model parameters, and in Section 5 we give a brief summary of our results and possible future work. | \label{sec:discussion} As shown in the previous section, disk thickness can have dramatic effects on the 2D reverberation transfer function, imprinting itself on the lag-frequency and lag-energy spectra of AGN. Assuming a lamp-post corona configuration and a scattering surface consistent with that of \cite{Shakura+Sunyaev1973}, one finds that self-shielding is the predominant effect in the area of parameter space this work explored, where the convex geometry of the inner disk acts as a barrier for coronal photons, resulting in the suppression of the irradiation profile (and thus the emissivity profile) at larger radii; this effect was first reported in our earlier work \cite{Taylor+Reynolds2018} in the context of the time-average reflection spectrum. This results in the suppression of the late-time "blue-wing" of the transfer function when $h$ is small and a "hollowing" when $i$ is large (i.e. when the disk is seen more edge-on). When $h$ is larger (e.g. 12 $r_{\rm g}$), while the blue-wing is no longer suppressed, one finds a change in the slope of the "red-wing" due to a decrease in the delay between the observed corona flash and the initial response from the disk. This suppression of late-time signatures results in an overall decrease in the lag magnitude of the lag-frequency spectrum with increasing disk thickness, the spread of the change of the lag decreasing with increasing black hole spin due to a inverse relationship between radiative efficiency $\eta$ and disk thickness. This suppression of the lag magnitude is also ubiquitous in the lag-energy spectrum, along with a suppression of frequency dependance to the lag-energy profile. In the context of observation, for a fixed reflection fraction, this overall decrease in the high-frequency lag signal would naturally cause an underestimation in the distance between the corona and the reprocessing material (or in the context of the lamp-post assumption, the coronal height $h$). For example, if we assume we knew $a$ and $i$ for the case presented in Figure \ref{transfers3}, the change in the lag-frequency spectrum ($\sim$ 7 $r_{\rm g}$/$c$ at $\nu$ = $10^{-3}$ $c$/$r_{\rm g}$) would likely result in a best fit height of $h$ $\sim$ 5 $r_{\rm g}$. This is interesting given that there is an abundance of small coronal heights quoted as best-fit values in the literature (e.g. \citealt{Dauser+2012, Kara+2015, Kara+2016, Frederick+2018}), however it must be noted that such an effect can also be achieved by decreasing the reflection fraction by approximately $\sim$ 33\% and thus diluting the lag signal by approximately the same amount \citep{Uttley+2014}. Thus, fitting the lag-frequency spectrum with both a free reflection faction and $\dot{M}$ is likely to result in further degeneracies in $\chi^{2}$ space. Ultimately, progress must be made by simultaneously using spectral and reverberation timing data to break these degeneracies. Finally, we have explored the scenario of an off-axis "disk-hugging" corona (absent a lamp-post), asking if such a corona could mimic a lamp-post-like signal, using both single point source flashes and an extended annulus. While irradiation by returning radiation from such a corona does spark curiosity, we find that any potential lag signal is likely to be diluted beyond detectability, as $\sim 95\%$ of the observed flux would have negligible lag times, coming from the disk immediately underneath the corona. This dilution would be further enhanced by the continuum itself, which has a null lag in the standard reflection paradigm (i.e. without incorporating low-frequency hard lags). Another point to note is that the transfer functions (see Figure \ref{example-multiphi_transfers}) suggest that this reflected flux would be primarily heavily red-shifted to below 5 keV, and thus inconsistent with observations of the time-averaged broad Fe K$\alpha$ line in Seyfert I galaxies, peaking towards the rest energy $\sim 6-7$ keV. Thus, while the exact coronal geometry is unknown and we cannot rule out the possibility of a corona that is partially extended over the disk, we can conclude that a significant portion of the irradiating flux must be coming from a source that "stands off" from the accretion disk, such as that of a lamp-post or an extended jet \citep{Zoghbi+2012, Kara+2016, Wilkins+2016}. We emphasize that this exploration does not take into account all complexities of reverberation modeling, and instead should be thought of as a proof of principle rather than a true statement of reality. While we have included a more physically-motivated accretion disk model as compared to the razor-thin approximation, the exact geometry of the accretion disk remains open to debate. Also, as the \cite{Shakura+Sunyaev1973} thin disk approximation breaks down at roughly $\dot{M}$ $>$ 0.3 $\dot{M}_{\rm Edd}$, exploring reflection and reverberation in super-Eddington systems would require the implementation of alternative disk models, such as a scale height derived from an analytic accretion model \citep{Abramowicz+1980, Abramowicz+1988} or from the output of a GRMHD simulation \citep{McKinney+2014,Jiang+2014,Jiang+2017}. In the future, we hope to be able to expand beyond the simple thin disk assumption, and {\tt Fenrir} is already well-suited to do that, as stated in Section \ref{sec:methods}. In most of this work, we have also assumed a point-source corona that varies only by its magnitude, with its spectral index $\Gamma$ being constant. These are common assumptions in the literature, which we have chosen to use for consistency, but the inclusion of an extended corona would almost certainly add in more phenomenological complexities and is also a likely necessity for explaining the low-frequency hard lag \citep{Wilkins+2016,Chainakun+Young2017}, the exploration of which is beyond the scope of this work. As noted in \cite{Mastroserio+2018}, the inclusion of a pivoting power-law (i.e. $d\Gamma$/$dt$ $\neq$ 0) adds in non-linearities, and thus could confound the linearity implicitly assumed in much of X-ray reverberation methodology. Finally, we have not included ionization effects into our calculations, instead simply assuming a rest-energy of Fe K$\alpha$ is 6.4 keV. It is incredibly common to assume a single ionization state in reflection modeling (e.g. {\tt RELXILL} \citealt{Garcia+2014, Dauser+2014}), but this not likely to be true in AGN given that the incredibly centrally-concentrated emissivity profiles inferred from observation implies a radial ionization gradient across the disk \citep{Ross+Fabian1993, Reynolds+Fabian2008, Wilkins+Fabian2011}. While there have been recent attempts to incorporate such complexities into reverberation modeling, such as in {\tt KYNREFREV} \citep{Caballero-Garcia+2017, Caballero-Garcia+2018}, we have chosen to our simplified model for clarity. As this is the first exploration of the relationship between reverberation signatures and disk geometries, we have opted for clean interpretations by eliminating possible degeneracies that may arise, instead allowing more thorough explorations to be performed in the future. The study of X-ray reflection and reverberation in BHB and AGN has proven extremely fruitful, allowing us to gain a deeper understanding of the central black holes, as well as the plasma that resides in the hot electron corona and the accretion flow. Modeling reverberation is accomplished via raytracing, calculating the photon orbits in Kerr spacetime from the corona to the disk, then disk to observer. In performing these calculations, it is common to make simplifications, such as approximating the corona as a lamppost or assuming that the disk thickness is negligible (a "razor-thin" disk). Using {\tt Fenrir} \citep{Taylor+Reynolds2018}, we have explored the effects that disk thickness has on reverberation lags as a function of Fourier frequency and photon energy, approximating the disk as an optically thick, geometrically thick, radiatively dominated \cite{Shakura+Sunyaev1973} accretion disk, while still using the lamppost approximation for a fiducial model. We found that the overall magnitude of the lag is consistently inversely correlated with disk thickness, with said change being inversely correlated with black hole angular momentum. This is apparent in both the lag-frequency and lag-energy spectra, with the decrease in the lag being greatest when the corona is close to the event horizon, where the inner edges of the disk act to prevent much of the flux from irradiating the outer regions of the disk. This "self-shielding" of the disk results in a truncating of the late-time "blue wing" of the 2D transfer function at all observer angles, while also "hollowing" out the transfer function at $i$ = 60\degree. Even with the corona well outside of the "bowl" of the disk, there is an overall decrease in the lag due to the decrease in the travel time between the corona and the disk, resulting in the changing of the slope of the relativistic "red wing" of the transfer function. We can conclude that, for a given reflection fraction, a non-zero disk thickness would result in an underestimation of the lamppost height, and would result in natural degeneracies between reflection fraction and disk thickness if one were to analyze the lag-frequency spectrum in isolation. The effects of disk geometry on the lag-energy spectrum are qualitatively different from simple dilution however, with the shape of the relation being relatively unchanged as a function of Fourier frequency. We expect that these degeneracies to be overcome by analyzing the complex cross-spectrum as a unified unit, and such exploration is planned for the future. Finally, we explored the possibility of off-axis "disk-hugging" corona, asking if such a source could produce similar reverberation characteristics as that of a lamppost, the lag signal being due to a coronal flash irradiating the side of the disk opposite itself. While reverberation "across the bowl" is possible, we find that such a scenario is inconsistent with observation. Most of the flux is observed to be coming from the region of the disk right under the corona (the primary region), with only a small fraction ($\sim$ 5\%) being seen coming from the secondary region opposite the primary. As the flux from the primary region would have a corresponding lag of $\sim$ 0, any potential lag signature would be diluted to the point of being undetectable. This is clearly inconsistent with the high-frequency soft lags observed in many Seyfert galaxies, thus requiring most of the irradiating to be coming from a source that is physically separated from the reprocessing material, such as a lamppost or an extended jet. \newline \newline We would like to thank Cole Miller, Erin Kara, Dan Wilkins, Drew Hogg, Matt Middleton, Adam Ingram, Dom Walton, Rob Fender, Chris Done, Misaki Mizumoto, Mariko Kimura, David Tsang, Thomas Dauser, and Javier Garc\'ia for many excellent and helpful conversations. We gratefully acknowledge support from NASA under grants NNX17AF29G and NNX15AU54G. Finally, we would like to thank the Department of Astronomy as the University of Maryland for allowing us to use part of their computational resources on the {\tt yorp} cluster. CSR thanks the UK Science and Technology Facilities Council (STFC) for support. \textbf{\software{Fenrir}} | 18 | 8 | 1808.07877 |
1808 | 1808.05043_arXiv.txt | { The wind-driving mechanism of asymptotic giant branch (AGB) stars is commonly attributed to a two-step process: first, gas in the stellar atmosphere is levitated by shockwaves caused by stellar pulsation, then accelerated outwards by radiative pressure on newly formed dust, inducing a wind. Dynamical modelling of such winds usually assumes a spherically symmetric star. }{ We explore the potential consequences of complex stellar surface structures, as predicted by three-dimensional (3D) star-in-a-box modelling of M-type AGB stars, on the resulting wind properties with the aim to improve the current wind models. }{ Two different modelling approaches are used; the CO$^5$BOLD 3D star-in-a-box code to simulate the convective, pulsating interior and lower atmosphere of the star, and the DARWIN one-dimensional (1D) code to describe the dynamical atmosphere where the wind is accelerated. The gas dynamics of the inner atmosphere region at distances of $R\sim1-2R_\star$, which both modelling approaches simulate, are compared. Dynamical properties and luminosity variations derived from CO$^5$BOLD interior models are used as input for the inner boundary in DARWIN wind models in order to emulate the effects of giant convection cells and pulsation, and explore their influence on the dynamical properties. }{ The CO$^5$BOLD models are inherently anisotropic, with non-uniform shock fronts and varying luminosity amplitudes, in contrast to the spherically symmetrical DARWIN wind models. DARWIN wind models with CO$^5$BOLD-derived inner boundary conditions produced wind velocities and mass-loss rates comparable to the standard DARWIN models, however the winds show large density variations on time-scales of 10-20 years. } {The method outlined in this paper derives pulsation properties from the 3D star-in-a-box CO$^5$BOLD models, to be used in the DARWIN models. If the current grid of CO$^5$BOLD models is extended, it will be possible to construct extensive DARWIN grids with inner boundary conditions derived from 3D interior modelling of convection and pulsation, and avoid the free parameters of the current approach.} | Low- to intermediate-mass stars, that is, 1-8 $M_\odot$ on the zero age main sequence (ZAMS), will lose a large portion of their mass during the asymptotic giant branch (AGB) phase, before turning into white dwarfs. The mass loss on the AGB is due to a slow atmospheric stellar wind, driven by radiation pressure on dust in the stellar atmosphere. Outward-propagating shockwaves caused by the pulsation of the AGB star will periodically levitate gas to distances where the conditions are favourable for dust formation, that is, with low temperature and high density. The dust particles will be accelerated outwards by interacting with the radiation field, through absorption and scattering, depending the type of dust. Momentum is transferred from the dust to the gas through collisions, inducing a wind. Observationally, this scenario is supported by, for example, high-resolution spectroscopy \citep[see][]{hinkle_time_1982,scholz_derivation_2000,nowotny_line_2010} and by high-angular interferometry modelling, and imaging (see e.g. for O-rich stars: \citealt{chandler_asymmetries_2007,karovicova_new_2013,ohnaka_spatially_2012,ohnaka_clumpy_2016,ohnaka_clumpy_2017}; while for C-rich stars: \citealt{ohnaka_temporal_2007,ohnaka_asymmetric_2008,ohnaka_amber-naco_2015,sacuto_observing_2011,rau_modelling_2015,rau_adventure_2017,wittkowski_aperture_2017}). Dynamical atmosphere models of AGB stars are used to simulate the wind-driving mechanism \citep[for a review see][]{hofner_mass_2018}. These wind models typically have an inner boundary situated just below the photosphere of the star, and reach out to around $20-30R_\star$, incorporating both the regions of dust formation and wind acceleration. Such models usually do not include any description of the stellar interior, where the pulsations originate. Therefore, the variations of the stellar surface layers and of the luminosity, which play a key role for the wind mechanism, are typically described by a parameterised inner boundary condition. Such an inner boundary condition was previously commonly assumed to be sinusoidal variations of both the stellar radius and the luminosity \citep[e.g.][]{hofner_dynamic_2003,hofner_dynamic_2016-1}. However both one-dimensional (1D) pulsation models \citep[e.g.][]{ireland_dynamical_2011} and observations \citep[e.g.][]{nowotny_line_2010,lebzelter_shapes_2011} suggest that this approach is an oversimplification. Previous studies have shown that assumptions made about the inner boundary may have substantial effects on both the dynamical properties of the resulting models and on the derived observables \citep{liljegren_dust-driven_2016,liljegren_pulsation-induced_2017}. A more realistic approach to predicting the mass-loss rate and wind velocity should ideally describe the dynamics of the stellar surface and the luminosity without free parameters, and be derived from variations of pulsation models. The stellar interior where these variations originate, an optical thick region dominated by convection, has however proven difficult to model. Historically the stellar envelope region has been modelled using 1D self-excited pulsation models, with mixing length theory for describing the convective motions. The mixing length description is often quoted as a shortcoming of such an approach \citep[for a detailed discussion see][]{barthes_pulsation_1998}. Recent findings further suggest that 1D radial pulsation models reproduce periods well for early AGB stars, which pulsate in overtone modes but are unreliable for evolved AGB stars, and Miras, which are thought to be fundamental pulsators \citep{trabucchi_new_2017-1}. A different approach to modelling the pulsation process of the more evolved AGB stars was explored by \cite{freytag_three-dimensional_2008} and \cite{freytag_global_2017}, with 3D star-in-a-box models of AGB stars simulated using the CO$^5$BOLD (COnservative COde for the COmputation of COmpressible COnvection in a BOx of L Dimensions, L=2,3) code. With a realistic 3D hydrodynamical description, the turbulent convective flows are modelled directly, avoiding crude recipes such as the mixing length theory. Pulsations emerge in the 3D models, with realistic periods for Mira stars \citep{freytag_global_2017}. The CO$^5$BOLD models encompass part of the atmosphere, with the outer boundary situated at $\sim 2 R_\star$. The AGB models presented by \cite{freytag_global_2017} do not include dust formation and therefore no wind driving. While there are plans to expand the current CO5BOLD modelling setup to include dust formation and the wind-driving region, such models will be very time consuming (the runtime is already typically a couple of CPU years per model, for parallelised code). They will therefore be impractical for extensive wind model grids used to derive wind properties for a wide range of stellar parameters. In this paper, we instead aim at improving the current 1D atmosphere and wind models (DARWIN code) by quantifying the dynamical behaviour in existing 3D convection and pulsation models (CO$^5$BOLD code) and applying the results in the 1D models. This is done by comparing the lower atmosphere for both modelling methods, which is a region in the range $\sim1-2R_\star$ where shockwaves induced by stellar pulsation dominate the dynamics before dust has condensed. The impact that the non-spherical morphology seen in the CO$^5$BOLD might have on the wind properties is discussed. The 3D models are then used to derive new inner boundary conditions for 1D atmosphere models, with similar stellar parameters, to try to emulate the effects of giant convection cells and pulsation, for a sample of models with eight different stellar parameter combinations. The resulting atmospheric dynamics are investigated, and compared to the standard DARWIN (Dynamic Atmosphere and Radiation-driven Wind models based on Implicit Numerics) model results. Both approaches describe M-type AGB stars, with oxygen-dominated atmospheric chemistry. | We try to estimate the effects of a non-spherical star, as predicted by CO$^5$BOLD 3D interior models, on the wind properties of AGB stars. To summerize the result: \begin{itemize} \item The gas velocities in a shock front in CO$^5$BOLD models are not uniform, but rather a distribution of velocities (Fig. \ref{fig:veld}). This might be important for the wind-driving in less-evolved AGB stars and could potentially lead to a weak dust-driven wind earlier on the AGB than predicted by the DARWIN models. \item Only about $70\%$ of the full surface of the CO$^5$BOLD models is covered by shockwaves during a cycle (Fig. \ref{fig:area}). This varies from cycle to cycle. \item The CO$^5$BOLD models do however show sporadic variations both in space and in time for the gas velocities and luminosity amplitudes, in contrast to the spherically symmetric DARWIN models where these quantities are assumed to vary sinusoidally (Fig. \ref{fig:veld}, \ref{fig:lvar} and \ref{fig:rvcomp}). \item The amplitudes of the luminosities and the gas velocities in the close, dust-free atmosphere of the CO$^5$BOLD 3D models are similar to those assumed for the DARWIN dynamical atmosphere models (Fig. \ref{fig:ramp}). \item When using the CO$^5$BOLD interior models as input for the DARWIN wind models the resulting average dynamical properties agreed well with the standard DARWIN u2 models (Fig. \ref{fig:veldmdt} and top panel of \ref{fig:diffcomp1}). The DARWIN u4 models have consistently higher mass-loss rates when compared to the DARWIN models using CO$^5$BOLD BC. \item DARWIN models with CO$^5$BOLD input show large variations with time, and mass-loss rates could vary by an order of magnitude and the wind velocity with $50\%$ over a timescale of 10-20 years (Fig. \ref{fig:timeevo}). Such large variations in the density of the wind might cause observable small-scale structures in the circumstellar envelope. \end{itemize} While the average dynamical properties were similar for the standard DARWIN models and the DARWIN models with CO$^5$BOLD input, the anisotropic star predicted by the CO$^5$BOLD models affect the wind. To see if such variability of the wind properties results in observable structures, more investigation is needed. The non-uniform behaviour of the shockwaves shown by the CO$^5$BOLD models might induce a dust-driven wind in less evolved AGB stars than predicted by the DARWIN models. CO$^5$BOLD models with relevant stellar parameters in combination with DARWIN models are needed to further explore this. Ideally, 3D models that include dust-driven winds should be used for studying the mass loss of AGB stars. However, such models are not available yet. Additionally, the computational time of such models would be several orders of magnitude higher than for the current spherical models, making it impractical, for example, in extensive wind model grids used to derive mass-loss rates, which span a wide range of stellar parameters, as necessary for stellar-evolution modelling. The methods developed in this paper, deriving pulsation properties from the CO$^5$BOLD models, can be used to mimic the effects of the pulsations and giant convection cells and avoid free parameters in DARWIN models. If the current grid of CO$^5$BOLD 3D models were expanded, it would therefore be possible to infer inner boundary conditions from a sparse grid of 3D models onto a well-sampled grid of DARWIN models. | 18 | 8 | 1808.05043 |
1808 | 1808.02725_arXiv.txt | On 3rd September 2015, the Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) successfully measured the linear polarization produced by scattering processes in the hydrogen Lyman-$\alpha$ line of the solar disk radiation, revealing conspicuous spatial variations in the $Q/I$ and $U/I$ signals. Via the Hanle effect the line-center $Q/I$ and $U/I$ amplitudes encode information on the magnetic field of the chromosphere-corona transition region (TR), but they are also sensitive to the three-dimensional structure of this corrugated interface region. With the help of a simple line formation model, here we propose a statistical inference method for interpreting the Lyman-$\alpha$ line-center polarization observed by CLASP. | \label{sec:intro} Recently, the Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) sounding rocket experiment provided the first ever successful measurement of the linear polarization $Q/I$ and $U/I$ profiles produced by scattering processes in the hydrogen Ly-$\alpha$ line of the solar disk radiation \citep{kano17}, as well as in the Si {\sc iii} resonance line at 1206 \AA\ \citep{Ishikawa17}. Such novel spectropolarimetric observations, with a spatial resolution of about 3~arcseconds, confirmed the following theoretical predictions for the Ly-$\alpha$ line \citep{jtb-stepan-casini11,belluzzi12,stepanjtb15}: \begin{enumerate} \item at the CLASP spatial resolution, the line-center $Q/I$ and $U/I$ signals, where the Hanle effect operates, are smaller than 1\% (see Fig.~\ref{fig:clasp}); \item the $Q/I$ and $U/I$ wing signals are larger than 1\%, with the $Q/I$ ones showing a clear center-to-limb variation (CLV) with negative amplitudes increasing towards the limb; \item both the line-core and wing signals show fluctuations along the spatial direction of the spectrograph's slit, which in the CLASP experiment was radially oriented from 20~arcseconds off-limb till 380~arcseconds on the solar disk. \end{enumerate} Although the CLASP observation of the hydrogen Ly-$\alpha$ line confirmed the above-mentioned theoretical predictions, it also revealed an interesting surprise, namely the lack of center-to-limb variation in the $Q/I$ line-center signal, in contrast with the predictions resulting from detailed radiative transfer calculations in one-dimensional (1D) semi-empirical and hydrodynamical models \citep{jtb-stepan-casini11,belluzzi12} and in \citet{carlsson16} three-dimensional (3D) magneto-hydrodynamical (MHD) model of the solar atmosphere \citep{stepanjtb15}. The CLASP observations encode unique information on the 3D structure of the upper solar chromosphere. In particular, via the Hanle effect the line-center $Q/I$ and $U/I$ signals encode information on the magnetic field of the chromosphere-corona transition region (TR), but the same linear polarization signals are also sensitive to the geometry of this complex interface region. In order to constrain the mean field strength and the geometrical complexity of the chromosphere-corona TR from the CLASP observation, it is necessary to develop suitable inference methods. In this paper, we propose a statistical inference method for interpreting the observed Ly-$\alpha$ line-center polarization, and illustrate its applicability with the help of a simple radiative transfer model of the formation of the Ly-$\alpha$ line-core radiation in the corrugated surface that delineates the transition region. In our next paper (Trujillo Bueno et al. 2018; in preparation) the statistical inference method explained here will be applied to the CLASP line-center data in order to constrain the magnetic field and the geometrical complexity of the solar transition region via radiative transfer calculations in suitably parametrized three-dimensional models of the solar atmosphere. | \label{sec:concl} Recently, unprecedented spectropolarimetric observations of the hydrogen Lyman-$\alpha$ line of the solar disk radiation have been provided by the CLASP sounding rocket experiment. The $Q/I$ and $U/I$ line-center signals observed along the spatial direction of the (radially oriented) spectrograph slit encode key information on the magnetic field and geometrical complexity of the corrugated layer that delineates the chromosphere-corona transition region. With only one spectral line it is not possible to determine the magnetic field of the solar transition region, unless the geometrical complexity of its defining corrugated layer is known beforehand. However, it should be possible to constrain the mean field strength and geometrical complexity via the application of a suitable statistical inference method. The aim of this paper has been to propose a statistical inference method, based on the concept of maximum likelihood, which we consider suitable for interpreting the CLASP observations. Here we have illustrated this method by applying it to the theoretical $Q/I$ and $U/I$ line-center signals resulting from a simple line formation model (the corrugated transition region model) that we have introduced for qualitatively understanding the CLASP observations. In our next paper (Trujillo Bueno et al. 2018; in preparation) we will apply the statistical inference method developed here in order to interpret the CLASP data themselves and estimate global properties of the quiet Sun atmosphere by means of more realistic models of the chromosphere-corona transition region resulting from 3D numerical simulations. | 18 | 8 | 1808.02725 |
1808 | 1808.05619_arXiv.txt | The positions of images produced by the gravitational lensing of background sources provide unique insight in to galaxy-lens mass distribution. However, even quad images of extended sources are not able to fully characterize the central regions of the host galaxy. Most previous work has focused either on the radial density profile of the lenses or localized substructure clumps. Here, we concentrate on the azimuthal mass asymmetries near the image circle. The motivation for considering such mass inhomogeneities is that the transition between the central stellar dominated region and the outer dark matter dominated region, though well represented by a power law density profile, is unlikely to be featureless, and encodes information about the dynamical state and assembly history of galaxies. It also happens to roughly coincide with the Einstein radius. We ask if galaxies that have mass asymmetries beyond ellipticity can be modeled with simpler lenses, i.e., can complex mass distributions masquerade as simple elliptical+shear lenses? Our preliminary study indicates that for galaxies with elliptical stellar and dark matter distributions, but with no mass asymmetry, and an extended source filling the diamond caustic, an elliptical+shear lens model can reproduce the images well, thereby hiding the potential complexity of the actual mass distribution. For galaxies with non-zero mass asymmetry, the answer depends on the size and brightness distribution of the source, and its location within the diamond caustic. In roughly half of the cases we considered the mass asymmetries can easily evade detection. | Multiple image, or strong gravitational lensing is a unique tool for determining the detailed mass distribution in galaxies. The very central few kpc of galaxies are dominated by baryons, in the form of stars. The density of stars falls off rapidly with distance from the center, and at larger radii the total mass becomes dominated by dark matter. The typical radius where the contributions of the two mass components are equal---what we will call the transition radius---is around 5-10 kpc, in projection. Despite the fact that the dominant mass component changes from stars to dark matter, strong lensing studies show that the 3D spherically averaged density profiles of galaxies are well represented by a single power law in radius, $\rho\propto r^{-\gamma}$, where $\gamma$ was estimated to be about $2$ \citep{koopmans09,barnabe11}. Because this transition is smooth, it is sometimes called the bulge-halo conspiracy \citep{vanalbada86}, in the sense that the stellar and the dark matter components conspire to keep the total mass density slope the same across the transition region. This smooth transition is also seen in numerical simulations \citep{schaller15a}, and is probably the consequence of the central regions of galaxies approaching relaxation. However, the transition region is not completely featureless. Both simulations \citep{schaller15a} and observations \citep{thomas07,chae14} show that with increasing distance from center, the total density slope becomes somewhat steeper, then shallower, and then steeper again. The presence of these features implies that full relaxation has not been achieved yet, even though the galaxies are likely in a stable mechanical equilibrium \citep{young16}. Both simulations \citep[e.g.,][]{nav04,springel08} and theory \citep{williams10} show that in a fully relaxed, collisionless system there should be no non-monotonic slope changes at these radii. If the central regions of galaxies are not fully relaxed, one should expect density perturbations, or asymmetries, not just in the radial, but also in the azimuthal directions. For example, if the ellipticity position angles of the dark matter and stellar distributions are misaligned, then the transition curve will not be elliptical. Most studies of the bulge-halo conspiracy have concentrated on the circularly (or spherically) averaged density profiles; in other words, used only the size of the Einstein radius in the analysis. But lensing can also map out density variations in the projected azimuthal direction, because the positions of images in the polar angle around the lens center are sensitive to the azimuthal distribution of mass at the Einstein radius. By coincidence, multiple images of background sources form roughly around the transition radius \citep[see Figure 12 of][]{GomerWilliams2017}. Thus the structure of this region, both in the radial as well as azimuthal directions, is reflected in the image positions. Future surveys will deliver hundreds or thousands of quad lenses \citep{agnello15,finet12,oguri10}, allowing the study of redshift evolution of the transition region in a statistical sense, leading to a better understanding of galaxy relaxation. We note that the mass asymmetries we are interested in are not the same as clumpy substructure, which has been detected through lens reconstruction, in several recent studies \citep{hez16,veg14,veg12,veg10}. What is the best way to extract the information about the azimuthal mass distribution in a lens? One could carry out mass reconstructions of individual lenses, using either parametric, or free-form techniques. The drawbacks of this approach are two-fold: (a) lensing degeneracies, for example the monopole degeneracy \citep{saha00,lie08,lie12}, can conceal the true features of the azimuthal mass distribution, especially when these features are higher order perturbations compared to pure ellipticity, and (b) individual lens modeling cannot take advantage of the fact that lenses belong to a population, and hence share some common properties. In this paper we examine the ability of mass modeling of individual lenses to extract information about the azimuthal mass distribution in the transition region. \cite{GomerWilliams2017} studied quad populations, with the same goal in mind.% It is known that most quad lenses are well modeled by elliptical+shear mass distributions. However, even the most sophisticated models, those that consist of a superposition of two different profiles---one representing dark matter, and the other, the distribution of stars \citep[e.g.][]{suyu09,gil17}---do not include the azimuthal complexities potentially associated with the transition region. Higher order perturbations in the galaxy isodensity contours may be present \citep{woldesenbet15,GomerWilliams2017}, but would elude mass modeling because of lensing degeneracies, which imply that there is an infinity of mass distributions that could reproduce the observed image properties. So an accurate fit to the images may not imply an accurately recovered mass distribution. The most well known is the mass sheet degeneracy \citep[MSD,][]{falco85}; its influence on the determination of $H_0$ from galaxy lenses was recently explored in \cite{xu16} and \cite{tagore18}. If one had a myriad of point sources at the same redshift, that covered the entire relevant portion of the source plane, and the multiple images of these sources were observed with infinite astrometric precision, then all degeneracies, except for MSD would be broken. These include the source plane transformation (SPT), which is a generalization of the MSD \citep{ss14}, and the monopole degeneracy, which reshapes the mass distribution between images. In addition, there could exist other degeneracies that have not been recognized and analyzed yet. These too would be broken by our idealized thought experiment. Such an idealized experiment is not possible. The next best thing is to use extended sources with variable surface brightness distributions, such as galaxies, or host galaxies of QSOs; \cite{KKM01,BSK01}, but see \cite{saha00}. These provide useful, but far from complete coverage of the source plane. In addition to (i) limited spatial extent, other shortcomings of realistic observations are, (ii) finite size of detector pixels, translating in to imprecise astrometry, and (iii) faintness, resulting in low signal-to-noise ratio. Compared to our idealised experiment, these allow degeneracies to creep in. In the present study, where we are interested in knowing how well, if at all, mass features of the transition region can be recovered through mass modeling, the most relevant degeneracy is not MSD or SPT, but probably the monopole degeneracy. However, our goal is not to identify specific degeneracies, but ask if quads of extended sources, generated by mass distributions that have transition radius features, can be used to recover these features. Specifically, we ask a closely related question: can quads produced by complex galaxies be successfully modeled by simpler mass distributions? The answer will naturally depend on properties mentioned in (i), (ii), and (iii) above, which we explore in the paper. For some combinations of properties, the situation is promising, but in cases where simple mass distributions can indeed mimic more complex ones, the true features of the dark matter-stars transition region cannot be uncovered by mass modeling of individual lenses, and quad population studies, such as those presented in \citet{woldesenbet15} and \citet{GomerWilliams2017} are needed. | Even though most individual quads are well represented by simple elliptical+shear lens models, the population of quads is not well represented by such lenses. \cite{GomerWilliams2017} studied the distribution of quads in the 3D space of relative image polar angles, and concluded that fold- and cusp-type quads arise, as expected, from lenses with a range of external shear values, whereas cross-type quads seem to arise only from lenses with small shear. Cross quads with large shears appear to be missing. This odd finding, which cannot be accounted for by selection effects, prompted the authors to consider other possible sources of mass perturbation, or asymmetry in the lenses. Having first ruled out $\Lambda$CDM substructures as the reason, they turned to mass asymmetries associated with the transition region, where the central stellar distribution gives way to dark matter. Because the central regions are not fully relaxed, azimuthal asymmetries are expected around this radius. The authors showed that these would give rise to 3D distribution of quad relative image angles consistent with the currently available sample of quad galaxy lenses. One might then ask, if such mass perturbations exist, why have they not been detected already, through mass modeling? In this paper our goal was to investigate how often, and under what circumstances, these asymmetries can evade detection, based on mass distributions recovered by modeling. In our preliminary tests presented in this paper we generated quad images of extended sources, using 2-component---stars and dark matter---galaxies, and then attempted to fit these using 1-component elliptical+shear models. The easiest way to mimic mass asymmetry at the image radius is to offset the two components. We represented extended sources with dense clusters of point-sources, and compared the ``observed'' images with modeled images, using $\rm {RMS}$ between the corresponding point-images comprising the extended images. Our $\rm {RMS}$ threshold to separate good from bad fits was set at $0.03\arcsec$, somewhat smaller than the HST ACS pixel, because point-images in the lens plane with smaller separations would not be distinguished. For 2-component galaxy lenses with small or zero offsets, 1-component models can successfully reproduce the images of even the large, caustic-filling sources; i.e., $\rm {RMS}$ were in general below $0.03\arcsec$. In these cases, the fact that a lens has two components will not be revealed by mass modeling. For 2-component lenses with non-zero offsets (up to $\sim 1h_{0.7}$~kpc) the source averaged $\rm {RMS}$ depends on several parameters. Sources with flat brightness distributions and further from the caustic centre are worse fit with 1-component models, and hence more likely to indicate the presence of mass perturbations beyond simple ellipticity. Also, if the average density profile slope of the 2-component galaxy at the location of the images differs from the assumed slope of the 1-component model, such models would have larger $\rm {RMS}$, and also signal the presence of additional mass perturbations. However, there is no guarantee that an improved mass model, one that has a lower $\rm {RMS}$, will recover the true mass distribution adequately well. Overall, we estimate that of order half of the quads will be able to eliminate simple models, though not necessarily lead to the true mass distributions. This is not an exhaustive study; a more detailed study would consider a wider range of possible galaxy models, and incorporate the effects of magnification bias. In this work we did not use any image time delay information, even though it is available for a subset of lenses, where the central quasar shows variability \citep[e.g.,][]{bon18,slu12}. If all three relative time delays between four images of a quad are known precisely, to better than a few percent, the ratios between these can be used as additional constraints to break degeneracies discussed in this paper, and help isolate the true mass solution. The same quad can then also be used to estimate $H_0$. However, most of the currently available quads have only one precisely measured time delay \citep[e.g.,][]{cor18}. In such a case, one can use the time delay either to constrain mass model asymmetries, or to estimate $H_0$, not both. Until larger samples of quads with multiple precise time delays become available, the best strategy for obtaining $H_0$ is to use ensembles of lenses and constrain them to share the same $H_0$ value, as was done in \cite{col08,par10,lub12}. In the present paper, we fitted the central point images of quads, and asked if these fitted mass models can also reproduce extended images within observational uncertainty. For the purposes of $H_0$ estimation, it is now common to use the entire area of extended images to do the mass fitting \citep[e.g.,][]{suy17}, which would require an approach different from the one we implemented here. For all these reasons, $H_0$-related investigation is postponed to a future work. | 18 | 8 | 1808.05619 |
1808 | 1808.02808_arXiv.txt | We apply the transit light curve self-contamination technique of Morris et al.\ (2018) to search for the effect of stellar activity on the transits of the ultracool dwarf TRAPPIST-1 with 2018 \spitzer photometry. The self-contamination method fits the transit light curves of planets orbiting spotted stars, allowing the host star to be a source of contaminating positive or negative flux which influences the transit depths but not the ingress/egress durations. We find that none of the planets show statistically significant evidence for self-contamination by bright or dark regions of the stellar photosphere. However, we show that small-scale magnetic activity, analogous in size to the smallest sunspots, could still be lurking in the transit photometry undetected. | TRAPPIST-1 is a system of seven approximately Earth-sized planets orbiting an M8V star \citep{Gillon2016, Gillon2017, Luger2017, Delrez2018}. It is the subject of much hope for characterization with the James Webb Space Telescope \citep{Gillon2016,Barstow2016,Morley2017,Batalha2018}, though stellar activity may complicate efforts to characterize the exoplanets \citep{Rackham2018}. The photosphere of TRAPPIST-1 may be described as a mixture of several photospheric components with different temperatures, according to Hubble Space Telescope (HST) spectra in the analysis by \citet{Zhang2018}. \citet{Roettenbacher2017} showed that the spots evolve on the apparent rotation timescale, and comparison of \kepler and \spitzer time-dependent modulation independently suggests that there are bright (hot) spots in the photosphere \citep{Morris2018c}. These hot spots appear to be correlated with strong flares in the K2 light curve, which calls into question the association of spot variability with stellar rotation. Recent analysis of the broadband transmission spectra of the TRAPPIST-1 planets yields a non-detection of spectral contamination by stellar activity \citep[upper limit of $200-300$ ppm in the spectra of planets b and d][]{Ducrot2018}. In this work, we analyze the \spitzer transit light curves of TRAPPIST-1 with the ``self-contamination'' technique of \citet{Morris2018f}. The self-contamination method fits the transit light curves of planets orbiting spotted stars, allowing the host star to be a source of contaminating positive or negative flux which influences the transit depths. Accounting for the contamination potentially allows for robust inference of the exoplanet radii from the transit ingress and egress durations, even in the presence of extreme starspot distributions, like those predicted for TRAPPIST-1 by some \citep{Rackham2018, Zhang2018}. Crucially, unlike spot occultation observations \citep[see e.g.][]{Sanchis-Ojeda2011, Morris2017a}, the self-contamination technique can detect nearly-homogeneous distributions of spots throughout the transit chord of an exoplanet, or surrounding the transit chord of an exoplanet, so long as the transit chord has a different mean intensity than the rest of the photosphere \citep{Morris2018f}. | We present a self-contamination analysis of the \spitzer transit light curves of the TRAPPIST-1 planets, using the transit light curve parameterization of \citet{Morris2018f}. We find insufficient evidence for contamination by bright or dark spots inside or outside of the transit chord using the self-contamination technique of \citet{Morris2018f}, measuring contamination $\epsilon = 0.22 \pm 0.10$ for planet b. This is a tighter constraint on the contamination than measured with \kepler photometry in \citet{Morris2018f}. This analysis suggests that the mean photosphere is similar to the photosphere occulted by the TRAPPIST-1 planets. However, we cannot exclude the possibility that small-scale magnetic activity analogous in size to the smallest sunspots may be occuring within (or outside) of the transit chords given the photometric precision of the \spitzer observations. \facilities{Spitzer} \software{\texttt{astropy} \citep{Astropy2018}, \texttt{emcee}, \citep{Foreman-Mackey2013}, \texttt{ipython} \citep{ipython}, \texttt{numpy} \citep{VanDerWalt2011}, \texttt{scipy} \citep{scipy}, \texttt{matplotlib} \citep{matplotlib}, \texttt{robin} \citep{Morris2018f}} | 18 | 8 | 1808.02808 |
1808 | 1808.04335_arXiv.txt | HD\,149277 is a rare SB2 system with a slowly rotating magnetic He-rich primary with $P_{\rm rot}=25.4$\,d. The CFHT/ESPaDOnS archive spectra revealed $P_{\rm orb}=11.5192 \pm 0.0005$\,d indicating strong subsynchronous rotation of the primary component. Such a strong subsynchronous rotation was not detected in any other SB2 system with a magnetic chemically peculiar component. Our inspection of the spectra revealed the presence of resolved Zeeman split spectral lines allowing us to determine the variability of the mean magnetic field modulus over the rotation period. The maximum of the magnetic field modulus concides roughly with the positive extremum of the longitudinal field, whereas the minimum of the modulus with the negative extremum of the longitudinal field. No evidence for a longitudinal magnetic field was seen in the circularly polarized spectra of the secondary component. Using archival data from the ASAS3 survey, we find in the frequency spectrum only one significant peak, corresponding to the period $P_{\rm phot}=25.390 \pm 0.014$\,d. This value is in good agreements with the previous determination of the rotation period, $P_{\rm rot}=25.380\pm0.007$\,d, which was based on longitudinal magnetic field measurements. | Using high-resolution polarimetric spectra of HD\,149277 acquired with ESPaDOnS at the Canada-France-Hawaii Telescope (CFHT), \citet{Shultz2018} recently reported on the presence of a rather strong longitudinal magnetic field with $\left<B_{\rm z}\right>_{\rm max}=3.3\pm0.1$\,kG. The authors determined a rotation period of 25.4\,d using these mean longitudinal magnetic field measurements. HD\,149277 is a member of the young open cluster NGC\,6178 at an age of $\log\,(t [\mathrm{yr}])=7.15\pm0.22$ \citep{Kharchenko2005}. Its physical properties, $T_{\rm eff}=22\,300\pm 500$\,K, $M=8.75\pm0.40$\,M$_{\odot}$, and $\log (L/L_{\odot})=3.7\pm 0.1$ were reported by \citet{Landstreet2007}. In the column ``remarks'' of their Table~1, \citet{Shultz2018} mention that HD\,149277 is an SB2 system with a B2IV/V magnetic primary, but give no information on the nature of the secondary component or the orbital parameters. According to previous studies by e.g.\ \citet{Carrier2002}, \citet{Hubrig2014}, and \citet{Landstreet2017}, close SB2 systems with magnetic Ap or Bp components are extremely rare. Among the studied binary systems with A and late B-type primaries, only two systems, HD\,98088 and HD\,161701, are known to possess a magnetic Ap star as a companion \citep{Babcock1958,Abt1968,Hubrig2014}, and only a few more SB2 systems with Bp components are currently known \citep{Landstreet2017}. Such systems are of considerable interest in the context of the magnetic field origin, which is still not properly understood. \citet{Ferrario2009} suggested that magnetic Ap and Bp stars are products of a merger of two lower mass protostars. In this scenario, the binaries that we observe now were triple systems earlier in their history. In the following we report on our analysis of the orbital parameters of HD\,149277 and give additional information on the spectral, magnetic, and photometric variability. | The analysis of the system HD\,149277 is of considerable interest as close main sequence SB2 systems only very rarely contain a magnetic Ap or Bp star as a component. We determined the orbital parameters of the system and studied a few characteristics of the individual components, such as spectroscopic and photometric variability. Similar to a few other SB2 systems with magnetic Bp components compiled in Table~5 in the work of \citet{Landstreet2017}, the orbit is quite eccentric with $e=0.237$, but the rotation period of the primary is the longest among the studied systems. The more massive of the two stars is rotating subsynchronously and exhibits a strongly variable magnetic field modulus. Among the previously studied SB2 systems, the primary in HD\,149277 exhibits the strongest magnetic field and the strongest subsynchronous rotation. The less massive component is apparently non-magnetic, but probably shows spectral variability, which should be analysed in more detail in future higher S/N observations. Such future high S/N observations should also be used to constrain the structure of the magnetic field of the primary in more detail. We note that studies of strongly magnetic stars using the mean magnetic field modulus, measured using magnetically resolved lines, are of importance because they provide the best opportunity to study the effect of a magnetic field on stellar atmospheres. At present, 84~Ap stars are known to show magnetically resolved lines, representing 2.3\% of the total number of known Ap stars \citep{Mathys2017}. The sample of early-type massive Bp stars currently consists of just three members (Hubrig et al., {\sl in preparation}). | 18 | 8 | 1808.04335 |
1808 | 1808.01726_arXiv.txt | The large columns of dusty gas enshrouding and fuelling star-formation in young, massive stellar clusters may render such systems optically thick to radiation well into the infrared. This raises the prospect that both ``direct'' radiation pressure produced by absorption of photons leaving stellar surfaces and ``indirect'' radiation pressure from photons absorbed and then re-emitted by dust grains may be important sources of feedback in such systems. Here we evaluate this possibility by deriving the conditions under which a spheroidal, self-gravitating, mixed gas-star cloud can avoid catastrophic disruption by the combined effects of direct and indirect radiation pressure. We show that radiation pressure sets a maximum star cluster formation efficiency of $\epsilon_{\rm max} \sim 0.9$ at a (very large) gas surface density of $\sim 10^5 \msun$ pc$^{-2} (\zsun/Z) \simeq 20$ g cm$^{-2} (\zsun/Z)$, but that gas clouds above this limit undergo significant radiation-driven expansion during star formation, leading to a maximum stellar surface density very near this value for all star clusters. Data on the central surface mass density of compact stellar systems, while sparse and partly confused by dynamical effects, are broadly consistent with the existence of a metallicity-dependent upper-limit comparable to this value. Our results imply that this limit may preclude the formation of the progenitors of intermediate-mass black holes for systems with $Z \gsim 0.2 \zsun$. | \label{sec:intro} It has been appreciated for some time that the direct radiation flux from young stars may be sufficiently intense to drive gas out of isolated protoclusters experiencing intense star formation. As such, direct radiation pressure -- i.e., the momentum flux imparted by starlight to gas mediated via the photons' initial absorption and scattering by the dust borne by the gas -- is an important agent of ``feedback'' in such systems, a view supported by both observational \citep{Scoville2001,Lopez2011,Lopez2014} and theoretical \citep{Krumholz2009a,Fall2010,Murray2010b,Murray2011,Skinner2015,Thompson2016} perspectives. In this article -- which leaves off from developments in our previous paper on star-forming discs \citep[][hereafter \citetalias{Crocker2018}]{Crocker2018} which, in turn, follows \citet{Krumholz2012,Krumholz2013} -- we show that {\it indirect} radiation pressure \citep[i.e., radiation pressure due to dust-reprocessed photons rather than direct starlight photons; cf.][]{Murray2010b} will also, in many cases, have an important dynamical effect in nascent star clusters. Indirect radiation pressure effects arise because the molecular gas, from which stars form, bears dust that reradiates absorbed UV and optical light at infrared (IR) wavelengths. This same dust may -- if it presents a sufficiently large column -- subsequently scatter or absorb and reradiate the starlight down-scattered into the IR. Indeed, at the large gas and, consequently, dust columns concomitant to the intense star formation surface densities encountered in local ultra-luminous infrared galaxies (such as Arp 220) or in sub-mm galaxies at higher redshifts, a star-forming environment may be optically thick to photons with wavelengths as long $\sim 100 \ \mu$m\footnote{Fits to such galaxies' spectral energy distributions imply gas columns of $\sim 0.01 - 1$ g cm$^{-2}$ \citep{Chakrabarti2008}, corresponding to optical depths of $\sim 10 - 100$ at 20 $\mu$m and $\sim 1 - 10$ at 100 $\mu$m.}. Most pertinent here, similar or even larger dust columns and consequent optical depths are also encountered in the densest star-forming clouds found in the Milky Way and other galaxies in the local Universe. For example, \citet{Clarkson2012} find that the stellar surface density in the central $0.4$ pc of the Arches cluster near the Galactic Centre is $\approx 4$ g cm$^{-2}$, and this is only a lower limit on the initial gas surface density, corresponding to optical depths of several at 100 $\mu$m. The young or still-forming super star clusters in M82 \citep{McCrady2007} and NGC 253 \citep{Leroy2018} have gas columns exceeding $10$ g cm$^{-2}$, so at 100 $\mu$m the optical depth is $\sim 10$. The existence of large optical depths at IR wavelengths in such systems raises the interesting possibility that, as the downshifted photons bang around inside the gas column, much more momentum can be extracted from them than is possible in the single-scattering limit pertinent to direct radiation pressure. Indeed, in the ``strong-trapping'' limit the momentum per unit time extracted from starlight is amplified from $L/c$ to $\sim \tau L/c$, where $\tau$ is the optical depth\footnote{Ultimately only bound, in principle, by energy conservation to $\lsim (c/v) L$ where $v$ is a characteristic velocity of the outflowing gas \citep[e.g.,][]{Lamers1999}.}. While such a trapped radiation field could in principle eject gas from galaxies \citep{Murray2011}, whether it does so in practice is a separate question. Both analytic calculations and simulations suggest that dust-reprocessed radiation pressure is a threshold effect: for a given column of gas and stars, there exists a critical maximum radiation flux that can be forced through the column while the gas remains in a stable hydrostatic equilibrium. As long as such an equilibrium exists, the gas plus radiation pressure forces self-adjust to be in balance with the gravitational force, and IR radiation pressure has little effect on the dynamics. Once the flux exceeds the critical value, however, the gas column becomes unstable and turbulent, and simulations show that the instability saturates into a state where the mass-averaged radiation force exceeds (though, as a result of radiation Rayleigh-Taylor instability, only slightly) the mass-averaged gravitational force, rendering the entire gas column super-Eddington and thus liable to ejection on a dynamical timescale \citep[e.g.,][]{Davis2014, Tsang2015, Zhang2017}. Thus the question of whether indirect radiation pressure is important for star formation reduces to the question of whether star forming systems have combinations of gas column and radiative flux that place them into the stable and sub-Eddington regime or the unstable and super-Eddington one. In \citetalias{Crocker2018} we showed that the radiative flux in most star-forming discs, averaged over the entire star-forming disc, fall into the former rather than the latter category. Consequently, for the vast majority even of starbursting galaxies, radiation pressure cannot be an important regulator of star formation or driver of winds at galactic scales. On the other hand, % as first shown by \citet{Thompson2005} and later confirmed in \citetalias{Crocker2018}, there is a very suggestive coincidence \citep[cf.][]{Andrews2011} between the upper boundary of the occupied region of the Kennicutt-Schmidt (KS) parameter space (of star formation surface density $\dot{\Sigma}_{*}$ vs.~gas surface density $\Sigma_{\rm gas}$) and the critical value of the star formation surface density ($\dot{\Sigma}_{\rm \star,crit} \sim 10^3 \msun$ pc$^{-2}$ Myr$^{-1}$, corresponding to a critical radiative flux of $F_{\rm \star,crit} \sim 10^{13} \lsun$ kpc$^{-2}$) where indirect radiation pressure effects preclude hydrostatic equilibrium. This strongly suggests that, while indirect radiation pressure is not an important agent of feedback {\it on global scales} for most systems, it nevertheless circumscribes the parameter space along the locus of the KS relation that may be occupied by real systems. Moreover, even if a star forming system is globally sub-Eddington, the fact that star formation is highly clumpy can render individual star-forming sub-regions (i.e., nascent star clusters and super star clusters forming out of individual giant molecular clouds) super-Eddington, driving outflows away from these sub-regions \citep{Murray2011}. Numerical exploration of this question in the context of the most massive star clusters, where the effect is expected to be most important, has been highly limited by computational costs. \citet{Skinner2015} and \citet{Tsang2018} both simulate indirect radiation pressure effects in a forming star cluster, and find them to be quite modest, but they survey a very small part of parameter space, and one where, as we show below, indirect radiation pressure effects are not expected to be significant. Moreover, these authors adopt a constant opacity to indirect radiation pressure, an assumption that we showed in \citetalias{Crocker2018} leads to fundamental changes in the dynamics of the problem. Motivated by the need to explore this problem over a wider range of parameters than simulations currently permit, here we direct our attention to the importance of indirect radiation and to its effects on local scales within regions experiencing intense star formation, e.g., individual molecular clumps that are collapsing to form stellar proto-clusters or, in principle, larger stellar spheroids. Furthermore, we simultaneously incorporate {\it direct} radiation pressure effects in our model following the treatment of \citet[hereafter \citetalias{Fall2010}]{Fall2010}. One might suspect that a threshold feedback mechanism such as indirect radiation pressure might be important for star-forming subregions because \citet{Hopkins2010} have compiled observations that support the existence of a universal, maximum {\it central}\footnote{That is, {\it not} the effective or mean surface density $M_{\star}/(\pi R_e^2)$ but the limiting surface mass density as $r \to 0$.} surface mass density $\Sigma_{\rm max} \sim 10^5 \msun/$pc$^{-2} \simeq 20$ g cm$^{-2}$ for spheroidal stellar systems across a span of $\sim$7 orders of magnitude in total stellar mass $M_{\star}$ and $\sim$5 in effective radius $R_e$. These dense stellar systems include globular clusters in the Milky Way and nearby galaxies, massive star clusters in nearby starbursts, nuclear star clusters in dwarf spheroidals and late-type discs, ultra-compact dwarfs, and galaxy spheroids spanning the range from low-mass ``cusp'' bulges and ellipticals to massive ``core'' ellipticals; these systems are all baryon dominated and likely formed in rapid, dissipational events. \citet{Hopkins2010} have already weighed a number of theoretical scenarios that might explain the existence of a universal $\Sigma_{\rm max}$ including that it is an effect of infrared radiation pressure mediated by dust. While seen as particularly promising by \citet{Hopkins2010}, these authors did note that an explanation invoking indirect radiation pressure faces a number of challenges and further, recent work involving some of the original authors \citep{Grudic2018a,Grudic2018b} seems to cast further doubt on this general scenario. The most significant challenge facing the scenario is presented by the differing metallicities of these systems and, therefore, the well-motivated expectation that their dust-to-gas ratio -- and therefore infrared opacity -- should vary. In particular, one would expect {\it ceteris paribus} that systems that form their stars at quite high redshift and which are observed to have low stellar metallicities today, would have higher maximum surface densities. Other challenges include that the mechanism would seem not to work if the stellar content of the system were built up in a number of star-formation events and that, again for systems formed at high redshift, there has been a lot of time for dynamical relaxation to diminish the central surface mass density. We revisit the question of whether the observed maximum stellar surface density can in fact be explained by radiation pressure effects in this work. In brief, this paper extends previous work in three ways: i) we determine the stability curve for star forming, dusty clouds subject to radiation pressure deriving from the nascent stars adopting a realistic temperature-dependent opacity $\kappa \propto T^2$ (rather than assuming a constant value); ii) we account simultaneously for direct and indirect radiation pressure effects; and iii) we follow the evolution of star clusters (forming out of giant molecular clouds) accounting for radiation pressure in our determination of the final state surface mass density as a function of initial state surface mass density. The remainder of this paper is as follows. In \autoref{sec:model} we present a theoretical calculation for the process of star formation limited by both direct and dust-reprocessed radiation. In \autoref{sec:discussion} we compare this theoretical calculation to observations of star clusters, and discuss further implications of our findings. We summarise and conclude in \autoref{sec:summary}. \subsection{A word on notation and symbols} To forestall any potential confusion, below we label (dimensionful and dimensionless) reference values of some general quantity $x$ with a subscript asterisk: $x_*$. Thus, for instance, $T_*$ is a reference (dimensionful) temperature and $\tau_*$ is a (dimensionless) reference optical depth (both defined below). Quantities connected to stars or star formation are labelled with a subscript ``$_\star$". Thus, for instance, $M_\star$ is the total stellar mass of the system and $\dot{\Sigma}_{\rm \star,crit}$ is the critical star formation surface density (defined below). | \label{sec:discussion} \subsection{Limits on surface density: observational comparison} The simple considerations set out above suggest that indirect and direct radiation pressure, acting in concert, should put an upper limit of $\sim 1.3 \times 10^5 \msun$pc$^{-2} \ (\zsun/Z) \ (\Psi_0/\Psi)$ for the maximum stellar surface density of star clusters. Interestingly, this finding is broadly consistent with observations. Indeed, as presaged above, \citet{Hopkins2010} pointed out the apparent existence of an empirical upper bound, at $\Sigma_{\rm max} \sim 10^5 \msun$pc$^{-2}$, to the central stellar surface mass density of compact stellar systems. \citet{Hopkins2010} remark that this rough limit holds over a $\sim$ 7 order magnitude range of total mass, a $\sim$ 5 order of magnitude range in physical size, and over $\sim 2$ orders of magnitude in metallicity. Given this, they tentatively conclude ``that feedback from massive stars likely accounts for the observed $\Sigma_{\rm max}$, plausibly because star formation reaches an Eddington-like flux that regulates the growth of these diverse systems". However, a problem for this explanation -- raised by \citet{Hopkins2010} and again recently by \citet{Grudic2018a,Grudic2018b} -- is the expectation that $\Sigma_{\rm max}$ should scale inversely as the metallicity (because of the expectation that the dust-to-gas mass ratio trace metallicity) whereas it did not seem to these authors that there was any such metallicity dependency evident in their data. \begin{figure}% \centering \includegraphics[width = 0.5 \textwidth]{plotCentralSurfaceDensityVsMetallicity.pdf} \caption{ Central surface mass density (measured, inferred, or lower limit as described below) versus metallicity for different compact stellar systems (data truncated below $10^3 \msun$ pc$^{-2}$). The systems included in the compilation are as follows: {\bf MW GCs:} Milky Way globular clusters ($N = 119$) with central mass surface density from \citet{Baumgardt2018} and with metallicities from \citet{Harris1996,Harris2010}; {\bf GCs, UCDs, cEs:} surface mass density within the effective half-light radius for massive globular clusters, ultracompact dwarfs, and compact elliptical galaxies ($N = 29$) from the Archive of Intermediate Mass Stellar Systems with metallicities compiled by \citet{Janz2016}; {\bf M31 GCs:} Central surface mass densities for globular clusters from M31 ($N = 18$) from the compilation by \citet{Barmby2007}; {\bf MW + satel.:} Central surface mass densities for massive clusters from Milky Way and satellites (the Large Magellanic Cloud, Small Magellanic Cloud and the Fornax dwarf spheroidal, $N = 153$) from the compilation by \citet{McLaughlin2005}; {\bf M82:} surface density inside half mass radius for super star clusters from M82 from \citet{McCrady2007} ($N = 15$) adopting gas phase metallicity of 0.6 $\zsun$ \citep{Origlia2004,Nagao2011}; {\bf NGC253:} total (gas+stars) surface density inside 2D FWHM radius nascent super star clusters from the central starburst in NGC 253 from \citet{Leroy2018} ($N = 14$) adopting gas phase metallicity of 1.0 $\zsun$ \citep{Webster1983}. The sloped orange line is for $\Sigma_{\rm 0,crit}(Z) = \Sigma_{\rm 0,crit}(\zsun/Z)$ with $\Psi = \Psi_0$ and a width encompassing the efficient convection and the pure radiative transfer limits (the horizontal orange line is for no metallicity evolution). The dashed horizontal line corresponds (cf.~\autoref{eq:SigmaCritIMBH}) \ roughly to the critical stellar volumetric number density of $n_* \sim 10^6$ pc$^{-3}$ where stellar mergers in cluster cores occur on a timescale less than the main sequence lifetime of massive stars, allowing the merger formation of giant stars, progenitors of intermediate mass black holes (assuming a large fraction of massive stars are in primordial hard binaries; see the text). The two systems that most surpass the expected upper limit are labelled; they are M85-HCC1, a hypercompact star cluster claimed as likely the remnant nucleus of a galaxy recently accreted on to its current host galaxy \citep{Sandoval2015}, and Liller 1, a Galactic globular cluster that is in core collapse \citep{Baumgardt2018}. } \label{fig_plotCentralSurfaceDensityVsMetallicity.pdf} \end{figure} Our compilation of the central surface mass density of a number of systems vs.~metallicity in shown in \autoref{fig_plotCentralSurfaceDensityVsMetallicity.pdf}. The data are still sparsely sampled and subject to selection effects that we have not rigorously characterised. Nevertheless, they do not seem to us to be inconsistent with such a metallicity-dependency for $\Sigma_{\rm max}$. A further point to keep in mind here is that the sloped limit line in \autoref{fig_plotCentralSurfaceDensityVsMetallicity.pdf} assumes a metallicity independent light to mass ratio $\Psi(Z) \to \Psi_0$. Were, for instance, the mean IMF to become systematically more ``top heavy" for lower metallicity, this would have the overall effect of attenuating and plausibly even totally cancelling out the metallicity evolution of the critical central surface mass density \citep[cf.~recent observations of the 30 Doradus local starburst:][where the expected $\sim 3-4$ increase in $L/M$ concomitant with the claimed top-heavy IMF would roughly cancel out the effect of the LMC's $\sim 0.4 \zsun$]{Schneider2018}. However we caution the reader that claims for strong metallicity effects on the IMF have frequently been contested or countered with seemingly contradictory examples or analysis \citep[e.g.,][]{Bastian2010, Offner2014}. Aside from obtaining more data, a fuller empirical analysis of the issue of the putative maximal central surface mass density would have to deal with a number of issues that revolve around questions of systematics connected to the dynamical evolution of stellar systems. One possible confound is that metal-rich GCs tend to have formed nearer the centres of their host galaxies than relatively metal poor ones, i.e., in a relatively stronger tidal fields. This will render the former more compact at the present time, independent of their initial configuration. In light of the complexity of applying our model to old stellar systems that may have undergone significant dynamical evolution, the data covering in-formation, embedded super star clusters in the NGC 253 nuclear star burst obtained by \citet{Leroy2018} provide a particularly interesting test of our model. From ALMA 350 MHz dust continuum observations, these authors find 14 candidate super star clusters ($M_{\star} \gsim 10^5 \msun$) within the $\sim 3 \times 10^8 \msun$ of molecular gas inside NGC 253's nucleus. Each cluster has a large gas fraction and is, consequently, highly extincted behind very high gas and dust columns (yielding optical depths $\tau \sim 5 -10$ at 100 $\mu$m). Nevertheless, \citet{Leroy2018} find no high velocity line wings in their data implying that each cluster's gas is gravitationally bound. This finding is broadly consistent with our scenario which suggests that indirect radiation pressure effects in the nascent NGC 253 star clusters, while likely to cause some of the clusters to expand, will not expel the clusters' gas (cf.~\autoref{fig_plotCentralSurfaceDensityVsMetallicity.pdf}). Overall, indeed, we would expect a large fraction of each cluster's original gas allocation to be turned into stars, consistent with the data and analysis presented by \citet{Leroy2018}. \subsection{Stellar Mergers and Intermediate Mass Black Holes} A possible consequence of our picture is that clusters formed at higher metallicities (approaching solar) may be prevented by indirect radiation pressure from reaching the volumetric stellar number densities required such that stellar mergers may occur sufficiently rapidly in their cores to form the giant stellar precursors of intermediate mass black holes (IMBHs). \citet{Bonnell2005} find that stellar mergers of massive stars can occur on a timescale less than their $\sim 10^6$ yr main sequence lifetimes -- thus allowing for the dynamical formation of giant stars via mergers -- for core cluster densities $n_* \gsim 10^6$ pc$^{-3}$ assuming that a large fraction of massive stars are born into hard binary systems. This corresponds to a rough critical surface density \begin{equation} \Sigma_{\rm crit,IMBH} \sim 8 \times 10^5 \msun \ {\rm pc}^{-2} \left(\frac{M_c}{10^6 \msun} \right)^{\frac{1}{3}} \left(\frac{\rho_{\rm crit,IMBH}}{10^6 \msun/{\rm pc}^3} \right)^{\frac{2}{3}} \, . \label{eq:SigmaCritIMBH} \end{equation} This critical surface density is shown, for the fiducial parameters, as the horizontal dashed line in \autoref{fig_plotCentralSurfaceDensityVsMetallicity.pdf}; compact stellar systems at $Z \gsim 0.2 \zsun$ may have trouble reaching this critical surface density (though it is to be acknowledged that there are a handful of star systems above this rough threshold at $Z \gsim 0.2 \zsun$ in our compilation). This effect is independent of and in addition to stellar mass loss due to Wolf-Rayet phase winds which also increases as a function of metallicity and may also preclude the formation of IMBHs \citep{Yungelson2008,Glebbeek2009}. In this paper we investigate the combined effects of indirect, dust-reprocessed and direct, stellar radiation pressure on the formation of the densest star clusters. Adopting our calculation from \citetalias{Crocker2018} of the largest column of dusty gas for which hydrostatic equilibrium is possible when the column is subject to the opposing forces of indirect radiation pressure and gravity and also drawing results on direct radiation pressure from \citetalias{Fall2010}, we construct here an evolutionary model for a dense protocluster gas cloud forming stars, and show that clouds with initial surface density $\gsim 10^5 \msun$ pc$^{-2}$ with Milky Way-like dust and dust-to-gas ratios will become super-Eddington with respect to indirect radiation pressure at some point during their star formation process. This effect is unlikely to push gas out of clusters in winds, abruptly cutting-off star formation. Rather, systems with sufficiently high initial surface mass densities probably suffer a rather gentle expansion under indirect radiation pressure effects. Only late in their evolution, once they have typically turned well more than 50\% of their original gas allocation into stars, will {\it direct} radiation pressure effects turn on in such clusters, pushing the remaining gas out of the cluster at greater than the escape speed. This process is complete well before core-collapse supernovae start going off in such clusters. The combined effect of direct and indirect radiation pressure is to set an upper limit of $\approx 10^5 \ (Z_\odot/Z)$ $M_\odot$ pc$^{-2}$ on the surface densities of star clusters, and to produce a star formation efficiency -- defined as the ratio of the initial gas surface density to the final stellar surface density -- that has a maximum of $\approx 90\%$ for gas clouds with surface densities near this upper limit, and falls off sharply at either lower or higher surface densities. This limit is likely to preclude the formation of intermediate mass black holes via stellar collisions in any star cluster with a metallicity above $\approx 20\%$ of Solar. The scenario suggested by our model is qualitatively and quantitatively consistent with the empirical determination \citep{Hopkins2010} that there seems to be an upper limit to the central surface mass density of compact stellar systems at $\sim 10^5 \msun$ pc$^{-2}$. We compare our model to an updated compilation of measured stellar surface densities in a wide variety of compact stellar systems, and find that it is qualitatively consistent with the observations, including the possibility that star clusters formed with lower metallicities and thus lower dust content might have systematically higher maximum surface densities. Further tests of this model, and in particular the prediction that the results should depend on metallicity, will require additional measurements of surface densities in low-metallicity systems, preferably young ones so as to minimise the confounding effects of dynamical evolution. | 18 | 8 | 1808.01726 |
1808 | 1808.08577_arXiv.txt | Some problems of spontaneous and gravitational baryogenesis are discussed. Gravity modification due to the curvature dependent term in gravitational baryogensis scenario is considered. It is shown that the interaction of baryonic fields with the curvature scalar leads to strong instability of the gravitational equations of motion and as a result to noticeable distortion of the standard cosmology. | \label{aba:sec1} Observations show that at least the region of the Universe around us is matter-dominated. Though we understand how the matter-antimatter asymmetry may be created, the concrete mechanism is yet unknown. The amount of antimatter is very small and it can be explained as the result of high energy collisions in space. The existence of large regions of antimatter in our neighbourhood would produce high energy radiation as a consequence of matter-antimatter annihilation, which is not observed. Any initial asymmetry at inflation could not solve the problem of observed excess of matter over antimatter, because the energy density associated with baryonic number would not allow for sufficiently long inflation. On the other hand, matter and antimatter seem to have similar properties and therefore we could expect a matter-antimatter symmetric Universe. A satisfactory model of our Universe should be able to explain the origin of the local observed matter-antimatter asymmetry. The term {\it baryogenesis} means the { generation of the asymmetry} between baryons (basically protons and neutrons) and antibaryons (antiprotons and antineutrons). In 1967 Andrey Sakharov pointed out 3 ingredients, today known as {\it Sakharov principles}, to produce a matter-antimatter asymmetry from an initially symmetric Universe. These conditions include: 1) non-conservation of baryonic number; 2) breaking of symmetry between particles and antiparticles; 3) deviation from thermal equilibrium. However, not all of three Sakharov principles are strictly necessary. In what follows we briefly discuss some features of spontaneous baryogenesis (SBG) and concentrate in more detail on gravitational baryogenesis (GBG). Both these mechanisms do not demand an explicit C and CP violation and can proceed in thermal equilibrium. Moreover, they are usually most efficient in thermal equilibrium. The statement that the cosmological baryon asymmetry can be created by spontaneous baryogenesis in thermal equilibrium was mentioned in the original paper by Cohen and Kaplan\cite{Cohen:1987vi} and developed in subsequent papers\cite{Cohen:1988kt,Cohen:1991iu}, for review see\cite{Dolgov:1991fr,Rubakov:1996vz}. The term "spontaneous" is related to spontaneous breaking of a global $U(1)$-symmetry, which ensures the conservation of the total baryonic number in the unbroken phase. This symmetry is supposed to be spontaneously broken and in the broken phase the Lagrangian density acquires the additional term \be {\cal L}_{SB} = (\partial_{\mu} \theta) J^{\mu}_B\, , \label{L-SB} \ee where $\theta$ is the Goldstone field and $J^{\mu}_B$ is the baryonic current of matter fields, which becomes non-conserved. For a spatially homogeneous field, $\theta = \theta(t)$, the Lagrangian is reduced to the simple form \be {\cal L}_{SB} = \dot \theta\, n_B\,, \ \ \ \ n_B\equiv J^0_B, \ee where time component of a current is the baryonic number density of matter, so it is tempting to identify ${\dot \theta}$ with the chemical potential, $ \mu_B$, of the corresponding system. However, such identification is questionable and depends upon the representation chosen for the fermionic fields\cite{Dolgov:1994zq,Dolgov:1996qq}. It is heavily based on the assumption ${\dot \theta \approx const}$, which is relaxed in the work\cite{Arbuzova:2016qfh}. But still the scenario is operative and presents a beautiful possibility to create an excess of particles over antiparticles in the Universe. Subsequently the idea of gravitational baryogenesis (GBG) was put forward~\cite{Davoudiasl:2004gf}, where the scenario of SBG was modified by the introduction of the coupling of the baryonic current to the derivative of the curvature scalar $R$: \be {\cal L}_{GBG} = \frac{1}{M^2} (\partial_\mu R ) J^\mu_B\, , \label{L-GBG} \ee where $M$ is a constant parameter with the dimension of mass. In the presented talk we demonstrate that the addition of the curvature dependent term (\ref{L-GBG}) to the Hilbert-Einstein Lagrangian of General Relativity (GR) leads to higher order gravitational equations of motion, which are strongly unstable with respect to small perturbations. The effects of this instability may drastically distort not only the usual cosmological history, but also the standard Newtonian gravitational dynamics. We discovered such instability for scalar baryons~\cite{Arbuzova:2016cem} and found similar effect for the more usual spin one-half baryons (quarks)~\cite{Arbuzova:2017vdj}. | } For more accurate analysis numerical solution will be helpful, which we will perform in another work. The problem is complicated because the assumption of slow variation of $\dot R$ quickly becomes broken and the collision integral in time dependent background is not so simply tractable as the usual stationary one. The technique for treating kinetic equation in non-stationary background is presented in Ref.~\cite{Arbuzova:2016qfh}. For evaluation of $R(t)$ in this case numerical calculations are necessary, which will be presented elsewhere. Here we describe only the basic features of the new effect of instability in gravitational baryogenesis. To conclude we have shown that gravitational baryogenesis in the simplest versions discussed in the literature is not realistic because the instability of the emerging gravitational equations destroys the standard cosmology. Some stabilization mechanism is strongly desirable. Probably stabilization may be achieved in a version of $F(R)$-theory. \vspace{1cm} \centerline{{\bf Acknowledgement}} This work was supported by the RSF Grant N 16-12-10037. The author expresses sincere gratitude to Harald Fritzsch for his invitation and for the opportunity to present the talk at the Conference on Particles and Cosmology. She would like to thank Kok Khoo Phua for his kind hospitality at NTU, Singapore. | 18 | 8 | 1808.08577 |
1808 | 1808.01456_arXiv.txt | This study expands the coverage and improves the homogeneity of the distribution of MILES template stars in the parameter space, as well as extends the wavelength coverage of the template spectra to the far red beyond the Ca\,{\sc{ii}} triplet. To achieve this we have carried out a major observational campaign using the OMR long-slit spectrograph mounted on the NAOC 2.16\,m telescope and the YFOSC long-slit spectrograph mounted on the YNAO 2.4\,m telescope. The original sample is based on the MILES library, supplemented by 918 stars selected from PASTEL database. In total, 822 OMR and 1,324 YFOSC spectra, covering respectively the wavelength ranges $\lambda\lambda$3800--5180 and $\lambda\lambda$5150--9000, have been collected and reduced. The spectra have a mean resolution FWHM (full-width at half-maximum) of $\sim 3.3$\,{\AA} and are wavelength- and flux-calibrated to an accuracy of $\sim 20$\,km\,s$^{-1}$ and $\sim 5$\,per\,cent, respectively. The spectra are further corrected for systematic errors in the wavelength calibration to an accuracy of $\sim 4$\,km\,s$^{-1}$ by cross-correlating with the theoretical spectra. Almost all the spectra have an average signal to noise ratio (SNR) better than 100 per pixel. Combined with the MILES spectra, there are now 1,731, 1,542, 1,324 and 1,273 stars with spectra covering respectively $\lambda\lambda$3800--5180, $\lambda\lambda$3800--7500, $\lambda\lambda$5150--9000 and $\lambda\lambda$3800--9000. This paper describes our template star selection, the observation and data reduction, and presents the reduced spectra collected hitherto. | A low- to medium-resolution spectral library with a good and homogenous coverage of the stellar atmospheric parameter space (i.e. effective temperature $T_{\mathrm{eff}}$, surface gravity $\log\,g$ and metallicity [Fe/H]) is an important tool in many astronomical applications, from the spectral synthesis analyses of stellar populations of galaxies \citep{Guiderdoni1987,Buzzoni1989,Worthey1994,Leitherer1996,1999ApJ...513..224V,Bruzual2003,Leitherer2010, 2012MNRAS.424..157V,Rock2016,Milone2014} to the stellar atmospheric parameters determinations by spectral template matching \citep{Adelman2008,Lee20081,Boeche2011,Wuyue,LSP3}. The latter has become increasing important, driven by a number of already completed or still on-going large scale spectroscopic surveys, such as the Sloan Extension for Galactic Understanding and Exploration \citep[SEGUE;][]{yanny-segue}, the Radial Velocity Experiment \citep[RAVE; ][]{2006AJ....132.1645S}, the Large sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) Galactic Spectroscopic Surveys \citep{2012RAA....12..723Z, deng-legue, liu-lss-gac, yuan-lamost}, and the APO Galactic Evolution Experiment \citep[APOGEE;][]{APOGEE}. These surveys are providing huge amounts of low- to intermediate-resolution spectral data to help improve our understanding of the structure, kinematics and chemistry, and formation and evolution of the Milky Way galaxy, and of other galaxies in general. Specifically, the on-going LAMOST Galactic Spectroscopic Surveys have hitherto collected over 7.5 million low-resolution ($R\sim 1800$) quality optical spectra \citep{LAMOST_preface}. To derive robust estimates of the stellar atmospheric parameters as well as the radial velocities from this huge data set, two stellar parameter determination pipelines based on the technique of spectral template matching, the LAMOST Stellar Parameter Pipeline \citep[LASP; ][]{lamost-dr1} and the LAMOST Stellar Parameter Pipeline at Peking University \citep[LSP3; ][]{LSP3}, have been developed. LASP determines both the atmospheric parameters as well as the radial velocities by template matching with the empirical spectral library ELODIE \citep{2001A&A...369.1048P}, whereas LSP3 uses ELODIE for the radial velocity determinations and another empirical spectral library MILES \citep{2006MNRAS.371..703S,2011A&A...532A..95F} for the atmospheric parameter determinations. Several either empirical \citep{2006MNRAS.371..703S,2011A&A...532A..95F,STELIB,ngsl,xsl,indo-us,2012MNRAS.424..157V,2001MNRAS.326..959C,Jones1999} or synthetic \citep{Lastennet2002,Barbuy2003,Murphy2004,Munari2005,Martins2005,Coelho2005} spectral libraries are now available (cf. the recent review by \citealt{Wuyue}). Compared to synthetic spectra, empirical spectra have the advantage that they represent {\em real} stars. On the other hand, empirical spectral libraries are always restricted by the available observations and thus limited in term of the parameter space coverage \citep{Martins2007,Wuyue}. Either due to the lack of a wide coverage of the stellar atmospheric parameter space or insufficiently accurate flux-calibration over a wide wavelength range, most of those currently available empirical spectral libraries are not suitable as template spectral libraries for the determinations of the stellar atmospheric parameters. For examples, STELIB \citep{STELIB}, NGSL \citep{ngsl} and XSL \citep{xsl} have insufficient atmospheric parameter space coverage, while INDO-US \citep{indo-us} and MIUSCAT \citep{2012MNRAS.424..157V} suffer from poor flux-calibration, and CaT \citep{2001MNRAS.326..959C} and Jones \citep{Jones1999} have narrow wavelength coverages. In comparison, MILES and ELODIE, adopted as the template library respectively LASP and LSP3, have broad atmospheric parameter coverages as well as wide wavelength ranges. MILES spectra were observed using a long-slit spectrograph with a spectral resolution comparable to that of the LAMOST spectra and were accurately flux-calibrated to a few per cent \citep{2006MNRAS.371..703S}. In comparison, ELODIE spectra were obtained by the ELODIE spectrograph with medium ($R\sim$10,000) to high spectral resolution ($R\sim$42,000) and were poorly flux-calibrated. Thus the MILES spectral library is ideal for the determinations of the atmospheric parameters, although ELODIE works much better for the radial velocity determinations, given the much higher spectral resolution of the spectra of the latter \citep{LSP3}. With MILES, LSP3 has achieved a precision of 150 K, 0.25 dex, 0.15 dex for the determinations of $T_{\mathrm{eff}}$, log\, $g$, and [Fe/H], respectively, for LAMOST spectra of FGK type stars of signal-to-noise ratios (SNRs) per pixel better than 10. As discussed in \cite{LSP3} and \cite{yuan-lamost}, there are several aspects of the MILES library that are desired of further improvement. Firstly, while the library has a decent coverage of the stellar parameter space, the distribution of stars in the parameter space is not uniform -- there are clusters and holes of stars in the distribution that produce systematic errors in the derived atmospheric stellar parameters \citep{LSP3}. A more acute problem is that the spectra only cover wavelength ranges up to 7500\,{\AA}. Given that the LAMOST Galactic Spectroscopic Surveys target stars of all colors in the Galactic disk and halo, there are a significant fraction (about 30\,per\,cent) of spectra that meet the survey SNR requirement, i.e. better than 10, in the red, but fail to do so in the blue, either because the stars are intrinsically red (i.e. of late spectral types) or heavily reddened by the interstellar dust grains, or both. The lack of suitable template spectra in the red is largely responsible for the fact that of all the spectra hitherto collected by LAMOST, only just over half have the atmospheric parameters determined \citep{lamost-dr1, yuan-lamost}. Although there are several empirical libraries e.g.\, MIUSCAT, INDO-US, STELIB, NGSL and XSL as mentioned above, that provide spectra covering almost the whole optical wavelength range, those spectra are either poorly flux-calibrated or have insufficient coverage of the atmospheric parameter space. Thus it is highly desirable to extend the wavelength coverage of all MILES template spectra to the far red, beyond the Ca\,{\sc ii} triplet for example. Finally, there is also room of expansion in the parameter coverage of MILES template stars, particularly toward low metallicities and low effective temperatures. With the above considerations in mind, we have embarked on a massive campaign to expand the MILES empirical spectral library. To maintain the maximum internal consistency, all spectra will be collected using long-slit spectrographs with a spectral resolution comparable to that of the MILES spectra and accurately flux-calibrated to a few per cent. Additional template stars with accurately known atmospheric parameters, mostly determined with high resolution spectroscopy, are selected and added to the library, and observed in order to increase the parameter coverage as well as to improve the homogeneity of the distribution of template stars in the parameter space. Spectra extending to the far red will also be collected such that LAMOST spectra of stars of either intrinsically red colors or heavily reddened by dust grains can also be properly analyzed with LSP3. The spectra collected will also be of interest for other applications such as the spectral synthesis analyses of stellar populations of galaxies as mentioned above. The observed high SNR (better than 100 per\,pixel) spectra collected in LEMONY--a Library of Empirical Medium-resolution spectra by Observations with the NAOC Xinglong 2.16 m and YNAO Gaomeigu 2.4 m telescopes, are accurately wavelength- and flux-calibrated, and cover almost the whole optical range of $\lambda \lambda $ 3800--9000 at a FWHM (full-width at half-maximum) resolution of $\sim 3.3$\,{\AA}. The spectra were collected with the NAOC 2.16m telescope in the blue and the YNAO 2.4m in the red. Here we present the final results of this observational campaign. The paper is organized as follows. In Section\,2 we describe the selection of additional template stars and observations. The data reduction is presented in Section\,3. We describe the new library LEMONY to guide its use in Section\,4. Qualities of the secured spectra are examined and discussed in Section\,5. In Section\,6, we discuss some improvements of LSP3 based on LEMONY. Finally, Section\,7 summarizes the main results of the paper. | In this work we built a new stellar spectral library, LEMONY, based on the observations using the OMR long-slit spectrograph mounted on the NAOC 2.16 m telescope and the YFOSC long-slit spectrograph mounted on the YNAO 2.4 m telescope. The coverage in the parameter space is originally based on MILES, but expanded through selecting targets from PASTEL catalogue in order to improve the coverage and homogeneity of the distribution of the MILES template stars. The wavelength coverage of the template spectra is also extended to the far red beyond the Ca~{\sc {ii}} triplet. Hitherto, 822 OMR (blue) and 1,324 YFOSC (red) spectra, covering respectively wavelength ranges $\lambda\lambda$3800--5180 and $\lambda\lambda$5150--9000, have been observed and reduced. The spectra has a FWHM resolution of about 3.3\,{\AA}, and a mean SNR higher than 100 per pixel for essentically all of them. An accuracy of $\sim 0.3$\,{\AA} and $\sim 5$\,per\,cent have been achieved for the wavelength- and flux-calibration. The wavelength-calibration is further improved to an accuracy of $\sim\,4$\,km\,s\,$^{-1}$ after corrected for the systematic errors in the spectral dispersion relations derived from the arc spectra. Comparison of broad band ($B-V$) colours calculated from the LEMONY spectra with those calculated from the MILES spectra and the photometric measurements from the Lausanne photometric database, and comparison between the LEMONY spectra with those from the MILES and CaT libraries for the common stars, all suggest that a flux-calibration accuracy of the LEMONY spectra of $\sim$\,5\,per\,cent. The Lick/IDS and the near-IR indices derived from the LEMONY spectra are also consistent with those derived from the spectra in the MILES, ELODIE and CaT libraries. Currently, the LEMONY library contains 822 blue and 1,324 red spectra. Together with the MILES spectra, one now has 1,731, 1,542, 1,324 and 1,273 stars with high quality spectra covering respectively wavelength ranges $\lambda\lambda$3800--5180, $\lambda\lambda$3800--7500, $\lambda\lambda$5150--9000 and $\lambda\lambda$ 3800--9000. Compared with the MILES library, the coverage and homogeneity of the distribution of the template stars in the LEMONY library in the parameter space are much improved. In addition, a significant fraction of the stars have red spectra extending in wavelength beyond the Ca~{\sc ii} triplet. The LEMONY library is expected to reduce the systematic errors of atmospheric parameters deduced with LSP3. The 1,324 LEMONY red spectra will be used as template spectra to estimate atmospheric parameters from the LAMOST red-arm spectra, for stars either intrinsically red (i.e. of late spectral types) or heavily reddened by the interstellar dust grains, increasing the number of stars surveyed by LAMOST with atmospheric parameters determined by $\sim$ 30 per\,cent. The LEMONY library should also be useful for stellar population syntheses of galaxies and clusters in a wide wavelength coverage. Of course, it should also benefit other studies, such as the spectral classification of stars, tests of the stellar atmospheric models,etc. | 18 | 8 | 1808.01456 |
1808 | 1808.06795_arXiv.txt | {Solar active region (AR) 12673 in 2017 September produced the two largest flares in Solar Cycle 24: the X9.3 flare on September 6 and the X8.2 flare on September 10. } {We attempt to investigate the evolutions of the two large flares and their associated complex magnetic system in detail. } {Combining observations from the \emph{Solar Dynamics Observatory} and results of nonlinear force-free field (NLFFF) modeling, we identify various magnetic structures in the AR core region and examine the evolution of these structures during the flares. } {Aided by the NLFFF modeling, we identify a double-decker flux rope configuration above the polarity inversion line (PIL) in the AR core region. The north ends of these two flux ropes were rooted in a negative- polarity magnetic patch, which began to move along the PIL and rotate anticlockwise before the X9.3 flare on September 6. The strong shearing motion and rotation contributed to the destabilization of the two magnetic flux ropes, of which the upper one subsequently erupted upward due to the kink-instability. Then another two sets of twisted loop bundles beside these ropes were disturbed and successively erupted within five minutes like a chain reaction. Similarly, multiple ejecta components were detected as consecutively erupting during the X8.2 flare occurring in the same AR on September 10. We examine the evolution of the AR magnetic fields from September 3 to 6 and find that five dipoles emerged successively at the east of the main sunspot. The interactions between these dipoles took place continuously, accompanied by magnetic flux cancellations and strong shearing motions. } {In AR 12673, significant flux emergence and successive interactions between the different emerging dipoles resulted in a complex magnetic system, accompanied by the formations of multiple flux ropes and twisted loop bundles. We propose that the eruptions of a multi-flux-rope system resulted in the two largest flares in Solar Cycle 24. } | Solar flares are explosive phenomena on the Sun that can be observed from X-ray to radio wavelengths, and that release dramatic free magnetic energy stored in the solar atmosphere via the process of magnetic reconnection (Priest \& Forbes 2002; Schmieder et al. 2015). In previous studies, the accumulation of free magnetic energy in the solar atmosphere is demonstrated to be mainly caused by three types of mechanisms: (1) magnetic flux emergence or cancellation (Wang \& Shi 1993; Chen \& Shibata 2000; Zhang et al. 2001; Sterling et al. 2010; Louis et al. 2015), (2) shearing motion (Wang et al. 1994; Meunier \& Kosovichev 2003; Sun et al. 2012), (3) sunspot rotation (Brown et al. 2003; Zhang et al. 2007; T{\"o}r{\"o}k et al. 2013). Although the energy accumulation has been investigated thoroughly, it is difficult for us to comprehend the detailed process of violent energy release in various solar eruptions. Because it is widely accepted that magnetic flux ropes play key roles in triggering eruptive events (Amari et al. 2000; Fan 2005; Kliem et al. 2010; Liu et al. 2010; Green et al. 2011; Li et al. 2016; Yan et al. 2017), we can understand these eruptive events such as solar flares and coronal mass ejections (CMEs) through studying magnetic flux ropes. \begin{figure*} \centering \includegraphics [width=0.96\textwidth]{fig1.eps} \caption{ Flares produced by AR 12673. Panel (a): GOES SXR 1-8 {\AA} flux variation from 2017 September 3 to September 11. Four X-class flares took place during this period, of which the two largest ones reached up to X9.3 (orange region) and X8.2 (green region), respectively. The blue horizontal dotted lines mark the threshold levels of M1.0 and X1.0 flares. Panels (b)-(d): overview of the X9.3 flare in AR 12673 on September 6. The AIA 94 {\AA} image in panel (b) shows this AR at the onset of the flare. HMI continuum intensitygram and LOS magnetogram in panels (c) and (d) display the sunspots and underlying magnetic fields in the AR core region, whose field of view (FOV) is outlined by the green square in panel (b). } \label{fig1} \end{figure*} A magnetic flux rope is a set of magnetic field lines winding around a central axis in classical eruptive flare models and many CME observations. A huge amount of effort has been made in numerical simulations of the formation and dynamic activity of flux ropes (Forbes \& Priest 1995; Aulanier et al. 2010). Amari et al. (2000, 2003) simulated the evolution of a flux rope and proposed that a slow converging motion of the footpoints of field lines toward the polarity inversion line (PIL) contributed to the formation of a flux rope through magnetic reconnection. With high-resolution observations, the existence of flux ropes in the solar atmosphere has also been recently evidenced (Guo et al. 2010, 2013; Cheng et al. 2011; Yang et al. 2014; Kumar et al. 2017; Guglielmino et al. 2017; Wang et al. 2017a; Yan et al. 2018a; Shen et al. 2018). Zhang et al. (2012) reported a flux rope observed as a hot extreme ultraviolet (EUV) channel before and during the solar eruption and proposed that the instability of this flux rope triggered the eruption. Li \& Zhang (2013a) investigated the successive eruptions of two flux ropes during an M-class flare. Li \& Zhang (2013b) presented four homologous flux ropes, which were formed successively at the same location in an active region (AR). These observations imply that flux ropes may be ubiquitous on the Sun (Zhang et al. 2015; Hou et al. 2016). In the present work, a magnetic flux rope is defined as a set of magnetic field lines winding around a central axis by more than one full turn (Liu et al. 2016). Then aided by nonlinear force-free field (NLFFF) modeling and the calculation of twist number, we can identify a magnetic flux rope without ambiguity. Flux ropes are often related to various magnetohydrodynamic (MHD) instability processes, which eventually trigger solar flares and CMEs (Alexander et al. 2006; Liu et al. 2007; Kumar \& Cho 2014). Kink MHD instability is triggered by the azimuthal twist of magnetic tubes. Numerical simulations of the kink instability suggest that if the twist of a flux rope exceeds a critical value, then this rope becomes unstable (Kliem et al. 2004). The exact value of required twist depends on various factors such as loop geometry and overlying magnetic fields (Hood \& Priest 1979; Baty 2001; Fan \& Gibson 2004; Leka et al. 2005). In addition, observations of kink instability were reported recently by many authors (Srivastava et al. 2010; Wang et al. 2017b). From 2017 September 4 to September 10, AR 12673 produced a total of 4 X-class flares, 27 M-class flares, and a multitude of smaller ones (see the details in Yang et al. 2017). The X9.3 flare on September 6 is the largest flare in Solar Cycle 24 and has been reported in several works (Wang et al. 2018; Verma 2018; Shen et al. 2018; Yan et al. 2018b; Jiang et al. 2018). In this work, we identify a double-decker flux rope configuration above the PIL in the AR core region and detect successive eruptions of multiple flux ropes and twisted loop bundles within five minutes before the peak of this large flare. A similar phenomenon was also observed during the X8.2 flare on September 10. Here we investigate the evolutions of the two large flares and the associated complex magnetic system in detail. The remainder of this paper is structured as follows. Section 2 contains the observations and data analysis taken in our study. The detailed process of the two flares and the evolution of the magnetic fields in the AR core region are presented in Sect. 3. Finally, in Sect. 4 we conclude this work and discuss the results. \begin{figure*} \centering \includegraphics [width=0.96\textwidth]{fig2.eps} \caption{ Double-decker flux rope configuration above the PIL in the AR core region revealed by NLFFF modeling at 11:24 UT on 2017 September 6. Panels (a)-(b): top view and side view of two flux ropes (FR1 and FR2) composing the double-decker configuration. The FOV of these panels is approximated by the white square in Fig. 1(d). Panel (c): isosurfaces of twist number $T_{w}$=--1 (white) and $T_{w}$=--1.75 (red) viewed from the same perspective as panel (a). Panel (d): twist number distribution in the vertical (x-z) plane along the green cut labeled in panel (c). } \label{fig2} \end{figure*} | Employing the \emph{SDO} observations, we investigate the two largest flares of Solar Cycle 24 occurring in AR 12673 and the evolution of the AR magnetic fields. On 2017 September 6, the largest flare of Solar Cycle 24 took place with its peak intensity reaching X9.3. Aided by NLFFF modeling, we identify a double-decker flux rope configuration above the PIL in the AR core region. The north ends of these two flux ropes were rooted at a negative magnetic patch, which began to move along the PIL and kept shearing with adjacent positive fields before the X9.3 flare on September 6. The strong shearing motion as well as a continuous rotation contributed together to the destabilization of the two magnetic flux ropes. Then the upper flux rope erupted upward due to the kink-instability and led to the successive eruptions of another two sets of twisted loop bundles beside the flux ropes within five minutes like a chain reaction. Similarly, during another X8.2 flare occurring on September 10, we also detected the successive eruptions of multiple ejecta components. The evolution of the AR magnetic fields shows that five dipoles emerged successively at the east of the main sunspot. The interactions between these dipoles took place continuously, accompanied by magnetic flux cancellations and strong shearing motions. Flux ropes have been thought to be closely connected with CMEs and solar flares (Lin \& Forbes 2000; Fan 2005; Liu 2013). Amari et al. (2000) proposed a model to approach the theory of CMEs and two-ribbon flares, in which twisted flux ropes play a crucial role. It was shown that the modeled magnetic configuration could not stay in equilibrium, and a considerable amount of magnetic energy was released during the eruption of the flux rope. Employing high-resolution observations from space platforms, Zhang et al. (2015) detected 1354 flux rope proxies over the solar disk from 2013 January to 2013 December. Hou et al. (2016) further implied the existence of multiple flux ropes during the evolution of AR 11897. The classical scenario assumes a single flux rope for each eruption, but it is easy to imagine multiple flux ropes if the AR is complex and has extended curved PIL (Liu et al. 2009; Liu et al. 2012; Shen et al. 2013; Awasthi et al. 2018). T{\"o}r{\"o}k et al. (2011) presented a 3D MHD simulation to investigate three consecutive filament eruptions. They considered a configuration that contains two coronal flux ropes located within a pseudo-streamer and one rope located next to it. It is found that a sequence of eruptions was initiated by the eruption of the flux rope next to the streamer. The expansion of this rope resulted in two successive reconnection events, each of which triggered the eruption of a flux rope by reducing the overlying stabilizing flux. In the observational domain, Shen et al. (2012) reported the simultaneous occurrence of a partial and a full filament eruption in two neighboring source regions. Cheng et al. (2013) investigated successive eruptions of two flux ropes with an interval of several hours. In the present work, we identify a double-decker flux rope configuration above the PIL in the AR core region. The two flux ropes (FR1 and FR2) erupted at the onset of the X9.3 flare due to the shearing motion and rotation of the negative magnetic patch where the ropes were rooted. Then another two sets of twisted loop bundles (LB1 and LB2) beside these ropes were disturbed and successively erupted within five minutes like a chain reaction. The results from NLFFF modeling show that the $\mid$$T_{w}$$\mid$ of FR1 and FR2 are beyond 1.0 and the $\mid$$T_{w}$$\mid$ of LB1 is beyond 0.5. If we take a lower standard for defining a magnetic flux rope (e.g., Chintzoglou et al. 2015, who consider a half turn to be sufficient), then LB1 could be regarded as the third flux rope in this event. Therefore, we propose that the eruptions of a multi-flux-rope system rapidly released enormous magnetic energy and led to the X9.3 flare on September 6, the largest flare in Solar Cycle 24. Similar phenomenon was also observed during another X8.2 flare occurring in the same AR several days later. In recent years, the concept of double-decker filament (flux rope) was proposed by Liu et al. (2012) to explain two vertically separated filaments (flux ropes) over the same PIL. The complex configuration of double-decker flux rope was observed and modeled to exist prior to solar eruptive events (Cheng et al. 2014; Kliem et al. 2014). Extrapolated NLFFF structures in this work reveal that before the onset of the X9.3 flare, two magnetic flux ropes were located separated vertically above the PIL in the AR core region, forming a typical double-decker flux rope configuration. At the onset of the X9.3 flare, the strong shearing motion and rotation of the north ends of the two magnetic flux ropes contributed to their destabilization (Kliem et al. 2004; Srivastava et al. 2010; T{\"o}r{\"o}k et al. 2013; Yan et al. 2018b). The brightening at the cross sites of these two ropes observed in EUV wavelength indicated the interaction (magnetic reconnection) occurring between the two flux ropes during their slow-rise phase. The subsequent AIA observations revealed that the lower rope lost its stability first and erupted outwards while the upper flux rope kept rising upward. Then the upper magnetic flux rope writhed into a sigmoid shape. The calculation of twist number based on the NLFFF results shows that the maximum $\mid$$T_{w}$$\mid$ of the two flux ropes were all beyond 1.75 half an hour before the onset of the flare. It is worth noting that the exact value of twist required of the kink instability depends on various factors such as the flux rope geometry and the surrounding magnetic fields. T{\"o}r{\"o}k et al. (2004) proposed that the threshold of instability increases with rising aspect ratio and the number is 1.75 (3.5 $\pi$) at a loop aspect ratio $R/a \approx 5$, which corresponds to a rather fat flux rope. Although the double-decker flux ropes in the present work may have a different aspect ratio, we approximate the threshold value of kink instability to 1.75 here. The facts that the twist of the flux rope is beyond the threshold value of kink instability and its conversion into the writhe support the occurrence of the kink instability during the eruption of the upper flux rope. The eruption of a kink-unstable flux rope during this event has also been investigated by Yang et al. (2017). The existence of multiple flux ropes and twisted loop bundles during the two X-class flares reported in the present paper implies a complicated magnetic system in AR 12673. Examining the evolution of the magnetic fields in the AR core region, we notice that significant flux emergence occurred in this region (Sun \& Norton 2017). Five dipoles emerged successively at the east of the main sunspot. The negative and positive patches of the first two dipoles separated along the east-west direction. However, the patches of the latter two dipoles separated along the north-south direction, perpendicular to the former one. The cross separation of these dipole patches with opposite polarities led to the continuous interactions between different dipolar fields, accompanied by magnetic flux cancellations at some places (Toriumi et al. 2013; Louis et al. 2015; Yang et al. 2017). Strong shearing motions between the patches with opposite polarities accumulated dramatic free energy (Shimizu et al. 2014; Toriumi \& Takasao 2017) and could result in magnetic reconnection (Moore et al. 2001), which would lead to the formation of flux ropes (Xue et al. 2017). The rotation of the associated magnetic patch also contributes to the magnetic flux rope buildup. In Sect. 3.3, we speculated on the detailed process concerning the formations of these flux ropes and twisted loop bundles. It is worth mentioning that during the impulsive phase of the X9.3 flare, a white-light signal was detected as well as anomalous magnetic transient near the PIL (see the animation corresponding to Fig. 4), indicating a violent release of energy (Hudson et al. 1992; Song et al. 2018). We propose that in AR 12673 significant flux emergence and successive cross-separations between the patches of different newly emerging dipoles resulted in the formation of multiple flux ropes and twisted loop bundles in the same AR and the storage of dramatic magnetic energy. | 18 | 8 | 1808.06795 |
1808 | 1808.03671_arXiv.txt | A prevailing open problem in planetary nebulae research, and photoionized gaseous nebulae research at large, is the systematic discrepancies in electron temperatures and ionic abundances as derived from recombination and collisionally excited lines. Peimbert (1967) proposed the presence of 'temperature fluctuations' in these nebulae, but the apparent amplitude of such fluctuations, as deduced from spectral diagnostics and/or abundance discrepancy factors, remain unexplained by standard photoionization modeling. While this and other alternative models to explain the temperature and abundance discrepancies remain inconclusive, recent observations seem to point at a connection between nebular abundance discrepancy factors and a binary nature of photoionizing stars. In this paper we show that large amplitude temperature fluctuations are expected to form in planetary nebulae photoionized by short-period binary stars. Resonant temperature fluctuations are first formed along the orbital disk around the binary stars, as the periodically varying ionizing radiation field induces periodic oscillations in the heating-minus-cooling function. Then, the temperatures fluctuations propagate vertically to the disk as thermal waves that later steepen into radiative shocks. The binary period of the ionizing stars is determinant in the formation and propagation of temperature fluctuations, as well as in associated density fluctuations. Fluctuations propagate efficiently only in systems with binary periods significantly shorter than the gas thermalization time, of the order of 10 days. Further, we propose temperature diagnostic line ratios that combine [\ion{O}{3}] collisionally excited lines and \ion{O}{2} recombination lines to determine the equilibrium temperature and the magnitude of resonant temperature fluctuations in nebulae. | Arguably, the most intriguing question left unanswered in photoionization modeling in astronomy pertains the origin of systematic discrepancies in ionic abundances derived from recombination and collisionally excited lines in a large fraction of known \ion{H}{2} regions and planetary nebulae (PNe). Such differences in derived abundances are generally quantified in terms of abundance discrepancy factors (ADF) that can reach up to two orders of magnitude for C, N, O, and Ne in some extreme PNe (e.g. McNabb et al. 2016; Corradi et al. 2015; Wesson et al. 2003). These ADF seem to be the result of temperatures associated with recombination spectra being considerably lower than those derived from forbidden collisionaly excited lines (Torres-Peimbert et al. 1980). Peimbert (1967) proposed the existence of ``temperature fluctuations" common to \ion{H}{2} regions and PNe, but the amplitude of such fluctuations needed to reconcile the abundance determination are too large, in general, to be reproduced by standard photoionization modeling (Kingdon and Ferland 1995). The existence of temperature variations of some sort has been supported by modern spectra from high sensitivity, high spatial resolution instruments. Liu et al. (2000, 2001) showed that the temperatures of PNe determined by ratios of collisionally excited lines (e.g. [\ion{O}{3}], [\ion{N}{2}], [\ion{S}{3}]) are typically larger than the temperatures derived in hydrogen by fitting the Balmer discontinuity to the Balmer recombination lines (Te(Bac)). Moreover, the ADF from collisional and recombination lines from optical and UV spectra of PNe and \ion{H}{2} regions are correlated with the difference between Te([\ion{O}{3}]) and Te(Bac) (Garc\'{\i}a-Rojas and Esteban 2007; Liu et al. 2004). Further, point-to-point electron temperature variations have been obtained for several high surface brightness PNe and \ion{H}{2} regions (Rubin et al. 2002, 2003; Krabbe and Copetti 2002, 2005; O'Dell et al. 2003, 2013; Garnett and Dinerstein 2001; Wesson \& Liu 2004), though the spatial scale of the variations is expected to be too small to be resolved in detail. Not surprisingly, temperature variations averaged over the smallest spatial scales that can be resolved observationally at present are too small to account for ADF (see the case of NGC~6543 by Wesson \& Liu 2004). At present, the idea that is receiving the most attention in explaining ADF is the hypothesis of chemically inhomogeneities. According to this hypothesis there would be in the nebula pockets of cold very metal-rich plasma mixed with the gas or an extended high metallicity gas embedded in a less dense ambient gas with lower metallicity (Tsamis et al. 2003). The former idea was first suggested by Torres-Peimbert et al. (1990) and has been studied most extensively by Liu et al. (2006). Though, this idea lacks workable models that explain the origin of such chemical inhomogeneities. Henney \& Stasi\'nska (2010) tried to explain the presence of metal-rich droplets in PNe by destruction of solid bodies; however, they concluded that the amount of solid bodies needed to reproduce the observations was anomaly large. In recent years, it has been found that a large fraction of all intermediate-mass stars, PNe progenitors are known to be in binary systems (Moe and De~Marco 2006; Miszalski et al. 2009). Moreover, there is now mounting observational evidence that binary stars play a significant role in the PN ejection process. In particular, it seems like all PNe with extreme abundance discrepancy factors host short-period binary stars (Corradi et al. 2015; Wesson et al. 2017). Observational searches for close binaries demonstrate that these are virtually all found in bipolar PNe (Mastrodemos and Morris 1999; Miszalski et al. 2009). Though, because searches for binary stars are mostly limited to near edge-on systems with significant photometric variability it remains unproven whether all non-spherical PNe, which in fact are the large majority of PNe, are ejected from a star in a binary system. Surveys have found that between $\sim$10\% and 20\% of all PNe central stars are close binary systems, with periods typically shorter than 3 days (Jones et al. 2016). Here we show that the periodically varying photoionizing radiation field of a short-period binary star will lead to resonant temperature fluctuations (RTF) in the orbital disk and these can propagate through the rest of the cloud as thermal waves that lead to radiative shocks. The mechanisms for this process are described in the next section. Further, Section 3 presents spectral diagnostics to determine the equilibrium and resonant temperature fluctuation amplitude from observed spectra. | We show that resonant temperature fluctuations, with amplitudes up to $\sim$90\% of the equilibrium temperature, are expected to form in PNe photoionized by short-period-binary stars. Such systems yield a periodically varying ionizing radiation field along the orbital disk, which induces periodic oscillations in the heating-minus-cooling function. As a result, temperature perturbations in the disk with frequencies similar to those of the ionizing source will undergo resonant amplification. Further, the temperature fluctuations in the disk cause thermal waves and shocks that propagate to the rest of the nebulae. Further, our study shows that the amplitude of the RTF depends critically on the occultation period of the binary star. Only short-period binaries, with period of few days, can sustain significant RTF. How the present mechanism for RTF applies to H~II regions remains to be studied. On the one hand, H~II regions are ionized by one of more young massive stars, which are believed to have a large binarity fraction. Many of these binary systems could be close binaries, see for instance S~106 (Comer\'on et al 2018). On the other hand, if the secondary star is much smaller than the primary it would lead to a very small and thin ecliptic disk, possibly unable to originate sustainable RTF. We present diagnostic line ratios that combine [\ion{O}{3}] collisional lines and \ion{O}{2} recombination lines. These ratios can be used to estimate the equilibrium temperature and RTF in the O$^{2+}$ region. Similar diagnostics can be created using different ions that also produce observable collisional and recombination lines in the nebular spectrum. This will be the subject of future publications. When applying these diagnostics to PNe with extremely large ADF and known binary central stars we find that they are characterized by equilibrium temperatures, $T_0$, between 5500~K and 10,000~K and $T_{rtf}/T_0$ between 0.6 and 0.9. Most of these objects also show density fluctuations out of phase with the RTF. By determining $T_0$ and $T_{rtf}$ one can then estimate the abundance fractions of different ions relative to hydrogen. These estimate should reflect the true chemical composition of the nebula by removing the long standing discrepancies between collisional and recombination lines. | 18 | 8 | 1808.03671 |
1808 | 1808.04051_arXiv.txt | The possible effect on the flavour spectra of astronomical neutrinos from a neutrino-dark matter interaction has been investigated for decoherent neutrinos \cite{DeSalas2016}. In this work, we report results calculated for coherent neutrinos. This was done with two different models for the neutrino dark-matter interactions: a flavour state interaction, as for the weak interaction in the Standard Model, and a mass state interaction, which is predicted by certain non-Standard Models (specifically Scotogenic models). It was found that using a coherent analysis dramatically increased the explorable parameter space for the neutrino-dark matter interaction. However, the detection of coherent astronomical neutrinos presents a significant challenge to experimentalists, because such a detection would require an improvement in energy resolution by at least six orders of magnitude, with similar improvements in astronomical distance determinations. | Astronomical observations over the last several decades have consistently shown that, in simple terms, galaxies spin too fast for the visible matter they contain to hold them together gravitationally. This means that either the standard theory of gravity needs to be modified or that there are other forms of matter present which do not participate in the other Standard Model interactions (the electroweak and strong interactions) or only do so extremely weakly. Given that no satisfactory alternative theory of gravity has been developed, it is generally presumed that there is a type of matter that is quite common but is currently undetectable. This matter is called ``Dark Matter" (DM) \cite{Lesgourgues2012,Duda2011}. % Neutrinos are electro-magnetically neutral leptons with a very small mass (the heaviest neutrino is at least six orders of magnitude lighter than the electron) \cite{Mertens2016}. Intrinsically connected to the massive nature of neutrinos is neutrino oscillations, also known as flavour mixing \cite{Bilenky2014}. (Indeed, the massive nature of neutrinos was proven by the discovery of neutrino oscillations \cite{Ahmad2001,Collaboration2001}.) The currently favoured model for neutrino oscillations is three-neutrino mixing whereby a neutrino produced in one of the three flavour states enters into a quantum superposition of the three mass states which then propogate at different velocities due to having different masses. These velocity differences produce interference effects which cause the flavour content of the wavepacket to change in an oscillatory manner. An interesting feature of these oscillations is that their exact form is dependent on the medium in which the oscillations take place. The most common form is the Mikheyev-Smirnov-Wolfenstein (MSW) effect, which occurs when neutrinos pass through a medium containing electrons \cite{Wolf1978,Barger,Renshaw2013}. The coupling of the electron-neutrino component to the medium causes a shift in the oscillation pattern, which is observable if the density of the medium is high enough. Theoretically, a similar effect would appear for any medium that couples to neutrinos strongly enough, regardless of the precise interaction involved. De Salas, Lineros and, T{\'o}rtola \cite{DeSalas2016} proposed that this effect could be used to observe neutrino-dark matter interactions. The idea was that if there is a significantly strong coupling between neutrinos and Dark Matter, then it would be observable at neutrino observatories, particularly high energy ones like IceCube \cite{Aartsen2013}. One attractive feature of their approach is that it does not presume any particular type of Dark Matter or any particular type of interactions, merely that there is Dark Matter and it couples to neutrinos. The formula for flavour transition probabilities when the wavepackets are coherent is: \begin{equation} f_{\beta}=\displaystyle\sum_{\alpha=e,\mu,\tau}{\left|\displaystyle\sum_{i=1}^{3}U_{{\beta}i}^{}U_{i{\alpha}}^{\dagger}\mathrm{e}^{-\mathrm{i}E_{i}t}\right|}^2f_{\alpha}, \label{oscprob} \end{equation} where \(f_{\alpha}\) is the emission flavour vector (i.e. a normalized vector containing the three flavour fractions), \(f_{\beta}\) is the flavour vector at the detector and U is the matrix translating between the flavour basis and the effective mass basis\footnote{A note about the effective mass basis: The effective mass basis is simply the one in which the Hamiltonian in the presence of a medium is diagonal. It is called the effective mass basis because, if it is calculated, then the equations for oscillations in a vacuum can be used with simple substitution.}. De Salas, Lineros and, T{\'o}rtola \cite{DeSalas2016} used the formula for decoherent wavepackets: \begin{equation} f_{\beta}=\displaystyle\sum_{\alpha=e,\mu,\tau}\left(\displaystyle\sum_{i=1}^{3}{\left|U_{{\beta}i}^{}U_{{\alpha}i}^{*}\right|}^2f_{\alpha}^0\right), \label{nooscprob} \end{equation} which can be obtained by expanding out the term in straight brackets in Eq.~\ref{oscprob} and then integrating over all \(t\) before recompressing the surviving terms. Since baseline is related to time, this effectively integrates over all possible source locations. Thus, the decoherent probability is an average of the coherent probability across all baselines. The coherent formula is valid as long as the different mass state wavepackets overlap. As the neutrinos propagate, the mass state wavepackets diverge due to minute differences in their group velocities \cite{Akhmedov2009}. Eventually, the wavepackets diverge to the point where they no longer overlap. When this happens, oscillations cease to occur as it is the interference between the wavepackets that produces oscillations; the neutrinos are now said to be decoherent and the valid formula is the decoherent one. The time it takes for neutrinos to decohere increases with energy \cite{Akhmedov2012}. Thus, neutrinos can maintain coherence, even across astronomical distances, if they have sufficiently high energy. (Coherence limits are discussed in more detail in Section 2.) This work examined the effects of using the coherent formula and how they differ from the decoherent formula. This was done by performing calculations using both formulas in the same manner as in \cite{DeSalas2016}, save that the coherent formula required the addition of a baseline dependency. The calculations were made using two different potentials, one corresponding to interactions with the neutrino flavour states (Section 3) and one corresponding to interactions with the neutrino mass states (Section 4). The flavour based potential is the standard choice and corresponds to DM that participates in the weak interaction (e.g. WIMPs). It was the potential used by \cite{DeSalas2016}. The mass based potential is an unconventional choice that is predicted by certain theories of neutrino mass that are beyond the Standard Model (i.e. Scotogenic models) \cite{Wilkinson2014}. These are models where neutrinos obtain mass radiatively via virtual intermediaries which can serve as DM candidates (see e.g. \cite{Ma2009,HiroshiOkada2014,Merle2015,Bonilla2016}). In addition to comparing results from the coherent formula with those from the decoherent formula, the results for the two potentials were compared to each other using the coherent formula. This is done by examining the distance dependency of the coherent formula for each potential (Section 5). The analysis in Section 3 was then carried out for neutrinos from blazar TXS 0506+056 at the energy observed by IceCube \cite{Collaboration2018,2041-8205-854-2-L32} in order to examine the effect of an increased baseline (Section 6). The implications of the analyses are discussed in Section 7 before the whole work is summarized in Section 8. | The work by \cite{DeSalas2016} showed possible ``Dark Matter effects" on the astronomical neutrino spectrum. This work showed that coherence effects can dramatically increase the sensitivity of the spectrum to dark matter interactions. The first major issue is that of coherence, specifically whether coherent astrophysical neutrino states can be detected anytime in the forseeable future. This would require neutrinos produced at not too great a distance at rather high energies detected by more sophisticated equipment than currently exists. Additionally, the object in question would require a physical size substantially less that the oscillation wavelength. As previously stated, these constraints imply that the most likely source is in the near vicinity of stellar-mass black holes. It is an open question as to whether stellar-mass black holes are indeed potential sources of sufficiently high energy neutrinos. How such neutrinos could be linked to a specific source is also an issue that needs to be addressed. Then there is the constraint on baseline uncertainty. Given that this is fixed by the neutrino energy and that black hole range-finding is somewhat difficult, overcoming this obstacle is arguably even more difficult than overcoming the energy resolution constraint. On the other hand, this question is of interest to other fields so there might be faster progress in this area. Even if the source was known and the coherence constraints could be overcome, there is the issue of detecting enough neutrinos to be able to conclude anything about the flavour spectrum, an issue which is compounded by the large distances involved and the inverse square law. The use of very high energy neutrinos helps somewhat, as these neutrinos are not produced in the Solar System, which reduces the background that needs to be accounted for (relative to lower energy neutrinos). Still, there needs to be a sufficiently large signal. For blazar neutrinos, there has, as of writing, only been a handful of confirmed events \cite{Collaboration2018}. This, coupled with the issues regarding detector energy resolution, means that this type of analysis cannot be performed in the near future (which most emphatically does not mean that it cannot be performed in the distant future). Unfortunately, the ranges for both interactions exceed the cosmological bound for a constant cross-section. This disfavours the mass state interactions as those interactions are predicted to have constant cross-sections. The flavour state interactions are predicted to be energy dependent like the SM weak interaction, and energy dependent interactions are far less bound by cosmological constraints\cite{Wilkinson2014}, meaning that a flavour state interaction is, perhaps unsurprisingly, more likely to be detected by this kind of experiment (presuming that one even exists and is sufficiently strong). If such an effect was observed it would yield valuable physics information. Depending on the type of interaction and the potential at which it occured (a distinction that can't be made with the de-coherent effect), it woud help to fix the absolute mass scale of the DM particle. Also, such experiments would complement cosmological observations rather well given the different energy scales being observed. All of that being said, given both the need for a large sample size and significant improvements in detector quality, it will probably be a very long time before making these kinds of observations becomes feasible. | 18 | 8 | 1808.04051 |
1808 | 1808.03501_arXiv.txt | In the cold dark matter (CDM) picture of structure formation, galaxy mass distributions are predicted to have a considerable amount of structure on small scales. Strong gravitational lensing has proven to be a useful tool for studying this small-scale structure. Much of the attention has been given to detecting individual dark matter subhalos through lens modeling, but recent work has suggested that the full population of subhalos could be probed using a power spectrum analysis. In this paper we quantify the power spectrum of small-scale structure in simulated galaxies, with the goal of understanding theoretical predictions and setting the stage for using measurements of the power spectrum to test dark matter models. We use a sample of simulated galaxies generated from the \texttt{Galacticus} semi-analytic model to determine the power spectrum distribution first in the CDM paradigm and then in a warm dark matter scenario. We find that a measurement of the slope and amplitude of the power spectrum on galaxy strong lensing scales ($k\sim 1$ kpc$^{-1}$) could be used to distinguish between CDM and alternate dark matter models, especially if the most massive subhalos can be directly detected via gravitational imaging. | \label{sec:Intro} Dark matter is a key component of the standard model of cosmology, but its fundamental nature remains uncertain. In the standard Cold Dark Matter (CDM) model of cosmological evolution, structures form through the accretion and merging of smaller structures. This bottom-up picture of structure formation leads to dark matter halos that contain substructure in the form of smaller, less massive subhalos. Cosmological simulations make specific predictions about the mass function and spatial distributions of this dark matter substructure \citep[e.g.,][]{springel, boylan, ponos_proj}. These predictions depend strongly on the type of dark matter particle considered. For instance, moving from CDM to a warm dark matter (WDM) model by decreasing the mass of the dark matter particle reduces the amount of substructure in galaxies \citep[e.g.,][]{wdm_goetz,Lovell:2013ola,Bose:2016irl}. This difference provides a possible way to learn about the fundamental nature of dark matter by observing the abundance of satellite galaxies within the Local Group \cite[see, e.g.,][]{Anderhalden:2012jc,2015MNRAS.448..792G,Schneider:2014rda}. In practice, the actual number of small dwarf galaxies surrounding the Milky Way depends not only on the dark matter physics, but also on the star formation efficiency in small dark matter subhalos \citep[e.g.,][]{Bullock,Benson02,Somerville,Behroozi:2012iw,Garrison-Kimmel:2013eoa,Brooks,Brook:2013laa,2017MNRAS.470..651R}. While there are still considerable uncertainties in the stellar content of small halos, it appears plausible that dark matter halos below a certain mass threshold may be entirely devoid of stars \cite[see, e.g.,][]{Dooley:2016xkj,Kim:2017iwr}. Therefore, directly observing the substructure content of the Local Group at the smallest scales is very challenging, although indirect methods based on the gravitational influence of small subhalos on the Milky Way disk \citep{Feldmann:2013hqa}, halo stars \citep{Buschmann:2017ams}, or stellar streams \citep{2014ApJ...788..181N,2016MNRAS.463..102E,2016ApJ...820...45C,2016PhRvL.116l1301B,2017MNRAS.466..628B,Banik:2018pjp} could potentially shed light on local small-scale structure. Since it is sensitive to the total projected mass distribution along the line of sight between the high-redshift source and the observer, gravitational lensing provides a means for detecting dark matter subhalos even if they do not contain any stars or gas. While the technique could in principle be applied to our local neighborhood \citep[see, e.g.,][]{Erickcek:2010fc,VanTilburg:2018ykj}, gravitational lensing is the only way to detect dark substructure in cosmologically distant galaxies. In observed gravitational lenses, substructure appears as localized perturbations to an otherwise ``smooth'' mass model responsible for setting the broad structure of the lensed images. These perturbations are usually detected through anomalies in the lensing observables that cannot be easily reabsorbed by a change to the smooth lens model \citep{Koopmans:aa,Vegetti:2008aa,Hezaveh:2012ai}. In some cases, these anomalies can be well fit by the inclusion of a mass clump in the model. This is often interpreted as evidence of the ability to detect individual dark matter subhalos with gravitational lensing \citep{Mao98,metcalf01,Vegetti_2010_1,Vegetti_2010_2,vegetti2012,Nierenberg:2014aa,2014MNRAS.442.2017V,hez_clump}. We note, though, that translating a substructure detection to the actual physical properties of a dark matter subhalo has important subtleties \citep{Minor:2016jou,Daylan:2017kfh}. Also, some of these anomalies could be caused by baryonic substructure, although it is statistically unlikely that all of the observed anomalies are caused by baryons \citep{gilman}. CDM theory predicts the existence of abundant small-scale structure and so it would be convenient to build inference models that are able to capture the collective effect of this substructure. There has been work done to this end that has incorporated a population of subhalos within lens models in a statistical way \citep{dalal_kochanek,fadely,Birrer2017}. Work has also been done to calculate what effect a population of subhalos can have on the image positions and relative time delay of multiply-imaged quasars \citep{FYCR}. Another way to capture the statistical properties of the small-scale structure within lens galaxies is with a power spectrum analysis. It has previously been shown that measuring the power spectrum of projected density fluctuations with current observations of strongly-lensed images is likely feasible \citep{hez_pow,Chatterjee,Bayer,Pksub}. Moreover, theoretical predictions for the shape and amplitude of the substructure convergence power spectrum from realistic populations of subhalos has recently been presented in \cite{Diaz}. There, it was shown that the substructure power spectrum contains important information about the abundance, masses, and density profiles of the subhalos inhabiting the lens galaxy. Substructure lensing is moving towards analyses that include a power spectrum piece that accounts for small-scale structure of the kind predicted by current dark matter theories. In order for measurements of the power spectrum to be useful for weighing competing theories of dark matter we must first determine what these theories look like in the language of power spectra. In this work we move beyond theoretical estimates to directly quantify the lensing convergence power spectrum in simulated galaxies with an eye towards informing future lensing measurements and with the hope that the power spectrum formalism becomes the new standard for analyzing the substructure content of lens galaxies. This paper is organized as follows. In Section \ref{sec:Methods} we describe our subhalo populations and outline the method for calculating the substructure power spectrum. In Section \ref{sec:Results-CDM} we present the results of our calculation of the power spectrum distribution for our CDM populations and show how it is affected by removing massive subhalos. We also test the validity of using multiple projections of individual subhalo populations as a proxy for having independent populations. Finally, in Section \ref{sec:Results-WDM} we compare our CDM and WDM subhalo populations in terms of their power spectrum distributions. | \label{sec:Conclusions} We have computed the convergence power spectrum of dark matter substructure using semi-analytic subhalo populations in both cold and warm dark matter scenarios. The power spectrum distributions for CDM and WDM have similar shapes and overall levels of power at low wavenumbers, but the scatter appears larger for WDM. The scatter in the power spectrum distribution is driven by the few most massive subhalos. Those subhalos could potentially be individually detected and directly included in the main lens model, so they can be excluded from the power spectrum analysis. When that is done, the resulting power spectrum distributions are statistically robust and show clear differences between CDM and WDM predictions on scales $k \gtrsim 0.1$ kpc$^{-1}$. This result is promising in connection with recent work on using galaxy-scale strong lensing to measure small-scale power. \citet{Pksub} recently developed a comprehensive likelihood-based formalism and used it to demonstrate that measuring power on scales of $k \sim 0.1$--10 kpc$^{-1}$ with lensing is likely feasible with deep, high-resolution observations. Our analysis indicates that even a few high-quality power spectrum measurements in this $k$ range could be sufficient to measure potential deviations from the CDM predictions for dark matter substructure within galaxies. | 18 | 8 | 1808.03501 |
1808 | 1808.06923_arXiv.txt | We examine the viability of Weyl conformal gravity as an alternative to the general theory of relativity. By using the extended rotation curve of the Milky Way and velocity dispersions of four globular clusters, we show that Weyl gravity predictions without resorting to dark matter comply with observations at the galactic scale. For the Milky Way, we demonstrate that the uncertainty in baryonic modelling results a bracket of possible rotational velocities which well encompasses the diversity in rotation curve construction. Such diversity generally arises from differences in measurements of velocity anisotropy parameter, and the circular speed and Galactocentric distance of the Sun. Furthermore, we explore the ability of Weyl gravity to account for the inferred acceleration of Abell cluster 1689. \pacs{} | The validity of Einstein's General Relativity (GR) is well-established in solar-system neighborhood and binary pulsar systems \cite{solar1}. The recent detection of gravitational wave by LIGO \cite{gw} has further extended its credibility to dynamical strong gravity regimes. However, the theory is plagued by an apparent `mass-discrepancy' in galaxies and clusters. These discrepancies have motivated the ad-hoc addition of mysterious `Dark Matter' (DM) in the current cosmological paradigm which considers GR to be valid at all length-scale. However, ambitious experiments designed to detect dark matter have so far failed to give any positive result \cite{bertone2005particle}.\\ Alternatively, the `mass-discrepancy' could be interpreted as the manifestation of new gravitational physics. The nature of gravity might be intrinsically different at galactic and cosmological scales. This idea encouraged the emergence of a number of modified or alternative theories of gravity. One of the most popular alternative gravity models is Weyl conformal gravity (CG). The theory has recently gained momentum because of its grounding in field theory, embedded local invariance principle and interesting cosmology with naturally arising inflation \cite{weylrot5}. The promises of fourth order terms in Weyl gravity to prevent the Big Bang singularity of GR \cite{weylmotivation1} and to be one-loop re-normalized \cite{weylmotivation2} has created further interest. Moreover, Mannheim and O'Brien have successfully explained the observed galactic rotation curves for a number of galaxies using Weyl gravity without invoking dark matter \cite{weylrot1,weylrot2,weylrot3,weylrot4}. Subsequent studies have confirmed that rotation curve analysis in Weyl gravity is consistent with perihelion precession of mercury \cite{perihelion} and bending of light issues \cite{bending1,sultana,cattani}.\\ One of the predictions of Weyl gravity is the eventual decline of galactic rotational curves \cite{weylrot3}. Galaxies with observational data for rotational velocity profiles extending way beyond the optical length could therefore be utilized to test Weyl gravity. Over the last decade, observed Milky Way (MW) rotation curve has been obtained starting from its innermost regions out to distances beyond 100 kpc from the galactic center using kinematical data of a variety of tracer objects [ Sofue et al (YS09) \cite{sofue1}; Xue et al (X08) \cite{xue}; Sofue (YS12) \cite{sofue2}; Bhattacharjee et al (BCK14) \cite{pijush}; Huang et al (YH15) \cite{yh16} ]. However, the construction of the Milky Way rotation curve heavily relies on three galactic parameters: galacto-centric distance $R_0$ and circular velocity of the Sun $V_0$ and anisotropy parameter $\beta$. Till date, these three fundamental parameters remain remarkably uncertain. O'Brien and Moss (OM15) \cite{obrien} has recently compiled the rotational velocity data from YS09, X08 and BCK14 and fitted within the context of Weyl gravity with mass-to-light ratio as the only free parameter in the model. Though they have found an acceptable mass-to-light ratio, it is to be noted that the differences between astronomical datasets are often systematic. A straight-forward fitting to the combined data set from different surveys could therefore potentially over or under-estimate the total mass in the Milky Way. Thus, a more stringent test for Weyl gravity with extended MW rotation curve is due.\\ Another intriguing set of testing grounds for modified gravity theories is the galactic globular clusters (GCs). The projected radial velocity dispersion for several GCs has been found to be maximum at the center and then to eventually decline towards an asymptotic constant value at large radii \cite{ngc1851a1904,ngc288,ngc5139,ngcothers,ngcothers2}. However, GCs are generally believed to contain little or no dark matter \cite{gcdm1,gcdm2,gcdm3}. Therefore, the velocity dispersion has been expected to follow a Keplerian fall-off and ultimately vanish at larger radii if GR (and Newtonian gravity, weak field limit of GR) would have been valid at GCs. Although classical phenomenon like tidal heating could have been a possible Newtonian gravity explanation for the apparent increase of velocity dispersion in the outskirts of GCs, no solid support for such hypothesis has been found \cite{gctidal}. On the other hand, the eventual flattening of velocity dispersions in GCs hints an interesting analogy with flat rotation curves in elliptical galaxies. Therefore, it might be more logical to argue that the flatting out of velocity dispersions in different GCs have a common origin and is linked to the breakdown of GR at those scale.\\ At this point, we identify a third front to test Weyl gravity predictions. Recently, acceleration profile of Abell cluster 1689 has been inferred \cite{nieu1} from lensing data. It has been claimed that popular alternative gravity theories like Modified Newtonian Dynamics (MOND) \cite{mond1} and Moffat's MOdified Gravity (MOG) or scalar-tensor-vector-gravity \cite{mog} cannot fit the acceleration profile unless an additional dark matter profile ( such as heavy neutrinos ) is assumed. The inferred acceleration profile of A1689 thus provides a crucial extra-galactic test for Weyl gravity.\\ This article aims to explore the astrophysical viability of Weyl gravity. Our work expands from galactic scale up to the length-scale of clusters. First, we test Weyl gravity against the Milky Way rotation curve data. Our approach differs significantly from OM15 \cite{obrien}. We intend neither to compile rotational data from different surveys nor to fit any of them. Rather, we adopt a state-of-art mass model from \cite{mcmillan,bulge,bulge2} and predict the mean rotation profile for the Milky Way up to around 120 kpc and then compare it with observed rotational velocity curve reported by BCK14 \cite{pijush}. The reason for choosing the data set from BCK14 \cite{pijush} is that the assumed values for the galactic constants [$R_0$,$V_0$] in their study closely matches with the most up-to-date measurements from VERA and VLBA surveys \cite{reid}. Furthermore, we show that the embedded uncertainties in the mass model results a `bracket' of rotational velocities possible in the Milky Way within the context of Weyl gravity. Whether this baryon bracketing of rotation curve can successfully encompass the variation in observational data \cite{sofue2,pijush,yh16}, which arises due to the uncertainty in velocity anisotropy parameter and circular velocity at the solar position, is a prime focus of our study. This analysis is done in Section \ref{sec3}. In subsequent section \ref{sec4}, we extend our analysis to globular clusters. We choose a set of four GCs whose distance (from galaxy center), luminosities and sizes are very different from each other. Therefore, we expect that if there is any systematic in their velocity dispersion which hints a Newtonian breakdown, Weyl gravity would be able to capture that. In Section \ref{sec5}, we construct the baryonic mass profile of A1689 with parameterized models for the galaxies \cite{abel1} and inter-cluster gas \cite{nieu2} and compute the Weyl gravity acceleration for the cluster. The predicted acceleration profile is then compared with the one inferred from lensing surveys. Finally, in Section \ref{sec6}, we discuss several aspects of our results and draw conclusions. | \label{sec6} We have tested Weyl gravity from galactic scale up to the scale of galaxy clusters. At galactic scale, we test the viability of Weyl gravity with the extended rotation curve of the Milky Way and velocity dispersions of four globular clusters. In our quest to find clues for modified gravity in the Milky Way rotation curve, we first identified that, as predicted in Weyl gravity, the rotation curve indeed falls at larger distances. We have demonstrated that including a central supermassive blackhole in the mass model improves the Weyl gravity predictions manifold. Furthermore, we find Weyl gravity predictions to be consistent with radial acceleration relation (RAR) in the Milky Way. Additionally, we compute a bracket of rotational velocities possible in the Milky Way within the context Weyl gravity and found that this bracket accommodates the diverse rotation curves for the Milky Way, which is a result of inherent assumptions for the different values of $R_0$, $V_0$ and $\beta$, made during the construction of rotation curve profile. In our analysis, we have used rotation curve data from three different groups: BCK14, YS12 and YH16 \cite{pijush,sofue2,yh16}. The range of values for several galactic constants assumed in these studies are: $8.0$ kpc $<$ $R_0 < 8.5$ kpc; 200 km/s $< V_0 <$ 244 km/s and 0 $< \beta <$ 1. Thus, rotational curve data used in our work truly represents the family of the MW rotation curves. Our result is therefore immune to current observational errors and uncertainties. This study thus is not only different from previous Weyl gravity analysis of the Milky Way rotation curve \cite{obrien}, it is actually complementary to that.\\ In the case of GCs, we have calculated the velocity dispersions for NGC 288, NGC 1851, NGC 1904 and NGC 5139. We assumed the GCs to be spherically symmetric and non-rotating. Furthermore, we adopted simple Hernquist mass profile for GCs. However, in reality, NGC 1851, NGC 1904 and NGC 5139 has been observed to be slowly rotating. Moreover, our analysis does not include any complicated tidal effects or external field effects due to the gravitational pool of the Milky Way. Still, we find good fits to the observed dispersion profiles with reasonable values of mass-to-light ratio. We note that Moffat \& Toth have obtained a similar fit within the context of MOG with $M/L=4.38$ for NGC 288 and $M/L=2.79$ for NGC 5139 \cite{moffattoth}. On contrary, our analysis results 0.5 $< M/L <$ 2.0. This range of mass-to-light ratio is more consistent with recent estimates \cite{gcml1,gcml2,gcml3}. On top of that, our sample of GCs are extremely diverse. They have different sizes, different luminosities, different concentrations, different dynamical histories and they lie at different radial distances from the galactic center. Thus, they experience different strength of gravitational pull. Still, simple Weyl gravity model can more-or-less describe their dispersion profile which is otherwise difficult to explain in Newtonian dynamics (or in GR). Such universal explanation for the eventual flattening of dispersion profiles in GCs should definitely be taken as a triumph for modified gravity and in particular for Weyl gravity.\\ We have then extended our study to Abell cluster 1689 (A1689). For A1689, we modelled the galaxy cluster in Weyl gravity and compared the results with inferred acceleration profile from lensing data. Weyl gravity acceleration has been found to keep increasing with distances from the center of the cluster and exceed the inferred profile by almost two to three orders of magnitude in the outer region (beyond 300 kpc). The essence of our result is similar to the claims of Horne \cite{weylcluster2} and Diaferio \& Ostorero \cite{weylcluster1}. Horne \cite{weylcluster2} found that Weyl gravity analysis of X-ray gas in Abell 2029 yields a total mass profile which is nearly 10 times greater than what is required to hold the hot gas in hydrostatic equilibrium. Such disagreement with observation has then further extended to temperature profile by Diaferio \& Ostorero who used adiabatic N-body/hydrodynamical simulations of isolated self-gravitating gas clouds in galaxy clusters within the framework of Weyl gravity and noted that the predicted temperature profile rises, rather than following a decreasing trend observed in real clusters. It suggests that the success of Weyl gravity at the galactic scale does not get translated in the scale of clusters.\\ However, we note that, in dark matter formalism, the acceleration (or velocity) is determined almost by dark matter distribution. Thus, a little uncertainty in baryonic mass does not affect the overall expectation. That is not the case for modified gravity theories like Weyl gravity. As the observed acceleration (or equivalently velocity) is completely determined by the visible baryonic mass distribution, extra caution must be taken while adopting a particular mass model. It is worth pointing out that the presence of foreground and background structures in the line of sight of A1689 can increase the uncertainty in the estimated mass (from lensing data) \cite{1689a}. Even any departure from spherical symmetry will have a similar effect \cite{1689b}. However, even if these factors have somehow contributed to the uncertainty of the mass profile used, it is highly unlikely that they will severely alter our result. Furthermore, the inferred acceleration data is no way an explicit acceleration profile. It shows a trend similar to the ones observed in several galaxies. Therefore, the inferred profile may be a good estimate for the actual centripetal acceleration profile. Still, it is not clear whether that is indeed the case. Existence of several structures aligned along the line of sight makes kinematic studies difficult at present \cite{1689c}. On a more theoretical ground, the appropriate inclusion of the shielding effects of nearby external matter of the cluster could help Weyl gravity to reconcile with inferred acceleration profile. However, such effects are currently poorly understood in Weyl gravity. Thus much more work is required in both Weyl gravity as well as kinematic studies of A1689 before reaching any strong conclusion and is left for future.\\ Before we conclude, we would like to point out an generally overlooked but important aspect of Weyl gravity. Weyl gravity, like all other fourth order gravity theories, does not possess any dimensional constant. Instead, it features a dimensionless constant $\alpha_{g}$ which has a value of order unity. However, when Weyl gravity is coupled with matter, the presence of a dimensional constant (namely Newtonian gravitational constant G) is assumed. There lies some well supported motivations behind such exercise. In fact, such dimensional constant is shown to be induced by different interactions in (quantum) Weyl gravity \cite{zee1983einstein}.\\ In summary, we have demonstrated that Weyl gravity can achieve high degree of success in describing the observed rotation curves of the Milky Way without invoking any dark matter profile. Our study has then extended the credibility of Weyl gravity to the scale of globular clusters. However, the Weyl gravity acceleration generated from the reported baryon mass in the cluster is found to exceed the inferred acceleration from lensing data. This apparent discrepancy may in principle be tackled by properly including the effects of the nearby external matter. This particular avenue of research needs to be explored further before reaching a final conclusion. | 18 | 8 | 1808.06923 |
1808 | 1808.05920_arXiv.txt | The direct detection of gravitational waves has provided new opportunities for studying the universe, but also new challenges, such as the detection and characterisation of stochastic gravitational-wave backgrounds at different gravitational-wave frequencies. In this paper we examine two different methods for their description, one based on the amplitude of a gravitational-wave signal and one on its Stokes parameters. We find that the Stokes parameters are able to describe anisotropic and correlated backgrounds, whereas the usual power spectra of the amplitudes cannot -- i.e. the Stokes spectra are sensitive to properties such as the spatial distribution of the gravitational-wave sources in a realistic backgrounds. | The observation of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors \citep{GW150914} was the result of several decades of work, both from the LIGO/Virgo collaborations and elsewhere. As of writing, there have been six confirmed (plus one probable) observations of black hole or neutron star binaries published, with varying degrees of localisation. These are single, individually separable sources but in the future it is predicted that detectors such as pulsar timing arrays \citep[PTAs; e.g.][]{Detweiler:1979, HellingsDowns:1983, Jaffe2003, Yardley:2011fk, Lentati:2015qwp, Arzoumanian:2018saf} and the Laser Interferometer Space Antenna \citep[LISA; e.g.][]{LISA:2017, Cornish:2001bb} will be able to observe a stochastic background -- i.e. one where there are multiple, nonseparable signals. Such a signal can have varying properties. It could be astrophysical \citep{Regimbau2011} or cosmological \citep{Caprini2015} in origin, monochromatic or polychromatic, isotropic or anisotropic \citep{msmv13, Ungarelli:2001xu, ThraneEtAl:2009}. It may also be made up of many individual sources that are theoretically resolvable but are too numerous/low amplitude to do so at the current time (e.g. galactic white dwarf binaries) or one that is not due to the fact that it simply exists everywhere (e.g. inflationary gravitational waves, e.g. \citealt{lms+16}). How best to analyse this broad range of multi-frequency stochastic backgrounds is the subject of this paper. Here we consider two methods to construct power spectra for a gravitational-wave background, using analogies to Cosmic Microwave Background (CMB) -- one involving a decomposition of the $h_+$ and $h_\times$ amplitudes \citep{Gair2014} and the other one of the GW Stokes parameters \citep{Seto:2008sr,Gubitosi2016,KatoSoda:2016}. The power spectral methods we use here make no major assumptions about properties of the background, only that it is observable and there is some directional dependence. As such, they are very general and can be applied to any gravitational frequency. We introduce the mathematics of the formalisms in Section~\ref{Sec:Form}. In Section~\ref{Sec:Backgrounds} we apply the formalisms to models of various backgrounds -- both astrophysical and cosmological -- and consider which method is appropriate for the description of different backgrounds and what can be learned from the power spectra in each case. Finally in Section~\ref{Sec:conclusions} we conclude and give an outlook for future work using these techniques.\footnote{Readers interested in the code used to produce the simulations and analyses presented here should contact the authors.} | \label{Sec:conclusions} We have compared the spin-2 spectra of the gravitational wave amplitude of a stochastic background to that of the spin-4 spectra of the gravitational Stokes parameters. We can see that, in many examples, the amplitude analysis gives white (constant amplitude) spectra of statistically equal strength for the autocorrelations and zero for the cross-correlations. As such, we cannot infer much information directly from the power spectra in these cases, other than a measure of the overall signal strength and an indication of the expected parity symmetry. While it is possible to construct examples where the amplitude auto-spectra are not equal and the cross-spectrum is not zero (e.g. a background with a small number of sources or by breaking parity) and where they are not white (requiring a correlation in phase which is very difficult to set up), these simple constraints hold for a majority of cases considered. However, this does mean that any detection of such non-standard power spectra indicates something unexpected about the background. The Stokes parameter analysis method, while still often giving white spectra, does show more information. Though the $C^{EE}_\ell$ and $C^{BB}_\ell$ spectra are usually equal, they differ from $C^{II}_\ell$ and $C^{VV}_\ell$. Further, in the Stokes case, it is easier to construct reasonable examples of backgrounds where the spectra are not white -- as can be seen in the white dwarf binary and the large-scale structure/SMBHB examples -- giving information on the distribution of sources. It should be further noted that the power spectra for Stokes parameters, other than $I$, share many of the same constraints as the amplitude spectra. That is, in the majority of examples they are white and $C^{EE}_\ell$ usually equals $C^{BB}_\ell$. The reasons for this are often similar: for example, in the case of binaries, the orientations of different binaries are unlikely to be correlated and so lead to white spectra in the same way as uncorrelated phases. Because of these observations, it is clear that the Stokes parameter method will often provide more information than the amplitude (and in the majority of cases, the most valuable spectrum to consider is that of the $I$ Stokes parameter -- consistent with what has been studied in the past). As such it will, in general, be the more appropriate method to analyse the background. We will apply these techniques to simulations of white dwarf binaries (Brevik et al., 2018, in preparation) as both a method characterise the background and distinguish it from other sources of gravitational radiation. For the application of these methods to real data, contaminated by noise and selection effects, much work will be necessary, going from pulsar-timing or gravitational-wave interferometer timestream data to maps of the background, e.g. \cite{RenziniContaldi2018}, and then to the spectra and related likelihood functions. Estimations of backgrounds made up of small numbers of sources, or examples with a single source that provides a significant part of the signal, will be subject to non-Gaussian statistics and it could be argued that the angular power spectra are not appropriate, or at least do not show the full picture. We expect that methods from the analysis of the CMB \citep[e.g.][]{BJK1998,Hivon2002,PlanckLikelihood2015}, large scale structure \cite[e.g.][]{BOSS2018}, and weak lensing \citep[e.g.][]{Alsing2017} will be particularly useful and we will pursue these techniques in future work. | 18 | 8 | 1808.05920 |
1808 | 1808.09938_arXiv.txt | The trans-Neptunian objects (TNOs) are small Solar System bodies at large distances from the Sun. As such, their physical properties are difficult to measure. Accurate determination of their physical parameters is essential to model and theorize the actual composition and distribution of the population, and to improve our understanding of the formation and evolution of the Solar System. The objective of this work is to construct phase curves in two filters, $V$ and $R$, of a large TNO sample obtaining absolute magnitudes ($H$) and phase coefficients ($\beta$), and study possible relations between them and other physical parameters (orbital elements, sizes, and albedos). We used our own data, together with data from the literature, to create the phase curves assuming an overall linear trend. We obtained new magnitudes for 35 TNOs, 27 in the V filter and 35 in the R filter. These magnitudes, together with data from the literature, allowed us to obtain absolutes magnitudes, 114 in the V filter and 113 in the R filter, of which 106 have both. From the search for correlations we found a strong anticorrelation between $H_V-H_R$ and $\Delta \beta=\beta_V-\beta_R$, which is probably more related to surface structure than to composition or size of the objects. | The trans-Neptunian objects, TNOs, are distant objects leftovers of the protoplanetary disk where the planets formed. The understanding of their physical properties sets important constrains to improve the evolution models of the Solar System \citep{mulle10}. Nowadays, the Minor Planet Center\footnote{http://www.minorplanetcenter.net/iau/mpc.html} lists around 2,300 TNOs. Unfortunately, just a few hundreds of them have high-quality physical studies, due to their orbital and size distributions, that produce few objects brighter than $V_{mag}~\sim~17$. Among the techniques used to study TNOs, photometry is the less expensive one (in terms of observing time). Photometric studies allow to obtain information of a good number of TNOs via apparent magnitudes and colors. The first are measurements of the integral reflected light by the TNO surface, subjected to the geometry of the observation and physical properties, such as diameter ($D$) and albedo ($p$), while the latter is a measure of the slope of the spectral reflectance of the object. Apparent magnitudes can be used to obtain absolute magnitudes ($H$) if the observational circumstances are known. The absolute magnitude is the mean apparent magnitude, over a rotation cycle of the object, observed at zero phase angle, and both at 1 AU from the Sun and the Earth. In practice, $H$ should be computed using phase curves and the formalism of \cite{muin10}. A phase curve shows the change of the apparent magnitude, normalized to unit distance from the Earth and the Sun, with the phase angle ($\alpha$). Nonetheless, due to the large distances where the TNOs reside, $\alpha$ (the arc that subtends the distance Sun-Earth as seen from the object) can only reach values as large as $\sim3^{\rm o}$, while the centaurs (representatives of the TNO population orbiting closer to the Sun) can be observed up to phase angles $\sim 7^{\rm o}$. In these small ranges the phase curves can be approximated by a linear function \cite[see, for instance,][]{alvarez-candal16} with due caution for possible opposition surges at phase angles close to zero. The absolute magnitude is of interest because it can be used as a proxy for size through \begin{equation}\label{eq1} D~[km] = C \times10^{-H/5}p^{-1/2}, \end{equation} \noindent where $C$ is a constant. On the other hand, colors are the difference of two magnitudes measured using two filters with different effective wavelengths, $\lambda_1$ and $\lambda_2$, and, as mentioned, are related to the reflectance spectrum of the objects, or, in other words, to their surface composition. However, even if different colors might imply different compositions, they cannot be used to infer it, but just as a first approach \citep{dores08,baruc11}. The TNOs show a great diversity of colors, ranging from neutral to very red \citep{baruc05}. It has been suggested that colors of TNOs together with other properties, such as sizes and albedos at different wavelengths, are used to help describe their surfaces properties and evolution \citep{Luu1996, Pike2017}. However, laboratory work of \citet{Kanuchova12} showed that fully weathered organic materials variate refractive properties of the materials and turn back in the color$-$color diagrams, such as a result suggest that colors themselves might not be entirely useful to explain the TNOs evolution. Thus, the color diversity of TNOs must be explained taking in account nurture and nature scenarios. For instance, \cite{peixe12} reported a bimodal $(B-R)$ distribution of centaurs and small TNOs with a gap in $(B-R)\sim 1.6$. Such a bimodality was independent of their orbital distribution and could be explained by different location of origin and/or disruptive collisions processes. Also, \cite{lacer14} reported two groups of mid-sized TNOs based in albedo and color: one bright and red, while the other is dark and neutral, with no dynamical segregation. Such a color-albedo separation was explained as different birth locations and is considered as evidence of a break in the composition continuity of the protoplanetary disk. In a previous work \citep[hereafter paper 1]{alvarez-candal16} we analyzed the absolute magnitudes ($H_V$) and phase coefficients ($\beta_V$), of 110 TNOs in the V band. The methodology we used in paper 1 was slightly different than the presented here. We only used $V$ magnitudes. In cases when only $R$ magnitudes were available, we transformed them to $V$ magnitudes using the weighed average $(V-R)$ for the object. In the present work we extend our analysis by including data in the $R$ band, i.e., $H_R$ and $\beta_R,$ and an updated list of magnitudes, some observed by ourselves and other from the literature not included before. With this, we aim at gaining a deeper comprehension on the surface characterization of TNOs. Of special interest is the ``absolute color'', $H_V-H_R$, that is proportional to the ratio of albedos (Eq. \ref{eq1}) and does not have any phase-related effect, providing a zero-phase approximation to the reflectance spectrum. We also define the ``relative phase coefficient'' as $\Delta\beta=\beta_V-\beta_R$ and study its relationship with the absolute color and their relation with other typical parameters. This paper is organized as follows: in the next section we described our new observations, in Sect. 3 we explain the method used, while in Sects. 4 and 5 we present and discuss our results. | \label{sec4} In this paper we present $H_V$ ($\beta_V$) for 114 objects and $H_R$ ($\beta_R$) for 113. These results were obtained from data observed by ourselves and from the literature. Note that 105 objects have both phase curves and therefore absolute colors. In paper 1 we had not included data in the $R$ filter, thus the present work expands our previous results. We tested for different correlations, among our data, orbital parameters, and data from the {\it TNOs are cool} survey. The most interesting correlation we found is between $H_V-H_R$ and $\Delta \beta$. The correlation holds if we consider different bins in semi-major axis (see Fig. \ref{Fig:colorvsbeta}, top) and separate between large an small objects (Fig. \ref{Fig:colorvsbeta}, bottom). Therefore, we conclude it is intrinsic to the TNO (and associated) population. This correlation indicates that redder objects have steeper phase curves in the $R$ filter than in the $V$ filter, while the opposite is true for bluer objects. As many different surfaces types, sizes, and dynamical evolutions are being sampled by our absolute colors we cannot assure that we are seeing an evolutionary effect, but probably something related to the porosity and compaction of the surfaces. The intrinsic brightness of the object depends of asteroid albedo, which is determined by the surface composition, compaction and grains size. There is a dependence of phase coefficient on surface texture \citep{shkur94, shkur94b}. However, given the inhomogenities of our data base, further studies are needed to clarify this interpretation. We separated our sample into two sub-groups: large and small, using $H_V=4.5$ as discriminant based on the results of \cite{brown12} in order to use all our dataset. Interestingly, there seems to be a gap in this region (Fig. 5 top) which remains to be confirmed. From our search for correlations among the two aforementioned groups (large and small) we found that: \begin{itemize} \item The correlation between $H_V-H_R$ and $\Delta \beta$ holds for both of them. As we do not expect the surface composition to be the same in both groups (in fact it is clear that the large objects do not have objects as red ad the small population) and the albedo distributions are different, we consider that the correlation is due to surface micro-structure (compaction, grain size) in a yet-to-be-understood way. Surface temperature does not seem to be a key factor here either, at least in first approximation, as the correlation holds for different bins in semi-major axis as well. \item There exists a significant correlation between $H_V-H_R$ and $p_V$ for the small objects (upper size limit at $\sim 500$ km). According to this correlation the redder objects have higher albedos. For the larger objects there is a marginal (opposite) trend. \item Regarding the small objects, the high-albedo tend, as well, to be the larger objects as shown in Fig. \ref{Fig:gapHV_D-p}. According to our understanding of collisional and resurfacing models, an initially neutral bright surface (ice-covered) under irradiation will decrease its albedo in the visible faster than in the red. Further irradiation will decrease the albedo in the red letting a dark carbon-covered surface with a neutral slope \citep[e.g.,][and references]{strazz91,thompson87,hud08}. The main opposing mechanism is collisional, that craterize the surface exposing sub-superficial material \cite[see][]{hutto02}. Therefore, the larger ``small'' objects, of higher albedo and red, are probably well processed, but not yet in the last stages of irradiation, while the smaller, bluer and lower-albedo, could be objects that are very processed. This is very curious, because these smaller objects (Fig. 6-right) should have suffered more impacts than larger ones \citep[e.g.,][]{Dohn71, farinelladavis92} and, in principle, there should be at least some objects with higher albedos. \end{itemize} We also searched for correlations among the different dynamical classes: Centaurs, Classical TNOs, Scattering objects (including Detached objects, and Resonant objects, following \cite{gladman08}. Although with a lower number of objects, the correlation between $H_V - H_R$ and $\Delta\beta$ appears in all subpopulations, pointing even more towards a property shared by all these minor bodies and that deserves further analysis. Following part of the discussion drawn in paper 1, it becomes clear that, although the $\beta$ distribution are clearly unimodal and that about 60 \% of the objects are close to the mode of the distribution, a non-negligible fraction of objects have values that can differ by a significant amount of the mode. Therefore an ``average'' value of the phase coefficient must be taken, and used, with extreme caution. A phase curve with negative values of $\beta$ do not have a direct physical interpretation in terms of photometric models, see our discussion in paper 1. Nevertheless, some plausible explanations are (i) underestimation of rotational amplitude, which could account for values of reduced magnitudes different than expected by our simple model (Eq. \ref{eq_rand}), (ii) the presence of material surrounding the body (ring systems, satellites, or binaries) which modify the total reflecting area as seen from Earth, and (iii) faint cometary-like activity. Further deeper, in quality and quantity, photometric studies are needed in order to discern between these scenarios. The absolute magnitudes and phase coefficients have been obtained from heterogeneous sources, with a variety of precisions, from a wide distribution of telescopes, instruments, and filters. Nevertheless, we have used homogeneous techniques to analyze them and produce an accurate database, although probably not as precise as desired, especially due to the large uncertainties introduced by unknown rotational properties. Also, our results are, in a way, mean values, as observations covering large intervals of time are being used here and some objects are known to suffer changes in relatively short time-scales, for instance the ring bearer Chariklo. Nevertheless, the statistical significance of our database is robust and we intend to continue increasing it, including new observations reported in the literature and our own forthcoming observations. | 18 | 8 | 1808.09938 |
1808 | 1808.07925_arXiv.txt | Extraterrestrial habitability has always fascinated humanity. The discovery of exoplanets makes the question of habitability of much practical importance. Current and future space missions, such as the Transiting Exoplanet Survey Satellite (TESS) and James Webb Space Telescope (JWST), will provide us with spectroscopic atmospheric characterizations. Improving constraints on habitability will provide us with better target filters for future observations. Metabolism requires energy, which life obtains in the process of electron transfer by redox chemical reactions \citep{McKay2014,Jelen2016}. One such reaction, analogous to photosynthesis on Earth, and invoked as a possible source of energy for life on Titan, is the production of organics from CH$_4$, followed by release of H$_2$. In addition, for the cryogenic temperatures on the surface of Titan, CH$_4$ replaces water as the surface liquid body, which is essential for cycling nutrients \citep{McKay2016}. Titan-like worlds may be favorable for habitability being out of harms reach around highly active M-dwarfs \citep{Lunine2009}, and should be common throughout our cosmos considering the ubiquity of water. Generalizing beyond Titan-like worlds, CH$_4$, in conjunction with atmospheric O$_2$ and O$_3$, is speculated to be a biosignature \citep{Kaltenegger2010}. Therefore, modeling the transport of CH$_4$ across the interiors of planets and moons, and its availability at the surface and atmosphere, are of paramount importance. Clearly, the data we have for Titan is far superior to what we will have in the foreseeable future for Titan-like exoplanets and exomoons. Therefore, although our aim is more general, this work will use Titan as our primary model object. During the epoch of its accretion Titan maintained an inner core of undifferentiated ice-rock mixture \citep[][]{Lunine198761,Barr2010858,Monteux2014377}. The ultimate source of CH$_4$ in present day Titan's atmosphere is this inner core \citep{Lunine198761}. However, this implies that CH$_4$ was able to traverse across the entire depth of Titan to reach the atmosphere. The moment of inertia estimated for Titan from Cassini gravity measurements suggests that Titan's interior is partially undifferentiated. The nature of the undifferentiated layer is still unknown. It may be either an ice-rock layer between a rocky core and a water rich outer mantle, or an outer rocky core composed of hydrous silicates \citep{Fortes2012c,lunine10}. If a mixed ice-rock layer indeed exists in the interior of Titan, then a newly discovered high pressure solid solution in the H$_2$O-CH$_4$ binary system called MH-III (also CH$_4$ filled-ice Ih) may hinder the outer transport of internal CH$_4$ into the atmosphere. The formation of MH-III was first reported in \cite{lovedaynat01}. Contrary to what was previously assumed for the H$_2$O-CH$_4$ system, upon increasing the pressure above about $2$\,GPa, at room temperature, the classical structure H cage clathrate transforms into MH-III, rather then experience phase separation into water ice VII and solid CH$_4$. In this way the solubility of H$_2$O and CH$_4$ is kept throughout the entire pressure range inside Titan. This is also likely true for the much higher pressures spanning water ice mantles of water-rich exoplanets, given that MH-III was found to be stable up to about $100$\,GPa \citep{hirai06}, and temperatures higher than $1000$\,K \citep{Machida2006}. We refer the reader to \cite{loveday01} for a detailed description of the crystallographic nature of MH-III. If CH$_4$ is indeed locked in grains of MH-III, scattered within a deep ice-rock layer above the rocky core of Titan, then how much of it may be transported outward depends on the buoyancy of these grains with respect to melt pockets and the solubility of CH$_4$ under such conditions. Such an analysis requires thermophysical data for MH-III at the appropriate conditions. In the context of Titan-like exoplanets, previous work on the transport of CH$_4$ across the interior pinpointed the necessary thermophysical data and the lack thereof \citep{Levi2013,Levi2014}. Quantifying the needed thermophysical data is the prime object of this work. In section $2$ we probe the pressure regime in a possible undifferentiated ice-rock layer inside Titan, to better pinpoint our molecular simulations and the possible role of MH-III. In section $3$ we explain our computational methods. In section $4$ we derive the thermal equation of state and thermal expansivity. Section $5$ is dedicated to the heat capacity. In section $6$ we estimate the thickness of a MH-III enriched layer in Titan's interior, and its carbon content capacity. In section $7$ we use a 1-D thermal evolution model to asses the stability of such a layer. Section $8$ is a discussion, and section $9$ is a summary. | MH-III is an important phase within the H$_2$O-CH$_4$ binary system that should be considered when modeling water-rich bodies. Its thermodynamic stability field is very wide, overlapping those of ice VI, VII and X. In addition it has a high capacity for storing CH$_4$ (H$_2$O:CH$_4$ mole ratio of $2$:$1$). We show that MH-III may exist in the interior of Titan for part of the parameter space describing Titan's inferred internal structure. However, this phase is likely dominant in the interior of super-Titans owing to the higher pressures reached within their water-rich ice mantles. This has two interesting consequences, (1) it may further constrain Titan's interior models, (2) it may create a dichotomy breaking analogies between Titan and super-Titans. We describe two modes for the outward transport of CH$_4$ across a MH-III enriched layer, either as a dissolved component within a buoyant melt, or largely as a separate phase (in addition to partially dissolved) if the melt is of a high enough temperature to dissociate MH-III in its path. These two modes represent different CH$_4$ transport efficiencies if the solubility value is low. The solubility of CH$_4$ when in equilibrium with MH-III is not known. If it is low, and dissolution of CH$_4$ is the prime mode of transport, then melt extraction may not be an efficient mechanism for the outward transport of CH$_4$ out of an MH-III enriched layer. In this case the abundant presence of CH$_4$ at the surface and atmosphere of Titan makes a high moment of inertia ($0.34$) more likely, since MH-III will not be stable in Titan's interior in this case. Another possibility is that the composition of the ice-rock mixed layer, assumed in our model, is poor in rock ($\lessapprox 0.2$ in mass fraction) resulting in a buoyant melt that is hot enough to dissociate MH-III along its path. In \cite{Levi2014} we have suggested that the presence of MH-III would shift adiabatic thermal profiles to higher temperatures when compared against adiabats in ice VII. Our new results for the volume thermal expansivity and isobaric heat capacity for MH-III confirm this earlier estimation which was not based on ab initio models for MH-III (see Fig.\ref{fig:Adiabats}). This shift to higher temperatures ought affect the dynamics of ice mantles, and couple between dynamics and composition along the history of CH$_4$ transport and outgassing. However, such an analysis would require a better understanding of the viscosity of high-pressure solid solutions. \begin{figure}[ht] \centering \includegraphics[trim=0.15cm 5cm 0.01cm 5.0cm , scale=0.60, clip]{f23.pdf} \caption{\footnotesize{Adiabatic profiles assuming a composition of ice VII (dashed red), and a composition of MH-III (solid red). Dashed-dotted (magenta) is the melting curve of ice VII from \cite{Lin2004}. }} \label{fig:Adiabats} \end{figure} The interiors of the icy moons of our solar system reach relatively low pressures. The highest pressure inside Titan is only about $6$\,GPa. Their total mass of volatiles is also likely small in comparison to what is stored inside a ice-rich planet or a super-Moon. Therefore, the high capacity of MH-III for storing volatiles makes it important, even if it is only stabilized over a narrow pressure range ($\sim 0.1$\,GPa). Observations beyond our solar system may detect super-Titans down to twice the mass of Mars \citep{Kipping2009,Heller2014}. \cite{Heller2015a,Heller2015b} have shown that super-Titans and super-Ganymedes can form in the accretion disks around super-Jovian planets, noting that hot Jupiters have already been detected. Polymorphs of filled ice likely play a major role in the transport and outgassing of volatiles for the case of the more massive super-Titans and water worlds. Filled ices form not just in the H$_2$O-CH$_4$ system (i.e. MH-III) but also in the H$_2$O-CO$_2$ and H$_2$O-N$_2$ systems \citep{Loveday2008}. Thus, separating between biotic and abiotic atmospheric signatures requires a better understanding of these phases and their thermophysical nature. We hope that the community of high-pressure experimentalists and computational material scientists would invest more resources in the study of filled-ices. Such knowledge for the lower pressure clathrate hydrates yielded a general framework for modeling multi-component systems. It is time to do the same for filled-ices if we wish to realistically constrain the uncertainty of biosignatures in water worlds. | 18 | 8 | 1808.07925 |
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1808 | 1808.00734_arXiv.txt | Based on the model of accretion induced the magnetic field decay of the neutron star (NS), the millisecond pulsars (MSPs) will own the minimum magnetic field when the NS magnetosphere radius shrinks to the stellar surface during the binary accretion phase. We find that this minimum magnetic field is related to the accretion rate $\dot{M}$ as $B_{\rm min}\sim2.0\times10^7{\,\rm G}\,(\dot{M}/\dot{M}_{\rm min})^{1/2}$, where $\dot{M}_{\rm min}=4.6\times10^{15}\rm\,g/s$ is the averaged minimum accretion rate required for the MSP formation and constrained by the long-term accretion time, which corresponds to the companion lifetime less than the Hubble time. The value of $B_{\rm min}$ is consistent with that of the observed radio MSPs and the accreting MSPs in low mass X-ray binaries, which can be found the case of the application on the minimum and present field strength of \1808. The prediction on the minimum magnetic field of MSPs would be the lowest field strength of NSs in universe, which could constrain the evolution mechanism of the magnetic field of accreting NSs. | Millisecond pulsars (MSPs) are with the spin period ($P$) less than $10\rm\,ms$ and the magnetic field ($B$) around {\bf $10^{8.5}\rm\,G$}. They are recycled pulsars (PSRs) through the accretion in the low mass X-ray binaries (LMXBs) (Stairs 2004; Lorimer 2008; van den Heuvel 2009, 2017; Manchester 2017). Since the first MSP (PSR B1937+21) discovered by Backer et al. in 1982, there have been over 300 MSPs recorded in ATNF pulsar catalogue until April of 2018 (Manchester et al. 2005). Their magnetic fields ($B$) are believed to decay from $\sim 10^{10.5-15.5}$ G (Ho 2013; Luo et al. 2015; Kaspi 2017) to $\sim10^{7.5-9.0}\rm\,G$ in LMXBs by accreting the mass of $\sim0.1-0.2\ms$, which can be inferred from the observations (Bhattacharya \& van den Heuvel 1991; Phinney \& Kulkarni 1994; Bhattacharya \& Srinicasan 1995; van den Heuvel 2004; Ruderman 2010; Zhang et al. 2011, 2016; Tauris 2015; Manchester 2017). As a comparison, the histogram of field strength of MSPs and normal PSRs are shown in Fig.\ref{hist_b}. The model of a MSP formed during the accretion in LMXB was first proposed in 1980s (Alpar et al. 1982). Then, from the observational statistics, Taam and van den Heuvel (1986) found that the magnetic field of neutron star (NS) decayed inversely with the accretion mass, based on which, an empirical formula about the field strength evolution of the X-ray PSR with the accretion mass was presented by Shibazaki et al. (1989). Furthermore, by assuming the frozen magnetic field in the NS crust, the model of the accretion induced the magnetic field decay was proposed (Zhang \& Kojima 2006), which was applied to simulate the B-P evolution of accreting NSs, whose results were suitable for those of the observed PSRs (Wang et al. 2011; Pan et al. 2013, 2015). The magnetic field of MSPs can be estimated by different methods. For the radio and non-accreting MSPs, their magnetic fields can be calculated through the spin period and period derivative ($\dot{P}$): $B\simeq3.2\times10^{19}{\,\rm (G)}\,(P\dot{P})^{1/2}$ (Shapiro \& Teukolsky 1983; Bhattacharya \& van den Heuvel 1991). For the anomalous X-ray PSRs, the magnetic field can be obtained through modeling the non-thermal X-ray spectra with cyclotron and magnetic Compton scattering processes in the magnetosphere (G$\rm\ddot{u}$ver, $\rm\ddot{O}$zel \& G$\rm\ddot{o}\breve{g}\ddot{u}s$ 2008). For the X-ray PSRs with high B (e.g. $B\geqslant10^{12} \rm\,G$), one can use the resonant electron cyclotron lines in the X-ray spectra (Caballero \& Wilms 2012). For the accreting X-ray MSPs (AMXPs), the magnetic field can be derived through comparing the magnetosphere radius to the co-rotation radius of accreting NS (Burderi et al. 1996, 2002), by which the magnetic fields of \1808 (Wijnands \& van der Klis 1998) and XTE J1751-305 and XTE J0929-314 were estimated in the order of $\sim10^{8}$ G (Wijnands et al. 2005). The magnetic field of a NS in LMXB (NS/LMXB) can also be constrained with its detected frequency of kilo-Hertz quasi-periodic oscillation (kHz QPO, van der Klis 2000; Zhang 2004). In addition, if the frequency derivative of an accreting NS/LMXB is detected, the magnetic field can be estimated by the spin up formula of X-ray NS (Ghosh \& Lamb 1979), by which the magnetic fields of a dozen NS/LMXBs are obtained as $10^{8-9}\rm\,G$ with their frequency derivatives about $\sim10^{-14}\rm\,Hz\,s^{-1}$ (Burderi \& Di Salvo 2013). In this paper, by the model of accretion induced the magnetic field decay of NS, we study the minimum field strength $B_{\rm min}$ of MSPs, which corresponds to the minimum accretion rate for the MSP formation in section 2. The consistence is investigated between our $B_{\rm min}$ of MSPs and that of the observed MSPs and AMXPs. We also figure out the magnetic field range of NS/LMXB whose companion is with the possible upper limit mass. Furthermore, the minimum magnetic field of AMXPs is discussed, including an application for the minimum and present field strength of the first discovered AMXP, \1808. The conclusion and discussion are given in section 3. \begin{figure} \includegraphics[width=8cm]{bhist1220.eps} \caption{Histogram of magnetic fields of 2636 pulsars (data from ATNF pulsar catalogue until April of 2018). The samples almost follow a bimodal distribution (Camilo et al. 1994): centered at $\sim10^{12.5}\rm\,G$ for normal pulsars labelled with the left-inclined bars and $10^{8.5}\rm\,G$ for MSPs labelled with the right-inclined bars. } \label{hist_b} \end{figure} \begin{figure} \includegraphics[width=8cm]{msp0206.eps} \caption{Binary pulsars and millisecond pulsars (labelled with the dot and crossing symbols) distributed in the magnetic field versus spin period diagram. The ones with $B<10^8\rm\,G$ are labelled with the quadrangles. Four solid lines represent the spin up lines with the accretion rates from $10^{18}\rm\,g/s$ (upper) to $10^{15}\rm\,g/s$ (bottom), and the dash line stands for the death line (Bhattacharya \& van den Heuvel 1991). The upper-left small B-P diagram is the enlarged close-up of MSPs. } \label{msp} \end{figure} | The minimum magnetic field of MSP appears when the NS magnetosphere is compressed onto the stellar surface, according to the model of accretion induced the field strength decay. We find that the minimum field strength is proportionally related to the accretion rate, shown as $B_{\rm min}\simeq2.0\times10^7{\rm\, G}\,(\dot M/\dot M_{\rm min})$ for a MSP with $m=1.4$, $R_6=1.5$ and $\dot M_{\rm min}\simeq4.6\times10^{15} \rm\,g/s$. $\dot M_{\rm min}$ is the critical minimum accretion rate for the MSP formation, which is constrained by two conditions: the accretion mass $0.1\ms$ required for the MSP formation at least, and the longest accretion time about 10\% of the main-sequence time of the companion star that closes to the Hubble age or the age of universe. With the accretion rate $\dot M_{\rm min}$, the minimum magnetic field $2.0\times10^7\rm\,g/s$ of a MSP is obtained, that is closed to the minimum field strength of the observed MSPs, as shown in Fig. \ref{hist_b} and Table 2. Thus, we propose that the calculated minimum magnetic field of MSP is also the minimum field strength of NS, which would be a limitation of the magnetic field decay of NS in the universe. When the accretion rate is from $\dot M_{\rm min}$ to $\dot M_{\rm Edd}$ in LMXBs, the magnetic field of MSPs will be $2.0\times10^7\rm\,G\leq B\leq2.8\times10^8\rm\,G$, which gives a requirement for the companions mass range in main sequence to be about $1.0\ms$ to $4.6$ or $5.6\ms$. Some approximations exist during the estimation of $B_{\rm min}$, such as the accretion time and ratio between the accretion disk radius and Alfv\'en radius of the NS, which may cause $B_{\rm min}$ a little change: (a) the accretion time is a fraction of the companion lifetime (10\%). The relaxation of this condition will modify $B_{\rm min}$; (b) the ratio between the magnetic sphere and Alfv\'en radius is 0.5 as a usual choice (Ghosh \& Lamb 1979; Wang 1996; Ho et al. 2017). A higher one, e.g. $0.8\sim1$ (Li \& Wang 1999), could also arise $B_{\rm min}$. When comparing $B_{\rm min}$ to the estimated field strengths of AMXPs, all AMXPs are with the higher magnetic field ($\sim 10^8 {\rm\, G}$) than the obtained minimum field value, e.g., the field strength calculation of the first AMXP, \1808. Its mean values of mass, radius and accretion rate of the source are selected based on the researches on its seven bursts in the past 20 years. With such conditions, the present magnetic field of the source is calculated to be $7.1\times10^7\rm\,G$, and the minimum value is $2.5\times10^7\rm\,G$. The results illustrate that \1808 will continue the evolution till the magnetic field decays to the minimum value. | 18 | 8 | 1808.00734 |
1808 | 1808.05327_arXiv.txt | {\bf In the present study, the magnetic field scaling on density, $|B| \propto \rho^{\kappa}$, was revealed in a single starless core for the first time. The $\kappa$ index of $0.78 \pm 0.10$ was obtained toward the starless dense core FeSt 1-457 based on the analysis of the radial distribution of the polarization angle dispersion of background stars measured at the near-infrared wavelengths. The result prefers $\kappa = 2/3$ for the case of isotropic contraction, and the difference of the observed value from $\kappa = 1/2$ is 2.8 sigma. The distribution of the ratio of mass to magnetic flux was evaluated. FeSt 1-457 was found to be magnetically supercritical near the center ($\lambda \approx 2$), whereas nearly critical or slightly subcritical at the core boundary ($\lambda \approx 0.98$). Ambipolar-diffusion-regulated star formation models for the case of moderate magnetic field strength may explain the physical status of FeSt 1-457. The mass-to-flux ratio distribution for typical dense cores (critical Bonnor--Ebert sphere with central $\lambda=2$ and $\kappa=1/2$--$2/3$) was calculated and found to be magnetically critical/subcritical at the core edge, which indicates that typical dense cores are embedded in and evolve from magnetically critical/subcritical diffuse surrounding medium. } \vspace*{0.3 cm} \clearpage | Magnetic fields are believed to play an important role in controlling the formation and contraction of dense cores in molecular clouds. The determination of the relationships between the magnetic field strength $|B|$ and the gas volume density $\rho$, usually expressed in a power law form as $|B| \propto \rho^{\kappa}$, is important because they are related to the accumulation history of both the magnetic flux and the cloud material (e.g., Crutcher 1999). The $|B|$--$\rho$ relationship is also crucial in order to compare the magnetic field and internal density structure observations with theory. \par If an initially uniform magnetic field pervading a diffuse medium is assumed as a starting condition of the mass accumulation to form dense cores, the $|B|$--$\rho$ relationship of the core depends on 1) the shape of the progenitor cloud (e.g., spherical, cylindrical), 2) the magnetic field geometry (i.e., parallel or perpendicular or inclined geometry with respect to the elongation axis of the core), and 3) the direction of contraction (i.e., isotropic contraction or contraction toward a specific direction). In the case of (spherical) isotropic contraction, the conservation of magnetic flux ($\Phi = \pi R^2 |B|$) yields $|B| \propto R^{-2}$ ($R$ is the radius of the core) and the conservation of mass $(M = (4/3)\pi R^3 \rho)$ yields $\rho^{2/3} \propto R^{-2}$, providing the $|B|$--$\rho$ relationship as $|B| \propto \rho^{2/3}$. This corresponds to the prediction of the relatively weak magnetic field case (Mestel 1966). Note that isotropic contraction does not necessarily mean spherical cloud shape, merely that the shape be conserved during the contraction. However, if the initial axial ratio of the cloud is large, the shape of the cloud becomes more elongated during the contraction by the effect of gravity. In the case of the plane-parallel or infinite thin disk geometry, the conservation of magnetic flux ($\Phi = \pi R^2 |B|$) and mass $(M = \pi R^2 z \rho)$ yields $\rho z / |B| = {\rm constant}$, where $z$ is the distance perpendicular to the plane. In this geometry, the force balance between self-gravity and internal thermal pressure along the symmetry axis is $2\pi G \rho z^2 \approx C_{\rm s}^2$ (Spitzer 1942), where $C_{\rm s}$ is the sound speed. Therefore, $|B| \propto (\rho T)^{1/2}$ ($T$ is the gas temperature), and in the isothermal case, $|B| \propto \rho^{1/2}$ (see, Crutcher 1999). \par On the basis of large samples with Zeeman measurements of the line-of-sight magnetic field strength $B_{\rm los}$ and Bayesian statistical analysis, Crutcher et al. (2010) concluded that the data prefer $\kappa \approx 2/3$ $(|B| \propto \rho^{0.65 \pm 0.05}$ for $\rho > 300$ cm$^{-3}$) and reject $\kappa \approx 1/2$. They also showed the existence of two distinct branches on the $B$ versus $\rho$ diagram, a flat region at low densities ($|B|$ independent of $\rho$, i.e., $\kappa \approx 0$) and a power-law scaling region at high densities ($\kappa \approx 2/3$). A recent study reported results contrary to those reported by Crutcher et al. (2010) based on the re-analysis of the same observational data ($\kappa \approx 1/2$ is preferred; Tritsis et al. 2015). Note that Crutcher et al. (2010) analyzed the full set of Zeeman data including non-detections, whereas Tritsis et al. (2015) only analyzed the observational data with Zeeman detection (this may cause the biased results with stronger magnetic field strength and smaller $\kappa$). \par Several $\kappa$ measurements with smaller samples have been conducted. Li et al. (2015) obtained $\kappa = 0.41 \pm 0.04$ toward the clouds and cores in the NGC 6334 complex based on the measurements of $B_{\rm pos}$ by comparing the curvature of the plane-of-sky magnetic field lines with self-gravity. Ching et al. (2017) obtained $\kappa = 0.54 \pm 0.30$ toward the cores in the dense filamentary cloud DR21 based on the submillimeter (submm) dust emission polarimetry and the Chandrasekhar--Fermi method (Chandrasekhar \& Fermi 1953). Hoq et al. (2017) obtained $\kappa = 0.73 \pm 0.06$ toward the filamentary infrared dark cloud (IRDC) G28.23-00.19 based on near-infrared (NIR) dust extinction polarimetry and the Chandrasekhar--Fermi method. Observations show a variety of $\kappa$ values ranging from $\kappa \approx 1/2$ to $\kappa \approx 2/3$. Therefore, it is important for observational studies to provide the definite value of $\kappa$ through much larger samples or much more accurate measurements, although it is possible that the value of $\kappa$ varies from region to region, depending on the shape of objects or the type of contractions or other characteristics. Note that there is no observation of the $|B|$--$\rho$ relationship determined using a single molecular cloud core. \par From a theoretical point of view, Mouschovias (1976a,b) showed that the ratio of magnetic and gas pressure ($B^2 / 8 \pi P$) tends to remain constant, $\approx 1$, inside the magnetized cloud during collapse. This yields $|B| \propto \rho^{1/2}$ for the isothermal case (i.e., $P=\rho C_{\rm s}^2$, where $C_{\rm s}$ is the isothermal sound speed). Numerical simulation of the ambipolar diffusion driven core contraction (Fiedler \& Mouschovias 1993) provided $\kappa \approx 0.47$ which is consistent with a $\kappa$ value of 1/2. Ciolek \& Mouschovias (1994) obtained relatively smaller values of $\kappa = 0.38 - 0.43$. Mouschovias (1991) suggested that the magnetic field in molecular clouds depends on both the density and the velocity dispersion $\sigma_v$ as $|B| \propto \rho^{1/2} \sigma_v$. Basu (2000) showed that there is a good correlation between $B_{\rm los}$ and $\rho \sigma_v$ in observations, providing $B_{\rm los}/\sigma_v \propto \rho^{0.50 \pm 0.12}$. If the velocity dispersion does not depend on the density, this is consistent with the relation of $|B| \propto \rho^{1/2}$. In contrast, recently Li, McKee \& Klein (2015) conducted a large-scale magneto-hydrodynamic (MHD) simulation of isothermal, self-gravitating gas with a slightly magnetically supercritical initial magnetic field. A $\kappa$ value of $0.70 \pm 0.06$ was obtained, and the result is consistent with the value obtained by Crutcher et al. (2010) of $\kappa \approx 2/3$ $(B_{\rm tot} \propto \rho^{0.65 \pm 0.05}$). The flat low density region and the high density region following a power law relation ($\kappa = 0.65$) on the $|B|$ vs. $\rho$ diagram are reproduced in their simulation. Furthermore, it was found that the velocity dispersion scales weakly with density as $\sigma_v \propto \rho^{0.14 \pm 0.05}$, which is also consistent with the result of $\kappa \approx 2/3$. Theoretical studies have revealed a variety of $\kappa$ values ranging from $\kappa \approx 1/2$ to $\kappa \approx 2/3$. Further theoretical studies are desirable in this field. \par Another critical parameter for magnetic field theories is the ratio of the mass $M$ in the flux tube to the magnitudes of magnetic flux $\Phi$, which is often expressed as the observational parameter normalized by the theoretical critical value, $\lambda = (M/\Phi)_{\rm obs}/(M/\Phi)_{\rm critical}$. Since the magnetic support and the gravity have same radial dependence, the collapse of dense cores cannot be stopped by magnetic fields once gravity overcomes magnetic fields. Theoretical determination of the critical value is thus important. The critical value suggested by theory can be written as $(M/\Phi)_{\rm critical} = c_{\Phi}/\sqrt{G}$, and Mouschovias \& Spitzer (1976) found $c_{\Phi} \approx 0.126$ for disks with support along magnetic field lines. Tomisaka et al. (1988) found a consistent value based on extensive numerical calculations as $c_{\Phi} \approx 0.12$. Nakano \& Nakamura (1978) derived $c_{\Phi}=1/2\pi$ with a linear perturbation analysis for the magnetized isothermal gaseous disk. Note that the mass-to-flux ratio depends on cloud geometries, and $(M/\Phi)_{\rm critical} = [3 \pi \sqrt{G/5}]^{-1}$ can be obtained for a uniform sphere under virial equilibrium between gravity and the magnetic field, $3GM^2 / 5R = B^2 R^3 /3$ (Crutcher 2004). Thus, $c_{\Phi} \approx 2/3\pi$ for the spherical case. Molecular cloud cores in various regions tend to show projected aspect ratios of 2:1 (e.g., Myers et al. 1991; Jijina et al. 1999), and de-projection analyses for revealing the intrinsic shape of dense cores were reported (e.g., Jones et al. 2001: triaxial shape, Tassis et al. 2007: oblate shape with finite thickness). Therefore, in general, observational studies need assumption on the shape of the core when choose and use the theoretical critical value, although the value of $c_{\Phi}=1/2\pi$ (Nakano \& Nakamura 1978) has been widely used. \par Without information of line-of-sight inclination angle of magnetic field direction, $\lambda$ was statistically estimated assuming random orientation of the inclination angle for many target cores. After statistical geometric correction, Crutcher (1999) and Troland \& Crutcher (2008) obtained $\lambda \approx 2$ based on the OH Zeeman observations of dark cloud cores, and the CN Zeeman observations by Falgarone et al. (2008) showed consistent results. Thus, typical dense cores seem to be in a state of slightly magnetically supercritical condition. However, these results have a problem that the statistical analysis eliminates the information of the diversity of the magnetic fields for each core. In order to know $\lambda$ for each core and discuss the magnetic field condition of the core in detail, it is necessary to obtain the information of the magnetic inclination angle $\theta_{\rm inc}$. If $\theta_{\rm inc}$ is known in addition to $\rho$ and $\kappa$, the distribution of $\lambda$ can be obtained from the center of the core to its envelope. As stated by Crutcher (2004), the $\lambda$ value at the cloud envelope provides a crucial test for magnetic support models of star formation. \par In the present study, the $|B|$--$\rho$ relationship was constructed for the starless dense core FeSt 1-457 based on the NIR polarimetric observations of the dichroic polarization of dust toward the background stars. A modified form of the Chandrasekhar--Fermi method, which enables the determination of the value of $\kappa$, was used. With information of the magnetic fields ($\kappa$ and $\theta_{\rm inc}$) and the cloud density distribution, the distribution of mass-to-magnetic flux was obtained, and physical status of FeSt 1-457 was discussed. The mass-to-flux ratio distribution for the case of critical Bonnor--Ebert sphere with $\lambda=2$ was calculated in order to evaluate the behavior of the distribution for typical dense cores. \par FeSt 1-457 is known to be accompanied by an hourglass-shaped magnetic field (Kandori et al. 2017a, hereafter Paper I), and the three dimensional (3D) modeling of the field provides the magnetic field curvature and the line-of-sight inclination angle of the magnetic field direction $\theta_{\rm inc}$ (Kandori et al. 2017b, Paper II). The total magnetic field strength of the core is $33.7 \pm 18.0$ $\mu$G with a ratio of the observed mass-to-magnetic flux to a critical value of $\lambda = 1.41 \pm 0.38$ (magnetically supercritical, Paper II). These analyses seem reliable, because observed NIR polarizations of stars show linear relationship with respect to the dust extinction, indicating that magnetic fields inside FeSt 1-457 is traced by the NIR polarimetry (Kandori et al. 2018, Paper III). The fundamental physical parameters of FeSt 1-457 have been well defined in an internal density structure study based on NIR extinction measurements of the background stars and fitting with the Bonnor--Ebert sphere model (Ebert 1955; Bonnor 1956). The radius, mass, and central density of the core are 18,500 AU (144$''$), $3.55$ $M_{\rm \odot}$, and $3.5 \times 10^{5}$ ${\rm cm}^{-3}$ (Kandori et al. 2005), respectively, at a distance of $130^{+24}_{-58}$ pc (Lombardi et al. 2006). \par Throughout this paper, the spherical shape was assumed for the core geometry, and $(M/\Phi)_{\rm critical} = 1/2 \pi \sqrt{G}$ (for disk geometry: Nakano \& Nakamura 1978) was used for the theoretical critical mass-to-flux ratio. Though FeSt 1-457 was well fitted using the Bonnor--Ebert sphere model, the elongation in column density structure appears around the core center, which may be the existence of disk-like structure around center. The theoretical critical value for spherical geometry is larger than that for disk geometry, and we thus use the value of $1/2 \pi \sqrt{G}$ as a lower limit of the theoretical critical value. | In the present study, the magnetic field scaling on density, $|B| \propto \rho^{\kappa}$, was revealed in a single starless core for the first time. The index $\kappa$ was obtained to be $0.78 \pm 0.10$ toward the starless dense core FeSt 1-457 based on the analysis of the radial distribution of the polarization angle dispersion of background stars measured at the near-infrared wavelengths. The result prefers $\kappa = 2/3$ (isotropic contraction), and the difference of the observed value from $\kappa = 1/2$ is 2.8 sigma. The relatively large $\kappa$ value indicates that the magnetic field in FeSt 1-457 is not very strong. This is consistent with the slightly magnetically supercritical feature of the core. The magnetic field in FeSt 1-457 can be strong enough to control the contraction of the core, because the magnetic field direction of the core is perpendicular to the elongation axis of the core. Observations of ordered magnetic field lines around the core also support this conclusion. These results are consistent with the recent theoretical MHD simulation calculated under the slightly magnetically supercritical condition. The total magnetic field strengths at the center and boundary of the core are 132 $\mu$G and 17 $\mu$G, respectively. The boundary value can be used as the estimation of the magnetic field strength in the diffuse inter-clump medium surrounding the core. On the basis of $\kappa$ and known density structure, the distribution of the ratio of mass to magnetic flux was evaluated. FeSt 1-457 was found to be magnetically supercritical near the center ($\lambda \approx 2$), whereas nearly critical (slightly subcritical) at the core boundary ($\lambda \approx 0.98$). Thus, the diffuse inter-clump medium surrounding the core can also be nearly magnetically critical. Ambipolar diffusion regulated star formation models for the case of moderate magnetic field strength may explain the physical status of FeSt 1-457. Note that though our obtained index of $\kappa = 0.78$ does not fit to the case of strong magnetic fields, it may not be inconsistent with the moderate magnetic field case. The mass-to-flux ratio distribution for typical dense cores (critical Bonnor--Ebert sphere with central $\lambda=2$ and $\kappa=1/2$--$2/3$) was found to be magnetically critical/subcritical at the core edge, which indicates that typical dense cores are embedded in and evolve from critical/subcritical diffuse surrounding medium. \subsection*{Acknowledgement} We are grateful to the staff of SAAO for their kind help during the observations. We wish to thank Tetsuo Nishino, Chie Nagashima, and Noboru Ebizuka for their support in the development of SIRPOL, its calibration, and its stable operation with the IRSF telescope. The IRSF/SIRPOL project was initiated and supported by Nagoya University, National Astronomical Observatory of Japan, and the University of Tokyo in collaboration with the South African Astronomical Observatory under the financial support of Grants-in-Aid for Scientific Research on Priority Area (A) Nos. 10147207 and 10147214, and Grants-in-Aid Nos. 13573001 and 16340061 of the Ministry of Education, Culture, Sports, Science, and Technology of Japan. RK, MT, NK, KT (Kohji Tomisaka), and MS also acknowledge support by additional Grants-in-Aid Nos. 16077101, 16077204, 16340061, 21740147, 26800111, 16K13791, 15K05032, and 16K05303. | 18 | 8 | 1808.05327 |
1808 | 1808.02441_arXiv.txt | We introduce {\it SimBAL}, a novel spectral-synthesis procedure that uses large grids of ionic column densities generated by the photoionization code {\it Cloudy} and a Bayesian model calibration to forward-model broad absorption line quasar spectra. We used {\it SimBAL} to analyze the {\it HST} COS spectrum of the low-redshift BALQ SDSS~J085053.12+445122.5. {\it SimBAL} analysis yielded velocity-resolved information about the physical conditions of the absorbing gas. We found that the ionization parameter and column density increase, and the covering fraction decreases as a function of velocity. The total log column density is 22.9 (22.4) [$\rm cm^{-2}$] for solar ($Z=3Z_\odot$) metallicity. The outflow lies 1--3 parsecs from the central engine, consistent with the estimated location of the torus. The mass outflow rate is 17--$28\rm \, M_\odot yr^{-1}$, the momentum flux is consistent with $L_{Bol}/c$, and the ratio of the kinematic to bolometric luminosity is 0.8--0.9\%. The outflow velocity is similar to the escape velocity at the absorber's location, and force multiplier analysis indicates that part of the outflow could originate in resonance-line driving. The location near the torus suggests that dust scattering may play a role in the acceleration, although the lack of reddening in this UV-selected object indictes a relatively dust-free line of sight. The low accretion rate ($0.06 L_{\rm Edd}$) and compact outflow suggests that SDSS~J0850$+$4451 might be a quasar past its era of feedback, although since its mass outflow is about 8 times the accretion rate, the wind is likely integral to the accretion physics of the central engine. | The optical and UV spectra of active galactic nuclei (AGN) and quasars offer powerful diagnostics of the physical conditions of gas in the vicinity of their central engines. Powered by photoionization, the broad emission lines trace the kinematics of the broad line region, likely dominated by Keplerian motions, while the broad absorption lines trace the outflow. A range of ionization states are seen from a number of different ground- and excited-state transitions. The broad emission lines are significantly Doppler-broadened by the motion of the gas in the vicinity of the black hole, with characteristic velocity widths of 1000s of $\rm km\, s^{-1}$, making line blending a considerable impediment to quantitative analysis. Emission-line studies are further compromised by the potential contributions to a single line from gas with a wide range of illumination patterns (e.g., the illuminated side of a cloud will emit differently than the back side of the cloud). Absorption line studies are more straightforward because only line-of-sight gas is important. Diagnostic power is lost when lines are saturated and complicated by the fact that the gas is known to partially cover the accretion disk, the source of the continuum emission. While we know that the gas must be clumpy in order to be dense enough to produce the emission and absorption that we see, there is no clear understanding of the characteristic scale and distribution of these clumps, or of how they are formed and maintained within the dynamic environment of the central engine. Nevertheless, emission and absorption lines in quasars provide insight into fundamentally important phenomena. The central engine of quasars is not only a bright beacon in the Universe, exhibiting a rich phenomenology, but it also may be contributing to regulating the rate of star formation in the host galaxy \citep[e.g.,][]{kp15}, thus contributing to the observed tight correlation between black hole mass and the mass of the bulge \citep[e.g.,][]{fm00,kh13}. Blue-shifted absorption lines, in particular, provide strong evidence for powerful outflows, and may prove to be key tracers of how accretion power may couple to the host galaxy's interstellar medium. Early quantitative analysis of broad absorption line quasar spectra focused on estimating the physical conditions of the gas, including ionization parameter, column density, and metallicity as a way of understanding the acceleration mechanism and potential for chemical enrichment of the intergalactic medium. Initially, these investigations proceeded with little concern for the width of the absorption lines. \citet{arav01b} reported the analysis of the low-redshift quasar PG~0946$+$301, which has a FWHM of the main \ion{C}{4} component of about $8000\rm \, km\, s^{-1}$. Once partial covering was discovered to be important, investigators started working on determining the covering fraction and nature of partial covering \citep[e.g.,][]{hamann01,dekool02c}. Around the same time, scientists began to appreciate the diagnostic power of absorption lines with easily-populated excited states for determining the density of the outflows \citep[e.g.,][]{dekool01,dekool02a,dekool02b}. An issue is that many of the diagnostic pairs of lines (e.g., \ion{C}{2} at 1334.0 and 1335.7 \AA\/, \ion{S}{4} at 1062.7 and 1073.0 \AA\/) lie quite close together in wavelength \citep[e.g.,][Fig.\ 15]{lucy14}, making blending a problem for lines that are broad. The focus on using excited states to determine the outflow density, and the accompanying problems with blending, means that much of the recent work to determine the physical conditions of the outflowing gas using spectroscopic diagnostics has been done on objects with relatively narrow lines. For example, HE~0238$-$1904 has several components with velocity widths of $500\rm\, km\, s^{-1}$ \citep{arav13}. FBQS~J0209$-$0438 shows an absorption system with overall width of $600\rm\, km\, s^{-1}$ \citep{finn14}. QSO~2359$-$1241 shows \ion{Fe}{2} absorption from various velocity components ranging in width from $<50\rm \,km\, s^{-1}$ to $\sim 100 \rm \, km\, s^{-1}$ \citep{bautista10}. SDSS~J1106$+$1939 shows \ion{S}{4} absorption with width of $\sim 2900\rm \, km\, s^{-1}$, while SDSS~J1512$+$1119 shows \ion{S}{4} absorption with width of $\sim 250\rm \, km\, s^{-1}$ \citep{borguet13}. Yet the population of BAL quasars shows an enormous range of velocity widths. \citet{baskin15} report analysis of the \ion{C}{4} line from 1596 BAL quasars taken from the SDSS DR7 quasar catalog \citep{shen11}. The distribution of \ion{C}{4} width peaks at around $2000\rm \, km\, s^{-1}$ with a long tail to larger velocities. A cumulative distribution shows that 25\% have velocity widths larger than $5200 \rm \, km\, s^{-1}$, while 10\% have velocity widths larger than $7500\rm\, km\, s^{-1}$. Limiting analysis to objects with narrow lines, or selecting out exactly those quasars with the strongest winds that are most likely to be important for feedback, may limit our understanding of quasar outflows. Another issue was revealed by \citet{lucy14}. In that paper, we analyzed the iron low-ionization broad absorption line quasar (FeLoBAL) FBQS~J1151$+$3822. We modeled the lines using a normalized absorption-line template developed from the \ion{He}{1}* absorption lines \citep{leighly11}. Following the procedure in the literature that has been used by many authors \citep[e.g.,][]{moe09, dunn10, borguet12,arav13, chamberlain15}, we fit the template to the spectrum in order to estimate the apparent column densities of line complexes. We compared the measured column densities with column densities predicted by the photoionization code {\it Cloudy} \citep{ferland13}, and used a figure of merit to determine the best-fitting values of ionization parameter $\log U$, density, and column density (parameterized as $\log N_H - \log U$). Our next step was novel. To check our best-fit result, we created a synthetic spectrum using the best-fitting parameters and overlaid it on the observed spectrum \citep[Fig.\ 3b,][]{lucy14}. The resulting fit was a very poor match to the observed spectrum, potentially implying that the physical parameters derived using this type of analysis may be wrong. Clearly a new approach is necessary, and we can take inspiration from work with other energetic systems. Supernovae are another type of astronomical object with broad absorption lines. In these objects, the lines can be so broad that identification of a feature can be difficult. Spectral synthesis codes have proven invaluable for both line identification \citep[SYNOW,][]{branch05} and for analysis of the physical conditions in the outflow \citep[PHOENIX,][]{hb99}. It stands to reason that a similar approach may be useful for broad absorption line quasars. To that end, we introduce {\it SimBAL}, a spectral-synthesis forward-modeling method for analyzing BAL quasar spectra. {\it SimBAL}, in essence, inverts the conventional method for analyzing absorption lines. Instead of fitting individual lines and then comparing those measurements with {\it Cloudy} models, synthetic spectra are constructed from {\it Cloudy} models and then compared with the observed spectrum. The spectral synthesis approach has several advantages. First, because we do not need to identify individual absorption lines, blending is not an issue, so the width of the line no longer is an impediment to selection of quasars for analysis. Second, the conventional analysis method outlined above focuses on the lines that are observed, neglecting the important information provided by lines that are {\it not} detected. Since the spectral synthesis approach models the whole spectrum, the information provided by absent lines is used to constrain the solution. Finally, we use a Markov Chain Monte Carlo method in physical parameter space to compare the synthetic spectrum with the observed spectrum. This method allows us to harvest uncertainties on the physical parameters from the posterior probability distributions. Along the way, we have also discovered that we can map the physical parameters of the outflow (e.g., ionization parameter, column density, and covering fraction) as a function of velocity, properties that may be important for constraining acceleration models for the outflows. With the physical properties of the outflow in hand and a few assumptions, we can estimate mass outflow rates, key for constraining the kinetic energy available for quasar feedback on the host galaxy. In this paper, we use {\it SimBAL} to analyze {\it HST} COS spectrum of the low redshift ($z=0.5422$) LoBAL quasar SDSS~J085053.12$+$445122.5, hereafter referred to as SDSS~J0850+4451. The observation and continuum model are described in \S\ref{observations}. A brief description of {\it SimBAL} is given in \S\ref{simbal}. The absorption modeling and extraction of the physical parameters of the outflow is described in \S\ref{absorption_modeling}. The implications of our analysis are discussed in \S\ref{discussion}, the summary of our principal results and future development of {\it SimBAL} are discussed in \S\ref{conclusions}, { and several potential systematic effects are discussed in an Appendix.} Vacuum wavelengths are used throughout. Cosmological parameters used depend on the context (e.g., when comparing with results from an older paper), and are reported in the text. | \label{discussion} \subsection{The Black Hole Mass}\label{black_hole_mass} As discussed above, we found that the outflow lies 1--3~pc from the central engine. In order to put this value into context, we estimated size scales in SDSS~J0850$+$4451, beginning with the black hole mass. To determine the radius of the broad line region, we referred to \citet{bentz13}, who found that $\log(R_{BLR})=K+\alpha \log[\lambda L_\lambda(5100)/10^{44}\rm \, erg\, s^{-1}]$. The continuum flux density at 5100\AA\/ was estimated from the SDSS spectrum to be $F_{5100} = 31.3 \times 10^{-17}\rm \, erg\, s^{-1}\, cm^{-2}$\AA\/$^{-1}$. Using the cosmological parameters used by \citet{bentz13} ($H_0=72\rm\, km/s/Mpc$, $\Omega_M=0.27$, and $\Omega_\Lambda=0.73$), we obtained a luminosity distance $D_L=3031\,\rm Mpc$. Using their best-fitting values $K=1.527^{+0.031}_{-0.031}$ and $\alpha=0.533^{+0.035}_{-0.033}$, we obtained an estimate of the radius of the broad-line region of 155 light days, corresponding to $0.13^{+0.024}_{-0.021}\rm \, pc$, where the uncertainties are based on the regression coefficient uncertainties. SDSS~J0850+4451 has been identified as having a disk-like H$\beta$ emission-line profile \citep{luo13}. \citet{luo13} fit the H$\beta$ line with a relativistic Keplerian disk model. They found inner and outer radii for the line of 450 and 4700 $r_g$ respectively. For our derived black hole mass, these values correspond to $r_{in}=0.035\rm \, pc$ and $r_{out}=0.37 \rm \, pc$ respectively, roughly consistent with the \citet{bentz13} regression-estimated H$\beta$ radius of 0.13 pc. We estimated the black hole mass from the H$\beta$ line in the SDSS spectrum in the usual way. The data and model are shown in Fig.~\ref{fig19}. We were able to obtain a good fit with a single Gaussian profile with velocity width of $8090 \pm 120 \rm \, km\, s^{-1}$. To estimate the virial mass, we referred to \citet{collin06}, who provide line-shape-based correction factors to the FWHM-based virial product used to estimate the black hole mass. For a Gaussian profile, $FWHM/\sigma_{line}=2.35$, and the scale factor for the mean spectrum is $f=0.835$. We estimated that the black hole mass is $1.6\times 10^9 \rm \, M_\odot$. With the log bolometric luminosity estimate of 46.1, SDSS~J0850+4451 is radiating at about 6\% of the Eddington limit. \begin{figure*}[!t] \epsscale{1.0} \begin{center} \includegraphics[width=4.5truein]{f13-eps-converted-to.pdf} \caption{A model of the SDSS spectrum in the region of the H$\beta$ line. The broad H$\beta$ line was modeled with a single Gaussian, yielding a FWHM of $8090 \pm 120 \rm \, km \, s^{-1}$ and a black hole mass estimate of $1.6\times 10^9\rm \, M_\odot$. The small narrow H$\beta$ is the contribution from the narrow-line region, estimated to be 10\% of the flux of [\ion{O}{3}]$\lambda 5007$ \citep{cohen83}. \label{fig19}} \end{center} \end{figure*} \subsection{The Location of the Outflow}\label{location} The analysis presented in \S \ref{derived} indicated that the outflow is located approximately 1--3 parsecs from the central engine, i.e., around the expected size of the torus in a quasar-luminosity object. Near-IR reverberation has shown that the location of the hot inner edge of the torus is correlated with the luminosity \citep{kishimoto07}. We used their Eq.\ 3 to estimate that the inner edge of the torus is $R_{\tau_K} = 0.46 \rm \, pc$, i.e., slightly smaller than the outflow distance. Another number characterizing the torus is the $12\, \mu \rm m$ half-light radius. This property does not have a clear luminosity scaling relationship like $R_{\tau_K}$ \citep{burtscher13}. We estimated a plausible limit for $R_{1/2}(12\, \mu\rm m)$ by comparing the SDSS~J0850$+$4451 bolometric luminosity with the objects in \citet{burtscher13} Table 6. Three objects have bolometric luminosities within 0.2 dex of SDSS~J0850+4451, and all of these have upper limits on their mid-IR half-light radius between 2.7 and 3.5 parsecs. These estimates are crude, but they indicate that the outflow is consistent with an origin near the torus in SDSS~J0850$+$4451. Interestingly, a torus location for the broad absorption line outflow in the Seyfert luminosity BALQ WPVS~007 was inferred based on variability arguments \citep{leighly15}. Since we have estimated the black hole mass ($1.6\times 10^9\rm \, M_\odot$) and the radius of the outflow (1--3 parsecs), we can estimate the escape velocity $v_{esc}=\sqrt{2GM_{BH}/R}$ at the location of the outflow. We find that $v_{esc}$ lies between 2100 and $3700 \, \rm km\, s^{-1}$, interestingly close to the range of velocities seen in the outflow. This result suggests that the outflow could have been accelerated from rest close to the location where it is observed, in contrast to large-distance outflows, where the outflow velocity is much greater than the escape velocity, and other acceleration mechanisms such as ``cloud crushing'' \citep[e.g.,][]{fg12} are required. \subsection{The Acceleration Mechanism}\label{mechanism} We explored the acceleration mechanism for the outflow by using {\it Cloudy} to compute the force multiplier as a function of velocity. We extracted the MAP values of the ionization parameter and column density in each velocity bin, and assumed that the density over the whole outflow was equal to the average MAP value in bins representing the concentration. The results are shown in Fig.~\ref{fig20}. As discussed in e.g., \citet{couto16}, the force multiplier extracted from {\it Cloudy} is defined as the ratio of the total absorption cross section, including both line (bound-bound) and continuum (bound-free) processes, to the Thompson cross-section. The absorber can be radiatively driven if $FM \ge (L_{Bol}/L_{Edd})^{-1}$. As discussed in \S \ref{black_hole_mass}, this quasar seems to be radiating at about 6\% of $L_{edd}$, which means that $\log FM$ should be greater than 1.2 for the outflow to be radiatively driven. Fig.~\ref{fig20} shows that for the solar metallicity case, the force multiplier is generally less than the required value, although it meets the required value for velocities between $-2600$ and $-1900\rm \, km\, s^{-1}$, implying that another source of acceleration \citep[e.g., perhaps an MHD model,][]{kraemer18} is necessary. On the other hand, for the $Z= 3 Z_\odot$ case, the force multiplier exceeds the required value significantly for velocities less than $\sim -2600\rm \, km\, s^{-1}$, suggesting that radiative driving may be important, at least at lower velocities in the outflow. \begin{figure*}[!t] \epsscale{1.0} \begin{center} \includegraphics[width=7.0truein]{f14-eps-converted-to.pdf} \caption{The force multiplier computed at the MAP solution as a function of velocity. The open symbols show the results for the first continuum model, and the solid symbols mark the solutions for the second continuum model. The left (right) panel shows the result for solar ($Z=3 Z_\odot$) metallicity. The horizontal line marks the force multiplier value above which the flow can be radiatively driven. See the text for details. \label{fig20}} \end{center} \end{figure*} The force multiplier is anti-correlated with the column density, and the ionization parameter (see Fig.~\ref{fig7} and Fig.~\ref{fig8}). At larger velocities the gas may be thick but it may be too ionized to provide sufficient opacity for radiative driving. Alternatively, the gas may be too thick at high velocities (especially in the region of the concentration); a very thick gas slab is difficult to accelerate due to the loss of continuum photons by absorption \citep[e.g.,][]{arav94a}. { This is shown by \citet{baskin14} in their Fig.~9.} What is the origin of the differences between the solar metallicity case and the $Z=3 Z_\odot$? We expect a larger force multiplier for a higher metallicity, as metals provide the bulk of the scattering opacity, as observed. The simulations also show that that a larger fraction of the acceleration in the higher metallicity case is attributed to bound-bound interactions. However, the offset between the $\log FM$ values is not constant between the two metallicity cases, suggesting a contribution from differences in the ionization state of the gas and column density as well. { The outflow in SDSS~J0850$+$4451 originates near the torus. This suggests that dust could play a role in the wind acceleration. The equivalent dust cross section to scattering is 500--1000 times the electron scattering cross section for a typical quasar SED, which means that a typical quasar is super-Eddington with respect to dust, and may imply that dust-driven outflows can contribute to feedback \citep[e.g.,][and references therein]{fabian12, roth12}. Some models for the torus that take into account radiation-driven outflows find that a strong wind is produced \citep[e.g.,][]{kk94,gallagher15}. For example, \citet{ck16} predict a wind along the inner edge of the torus with velocity $\sim 5000 (M/10^7M_\odot)^{1/4} [L_{UV}/(0.1L_{Edd})]^{1/4} \rm \, km\, s^{-1}$ that carries $\sim 0.1 (M/10^7 M_\odot)^{3/4} [L_{UV}/(0.1 L_{Edd}]^{3/4} \rm M_\odot\, yr^{-1}$ where $M$, $L_{UV}$, and $L_{Edd}$ are the black hole mass, UV luminosity, and Eddington luminosity respectively. Recent models of the broad line region also appeal to radiation pressure on dust \citep{ch11,czerny17,bl18}. Thus, it seems that radiative acceleration on dust may provide more than enough energy to power winds that originate in the vicinity of the torus and perhaps beyond. The difficulty with this scenario is that while BALQ spectra are typically more reddened than quasars without broad absorption lines, only a small fraction show large amounts of reddening \citep[e.g., 13\% show $E(B-V) > 0.1$ and 1.3\% show $E(B-V) > 0.2$,][]{krawczyk15}. SDSS~J0850$+$4451, being UV selected, shows no evidence for reddening. In contrast, for a standard dust-to-gas ratio \citep{bohlin78}, a log hydrogen equivalent column density of 22.9 predicts $E(B-V)=13.7$, far too large to be realistic. So the dust must be separated from the gas. Dust is bound to the gas by collisions \citep{wick66}, and that mechanism becomes inefficient at low densities, allowing the dust to drift. Evidence for this mechanism is found in AGB stars \citep[][and references therein]{ho18}. We speculate that it is conceivable that the dusty wind is accelerated from the vicinity of the torus, and when it reaches a certain density, the dust continues to be accelerated, perhaps ultimately forming a scattering halo that may be observed as a polar outflow \citep{honig13, hk17}, or be responsible for polarization in BALQs \citep{ogle99} and red quasars \citep{alexandroff18}. The gas, which is left behind, would still have the momentum imparted during the dust acceleration phase, and could then be responsible for the broad absorption lines. } \subsection{Where Does SDSS J0850$+$4451 Fit In?}\label{context} In this paper, we have performed a detailed analysis of the absorption lines in SDSS~J0850$+$4451. In this section, we compare SDSS~J0850$+$4451 with other BALQs in order to gauge how typical this quasar is. SDSS~J0850$+$4451 was selected for observation using {\it HST} COS from a small sample of SDSS LoBAL quasars for which we had observations of \ion{He}{1}*$\lambda 10830$ using either Gemini GNIRS and/or LBT LUCI. Our intention was to compare the optical depths of \ion{He}{1}*$\lambda 10830$ and \ion{P}{5} to investigate the nature of partial covering; this is discussed in Paper II (Leighly et al.\ in prep.). We used {\em GALEX} to ensure that the target objects would be bright enough for {\it HST} to obtain a good signal-to-noise ratio in a reasonable exposure time. Thus, SDSS~J0850$+$4451 is relatively blue. { SED fitting, to be presented in Paper II (Leighly et al.\ in prep.) reveals no evidence for significant intrinsic reddening.} In contrast, BALQs tend to be reddened compared with the normal quasar population, although many BALQs with little reddening are found \citep[e.g.,][]{krawczyk15}. Indeed, SED fitting of the optical and IR photometry shows that the torus emission is relatively weak (Paper II, Leighly et al.\ in prep.) suggesting that SDSS~J0850$+$4451 might be relatively dust-free altogether. Despite the lack of reddening, SDSS~J0850$+$4451 was found to be X-ray weak in a {\it Chandra} observation \citep{luo13}. Only three hard photons, all with energies greater than 6.2 keV in the rest frame were detected. Assuming a typical quasar X-ray spectrum, \citet{luo13} found that a column of $N_H \approx 7 \times 10^{23}\rm \, cm^{-2}$ was necessary to produce three hard photons and no soft photons. BALQs are known to be X-ray weak, and LoBAL quasars are known to be generally significantly X-ray weaker than high-ionization BALQs \citep[e.g.,][]{green01, gallagher02b,gallagher06}. Generally, this X-ray weakness is inferred to be due to absorption. Sometimes the column densities can be measured directly from the X-ray spectrum \citep[e.g.,][]{gallagher02}, but often, only a few photons are detected, and the attenuation in the X-ray band compared with the optical band is assumed to originate from absorption, and in that case, the column density can be estimated. \citet{luo14} (their Fig.~4) shows that the $N_H$ estimated for SDSS~J0850$+$4451 is relatively large compared with other BALQs. Alternatively, some BALQs have been shown to be intrinsically X-ray weak \citep[e.g.,][]{luo14}. That may not be the case for SDSS~J0850$+$4451 as it shows relatively typical UV emission lines and ratios, in comparison with the weak line emission in the intrinsically X-ray weak quasar PHL~1811 \citep{leighly07a, leighly07}. Nevertheless, it appears that SDSS~J0850$+$4451 is typical LoBAL in its X-ray properties. The broad absorption lines in SDSS~J0850$+$4451 have a maximum velocity of $\sim -5500\rm \, km\, s^{-1}$ and a minimum velocity of $\sim -1400\rm \, km\, s^{-1}$, and therefore a width of about $4000\rm \, km\, s^{-1}$, and a middle velocity offset of $\sim -3500\rm \, km \, s^{-1}$. This velocity width appears to be rather typical of BALQs \citep{baskin15}. Several investigators have observed a rough upper envelope of maximum velocity with optical luminosity \citep{laor02, ganguly07}. For $H_0=70\rm \, km\, s^{-1}\, Mpc^{-1}$, $\Omega_M=0.3$, $\Omega_\Lambda=0.7$, $\log \lambda L_\lambda$ at 3000\AA\/ is 45.4 [$\rm erg\, s^{-1}$]. Fig.\ 7 in \citet{ganguly07} shows that a maximum outflow velocity of $5500 \rm \, km\, s^{-1}$ appears to be consistent with the average for an object with this luminosity. As discussed in \S \ref{black_hole_mass}, the rather broad Balmer line observed in SDSS~J0850$+$4451 yields a large black hole estimate of $1.6 \times 10^9 \rm \, M_\odot$, and for a bolometric luminosity estimate of $46.1 \, \rm [erg\, s^{-1}]$ \citep{luo13}, the object is radiating at only 6\% of Eddington. This value is low for a type 1 object. In contrast, \citet{yw03} observed $z\sim 2$ BALQs in the infrared band and found high (of order $\sim 1$) Eddington ratios. They noted that this might be a selection effect due to observing the brightest objects; on the other hand, they found that most objects had strong ``Eigenvector 1'' line emission patterns including very strong \ion{Fe}{2} and weak [\ion{O}{3}], also an indication of a high Eddington ratio. In contrast, SDSS~J0850$+$4451, with its broad Balmer lines and modest \ion{Fe}{2} emission has emission line properties mostly consistent with a low (for a Seyfert 1) accretion rate. The [\ion{O}{3}] appears too weak for an object with such a broad H$\beta$ line, but weak [\ion{O}{3}] seems to be common among LoBAL quasars \citep[e.g.,][and references therein]{schulze17}. Empirically, it has been suggested that BALQs are typically high Eddington objects \citep[e.g.,][]{boroson02}, and this has also been suggested on theoretical grounds \citep{zk13}. SDSS~J0850$+$4451's low Eddington ratio would seem to make it anomalous, because, as shown in \citet{ganguly07} (their Fig.~6), very few of the \citet{trump06} BALQs radiate at less than 10\% Eddington. However, a more recent study by \citet{schulze17} revealed no difference in black hole mass and Eddington ratio between a sample of 22 LoBAL quasars and unabsorbed objects, and several of their $z \sim 0.6$ sample showed Eddington ratios less than 10\%. Thus general claims that all LoBALQs are high Eddington-ratio objects do not seem justified, although high Eddington-ratio objects may be over-represented in this population. SDSS~J0850$+$4451 has a kinetic-to-bolometric luminosity ratio for the broad absorption lines of 0.8--0.9\% (Fig.~\ref{fig12}). We note that there is also a blueshifted component of the [\ion{O}{3}] line, modeled as an additional Gaussian with velocity offset of $-1150\rm \, km\, s^{-1}$ (\S~\ref{black_hole_mass}), although we have no information about the spatial extent of this emission. \citet{fiore17} attempt to bring together a compendium of outflow indicators. While their information is incomplete for BALQ measurements, their results are nevertheless useful for comparison. Our $\dot E_{kin}/L_{bol}$ ratio is comparable to other BALQs and ionized winds for objects of the same bolometric luminosity. Like the other BALQs, our $v_{max}$ lies between the relatively low-velocity ionized gas and molecular outflows, and the ultra-fast outflows (UFOs). Our momentum flux ratio $\dot P_{OF}/\dot P_{AGN}$ is approximately 1, and is typical of ionized winds and UFOs, and less than the molecular outflows. The outflow in SDSS~J0850$+$4451 is located 1-3 parsecs from the central engine, consistent with the estimated location of the torus. Interestingly, a similar location was inferred for the broad absorption line outflow in the Seyfert-luminosity Narrow-line Seyfert 1 Galaxy WPVS~007 based on variability arguments \citep{leighly15}. Density-constrained distances have been measured for a handful of objects, and these span a wide range, from the vicinity of the torus (parsec scale) to kiloparsec scale \citep[e.g.,][]{lucy14, dabbieri18, arav18}. In comparison with the kiloparsec-scale outflows, the outflow in SDSS~J0850$+$4451 appears to be relatively compact. The discussion and comparisons above indicate that SDSS~J0850$+$4451 has an outflow characterized by typical offset velocity and velocity width. But compared with other BALQs, it radiates at a relatively low Eddington ratio, has relatively broad emission lines, and has relatively low reddening and weak torus emission that suggest a low dust content. The outflow is observed near the torus, rather than at kiloparsec distances as has been found in some other BALQs, and therefore seems relatively compact. Although a conclusive comparison will have to wait until we have analyzed more objects, we suggest that the feedback interaction between the quasar nucleus and the host galaxy is not currently ongoing, although it may have been in the past. Indeed, SED fitting gave only an upper limit on the star-formation rate \citep{lazarova12}. Nevertheless, the outflow SDSS~J0850$+$4451 hosts is likely to be important to the operation of the central engine. The accretion rate is estimated to be only $2.2 \rm \, M_\odot\, yr^{-1}$, while the outflow rate is about 8 times higher. So if this object did not host an outflow, it might accrete at a higher rate, and the central engine and emission line properties might be much different. | 18 | 8 | 1808.02441 |
1808 | 1808.05866_arXiv.txt | {The heliospheric magnetic field (HMF) is structured into large sectors of positive and negative polarity. The parts of the boundary between these sectors where the change in polarity matches that of the leading-to-following sunspot polarity in that solar hemisphere, are called Hale Sector Boundaries (HSB).} {We investigate the flare occurrence rate near HSBs and the association between HSBs and active longitudes.} {Previous work determined the times HSBs were at solar central meridian, using the detection of the HMF sector boundary crossing at the Earth. In addition to this, we use a new approach which finds the HSB locations at all times by determining them from Potential Field Source Surface (PFSS) extrapolations of photospheric magnetograms. We use the RHESSI X-ray flare list for comparison to the HSB as it provides accurate flare locations over 14 years, from February 2002 to February 2016, covering both Cycles 23 and 24. For the active longitude positions we use previously published work based on sunspot observations.} {We find that the two methods of determining the HSB generally agree and that $41\%$ (Cycle 23) and $47\%$ (Cycle 24) of RHESSI flares occur within $30^\circ$ of the PFSS determined-HSB. The behaviour of the HSBs varies over the two Cycles studied, and as expected they swap in hemisphere as the Cycles change. The HSBs and active longitudes do overlap but not consistently. They often move at different rates relative to each other (and the Carrington solar rotation rate) and these vary over each Cycle. The HSBs provide a useful additional activity indicator, particularly during periods when active longitudes are difficult to determine.} {} | \label{nsec:intro} \begin{figure*} \centering \includegraphics[width=0.7\linewidth]{hsb_cartoon.pdf} \caption{Cartoon of the Hale Sector Boundary (thick purple lines) for odd (left) and even (right) Cycles during periods when four-sector boundary crossings would be detected at the Earth. The HSBs are the parts of the sector boundary where the magnetic polarity change, from leading-to-following (right to left in each panel), matches the magnetic polarity change of the sunspots in that hemisphere. Positive magnetic polarity is indicated by yellow, negative by blue. Based on the Cycle 20 example in \citet{1976SoPh...49..177S}.} \label{fig:hsb_cartoon} \end{figure*} Predicting solar magnetic activity such as flares and coronal mass ejections is difficult, but high degrees of organisation in both time and position do exist. With each new 11-year activity Cycle, sunspots appear at high latitudes. As the cycle evolves, new groups appear closer to the equator, producing the classic Butterfly Diagram \citep{1904MNRAS..64..747M}. In addition, sunspots tend to occur in pairs with oppositely directed magnetic field and have the same configuration of leading-to-following polarity (in the direction of solar rotation) in each hemisphere. This is reversed between northern and southern hemispheres and then swaps for each solar Cycle, i.e. Hale's law \citep{1919ApJ....49..153H}. As the solar wind carries the magnetic field into the heliosphere, it simplifies into large sectors of different magnetic polarities separated by the Heliospheric Current Sheet (HCS) \citep{1973Ap&SS..24..371S}. This boundary separating the different sectors of magnetic polarity is detectable at the Earth. In this paper, we study its association with solar activity and also compare it with the phenomenon of active longitudes. Concentration of activity in terms of longitude have been suggested since the time of \citet{1863spots...C}. Initial studies of ``active longitudes'' \citep[e.g.][]{1939POMic...7..127L} found substantial ambiguities in their existence and precise location. A copious literature has developed to characterise these regions, testing their usefulness for solar activity prediction and probe their source and implications for dynamo theory \citep[e.g.][]{2007AdSpR..40..951U}. Several terms have been used for these regions, including ``nests of activity'' \citep{1983ApJ...265.1056G,1987ARA&A..25...83Z}, but all these describe locations where there is a strong tendency for flux emergence to persist over long timescales. The general approach for finding active longitudes is to filter the activity tracer, i.e. sunspots or flares, so that only the most dominant regions per time remain, often requiring a correction for rotation at rates differing from those of the Carrington synodic period \citep[e.g.][]{2007AdSpR..40..951U}. A variety of techniques have been applied to active longitude studies but these can sometimes produce artefacts \citep[e.g.][]{2010A&A...513A..48P} that can lead to ambiguities in the quantitative properties of active longitudes. The work of \citet{2003A&A...405.1121B} and \citet{2005A&A...441..347U} used the Greenwich sunspot data, finding two active longitudes in each hemisphere about $180^\circ$ apart. This pattern lasted for several solar Cycles. At any given time one of the active longitudes was more dominant than the other, with the activity ``flip-flopping'' between them. These active longitudes were affected by differential rotation but at a different rate to the sunspots and were asynchronous between hemispheres. \citet{2006A&A...445..703B} provided a qualitative explanation for their results in terms of the internal solar dynamo, with it either being a differentially rotating magnetic structure or a solid rotator with a stroboscopic effect producing the observed behaviour. Similarly behaving active longitudes have been identified via EUV observations of coronal streamers \citep{2011ApJ...735..130L}, as well as flare locations during solar Cycles 19-23 \citep{2003ApJ...585.1114B} and Cycles 21-23 \citep{2011JASTP..73..258Z}. The Debrecen photoheliographic sunspot data have contributed to active longitude studies \citep{2012CEAB...36....9G,2014SoPh..289..579G,2016ApJ...818..127G}, leading to the conclusion that about 60\% of X-ray flares occurred with $\pm36^\circ$ of an active longitude. This work again shows two bands of activity, with one being more productive than the other and this varying over time (the ``flip-flop'' behaviour). These regions were narrow during the starting and decay phases of each Cycle (about $20^\circ-30^\circ$) but wider ($60^\circ$) during maximum. They also showed how the active longitudes' rotation rates vary over each Cycle. Initially they are faster than the Carrington rate but near solar maximum start to slow down, resulting in a ``parabolic migration path'' relative to the Carrington rate \citep{2016ApJ...818..127G}. This time evolution of their location was previously noted by \citet{2005A&A...441..347U}. The properties of the sunspot groups near active longitudes, such as complexity and helicity, were also found to be more preferential for CMEs to occur \citep{2017ApJ...838...18G}. Despite ambiguity about the specific nature of active longitudes it is clear that they have something to do with the internal dynamo of the Sun, and that this and other related phenomena should manifest themselves in the global solar magnetic field. The discovery of the sector boundaries in the heliospheric magnetic field \citep{1965JGR....70.5793W} provided an alternative physical framework for characterising the large-scale distribution of solar activity, and one with links to solar-terrestrial impacts via ``proton flares'' \citep{1969SoPh....6..104B}. We now understand the sector structure to be the result of the natural simplification of the Sun's large-scale magnetic field as the solar wind drags it out into an almost bipolar configuration \citep[e.g.][]{2013LRSP...10....5O}. The heliospheric current sheet (HCS) is the warped surface that separates the sectors of positive and negative polarity, and where this intersects the Earth's orbit we detect the polarity reversal. The HMF essentially has the polarity pattern of a dipole, but with an inverse-square falloff with radial distance as dictated by the solar wind. A simple tilted dipole, relative to the ecliptic, results in two sector boundary crossings detectable at the Earth. The seasonal variation of sector widths reveals the presence of the tilt \citep{1969JGR....74.5611R}. This two-sector structure is mostly seen during the weaker phases of the solar Cycle (declining and minimum) with a more complicated four-sector structure arising from the periods when the quadrupole component is relatively stronger compared to the dipole \citep[e.g.][]{2017SoPh..292..174G}. During these times, the HCS has a significant warp, as well as a tilt relative to the solar rotation axis. Early work showed that the sector boundary locations, identified solely via the polarity reversal in the solar wind near 1~AU, was associated with enhancements in activity in terms of both the green line corona \citep{1974SoPh...36..115A} and flares \citep{1975SoPh...41..227D}. In the latter case, a superposed epoch analysis of flares from 1964 to 1970 (Cycle 20) showed a marked increase in occurrence with the negative leading positive (-,+) sector boundary crossing. This preference was more noticeable for northern hemisphere flares, where the magnetic polarity matched Hale's law. This pattern was further shown by \citet{1976SoPh...49..177S} for the green line corona, with the maximum occurring above the ``Hale Sector Boundary'' (HSB), the part of the sector boundary with the same polarity change as Hale's law gives for sunspots in that solar hemisphere. As the sunspots' leading magnetic polarities swap between alternate 11-year sunspot Cycles \citep{1919ApJ....49..153H}, the location of the HSB of a particular polarity change will be different for odd and even numbered Cycles. Fig.~\ref{fig:hsb_cartoon} illustrates this relationship for each Cycle during periods when four sectors are detected at the Earth. Specifically we have \begin{itemize} \item For an odd Cycle (left panel, Fig. \ref{fig:hsb_cartoon}), the positive leading negative $(+,-)$ HSB will be in the northern hemisphere while the negative leading positive $(-,+)$ will be in the southern hemisphere; \item For an even Cycle (right panel, Fig. \ref{fig:hsb_cartoon}), the positive leading negative $(+,-)$ HSB will be in the southern hemisphere while the negative leading positive $(-,+)$ will be in the northern hemisphere; \end{itemize} The sector boundaries detected via the crossing of the HCS at the Earth usually have clear signatures. From these epochs, a ballistic assumption about solar wind transport can be used to estimate how many days beforehand the structure was at central meridian at the Sun. \citet{2011ApJ...733...49S} used a range of 4.5 to 6.5 days, with superposed epoch analysis on magnetograms from Cycles 21 to 24 and X-ray flare positions, from RHESSI and GOES, covering 2002 to 2008 and 1996 to 2008 respectively. In both cases, there was a strengthening of activity in the expected hemisphere at central meridian corresponding to the HSB location. This approach was repeated for sunspots over Cycles 16 to 24, again finding a concentration at times when the HSB was expected to be at the central meridian in each hemisphere \citep{2014SSRv..186...17H}. It has also been shown that sunspot pairs are more likely to develop near the HSB \citep{2015GeoRL..42.2571A}. This work again showed that even though the structure is being detected at the Earth, it could be clearly related to a concentration of activity back at the Sun. \citet{2017SoPh..292..174G} carefully looked at the Earth sector boundary crossings for Cycles 21 to 24 compared to photospheric magnetograms. Instead of using a fixed timelag (constant solar wind speed) to get the HSB back at central meridian, they took into account the observed speeds, which produced a sharper mapping back to the Sun. Overall they found that this refined technique, compared to the approach of \citet{2011ApJ...733...49S}, yields similar patterns. With their refined HSB approach they found that the HSB mapping into the magnetograms was statistically significant, particularly during the maximum and declining phases of each Cycle. They also found that the clearest HSB association was in the northern hemisphere during the odd Cycles studied, but was weaker in the southern hemisphere during even Cycles. No difference was found between Cycles for the (-,+) HSB, with a consistent association with activity. In this paper we extend the work of \citep{2011ApJ...733...49S} by comparing the HSB found via the detection of the boundary crossing at the Earth (which we call HSB-Earth, to distinguish it from the HSB at the Sun) to RHESSI X-ray flares into Cycle 24, detailed in \S\ref{nsec:findhsbesc}. Then in \S\ref{nsec:hsbvsal}, we compare these HSBs to the active longitudes determined by \citet{2016ApJ...818..127G} over Cycles 21 to 24 to investigate how these phenomena relate. Even with the refined approach of \citet{2017SoPh..292..174G}, the HSB can only be found at times corresponding to central meridian passage. So to be able to determine the HSB locations for all times we instead determine it from daily Potential Field Source Surface (PFSS) maps, described in \S\ref{nsec:findhsbpfss} (which we call HSB PFSS). This also has the advantage that the HSB can be found closer to the Sun, minimising the uncertainty introduced by the variable solar wind speed in the HSB-Earth approach. We compare these two HSB approaches in \S\ref{nsec:escvspfss} and then determine the closest HSB PFSS for each RHESSI X-ray flare, investigating their association in \S\ref{nsec:pfssvsfl}. | \label{nsec:discon} With both the HSB-Earth and HSB PFSS approaches we have been able to show that this magnetic phenomenon maps back to the solar surface and is associated with RHESSI X-ray flares.This HSB-flare association is shown quantitatively in Figs.~\ref{fig:lesslng} and \ref{fig:bothcyc}, finding that overall nearly half of RHESSI flares occur within a longitude of $\pm30^\circ$ of a HSB. Our extension of the work of \citet{2011ApJ...733...49S}, has shown that the HSB hemispheres do swap as we change from Cycle 23 to 24. However the HSB-Earth association is not as clear in Cycle 24, especially in the northern hemisphere. Our comparison between this and the HSB PFSS approach seems to suggest that in Cycle 24 the mean solar wind is faster than we assumed, with the actual HSB lagging behind where HSB-Earth predicted it to be. \citet{2017SoPh..292..174G} used the observed solar wind speed to determine the time of HSB at central meridian, finding a sharper association to flares. Although even this approach found a weaker occurrence pattern for Cycle 24 in both hemispheres compared to Cycle 23. Despite this, we are still able to show a concentration of flares in the expected hemisphere associated with the HSB, even separated by GOES class. The same association works for large X-class flares down to A-class microflares. Determining the HSB via PFSS allows it to be found for all times and flares. This provides a clearer picture of the sector structure closer to the solar surface, and one that is not affected by variations in the solar wind speed. From this approach we find that about $41\%$ (Cycle 23), $47\%$ (Cycle 24) of RHESSI flares occur within $30^\circ$ of the HSB PFSS. The advantage of the PFSS approach is that we achieve a near-instantaneous view of the current structures on the Sun. We therefore provide a webpage\footnote{\url{http://www.astro.gla.ac.uk/~iain/hsb}} where the daily HSB PFSS are shown relative to the current active regions and recent flare activity. The confirmation that the HSB and active longitudes do overlap sometimes is expected, since the former has an association with activity and the latter is directly derived from activity indicators. However it is clear that they are not exactly the same thing, and show differences in migration paths; the parabolic passage of the active longitudes over time, as found by \citep{2005A&A...441..347U, 2016ApJ...818..127G} are not apparent in the HSB. The closest matching occurs when both are rotating at about, or slightly faster, than the Carrington rate, with the ``flip-flop'' between dominate active longitudes seen as jumping between a two-sector structure in that hemisphere (during a period of overall four-sectors). Considering the difference in Carrington phase between the active longitudes and HSB does help quantify this association, with some concentration near zero. However this varies between hemispheres and the majority of phase differences are positive, showing that the HSB Carrington phase is mostly larger than the active longitude's. This might be due to the observed migration paths, with the HSB mostly appearing to steadily increase in phase with time, whereas the active longitudes' phases increase and decrease with time. However there are several limitations and assumptions to this HSB and active longitude comparison presented in this paper that merit investigation in future studies. It is problematic that the active longitudes are not detected at all times, and linear interpolation has to be used for a full comparison to the HSB. In addition, we only considered the most dominant active longitudes, so future work could benefit from comparing the HSB to both active longitude bands. Using the HSB found from the PFSS approach could help, removing uncertainties arising from a variable solar wind speed, but this would be limited to more recent Cycles due to the availability of suitable magnetograms. Another discrepancy is that the identified active longitudes persist across several cycles while the HSB of each type swaps hemisphere as the cycle changes. As this occurs during solar minimum, it is not a major issue for the HSB-flare association, but would certainly merit further work to determine how the location of the HSB evolves as the Cycles changes, especially in comparison to the active longitudes. It is a remarkable feature that a magnetic phenomenon detected at the Earth can be mapped back to activity on the Sun, providing a fast and simple approach to determine longitudinal regions of concentrated activity compared to the longterm averaging and filtering required in active longitude studies. Given that the HSB can often be determined at times when the active longitude cannot be found, a combination of both could be vital for not only helping to predict future activity but for understanding the internal source of the phenomena. It is possible to speculate as to why active emerges repeatedly at similar longitudinal regions \citep[e.g.][]{2004ApJ...604..944B,2006A&A...445..703B,2007AdSpR..40..951U}, but why this should be reflected in the large-scale magnetic field through the HSB is still not clear and requires further investigation. | 18 | 8 | 1808.05866 |
1808 | 1808.10254_arXiv.txt | {In early-type Be stars, groups of nonradial pulsation (NRP) modes with numerically related frequencies may be instrumental for the release of excess angular momentum through mass-ejection events. Difference and sum/harmonic frequencies often form additional groups. } {The purpose is to find out whether a similar frequency pattern occurs in the cooler third-magnitude B7-8\,IIIe shell star \object{$\nu$ Pup}.} {Time-series analyses are performed of space photometry with BRITE-Constellation (2015, 2016/17, and 2017/18), SMEI (2003--2011), and Hipparcos (1989--1993). Two {\it IUE} SWP and 27 optical echelle spectra spanning 20 years were retrieved from various archives.} {The optical spectra exhibit no anomalies or well-defined variabilities. A magnetic field was not detected. All three photometry satellites recorded variability near 0.656\,c/d which is resolved into three features separated by $\sim$0.0021\,c/d. First harmonics form a second frequency group, also spaced by $\sim$0.0021\,c/d. The frequency spacing is very nearly but not exactly equidistant. Variability near 0.0021\,c/d was not detected. The long-term frequency stability could be used to derive meaningful constraints on the properties of a putative companion star. The IUE spectra do not reveal the presence of a hot subluminous secondary.} { $\nu$\,Pup is another Be star exhibiting an NRP variability pattern with long-term constancy and underlining the importance of combination frequencies and frequency groups. The star is a good target for efforts to identify an effectively single Be star.} | \label{intro} When a rapidly rotating massive star evolves, it may have to solve a problem when angular momentum is transported from the contracting core to the outer layers \citep{2011A&A...527A..84K, 2013A&A...553A..25G}. Apart from mixing, nonradial $g$-modes may be involved in the angular-momentum transport process \citep[][and references therein]{2013ASPC..479..319N}. These stars may appear as Be stars which are unique in that only Be stars seem to possess circumstellar disks built from self-ejected matter \citep{2013A&ARv..21...69R}. In these little to moderately evolved stars, radiative winds do not produce major mass-loss rates \citep{2014A&A...564A..70K}. Broad consensus exists that the near-critical rotation \citep{2005A&A...440..305F, 2012A&A...538A.110M, 2013A&ARv..21...69R} is a necessary condition for the mass loss. Numerous observational studies \citep{1998ASPC..135..343R, 2009A&A...506...95H, 2013A&ARv..21...69R, 2017sbcs.conf..196B, 2018A&A...610A..70B} suggest that much of the star-to-disk mass-transfer process takes place in discrete events, which cover a wide range in cadence and amplitude \citep{2018A&A...613A..70S, 2018MNRAS.479.2909B}. Although having the appearance of mass-loss events, they may actually be more accurately described as angular-momentum-loss events. Angular-momentum-loss rates were recently measured for a large sample of Be stars \citep{2018MNRAS.476.3555R}. Evidence is broadly increasing \citep{1998ASPC..135..343R, 2017arXiv170808413B} that multi-mode nonradial pulsation (NRP) plays a central role in the conditioning of the stellar atmosphere for outbursts. Which specific conditions do lead to an outburst is entirely unknown except that temporarily much increased NRP amplitudes can have triggering power. Interacting NRP modes may operate the valves of the angular-momentum-loss process. \citet{2017arXiv170808413B} have presented a scheme of nested clocks with hierarchically decreasing frequencies, which all derive from stellar pulsation frequencies and govern the opening and closing of the angular-momentum-loss valves. More massive stars may have to open these valves more often and/or more widely because they evolve more rapidly. This mass-dependence of the activity seems confirmed by the long-term photometry of large numbers of Be stars with a wide range of spectral subclasses \citep[e.g.,][]{1998A&A...335..565H, 2018MNRAS.479.2909B}. Brightenings indicate ejections of gas, which reprocesses the stellar light; in edge/equator-on systems such events lead to fadings when the disk attenuates the stellar light \citep{2014ApJ...785...12H}. \begin{figure*} \includegraphics[width=18.3cm,angle=-90]{LCmulti.eps} \caption{All main strings of BRITE observations of $\nu$\,Pup in 2015, 2017, and 2018. Very long segments are split with partial duplications. The ordinate is in units of instrumental magnitudes with arbitrary zero point. Symbols: red $+$: BHr2015; red $\circ$: BHr2017; red $\times$: BTr2017; blue $+$: BLb2017; red $\square$: BHr2018. Intercomparison of observations in identical time intervals but from different satellites shows that the most regular segments of the light curves are representative and the others deviate as a result of noise. The amplitude was largest in 2017 and lowest in 2018. In the bottom panel, between days 1145 and 1150 and shortly before day 1160, there may have been some mini outbursts. } \label{LCmulti} \end{figure*} \begin{figure*} \includegraphics[width=5.9cm,angle=-90]{BLC2017.eps} \caption{A 10-d stretch (in 2017) of observations of $\nu$ Pup with BRITE satellites BLb (blue filled triangles), BHr (red asterisks), and BTr (red crosses). The zeropoints of the magnitude scale are arbitrary. Black dots represent a sine fit to the BHr data. The deviation from sinusoidality is most clearly seen in the BHr data.} \label{BLC} \end{figure*} \begin{table*} \caption{Overview of the BRITE, Hipparcos, and SMEI observations. Information not available for Hipparcos and SMEI is flagged as 'N/A'. Suffixes 'b' and 'r' in the acronyms of BRITE satellites identify the spectral passband (blue/red). 'CCDT' is the detector temperature range. 'Contig.\ time' denotes the typical time interval per satellite orbit during which exposures were made. 'No.\ of TSA data points' is the number of data points (in the case of BRITE formed as orbital averages from the elementary measurements) and used for time-series analysis. Intervals between start and end dates include gaps.} \label{obslog} \centering \begin{tabular}{l c c c c c c c c c} \hline\hline Satellite name & P$_{\rm orbit}$ & Year(s) & JD--2,400,000 & CCDT & Contig.\ time & No.\ of & t$_{\rm exp}$ & No.\ of & No.\ of TSA \\ (acronym) & [min] & & (start-end) & [\degr C] & [min] & setups & [s] & observ. & data points \\ \hline Hipparcos & 637.2 & 1989-1993 & 47860-49051 & N/A & N/A & N/A & $\sim$20 & 115 & 115 \\ SMEI & 101.5 & 2003-2011 & 52673-55833 & N/A & N/A & N/A & $\sim$900 & 38617 & 31707 \\ BRITE-Heweliusz & 97.1 & 2015 & 57098-57176 & 9.3-18.8 & 2.6-29.8 & 3 & 1 & 47816 & 487 \\ (BHr) & & 2017 & 57760-57784 & 13.3-22.2 & 4.7-20.1 & 1 & 4 & 15542 & 257 \\ & & 2017/18 & 58066-58222 & 0.9-23.8 & 3.0-21.4 & 7 & 4 & 63886 & 1433 \\ BRITE-Lem & 99.6 & 2016/17 & 57738-57910 & 18.2-34.6 & 4.0-13.9 & 5 & 2 & 82516 & 1382 \\ (BLb) & & & & & & & & & \\ BRITE-Toronto & 98.2 & 2016/17 & 57697-57877 & 2.9-20.4 & 3.7-15.7 & 6 & 4 & 65260 & 1822 \\ (BTr) & & & & & & & & & \\ \hline \end{tabular} \end{table*} At the cool limit of the so-called Be phenomenon, spectroscopic evidence of a disk is often restricted to shell absorption lines. However, recent observations by \citet{2018A&A...609A.108S} have demonstrated that, with the help of high-quality spectral line profiles, weak H$\alpha$ emission can be detected in many more late B-type stars than previously thought. The variability of their emission lines seems to be much slower and reach lower amplitudes than displayed by many early-type Be stars \citep{2013A&A...556A..81B}. Photospheric line-profile variability is also much less pronounced in late-type Be stars \citep{1989A&A...222..200B}. With the advent of powerful space photometers, a substantially more detailed view of the variability of late-type Be stars is emerging. Recently, {\it Kepler} observations of \object{KIC\,11971405} (HD\,186567) \citep[B5\,IV-Ve;][]{2017A&A...598A..74P} revealed one of the most intricate networks of NRPs known in Be stars. Most variabilities have sub-mmag amplitudes. At B5, HD\,186567 is also one of the cooler Be stars with detected NRPs. Still cooler is \object{$\beta$\,CMi} at B8, for which {\it MOST} recorded many NRP modes with similarly low amplitudes \citep{2007ApJ...654..544S}. In observations of the B7\,V star \object{CoRoT 101486436}, \citet{2018A&A...613A..70S} find this star's variability to resemble that of $\beta$\,CMi; however, the peak-to-valley amplitude of a 0.03\,c/d beat (perhaps: difference) frequency has an amplitude of 12,000\,ppm with individual frequencies near 5\,c/d reaching up to 3,000\,ppm. During the monitoring period with {\it Kepler}, also KIC\,11971405 underwent some small outbursts. As \citet{2017arXiv170808413B} showed, the spacing in time of some of these events can be related to difference frequencies of some NRP modes with the highest amplitudes. Such coupling had previously been found in BRITE, {\it Kepler}, and CoRoT observations of several early-type Be stars \citep[][Rivinius et al., in prep.]{2016A&A...588A..56B, 2016A&A...593A.106R, 2017arXiv170808413B}. \citet{2017MNRAS.471.2882W} conclude that {\it Kepler}/K2 observations of four Be stars in the Pleiades are consistent with this hypothesis for the two least evolved Be stars, \object{Merope} (B6\,IVe) and \object{Pleione} (B8\,Vne). Late-B spectral types are also the realm of the historically mythical Maia variables. Maia itself (\object{20\,Tau}, B7\,III) was finally shown not to be pulsating but exhibiting slow rotational modulation \citep{2017MNRAS.471.2882W}. However, there do exist probable $g$-mode pulsators between the conventional Slowly Pulsating B Star (SPB) and $\gamma$ Dor domains \citep[e.g.][]{2013A&A...554A.108M}; this includes late B-type stars. Whether the pulsations of the other six B stars in the Pleiades studied by \citet{2017MNRAS.471.2882W} fall into just one single category is unknown. The light curves of \object{Alcyone} (B7\,IIIe), \object{Electra} (B6\,IIIe), \object{Merope} (B6\,IVe), and \object{Pleione} (B8\,Vne) exhibit clear variations of their upper and lower envelopes which may be due to the beating of a few single frequencies. A similar pattern is absent in the normal binary B star \object{Atlas} (B8\,III\,$+$\,B8\,V) and much less prominent in the other normal B-type star Taygeta (B6\,IV) if present at all. \citet{2017MNRAS.471.2882W} explicitly report frequency groups for the Be stars Alcyone, Electra, and \object{Taygeta} and describe the variability of Merope (Be) and Taygeta (B) in terms of closely spaced frequencies, which is consistent with the presence of frequency groups. Frequency groups are characteristic of Be stars \citep{2011MNRAS.413.2403B, 2017sbcs.conf..196B, 2018A&A...613A..70S} but do not seem limited to them \citep{2015MNRAS.450.3015K}, and not all pulsating Be stars display frequency groups. The latter authors proposed that frequency groups may be understood as clusters of combination frequencies of NRP modes. This was confirmed by \citet{2017A&A...598A..74P} in the same data. In the early-type Be star \object{25\,Ori}, \citet[][an extended version of this work with additional BRITE and revised SMEI observations is in preparation]{2017arXiv170808413B} tentatively identified an extremely rich pattern of grouped combination frequencies. It has been proposed \citep{2008ApJ...685..489C, 2016A&A...593A.106R, 2017MNRAS.471.2882W} that Be stars may be rapidly rotating SPB stars. However, among the B-type stars without Be characteristics, neither SPB stars nor any other type of pulsating star span such a wide range in effective temperature as the Be phenomenon does. On the other hand, pulsations of Be stars do not seem to significantly extend to lower or higher temperatures than other pulsating OB stars do, and the combined role of rapid rotation and mass and angular-momentum leakage is still to be explored in detail. The third-magnitude late-type Be star \object{$\nu$\,Pup} (HR\,2451, HIP\,31685, HD\,47670) has not been given much attention by spectroscopists. \citet{1909ApJ....29..232C} described H$\gamma$ as consisting of a broad absorption with superimposed fairly sharp central absorption. Such shell components occur in Be stars if the star is viewed equator-on and the line of sight passes through the disk. In eight spectra, the radial velocity of the narrow component varied from $+$33\,km/s in 1904 to $+$20\,km/s in 1908. Temporary shell absorption flanked by weak line emission in H$\alpha$ was also detected by \citet{1999A&A...348..831R, 2006A&A...459..137R}. Shell absorptions were not reported by \citet{1897ApJ.....6..349P} and by \citet{1975ApJS...29..137S} so that the disk is probably not persistent. \citet{1987SAAOC..11...93C} treated $\nu$\,Pup as a secondary photometric standard. On the other hand, from Hipparcos observations, \citet{2002MNRAS.331...45K} reported a variability with frequency 0.15292\,c/d and amplitude 0.00117\,mag. At other wavelengths, $\nu$\,Pup has remained inconspicuous: It was not detected in the ROSAT All Sky X-ray Survey \citep{1996A&AS..118..481B}, and \cite{2018arXiv180601294B} did not find it embedded in a mid-IR nebulosity. \citet{2008MNRAS.389..869E} do not list $\nu$\,Pup as multiple. $\nu$\,Pup was selected from the Be stars observed with BRITE-Constellation because of its relatively low temperature (extending earlier studies with BRITE of hotter Be stars), its brightness (yielding a better signal-to-noise ratio with BRITE), and the, at a first glance, unusual simplicity of its frequency spectrum. | The time spanned - three decades from 1989 through 2018 - and significantly covered by the space photometry of $\nu$\,Pup is not exceeded by space observations analyzed for other Be stars. This has permitted an unprecedented study of the long-term behavior of the variability of a Be star. $\nu$\,Pup is a spectroscopically normal B7-B8\,IIIe star. It exhibits a $\sim$10-mmag variability near 0.6556\,c/d split into three frequencies f1 to f3 spaced by $\sim$0.0021\,c/d. The frequency spacing is nearly but not exactly equidistant; neither appear the periods equidistant. Five much weaker variabilities form a second nearly equidistant frequency group near 1.31\,c/d; three of them are harmonics of f1 to f3. Similarly narrow groups of high-amplitude NRP modes are not known from other Be stars unless similar frequency groups in HD\,175869 were not resolved by the one-month observations \citep{2009A&A...506..133G}. However, the narrowness may be the result of the insensitivity of the observations to sub-mmag variations. The frequency spacing is very much smaller than any expected rotational splitting of NRP modes. The similarity of the spacing between all frequencies in both groups suggests that they are somehow coupled. This coupling along with the large amplitudes may be responsible for the strong and varying asymmetry of the light curve. In early-type Be stars, difference frequencies seem to be involved in the triggering of mass-loss events. The existence of very effective selection rules of NRP modes, which are also implied by other observations, may be part of the DNA of the stellar component of the Be phenomenon. Because the mass-loss process in $\nu$\,Pup is very weak but frequency combinations are still very prominent, NRP-enabled mass loss from Be stars should only be the consequence of coupled NRP modes, not also their cause. A causal element may lie in the radial transport of excess angular momentum. Because Be stars are not destroyed by the angular momentum rising to the surface, the unknown mode-selection process may favor difference frequencies effective in preventing an angular-momentum catastrophe. Before the availability of space photometry, Be stars were notorious for their seemingly unpredictable, erratic behavior. Satellite observations have revealed complex variability patterns, which can be governed by multiply nested clocks and, therefore, can be repetitive. However, the duration of observations required to recognize such repetitive patterns is long, especially if multiple and/or closely spaced frequencies rule the light curve. The 0.0021-c/d frequency spacing in $\nu$\,Pup has extended the range of these timescales to $\sim$1000\,d. The synchronization over two very similar $\sim$0.0021-c/d beat cycles in $\nu$\,Pup of f1 to f3 takes decades, possibly in agreement with the spacing of shell episodes. Late-type Be stars are also a source of valuable observational data for the analysis of the disk dissipation process: Compared to hotter Be stars, radiative effects on the disk are much lower, the dissipation is much less likely to be disturbed or reversed by new outbursts, and the sensitivity to a continuous star-to-disk mass-transfer process, if any, could be much higher. This may enable a more precise determination of the viscosity parameter, its radial and vertical distribution in the disk, and its temporary evolution \citep[cf.\ the work on the early-type Be star \object{28\,CMa} by][]{2018MNRAS.479.2214G}. Motivated by the expectation that Be stars result from the evolution of binary stars, searches have been carried out, and many actual and candidate binary systems have been idemtified. It would be most valuable to complement such efforts with deep analyses of a few Be stars with the goal of finding out whether effectively single Be stars also exist. The edge-on perspective, relatively low mass, very large photometric amplitude, and simple frequency spectrum render $\nu$\,Pup a promising test target. By the example of $\nu$\,Pup it could be shown, for the first time in Be stars, that photometric Doppler shifts can place useful constraints on the properties of companion stars. Other Be stars worth investigating in this way include KIC\,11971405 and Achernar \citep{2011MNRAS.411..162G}. If effectively single Be stars can be identified, it will be most illuminating to learn whether pulsations can distinguish the formation histories of different populations of Be stars. | 18 | 8 | 1808.10254 |
1808 | 1808.04392_arXiv.txt | We present results of recent {\it Neutron Star Interior Composition Explorer} observations of the accreting millisecond X-ray pulsar IGR J17062$-$6143 that show that it resides in a circular, ultracompact binary with a 38 minute orbital period. {\it NICER} observed the source for $\approx 26$ ksec over a 5.3 day span in 2017 August, and again for 14 and 11 ksec in 2017 October and November, respectively. A power spectral analysis of the August exposure confirms the previous detection of pulsations at 163.656 Hz in {\it Rossi X-ray Timing Explorer} data, and reveals phase modulation due to orbital motion of the neutron star. A coherent search for the orbital solution using the $Z^2$ method finds a best-fitting circular orbit with a period of 2278.21 s (37.97 min), a projected semi-major axis of 0.00390 lt-sec, and a barycentric pulsar frequency of 163.6561105 Hz. This is currently the shortest known orbital period for an AMXP. The mass function is $9.12 \times 10^{-8}$ $M_{\odot}$, presently the smallest known for a stellar binary. The minimum donor mass ranges from $\approx 0.005 - 0.007$ $M_{\odot}$, for a neutron star mass from 1.2 - 2 $M_{\odot}$. Assuming mass transfer is driven by gravitational radiation, we find donor mass and binary inclination bounds of $0.0175 - 0.0155 M_{\odot}$ and $ 19^{\circ} < i < 27.5^{\circ}$, where the lower and upper bounds correspond to 1.4 and 2 $M_{\odot}$ neutron stars, respectively. Folding the data accounting for the orbital modulation reveals a sinusoidal profile with fractional amplitude $2.04 \pm 0.11 \%$ (0.3 - 3.2 keV). | \label{sec:introduction} The accreting neutron star binary IGR J17062$-$6143 (hereafter, J1706) is one of the most recently identified accreting millisecond X-ray pulsars (AMXP). First observed in outburst in 2006 \citep{2007A&A...467..529C, 2008ATel.1840....1R, 2008ATel.1853....1R}, it has since then been persistently accreting at luminosities in the range 5.8 - $7.5 \times 10^{35}$ erg s$^{-1}$ (2 - 20 keV), assuming a distance of 7.3 kpc \citep{2013ApJ...767L..37D, 2017ApJ...836..111K, 2017ApJ...836L..23S, 2018MNRAS.475.2027V}. The object's neutron star nature was first revealed by the detection of thermonuclear X-ray bursts. The first of these was observed by {\it Swift} in 2012 \citep{2013ApJ...767L..37D}, and most recently \citet{2017ApJ...836..111K} reported on {\it Swift} observations of a long duration burst first detected with {\it MAXI} \citep{2015ATel.8241....1N} that was likely powered by burning of a deep helium layer. The properties of these long duration (tens of minutes) thermonuclear X-ray bursts are consistent with the accumulation of helium rich material on the neutron star surface, which could be accommodated by accretion from a degenerate helium dwarf in an ultracompact system. However, accretion of hydrogen-rich fuel under certain conditions can also lead to thick, combustible helium layers, so the observation of apparently helium-powered nuclear flashes is not necessarily a definitive indication of an ultracompact system \citep{1981ApJ...247..267F, 2006ApJ...652..559G}. \citet{2017ApJ...836L..23S}, hereafter SK17, reported the detection ($4.3 \sigma$) of 163.656 Hz pulsations in a single $\approx 1200$ s observation with the {\it Rossi X-ray Timing Explorer} ({\it RXTE}; \cite{1993A&AS...97..355B}). They found a fractional pulsed amplitude (after background subtraction) of $9.4 \pm 1.1 \%$, but could not determine the orbital period of the system due to the single, short {\it RXTE} observation. They were able to place a lower limit on the orbital period of about 17 minutes. The source has recently been studied extensively with {\it Swift}, {\it NuSTAR}, {\it Chandra} and {\it XMM-Newton}. For example, \citet{2017MNRAS.464..398D} reported the presence of Fe K$\alpha$ reflection features in {\it NuSTAR} data, modeling of which suggested an inner disk that may be truncated out to $\approx 100 R_g$, where $R_g = GM/c^2$. Most recently, \citet{2018MNRAS.475.2027V} presents results of simultaneous {\it NuSTAR} and {\it XMM-Newton} observations. They report the presence of reflection features as well, and suggest a similarly truncated disk as in \citet{2017MNRAS.464..398D}. They note, however, that a disk extending down to the neutron star cannot be excluded if the binary inclination is very low. Based on analysis of {\it XMM-Newton} Reflection Grating Spectrometer (RGS) data they also suggest the system may have an oxygen-rich circumbinary environment, perhaps due to an outflow. Interestingly, they also searched for pulsations using the {\it XMM-Newton} EPIC timing mode data but did not detect them. They placed an upper limit on the pulsed fraction in those data of $5.4 \%$ ($0.5 - 10$ keV). They concluded that the persistently faint X-ray luminosity could be indicative of either an ultracompact binary system or perhaps magnetic truncation, but the spectroscopic data alone were not decisive between these two possibilities. \citet{2018arXiv180103006H} have recently reported on broad-band optical to near-infrared (NIR) photometry of \source{} that they modeled as emission from an irradiated accretion disk. Their modeling indicates an accretion disk size consistent with an ultracompact orbit, and they argued for an orbital period in the range from 0.4 - 1 hr. Additionally, their optical spectroscopy showed no H-$\alpha$ emission, consistent with a hydrogen-deficient donor and an ultracompact system. Thus, sensitive, new timing observations to determine the binary orbital parameters, and the nature of the system, were clearly warranted. In this paper we report results of recent {\it Neutron Star Interior Composition Explorer} (NICER) observations of \source{}. The principal goals of the {\it NICER} observing campaign were to confirm (or not) the {\it RXTE} detection of 163.656 Hz pulsations and, if pulsations could be detected, to determine the system's orbital parameters. We show below that the new {\it NICER} data confirm that \source{} is an 163.656 Hz pulsar, and also reveal an ultracompact orbit with similarities to other ultracompact AMXPs \citep{2012arXiv1206.2727P}. The plan of the paper is as follows. We first describe the observations, data selection, and our initial pulsation search and detection, confirming that \source{} is a 163.656 Hz pulsar. We next discuss our orbit search and detection, and we summarize the properties of the system given the orbit solution. We conclude with a brief summary and discussion of the implications of our findings for the nature of \source{}. | Our analysis of observations of \source{} with {\it NICER} obtained in 2017 August, October and November confirms the discovery by SK17 that it is a 163.656 Hz AMXP, and allowed us to derive the orbital parameters of the system for the first time. The 37.97 min orbital period of \source{} is the shortest currently known for an AMXP, and our measurement confirms several previous indirect indications that the system is an ultracompact binary \citep{2018arXiv180103006H, 2018MNRAS.475.2027V}. We measure a mass function, $f_x = (m_d \sin i)^3 / (m_{ns} + m_d)^2 = ( (a_x\sin i)^3 \omega_{orb}^2 )/G = 9.12 \times 10^{-8} M_{\odot}$, which is also the smallest among stellar binaries. The mass function defines a lower limit to the mass of the donor star, $m_d$. For a neutron star mass in the range from $m_{ns} = 1.2 - 2 M_{\odot}$ we find a minimum donor mass in the range from $0.005 - 0.007 M_{\odot}$. Given the orbital period and a plausible range of total system mass, the separation between the components is of order $300,000$ km, and would fit within the Earth - Moon distance. The reasonable assumption that the donor star fills its Roche lobe provides a constraint on the mean density of the donor. This can be expressed as a constraint on its radius in units of the component separation, $a$, that depends principally on the system's mass ratio, $q = m_d / m_{ns}$ \citep{1983ApJ...268..368E}. We combine this constraint with that from the measured mass function to explore the implications for the nature of the donor star and the system's orbital inclination. Our results are summarized in Figure 7 which shows constraints on the donor mass and radius. We plot the Roche lobe constraint for three different neutron star masses, $1.2$ (green), $1.4$ (black), and $1.8$ $M_{\odot}$ (red). The closeness of the three curves is a visual demonstration of how insensitive this constraint is to the assumed neutron star mass. The different symbols along the curve mark inferred donor masses from the mass function constraint for different assumed orbital inclinations, $i$, and for two values of the neutron star mass at each inclination. For each pair of symbols the left- and right-most correspond to a neutron star mass of $1.2$ and $1.8 M_{\odot}$, respectively. The left-most symbol for $i = 90^{\circ}$ marks the minimum donor mass for a $1.2 M_{\odot}$ neutron star. First, we note that the constraints require hydrogen-deficient donors, as is expected for systems with an orbital period less than about 80 min \citep{1984ApJ...283..232R, 2002ApJ...577L..27B}. For additional context we show mass - radius relations obtained from the literature for several donor types. The dashed curve is the mass - radius relation for low mass, cold, pure helium white dwarfs from \cite{1969ApJ...158..809Z}, as corrected by \cite{1984ApJ...283..232R}. Here we have plotted it using the fitting formula of \cite{2001A&A...368..939N}. The dotted curves denote a range of mass - radius values from the binary evolutionary calculations of \citet{2007MNRAS.381..525D} for the helium donors of AM CVn systems. The region between the upper and lower dotted curves gives an indication of the allowed range in mass and radius for donors at different evolutionary stages, and with different values of central degeneracy at the onset of mass transfer (see Deloye et al. 2007 for details). Lastly, the dash-dotted curves show mass - radius relations for carbon white dwarfs with central temperatures of $10^4$ (lower) and $3 \times 10^6$ K (upper), from \citet{2003ApJ...598.1217D}. Thus, \source{} appears to be a somewhat more extreme example of the currently known ultracompact AMXPs \citep{2007ApJ...668L.147K, 2012arXiv1206.2727P}. For a random distribution of inclination angles the chance probability to observe a system with an inclination less than or equal to $i$ is $1 - \cos(i)$. The probability to observe an inclination angle less than or equal to $\approx 18.2^{\circ}$ is $5\%$. From this, and assuming a $1.8 M_{\odot}$ neutron star mass, we deduce a $95\%$ confidence upper limit to the donor mass of $0.0216 M_{\odot}$, with a corresponding radius of $0.05 R_{\odot}$, substantially less than that of any hydrogen-rich brown dwarfs \citep{2000ApJ...542..464C}. We use this upper limit on the donor radius to place an upper limit on the inclination of $\approx 84^{\circ}$, since no eclipses are seen in the light curve. Additional insight is provided by estimates of the long term mass accretion rate, $\dot M$, and the realization that the mass transfer in such systems is driven by angular momentum loss due to gravitational radiation \citep{1984ApJ...283..232R, 2001ApJ...557..292B}. Interestingly, for \source{} we have $\dot M$ estimates from both persistent X-ray flux measurements and modeling of its thermonuclear X-ray bursts that are in substantial agreement \citep{2017ApJ...836..111K}, and suggest $\dot M \approx 2.5 \times 10^{-11}$ $M_{\odot}$ yr$^{-1}$. This value for \source{} is also in general agreement with the calculations of $\dot M$ versus $P_{orb}$ reported by Deloye et al. (2007, see their Figure 15). Based on this, and the reasonable assumption that the donor responds to mass loss like a degenerate star \citep{2001ApJ...557..292B}, we can estimate the donor mass as $m_d = 0.0175 (m_{ns}/ 1.4 M_{\odot})^{-1/3} \; M_{\odot}$. Using this result we additionally show in Figure 7 (with blue ``$+$'' symbols) the donor masses and corresponding radii for neutron star masses of 1.4 and 2 $M_{\odot}$, where the higher donor mass estimate corresponds to the lower mass neutron star (1.4 $M_{\odot}$). These mass estimates further imply constraints on the binary inclination angle of $19^{\circ} < i < 27.5^{\circ}$, where the lower and upper bounds correspond to neutron star masses of 1.4 and 2 $M_{\odot}$, respectively. The constraints summarized in Figure 7 suggest that \source{} is observed at relatively low inclination, and the donor mass - radius constraints appear to be consistent with the helium donors of AM CVn systems explored by \citep{2007MNRAS.381..525D} (the dotted curves in Figure 7). We note that these authors also provide estimates of the expected orbital period evolution, $\dot P_{orb}$, for these systems. Given the observed orbital period of \source{}, the predicted values are in the range $\dot P_{orb} \approx 1 - 3 \times 10^{-6}$ s yr$^{-1}$, which can be probed with additional {\it NICER} timing observations. Clues to the donor composition in a neutron star X-ray binary can in principle be provided by the properties of its thermonuclear flashes. The energetic, long duration burst events seen to date would appear to be consistent with deep ignition of a helium-rich layer \citep{2017ApJ...836..111K}. As noted previously, under certain conditions the stable burning of accreted hydrogen into helium can result in helium-powered thermonuclear flashes \citep{1981ApJ...247..267F, 2006ApJ...652..559G}. Our measurements confirm the previous indications for a hydrogen-deficient donor in \source{} \citep{2018arXiv180103006H, 2018MNRAS.475.2027V}, and definitively rule out this option, since the accreted fuel cannot contain a significant fraction of hydrogen. While a helium donor in \source{} appears quite plausible given the measurements presented here, as well as its bursting properties, prior X-ray spectroscopy results have suggested \source{} may have an oxygen-rich circumbinary environment, perhaps associated with an outflow \citep{2018MNRAS.475.2027V}. In addition, spectral modeling of the Fe K$\alpha$ reflection feature appears to favor a higher inclination than suggested by our constraint derived from the assumption of gravitational radiation driven mass loss \citep{2017MNRAS.464..398D, 2018MNRAS.475.2027V, 2017ApJ...836..111K}. Based on these indications, \cite{2018MNRAS.475.2027V} favor a CO or O-Ne-Mg white dwarf donor. Given the constraints on the donor summarized in Figure 7 this remains a viable option, particularly in the case of non-conservative mass transfer, as would occur in the presence of an outflow. However, such a conclusion would also open up additional questions, such as the nature of the fuel for the observed X-ray bursts, which is presumably helium \citep{2017ApJ...836..111K}, though we note that \cite{2018arXiv180103006H} did not detect helium in their optical spectra of \source{}. Further to this final point, the bursting low mass X-ray binary 4U 0614$+$091 is another source with apparently helium-powered X-ray bursts \citep{2010A&A...514A..65K}, but whose optical spectra are suggestive of a CO donor with little to no helium \citep{2006A&A...450..725W, 2004MNRAS.348L...7N}. Additional observations will likely be needed to definitively pin down the nature of the donor in \source{}. While most AMXPs are transient systems, \source{} is distinctive in that it has been in outburst now for about a decade. This provides an exciting opportunity to study the long-term spin and orbital evolution with additional {\it NICER} observations. Moreover, we now have detections of pulsations from \source{} at two widely spaced epochs, in 2008 May with {\it RXTE}, and the present 2017 August, October and November observations with {\it NICER}. Interestingly, the source shows some indications of a significant change in pulsed amplitude in that time-frame. The estimated source pulsed amplitude measured by SK17 with {\it RXTE} was $9.4 \pm 1.1\%$ ($2 - 12$ keV), whereas we find $2.04 \pm 0.11 \%$ ($0.3 - 3.2$ keV) with {\it NICER}. We note that given the current uncertainties associated with modeling the {\it NICER} background, combined with the fact that the source count rate is dropping steadily above $\approx 5$ keV, it is presently challenging to accurately determine the pulsed amplitude above this energy. Nevertheless, with the present data we can measure the pulsed amplitude in the $2 - 5$ keV band with reasonable precision, and we find a value of $3.2 \pm 0.3 \%$. Based on this we think it likely that the smaller amplitude measured by {\it NICER} is a real effect and likely represents some secular change within the system, perhaps associated with the effect of accretion on the magnetic field, as, for example, suggested by \cite{2012ApJ...753L..12P}. More definitive conclusions in this regard should become feasible as the {\it NICER} background calibration improves. We will pursue this, as well as searches for energy dependent phase lags and a detailed spectroscopic study in subsequent work. \label{sec:conclusions} | 18 | 8 | 1808.04392 |
1808 | 1808.02532.txt | We consider the 21cm absorption signal expected at high redshift in cosmologies with and without non-baryonic cold dark matter. The expansion of the early universe decelerates strongly with dark matter, but approximately coasts without it. This results in a different path length across the epochs when absorption is expected, with the consequence that the absorption is predicted to be a factor of $\sim 2$ greater without dark matter than with it. Observation of such a signal would motivate consideration of extended theories of gravity in lieu of dark matter. | The nature of the missing mass remains one of the great unsolved problems in physics. The existence of non-baryonic cold dark matter (CDM) is an apparent requirement of modern cosmology for a variety of reasons \cite{Peebles}, perhaps most notably \cite{WMAP3,Planck15} the cosmic microwave background (CMB). This cosmic dark matter is widely assumed to be a weakly interacting massive particle (WIMP), yet decades of direct detection experiments have so far yielded only null results \cite{Akerib,PandaX,Xenon1T}. These non-detections have repeatedly excluded regions of parameter space where positive detections had been expected \cite{Trotta}. More generally, there is no positive experimental evidence for supersymmetry, a necessary prerequisite for the hypothesized WIMPs. Meanwhile, some astronomical data provide reason to doubt the existence of CDM outright \cite{sandersNOCDM,Kroupa2012,MdB98a}. This situation motivates consideration of alternatives to WIMP dark matter. Here we consider the possibility that the effects we have been interpreting as dark matter might in fact point to a need for an extended theory of gravity. Such a possibility is observationally well motivated \cite{SMmond,FM12}, with powerful arguments that can be made for and against both the dark matter and extended gravity interpretations \cite{CJP}. The modified Newtonian dynamics (MOND) hypothesized by Milgrom \cite{MONDorig} has had many a priori predictions \cite{milgrom83} come true \cite{BBS,MdB98b,PRL11,MM13a,MM13b,RAR,LMSP,LLMS18}. This should not happen if dark matter is the correct interpretation of the observed discrepancies. However, while MOND has the interesting property that dynamics \footnote{Though it has become conventional to discuss modifications of gravity, MOND might also be interpreted as a modification of inertia.} become scale invariant \cite{scaleinvar}, attempts to incorporate it into a generally covariant framework have been frustrating. The most prominent example of such a theory, TeVeS \cite{TeVeS}, fails to fit the CMB \cite{TVSforcing}, grow structure \cite{Dod2011}, or be consistent with observations of gravitational waves \cite{SandersGW}. The failure of the specific theory TeVeS does not falsify the more general hypothesis of scale invariant dynamics \footnote{Dynamics in the deep MOND regime are scale invariant under transformations $(t, \mathbf{r}) \rightarrow (\lambda t, \lambda \mathbf{r})$}, but we are left without a clear theory for cosmology in this context. Fortunately, the physics of the 21cm absorption is straightforward, depending only on atomic physics and the fact that the universe is expanding. This provides the opportunity to outline some very general expectations. Generically, we expect a universe devoid of non-baryonic dark matter (\Lnoob) to be low density, and thus experience less deceleration at early times \cite{Felten} than the conventional \LCDM\ \footnote{One might interpret the need to invoke both dark matter and dark energy as a failing of current theory: these are auxiliary hypotheses invoked to save the phenomena of a Friedmann-Robertson-Walker cosmology.} universe. As a consequence, there is a greater path length to the surface of last scattering that leads to a stronger absorption signal. | A challenge for modern cosmological theory is to identify definitive predictions by which \LCDM\ would be subject to falsification \cite{Kroupa2012,Kroupa2014}. Previous attempts \cite{M1999CMB} with the CMB succeeded \cite{M2000,M2004CMB} before failing \cite{CJP} due to previously unacceptable degrees of freedom \footnote{It was long believed that BBN required $\omega_b = 0.0125$ until fitting CMB data required $\omega_b = 0.0224$. No BBN measurements prior to the first relevant CMB measurements had suggested $\omega_b > 0.020$}. I worry that the current picture allows so much room for auxiliary hypotheses that there is no possibility of discerning that it is incorrect, should that happen to be the case. Here I have highlighted the amplitude of the 21cm absorption as a possible test. Generically, I predict that a universe devoid of CDM will exhibit about twice as much absorption as is possible in \LCDM. Taken at face value, the EDGES \cite{EDGES} detection is in serious conflict with \LCDM\ \cite{DMsanetalk} while corroborating the \Lnoob\ calculation made here. The various auxiliary hypotheses \cite{lightDMcrazytalk} that have been offered to reconcile the EDGES signal with \LCDM\ highlight my concern for its falsifiability. \medskip | 18 | 8 | 1808.02532 |
1808 | 1808.03321_arXiv.txt | Io is the only object in the Solar System with an atmosphere that is dynamically created by active volcanism. Interactions with Jupiter's plasma environment strip material from the atmosphere at a rate of $\sim$1 ton/second (Schneider \& Bagenal, 2007). Meanwhile, a combination of volcanic outgassing and sublimation of surface frost replenish atmospheric species, predominantly SO$_2$ (Lellouch et al. 2007). Numerous studies have investigated the role of both of these processes in sustaining Io's atmosphere, but have led to inconsistent conclusions regarding which process is dominant (e.g. Jessup and Spencer 2015; Jessup et al. 2004; Feaga et al. 2009; Spencer et al. 2005; Retherford et al. 2007; Roth et al. 2011; Tsang et al. 2012). Recent 19-$\mu$m observations have provided strong evidence that Io's SO$_2$ atmosphere decreases in column density by a factor of $\sim$5 during eclipse (Tsang et al. 2016). Although the discrepancies between various datasets remain unresolved, these authors suggest that differences could be explained if different atmospheric support mechanisms dominate at different Ionian longitudes. \par Although Io's bulk atmosphere can be studied at wavelengths from millimeter through ultraviolet (e.g. Retherford et al. 2007; Tsang et al. 2012; Moullet et al. 2013), the direct volcanic component is challenging to isolate. In 1999, de Pater et al. (2002) detected emission near 1.7 $\mu$m while observing Io in Jupiter's shadow, and attributed the emission to the rovibronic band associated with the forbidden ${\rm a}^1\Delta \rightarrow {\rm X}^3 \Sigma^-$ transition of SO. The shape and the forbidden nature of the emission were indicative of high gas temperatures ($\geq$1000 K), and the emission was attributed to hot, excited SO gas directly released from a volcanic vent. Follow-up observations on four nights between 2000 and 2003 found a tentative correlation between the strength of the emission and activity at Loki Patera (Laver et al. 2007). De Pater et al. (2007) performed the first spatially-resolved spectroscopy of the emission band and detected a hot plume over the volcano Ra Patera, which was undergoing a powerful eruption at the time. \par Models of the 1.7-$\mu$m emission band have treated the SO source as a single gas in thermodynamic equilibrium, with gas temperatures of 500-1000 K (de Pater et al. 2002; Laver et al. 2007; de Pater et al. 2007). However, such models were unable to fit the shape of the band, and underpredicted emission both at 1.71-1.715 $\mu$m and around 1.69 $\mu$m. The authors speculated that the source gas may be out of local thermodynamic equilibrium (LTE), but the low signal-to-noise in the wings of the band prevented more detailed modeling. \par We observed the 1.7-$\mu$m emission band on three occasions between 2012 and 2016, during eclipses of Io by Jupiter, including two observations with a factor of $\sim$10 higher spectral resolution than all previous data. Leveraging this significant improvement to spectral resolution, and the corresponding improvement in signal-to-noise, we investigate the source of the emitting gas via more complex models than were previously warranted. The observations, data reduction and calibration procedures are described in Section \ref{sec:data}. In Sections \ref{sec:models} and \ref{sec:results} we describe our models and results; more details on the statistical methods are given in \ref{sec:appendix}. The implications are discussed in Section \ref{sec:disc}, and summarized in Section \ref{sec:conc}.\par | \label{sec:conc} We observed Io in Jupiter eclipse on three occasions in 2012-2016 and detected the 1.7-$\mu$m rovibronic band associated with the forbidden a$^1\Delta \rightarrow {\rm X}^3 \Sigma^-$ transition of SO. On two of these dates, observations were made at a spectral resolution of R$\sim$15,000, an order of magnitude improvement over all prior datasets. The high spectral resolution of these data permits a more detailed modeling treatment than has been possible in the past. Analysis of the spectra indicates a contribution from gas components at both high and low rotational temperatures. The high-temperature component is consistent with volcanic gas emission (1000-1500 K), while the low-temperature component is consistent with the temperature of Io's bulk atmosphere: 172-217 K during observations of Io just entering eclipse (in December 2015), and 76-119 K after Io had been in shadow for an hour (in May 2016). This is suggestive of a hot volcanic gas that has partially equilibrated rotationally to the bulk atmospheric temperature prior to de-exciting to the ground electronic state, a scenario which is consistent with the radiative properties of SO for a gas density of $\sim 10^{11}$ cm$^{-3}$ and a pressure of $\sim$1-3 nbar in the emitting region, if the atmosphere cools through the eclipse. These values are consistent with past observational and modeling work for Io's dayside temperature (e.g. Walker et al. 2010; Lellouch et al. 2007). \par This interpretation is challenged by the fact that Io's surface cools after entering eclipse over a timescale of $\sim$10 minutes (Tsang et al. 2016), while individual spectra taken throughout the first 30 minutes of eclipse do not show any systematic trends in gas temperature (though we note that if such a change were subtle, it would not be distinguished in the individual spectra due to low signal-to-noise). If the low-temperature SO emission is indeed probing the bulk atmospheric temperature, the atmospheric cooling must be delayed relative to that of the surface. In addition, the overall band strengths and best-fit gas densities are very similar between the two observing dates. This would seem to contradict recent evidence for the collapse of Io's bulk SO$_2$ atmosphere in eclipse (Tsang et al. 2016). However, we note that uncertainties on the inferred densities are high, and rely on several assumptions; a collapse by a factor of 5$\pm$2, as found by Tsang et al. (2016), is fully consistent with our results.\par These three datasets bring the total number of detections of this emission band to eight. Analysis of the total band strength across all eight dates does not find any significant correlation between the observed SO emission and incident sunlight, Io's orbital phase, time since Io was last in sunlight, Jupiter's System III longitude, nor thermal hot spot activity. If the SO producing the emission band is indeed of volcanic origin, this indicates that thermal hot spot activity is not a good indicator of the gas emission. \par The two-temperature models that provide a good fit to the high-resolution data are unable to reproduce an excess of emission near 1.69 $\mu$m that is seen in the low-resolution data, which cover a wider spectral range. Simple non-LTE models are able to match this emission by over-populating high rotational states, but a detailed analysis is limited by the coarse spectral resolution. Future observations with high spectral resolution across the entire 1.67-1.74 $\mu$m region will allow for a more in-depth characterization of the thermodynamic equilibrium state of the gas, which reflects on the gas origins and potentially the vent conditions. Continued observations with high spectral resolution after Io has been in shadow for differing time intervals would confirm or refute the tentative correlation between the temperature of the low-T gas component and the amount of time Io has been in shadow; if the correlation is confirmed, such studies would then provide a new way of studying how Io's atmospheric temperature and density drop at night. \par \centerline {\bf Acknowledgments} K. de Kleer is supported by the Heising-Simons Foundation \textit{51 Pegasi b} postdoctoral fellowship; this work was also partially supported by the National Science Foundation grant AST-1313485 to UC Berkeley. This work made use of the JPL Solar System Dynamics high-precision ephemerides through the HORIZONS system. Data were obtained with the W.M. Keck Observatory, which is operated by the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. Data were also obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnolog\'{i}a e Innovaci\'{o}n Productiva (Argentina), and Minist\'{e}rio da Ci\^{e}ncia, Tecnologia e Inova\c{c}\~{a}o (Brazil). The authors extend special thanks to those of Hawaiian ancestry on whose sacred mountain we are privileged to be guests. Without their generous hospitality, none of the observations presented would have been possible. \par \appendix | 18 | 8 | 1808.03321 |
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1808 | 1808.00052_arXiv.txt | The orbital period of the hot Jupiter WASP-12b is apparently changing. We study whether this reflects orbital decay due to tidal dissipation in the star, or apsidal precession of a slightly eccentric orbit. In the latter case, a third body or other perturbation would be needed to sustain the eccentricity against tidal dissipation in the planet itself. We have analyzed several such perturbative scenarios, but none is satisfactory. Most likely therefore, the orbit really is decaying. If this is due to a dynamical tide, then WASP-12 should be a subgiant without a convective core as \citet{Weinberg+2018} have suggested. We have modeled the star with the \textsc{mesa} code. While no model fits all of the observational constraints, including the luminosity implied by the GAIA DR2 distance, main-sequence models are less discrepant than subgiant ones. | Much circumstantial evidence indicates that tidal dissipation sculpts the orbits of short-period binary stars and exoplanets. First-principles tidal theories often have difficulty explaining the observations quantitatively, however. For example, among low-mass main-sequence binaries, the period below which orbits circularize appears to increase with system age up to periods $\sim 20\unit{d}$, whereas standard dissipation mechanisms become ineffective beyond $\sim 10\unit{d}$ \citep{Zahn2013}. Transiting exoplanets offer the prospect of testing tidal dissipation in real time. Massive exoplanets with very short periods are expected to exhibit orbital decay due to tidal dissipation in their host stars, whose rotation is usually sub-synchronous, on timescales short compared to the star's main-sequence lifetime \citep{Levrard+2009}. (This should not occur for stellar binaries because of the much greater angular momentum in the orbit, only a small fraction of which is needed to bring the stars into synchronous rotation.) In favorable cases where the inspiral time is $\lesssim 10^7\unit{yr}$, transit timing with sub-minute accuracy may be expected to detect the period change after a decade or so. Currently the most promising tentative detection has been made for WASP-12b, a planet with mass $m_{\mathrm b}\approx 1.5\ M_{\rm J}$ in a $1.0914\,\mathrm{d}$ orbit around a main-sequence F star \citep{Hebb+2009}. Highly statistically significant departures from a linear transit ephemeris have been measured by \citet{Maciejewski+2016} and recently confirmed by \citet{Patra+2017}. According to the latter authors, the measured rate of change of orbital period is $\dot P = -29\pm 3\unit{ms\,yr^{-1}}$, and $P/\dot P=3.2\unit{Myr}$. Three hypotheses for the orbital period change have been discussed. One is orbital decay. A second is precession of the periapse of a slightly eccentric orbit with a period $\sim 10\unit{yr}$ \citep{Maciejewski+2016}. The required eccentricity is on the order of $10^{-3}$, well below the limit $e<0.05$ set by \citet{Husnoo+2012}. \citet{Patra+2017} find that this explanation is disfavored by times of planetary occultation (secondary eclipse) as measured with {\it Spitzer}: an eccentric orbit would tend to displace the times of primary and secondary eclipses in opposite directions, whereas the data seem to prefer an advance of both. Furthermore, it seems unlikely that even such a small eccentricity could have survived tidal dissipation in the planet. Nevertheless, \citet{Patra+2017} conclude that apsidal precession cannot yet be definitively ruled out on the basis of the timing data. The third possible explanation for $\dot P$ is acceleration by a companion. In fact WASP-12 is accompanied by a pair of M stars at projected separation $\approx 1\arcsec$, \citep{Bechter+2014}. Given that the estimated mass of this pair is $\approx 0.75\,M_\odot$ and the distance to WASP-12 is $432.5\pm6.1\unit{pc}$ \citep{GaiaDR2}, the maximum line of sight acceleration is $\approx 0.33\unit{m\,s^{-1}\,yr^{-1}}$, corresponding to $|\dot P|< 0.1\unit{ms\,yr^{-1}}$, far smaller than the observed value. More to the point---because there might be unseen massive planets closer in---\citet{Knutson+2014} have used their radial-velocity data to place a limit $\lesssim 4\unit{m\,s^{-1}\,yr^{-1}}$ on this acceleration, and this is still almost an order of magnitude too small to explain $\dot P$. In the absence of a plausible fourth hypothesis, orbital decay would therefore seem to be the best explanation for the observed departures from a linear ephemeris. There are, however, reasons for doubt. If the orbital decay timescale is in fact only $\sim 3\unit{Myr}$, whereas the main-sequence lifetime of the host star is $\gtrsim 1\unit{Gyr}$ (see \S\ref{sec:models}), we must be viewing the system at a special time. On the other hand, WASP-12 is perhaps the best current candidate for measurable orbital decay out of hundreds of hot Jupiters, so perhaps such a ``coincidence'' should be less surprising. A potential concern is the small measured rotation: $v\sin i<2.2\unit{km\,s^{-1}}$ \citep{Hebb+2009}, $v\sin i<5.1\unit{km\,s^{-1}}$ \citep{Fossati+2010b}, or $v\sin i=3.4\pm0.9\unit{km\,s^{-1}}$ \citep{Torres+Fischer+2012}. If the planetary orbit has donated much of its original angular momentum to the star, one might expect the star to have a larger $v\sin i$: the converse argument has been used by \citet{Penev+2016} to suggest orbital decay in the HATS-18 system. In \S\ref{sec:eq} and \S\ref{sec:spinup} however, we demonstrate that this expectation is incorrect and that tidal mechanisms are insufficient to bring WASP-12 to full synchronous rotation. Instead, tidal mechanisms should spin-up only a small core region of the star--the observational effect of which we explore. The orbital decay explanation has been previously investigated by \citet{Weinberg+2018} who offer the novel suggestion that WASP-12 is a subgiant star. But because this particular system holds a unique and valuable place within the context of tidal theories and planet-star interaction, we felt it necessary to investigate this system further. We make a more thorough examination of stellar models before independently coming to similar interpretations as \citet{Weinberg+2018}. Our analysis also benefits from the most recent luminosity estimates for WASP-12 (see \S\ref{sec:lum}) and while the results are inconclusive, this new luminosity favors a higher mass main-sequence model. Bearing in mind this preference for a main-sequence model, we present a comprehensive investigation of alternative explanations for the observed period change in \S\ref{sec:disc}. | \label{sec:disc} We have seen that the apparent period change ($\dot P$) observed in the transits of WASP-12b cannot easily be explained as secular orbital decay. Standard mechanisms of tidal dissipation are too slow, unless the orbit happens to be close to resonance with a global g~mode. We have estimated the probability for this to be quite small. The leading alternative explanation for the anomalous transit times is that the planetary orbit is slightly eccentric, $e\approx 2\times 10^{-3}$. In this interpretation, the true orbital period is constant, but the transit times depart slightly from a linear ephemeris due to precession of periastron at a rate $\dot\omega\approx 26\unit{deg\,yr^{-1}}$ \citep{Maciejewski+2016,Patra+2017}. The latter authors estimate that for a reasonable tidal quality factor of the planet itself, $Q_{\rm p}\le 10^6$, any primordial eccentricity would have decayed to $e < 10^{-3}$ after a few million years, whereas the system age appears to be $> 1\unit{Gyr}$. Therefore, the eccentricity would have to be recently excited or continually forced. We now briefly examine mechanisms for forcing the eccentricity or modulating the period of the orbit via changes in host star or third bodies. In the following, unless otherwise noted, we take $M_*=1.4\,M_\odot$, which is slightly higher than any of the values in Table~\ref{tab:models}. Therefore $R_*=1.64\,R_\odot$ based on the mean density adopted in Table~\ref{tab:properties}. With \cite{Southworth2012}'s result that $R_{\rm b}/R_*\approx0.1159\pm0.0033$, we then have $R_{\rm b}\approx 1.89 R_{\rm J}$ for the planetary radius. Both radii would scale $\propto M_*^{1/3}$ to other assumed values of the stellar mass. Adopting the radial velocity amplitude $K= 221.9\pm3.1\unit{m\,s^{-1}}$ from \cite{Knutson+2014} and the inclination $I=(83\pm0.5)^\circ$ from \cite{Maciejewski+2013}, and since $m_{\mathrm{b}}(M_*+m_{\mathrm{b}})^{-2/3}= K_*\sec I (P/2\pi G)^{1/3}$, we then have $m_{\mathrm{b}}=1.41\,M_{\rm J}$; this scales approximately as $M_*^{1/3}$. Finally the semimajor axis becomes $a=(P/2\pi)^{2/3}[G(M_*+m_{\mathrm{b}})]^{1/3}\approx 0.02322\unit{au}$. \subsection{Eccentricity from convection} \citet{Phinney1992} proposed that the small measured eccentricities of binary millisecond pulsars with white-dwarf companions can be explained by potential fluctuations associated with convection in the envelope of the companion when on the giant or asymptotic-giant branch. With few exceptions, the orbits of subsequently discovered binary millisecond pulsars have conformed well to the predictions of this model \citep{Lorimer2008}. Adapted to the WASP-12 system, so that the reduced mass $\mu\approx 1.4\,M_{\rm J}$, Phinney's equation (7.33) reads \begin{equation} \label{eq:ePhinney} \langle e^2\rangle^{1/2} \approx 2\times 10^{-5} \left(\frac{L_*R_{\rm env}}{5\,L_\odot R_\odot}\cdot \frac{1.4 M_\odot}{M_*}\right)^{1/3} \left(\frac{M_{\rm env}}{0.0004\,M_\odot}\right)^{1/6}\,, \end{equation} in which $R_{\rm env}\approx 1.4\,R_\odot$ is the radius at the base of the outer convection zone in our preferred model for WASP-12. $M_{\rm env}$, the mass of that zone, is sensitive to the effective temperature, metallicity, and evolutionary state of the star, but in view of the sixth root, no plausible value of $M_{\rm env}$ could make up the two orders of magnitude by which the r.m.s. eccentricity predicted by eq.~\eqref{eq:ePhinney} falls short of the value required to explain the quadratic term in the transit ephemeris. Furthermore, as Phinney remarks, his eq.~(7.33) probably overestimates the eccentricity expected when the turnover time of the largest convective eddies exceeds the tidal period, as occurs in WASP-12 by at least one order of magnitude. \subsection{The Applegate effect} \citet{Applegate+Patterson1987} and \citet{Applegate1992} suggested that long-term modulations observed in the eclipse times of some close stellar binaries, including V471~Tau and Algol, are caused by slow changes in the quadrupole moment of one or both stars induced by their magnetic cycles. In the later version of this idea, the magnetic stress is not large enough to distort the equilibrium shape of the star directly, but rather slowly redistributes angular momentum within the star(s), leading to changes in the rotationally-induced quadrupole. Because the changes are slow, they would not excite the eccentricity of the orbit, but the quadrupole contributes to the central force between the stars and hence to the orbital period itself. \citet[hereafter WM10]{Watson+Marsh2010} have scaled \citet{Applegate1992}'s model to several exoplanet systems. For WASP-12b, they estimate that the anomaly in the transit time ($O-C$, observed minus calculated) could be as much as $42~(T/50\,\mathrm{yr})^{3/2}$, where $T$ is the period on which the dynamo modulates the internal differential rotation. This last could be the same as the period of the magnetic dipole, or half that, depending on the type of dynamo. MW10's predicted variation is not a great deal smaller than the $\sim$2-minute departure from a linear transit ephemeris found by \citet{Patra+2017}. It depends on several several uncertain parameters besides the dynamo period $T$, so one ought to consider whether the uncertainties in these parameters might allow the Applegate effect to explain the WASP 12 data. The relevant parameters are the rotation period of the star, for which WM10 take $P_{\rm rot}=36\,\mathrm{d}$, the fractional mass of the convection zone, for which they take $M_{\rm env}/M_*=0.1$, and the portion of the mean luminosity that is converted to mechanical form to change the differential rotation. For the latter they take $\Delta L=0.1\,L$; this seems large, but perhaps not in direct conflict with observations because, as they point out, the luminosity variation at the photosphere could be much smaller due to the thermal inertia of the convection zone (i.e., the ratio of its total thermal energy to the luminosity of the star; this is about 300~yr for WASP 12). WM10's equations imply that the transit-time anomalies scale with these parameters as follows: \begin{equation} \label{eq:MWscalings} (O-C)_{\rm max}\propto T^{3/2}P_{\rm rot}^{-1}\left(\frac{M_{\rm env}}{M_*}\right)^{1/2}(\Delta L)^{1/2}\,. \end{equation} The mass of the convective envelope of WASP~12 is probably $\lesssim 10^{-3}\,M_*$, as remarked above; following eq~\eqref{eq:MWscalings}, this would reduce the predicted $O-C$ by an order of magnitude. On the other hand, the rotation period may be rather less than the assumed value if the star is viewed near pole on, as Rossiter-MacLaughlin measurements suggest \citep{2012ApJ...757...18A}. The median rotation period for main-sequence F8 stars\footnote{\citet{Hebb+2009} classify WASP 12 as F9V} is $\approx 8\,\mathrm{d}$ \citep{Nielsen+2013}. Since dynamo periods appear to correlate positively with stellar rotation periods \citep{Saar+Brandenburg1999,Boehm-Vitense2007}, however, the positive scaling with $T$ seems likely to overwhelm the negative scaling with $P_{\rm rot}$ in eq.~\eqref{eq:MWscalings}. If MW10's scalings are applied to the Sun, they predict a variation $\Delta J_2\gtrsim 5\times 10^{-8}$ in its rotationally-induced dimensionless quadrupole moment over the dynamo cycle. The internal differential rotation of the Sun has been directly constrained by helioseismology, and for a significant fraction of a cycle. \citet{Antia+2008} have used these data to estimate that $\langle J_2\rangle_\odot=2.2\pm0.01\times 10^{-7}$, and the variation over a nine-year period to be $\lesssim 1\times 10^{-10}$, i.e. several orders of magnitude smaller than MW10's assumptions would predict. For these reasons (i.e., both our estimates of the actual parameters of WASP-12, as well as comparision with heliosesimological inferences for the Sun), it is unlikely that the Applegate effect explains the transit-time anomolies of WASP-12b. \subsection{Bow shock} Ultraviolet absorption is seen just before each transit of WASP-12b and has been interpreted as evidence for mass loss from the planet through its inner Lagrange point \citep{Fossati+2010a}. Alternatively, this could be the signature of a bow shock ahead of the planet encountering a wind from the star \citep{Lai+2010,Vidotto+2010}. Such a shock would exert a drag on WASP-12b's orbit. As shown here, however, an improbably dense wind would be required to explain the observed $\dot P$. The torque exerted on the planet by the shock is $C_D\pi R_{\mathrm{b}}^2\rho_{\mathrm{w}} (v_{\mathrm{b}}^2+v_{\mathrm{w}}^2)^{1/2}v_{\mathrm{b}}a$, in which $C_D$ is a factor of order unity (the drag coefficient), $\rho_{\mathrm{w}}$ the pre-shock density of the wind, $v_{\mathrm{w}}$ the wind velocity, $R_{\mathrm{b}}\approx 1.9\,\mathrm{R_{\rm J}}$ the radius of the planet, and $v_{\mathrm{b}}\approx (GM_*/a)^{1/2}$ the orbital velocity. The decay timescale is then \begin{equation} \label{eq:drag} \frac{P}{\dot P} = \frac{m_{\mathrm{b}}}{3\pi C_D R_{\mathrm{b}}^2\rho_{\mathrm{w}}(v_{\mathrm{b}}^2+v_{\mathrm{w}}^2)^{1/2}} \approx 4\times10^{12}\unit{yr}. \end{equation} For the numerical estimate, we have taken $C_D=0.3$, and $\rho_{\mathrm{w}}=2\times10^{-18}\unit{g\,cm^{-3}}$ (i.e. $n_{\mathrm{H}}=1.5\times10^6\unit{cm^{-3}}$); the latter follows \cite{Vidotto+2010} and implies a stellar mass-loss rate of $10^{-12.3}(v_{\rm wind}/100\unit{km\,s^{-1}})\unit{M_\odot\,yr^{-1}}$. In order to explain the apparent decay rate ($P/\dot P\approx 3\unit{Myr}$), the wind density would have to increase some six orders of magnitude, making the mass-loss timescale of the star $\lesssim 10\unit{Myr}$. This is unreasonable as the star is probably older than $1\unit{Gyr}$. \subsection{Kozai-Lidov oscillations}\label{subsec:KL} We consider the possibility that a non-transiting third body in the system continuously excites a small eccentricity in the orbit of WASP-12b so that, as suggested by \citet{Maciejewski+2016}, the transit-time anomolies result from apsidal precession of the slightly elliptical orbit. Apsidal precession itself imposes a lower bound on the perturbations that such a hypothetical companion must exert to excite WASP-12b's eccentricity. Let the companion have mass $m_{\mathrm{c}}$, semimajor axis $a_{\mathrm{c}}$, and orbital eccentricity $e_{\mathrm{c}}$, and let $\{m_{\mathrm{b}},a_{\mathrm{b}},e_{\mathrm{b}}\}$ be those of WASP-12b itself. By a standard calculation in secular perturbation theory, one can show that if $e_{\mathrm{b}}\ll 1$ initially, then $e_{\mathrm{b}}$ will grow by the Kozai-Lidov mechanism (hereafter KLM) only if \begin{equation} \label{eq:KLlimit} \frac{m_{\mathrm{c}}}{a_{\mathrm{c}}^3(1-e_{\mathrm{c}}^2)^{3/2}} > \frac{10}{3} k_{2\mathrm{b}} \frac{M_*^2R_{\mathrm{b}}^5}{m_{\mathrm{b}} a_{\mathrm{b}}^8}\,, \end{equation} in which $R_{\mathrm{b}}$ is the radius of WASP-12b and $k_{2\mathrm{b}}$ its Love number, these two quantities being important for the apsidal precession rate. The inequality \eqref{eq:KLlimit} assumes that the orbital planes of $m_{\mathrm{c}}$ and $m_{\mathrm{b}}$ are orthogonal, which maximizes the efficiency of the KLM. We are also assuming $a_{\mathrm{c}}>a_{\mathrm{b}}$, i.e. the third body's orbit is exterior to that of WASP-12b. The orbits should not cross, whence $a_{\mathrm{c}}(1-e_{\mathrm{c}})>a_{\mathrm{b}}$, and therefore $a_{\mathrm{c}}(1-e_{\mathrm{c}}^2)^{1/2}>\sqrt{a_{\mathrm{b}}a_{\mathrm{c}}}$. With $k_{2\mathrm{b}}\approx0.6$, the lower bound on the companion's mass for the KLM becomes \begin{equation} \label{eq:KL2} m_{\mathrm{c}} > 77. \left(\frac{a_{\mathrm{c}}}{a_{\mathrm{b}}}\right)^{3/2}\unit{M_\oplus} \end{equation} An upper bound on $m_{\mathrm{c}}$ follows from the published radial-velocity data \citep{Hebb+2009,Husnoo+2011,2012ApJ...757...18A,Bonomo+2017}. After subtraction of the WASP~12b signal\footnote{We subtract an optimally scaled multiple of the photometric ephemeris of \cite{Patra+2017}, including their secular period derivative $\dot P= (0.92\pm0.01)\times 10^{-9}$. Thus this limit applies to companions with periods less than the span, of the data, $\sim 7$~yr.} and correction for the nominal measurement errors, these data have variance $\approx (9\unit{m\, s^{-1}})^2$. The RV signal of the hypothetical WASP-12c should be no larger than this. Therefore \begin{equation} \label{eq:mcrv} m_{\mathrm{c}} < 18\,f^{-1/2} \left(\frac{a_{\mathrm{c}}}{a_{\mathrm{b}}}\right)^{1/2}\unit{M_\oplus}\,, \end{equation} with $f$ being a geometrical factor that determines the mean-square projection of the orbital velocity onto the line of sight: \begin{equation} \label{eq:ffac} f(e_{\mathrm{c}},\omega_{\mathrm{c}},I_{\mathrm{c}}) = \frac{\sin^2\omega_{\mathrm{c}} +\sqrt{1-e^2_{\mathrm{c}}}\,\cos^2\omega_{\mathrm{c}}}{1+\sqrt{1-e^2_{\mathrm{c}}}}\sin^2I_{\mathrm{c}}\,. \end{equation} In order that the KLM operate, the relative inclination of the two planetary orbits must be greater than $\sin^{-1}\sqrt{2/5}\approx 39.2^\circ$, so \begin{equation*} \cos I_{\mathrm{c}}\cos I_{\mathrm{b}} +\sin I_{\mathrm{c}} \sin I_{\mathrm{b}}\cos(\Omega_{\mathrm{c}}-\Omega_{\mathrm{b}}) < \sqrt{3/5} \end{equation*} with $\Omega_{\mathrm{b,c}}$ being the longitudes of the ascending nodes. Since the inclination of WASP~12b is $I_{\mathrm{b}}\approx (83\pm0.5)^\circ$ \citep{Maciejewski+2013}, the above constraint is compatible with $I_{\mathrm{c}}\approx 0$, and of course also with any eccentricity $e_{\mathrm{c}}$ or argument of periastron $\omega_{\mathrm{c}}$. So the factor $f$ could be arbitrarily small. The two inequalities \eqref{eq:KL2} \& \eqref{eq:mcrv} could therefore both be satisfied by an exterior perturber ($a_{\mathrm{c}}>a_{\mathrm{b}}$), although this becomes less probable as the separation between the orbits increases because of the different scalings with $a_{\mathrm{c}}/a_{\mathrm{b}}$. Furthermore, eqs.~\eqref{eq:mcrv}-\eqref{eq:ffac} suppose that the radial velocity is measured continuously, whereas in fact it is sampled somewhat sparsely and irregularly: nearly half of the $\sim 90$ measurements were made by \citet{2012ApJ...757...18A} in a single night. If WASP~12c's orbit were highly eccentric, and thus hovering usually near apastron, its full radial-velocity amplitude might not be sampled. We have not systematically investigated the probability that both of the mutually antagonistic bounds \eqref{eq:KL2} and \eqref{eq:mcrv} could be satisfied. Nevertheless, the Kozai-Lidov mechanism does not seem to provide a natural explanation for the quasi-secular transit-time anomalies of WASP~12b. The hypothesis is attractive only in comparison to all of the other possibilities that we have investigated. \subsection{Resonance} We have considered the possibility that the orbital variations of WASP~12b are caused by resonant interactions with an unseen planet. We focus on mean-motion resonances. Suppose first a 1:1 resonance, in other words, a small trojan planet librating around the stable Lagrange points of the WASP~12+WASP~12b system.\footnote{We thank Scott Tremaine for suggesting that we look into this.} The inferred amplitude of the period variation is $29\pm3\unit{ms\,yr^{-1}}$ \citep{Patra+2017}, amounting to $\Delta\ln P\approx 3\times 10^{-6}$ over the 9 years that transits have been monitored. We estimate that a roughly lunar mass in a ``horseshoe'' 1:1 resonant libration could modulate WASP~12b's period at this amplitude. This would easily satisfy the limit $m_{\mathrm c}<34\,\mathrm{M}_\odot$ on Trojan companions to WASP-12b found by \cite{Lillo-Box+2018}, who based their analysis on archival radial velocities. The difficulty, however, is in the period of the modulation. It is well known that small-amplitude librations around the Lagrange points in the coplanar restricted three-body problem have period $P_{\rm lib} = P_{\rm orb}\times 2(1+q)/\sqrt{27 q}$, where $P_{\rm orb}$ is the orbital period of the massive bodies and $q<0.04$ is their mass ratio. In the present case where $P_{\rm orb}=1.09\unit{d}$ and $q\approx 10^{-3}$, $P_{\rm lib}\approx 13\unit{d}$. A large-amplitude libration can have a somewhat longer period than this, but not by more than a factor $\sim 2$ unless very close to the separatrix between libration and circulation, as we have convinced ourselves by numerical experiments. Such a $P_{\rm lib}$ is far too short to mistaken for a secular trend over 9~yr unless severely aliased, which seems unlikely in view of the density of transit observations [see the tabulation in \citet{Patra+2017}]. We have also examined first-order mean motion resonances $P_{\mathrm c}:P_{\mathrm b} \approx (j+1):j$, with $j\ge 1$ an integer. Our analysis is restricted to coplanar, near-circular cases, but the main conclusions would probably be similar even for strongly misaligned orbits. The unseen body WASP-12c is presumed to be much less massive than WASP-12b. Close to such a resonance, the $j^{\mathrm{th}}$ azimuthal harmonic of the potential of the orbit of b directly forces the eccentricity of c's orbit ($e_{\mathrm{c}}$), and the $(j+1)^{\mathrm{th}}$ harmonic of c forces $e_{\mathrm{b}}$. In the first case, or ``exterior'' resonance, $e_{\mathrm{b}}$ is neglected to leading order, while $e_{\mathrm{c}}$ is neglected for the interior resonance \citep[e.g.][]{Murray+Dermott2000}. The forced eccentricities depend not only on the masses $m_{\mathrm{c}}$ and $m_{\mathrm{b}}$ but also on the distances from exact resonance; these differ because of the unforced apsidal precession rates of the two planets. As already noted in \S\ref{subsec:KL}, the apsidal precession of b is dominated by its tidal distortion: $\varpi_{\mathrm{b}0}\approx 3.9\times10^{-4} n_{\mathrm b}$, with $n_{\mathrm{b}}=2\pi P_{\mathrm{b}}^{-1}$ being its mean motion. If c is a smaller body such as a super-earth, its apsidal motion is dominated by the axisymmetric potential of b's orbit. Near the 2:1 resonances, we estimate that $\dot\varpi_{\mathrm{c}0}\approx 3.8\times10^{-4}n_{\mathrm{b}}$. Because of the coincidence that $\dot\varpi_{\mathrm{b}}\approx \dot\varpi_{\mathrm{b}}$, the slow frequencies that measure the distance from resonance, namely $\nu_{\mathrm{b}}\equiv j n_{\mathrm{b}}-(j+1) n_{\mathrm{c}}-\dot\varpi_{\mathrm{b}0}$ and $\nu_{\mathrm{c}}\equiv j n_{\mathrm{b}}-(j+1) n_{\mathrm{c}}-\dot\varpi_{\mathrm{c}0}$ will usually be nearly equal, at least for the 2:1 resonances ($j=1$). Tidal dissipation within the planets damps the forced eccentricity at the rate \begin{equation} \label{eq:Qcirc} \gamma_{\rm p}\equiv -\left(\frac{d\ln e}{dt}\right)_{\rm tide} = \frac{63}{4Q'_{\mathrm{p}}}\frac{M_*}{m_{\mathrm{p}}}\left(\frac{R_{\mathrm{p}}}{a_{\mathrm{p}}}\right)^5 n_{\mathrm{p}} \end{equation} where $Q'_{\mathrm{p}}$ is the tidal quality factor of planet p corrected for its Love number. On short timescales $\sim \nu^{-1}$, an equilibrium holds between forcing and damping. Secularly however, at second order in eccentricity and first order in the damping rate \eqref{eq:Qcirc}, there is a transfer of orbital energy and angular momentum between planets. The transfer is always outward, i.e. from b to c in our case, but in the proportion $\Delta E = n_{\mathrm{c}}\Delta J$ for the interior resonance (where the orbit of c is approximated as circular), and $\Delta E = n_{\mathrm{b}}\Delta J$ for the exterior resonance (where $\Delta e_{\mathrm{b}}$ is neglected). The rate of transfer of angular momentum is related to the tidal dissipation rates $\mathcal{\dot E}_{\mathrm{b,c}}>0$ by \begin{equation} \label{eq:dJdt} \frac{dJ_{\mathrm c}}{dt}=- \frac{dJ_{\mathrm b}}{dt} = \frac{\mathcal{\dot E}_{\mathrm{b}}+\mathcal{\dot E}_{\mathrm{c}}}{n_{\mathrm{b}}-n_{\mathrm{c}}} \end{equation} The effect of this torque is to increase the slow frequencies $\nu_{\mathrm{b}}$ and $\nu_{\mathrm{c}}$, and hence to increase the distance from resonance if these frequencies are already positive. If body c is a super-earth, we estimate that $\mathcal{\dot E}_{\mathrm{b}}>\mathcal{\dot E}_{\mathrm{c}}$ by a factor of at least a few at the first few mean-motion resonances ($j\lesssim 6$): \begin{equation} \label{eq:Edotb} \mathcal{\dot E}_{\mathrm{b}} = \frac{\gamma_{\mathrm{b}} m_{\mathrm{b}} A^2_{\mathrm{b}}/4}{\nu_{\mathrm{b}}^2+\gamma^2_{\mathrm{b}}}\,, \end{equation} where \begin{equation} \label{eq:Ab} A_{\mathrm{b}} = \frac{Gm_{\mathrm{c}}}{a_{\mathrm{b}}a_{\mathrm{c}}} \left[\frac{d}{d\ln\alpha} b_{1/2}^{(j+1)} (\alpha)+2j b_{1/2}^{(j+1)}(\alpha)\right]_{\alpha =a_{\mathrm{b}}/a_{\mathrm{c}}}, \end{equation} in which the functions $b_{1/2}^{(j+1)}(\alpha)$ are the usual Laplace coefficients. The last equation follows from first-order epicyclic theory if the damping term is inserted by hand. (These equations also determine $\mathcal{\dot E}_{\mathrm{c}}$ if all subscripts ``b'' and ``c'' are interchanged and $j+1$ is replaced by $j$.) For definiteness, let us focus on the 2:1 resonance, $j=1$, so that $\nu_{\mathrm{b}}\approx\nu_{\mathrm{c}}$ by the numerical coincidence noted above. Presuming that $m_{\mathrm{c}}\ll m_{\mathrm{b}}$, the increase in $\nu$ due to the torque \eqref{eq:dJdt} is dominated by the change in the mean motion of c, but $dE_{\mathrm{c}}/dJ_{\mathrm{c}}\approx n_{\mathrm{c}}$ because dissipation occurs mainly in body b. Hence $dn_{\mathrm{c}}/dJ_{\mathrm{c}}\approx -3/m_{\mathrm{c}}a^2_{\mathrm{c}}$. In the relevant regime where $\nu\gg\gamma$, $d\nu/dt\propto\nu^{-2}$ because of the denominator in eq.~\eqref{eq:Ab}, the other terms in eqs.~\eqref{eq:Edotb}-\eqref{eq:Ab} being effectively constant when $|\nu|\ll n_{\mathrm{b,c}}$. Integrating this relation with the constants included yields \begin{equation} \label{eq:nuest} \nu\approx 0.02\left(\frac{10^6}{Q'_{\mathrm{b}}}\frac{m_{\mathrm{c}}}{M_\oplus}\frac{T}{\mathrm{Gyr}}\right)^{1/3}\,n_{\mathrm{b}}\,, \end{equation} presuming that the system started from exact resonance at time $T$ in the past. The quantities in parentheses in eq.~\eqref{eq:nuest} are uncertain, but because of the cube root, it is unlikely that the distance from resonance ($\nu/n_{\mathrm{b}}$) is much less than $10^{-2}$. Now at a $(j+1):j$ resonance, the combination $(j+1)n_{\mathrm{c}}-jn_{\mathrm{b}}$ is the \emph{forced} apsidal precession rate, $\dot\varpi_{\mathrm{b}}$. Therefore $\nu_{\mathrm{b}}=\dot\varpi_{\mathrm{b0}}-\dot\varpi_{\mathrm{b}}$. Since we have previously estimated that $\dot\varpi_{\mathrm{b0}}\approx 4\times 10^{-4}n_{\mathrm{b}}$, it follows from eq.~\eqref{eq:nuest} that $\dot\varpi_{\mathrm{b}}<0$, with a period $\sim 50\times P_{\mathrm{b}}\approx 55\,\mathrm{d}$. Thus while it is possible to choose $m_{\mathrm{c}}$ so that the amplitude of the forced eccentricity $e_{\mathrm{b}}=2\times10^{-3}$, the period of the apsidal precession is much too rapid to explain the observed quasi-secular $\dot P$. We have revisited the possible causes of WASP-12b's departure from a linear ephemeris. Either the orbit is decaying, or some dynamical perturbation maintains a small eccentricity and the apsides precess on some period longer than a decade. We have considered various perturbations induced by unseen third bodies or distortions of the star WASP-12 itself, but none is consistent with all of the observational constraints, at least not without fine tuning. The conclusion therefore seems inescapable that the orbit is indeed decaying, presumably because of tidal dissipation in the star. Indeed, the dynamical tide---computed for a circular orbit and a negligibly rotating star---naturally yields an orbital lifetime comparable to what is inferred from transit timing. But this requires that the star has evolved onto the subgiant branch and lost its convective core, as \citet{Weinberg+2018} have suggested. In that case, the g~modes excited at the base of WASP-12's thin surface convection zone might be just strong enough to damp nonlinearly in the core, which would broaden the g-mode resonances so that they overlapped. If WASP-12 were still on the main-sequence and still had its convective core, the resonances would be very sharp, and the orbit would have to be implausibly close to resonance to explain the current rate of orbital evolution. Alternatively, if the star had a \emph{rapidly rotating} core, with a rotation period as short or shorter than the period of the orbit, then the tidally excited g-modes would be absorbed at the critical (corotation) layer \citep{Barker+Ogilvie2010}; the torque applied by absorption of the ingoing waves would then maintain the rapid rotation of the layer and presumably of the core beneath it. This begs the question how the core could have started out with such rapid rotation, however. Moreover, unlike the subgiant hypothesis, it does not naturally explain why the decay timescale is so much shorter than the age of the star. The observational constraints on WASP-12 itself, when fit to theoretical models for its structure made with the \textsc{mesa} code, favor a main-sequence star rather than a subgiant. Actually, we have not been able to find any \textsc{mesa} model that fits all of the observations comfortably: the spectroscopically inferred $T_{\rm eff}$ and [Fe/H] are in tension with the luminosity inferred from the GAIA-DR2 distance and \citet{Stassun+2017}'s bolometric flux. This problem would exist even if there were no evidence for orbital decay, though the transit light curves are essential for constraining the star's mean density. \bigskip We thank Josh Winn for introducing us to this problem and for much helpful advice and conversation. | 18 | 8 | 1808.00052 |
1808 | 1808.00709_arXiv.txt | Herein, we present the $^{12}$CO ($J$=1--0) and $^{13}$CO ($J$=1--0) emission line observations via the FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45-m telescope (FUGIN) toward a {\it Spitzer} bubble N4. We observed clouds of three discrete velocities: 16, 19, and 25\,km\,s$^{-1}$. Their masses were $0.1\times 10^{4}$\,$M_{\odot}$, $0.3\times 10^{4}$\,$M_{\odot}$, and $1.4\times 10^{4}$\,$M_{\odot}$, respectively. The distribution of the 25-km\,s$^{-1}$ cloud likely traces the ring-like structure observed at mid-infrared wavelength. The 16- and 19-km\,s$^{-1}$ clouds have not been recognized in previous observations of molecular lines. We could not find clear expanding motion of the molecular gas in N4. On the contrary, we found a bridge feature and a complementary distribution, which are discussed as observational signatures of a cloud--cloud collision, between the 16- and 25-km\,s$^{-1}$ clouds. We proposed a possible scenario wherein the formation of a massive star in N4 was triggered by a collision between the two clouds. % The time scale of collision is estimated to be 0.2--0.3\,Myr, which is comparable to the estimated dynamical age of the H{\sc ii} region of $\sim$0.4 Myr. In N4W, a star-forming clump located west of N4, we observed molecular outflows from young stellar objects and the observational signature of a cloud-cloud collision. Thus, we also proposed a possible scenario in which massive- or intermediate-mass star formation was triggered via a cloud--cloud collision in N4W. | % \subsection{Massive star formation} Massive stars are important objects in the galactic environment due to their powerful influence on the interstellar medium via ultraviolet radiation, stellar winds, and supernova explosions. It is therefore of fundamental importance to understand the mechanisms of massive star formation, although these mechanisms still remain elusive (e.g., \cite{2007ARA&A..45..481Z, 2014prpl.conf..149T}). Recently, supersonic cloud--cloud collision (CCC) has been discussed as an important triggering mechanism of massive star formation because of the large mass accretion associated with the compressed region between colliding two clouds. Observational studies have suggested the possible evidence of CCCs in H{\sc ii} regions (with one or several young O-stars) and in super star clusters (with 10--20 O-stars) in the Milky Way and the Large Magellanic Cloud (\cite{2014ApJ...780...36F, 2015ApJ...807L...4F, 2018ApJ...859..166F, 2018PASJ...70S..60F, 2018PASJ...70S..46F, 2009ApJ...696L.115F, 2018PASJ...70S..49E, 2018PASJ...70S..48H, 2018PASJ...70S..50K, 2018PASJ...70S..42N, 2017arXiv170606002N, 2010ApJ...709..975O, 2018PASJ...70S..45O, 2018PASJ...70S..47O, 2017arXiv170808149S, 2018PASJ...70S..43S, 2013ApJ...768...72S, 2011ApJ...738...46T, 2015ApJ...806....7T, 2017ApJ...835..142T, 2017arXiv170607164T, 2018PASJ...70S..51T, 2015PASJ...67..109T, 2017arXiv170605664T}). Magneto-hydrodynamical simulations of the formation of the massive clumps that may form massive stars in the collision-compressed layer have also been discussed (\cite{2013ApJ...774L..31I, 2018PASJ...70S..53I}). Furthermore, comparisons between the observations and numerical calculations (\cite{1992PASJ...44..203H, 2010MNRAS.405.1431A, 2014ApJ...792...63T, 2017arXiv170608656T}) have indicated two important observational signatures of CCCs: the ``bridge feature'' in position-velocity diagrams and the ``complementary spatial distribution'' in the sky between two colliding clouds, which provide useful diagnostics to identify CCCs using molecular line observations (\cite{2018ApJ...859..166F}). Bridge features are relatively weak CO emissions at intermediate velocities between two colliding clouds with different velocities. When a smaller cloud drives into a larger cloud, the smaller cloud caves the larger cloud owing to the momentum conservation (\cite{2015MNRAS.450...10H}), and a dense compressed layer is formed at the collision interface, resulting in a thin, turbulent layer between the larger cloud and the compressed layer. If one observes a snapshot of this collision with a viewing angle parallel to the axis of collision, two separated velocity peaks connected by an intermediate--velocity emission with lower intensity feature could be observed in position-velocity diagrams. \subsection{{\it Spitzer} bubble N4} Churchwell et al. (2006, 2007) listed $\sim$600 objects with {\it Spitzer} 8 $\mu$m emission in a ring-like morphology on the Galactic plane ($l=10^\circ$--$65^\circ$ and $295^\circ$--$350^\circ$) and termed these objects as {\it Spitzer} bubbles. The 8 $\mu$m emission [from hot dust and polycyclic aromatic hydrocarbon (PAH) molecule] of {\it Spitzer} bubbles surrounds the radio continuum (from ionized gas) and the 24 $\mu$m emission (from warm dust). According to \citet{1977ApJ...214..725E}, ultraviolet radiation from massive stars creates an expanding H{\sc ii} region and the interstellar gas and dust can be collected in the circumference of the H{\sc ii} region. As a result, dense ring- or shell-like gas/dust clouds are formed, which collapse to form stars. This is called as the ``collect and collapse'' process. This process has been suggested by some observational studies to operate in {\it Spitzer} bubbles (e.g., \cite{2009A&A...496..177D, 2010A&A...523A...6D, 2010A&A...518L..81Z}). Figure\,\ref{fig:RGB_all}(a) shows a composite color image of the {\it Spitzer}/MIPSGAL 24 $\mu$m (red) and {\it Spitzer}/GLIMPSE 8$\mu$m (green) emissions around N4 and N4W. N4 and N4W are located a little far from the middle of the Galactic plane, and seem to be relatively isolated objects from the surrounding H{\sc ii} regions. Figure\,\ref{fig:RGB_all}(b) shows a closeup figure of Figure\,\ref{fig:RGB_all}(a). N4 has an almost complete ring-like structure in the 8 $\mu$m emission and the H{\sc ii} region inside the ring. In previous studies, molecular clouds associated with N4 have been detected and the clouds show a ring-like structure (\cite{2013RAA....13..921L}), and their radial velocities ($V_{\rm LSR}$) are centered on $\sim$25\,km\,s$^{-1}$. According to the parallax-based distance estimator (\cite{2016ApJ...823...77R}), this $V_{\rm LSR}$ and direction corresponds to a probable distance of 2.80\,kpc$\pm$0.30\,kpc, and hence, we adopted a distance of 2.8\,kpc to N4. The radius of the ring is $\sim$2$'$, which corresponds to $\sim$1.6\,pc. The estimated total Lyman continuum [log($N_{\rm Lym}$\,s$^{-1}$) = 48.18] indicates that a main O8.5--O9V star is responsible for the ionization of N4 (\cite{2016ApJ...818...95L}). \citet{2010ApJ...716.1478W} investigated the distribution of young stellar object (YSO) candidates around N4, and found that there does not appear to be an overdensity of YSOs along the shell. Therefore \citet{2010ApJ...716.1478W} suggested that there is no evidence for the triggered star formation via the ``collect and collapse'' process, although they claimed that the triggered star formation could not be ruled out because YSO samples are not complete in this region. On the contrary, by observing the $^{12}$CO ($J$=1--0), $^{13}$CO ($J$=1--0), and C$^{18}$O ($J$=1--0) emissions, \citet{2013RAA....13..921L} found an expanding motion of the molecular clouds associated with N4. They suggested that the formation of a massive star candidate (labeled as S2 in \citet{2013RAA....13..921L}) on the ring may be triggered by the expansion of the H{\sc ii} region formed by a massive star candidate (labeled as S1 in \citet{2013RAA....13..921L}); however, the formation mechanism of S1, which is the star exciting N4 and located inside the ring, remains unclear in this scenario. N4W, located $\sim 5'$ west of N4, is a star-forming clump hosting YSOs and a submillimeter source (\cite{2016ApJ...822..114C}). \citet{2016ApJ...822..114C} identified four YSOs with at least intermediate mass in the innermost area by the observations of J, H, and Ks bands and found that these YSOs are almost coeval. \subsection{Paper overview} In this paper, we report an observational study of the {\it Spitzer} bubble N4 and N4W using the $^{12}$CO ($J$=1--0) and $^{13}$CO ($J$=1--0) dataset obtained via the FUGIN project (\cite{2016SPIE.9914E..1ZM, 2017PASJ...69...78U}), whose spatial resolution is approximately 3\,times higher than the previous CO observations, to investigate the formation process of N4 and N4W. Section\,\ref{sec:Dat} describes these datasets. In Section\,\ref{sec:Res}, we describe the large-scale CO distribution (Subsection\,\ref{sec:COdist}), present the velocity structure of the molecular clouds (Subsection\,\ref{sec:COvelo}), compare the $^{12}$CO ($J$=1--0) emission with the $^{12}$CO ($J$=3--2) archive data obtained using the James Clerk Maxwell Telescope (JCMT; Subsection\,\ref{sec:COratio}), and estimate the physical parameters of the molecular outflow associated with N4W (Subsection\,\ref{sec:outflow}). In Section\,\ref{sec:Dis}, we discuss massive star formation and the H{\sc ii} region in N4 via a comparison with other massive-star forming regions, and the star formation in N4W. \begin{figure}[h] \begin{center} \plotone{f1_.eps} \end{center} \caption{(a) A composite color image of the {\it Spitzer}/MIPSGAL 24 $\mu$m (red) and {\it Spitzer}/GLIMPSE 8$\mu$m (green) emissions. (b) Same as (a), but a closeup figure toward N4 and N4W. Square symbols represent the massive star candidates identified by \citet{2013RAA....13..921L}. In particular, the larger square symbols represent S1 and S2. Crosses represent the YSOs identified by \citet{2016ApJ...822..114C}.}\label{fig:RGB_all} \end{figure} | \label{sec:Dis} \subsection{Expanding motion of the molecular gas in N4}\label{sec:Dis_exp} \citet{2013RAA....13..921L} observed N4 with $^{12}$CO ($J$=1--0), $^{13}$CO ($J$=1--0), and C$^{18}$O ($J$=1--0) and speculated that N4 is more likely an inclined expanding ring than a spherical-bubble, although they also noted that observations with higher resolution are necessary to confirm this speculation. \citet{2013RAA....13..921L} also speculated that the formation of S2 on the ring was triggered by the compression due to the expanding motion of the ring. On the contrary, \citet{2017ApJ...838...80C} observed a magnetic field derived from near-IR polarization of reddened diskless stars located behind N4. They found that the direction of the magnetic field is curved and parallel to the ring and suggested that the star formation on the ring triggered by expanding motions might not easily occur because the estimated magnetic field is strong enough ($\sim$120\,$\mu$G). We investigate the detailed velocity structure of the 25-km\,s$^{-1}$ cloud by using our approximately 3\,times high-angular resolution CO dataset. Figure \ref{fig:circ_dist}(a) shows the $^{13}$CO ($J$=1--0) integrated intensity between the velocities of 12 and 37\,km\,s$^{-1}$. Figures \ref{fig:circ_dist}(b) and \ref{fig:circ_dist}(c) show the $v$--$b$ diagram and $l$--$v$ diagram of the $^{13}$CO ($J$=1--0) emission, respectively, integrated between the blue dotted-lines in Figure\,\ref{fig:circ_dist}(a). \textcolor{black}{The lowest contour indicates $\sim 5\sigma$ level.} If the molecular gas in N4 has an expanding spherical-bubble structure, elliptical shapes should be observed in Figures \ref{fig:circ_dist}(b) and \ref{fig:circ_dist}(c) as suggested by Figure\,5 in \citet{2011ApJ...742..105A}, which is a model of an expanding spherical-bubble inside a turbulent medium. However, we can not observe clear ellipse in Figures \ref{fig:circ_dist}(b) and \ref{fig:circ_dist}(c), which is consistent with the result of \citet{2013RAA....13..921L}. On the other hand, Figure \ref{fig:circ_dist}(d) shows the $p$--$v$ diagram of the $^{13}$CO ($J$=1--0) emission along the ring with a width of 1$'$ (between the black circles in Figure \ref{fig:circ_dist}(a)). \textcolor{black}{The lowest contour indicates $\sim 5\sigma$ level.} If the molecular gas in N4 has an expanding ring structure as proposed by \citet{2013RAA....13..921L}, Figure \ref{fig:circ_dist}(\textcolor{black}{d}) should show a sinusoidal wave with a length of 2$\,\pi$ radian (one cycle) unless the expanding motion is perpendicular to the line-of-sight. However, we can not find a clear sinusoidal wave of the 25-km\,s$^{-1}$ cloud in Figure \ref{fig:circ_dist}(d), though some velocity gradients are observed. For these reasons, we concluded that the molecular gas in N4 may not be expanding. \begin{figure}[h] \begin{center} \plotone{f9_.eps} \end{center} \caption{(a) The $^{13}$CO ($J$=1--0) integrated intensity between the velocities of 12 and 37\,km\,s$^{-1}$. The green contours show the intensity of 20-cm radio continuum taken from the Multi-Array Galactic Plane Imaging Survey (MAGPIS, \cite{2006AJ....131.2525H}) archive, and are plotted by 0.75 ($\sim 5\sigma$), 1.95, 3.15, 4.35, and 5.55 mJy\,Beam$^{-1}$. Square symbols represent the massive star candidates identified by \citet{2013RAA....13..921L}. (b) The $v$--$b$ diagram of the $^{13}$CO ($J$=1--0) emission integrated between the vertical blue dotted-lines in Figure\,\ref{fig:circ_dist}(a). \textcolor{black}{Contours are plotted at every 0.018\,K\,degree from 0.018\,K\,degree ($\sim 5\sigma$).} (c) The $l$--$v$ diagram of the $^{13}$CO ($J$=1--0) emission integrated between the horizontal blue dotted-lines in Figure\,\ref{fig:circ_dist}(a). \textcolor{black}{Contours are plotted at every 0.018\,K\,degree from 0.018\,K\,degree ($\sim 5\sigma$).} (d) The $p$--$v$ diagram of the $^{13}$CO ($J$=1--0) emission along the ring with a width of 1$'$ indicated by the black circles in Figure \ref{fig:circ_dist}(a). \textcolor{black}{Contours are plotted at every 1.0\,K from 1.0\,K ($\sim 5\sigma$).}}\label{fig:circ_dist} \end{figure} \subsection{Cloud--cloud collisions in N4 and N4W as an alternative scenario}\label{sec:Dis_ccc} \subsubsection{N4} As shown in Figures\,\ref{fig:12COchmap}, \ref{fig:integ_ratio}(c), and \ref{fig:integ_ratio}(f), the 25-km\,s$^{-1}$ cloud is clearly associated with N4. The 16-km\,s$^{-1}$ cloud is also possibly associated with N4 because it has slightly elevated $R^{12}_{3210}$, as shown in Figure\,\ref{fig:integ_ratio}(d). Meanwhile, it is not certain whether the 19-km\,s$^{-1}$ cloud is interacting with the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud. $R^{12}_{3210}$ of the 19-km\,s$^{-1}$ cloud is lower than those of the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud, and hence, it seems that the 19-km\,s$^{-1}$ cloud is not interacting with the H{\sc ii} region. The location of N4 is the inner Galaxy, $l=11\fdg8$, where heavy contamination is expected in these velocities. Therefore, the 19-km\,s$^{-1}$ cloud is possibly not directly interacting with N4, but it is overlapping with other clouds at the line-of-sight. Herein, we found that the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud are connected in the $p$--$v$ diagram (Figure\,\ref{fig:pvs}) toward N4. This is a bridge feature, which is discussed as a possible observational signature of CCC by previous studies (e.g., \cite{2015MNRAS.450...10H, 2015MNRAS.454.1634H}). Figure\,\ref{fig:integ_overlay}(a) shows an integrated intensity map of the $^{12}$CO ($J$=1--0) emissions of the 25-km\,s$^{-1}$ cloud (color scale) and the 16-km\,s$^{-1}$ cloud (blue contours). The Galactic east end of the 16-km\,s$^{-1}$ cloud in the map is located at the center of the ring structure of the 25-km\,s$^{-1}$ cloud, where the massive star candidates have been identified. Figure\,\ref{fig:integ_overlay}(b) shows an integrated intensity map of the $^{13}$CO ($J$=1--0) emissions. At the Galactic west side of the 25-km\,s$^{-1}$ cloud in the map, the two clouds show spatially complementary distributions, which is also discussed as a possible observational signature of CCC (\cite{2018ApJ...859..166F}). Figure\,\ref{fig:pv_N4_N4W_1}(a) shows the $p$--$v$ diagram between B and B$'$ in Figure\,\ref{fig:integ_overlay}(a) through the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud. A bridge feature connecting the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud can be observed, and it further shows a V-shaped structure (black dashed lines). Such V-shaped structures in $p$--$v$ diagrams have been observed in other CCC objects (e.g., \cite{2018ApJ...859..166F, 2018PASJ...70S..47O}). We can also observe the 19-km\,s$^{-1}$ cloud in the $p$--$v$ diagram, but this can be determined to be distinct from the bridge feature. We here test dynamical binding of the 16- and 25-km\,s$^{-1}$ clouds. If we tentatively assume that the two clouds are separated by 6\,pc (same as lengths of the 16- and 25-km\,s$^{-1}$ clouds in N4) in space and by $9\,\times \,\sqrt{2}$ km\,s$^{-1}$ in velocity (we also assume the viewing angle of the relative motion between the two clouds as 45$^{\circ}$ to the line-of-sight), the total mass required to gravitationally bind these two clouds can be calculated as $M=\frac{rv^2}{2G}=1.1\,\times 10^5M_{\odot}$. This is larger than the total molecular mass of N4 ($2.8\,\times 10^4M_{\odot}$) estimated in Section \ref{sec:COdist}, indicating that the co-existence of the two velocity clouds in N4 can not be interpreted as the gravitationally bound system. For these reasons, we proposed a CCC between the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud in N4. After the collision, a cavity was created in the molecular clouds, which permitted the formation of one or more massive stars at the compressed layer. At present, gas near the collision interface of the 16-km\,s$^{-1}$ cloud is \textcolor{black}{broken up} and ionized via UV radiation from the massive star(s). The timescale of the collision (between the time when collision occurred and the present time) in N4 can be approximated estimated from the size of the cavity and the relative velocity between the two clouds. The size of the cavity in the $l$--$b$ plane is $\sim$3\,pc. If we assume that the relative velocity parallel to the $l$--$b$ plane is same as the relative radial velocity and that the cavity is spherical, the estimated timescale of the collision is $3\,$pc$/9\,$km\,s$^{-1}=0.2$--$0.3$\,Myrs. The red and blue triangles in Figure\,\ref{fig:integ_overlay}(a) represent Class I YSOs and Class II YSOs, respectively, and the uncolored triangles represents transitional disk YSOs (\cite{2016ApJ...818...95L}). Class I and Class II YSOs are located at the extension line of the 16-km\,s$^{-1}$ cloud elongation and at the left edge of the 16-km\,s$^{-1}$ cloud in the map. The formation of these YSOs is \textcolor{black}{most likely} triggered by the collision of the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud, although the formation of the other YSOs in N4 could not has been triggered because the age of the transitional disk YSOs is generally greater than 1\,Myr (\cite{2011ApJ...732...24C}). \subsubsection{N4W} As seen in Figures\,\ref{fig:12COchmap}, and \ref{fig:integ_ratio}(c) the 25-km\,s$^{-1}$ cloud is associated not only with N4 but also with N4W. Figure\,\ref{fig:pv_N4_N4W_2} shows the $v$--$b$ diagram of the $^{12}$CO ($J$=1--0) emission from C to C$'$ in Figure\,\ref{fig:integ_overlay}(a). We can see a diffuse component between the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud at a $b$ value of $\sim 0\fdg80$ \textcolor{black}{with the intensity of the $^{12}$CO ($J$=1--0) emission of $>5\sigma$}. Figure\,\ref{fig:N4W_12CO_chmap_3} shows the average spectra within the squares B and C in Figure\,\ref{fig:N4W_12CO_chmap_1}. Although the high-velocity wing emission of the molecular outflows from the YSOs is confined to within the area of square B, a faint emission connecting the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud can be detected within the area of square C. For these reasons, the diffuse component between the two clouds may be a bridge feature similar to that observed in N4. In other words, even in N4W, a similar scenario of massive star formation triggered by the collision of the 16-km\,s$^{-1}$ and the 25-km\,s$^{-1}$ clouds is conceivable. Because the estimated $t_{\rm dyn}$ of the outflow from the YSOs is $<$\,0.1\,Myr (Subsection \ref{sec:outflow}) and H{\sc ii} regions in N4W have not grown compared to those of N4, the molecular clouds in N4W were collided probably after the collision in N4 in this scenario. \citet{2016ApJ...822..114C} suggested the possibility that the four YSOs in N4W are coeval. The CCC scenario in N4W could explain the small age range of the reported YSOs since CCC can trigger star formation over a short time scale. We speculate that the non-uniform cloud morphology and density caused massive star formations in two places (N4 and N4W) despite the single pair of collisions. \begin{figure}[h] \begin{center} \includegraphics[width=18cm]{f10_.eps} \end{center} \caption{(a) Integrated intensity map of the $^{12}$CO ($J$=1--0) emission with a velocity range from 24.8 to 26.1\,km\,s$^{-1}$ (color scale) (the 25-km\,s$^{-1}$ cloud) and from 15.1 to 16.4\,km\,s$^{-1}$ (blue contours) (the 16-km\,s$^{-1}$ cloud). Contours are plotted every 6\,K\,km\,s$^{-1}$ from 6\,K\,km\,s$^{-1}$ ($\sim 5\sigma$). Square symbols represent the massive star candidates identified by \citet{2013RAA....13..921L}. Triangle symbols represent the YSOs identified by \citet{2016ApJ...818...95L}, and red, blue, and non-colored indicate Class I, Class II, and transitional disk, respectively. Green contours show the {\it Spitzer}/GLIMPSE 8$\mu$m intensity at 100\,MJy\,str$^{-1}$ (b) Same as (a) but for the $^{13}$CO ($J$=1--0) emission \textcolor{black}{at the red square region in (a)}. Contours are plotted every 1\,K\,km\,s$^{-1}$ from 3\,K\,km\,s$^{-1}$ ($\sim 5\sigma$). }\label{fig:integ_overlay} \end{figure} \begin{figure}[h] \begin{center} \includegraphics[width=9cm]{f11_.eps} \end{center} \caption{(a) $p-v$ diagram of the $^{12}$CO ($J$=1--0) along black axis in Figure\,\ref{fig:integ_overlay}(a) from B to B$'$. Contours are drawn at every 0.08\,K\,degree from 0.08\,K\,degree ($\sim 10\sigma$). (b) Median intensity (perpendicular to the B--B$'$ line) of the {\it Spitzer}/MIPSGAL 24 $\mu$m (red) and {\it Spitzer}/GLIMPSE 8$\mu$m (green) along the B--B$'$ line in (a) with a width of 1.2$'$. }\label{fig:pv_N4_N4W_1} \end{figure} \begin{figure}[h] \begin{center} \includegraphics[width=9cm]{f12_.eps} \end{center} \caption{$v-b$ diagram of the $^{12}$CO ($J$=1--0) from C to C$'$ in Figure\,\ref{fig:integ_overlay}(a). Contours are plotted at every 0.05\,K\,degree from 0.05\,K\,degree ($\sim 5\sigma$). }\label{fig:pv_N4_N4W_2} \end{figure} \begin{figure}[h] \begin{center} \plotone{f13_.eps} \end{center} \caption{Averaged spectra of $^{12}$CO ($J$=1--0) emission (solid line) and $^{12}$CO ($J$=1--0) emission (broken line) in the squares B (left) and C (right) in Figure\,\ref{fig:N4W_12CO_chmap_1}, respectively. }\label{fig:N4W_12CO_chmap_3} \end{figure} \subsection{Ages of the H{\sc ii} region in N4}\label{sec:Dis_age} One can calculate a dynamical age of the H{\sc ii} region using the analytical model of the D-type expansion developed by \citet{1978ppim.book.....S}. The Lyman continuum photon flux of N4 was estimated to be $log(N_{\rm ly}\,{\rm s^{-1}})=48.18$ (\cite{2016ApJ...818...95L}). The initial volume density of the gas was estimated to be approximately 4$\times$10$^3$\,cm$^{-3}$ when assuming a uniform spherical distribution with a radius of 4\,pc with a total molecular mass of $\sim 2.8\times$10$^4$\,M$_{\odot}$. In addition, we assumed an electron temperature of 8000\,K. Given these parameters, the age of the H{\sc ii} region with a radius of 1.5\,pc is estimated to be $\sim$0.4\,Myr. This is almost consistent with the age of the time scale of the CCC estimated above \textcolor{black}{0.2--0.3\,Myr}, which supports the CCC scenario that explains the formation of the massive star(s). \subsection{Massive stars in N4 and N4W}\label{sec:Dis_star} Figure\,\ref{fig:RGB_closeup} shows a closeup of Figure\,\ref{fig:RGB_all}, where the blue contours indicate the intensity of the 20-cm radio continuum taken from the Multi-Array Galactic Plane Imaging Survey (MAGPIS, \cite{2006AJ....131.2525H}) archive. As mentioned above, \citet{2013RAA....13..921L} suggested that the \textcolor{black}{most massive and luminous} star in N4 is S1, which is located at the center of the ring, and that the formation of star S2, located on the ring, was triggered by the expansion of the H{\sc ii} region. However, the brightest massive stars in the {\it Spitzer} bubbles are not necessarily located at the center (e.g., \cite{2015ApJ...806....7T, 2018PASJ...70S..45O}). In N4, \citet{2013RAA....13..921L} showed that the brightest massive star candidate in the $J$ band and the $J-H$ is S2. Figure\,\ref{fig:pv_N4_N4W_1}(b) shows a plot of the median intensity (with the direction perpendicular to the B--B$'$) of {\it Spitzer}/MIPSGAL 24 $\mu$m (red) and {\it Spitzer}/GLIMPSE 8$\mu$m (green) along the B--B$'$ line in Figure\,\ref{fig:integ_overlay}(a) with a width of 1.2$'$. Of all massive star candidates reported by \citet{2013RAA....13..921L}, the closest to the peak of the 20-cm radio continuum emission, which traces H{\sc ii} regions, is S2, as observed in Figures\,\ref{fig:pv_N4_N4W_1}(b) and \ref{fig:RGB_closeup}. For these reasons, we speculate that the \textcolor{black}{most massive and luminous} star in N4 is most likely S2\textcolor{black}{, although we can not rule out the possibility that S1 was most influential on the IR bubble morphology}. Follow-up near-IR and optical observations would reveal the position and spectral type of the massive star(s) in N4. On the contrary, in N4W, no massive star candidates were identified, although \citet{2016ApJ...822..114C} identified one Class I and three Class II YSOs in the innermost area from observations of the $J$, $H$, and $Ks$ bands. For these YSOs, the authors derived the crude lower limits of their $L_{\rm bol}$ to be $1$--$2\,\times 10^2\,L_{\odot}$, suggesting at least intermediate masses for the YSOs. Using AKARI far-IR data (60, 90, and 140\,$\mu$m) (\cite{2007PASJ...59S.389K}), we estimated the far-IR total luminosity of N4 and N4W by employing the method of \citet{2016A&A...592A.155S}. As a result, $7.9\,\times 10^4\,L_{\odot}$ and $3.7\,\times 10^4\,L_{\odot}$ were derived for N4 and N4W, respectively. Since these values correspond to approximately a single O8V star and a single O9.5V star, respectively (\cite{2005A&A...436.1049M}), there might be an embedded massive star in N4W, which has not yet been identified. Figure\,\ref{fig:sche} shows a summary of the assumed CCC scenario discussed in Subsection\,\ref{sec:Dis_ccc}, which considers the location of the massive star in N4 and the YSOs in N4W. Figure\,\ref{fig:sche}(a) shows a schematic view from the Galactic \textcolor{black}{east} at the time the collision started (a few $10^5$--$10^6$ years ago) and when the molecular clouds in N4 began to be compressed. As a result, the 16-km\,s$^{-1}$ cloud created a cavity (the ring-like structure) in the 25-km\,s$^{-1}$ cloud \textcolor{black}{as demonstrated by the numerical simulation of CCC (see Figure\,6 in \citet{2014ApJ...792...63T}). Thereafter} the massive star S2 was formed in the compressed layer according to the model proposed in a study of \citet{1992PASJ...44..203H}. Figure\,\ref{fig:sche}(b) shows a schematic view from the Galactic \textcolor{black}{east} at the present time. S2 has either ionized or \textcolor{black}{broken up} the surrounding neutral materials. The ionized gas fills up the cavity and erodes the inner surface of the cavity, which is the ring structure observed at 8\,$\mu$m. This CCC scenario is able to explain the formation of both the massive star and the ring in N4. In addition, the molecular clouds in N4W began to be compressed and YSOs were formed. \textcolor{black}{Note that, the curve of the 16-km\,s$^{-1}$ cloud in this sketched diagrams Figure\,\ref{fig:sche}(a) and \ref{fig:sche}(b) is one instance to explain the star formation history in both N4 and N4W.} Figures\,\ref{fig:sche}(c1) and \ref{fig:sche}(c2) show schematic views of the sky plane and integrated intensity map of the CO gas, respectively. \begin{figure}[h] \begin{center} \includegraphics[width=9cm]{f14_.eps} \end{center} \caption{Closeup figure of Figure\,\ref{fig:RGB_all}, but the blue contours show the intensity of 20-cm radio continuum taken from the Multi-Array Galactic Plane Imaging Survey (MAGPIS, \cite{2006AJ....131.2525H}) archive ($b<0\fdg 8$), and are plotted by 0.75 ($\sim 5\sigma$), 1.95, 3.15, 4.35, and 5.55 mJy\,Beam$^{-1}$. Triangle symbols represent the YSOs identified by \citet{2016ApJ...818...95L}. }\label{fig:RGB_closeup} \end{figure} \begin{figure}[h] \begin{center} \plotone{f15_.eps} \end{center} \caption{(a) Sketched diagrams of N4 and N4W as viewed from the Galactic \textcolor{black}{east} when the collision started. Blue and orange show the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud, respectively. Green region indicates the compressed layer between the two clouds, where star(s) form. (b) The sketched diagrams of N4 and N4W as viewed from the Galactic east at the present. Red indicates ionized region. (c1) The sketched diagrams of N4 and N4W on the sky view. (c2) Color scale shows the $^{13}$CO ($J$=1--0) integrated intensity of the 25-km\,s$^{-1}$ cloud (15\,K\,km\,s$^{-1}$). Blue contours shows the $^{12}$CO ($J$=1--0) integrated intensity of the 16-km\,s$^{-1}$ cloud (12\,K\,km\,s$^{-1}$). }\label{fig:sche} \end{figure} \subsection{Comparison of the molecular clouds and massive stars in N4 with those of the other massive-star forming regions}\label{sec:Dis_com} In Table\,\ref{tab:comparison}, we compare the properties of the colliding molecular clouds in N4 with those of the other massive star-forming regions of RCW 120, RCW 38, and W51A that are also suggested to feature CCC. {\it Spitzer} bubble RCW 120 is comparable to N4 in terms of size and its ring appearance in near-IR. RCW 38 is known as a super star cluster. \citet{2016ApJ...820...26F} suggested that the formation of multiple O-stars was triggered at the point of collision of two clouds. The spatial distributions of these two colliding clouds resemble those of the 16-km\,s$^{-1}$ cloud and the 25-km\,s$^{-1}$ cloud in N4. W51A is the one of the most active star-forming region in the Galaxy. Multiple previous studies (e.g., \cite{1998AJ....116.1856C, 2001PASJ...53..793O, 2017arXiv171101695F}) suggested that a number of velocity components in W51A have been continuously colliding with each other, resulting in active massive star formation. \citet{2018ApJ...859..166F} suggested that the molecular column density [$N({\rm H_2})$] of the colliding clouds can be an important parameter for determining the number of the end produce of O-stars. $N({\rm H_2})$ and the number of O-stars between N4 and RCW 120 were approximately the same, whereas the mass of the associated molecular clouds of RCW 120 were larger by a factor of $\sim$3. On the contrary, the number of O-stars in RCW 38 is much larger ($\sim$20), although the mass of the associated molecular clouds of RCW 38 is approximately same as that of N4. This could be attributed to the higher $N({\rm H_2})$ in RCW 38. In W51A, multiple collisions of clouds with high $N({\rm H_2})$ resulted in active massive star formation. The relationship between the $V_{\rm LSR}$ separations and the number of O-stars can not be discussed from these data. To establish a quantitative scenario for forming massive stars via a CCC, more observational studies and statistical studies are required. \begin{deluxetable*}{ccccccc} \tablenum{1} \tablecaption{Properties of the colliding molecular clouds associated with N4, RCW120, RCW 38, and W51A \label{tab:comparison}} \tablewidth{0pt} \tablehead{ \colhead{Name} & \colhead{Number of O-stars} & \colhead{Cloud Mass} & \colhead{Typical $N({\rm H_2})$} & $V_{\rm LSR}$ Separation & Age of H{\sc ii} region & References \\ \colhead{} & \colhead{} & \colhead{($10^4\ M_{\odot}$)} & \colhead{($10^{22}\ {\rm cm^{-2}}$)} & \colhead{(km\,s$^{-1}$)} & \colhead{(Myr)} & \colhead{} } \startdata N4 & $\sim$1 (O8.5--O9V$^\dagger$) & (1.7, 0.1) & (3--4, 0.3) & 9 & $\sim$0.4 & This study\\ RCW 120 & 1 (O8--O9V) & (5.0, 0.4) & (3, 0.8) & 20 & $\sim$0.2 & \cite{2015ApJ...806....7T}\\ RCW 38 & $\sim$20 O-stars & (2.0, 0.3) & (10, 1) & 12 & $\sim$0.1 & \cite{2016ApJ...820...26F}\\ W51A & $\sim$30 O-stars & (11, 13, 19, 13) & $\sim$10 each & 6--18 & several 0.1 & \cite{2017arXiv171101695F}\\ \enddata \tablecomments{$\dagger$ \cite{2016ApJ...818...95L}} \end{deluxetable*} | 18 | 8 | 1808.00709 |
1808 | 1808.09628_arXiv.txt | The gamma-ray emission detected from several microquasars can be produced by relativistic electrons emitting through inverse Compton scattering. In particular, the GeV emission detected from \cyg, and its orbital phase dependence, strongly suggest that the emitting electrons are accelerated in a relativistic jet, and that the optical companion provides the dominant target. Here, we study the effects related to particle transport in the framework of the relativistic jet scenario. We find that even in the most compact binary systems, with parameters similar to \cyg, particle transport can have a substantial influence on the GeV lightcurve unless the jet is slow, \(\beta < 0.7\). In more extended binary systems, strong impact of particle transport is nearly unavoidable. Thus, even for a very compact system such as \cyg, particle transport significantly affects the ability of one-zone models to infer the properties of the gamma-ray production site based on the shape on the GeV lightcurve. We conclude that a detailed study of the gamma-ray spectrum can further constrain the structure and other properties of the gamma-ray emitter in \cyg, although such a study should account for gamma-gamma attenuation, since it may strongly affect the spectrum above \(5\rm\,GeV\). | Microquasars (\muq) are binary systems that host a companion star and an accreting compact object (CO) from which jets are produced. Several microquasars have been detected in the GeV gamma-ray range with \ag\, and \fer\, \citep{2009Natur.462..620T,2009Sci...326.1512F,2011ApJ...733L..20W,2012A&A...545A.110P,2012A&A...538A..63B,2012MNRAS.421.2947C,2013MNRAS.434.2380M,2013ApJ...775...98B,2016A&A...596A..55Z,2017ApJ...839...84P}. The variability found in the GeV emission in some of these sources is consistent with inverse Compton (IC) scattering of stellar photons by relativistic electrons accelerated in the jets \citep[e.g.,][]{2010MNRAS.404L..55D,2016A&A...596A..55Z,2018MNRAS.479.4399Z}. The IC origin of the gamma-ray emission detected from \muq is supported by arguments based on higher efficiency of leptonic radiation mechanisms, as compared to hadronic ones, under conditions of compact binary systems \citep{2009IJMPD..18..347B}. If the dominant target photon field is provided by the stellar companion, IC scattering will be strongly anisotropic \citep[see, e.g.,][]{2005AIPC..745..359K,2008MNRAS.383..467K}, and the scattering angle will change along the orbit. This variability of the scattering angle is imprinted in the emission intensity, and may be the dominant factor shaping the GeV lightcurve \citep[e.g.,][for \cyg]{2010MNRAS.404L..55D}. The specific dependence of the scattering angle on the orbital phase is determined by the jet and counter-jet orientations, and the location of the acceleration and the emission sites in the jet. Thus, gamma-ray light curves can help in constraining the emitter location in \muq. \cyg is the brightest and best studied gamma-ray emitting \muq \citep[e.g.][]{2009Natur.462..620T,2009Sci...326.1512F}. The high luminosity of this source may favour, from energetic arguments, relativistic jet velocities, as they could alleviate the demanding energy requirements through Doppler boosting. In such a jet, the non-thermal distribution of particles and their emission would be significantly affected by relativistic effects. Nevertheless, a highly relativistic jet is somewhat in tension with \fer\, data in the context of a one-zone IC emitter \citep{2010MNRAS.404L..55D,2018MNRAS.479.4399Z}. On the other hand, radio VLBI observations of the jets of \cyg, from milliarcsecond-to-arcsecond scales (\(\sim 10-10^4\)~AU), favour an at least moderately relativistic jet \citep{2001ApJ...553..766M,2001A&A...375..476M}, which may point to an even more relativistic flow on the scales of the binary (\(\sim 0.1\)~AU). In this paper, we derive the formulas for the IC emission from a relativistic jet using the distribution function of electrons in the phase space \((\br,\bp)\), with \(\br\) and \(\bp\) being the particle spatial and momentum coordinates in the laboratory reference frame (RF), respectively. This function is a Lorentz invariant, which allows us to avoid cumbersome RF transformations {in the case when the contribution from synchrotron self-Compton (SSC) is negligible\footnote{Note that in the case of a very clumpy jets, the SSC mechanism may provide a non-negligible contribution \citep[see][for the case of \cygl]{2017MNRAS.471.3657Z}}}. This approach also allows us to obtain the results in a form that consistently describes the advection and radiation of gamma rays by particles in the case of an extended emitter. In the derivation, we account both for the transformation of the particle distribution to the laboratory frame, and for the impact of relativistic effects on the particle cooling in the plasma frame. We obtain an analytic solution for the invariant distribution function under the assumption of dominant Thomson IC losses, and numerically compute the IC radiation accounting for changes in the target density and scattering angle along the jet. We discuss the impact of the synchrotron and adiabatic losses, and characterize the conditions when synchrotron losses dominate, under which an analytic solution for the particle distribution can be obtained. An approach based on the invariant distribution function was earlier suggested to describe the beaming pattern of the external IC emission produced by blobs moving relativistically in blazar jets \citep{2001ApJ...561..111G}. This approach was later applied to study variable IC emission in binary systems \citep[see, e.g.,][]{2002A&A...385L..10K,2002A&A...388L..25G,2002A&A...393L..61R}. In contrast to these studies, in our paper we consider the emission produced in a jet which implies a different beaming pattern, as compared to an emitting blob. Another difference with the calculations presented by \citet{2001ApJ...561..111G} is that we use the invariant distribution function to describe the propagation and cooling of relativistic electrons in an extended emitter, which appears to be an important factor for interpreting the gamma-ray emission detected from gamma-ray binary systems. As compared to other models, which involve extended emitters in \muq \citep[see, e.g.,][]{2010MNRAS.403.1457V,2012A&A...538A..97V,2014MNRAS.440.2238Z,2014MNRAS.442.3243Z,2015A&A...584A..95P} and rely on the conventional approach with RF transformations, our method significantly simplifies the computation of the external IC emission. Thus, this paper allows us to extend the existing models focusing on the GeV gamma-ray emission from \muq \citep[e.g.,][]{2010MNRAS.404L..55D,2012MNRAS.421.2956Z,2018MNRAS.479.4399Z}, and to study consistently the influence of particle advection on the gamma-ray spectra and lightcurves. Under conditions typical for \muq, in the TeV energy band the Klein-Nishina regime and gamma-gamma attenuation can affect the IC scattering and propagation of gamma rays, respectively \citep[see, e.g.,][]{2009IJMPD..18..347B}. In some systems with particularly hot stellar companions, e.g. as \cyg, these effects may influence the production of GeV gamma rays \citep[see, e.g.,][]{1987ApJ...322..838P,1993MNRAS.260..681M,1997A&A...322..523B,2011A&A...529A.120C,2012MNRAS.421..512S}. Therefore, we also consider the influence of the Klein-Nishina effect on the electron transport and the impact of the gamma-gamma absorption on the spectrum adopting system parameters similar to \cyg. | We have studied the properties of the gamma-ray emitting region in a relativisitc jet in a binary system. To facilitate the interpretation of the results, we have used an approach based on the distribution function in the phase space, which is Lorentz invariant. This allows obtaining results in a compact form that permits studying the influence of different parameters in a clearer way. The main focus of the study was on the impact of advection on the gamma-ray spectrum and lightcurve. For the case of a compact production site we have obtained an analytic representation of the energy distribution of the emitting electrons. When IC cooling dominates over advection, the gamma-ray spectrum, given by Eq.~(\ref{eq:spectrum_compact}), has a simple form that allows one to determine the process that affects the variability of the emission. Namely, it contains three factors that change with orbital phase: (i) IC proceeds in the anisotropic regime, and the scattering angle varies along the orbit \citep{2008MNRAS.383..467K,2010MNRAS.404L..55D,2012MNRAS.421.2956Z}; (ii) the Doppler boosting factor, \(\left[{\Db^{2\alpha_\gamma+1}\Gamma^{-1} }\right]\), which accounts for the relativistic transformation of radiation produced in a stationary jet \citep{1997ApJ...484..108S}; and (iii) in the case of dominant IC losses, an additional factor, \(\Db_*^2\), should be introduced. The stellar photon boosting effect on cooling can be ignored if the dominant losses are due to synchrotron cooling. {Adiabatic losses can be relevant only if relativistic particles are advected along the jet over a distance in which the jet material density undergoes a significant change.} In particular, this can be the case for low-energy electrons that are subject to slower radiative losses. In the case of a (at least) mildly relativistic jet, \(\Gamma\geq2\), advection might be important for GeV emitting electrons even in the most compact binaries like \cyg. In the case of dominant radiative losses, we have obtained an analytic solution that describes the properties of non-thermal electrons in a relativistic inclined jet. This solution can however be generalized to the case when adiabatic losses are important under weak IC losses, i.e., covering a broad range of synchrotron and adiabatic losses. It is generally expected that in gamma-ray emitting \muq IC losses should dominate over synchrotron for GeV electrons \citep[see, e.g.,][]{2012MNRAS.421.2956Z}. Thus, as test cases, we have considered two cases for extended emitters: (i) dominant IC losses, which allow an analytic solution for the particle density, Eq.~\eqref{eq:extended_solution}; and (ii) the case with IC and adiabatic losses, the latter being expected in a conical jet, for which a numerical treatment has been applied. The simulations have shown that, in systems similar to \cyg, particle advection may have a significant impact on the gamma-ray lightcurve if the jet velocity is high, \(\beta\geq 0.7\). For even faster jet velocities, \(\beta\sim0.9\), one should also expect a strong transformation of the gamma-ray spectrum from different orbital phases. In a more extended system, e.g., in \cygl, advection is very important unless synchrotron losses prevent efficient particle transport (see Eq.~\eqref{eq:b_dominant}), which is probably not very realistic. In the specific case of \cyg, the stellar companion should be very hot, \(T_*\simeq10^5\rm\,K\). For such a target photon field, two QED effects may influence the electron transport and gamma-ray spectrum in the GeV energy band. The Klein-Nishana effect weakens the IC energy losses and affect the gamma-ray spectrum, and gamma-gamma absorption can significantly suppress the flux above a few GeV. To study the influence of these effects we have performed detailed calculations of the electron transport, radiation, and gamma-gamma opacity. Since in the case of \cyg, the orbital separation is comparable to the stellar radius, in the calculations of the gamma-gamma opacity we have accounted for the finite size of the optical star. The simulations show that the Klein-Nishina effect has a small impact on the intrinsic gamma-ray spectra. Unless the gamma-ray production site is located at large distance from the CO, \(x\gg3d\), the gamma-gamma attenuation should significantly affect the spectrum at multi-GeV energies, \(E_\gamma>5\rm\,GeV\). To summarize, we have performed a detailed study of the IC process in realistic jets in compact binary systems. The performed study has revealed that the particle advection along the jet might be important even in a very compact binary system, e.g., in \cyg. In systems similar to \cygl, advection should be accounted for even in the case of a weakly relativistic jet. If adiabatic losses are weak, which would be the case, e.g., in cylindrical jets, advection can impact significantly the gamma-ray emission, potentially leading to a strong dependence of the gamma-ray spectrum shape on the orbital phase. For advection in a conical jet, adiabatic losses weaken the effects on the spectrum. Independently of the dominant cooling channel, advection results in a significant weakening of the orbital phase dependence. Thus, if the properties of the accelerator in \cyg and \cygl are similar, one should expect differences in the orbital phase dependency of the GeV emission between these two systems. {To illustrate the relevance of this effect, in Fig.~\ref{fig:cygx1_lc} we show the lightcurves computed for a system similar to \cygl (the temperature and luminosity of the optical star are taken as \(T_*=3\times 10^4\rm\,K\) and \(L_*=8\times10^{38}\,\ergs\), respectively; the CO was assumed to be in a circular orbit with \(d=3.2\times10^{12}\rm \,cm\)). The IC emission shown in Fig.~\ref{fig:cygx1_lc} was averaged over two orbital phase bins: \(|\phi|<0.25\) and \(|\phi|>0.25\), the orbit being \(-0.25<\phi<0.75\)). The injection point was assumed to be located at \(x_0=4d\), and the injection spectrum and jet velocity were assumed to be \(\propto\ve^{-4}\) and \(\beta=0.5\), respectively. The orbital inclination was selected to be \(i_\textsc{orb}=\pi/3\) and the figure includes only the contribution from the jet (i.e., the counter-jet emission is not accounted for because it is expected to be relatively small and to weaken the orbital phase dependence even stronger). The data points are from \citet{2017MNRAS.471.3657Z}, and the open and filled squares correspond to the emission expected from a CE and a EE, respectively. The adiabatic losses were assumed to be weak and the magnetic field set to \(B=0\), so the dominant cooling mechanism is the Thomson scattering. As seen from Fig.~\ref{fig:cygx1_lc}, the advection may provide a possible explanation for a weaker orbital phase dependence of the GeV emission from \cygl, and alleviate the requirement for a SSC contribution. \citet{2017MNRAS.471.3657Z} studied the broadband emission and gamma-ray variability in \cygl for the parameter space with \(x_0\ll d\). In that parameter space, it was found that external Compton models, including those with an extended emitter, are incompatible with the \fer emission from \cygl, and a better agreement can be achieved if one assumes a highly clumpy jet, which enhances the SSC emission. In the case of a conical jet \citep[as was assumed by][]{2017MNRAS.471.3657Z}, adiabatic losses lead to considerable cooling at distances \(x\sim x_0\), so plasma cools down on a scale in which the IC regime does not change for \(x_0\ll d\). Thus, advection cannot considerably affect the IC lightcurve for parameters adopted by \citet{2017MNRAS.471.3657Z}. The simulations shown in Fig.~\ref{fig:cygx1_lc} show that for \(x_0\geq d\), advection can improve the agreement between the observational data from \cygl and predictions of models that account for stellar IC only. We note, however, that the calculations presented in Fig.~\ref{fig:cygx1_lc} are for illustrative purposes only and cannot substitute a detailed broadband study (as the one presented in \citealt{2017MNRAS.471.3657Z}). } The influence of advection on the gamma-ray light curve also significantly affects the ability of one-zone models \citep{2010MNRAS.404L..55D,2012MNRAS.421.2956Z,2018MNRAS.479.4399Z} to accurately infer the properties of the gamma-ray production sites even in the case of the most compact binary systems. For example, \citet{2018MNRAS.479.4399Z} suggested that the \fer emission in \cyg is best explained by IC scattering from a production site located at \(x=2.3d\) in a jet with \(\beta=0.73\). As shown by our simulations, for this location of the production site the transport effects might be relevant. We present in this paper the theoretical framework and discuss the impact of advection on the GeV gamma-ray spectrum and lightcurve. A detailed application to the gamma-ray data of \cyg will be presented in a forthcoming paper. \begin{figure} \includegraphics[width=\columnwidth]{cygx1_lc} \caption{Lightcurves of the IC emission from a system similar to \cygl: \(T_*=3\times 10^4\rm\,K\), \(L_*=8\times10^{38}\,\ergs\),\(d=3.2\times10^{12}\rm \,cm\) (circular orbit), \(\beta=0.5\), and \(i_\textsc{orb}=60^\circ\). The jet was assumed to be perpendicular to the orbital plane, \(\alpha=\pi/2\). The case with weak adiabatic losses is shown with filled squares and the emission expected from a CE is shown with open squares. The data points are adopted from \citet{2017MNRAS.471.3657Z}. Other model parameters were set as \(B=0\) and \(x_0=4d\).} \label{fig:cygx1_lc} \end{figure} | 18 | 8 | 1808.09628 |
1808 | 1808.00015_arXiv.txt | { Large stellar surveys are sensitive to interstellar dust through the effects of reddening. Using extinctions measured from photometry and spectroscopy, together with three-dimensional (3D) positions of individual stars, it is possible to construct a three-dimensional dust map. We present the first continuous map of the dust distribution in the Galactic disk out to 7 kpc within 100 pc of the Galactic midplane, using red clump and giant stars from SDSS APOGEE DR14. We use a non-parametric method based on Gaussian Processes to map the dust density, which is the local property of the ISM rather than an integrated quantity. This method models the dust correlation between points in 3D space and can capture arbitrary variations, unconstrained by a pre-specified functional form. This produces a continuous map without line-of-sight artefacts. Our resulting map traces some features of the local Galactic spiral arms, even though the model contains no prior suggestion of spiral arms, nor any underlying model for the Galactic structure. This is the first time that such evident arm structures have been captured by a dust density map in the Milky Way. Our resulting map also traces some of the known giant molecular clouds in the Galaxy and puts some constraints on their distances, some of which were hitherto relatively uncertain. } | Attempts to map our Milky Way date back to the 18th century. One of the most important works was by William Herschel, who constructed a map of the Milky Way by counting stars in more than 600 different lines of sight. He concluded that the Milky Way is a flattened disk and the Sun is located very close to the centre \citep{Herschel75}. Jacobus Kapteyn improved Herschel's map using photometric star counts and parallaxes and proper motions of stars and estimated the size and shape of the Milky Way \citep{Kapteyn22}. However, neither Kapteyn nor Herschel were aware of the importance of the extinction of light by interstellar dust, which resulted in erroneous estimates of the size and shape of the Galaxy. Robert Trumpler found the first evidence of the interstellar reddening and demonstrated how significant the interstellar dust extinction is \citep{Trumpler30} that makes distant objects look fainter than they would in the absence of dust. Recognising the effects of the interstellar dust on the observations, many attempts were made by astronomers to map the extinction in the Milky Way. One of the significant studies in this regard is the work by \citet*{Schlegel98} who mapped the dust column density using far-infrared dust emission from the IRAS and COBE satellites. A more sensitive 2D map with higher resolution was made by \cite{Planck14} using a similar method to \citet*{Schlegel98}. However, for many Galactic studies, 2D measurements do not suffice; we often need an estimate of the three-dimensional location of the emitting/extinguishing sources in the Galaxy. Moreover, dust plays an important role in creating and shaping the Galaxy and forming stars and planets. Knowing the local distribution of dust provides valuable information about the Galactic structure and the probable sites of star formation. This opened a new area of studies in which various groups have been trying to map the Galactic dust extinction in 3D using different data sets and techniques. \cite{Marshall06} presented a 3D extinction model in the Galactic plane using a Galactic model and the near infrared colour excess to estimate distances and extinctions. \cite{Schlafly10} used the blue tip of the distribution of stellar colours to measure the colour of the main sequence turnoff stars and measured the reddening of stars in the SDSS-III footprint. \cite{Sale12} developed a hierarchical Bayesian model to simultaneously infer extinction and stellar parameters from multi-band photometry, and \cite{Sale14} used this method to build a 3D extinction map of the northern Galactic plane using IPHAS photometry. A similar probabilistic method was developed by \citet*{Hanson14} to estimate the effective temperature and extinction based on a method previously introduced by \citet*{CBJ11}. They used a Bayesian framework to account for the degeneracy between extinction and stellar effective temperature to produce a 3D extinction map of the Galactic high latitudes (b > $\sim30^{\circ}$) using SDSS and UKIDSS. \cite{Hanson16} then used photometry from Pan-STARRS1 and Spitzer Glimpse surveys to map the dust extinction in the Galactic plane. \cite{Green14} introduced a method similar to \cite{Sale12} to determine dust reddening from stellar photometry which was then used by \cite{Schlafly14} to map the dust reddening of the entire sky north of declination $-30^{\circ}$. This was also used later by \cite{Green15} to build a 3D map of dust reddening for three-quarters of the sky using Pan-STARRS1 and 2MASS. \cite{Green18} recently introduced an updated version of the map using a more accurate extinction law and additional new data from Pan-STARRS1. The main drawback of these methods is that they treat each line of sight (l.o.s) independently from one another. This creates artefacts and discontinuities in their results. \cite{Vergely10} used a method with a smoothing kernel to account for gaps in the data, and mapped the dust opacity (mag/pc) in the Sun's vicinity. A similar approach was taken by \cite{Lallement14} who presented a 3D map of the local opacity. They later updated this map in \citet{capitanio17} using distance information from Gaia TGAS and colour excess estimates from diffuse interstellar bands (DIBs) from SDSS/APOGEE spectra, adopting a low-resolution map based on Pan-STARRS1 reddening measurements as a prior. \citet*{SaleM14} introduced a new method to map the Galactic extinction and dust in which the logarithm of the extinction (log A) is modelled as a Gaussian random field. Its covariance function has a Kolmogorov-like power spectrum which is motivated by a physical model of the interstellar medium. Dust is also modelled as a semi-stationary random field which produces a log A distribution that is very close to Gaussian. Evidence for spiral structure in the Milky Way dates back to 1951 when W.W. Morgan and collaborators determined the distances towards emission regions \citep{Oort52,Morgan53}. This was confirmed shortly after by the discovery of 21 cm radio observations \citep{Hulst54,Morgan55}. Despite several attempts at 3D dust mapping, none of the current dust maps reveal the Galactic spiral arm structure. This is in contrast with the fact that spiral arms are rich in gas and dust where many stars are formed \citep{Kennicutt11, Schinnerer17}. The reason for this failure of extinction maps is mainly due to the lack of precise distance measurements as well as the assumptions behind dust mapping techniques. Most of the aforementioned maps illustrate dust extinction or reddening which is an integrated property, and so cannot trace local properties of the Galaxy. In addition, many of these methods treat each l.o.s separately such that no information is propagated from neighbouring points, resulting in discontinuities between neighbouring lines of sight in the resulting maps. We address issues of previous 3D dust extinction maps in our approach by using a non-parametric method to capture complex structures present in the observed data. Furthermore, we directly map dust density - which represents local properties of the Galaxy - rather than the integrated extinction. We take into consideration the correlation between dust points in space using an isotropic Gaussian process that provides a continuous map without l.o.s artefacts. In \citet{Rezaei_Kh_17} we described our approach in detail. We have since improved the method in some ways: these we explain in section \ref{method}. In section \ref{data} we explain our data selection from the Sloan Digital Sky Survey IV's Apache Point Observatory Galactic Evolution Experiment \citep[APOGEE-2,][]{Blanton17, Majewski17, Abolfathi17} which, being an infrared survey, enables to probe to greater distances and/or through dustier regions. We show our map of the Galactic disk in section \ref{map} and discuss the limitations and future possible improvements in section \ref{discussion}. | We have presented a map of the Galactic disk using RC stars and giants from APOGEE DR14. This is the first time that such a continuous map of the dust in the disk is presented out to 7 kpc from the Sun. We showed that some of the dust features in our map are possibly associated with spiral arms in our Galaxy. However, our result is limited by the spatial coverage of the input data and observational artefacts due to the APOGEE target selection, plus a limited distance precision of 5\%. Future data from APOGEE south and SDSS-V will be great compliments to the current data by covering the southern hemisphere and providing continuous observation. In addition, the upcoming Gaia DR2 data will be able to cover some of the missing l.o.s in our current APOGEE sample, although the fact that it is an optical survey limits the depth it can probe in dusty regions. | 18 | 8 | 1808.00015 |
1808 | 1808.02360_arXiv.txt | {One of the main problems for extracting the Cosmic Microwave Background (CMB) from submm/mm observations is to correct for the Galactic components, mainly synchrotron, free - free and thermal dust emission with the required accuracy. Through a series of papers, it has been demonstrated that this task can be fulfilled by means of simple neural networks with high confidence. The main purpose of this paper is to demonstrate that the CMB BB power spectrum detected in the Planck 2015 polarization maps is present in the improved Planck 2017 maps with higher signal-to-noise ratio. Two features have been detected in the EB power spectrum in the new data set, both with S/N $\sim$4 . The origin of these features is most likely leakage from E to B with a level of about 1 per cent. This leakage gives no significant contribution to the detected BB power spectrum. The TB power spectrum is consistent with a zero signal. Altogether, the BB power spectrum is not consistent with the 'canonical' tensor-to-scalar models combined with gravitational lensing spectra. These results will give additional strong arguments for support to the proposed polarization satellite projects to follow up on the Planck mission .} | Since the discovery of the Cosmic Microwave Background radiation (CMB) by Penzias and Wilson(1965), investigations of this radiation has been a central feature in order to get new information about the earliest evolution of the Universe. Due to technical limitations, until recently most of the observational effort has been concentrated to obtain very accurate temperature measurements. Rees (1968) showed that polarization observations of CMB on larger scales could be a very important way to study the very early history of the Universe. Symmetries in the production and growth of the polarization signal are constraining the configurations of the CMB polarization. Density (scalar) perturbations produce temperature (T) fluctuations and E (curl - free) polarization modes, while tensor (gravitational waves) produce both T, E and B (divergence free) modes. It is generally assumed that the initial inhomogeneities in the Universe were Gaussian distributed. Linear theory predicts that the CMB fluctuations are also Gaussian, and that the CMB spectrum can be fully described by 4 power spectra TT, EE, BB and TE while the TB and EB power spectra should zero due to parity constraints (e.g. Kamionkowski et. (1997). CMB polarization measurements were provided by the WMAP satellite, the final results given in Bennett et al. (2013). For r, the tensor-to-scalar ratio, Bennett et al. found, for WMAP-only data, an upper limit of 0.38. Ade et al. (2014) report a detection of B-modes in a 400 sq. degree area on the sky with the BICEP2 instruments, observing from the South Pole. These observations were done at only one frequency, 150 GHz, implying that their estimate of polarized Galactic emission in this small area on the sky is uncertain. Ade et al. (2015) attacked this problem by combining BICEP2 + Keck 150 GHz data and Planck 30 GHz-353 GHz observations in this area. This investigation determined the amplitude of the lensing spectrum 1.12 $\pm$ 0.18, relative to the standard $\lambda$CDM model, and an upper limit on the tensor-to-scalar ratio r $<$ 0.13, with 95 percent confidence. The Planck Collaboration XV (2016) determined the CMB lensing potential at a level of 40$\sigma$, while the Planck Collaboration XIII (2016) found an upper limit of 0.11 on the tensor-to-scalar ratio. For the Planck Collaboration, a key issue has always been to carefully investigate the data flows from the detectors and find ways to correct for systematic errors. Since the release of the Planck data in 2015, this effort has been continued and significant improvement in the final Planck frequency maps has been obtained. Since no new observations have been obtained between 2015 and 2017 , the improvements are mainly due to removal of remaining systematic errors. In a series of papers, the capabilities of neural networks for dealing with mm/submm observations have been investigated by N{\o}rgaard - Nielsen \& J{\o}rgensen (2008), N{\o}rgaard - Nielsen \& Hebert (2009), N{\o}rgaard - Nielsen (2010), and N{\o}rgaard - Nielsen (2012). The last two papers showed, by using data from the WMAP satellite, that simple neural networks can extract the CMB temperature and polarization signals with excellent accuracy. In N{\o}rgaard - Nielsen (2016, hereafter NN1) the Planck polarization frequency maps, released in 2015, the Stoke Q and U parameters were extracted by means of simple neural networks. The BB power spectrum was detected in 100 $\leq$ l $\leq$ 275 with S/N = 4.5. It was demonstrated that the contribution from Galactic emission and remaining systematic errors in the maps were very small, but they could not be completely ruled out. Due to the improvement in the Planck 2017 polarizations maps, it is feasible to repeat the 2016 analysis. As in NN1, the this paper is concentrated on the reliability of the detected polarization power spectra. The structure of the paper is the following: Sect. 2 and 3 give a short overview of the different analysis tools applied in NN1, the power spectra from the extracted Q and U maps are presented in Sect. 4, while the fully calibrated power spectra are shown in Sect. 5, the contamination of the power spectra is discussed in Sect. 6. Conclusions are given in Sect.7 . | It has been demonstrated that with the improved accuracy of the final Planck polarization maps compared the 2015 release, the detection of the BB power spectrum in NN1 is confirmed, with a higher confidence. Possible contamination from Galactic emission and remaining systematic errors in the Planck frequency maps has been ruled out. Two features in the EB power spectrum have been found each detected with a S/N $\sim$4 . At this stage, the most likely origin of these features is leakage from E modes to B modes of the order of 1 per cent. This level of leakage gives no significant contribution to the detected BB power spectrum. The TB power spectrum is found to be consistent with a zero spectrum. The confirmation of the BB power spectrum will, no doubt, give new strong arguments for the proposed polarization missions to follow up on Planck. | 18 | 8 | 1808.02360 |
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