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1808 | 1808.09558_arXiv.txt | Chromospherically sensitive atomic lines display different spectra in stellar active regions, spots, and the photosphere, raising the possibility that exoplanet transmission spectra are contaminated by the contrast between various portions of the stellar disk. To explore this effect, we performed transit simulations of G and K-type stars for the spectral lines \ion{Ca}{2} K at 3933 \AA, \ion{Na}{1} 5890 \AA, \ion{H}{1} 6563 \AA\ (H$\alpha$), and \ion{He}{1} 10830 \AA. We find that strong facular emission and large coverage fractions can contribute a non-negligible amount to transmission spectra, especially for H$\alpha$, \ion{Ca}{2} K, and \ion{Na}{1} D, while spots and filaments are comparatively unimportant. The amount of contamination depends strongly on the location of the active regions and the intrinsic emission strength. In particular, active regions must be concentrated along the transit chord in order to produce a consistent in-transit signal. Mean absorption signatures in \ion{Na}{1} and H$\alpha$ for example, can reach $\approx 0.2\%$ and 0.3\%, respectively, for transits of active latitudes with line emission similar in strength to moderate solar flares. Transmission spectra of planets transiting active stars, such as HD 189733, are likely contaminated by the contrast effect, although the tight constraints on active region geometry and emission strength make it unlikely that consistent in-transit signatures are due entirely to the contrast effect. \ion{He}{1} 10830 \AA\ is not strongly affected and absorption signatures are likely diluted, rather than enhanced, by stellar activity. \ion{He}{1} 10830 \AA\ should thus be considered a priority for probing extended atmospheres, even in the case of active stars. | \label{sec:intro} Transmission spectroscopy has been the workhorse for measuring the physical properties of exoplanet atmospheres, probing from the deep molecular layers of hot planets \citep{sing16} out to the thermosphere \citep{redfield08,wyttenbach15} and beyond to the unbound exosphere \citep{vidal03,ehren15}. These observations have revealed a variety of molecular \citep[e.g.,][]{knutson07,snellen10,deming13,kreidberg15,brogi16} and atomic species in exoplanet atmospheres \citep[e.g.,][]{jensen11,pont13,cauley15,wilson15,wyttenbach17,casasayas17,spake18}, detailed the presence of cloud layers \citep{kreidberg14}, and even probed the dynamics of bound and unbound material \citep{bourrier15,louden15,brogi16}. The \textit{James Webb Space Telescope} and upcoming extremely large ground-based telescopes will greatly expand the sample of planetary atmospheres that can be recorded in transmission. Exoplanet transmission spectra are always contaminated by star spots and faculae to some degree: the stellar disk is heterogeneous and the weighting of the integrated in-transit signal towards the unocculted regions of the stellar disk can produce spurious features in the transmission spectrum \citep{berta11,sing11,cauley17a,rackham18}. We hereon refer to this phenomenon as the \textit{contrast effect} due to its origin in the stark differences between the spectra of various active region features. Time-variable levels of stellar activity, as opposed to the effects induced on the observed spectrum by the planet's shadow, can also impact transmission spectra created by combining data from different epochs \citep{zellem17}. While more attention has recently been paid to the magnitude of the contrast effect, which, for example, has been used to estimate faculae coverage for GJ 1214 \citep{rackham17} and possible contamination of H$\alpha$ transmission spectra for HD 189733 b \citep{cauley17a}, a more complete understanding is needed of the magnitude of contrast contamination in exoplanet transmission spectra. Progress on this front has been made by \citet{rackham18}, who showed how active regions and spots on M-dwarfs can affect the strength of molecular features in the transmission spectra of small rocky planets. For many faculae and spot configurations, important molecular features, such as O$_2$, H$_2$O, and CO$_2$, can be contaminated at the level of $\approx 10-30\%$. These results highlight the need for stronger constraints on facular and spot coverage fractions in order to interpret transmission spectra of transiting planets around M-dwarfs. While molecular features such as H$_2$O and CO are observed at pressures of $\approx 1$ bar in exoplanet atmospheres \citep[e.g.,][]{kreidberg15}, the cores of atomic lines such as \ion{Na}{1} D, H$\alpha$, and \ion{He}{1} 10830 \AA\ sample pressures of $\approx 1$ $\mu$bar at higher altitudes \citep{huang17,oklopcic18}. Atomic transitions were the first detections in exoplanet atmospheres \citep{charbonneau02,redfield08,snellen08} and continue to be important diagnostics of the thermosphere \citep[e.g.,][]{cauley16,barnes16,cauley17a,cauley17b,chen17,khalafinejad17,wyttenbach17,casasayas17}. Recently, \citet{spake18} reported the first detection of helium in the extended atmosphere of WASP-107 b, confirming the potential of the \ion{He}{1} 10830 \AA\ line as a probe of hot planet exospheres, as suggested by early theoretical studies in atmospheric characterization \citep{seager00}. High-resolution observations of atomic lines can also provide information on velocity flows in the atmosphere \citep[e.g.,][]{wyttenbach15,louden15,cauley17a} and cross-correlation analysis of high-resolution molecular absorption can yield constraints on planetary rotation \citep{snellen10,snellen14,brogi16}. If non-negligible for hot Jupiter systems, the contrast effect can contaminate the magnitude of the measured absorption and may bias cross-correlation signatures towards active region features. In this paper we explore the effect of faculae and spots on the strength of observed atomic absorption features in exoplanet transmission spectra. We focus on G and K stars and spectral lines which have a significant contribution from the chromosphere, specifically the transitions of \ion{Ca}{2} K at 3933 \AA, the \ion{Na}{1} 5896 \AA\ component of the \ion{Na}{1} D doublet, \ion{H}{1} 6563 \AA\ (H$\alpha$), and \ion{He}{1} 10830 \AA. The details of the simulations are outlined in \autoref{sec:model} and the model results are given in \autoref{sec:results}. Included in \autoref{sec:results} is a transit of the resolved solar disk in order to provide some context for the rest of the simulation parameters. A discussion of how the results compare with observations is presented in \autoref{sec:discussion} and a brief summary of our conclusions is given in \autoref{sec:conclusion}. | \label{sec:conclusion} We have explored how stellar activity in the form of spots and bright facular or plage regions can contribute to the high-resolution optical transmission spectra in chromospherically active lines for giant planets. Overall, the emission from stellar active regions in the simulated lines has a weak effect on the transmission spectrum and varies little with $T_\text{eff}$. Only specific geometries, where the active region distribution is within $\approx 5^\circ$ of the planet's transit chord, combined with coverage fractions $\gtrsim 20\%$ and active region emission strengths $2-3\times$ the photospheric line strength can produce signatures similar to those observed for certain hot planet systems. In particular, observed H$\alpha$ and \ion{Na}{1} D absorption can most likely be attributed to the planet's atmosphere in the case of HD 189733 b, although some of the signal probably originates in stellar active regions, especially in the case of H$\alpha$. \ion{He}{1} 10830 \AA\ is a promising exosphere diagnostic \citep{spake18} and we find that atmospheric absorption should be depressed relative to the true values due to \ion{He}{1} 10830 \AA\ being in absorption in stellar chromospheres. However, the effect is on the order of $\approx 0.1\%$ even for active region coverage fractions of $\approx 0.4$, suggesting that stellar activity should be unimportant for exoplanets with moderate predicted \ion{He}{1} 10830 \AA\ absorption \citep[e.g., GJ 436 b and HD 209458 b;][]{oklopcic18}. This strengthens the case for the utility of the 10830 \AA\ line as a diagnostic of exoplanet atmospheres. The era of extremely large telescopes (ELTs) will enable high-resolution transmission spectra of super-Earths and small rocky planets. The effects of planets transiting active regions scales with the value of $(R_\text{p}/R_*)^2$, suggesting that the relative magnitude of the contrast effect should be similar for super-Earths and rocky planets. However, transmission spectrum light curves will likely exhibit higher levels of temporal variability since the relative size of the planet to spots and active regions decreases, increasing the frequency with which the planet transits individual active regions. Simulations of the contrast effect for super-Earths and rocky planets should be pursued. While we have attempted to explore a broad parameter space for giant planet transits of active stellar surfaces, we caution against specific comparisons of exoplanet systems with absorption values derived here. More precise knowledge of the active region distributions and emission strength for exoplanet host stars is needed to reach firmer conclusions about the absolute contribution of active regions to exoplanet transmission spectra. Magnetic mapping and modeling of faculae and spot contributions to the spectra and brightness variations of planet hosting stars will be useful in this respect \citep[e.g.,][]{dumusque14,herrero16,fares17}. Non-LTE effects should also be included in order to produce more precise estimates of the contrast effect in specific spectral lines. \bigskip {\bf Acknowledgments:} We thank the anonymous referee for their comments and suggestions, which helped improve the manuscript. This work is supported by NASA Origins of the Solar System grant No. NNX13AH79G (PI: E.L.S.). A portion of this work is also supported by the National Science Foundation through Astronomy and Astrophysics Research Grant AST-1313268 (PI: S.R.). CD, CK, and MV were supported by grant DE 787/5-1 of the Deutsche Forschungsgemeinschaft (DFG). This work has made use of NASA's Astrophysics Data System. Vacuum Tower Telescope in Tenerife and ChroTel are operated by the Kiepenheuer-Institute for Solar Physics, Freiburg, Germany, at the Spanish Observatorio del Teide, of the Instituto de Astrof{\'i}sica de Canarias. The ChroTel filtergraph has been developed by the Kiepenheuer-Institute in co-operation with the High Altitude Observatory in Boulder, CO, USA. \software{SPECTRUM, \citet{gray94}, http://www.appstate.edu/~grayro/spectrum/spectrum.html} | 18 | 8 | 1808.09558 |
1808 | 1808.05540_arXiv.txt | {Recently reported coincidences between high-energy neutrino events and major blazar outbursts reinforce the relevance of lepto-hadronic emission models for blazars. We study the influence of physical parameters on the neutrino output modeling blazar spectral energy distributions self-consistently assuming a relativistically propagating acceleration zone surrounded by a larger cooling zone. We find that the gross features of the spectral energy distribution can readily be explained with the model. A rigorous test requires time-resolved measurements of blazar spectral energy distributions during an outburst and high-statistics neutrino measurements to discriminate the leptonic and hadronic emission components.} | Active Galactic Nuclei (AGN) with radio jets are promising candidates for generating high-energy neutrinos with a flux that exceed the atmospheric flux at energies of around 100~TeV \citep{mannheim1995}. It is commonly adopted that particles are accelerated to relativistic energies in localized regions in the jet, presumably due to shock acceleration, producing non-thermal emission across the entire observable electromagnetic spectrum. The emission from objects that have their jet pointed towards Earth is boosted by the relativistic bulk motion of the emission regions. These objects are highly time-variable and therefore coined ``blazars'' \citep{angel1980, schlickeiser1996}. The spectral energy distribution (SED) of blazars typically exhibits two broad bumps in a log$\nu$-log$\nu$F$_{\nu}$ diagram. The low-energy bump is assumed to result from synchrotron emission by electrons, but the high-energy bump can be explained by either a leptonic or a hadronic scenario \citep[e.g.][]{mannheim1993, dermer1997, sikora2009, boettcher2013}. In the leptonic case the X-ray and $\gamma$-ray emission can be produced through Inverse-Compton scattering, where photons scatter off electrons and gain more energy. If this process occurs on the synchrotron photons produced by the same population of electrons, it is called synchrotron-self Compton (SSC), otherwise, in the presence of an external photon field, it is external Compton (EC) emission. If protons are present in the jet, photo-hadronic interactions can take place. The resulting pions from these interactions decay and cause particle cascades that produce $\gamma$-rays, electrons, positrons, muons and also neutrinos \citep{mannheim1989}. Because neutrinos are of neutral charge and nearly massless, they move undisturbed through space, while other particles and photons created in the jet get deflected by magnetic fields or can be absorbed, respectively. As both scenarios describe the SEDs of many sources equally well, a distinction could be made for a neutrino detection that can be traced back to a specific AGN.\\ The large-volume Cherenkov detector IceCube, which is built in the Antarctic ice at depths from 1450 to 2450\,m, can detect neutrinos in a range from TeV to PeV energies \citep{icecube2006}. Depending on the neutrino flavour, the detected neutrino event has a showerlike or a tracklike appearance for an electron neutrino or a muon neutrino, respectively. While for a cascade-like event the energy of the neutrino can be constrained well, the angular resolution is better for a track-like event. So far, only a few petaelectron neutrinos have been detected. The neutrino detection of the so-called neutrino "Big Bird" (formally high-energy starting event 35) was a cascade-like event, which had a positional uncertainty of $15.9^{\circ}$. \citet{kadler2016} showed that the field of interest contained 20 $\gamma$-ray bright AGN, but the blazar PKS B1424$-$418, which showed a major outburst in the months around the detection of the neutrino and it's calorimetric output was sufficiently high to explain the measured neutrino event. The recently detected very-high-energy event 170922A is a track-like event that has been spatially and temporally coincident with an increased $\gamma$-ray activity of the blazar TXS\,0506+056, detected by Fermi/LAT \citep{atelfermi}. Several multiwavelength follow-up observations confirmed an increase of X-ray \citep{atelswift} and optical activity \citep{atelasas}. MAGIC also detected VHE $\gamma$-rays after the neutrino event \citep{atelmagic}, while H.E.S.S. could not detect any significant $\gamma$-radiation from a point source located in the uncertainty area of the neutrino event \citep{atelhess}.\\ The blazar TXS\,0506+056 has a redshift of $z=0.3365$ \citep{paiano2018}. The classification of this source is unclear yet as \citet{bllac} identified the source to be a BL Lac according to optical observations, while \citet{crates} state that TXS\,0506+056 is a flat spectrum radio source. The SED of TXS\,0506+056 is shown in Fig.~\ref{fig:archivedata} constructed from archival (non-simultaneous) data. Although the source is present in several surveys and has been observed since 1986, TXS\,0506+056 has not been of special interest so far. \begin{figure}[t] \centerline{\includegraphics[width=.48\textwidth]{archive_SED_TXS0506}} \caption{Historical SED of TXS\,0506+056, using data from the time range 1986 to 2016. Radio observations (red) have been performed by ATCA \citep{atca}, CGRaBS \citep{cgrabs}, CLASSCAT \citep{classcat}, CRATES \citep{crates}, the Green Bank Telescope \citep{gbt1, gbt2, gbt3, gbt4}, the NRAO VLA Sky Survey \citep{nvss}, the Parkes-MIT-NRAO Survey \citep{pmn1, pmn2}, OVRO \citep{ovro1, ovro2}, Planck \citep{planck1, planck2, planck3}, the Texas Interferometer \citep{texas}, VERA \citep{vera}, VLBA \citep{vlba, mojave} and the VLBI Space Observatory Program \citep{vsop1, vsop2}. Optical and near-infrared observations (yellow) have been made by the Kitt Peak National Observatory \citep{kittpeak}, the Swift Satellite \citep{swift} and 2MASS \citep{2mass}. UV observations (purple) were performed by GALEX \citep{galex} and Swift \citep{swift}. Observations in the X-rays (blue) has been done by ROSAT \citep{rosat2,rosat1}. $\gamma$-ray data (green) is from all catalogs from Fermi/LAT \citep{fermi1fgl, fermi2fgl, fermi3fgl} and ARGO2LAC \citep{argo}.\label{fig:archivedata}} \end{figure} | The long-standing debate about the relative contributions of hadronic versus leptonic emission components in AGN jets is far from being settled, but the detection of neutrinos in the PeV energy regime can help to answer this question as AGN jets are one of the most probable accelerators to produce particles to sufficiently high energies. The self-consistent model employed here, simultaneously treats synchrotron-self Compton and photohadronic processes together with particle acceleration to study the blazar SED. We find that several parameters can change the shape and intensity of the SED, leading to very different expected neutrino fluxes. Until high-statistics measurements will become available, time-resolved studies of blazar spectral energy distributions are a promising avenue to resolve the issue in the frame of the model assumptions (Fermi acceleration at relativistically moving shocks), emphasizing the need for coordinated multi-frequency campaigns for blazar observations. | 18 | 8 | 1808.05540 |
1808 | 1808.07897_arXiv.txt | Testing General Relativity and exploring possible departures has received further input with the possibility to do so through gravitational waves emitted in strongly gravitating/highly dynamical scenarios and also through the availability of exquisitely sensitive cosmological observations. However, most extensions suffer from severe pathologies at the mathematical level which have stymied a thorough exploration of putative theories. With the aid of a model problem which captures typical pathologies, we explore suggested methods to control them. We find that the approach that modifies the equations to control higher-order gradients is both robust and efficient. | The availability of increasingly sensitive cosmological and astrophysical data is accompanied by further scrutiny on General Relativity (GR) as the theory of gravity governing the universe (e.g.~\cite{Will:2014bqa,Freire:2012mg,Baker:2012zs,Yunes_Siemens13,Berti_etal15,Yunes_etal16}). GR continues to successfully meet tests so far enabled by such data; indeed, examples include GR's successful role in $\Lambda$CDM (e.g.~\cite{Aghanim:2018eyx}), binary pulsar timing (e.g.~\cite{Freire:2012mg}), and gravitational waves from compact binary systems (e.g.~\cite{Abbott_etal16}). Nevertheless GR should eventually show cracks\footnote{Though a part of the theoretical physics community argues this is already the case due to the need for dark matter and dark energy.} and the search for possible deviations together with their physical implications, are greatly enhanced through theoretical analysis of putative extensions to GR. Of particular interest is the highly dynamical, strongly gravitating regime which, arguably, presents the likeliest scenario to detect such deviations. The analysis in such regimes is however hindered by several facts. First, it is yet unclear which specific theory (theories) one should focus on. Many theories have been proposed motivated by quantum gravity ideas, explorations of specific violations of fundamental principles of GR, alternatives to dark matter/dark energy, etc. While many of them are certainly appealing from academic reasons, no subset of theories has yet arisen as a preferred one. Second, and at a mathematical level, many such theories do not lend themselves to defining well-posed problems --especially in the regime of interest. That is, given suitable initial conditions, a unique solution can be determined which depends continuously on such conditions~\cite{jH02}. Indeed, with the exception of just a few theories (within the subset of scalar-tensor or scalar-vector-tensor theories), which have been explored nonlinearly in compact binary mergers~\cite{Healy:2011ef,Barausse:2012da,Sagunski:2017nzb,Hirschmann:2017psw}, lack of well-posedness presents a severe obstruction to the study of such theories. Of particular relevance is the understanding of compact objects, their stability and behavior in compact binary mergers, as well as cosmologies near the big-bang/or bounce, both of which are nonlinear regimes that naturally involve relativistic speeds and strong gravitational fields. Of course, mathematical difficulties have been identified before in some theories and to different degrees. For instance, efforts have been directed towards avoiding so-called Ostrogradski's instabilities (e.g.~\cite{Woodard:2006nt,tCmFeLaT13,deRham:2014zqa,Solomon:2017nlh}). Such instability, when present, invariably leads to ill-posed problems. Unfortunately, even in theories free of such instability, well-posedness is far from guaranteed, as several aspects still need to be determined (see, e.g.~\cite{Sarbach:2012pr}). One traditional way to assess well-posedness --which relies on energy estimates-- involves understanding the structure of the (principal part of the) evolution equations and assess whether they are: (i) symmetric/strongly hyperbolic, (ii) merely weakly hyperbolic or even if (iii) the system can transition from hyperbolic to elliptic within the domain of interest. Property (i), together with appropriate initial and boundary conditions, is essentially sufficient to guarantee well-posedness, irrespective of the lower-order terms of the equations. Property (ii), however, requires a careful analysis of lower-order terms and, with the exception of rare circumstances and in rather simple problems, ill-posedness typically follows in this case. As examples, one could mention that in Horndenski theories, weak hyperbolicity in all but a narrow corner has been recently demonstrated~\cite{Papallo:2017qvl} and similarly concerning aspects have been discussed for gravitational Dynamical Chern Simons theory~\cite{Delsate_etal15}. Also, numerical simulations in theories invoking a Vainshtein-like mechanism have explicitly shown pitalls presented by some of the mathematical roadblocks~\cite{Brito:2014ifa} aluded. Last, property (iii) indicates there exist severe obstructions to determining the solution beyond where/when the hyperbolic/elliptic transition takes place. A second hurdle, even with a strongly/symmetric hyperbolic system, is the fact that nonlinearities --in the principal part-- typically imply that characteristics can cross. Once they do, uniqueness of the solution is lost --and hence well-posedness. Such difficulties are already encountered at the level of hydrodynamical equations but, in such cases, further requirements --the so called Rankine–-Hugoniot conditions-- ~\cite{Rankine01011870,Hugoniot} are invoked to single out a unique solution and restore well-posedness. As far as we know, the analog of such conditions in gravitational theories has yet to be developed. Finally, there exist theories for which partial differential equations theory is still to be developed. An example of such a case is given by the ``simple looking'' equation $\Box \phi = \lambda (\Box \phi)^p + ... $ with $p>1$, for which there is no mathematical guidance on how to even formally define an initial value problem. The above discussion paints, at first sight, a rather bleak picture with regards to the degree to which most extensions to GR can be thoroughly analyzed. But it might not be the case in practice. On one hand, in perturbative regimes --i.e. cosmology applications-- the study of the linear perturbations with respect to a preferred solution allows from introducing an ultraviolet cutoff that circumvents many of the aforementioned problems. Thus, specific predictions can be drawn to test for possible deviations from GR and, with them hopefully draw lessons for the full theory\footnote{Note however this assumes {\em linearization stability} of the theory. That is, solutions to the linearized problem are consistent with those of the full problem linearized. In the case of General Relativity, the conditions for this being the case were discussed in~\cite{fischer1973}.}. At the nonlinear level however, the situation is more uncertain. In such case, nonlinearities could be responsible for runaway energy cascades to the UV, rendering effective cutoffs delicate to impose without severely affecting the physics. Moreover, as such regimes require numerical simulations --which at the level of truncation error typically do source all frequencies allowed by the computational grid-- sensitivity/uncontrolled growth at high frequencies represents a significant practical shortcoming standing in the way of exploring such regimes. Last, it is important to keep in mind that often extensions of GR are obtained from an effective field theory approach. A strong direct energy cascade to the UV takes the solution away from the regime of applicability of the theory and conclusions drawn in such a case need not be connected to the true phenomenology from the putative parent theory from which the EFT is, in principle, derived. The aforementioned shortcomings are sufficiently delicate that, in a sense, they have prevented significant advances in the study of extensions to GR in nonlinear regimes. However, the detection of gravitational waves by LIGO/VIRGO, together with our current rather robust understanding of compact binary mergers in General Relativity, give hope to shedding light on this enterprise. Namely, current observations are consistent with no significant energy cascade to the UV in these systems. Remarkably, GW150914 has, in a rather spectacular fashion, allowed observing such waves even without invoking a specific theory!~\cite{Abbott:2016blz}. Whatever the true theory of gravity is, it seems not to significantly alter the behavior from that of GR --at least in the context of binary mergers-- and putative higher-order corrections to GR seem to remain relatively small. Furthermore, this lack of a strong direct energy cascade to the UV in the context of compact binary mergers is also what is observed in fully nonlinear simulations within General Relativity (see for instance~\cite{Lehner:2014asa,Choptuik:2015mma,Duez:2018jaf} and references cited therein). These observations present both opportunities and challenges. An exciting opportunity is to study extensions of GR which, as mentioned, even with pathologies might allow one to devise suitable techniques to effectively control them while still capturing the essence of GR departures. After doing so, the challenge is to obtain sufficiently accurate predictions that can be tested or constrained through ever more sensitive detections. In the current work, we concentrate on assessing proposed techniques to deal with extensions to GR. As the techniques we study are sufficiently general, we will refrain from making contact with any specific extension. Instead, we find it more informative to study a toy model which captures essentially all problems commonly found in extensions to GR. Crucially, being ``UV-complete'' allows for checking to what extent the solution to the EFT problem stays close to that from the original theory. This is a luxury not yet afforded by extensions to GR. To fix ideas and briefly anticipate the strategies we will consider, let us assume the equations from a given theory can be schematically expressed as $G(g) = \lambda S(g)$. Here, and for our current purposes, $G$ stands for the Einstein tensor and $S$ some nonlinear, perhaps higher derivative operator, $\lambda$ is a coupling parameter considered small and $g$ the metric tensor\footnote{Also, further coupled fields can be considered, with their own equations of motion}. One of these strategies, often referred to as {\em ``reduction of order''}, extends a successful technique from ordinary differential equations~\cite{FORD1991217} to the less certain partial differential equation arena. In this technique, one first solves for $G=0$ (i.e. GR); the solution to this problem $g^{(0)}$ is used to evaluate the ``source'' $S(g^{(0)})$ and a new solution $g^{(1)}$ is obtained from $G(g^{(1)})=\lambda S(g^{(0)})$. This process is iterated to a certain desired tolerance of the difference between two subsequent solutions, i.e. $|g^{(i)}-g^{(i-1)}| < \epsilon$. The second strategy, which we refer to as {\em ``fixing equations''} introduced in~\cite{Cayuso:2017iqc}, extends a suggestion by Israel and Stewart to address ill-posedness of relativistic hydrodynamics. Here, a new variable $\Pi$, and its evolution equation (of the form\footnote{A second-order form with the Box operator is also possible, see~\cite{Cayuso:2017iqc}} $\tau \Pi_{,t} = -\Pi + \lambda S$), are introduced such that $\Pi$ asymptotes to $\lambda S$ (in a timescale determined by $\tau$) and controls higher gradients of $\Pi$. Thus it remains consistent with the original system in the IR while restraining a runaway direct energy cascade to the UV. Both the above prescriptions rely on the assumption that the physical system, for the regime of interest, does not naturally transfer energy to shorter wavelengths in a significant way. The former as it assumes $S$ stays as a small correction and the latter as it controls the shorter wavelengths. As mentioned, observations of gravitational waves by LIGO/VIRGO seem to support such an assumption in at least some regimes\footnote{As well as fluid-gravity duality and related arguments, see~\cite{Cayuso:2017iqc}} and thus, invigorates examining these strategies in detail. This is the purpose of this work. | 18 | 8 | 1808.07897 |
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1808 | 1808.08597_arXiv.txt | The Next Generation Balloon-borne Large Aperture Submillimeter Telescope (BLAST-TNG) is a submillimeter mapping experiment planned for a 28 day long-duration balloon (LDB) flight from McMurdo Station, Antarctica during the 2018-2019 season. BLAST-TNG will detect submillimeter polarized interstellar dust emission, tracing magnetic fields in galactic molecular clouds. BLAST-TNG will be the first polarimeter with the sensitivity and resolution to probe the $\sim$0.1 parsec-scale features that are critical to understanding the origin of structures in the interstellar medium. With three detector arrays operating at 250, 350, and 500 \um (1200, 857, and 600 GHz), BLAST-TNG will obtain diffraction-limited resolution at each waveband of 30, 41, and 59 arcseconds respectively. To achieve the submillimeter resolution necessary for its science goals, the BLAST-TNG telescope features a 2.5 m aperture carbon fiber composite primary mirror, one of the largest mirrors flown on a balloon platform. Successful performance of such a large telescope on a balloon-borne platform requires stiff, lightweight optical components and mounting structures. Through a combination of optical metrology and finite element modeling of thermal and mechanical stresses on both the telescope optics and mounting structures, we expect diffraction-limited resolution at all our wavebands. We expect pointing errors due to deformation of the telescope mount to be negligible. We have developed a detailed thermal model of the sun shielding, gondola, and optical components to optimize our observing strategy and increase the stability of the telescope over the flight. We present preflight characterization of the telescope and its platform. | 18 | 8 | 1808.08597 |
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1808 | 1808.04546_arXiv.txt | The formation of multiple close-in low-mass exoplanets is still a mystery. The challenge is to build a system wherein the outermost planet is beyond 0.2~AU from the star. Here we investigate how the prescription for type I planet migration affects the ability to trap multiple planets in a resonant chain near the inner edge of the protostellar disc. A sharp edge modelled as a hyperbolic tangent function coupled with supersonic corrections to the classical type I migration torques results in the innermost planets being pushed inside the cavity through resonant interaction with farther planets because migration is starward at slightly supersonic eccentricities. Planets below a few Earth masses are generally trapped in a resonant chain with the outermost planet near the disc edge, but long-term stability is not guaranteed. For more massive planets the migration is so fast that the eccentricity of the innermost resonant pair is excited to highly supersonic levels due to decreased damping on the innermost planet as it is pushed inside the cavity; collisions frequently occur and the system consists one or two intermediate-mass planets residing closer to the star than the disc's inner edge. We found a neat pileup of resonant planets outside the disc edge only if the corotation torque does not rapidly diminish at high eccentricity. We call for detailed studies on planet migration near the disc's inner edge, which is still uncertain, and for an improved understanding of eccentricity damping and disc torques in the supersonic regime. | Preventing low-mass planets from migrating to their host star is a long-standing problem. Mergers with their host star can be prevented if the protostellar disc has a sharp inner edge at a few stellar radii \citep{Masset06,O10}. \cite{TP07} showed that migrating protoplanets usually end up in resonances. Some of these resided inside the disc's inner cavity. \cite{OI9} also build a resonant chain of low-mass protoplanets that stalled near the disc's inner edge when the migration was artificially slowed down and the reduction of the corotation torque was ignored. Recently \cite{I17} trapped a high number of low-mass planets outside the disc edge in a resonant chain, that subsequently needed to break to account for the currently-observed exoplanet period distribution. On the other hand, \cite{Mat17} had trouble trapping multiple planets near the disc's inner edge, even though their migration prescription was very similar to that of \cite{I17}: both include supersonic corrections to the migration and eccentricity damping timescales. \cite{TP07} also included such corrections, but they followed the prescription of \cite{PL00} while \cite{I17} and \cite{Mat17} followed \cite{CN14}. The simulations of \cite{Mat17} usually resulted in one or two hot Neptune planets rather than a multiplet of smaller planets. The disparity between all of these results warrants further study. | The ability to trap multiple low-mass planets in a resonant chain outside the inner edge of the protostellar disc has been investigated. These low-mass planets execute type I migration which pulls them invariably towards the star. In the absence of a barrier these would all collide with the star. The disc's inner edge could provide a trapping mechanism \citep{Masset06}. We have tested two types of sharp inner edges of the disc: a hyperbolic tangent and a linear function, along with different migration prescriptions.\\ We find that a neat pileup of resonant planets outside the disc edge is established if the corotation torque does not rapidly diminish at high eccentricity. The expectation is that if the resonant chain of the planets remains outside the inner disc edge they eventually start orbit crossing and instigate a phase of giant impacts. This may account for formation of similar-sized, regularly spaced, non-resonant low-mass planets that are found to be common in relatively close-in regions by Kepler observations. However, the eccentricity damping and disc torques in the supersonic regime remain uncertain near the disc’s inner edge. Due to resonant interactions, eccentricity is generally excited to values $e \sim h$ for which the migration is generally inward. Therefore we call for detailed studies on eccentricity damping and disc torques in the supersonic regime and near the disc edge. Such a study will play an important role in understanding the common architecture of compact systems. | 18 | 8 | 1808.04546 |
1808 | 1808.03016_arXiv.txt | In spite of making a small contribution to total protoplanetary disk mass, dust affects the disk temperature by controlling absorption of starlight. As grains grow from their initial ISM-like size distribution, settling depletes the disk's upper layers of dust and decreases the optical depth, cooling the interior. Here we investigate the effect of collisional growth of dust grains and their dynamics on the thermal and optical profile of the disk, and explore the possibility that cooling induced by grain growth and settling could lead to gravitational instability. We develop a Monte Carlo dust collision model with a weighting technique and allow particles to collisionally evolve through sticking and fragmentation, along with vertical settling and turbulent mixing. We explore two disk models, the MMEN (minimum-mass extrasolar nebula), and a ``heavy'' disk with higher surface density than the MMEN, and perform simulations for both constant and spatially variable turbulence efficiency profile $\alpha(R,z)$. We then calculate mean wavelength-dependent opacities for the evolving disks and perform radiative transfer to calculate the temperature profile $T(R,z)$. Finally, we calculate the Toomre Q parameter, a measure of the disk's stability against self-gravity, for each disk model after it reaches a steady state dust-size distribution. We find that even weak turbulence can keep sub-micron sized particles stirred in the disk's upper layer, affecting its optical and thermal profiles, and the growth of large particles in the midplane can make a massive disk optically thick at millimeter wavelengths, making it difficult to calculate the surface density of dust available for planet formation in the inner disk. Also, for an initially massive disk, grain settling and growth can produce a drop in the Toomre Q parameter, driving the disk to $Q < 1.4$ and possibly triggering spiral instabilities. | \label{sec:intro} While most planets form ``bottom-up'' from dust particles accumulating into pebbles, planetesimals, and then solid cores \citep{lissauer93, pollack96, morbidelli12}, some massive giant planets and brown dwarfs may form by top-down collapse in fragmenting protostellar disks \citep{kratter16, boss97}. Despite inferred low disk masses \citep{andrews13, ansdell16, pascucci16} and stringent cooling requirements for fragmentation \citep{gammie01, boley06, stamatellos08, stamatellos09} observational evidence has been emerging that suggests some disks are gravitationally unstable \citep{kwon11, jin16, perez16, tobin16}. Furthermore, disk masses may be substantially underestimated due to the assumed value of the gas-to-dust ratio \citep{bergin13, mcclure16, miotello17, tsukamoto17, yu17}, and the companion mass-ratio distribution for B- and A-type primaries is separation-dependent, suggesting that close companions may originate in circumprimary disks rather than cloud core fragments \citep{gullikson16}. Evidence that instability and fragmentation are taking place in at least a few astrophysical systems gives theorists a mandate to identify plausible ways to trigger them, at least in disks with high gas masses. Disk cooling, which must occur on dynamical timescales for fragments to form \citep{gammie01}, is regulated by opacity \citep{cai06, boley10, cossins10, podolak11, lin16}. The odds of fragmentation increase when the disk becomes optically thin to its own thermal radiation, allowing it to cool quickly \citep{meru10}. Grain growth, which significantly lowers disk opacity, proceeds rapidly: even some Class 0 YSOs, which have ages under 200,000 years \citep{enoch09}, show some degree of dust growth via the core-shine effect \citep{steinacker10, steinacker15}, or have non-ISM spectral indices \citep{jorgensen07, ricci10, chiang12}. As disks evolve, the largest observed (or inferred) grain sizes increase from millimeter in the Class-I phase \citep{miotello14} to centimeter in the T-Tauri phase \citep{perez12, perez15, tazzari16}. Here we examine the extent to which grain growth alone---with no other triggers such as infall---can alter a disk's gravitational stability to axisymmetric perturbations. The effect of self-gravity in a protoplanetary disk is multifaceted. Apart from implications for planet formation, gravitational instability (GI) can contribute to angular momentum transport by producing turbulent stresses \citep{gammie01, baehr17}. Our work thus also helps address the broader question of how dust can affect gas dynamics in disks. This paper is organized as follows: In \S \ref{sec:diskmodel} we discuss our models of the gas disk and dust sub-disk. In \S \ref{sec:dustmodel} we describe our prescription for collision speeds and outcomes. \S \ref{sec:numericalalgorithm} explains our Monte Carlo method for simulating dust growth and settling, while in \S \ref{sc:results} we present results from each disk model. In \S \ref{sec:opacity} we describe our opacity-calculation method and radiative transfer simulations, and in \S \ref{sc:discussion} we discuss the implications of our results for opacities, thermal profiles and disk instability, and examine the limitations of our model. We present our conclusions in \S \ref{sc:conclusion}. | \label{sc:conclusion} In this paper, we have developed a new weighted Monte Carlo model of collisional sticking and fragmentation along with a Monte Carlo Lagrangian prescription for settling, and turbulent stirring, combined with wavelength dependent opacity calculations and radiative transfer. We have used three disk models with different surface densities and have employed both spatially constant and variable turbulence efficiency $(\alpha)$ prescriptions. Our main findings are: \begin{itemize} \item The collisional growth of dust grains through sticking and fragmentation transfers most of the solid mass to larger particles, leaving a small portion of the total dust mass in the $\micron$ and sub-$\micron$ dust grains which provide most of the surface area for photon absorption. This results in a reduction in midplane opacities at smaller wavelengths by $3-4$ orders of magnitude compared to the initial values. At the disk surface, however, the opacities decreases mainly due to depletion of dust grains by settling and inefficient growth of the dust particles due to weak coupling between dust and gas. \item Grain growth and settling tend to decrease the optical depths $(\tau)$ from disk's surface to the midplane at short wavelengths $(\lambda \la 10\micron)$ by a couple of orders of magnitude, while increasing $(\tau)$ at mm and sub-mm wavelengths. For a typical value of $\alpha=10^{-4}$, the optical depths at $1$~mm inside $30$ au exceed unity, which may be problematical for disk mass calculations from (sub)millimeter observations. \item In spite of the depletion of solids in the upper layers of the disk, grains of (sub)micron sizes are stirred high up in the inner disk even when the turbulence strength is small. This effect becomes more prominent when a strong turbulence in the disk surface is considered. Because of strong coupling, these dust particles would follow the gas motion in case a disk wind is present, altering the opacities in the disk atmosphere, an essential physical process requiring an in-depth investigation. \item The optical and thermal profiles of the disk is sensitive to the fragmenting threshold velocity $(v_{frag})$, chosen for modeling the collisional dust growth. We found the opacities at short wavelengths to be $5-10$ times smaller for $v_{frag}=100$~cm~s$^{-1}$ compared to $50$~cm~s$^{-1}$. An even higher value value of $v_{frag}$, traditionally chosen for porous icy aggregates would alter the outcomes significantly. \item Grain growth and settling can bring an initially marginally stable protoplanetary disk down below a Toomre $Q=1.4$ threshold at which non-axisymmetric gravitational instabilities may grow. We find that the disk interior cools as the disk's surface layers are heavily depleted of small grains once the size distribution reaches steady state, decreasing its stability to gravitational perturbations. As disks with low turbulent efficiency $\alpha(R,z)$ have lower collision speeds, and allow grains to grow and settle more efficiently than disks with active turbulence, we expect to find grain-triggered instability primarily in weakly turbulent disks. The model in which we find $Q < 1.4$ throughout most of the disk is extremely massive, with almost ten times the surface density of the minimum-mass solar nebula. Interestingly, this massive disk is consistent with what theorists propose is necessary for giant planet formation \citep[e.g.][]{lissauer09}, but is much larger than typical values inferred from disk observations \citep[e.g.]{andrews13, ansdell16, pascucci16}. However, given the evidence that disk masses are systematically underestimated \citep[e.g.]{mcclure16,yu17}, our model H1 ``heavy'' disk mass may be physically plausible. \item Finally, we note that disk instability may not necessarily lead to brown dwarf or star formation, though companions can form in overdense spiral arms \citep[e.g.][]{kratter16}. Disks that become gravitationally unstable may transport angular momentum by gravitoturbulence \citep[e.g.]{gammie01, shi14}, or growing spiral modes may saturate \citep{cossins09}, keeping the disk marginally stable. Further work would be necessary to track the eventual dynamical outcome of the grain growth and settling studied here. \end{itemize} | 18 | 8 | 1808.03016 |
1808 | 1808.02630_arXiv.txt | Much evidence suggests that the solar corona is heated impulsively, meaning that nanoflares may be ubiquitous in quiet and active regions (ARs). Hard X-ray (HXR) observations with unprecedented sensitivity $>$3~keV are now enabled by focusing instruments. We analyzed data from the \textit{Focusing Optics X-ray Solar Imager (FOXSI)} rocket and the \textit{Nuclear Spectroscopic Telescope Array (NuSTAR)} spacecraft to constrain properties of AR nanoflares simulated by the EBTEL field-line-averaged hydrodynamics code. We generated model X-ray spectra by computing differential emission measures for homogeneous nanoflare sequences with heating amplitudes $H_0$, durations $\tau$, delay times between events $t_N$, and filling factors $f$. The single quiescent AR observed by \textit{FOXSI-2} on 2014 December 11 is well fit by nanoflare sequences with heating amplitudes 0.02 erg cm$^{-3}$ s$^{-1}$ $<$ $H_0$ $<$ 13 erg cm$^{-3}$ s$^{-1}$ and a wide range of delay times and durations. We exclude delays between events shorter than $\sim$900 s at the 90\% confidence level for this region. Three of five regions observed by {\nustar} on 2014 November 1 are well fit by homogeneous nanoflare models, while two regions with higher fluxes are not. Generally, the {\nustar} count spectra are well fit by nanoflare sequences with smaller heating amplitudes, shorter delays, and shorter durations than the allowed \textit{FOXSI-2} models. These apparent discrepancies are likely due to differences in spectral coverage between the two instruments and intrinsic differences among the regions. Steady heating ($t_N$ = $\tau$) was ruled out with $>$99\% confidence for all regions observed by either instrument. | It has been known for nearly eighty years that the solar corona is significantly hotter than the solar photosphere \citep{Gro1939, Edl1943}. However, a complete explanation of this temperature gap has been difficult to achieve. While significant progress has been made in recent years, it is still unclear what the energetic contributions of different physical mechanisms such as waves, reconnection, and spicules are \citep{Kli2015,Par2012}. Two primary physical mechanisms are thought to contribute to high coronal temperatures: magnetic reconnection of stressed field lines and dissipation of MHD waves. Both involve heating on timescales much smaller than the cooling time of individual magnetic strands, and can therefore be characterized as impulsive heating \citep{Kli2006}. \citet{Par1988} coined the term ``nanoflare'' to describe magnetic reconnection between individual flux tubes, a process that can lead to subsequent heating and particle acceleration. However, the term is now widely used to describe impulsive heating events acting on individual flux tubes, in which cooling timescales are longer than heating timescales, without any preference for physical mechanism. As pointed out by \citep{Kli2006}, all plausible mechanisms of coronal heating under realistic conditions predict that the heating is impulsive. This includes wave heating, whether the waves are dissipated by resonance absorption, phase mixing, or Alfvenic turbulence. Nanoflares can be characterized by their volumetric heating amplitude $H_0$, duration $\tau$, and characteristic delay time between events $t_N$. A significant amount of research has focused on the nanoflare heating frequency (1/$t_N$) and how it compares to the characteristic cooling time $t_{cool}$ of a loop strand. High-frequency heating occurs for $t_N << t_{cool}$, while low-frequency heating occurs for $t_N >> t_{cool}$. Steady heating is simply the limit as $t_N$ approaches 0. If low-frequency nanoflares are prevalent, they will produce hot ($\ge$5~MK) plasma throughout the solar corona. However, emission at these temperatures is difficult to detect directly for two reasons: only small amounts of this plasma are predicted, and ionization non-equilibrium can prevent the formation of spectral lines that would form at those temperatures under equilibrium conditions \citep{Gol1989, Bra2006, Rea2008, Bra2011}. Field-aligned and field-line-averaged hydrodynamic simulations have been used to predict the differential emission measure distributions DEM(T) = $n^2 dh/dT$ produced by nanoflares with a wide range of physical properties \citep{Car2014, Bar2016a, Bar2016b}. Here $n$ is the plasma density, and $dh/dT$ corresponds to spatial variations in the temperature field along a particular line of sight. In addition, the DEM distributions of active regions have been measured by extreme ultraviolet (EUV) and soft X-ray (SXR) instruments including the \textit{Solar Dynamics Observatory's} Atmospheric Imaging Assembly (AIA, \citealt{Lem2012}), the \textit{Hinode} X-Ray Telescope (XRT, \citealt{Gol2007}) and the \textit{Hinode} EUV Imaging Spectrometer (EIS, \citealt{Cul2007}). In general these distributions peak close to 4 MK and fall off steeply at higher and lower temperatures \citep{Tri2011, War2012, Sch2012}. \citet{Car2014} and \citet{Car2015} found, through large numbers of simulations, that nanoflare sequences with delay times of hundreds to $\sim$2000 s ($t_N \sim t_{cool}$) give results that are consistent with AR observations. In addition, these studies found that delay times proportional to the total nanoflare energy are required to match the broad range of $EM$ slopes found in previous studies. \citet{Bra2016} created model active regions heated by nanoflares and showed that the best agreement with AR observations occurs for delay times on the order of a loop cooling time (several thousand seconds). Time-lag measurements of ARs at multiple wavelengths have shown signs of widespread cooling and are also consistent with $t_N$ values on the order of several thousand seconds \citep{Via2012, Via2017}. While active region observations with AIA, XRT, and EIS can strongly constrain AR emission below $\sim$5~MK, constraints are less stringent at higher temperatures \citep{Win2012}. Hard X-ray (HXR) instruments can be used to detect or constrain plasma at temperatures $\gtrsim$5~MK. HXR emission is not sensitive to ionization non-equilibrium effects, which can suppress line emission from high-temperature plasmas. However, such plasma can still be difficult to detect because the temperature of a cooling, post-nanoflare flux tube peaks well before the luminosity (which is proportional to the DEM in a given temperature bin). Searches for hot plasma from nanoflares have been performed during periods of low solar activity, in order to avoid contamination from resolvable flares. Long duration, spatially-integrated observations from the \textit{Reuven Ramaty High Energy Solar Spectroscopic Imager} ({\rhessi}, \citealt{Lin2002}) the \textit{Solar PHotometer IN X-rays} (\textit{SphinX}, \citealt{Syl2008}), the X-123 spectrometer and the EUNIS rocket experiment have all shown evidence of plasma at $T>$5~MK during non-flaring times \citep{McT2009,Mic2012,Cas2015, Bro2014}. The combination of XRT and {\rhessi} was used to set constraints on a high-temperature component in active regions by \citet{Rea2009} and \citet{Sch2009}. Large uncertainties in these analyses prevented a definitive detection; although {\rhessi} is more responsive to high-temperature plasma than the instruments on \textit{Hinode}, it lacks the sensitivity to reliably obtain images and spectra from non-flaring active regions. Improved sensitivity and dynamic range can be obtained at energies $>$3~keV by the use of HXR focusing optics. This technology has enabled direct imaging of HXR photons in place of the indirect images obtained by previous instruments such as {\rhessi}. The \textit{Focusing Optics X-ray Solar Imager (FOXSI)} sounding rocket payload uses focusing optics to image the Sun with much higher sensitivity and dynamic range than {\rhessi} \citep{Gle2016}. {\foxsi} has flown twice (in 2012 and 2014) and is expected to fly again in 2018. The \textit{Nuclear Spectroscopic Telescope Array (NuSTAR)} is a NASA Astrophysics Small Explorer launched on 2012 June 13 \citep{Har2013}. While it was not designed to observe the Sun, {\nustar} has successfully done so on thirteen occasions without any damage to the instrument; for a summary of the first four solar pointings see \citealt{Gre2016}. Both {\foxsi} and {\nustar} have been used to perform imaging spectroscopy of active regions and to set limits on hot plasma in those regions \citep{Ish2014, Han2016, Ish2017}. \begin{figure}[htp] \centering \includegraphics[width=\columnwidth]{am_ebtel_fig.eps} \includegraphics[width=\columnwidth]{nustarD1_alldets_model_data_spec.eps} \caption{(Top) Combined EUV and HXR image of five active regions observed by {\nustar} on 2014 November 1, with an effective HXR exposure time of 3.11 s. {\nustar} 2--4~keV flux contours (5, 10, 25, 50, and 80\%) from the FPMA telescope are overlaid in yellow on a co-temporal AIA 94~$\angstrom$ image. The {\nustar} image is co-aligned with the AIA data and smoothed (7$''$ Gaussian smoothing). White boxes are the areas used for this analysis. (Bottom) {\nustar} count spectra from the FPMA and FPMB telescopes for one of the on-disk active regions (D1) observed on 2014 November 1. The fit energy range is shown by the dashed box. Isothermal fit parameters and uncertainties are given in the upper right corner. As shown in this paper, there are a wide variety of energy distributions (going far beyond this isothermal model) that can well fit these data.} \label{fig:nustar_image_spec} \end{figure} In this paper we use active region observations from {\nustar} and \textit{FOXSI-2} to constrain the physical properties of nanoflares, particularly their heating amplitudes, durations, and delay times. We utilize {\nustar} and \textit{FOXSI-2} datasets that were analyzed in \citet{Han2016} and \citet{Ish2017}, respectively. We describe solar observations with these instruments in $\S$\ref{observing}, discuss our analysis methods in $\S$\ref{methods}, present our results in $\S$\ref{discussion}, and describe our conclusions and future work in $\S$\ref{conclusions}. | \label{conclusions} We modeled homogeneous sequences of nanoflares with variable heating amplitudes, durations, delays, and filling factors and compared their synthetic spectra to HXR AR spectra from {\nustar} and \textit{FOXSI-2} observations, first presented in \citet{Han2016} and \citet{Ish2017} respectively. We were able to generate good fits for the \textit{FOXSI-2} HXR data, subject to energetic and observational constraints, using homogeneous nanoflare sequences with a wide range of durations and delays. Although $t_N$ is unconstrained at the 99\% level, the best fits occur for $t_N$ $>$ 900 s in agreement with previous AR studies that did not utilize HXR data. The heating amplitudes required to fit the \textit{FOXSI-2} data are relatively high (0.02--13 erg cm$^{-2}$ s$^{-1}$), most likely because the count spectra correspond to the high-temperature ($\sim$11~MK) tail of the AR DEM. The fit quality is relatively insensitive to the nanoflare duration, which can vary from $\tau$ $<$ 5 s to $\tau$ $>$ 500 s (beyond the range of our analysis). For the cooler regions (characteristic temperature 3--4~MK) observed by {\nustar}, the instrument count fluxes are higher and therefore the absolute likelihoods are smaller. However, a fairly wide range of homogeneous nanoflare models yield good fits to the data (Figure \ref{fig:nustar_multimodel}). The shapes of the likelihood CIs for the {\nustar} ARs are fairly similar to each other and set limits on $H_0$, $\tau$, and $t_N$ from above, not from below. The $H_0$ vs. $\tau$ CI contours follow an approximate power-law, just like the \textit{FOXSI-2} CI contours but for smaller values of both parameters. On the other hand, the CI contours for the other {\nustar} likelihood maps ($H_0$ vs. $t_N$, $t_N$ vs. $\tau$) are distinctly different from the corresponding \textit{FOXSI-2} AR 12234 maps. In particular, $t_N$ is bounded from above by both the 90\% and 99\% contours, as is $\tau$. $H_0$ has a smaller maximum value for these regions than for AR 12234, as well as a minimum value that is below 0.005 erg cm$^{-3}$ s$^{-1}$ (the threshold of our analysis). The range of acceptable parameters for each region are consistent with the temperatures derived from isothermal fits to each region's HXR spectra, although these fits characterize only a limited portion of each region's full DEM. As mentioned above, large values of $t_N$ (low-frequency heating) will result in hotter plasma than small values (high-frequency heating). It is therefore logical that the hotter \textit{FOXSI-2} AR is fit best by nanoflare sequences with longer delays, and the cooler {\nustar} ARs are fit best by nanoflare sequences with shorter delays. Similar logic can be applied to $H_0$ and $\tau$: higher values of these parameters will produce greater energy fluxes and higher temperatures. Therefore, higher heating amplitudes and longer durations should be expected to produce the best fits to AR 12234, and in fact they do. Crucially, quasi-continuous heating is excluded with $>$99\% confidence for every active region in our sample. In other words, there is no region for which the delay and duration can have the same value (500 s) within the likelihood CIs. This is a further validation of the nanoflare model, as virtually any coronal heating mechanism should be impulsive on the spatial scale of a single loop strand \citep{Kli2006,Kli2015}. Because \textit{FOXSI-2} and {\nustar} have limited spectral range, it is difficult to determine if the parameter space results for each instrument are different due to intrinsic properties of the ARs, or because each instrument is sampling a different component of each region's DEM distribution. According to Figure 5 of \citet{Han2016}, the best-fit parameters for \textit{FOXSI}-observed AR 12234 (T$_{high}$ = 11.6 MK, EM = 3.0$\times$10$^{43}$ cm$^{-3}$) are right at the {\nustar} 2-sigma sensitivity limit for this sample of active regions. Therefore the NuSTAR-observed regions could have had high-temperature components in their DEM distributions with similar or lower intensities as the isothermal fit to the \textit{FOXSI}-observed AR 12234. We tested the multi-thermal nature of the \textit{FOXSI}-observed region by adding additional low-temperature components to the best-fit model. First we added a model with spectral parameters roughly centered between the fit parameters from the cooler {\nustar} regions D1, D2, and L1 (T$_{low1}$ = 3.3 MK, EM = 3.5$\times$10$^{46}$ cm$^{-3}$). Next, we tried the same procedure with spectral parameters roughly centered between the fit parameters from the hotter {\nustar} regions L2 and L3 (T$_{low2}$ = 4.4 MK, EM = 5.0$\times$10$^{46}$ cm$^{-3}$). The first 2-temperature model spectrum (T$_{high}$ plus T$_{low1}$) resulted in approximately 15\% increased flux in the lowest \textit{FOXSI-2} energy bin (4-5 keV), and neglible changes above 5 keV. However, the other 2-temperature model (T$_{high}$ plus T$_{low2}$) gave fluxes $>$6 times larger in the lowest bin and fluxes $>$2 times larger in the adjacent bin. Therefore, it is certain that AR 12234 could not be fit by a 2-temperature model in which the lower T and EM were similar to what {\nustar} observed from ARs L2 and L3. However, a 2-temperature model with low-temperature parameters similar to {\nustar}-observed regions D1/D2/L1 could agree reasonably well with the \textit{FOXSI-2} AR spectrum. Although we were able to obtain good agreement with HXR data from homogeneous nanoflare sequences, previous work by e.g. \citet{Ree2013} and \citet{Car2014} has shown that it is difficult to produce the range of observed AR DEM slopes with equally spaced, constant energy nanoflares. \citet{Car2014} and \citet{Car2015} showed that it is possible to reproduce a broad range of slopes with nanoflare sequences if there is a correlation between the nanoflare energy and the delay between successive events. This is a more physically motivated model, as more magnetic free energy would presumably be released by (and required for) larger events. Other authors (e.g. \citealt{Bar2016b, Bra2016, Lop2016}) have used heating amplitudes drawn from a power-law distribution instead of equal-energy nanoflares. The use of power-law distributions in energy and variable delay times is beyond the scope of this analysis, but will be explored in future work. Future work will also include the addition of ion heating to the EBTEL simulations. In addition, comparisons with field-aligned simulations can put additional constraints on which regions of parameter space can model active region HXR fluxes within the constraints of low-temperature EUV/SXR observations. Finally, {\nustar} has observed multiple active regions since 2014 November 1, several of which were quiescent and therefore suitable for nanoflare modeling studies. Future publications will model non-homogeneous nanoflares in field-line-averaged and field-aligned using data from multiple {\nustar} and \textit{FOXSI} ARs. \null This paper made use of data from the {\nustar} mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. This research also made use of the {\nustar} Data Analysis Software (NUSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). We thank the {\nustar} Operations, Software and Calibration teams for support with the execution and analysis of these observations. The \textit{FOXSI-2} sounding rocket was funded by NASA LCAS grant NNX11AB75G. The \textit{FOXSI} team would like to acknowledge the contributions of each member of the \textit{FOXSI} experiment team to the project, particularly our team members at ISAS for the provision of Si and CdTe detectors and at MSFC for the fabrication of the focusing optics. The authors would like to thank P.S. Athiray for providing AIA data co-temporal with the \textit{FOXSI-2} observations. Additional thanks goes to Will Barnes for helpful discussions about ebtel++ and the physics of small heating events. AJM was supported by NASA Earth and Space Science Fellowship award NNX13AM41H. LG was supported by NSF grant AGS-1429512. SJB was supported in this effort by NSF CAREER award AGS-1450230. IGH was supported by a Royal Society University Research Fellowship. This work was supported by NASA grants NNX12AJ36G and NNX14AG07G. \facility{NuSTAR}. | 18 | 8 | 1808.02630 |
1808 | 1808.06964_arXiv.txt | {The well established negative correlation between the $\alpha_{OX}$ spectral slope and the optical/UV luminosity, a by product of the relation between X-rays and optical/UV luminosity, is affected by a relatively large dispersion. The main contributions can be variability in the X-ray/UV ratio and/or changes in fundamental physical parameters.} {We want to quantify the contribution of variability within single sources (\textit{intra-source} dispersion) and that due to variations of other quantities different from source to source (\textit{inter-source} dispersion).} {We use archival data from the XMM-Newton Serendipitous Source Catalog (XMMSSC) and from the XMM-OM Serendipitous Ultra-violet Source Survey (XMMOM-SUSS3). We select a sub-sample in order to decrease the dispersion of the relation due to the presence of Radio-Loud and Broad Absorption Line objects, and to absorptions in both X-ray and optical/UV bands. We use the Structure Function (SF) to estimate the contribution of variability to the dispersion. We analyse the dependence of the residuals of the relation on various physical parameters in order to characterise the inter-source dispersion.} {We find a total dispersion of $\sigma\sim$0.12 and we find that intrinsic variability contributes for 56$\%$ of the variance of the $\alpha_{OX} - L_{UV}$ relation. If we select only sources with a larger number of observational epochs ($\ge\,$3) the dispersion of the relation decreases by approximately 15\%. We find weak but significant dependences of the residuals of the relation on black-hole mass and on Eddington ratio, which are also confirmed by a multivariate regression analysis of $\alpha_{OX}$ as a function of UV luminosity and black-hole mass and/or Eddington ratio. We find a weak positive correlation of both the $\alpha_{OX}$ index and the residuals of the $\alpha_{OX} - L_{UV}$ relation with inclination indicators, such as the FWHM(H$\beta$) and the EW[O$_{III}$], suggesting a weak increase of X-ray/UV ratio with the viewing angle. This suggests the development of new viewing angle indicators possibly applicable at higher redshifts. Moreover, our results suggest the possibility of selecting a sample of objects, based on their viewing angle and/or black-hole mass and Eddington ratio, for which the $\alpha_{OX} - L_{UV}$ relation is as tight as possible, in light of the use of the optical/UV - X-ray luminosity relation to build a distance modulus (DM) - $z$ plane and estimate cosmological parameters. } {} | The X-ray/UV ratio is a powerful tool which can be used to investigate distribution of Active Galactic Nuclei (AGN) X-ray and optical/UV properties \citep{LussoRisaliti2016,AvniTananbaum,Strateva2005} and their dependence on fundamental quantities like Eddington ratio, black-hole mass and redshift. The X-ray/UV ratio is usually defined in terms of the $\alpha_{OX}$ index as \begin{equation} \alpha_{OX}=\log{\frac{L(\nu_X)}{L(\nu_{UV})}}/\log{\frac{\nu_X}{\nu_{UV}}} \end{equation} but it is not rare to find it defined with a minus sign \citep[e.g.][]{Tananbaum1979,LussoRisaliti2016}, and it is usually considered $2\,$keV for the X-ray frequency and $2500{\si{\angstrom}}$ for the Optical/UV frequency \citep[e.g.][]{Vagnetti2010,LussoRisaliti2016}. The $\alpha_{OX}$ index can be thought as the energy index or slope associated to a power law connecting the X-ray and Optical/UV bands \citep{Tananbaum1979}. In literature it has been studied the dependence of the X-ray/UV ratio on redshift, finding no significant dependence \citep[e.g.][]{VignaliBrandtSchneider2003, Strateva2005, Steffen2006, Just2007, Vagnetti2010, Vagnetti2013, DongGreenHo32012}. This means that energy generation mechanisms have not changed from early epochs: already at high redshift, AGNs were almost completely built-up systems, notwithstanding short available time to grow (Vignali, Brandt \& Schneider 2003; Strateva et al. 2005; Just et al. 2007). This picture is consistent with studies finding no significant evolution in AGNs continuum shape even at high redshift from radio \citep{Petric2003}, Optical/UV \citep{Pentericci2003} and X-ray \citep{Page2005}. The $\alpha_{OX}$ dependence on other parameters is still matter of debate. Some authors have found a significant correlation with the Eddington ratio $L/L_{Edd}$ \citep{Lusso2010} while other authors find no significant correlation with $L/L_{Edd}$ \citep{DongGreenHo32012, Vasudevan2009} and a significant one with $M_{BH}$ \citep{DongGreenHo32012}. It has been found in literature a strong, non-linear correlation between the X-ray/UV ratio and the monochromatic UV luminosity at $2500{\si{\angstrom}}$ in the form $\alpha_{OX}=a{\log{L_{UV}}}+b$, with $a$ in the interval $\sim\,-0.2\div-0.1$. However, this anti-correlation is the by-product of the well-established positive non-linear correlation between X-ray and Optical/UV luminosity ${L_X}{\propto}L_{UV}^{\gamma}$ with ${\gamma}\sim{0.5}\div{0.7}$ \citep[e.g.][]{AvniTananbaum, VignaliBrandtSchneider2003, Strateva2005, Steffen2006, Just2007, GibsonBrandtSchneider2008, Lusso2010, Vagnetti2010, Vagnetti2013, LussoRisaliti2016}. Moreover, \citet{Buisson} analysed the variable part of the UV and X-ray emissions for a sample of 21 AGN, finding that they are also correlated with slopes similar to those found for the average luminosities. These two relations are symptoms of a tight physical coupling between the two regions responsible for the Optical/UV and X-rays, i.e. the accretion disk and X-ray corona, respectively. Indeed, standard accretion disk-corona models postulates an interaction between photons emitted from the accretion-disk and a central plasma of relativistic electrons constituting the corona, responsible for the emission of X-rays radiation. Following standard picture by Haardt \& Maraschi (1991,1993), the soft thermal photons from disk, parametrised by $L_{2500{\si{\angstrom}}}$, are energised to X-rays by means of inverse Compton scattering on hot ($T_e\sim10^8\,K$) corona electrons, resulting in a power-law like component observed in AGNs X-ray spectra, with a cut-off corresponding to electron temperature \citep[e.g.][]{LussoRisaliti2016,Tortosa2018}. In this picture, the study of the $\alpha_{OX} - L_{UV}$ relation, or equivalently of the ${L_X} - {L_{UV}}$ relation, is of fundamental importance as we still lack a quantitative physical model explaining the existence of this correlation. However, in a recent paper \citet{LussoRisaliti2017} advanced a simple, \textit{ad-hoc} physical model for the accretion disk-corona system, predicting a dependence of the X-ray monochromatic luminosity on the monochromatic UV luminosity and the emission line full-width at half maximum of the form $L_X{\propto}{{L_{UV}}^{4/7}}{{v_{FWHM}}^{4/7}}$. Their model is based on accretion disk-corona models by \citet{SvZd1994}, in which magnetic loops and reconnection events above a standard Shakura-Sunyaev \citep{ShakuraSunyaev1973} accretion disk may be responsible for the emission of X-ray radiation \citep{LussoRisaliti2016}. The $\alpha_{OX} - L_{UV}$ and $L_{X} - L_{UV}$ relations are however characterised by dispersion due to several causes: the Radio-Loud (RL) and Broad Absorption Lines (BAL) nature of some AGN, host galaxy effects, variability \citep{LussoRisaliti2016} (see Section \ref{sec:dispersion} for an extended discussion). AGN are variable in both Optical/UV and X-rays band. In the Optical/UV range many authors have confirmed variability \citep[e.g.][]{Cristiani1996,Giallongo1991,diClemente1996}, and the most reliable hypothesis is that of accretion disk instabilities \citep[e.g.][]{Vandenberk2004}. Variability in the X-rays band has been extensively studied with different methods like fractional variability \citep{Almaini, Manners2002}, the Power Spectral Density \citep{Papadakis2004, ONeill2005, UttleyMcHardy2005, McHardy2006,Paolillo2018}, the SF \citep{Vagnetti2011, Vagnetti2016, Middei2017}, and these works indicate that variations occur preferentially at long timescales \citep[e.g.][]{Middei2017}. Variability is a major source of scatter in the above relations, and, once simultaneous observations are selected, its contributions reduces to essentially two factors: an intrinsic variations in the X-ray/UV ratio for single sources, and inter-sources variations. Previous works have estimated the contribution of the intrinsic variability in X-ray/UV ratio to the total variance of $\alpha_{OX} - L_{UV}$ relation to be roughly $\sim{30}\div{40\%}$ \citep{Vagnetti2010,Vagnetti2013}, but we still lack a physical explanation for the residual dispersion, and in this work we want to spread light on this topic. In recent period, the study of the $L_X - L_{UV}$ relation has become more and more important as it has been used to built up a Hubble diagram for Quasars \citep{Risaliti2015,BisogniRisalitiLusso2017}. In order to achieve such a goal, the dispersion of the relation must be reduced as much as possible, and \citet{LussoRisaliti2016} proved that it is possible to do that by carefully selecting the sample. The use of this relation represents a valid alternative to the supernovae, as it can be used at higher redshift and it has a better statistics, but it has also shortcomings, as it relies on the tightness of the relation. For this very reason, a thorough study of the relation and of the physical origin of its dispersion is of fundamental importance, as it will aid in the selection of a sample of objects suited for the construction of a Hubble diagram. In section 2 and 3 we describe the data from which we derived the sample we work with, in section 4 and 5 we describe the data analysis procedure together with results, in section 6 we discuss implications of our results in light of present and past works in literature. Throughout the paper we use a $\Lambda$-CDM cosmological model: $H_{0}=70\,km\,{s^{-1}}{Mpc^{-1}}$, $\Omega_m=0.3$ and $\Omega_{\Lambda}=0.7$. | The purpose of our work is to estimate the contribution of intrinsic variation of the X-ray/UV ratio to the dispersion of the $\alpha_{OX} - L_{UV}$ relation, and in particular to understand the origin of the residual dispersion of the relation with simultaneous X-ray and UV observations coming from the MEXSAS2 catalogue and the XMM-SUSS3, respectively. Indeed, once simultaneous X-ray and UV observations are used, the dispersion of the $\alpha_{OX} - L_{UV}$ relation is given by two contributions: an intra-source dispersion, due to intrinsic variations in the X-ray/UV ratio in single sources, and an inter-source dispersion, which may be due to fundamental quantities like BH mass, Eddington ratio, and/or viewing angle. Starting from the parent sample, which is the result of the cross-match between MEXSAS2 and the XMM-SUSS3, we applied stringent constraints in order to decrease as much as possible the dispersion of the relation, following the strategy adopted by \citet{LussoRisaliti2016}. We considered only non-BAL and non-RL objects, as they would increase the dispersion, we took into account for the effects of intergalactic $H_{I}$ absorption and extinction, and we considered only non-absorbed (in X-rays) sources with reliable photon-index estimates. We have shown that by carefully selecting the sample with the constraints described above, it is possible to decrease the dispersion of the $\alpha_{OX} - L_{UV}$ relation, in agreement with \citet{LussoRisaliti2016}. We have confirmed the negative correlation between the two quantities, with a slope of -0.159${\pm}$0.007, comparable to slopes obtained by other autors \citep[e.g.][]{Just2007,Lusso2010,Vagnetti2010}, and we obtained a dispersion of $\sim$0.12, consistent with \citet{Vagnetti2010}. Moreover, we performed an ensemble variability analysis of the $\alpha_{OX}$ index by means of the Structure Function. Indeed, the variance of the $\alpha_{OX} - L_{UV}$ relation can be written as the sum of two contributions, an \textit{intra-source} and an \textit{inter-source} dispersion, and from the SF value at long time-lags we estimated that a true variability in the X-ray/UV ratio contributes for the 56$\%$ to the total variance of the relation (intra-source dispersion). Considering \citet{LussoRisaliti2016}, they found for the $L_{X} - L_{UV}$ relation a residual dispersion of $\sigma\sim0.19$, i.e. dispersion which is not explained by a true variability in the X-ray/UV ratio. Our result means that the dispersion which cannot be explained with a true variability in the X-ray/UV ratio is approximately ${\sim{\sqrt{1-0.56}}\sigma\sim0.2}$ (see Equation \ref{eqn:variability}), similar to that derived by \citet{LussoRisaliti2016}. In order to decrease the dispersion of the relation, we made an attempt by removing sources with only one or two observations, finding that it can decrease by approximately 15\%. The residual dispersion in the relation may be due to other physical quantities, like black-hole mass, Eddington ratio and inclination angle. First, we studied the dependence of the relation on redshift and optical/UV luminosity. We have performed a partial correlation analysis for the $\alpha_{OX} - L_{UV}$ relation taking into account the effect of redshift and for the $\alpha_{OX} - z$ relation taking into account the effect of UV luminosity, and we found $r_{\alpha\,z,L}=0.1$ with $P(>r)=0.012$: our result is not as strong as previous works \citep[e.g.][]{Just2007,Vagnetti2010,Vagnetti2013}, so we can not rule out a residual dependence on redshift. For the future, larger samples with wider and more uniform covering of the $L_{UV} - z$ plane will allow to obtain more robust results in this sense. Second, we studied the dependence of the residuals of the $\alpha_{OX} - L_{UV}$ relation on black-hole mass and Eddington ratio, and of the $\alpha_{OX}$ index on these quantities. We have found weak but significant trends indicating an increase of the residuals of the relation with black-hole mass and a decrease with Eddington ratio. However, the dependence on these quantities may be masked by the dependence on UV luminosity. To test this issue, we performed a multivariate regression analysis considering $\alpha_{OX}$ as a function of UV luminosity and black-hole mass or Eddington ratio. The results we have found are in agreement with the trends in the residuals. We also studied the dependence of the $\alpha_{OX}$ index and the residuals of the $\alpha_{OX} - L_{UV}$ relation on the inclination angle, and we considered as indicator the FWHM(H$\beta$), following \citet{Marziani2001,Marziani2018} and \citet{ShenHo2014}. We have found that the residuals of the relation and the $\alpha_{OX}$ index are positively correlated with FWHM(H$\beta$), with slopes of 0.13${\pm}$0.06 and 0.18$\pm$0.09, respectively, with the latter result in agreement with the scenario depicted by \citet{You2012}, according to which, in a GR model of an accretion disk+corona around a Kerr black-hole, higher inclination-angle objects would be characterised by higher $\alpha_{OX}$ values. We have performed the same analysis considering another inclination indicator, the EW[O$_{III}$], and we have found similar results. However, due to the poor statistics of our sample when considering the two quantities, these results are not robust. Nevertheless, they can represent a starting point for possible future studies. Indeed, a sample for which estimates of the FWHM(H$\beta$) (as well as EW[O$_{III}$]) are available for a larger number of objects, uniformly distributed in inclination angle, would for sure allow more robust studies. In particular, in light of the use of the $L_{X} - L_{UV}$ relation in cosmology, it would allow the possibility to divide the sample in intervals of inclination and select only those objects characterised by low values of the residuals, in order to decrease the dispersion of the relation. | 18 | 8 | 1808.06964 |
1808 | 1808.07889.txt | { The distributions of the initial main-sequence binary parameters are one of the key ingredients in obtaining evolutionary predictions for compact binary (BH-BH\,/\,BH-NS\,/\,NS-NS) merger rates. Until now, such calculations were done under the assumption that initial binary parameter distributions were independent. For the first time, we implement empirically derived inter-correlated distributions of initial binary parameters primary mass ($M_1$), mass ratio ($q$), orbital period ($P$), and eccentricity ($e$). Unexpectedly, the introduction of inter-correlated initial binary parameters leads to only a small decrease in the predicted merger rates by a factor of $\lesssim 2-3$ relative to the previously used non-correlated initial distributions. The formation of compact object mergers in the isolated classical binary evolution favours initial binaries with stars of comparable masses ($q\approx$\,0.5\,$-$\,1) at intermediate orbital periods ($\logpday$ = 2\,$-$\,4). New distributions slightly shift the mass ratios towards lower values with respect to the previously used flat $q$ distribution, which is the dominant effect decreasing the rates. New orbital periods ($\sim$ 1.3 more initial systems within $\logpday$ = 2\,$-$\,4), together with new eccentricities (higher), only negligibly increase the number of progenitors of compact binary mergers. Additionally, we discuss the uncertainty of merger rate predictions associated with possible variations of the massive-star initial mass function (IMF). We argue that evolutionary calculations should be normalized to a star formation rate (SFR) that is obtained from the observed amount of UV light at wavelength 1500$\AA$ (an SFR indicator). In this case, contrary to recent reports, the uncertainty of the IMF does not affect the rates by more than a factor of $\sim 2$. Any change to the IMF slope for massive stars requires a change of SFR in a way that counteracts the impact of IMF variations on compact object merger rates. In contrast, we suggest that the uncertainty in cosmic SFR at low metallicity can be a significant factor at play. } | The Laser Interferometer Gravitational-wave Observatory (LIGO) began its first upgraded observational run (O1) in September 2015; the first ever detection of a gravitational wave signal from a binary black hole (BH-BH) coalescence came shortly afterwards: i.e. GW150914 \citep{LIGO2016_first,LIGO2016_GW150914}. Since then, four additional BH-BH mergers and, most recently, a double neutron star (NS-NS) merger, were detected and reported to the community: i.e. GW151226 \citep[BH-BH,][]{LIGO2016_GW151226}, GW170104 \citep[BH-BH,][]{LIGO_GW170104}, GW170608 \citep[BH-BH,][]{LIGO2017_GW170608}, GW170814 \citep[BH-BH,][]{LIGO2017_GW170814}, and GW170817 \citep[NS-NS,][]{NSNS_discovery_paper}. The last three events were observed during the second observational run (O2); the Advanced Virgo detector \citep{AdvancedVirgo} joined the run on August 1, 2017 and contributed to the analysis of GW170814 and GW170817. The LIGO discovery marks the beginning of the gravitational-wave era. Detections of the coalescence signals from compact binary mergers (CBM) are of utmost astrophysical significance as, among other applications, they will constrain potential formation scenarios, stellar evolution models, and other assumptions associated with theoretical predictions \citep[e.g.][]{Stevenson2015,Richard2017,Barrett2018}. Various formation scenarios for CBM have been proposed. Those most widely discussed include the isolated binary evolution channel involving a common envelope (CE) phase \citep[][]{Eldridge2016,B16Nat,Chruslinska2018,Mapelli2017,Giacobbo2018,Stevenson2017_compas} or stable mass transfer \citep{vandenHeuvel2017}, isolated evolution of field triples \citep[eg.][]{Antonini2016}, dynamical evolution in dense stellar environments such as globular clusters \citep[GCs;][]{Rodriguez2016a,Rodriguez2016b,Askar2017,Park2017}, nuclear star clusters \citep[][]{Miller2009,Antonini2016} or even discs of active galactic nuclei \citep{Stone2017}), and the formation of compact objects in very close and tidally locked binaries through chemically homogeneous evolution \citep{deMink2016,Mandel2016,Marchant2016}. We note that while it is still possible to distinguish between different types of mergers (i.e. BH-BH, BH-NS, or NS-NS) in a model-independent way \citep{Mandel2015,Mandel2017} using their gravitational-wave signatures, we still lack a reliable way to determine the formation channel of an observed merger. This is especially true in case of the LIGO/Virgo NS-NS merger \citep{Belczynski_NSNS_origin}. In the case of BH-BH mergers there is some hope connected to the measurement of the BH-BH spin-orbit misalignments \citep{Stevenson2017_compas,Farr2017,FarrHolzFarr2018}, although this may not work if the BH spins are intrinsically very small \citep{Belczynski2017_GW170104}. Regardless of the formation scenario, the theoretical predictions for the compact binary merger rates are burdened with significant uncertainties due to numerous assumptions and models with poorly constrained parameters, for example the infamous CE phase \citep{Dominik2012} or the BH/NS natal kicks \citep{Repetto2015,Belczynski2016_kicks}). One of the key ingredients in the calculations are the initial conditions for the simulations: the birth properties of stellar clusters in the case of dynamical scenarios and the characteristics of primordial binaries in the case of isolated binary evolution channels. Recently, \citet{dMB15} incorporated the updated primordial binary parameter distributions obtained by \citet{Sana2012} from spectroscopic measurements of massive O-type stars in very young ($\sim$ 2 Myr) open star clusters and associations. The updated distributions included a much stronger bias towards close binary orbits with respect to the previously adopted {\"O}pik's law, i.e. a flat in logarithm distribution \citep{Opik1924,Abt1983}. Intuitively, this change should favour interacting binaries (including those undergoing the CE phase) and possibly cause a notable increase in merger rates. However, \citet{dMB15} found only a very small increase of less than a factor of 2. This is because the distributions obtained by \citet{Sana2012} also show a heavy bias towards low eccentricities with respect to the thermal-equilibrium distribution of \citet{Heggie1975}; this distribution results in a nearly unchanged distribution of periastron separations, which is the essential separation regulating the onset of mass transfer. The sample of binaries observed by \citet{Sana2012} suffers from a significant limitation: it is restricted to systems with $\logpday$ $<$ 3.5 (spectroscopically detectable binaries) and dominated by very short-period orbits with P $<$ 20 days (hence the huge fraction of circularized systems). Since the BH-BH mergers can originate from primordial binaries of up to log P $\sim$ 5.5 \citep{dMB15} the binary parameter distributions obtained by \citet{Sana2012} need to be extrapolated to longer periods, which automatically assumes no intrinsic correlations between parameters. However, the joint probability density function cannot be decomposed into independent distribution functions of the individual parameters, i.e. $f(M_1, q, P, e) \ne f(M_1)f(q)f(P)f(e)$. Observational studies have hinted at probable correlations \citep{Abt1990,Duchene2013}, but hitherto the selection biases have been too large to accurately quantify the intrinsic interrelations. Recently, \citet[][hereafter \citetalias{md16}]{md16} % hereafter \citetalias{md16} analysed more than 20 surveys of massive binary stars, corrected for their respective selection effects, combined the data in a homogeneous manner, and fit analytic functions to the corrected distributions. These authors confirm that many of the physical binary star parameters are indeed correlated at a statistically significant level. \label{sec:var_with_Z} \citet{dMB15} concluded that the most significant variations of merger rates associated with the initial parameters are due to uncertainties of the initial mass function (IMF) power-law slope for massive stars (merger rates going up and down by a factor of six in the case of BH-BH). Cosmological calculations of the BH-BH merger rates \citep[e.g.][]{Dominik2013,Dominik2015,B16Nat,Kruckow2018,Mapelli2017} are performed based on the assumption of a universal IMF across the cosmic time. Often assumed is a so-called ``canonical'' IMF, which is a multi-part power-law distribution $dN/dM = \xi(M) \propto M^{-\alpha_i}$, where $\alpha_1 = 1.3$ for $M/M_{\odot} \in [0.08,0.5]$ and $\alpha_2 = \alpha_3 = 2.3$ for $M/M_{\odot} \in [0.5,1.0]$ and $[1.0,150.0]$, respectively \citep{Kroupa2001}. Although clear evidence for strong IMF variations with environmental conditions is still lacking, there are a growing number of results hinting at departures from the IMF universality \citep[see reviews by][]{Bastian2010,Kroupa2013}. Notably, a recent spectroscopic survey of massive stars in the 30~Doradus star-forming region in the Large Magellanic Cloud has led to a discovery of an excess of stars with masses above $30 \msun$ with respect to the canonical IMF \citep{Schneider2018}; the best-fitted single power-law exponent for $M > 1 \msun$ is $\alpha_3 = 1.90_{-0.26}^{+0.37}$ \citep[although see a technical comment on the data analysis from][suggesting somewhat larger values for $\alpha_3$]{Farr2018}. The unknowns associated with the massive-star IMF are often considered to be one of the significant contributors to uncertainty of compact binary merger rates calculated based on population synthesis. In this work, we argue that by normalizing the simulated stellar population to the total amount of far-UV light that it emits, rather than to its total mass, one can significantly reduce the uncertainty associated with possible variations of the IMF slope in different environments; see Sect.~\ref{sec:small_imp}. As an example of such a variation and its impact on merger rate calculations, we study in detail the case of a possible correlation between the massive-star IMF slope and metallicity Z. With the exception of above-mentioned results of \citet{Schneider2018}, numerous observations of OB associations and clusters in the Local Group did not reveal any significant deviations from the canonical IMF slope for massive stars $\alpha_3 \approx 2.3$ \citep{Massey2003}. These included surveys of the Milky Way \citep[Z $\approx \zsun$ = 0.02; ][]{Daflon2004} \footnote{throughout this study, we adopt $\zsun$ = 0.02 \citep{Villante2014}}, the Small Magellanic Cloud \citep[Z $\approx$ 0.004; ][]{Korn2000} and the Large Magellanic Cloud \citep[Z $\approx$ 0.008; ][]{Korn2000}, indicating that for Z $\geq$ 0.004 ([Fe/H] $\gtrsim -0.7$) the high-mass end of IMF does not significantly depend on metallicity. \citet{Moe2013} showed that the same is true for the parameters of close binaries with massive stars. Even at solar metallicity, the discs of massive protostars are already highly prone to gravitational instability and fragmentation, explaining why the close binary fraction of massive stars is so large \citep{Kratter2006,Kratter2008,Kratter2010,md16}. Further reducing the metallicity can therefore only marginally increase the close binary fraction of massive stars \citep{Tanaka2014,Moe2018}. However, as we show, the vast majority of BH-BH mergers evolving from the CE channel are expected to originate from Z $<$ 0.004 environments, for which there is no direct observational evidence for the persistence of the canonical IMF. From a theoretical point of view, both the Jeans-mass formalism \citep{Jeans1902,Larson1998,Bate2005,Bonnell2006} and the model of stellar formation as a self-regulated balance between the rate of accretion from the proto-stellar envelope and the radiative feedback from the forming star \citep{Adams1996} predict that at a certain sufficiently low metallicity the IMF becomes top heavy \footnote{ an IMF shifted towards higher stellar masses with respect to the canonical IMF, i.e. $\alpha_3 < 2.3$}. In the first case, the prediction comes from the fact that the Jeans mass has to be larger at lower Z owing to less effective cooling of the proto-stellar cloud ($M_J \propto \rho^{-1/2} T^{3/2}$). The radiative feedback, on the other hand, is also metallicity dependent since photons couple less effectively to gas of lower metallicity. Hydrodynamical simulations of the formation of Population III stars ($\rm Z/Z_{\odot}$~$<$~10$^{-6}$) demonstrate that the first generation of stars were almost exclusively massive OB-type main-sequence (MS) stars \citep{Bromm1999,Yoshida2006,Clark2011}. However, by redshift $z$~$\approx$~10, the mean metallicity of actively forming stars was $\rm Z/Z_{\odot}$~$\approx$~10$^{-3}$ \citep{Tornatore2007,Madau2014}. For such Population II stars with intermediate metallicities, the IMF is expected to be only moderately top heavy compared to the canonical IMF \citep{Fang2004,Daigne2006,Greif2008}. From the observational side, there is indirect evidence for top-heavy IMF variations at cosmological times. The relative paucity of metal-poor G-dwarf stars in the Milky Way \citep[the so-called G-dwarf problem; ][]{Pagel1989} can be explained by applying an IMF, which is increasingly deficient in low-mass stars the earlier the star formation took place \citep{Larson1998}. By modelling the abundances of Lyman-break and submillimetre galaxies in the $\Lambda$CDM cosmology, \citet{Baugh2005} found that the observations can be reproduced only if some episodes of star formation with a top-heavy IMF were also present in addition to the canonical IMF. \citet{Nagashima2005} used the same model with two modes of star formation to explain the elemental abundances in the intracluster medium of galaxy clusters. \citet{Wilkins2008} pointed out that the local stellar mass density is significantly lower than the value obtained from integrating the cosmic star formation history with a Salpeter IMF \citep[single slope, $\alpha = 2.35$; ][]{Salpeter1955}. At low redshifts (z $<$ 0.5) they manage to match the observations using a slightly top-heavy ($\alpha_3 = 2.15$) IMF. For higher redshifts, however, \citet{Wilkins2008} argued that no universal IMF can reproduce the measured stellar mass densities. The only quantitative calibration of the relation between the high-mass IMF and metallicity obtained thus far has been made possible thanks to the observations of some GCs in the Milky Way. \citet{Djorgovski1993} noticed that the higher metallicity GCs tend to have a bottom-light present day mass function (i.e. a deficit of low-mass stars). \citet{DeMarchi2007} later found that these GCs are also the least concentrated sources in their observed sample. Such a trend contradicts basic cluster evolution theory -- GCs are expected to be losing low-mass stars from their outer regions owing to their collapse into dense, highly concentrated clusters. An explanation was put forth by \citet{Marks2008}, who proposed that low-mass stars could be unbound from mass-segregated GCs during expulsion of their residual gas. This introduces a dependence on metallicity, since the process of gas expulsion is expected to be enhanced in metal-rich environments \citep{Marks2010}. Finally, \citet{Marks2012b} concluded that in order to provide enough radiative feedback to expel the residual gas and match the characteristics of the observed GCs, their IMF had to be top heavy with the value of $\alpha_3$ decreasing with cluster metallicity. It should be noted, however, that the model of residual gas expulsion applied by \citet{Marks2012b} relies on simplified assumptions concerning the radiative feedback. First, the amount of energy deposited from stars into the ISM is fitted to stellar models of only three different masses \citep[35, 60, and 85 $\msun$;][]{Baumgardt2008}, and second there is no metallicity dependence. Additionally, \citet{Marks2012b} assumed that the energy needed for residual gas removal is provided by the stellar winds and radiation only (e.g. no feedback from supernova taken into account) and that all the energy radiated by the stars is deposited into the ISM. Thus, the exact relation between the high-mass IMF slope and metallicity remains highly uncertain. \newline The purpose of this study is twofold. First, we aim to incorporate the interrelated initial binary parameter distributions and multiplicity statistics obtained by \citetalias{md16} to determine their effects on the predicted rates and properties of CBM. Second, we investigate the importance of possible IMF variations for the merger rate calculations using the \citet{Marks2012b} calibration of the IMF dependency on metallicity as an example of such a variation. To achieve this, we perform comparative population synthesis where we use the works of \citet{dMB15} and \citet{B16Nat} as references (hereafter \citetalias{dMB15} and \citetalias{B16Nat}, respectively). % \LEt{When listing references in the running text of a sentence, please separate by commas and place an "and" between % the last comma and the reference or an "and" and no comma if there are only two references. % Please check for this throughout the paper. If you have trouble with the formatting, highlight the references in red.} In Sect.~\ref{sec:init_distr} we describe the new initial conditions and compare these with the previously used distributions. In Sect.~\ref{sec:comp_method} we describe our computational method. In Sect.~\ref{sec:results} we compare the distributions of the initial parameters of double compact merger progenitors in our simulations. In Sect.~\ref{sec:res_merger_rates} we present the impact of the incorporated changes on the cosmological merger rates. In Sect.~\ref{sec:discussion} we discuss the metallicity distribution of BH-BH mergers in our simulations and the significance of the top-heavy IMF in low-Z environments for the LIGO predictions. We conclude in Sect.~\ref{sec:summary}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | (a) The introduction of the updated initial ZAMS binary distributions from \citetalias{md16} (model I1) decreases the formation efficiency and, consequently, merger and detection rates of all types of CBM by a factor of about 2.1\,-\,2.6 with respect to the old simulations adopting \citet{Sana2012} distributions (model M10); see Sect.~\ref{sec:res_merger_rates}. This is a very small change in comparison to uncertainties associated with the binary evolution \citep[e.g.][]{Eldridge2016,Mapelli2017,Stevenson2017_compas,Chruslinska2018, Kruckow2018}. \\ In the case of BH-BH and NS-NS mergers, the major factor in play is the difference in the initial mass ratio distributions. \citet{Sana2012} obtaiedn their binary statistics based on the spectroscopic measurement of massive O-type stars. For that reason their sample is limited to $\logpday<$ 3.5 (spectroscopically detectable binaries) and dominated by very short-period orbits with P $<$ 20 days, to which they fit a flat mass ratio distribution. However, \citetalias{md16} have shown that wider binaries are weighted towards considerably smaller mass ratios (Fig.~\ref{fig:qdist}). According to their updated distributions, across intermediate periods $\logpday$ = 2\,-\,4, there are $\sim2.5$ fewer systems with $q>0.5$, which is the range of orbital periods and mass ratios at which BH-BH and NS-NS mergers are formed (see Fig.~\ref{fig.ZAMS_properties}). \\ Of secondary importance is the difference between the orbital period distributions (up to 40\% more system in the orbital period range $\logpday$ = 2\,-\,4, depending on metallicity), whereas the changes in the eccentricity statistics have negligible influence on merger rates even though an increase from $<$e$> = 0.3$ to $<$e$> = 0.6$ may seem significant at first. (b) The introduction of a top-heavy IMF at low metallicities \citep[Sect.~\ref{sec:imf_z_dependance_introduced},][]{Marks2012b} results in a small increase of BH-BH merger rates by only a factor of $\sim2$, and even less significant differences in the case of BH-NS and NS-NS mergers (Table~\ref{tab.det_rates}). This might seem surprising because for the values of power-law exponent $\alpha_3$ for the IMF of massive stars of $\alpha_3 \approx 1.8$ at $Z=0.05\zsun$ and even $\alpha_3 \approx 1.3$ at $Z=0.01\zsun$, we could expect an increase in the number of massive BH-BH progenitors (for a fixed stellar mass formed) by a factor of $\sim$4$-$5 with respect to the standard value $\alpha_3 = 2.3$. Interestingly, recent spectroscopic observations of 247 massive stars in the 30 Doradus star formation region reveal an IMF slope of $\alpha_3 = 1.90^{+0.37}_{-0.26}$ in the range 15\,$-$\,200$\msun$ \citep{Schneider2018}. However, because the formation of CBM likely occurs at cosmological scales \citep[e.g.][]{Dominik2013,Mapelli2017}, we argue that the simulations should be normalized to a fixed amount of UV light at wavelength $\rm 1500 \AA$ (used as an SFR indicator) produced by a star-forming population. A more top-heavy IMF produces more UV light per unit of stellar mass, which forces a rescale of the cosmic SFR to a lower value and prevents the BH-BH merger rates from increasing by more than a factor of $\sim2$. This is true even for very top-heavy IMFs with $\alpha_3$ value as low as $1.0$ (Fig.~\ref{fig.relative_numbers}). We conclude that the previously reported uncertainty by a factor of 6 up and down of the merger rate predictions due to possible variations in the IMF \citep{dMB15} is, in fact, not more significant than a factor of $\sim$2. | 18 | 8 | 1808.07889 |
1808 | 1808.06539_arXiv.txt | {Scattering polarization in the Sr I 4607.3 \AA \ line observed with high resolution is an important diagnostic of the Sun's atmosphere and magnetism at small spatial scales. Investigating the scattering polarization altered by the Hanle effect is key to constraining the role of small-scale magnetic activity in solar atmospheric activity and energy balance. At present, spatially resolved observations of this diagnostic are rare and have not been reported as close to the disk center as for $\mu=0.6$.} {Our aim is to measure the scattering polarization in the Sr I line at $\mu=0.6$ and to identify the spatial fluctuations with a statistical approach.} {Using the Fast Solar Polarimeter (FSP) mounted on the TESOS filtergraph at the German Vacuum Tower Telescope (VTT) in Tenerife, Spain, we measured both the spatially resolved full Stokes parameters of the Sr I line at $\mu=0.6$ and the center-to-limb variation of the spatially averaged Stokes parameters.} {We find that the center-to-limb variation of the scattering polarization in the Sr I line measured with FSP is consistent with previous measurements. A statistical analysis of Stokes $Q/I$ (i.e., the linear polarization component parallel to the solar limb), sampled with 0.16\arcsec \ pixel$^{-1}$ in the line core of Sr I reveals that the signal strength is inversely correlated with the intensity in the continuum. We find stronger linear polarimetric signals corresponding to dark areas (intergranular lanes) in the Stokes $I$ continuum image. In contrast, independent measurements at $\mu=0.3$ show a positive correlation of $Q$/$I$ with respect to the continuum intensity. We estimate that the patch diameter responsible for the excess $Q/I$ signal is on the order of 0.5\arcsec-1\arcsec.} {The presented observations and the statistical analysis of $Q$/$I$ signals at $\mu=0.6$ complement reported scattering polarization observations as well as simulations. The FSP has proven to be a suitable instrument to measure spatially resolved scattering polarization signals. In the future, a systematic center-to-limb series of observations with subgranular spatial resolution and increased polarimetric sensitivity (<$10^{-3}$) compared to that in the present study is needed in order to investigate the change in trend with $\mu$ that the comparison of our results with the literature suggests.} | The quiet solar photosphere is thought to be filled by small-scale and weak magnetic fields, as predicted by small-scale dynamo simulations of \citet{Vogler2007} and \citet{Rempel2014}. To test this model, detailed measurements of the often weak magnetic field and its spatial distribution is required. However, observations draw an inhomogeneous picture on magnetic field strength, inclination and distribution, see \citet{Lagg2016a}, \citet{Stenflo2011} and reviews on this topic by \citet{deWijn2009}, \citet{Steiner2012} and \citet{Borrero2015}. Observationally determining properties of fields weaker than a few hundred Gauss, which are tangled at spatial scales close to the observations' spatial resolution is quite a challenge, as the Zeeman effect as a diagnostic tool has two major intrinsic disadvantages for extracting information about these fields. Firstly, the sensitivity to weak magnetic fields is low, particularly to the component perpendicular to the line-of-sight, and secondly, if the magnetic field is turbulent, signal cancellation within a resolution element is possible. This makes it particularly difficult to probe the magnetic field's properties in inter-network regions, as the results conspicuously depend on the method and spectral line employed, see e.g., \citet{Borrero2015}. To a large extent, these disadvantages are overcome by employing the Hanle effect, see for example, \citet{LandiDeglInnocenti} and \citet{Stenflo1994}. \par A photospheric line widely used for Hanle diagnostics is Sr I 4607.3 \AA, which has the advantage of providing scattering signals at $\mu=0.1$ above 1\% (see, e.g., \citealp{Stenflo1997a} and \citealp{Gandorfer2002}). Here $\mu= \cos(\theta)$, where $\theta$ is the heliocentric angle and $\mu=0$ at the solar limb. So far, measurements with the required polarimetric sensitivity of the scattering polarization signals in this line suffer from insufficient spatio-temporal resolution (see \citealp{TrujilloBueno2007} and references therein). Additionally, the observed target needs to be sufficiently far from the solar limb to confidently correlate the granulation pattern with the detected polarimetric signals for interpretation. Observations with a spatial resolution of about 0.6\arcsec \ by \citet{Malherbe2007} at $\mu=0.3$ from the west limb display a positive correlation between the Stokes $Q$/$I$ signal in the Sr I line core and continuum intensity. Their findings possibly hint at a Hanle effect acting in the intergranular regions where higher magnetic fields are expected, in agreement with simulations carried out by \citet{Bueno2004}. However, close to the disk center, \citet{TrujilloBueno2007} predicted theoretically that most of the scattering polarization is produced by local symmetry breaking of the radiation field by atmospheric inhomogeneities. In this case, the theoretically expected $Q$/$I$ signal fluctuations lie between $-0.08$\% and 0.9\%, as they would be observed with a 1 m telescope and a spectral resolution of 25 m\AA \ at $\mu=0.5$, without considering a depolarizing magnetic field. \par Here we present the results of two sets of observations carried out at the German Vacuum Tower Telescope (Tenerife, Spain) in the Sr I 4607.3 \AA \ line taken with the Fast Solar Polarimeter \citep{Iglesias2016} attached to the TESOS filtergraph \citep{Kentischer1998,Tritschler2002}. First we check if the data obtained with the Fast Solar Polarimeter are consistent with those in the literature by measuring the center-to-limb variation of the linear polarization in Sr I and in a neighboring Fe I line that does not show scattering polarization. This center-to-limb variation of the $Q$/$I$ amplitude is compared with published results. In a second step, we use a statistical approach to analyze photon-noise limited spatial fluctuations of the $Q$/$I$ signal at subgranular resolution and (1) search for a correlation between the $Q$/$I$ amplitude in the line core and continuum intensity and (2) estimate the structure size of scattering polarization signals. | We performed scattering polarization measurements in the Sr I 4607.3 \AA \ line with the Fast Solar Polarimeter mounted on TESOS at the VTT on Tenerife. To our knowledge, this is the first time a measurement of the scattering polarization in the Sr I line was done with a filtergraph instrument. In a first step, we have tested the reliability of the FSP by comparing the spatially averaged center-to-limb variation of the polarization signal in Sr I with previous results obtained with other instruments. In addition we verified that the center-to-limb variation of Stokes $Q$/$I$ in the neighboring scattering-insensitive Fe I 4607.6 \AA \ line is indeed consistent with zero signal. In a second step we analyzed a quiet Sun dataset in the Sr I line recorded at $\mu=0.6$ with a spatial resolution sufficient to clearly separate granules and intergranules in the Stokes $I$ continuum image. After temporal and spatial binning to a nominal resolution of 0.16\arcsec pixel$^{-1}$ and 2.5 s integration time per wavelength and Stokes parameter, the noise per pixel in the linear polarization is 0.3\%. We find a negative correlation of $r=-0.17$ between Stokes $Q$/$I$ in the line core and the Stokes $I$ continuum intensity. We rule out Doppler-shift induced fluctuations as the source of this correlation. We stress that our measurement is photon noise limited and seeing-induced cross-talk can be ruled out. Despite the small value of the correlation coefficient, our analysis shows statistically robust evidence of an anti-correlation of Stokes $Q$/$I$ with the continuum intensity in the Sr I line core. The negative correlation found here seemingly contradicts the positive correlation reported by \citet{Malherbe2007} and \citet{Bianda2018}, both obtained by using a spectrograph and at $\mu=0.3$, hence, closer to the solar limb. The correlation coefficient by \citet{Bianda2018} is $r=0.19$, which is close to what has been found in this study, but with opposite sign. The spatial resolution achieved by \citet{Malherbe2007} cannot be better than the used slit width of 0.6\arcsec. We speculate that the difference in sign of the correlation found by these authors compared to that observed here could be due to the lower $\mu$ value at which the measurements were made. The contrast and shape of granulation and the sampled atmospheric height range changes considerably with $\mu$. This could lead to different signs of the correlation between Stokes $Q$/$I$ and continuum intensity. Results by \cite{DelPinoAleman2018} suggest that the positive sign is an artifact due to the reduced statistical significance arising from using a spectrograph. In order to uncover the cause of different dependences of Stokes $Q$/$I$ in the line core of Sr I on continuum brightness at different $\mu$ values, both, lower noise, high resolution full Stokes measurements and theoretical calculations of the spatial structure of $Q$/$I$ in the Sr I line in realistic MHD simulations \citep{Rempel2014,Vogler2007,DelPinoAleman2018} at multiple $\mu$ values, are needed. From our measurements we furthermore conclude that in order to spatially resolve polarimetric signals the noise level needs to be significantly lower than $3\cdot 10^{-3}$. The closest $\mu$ value to our observations at which $Q$/$I$ images are presented in the most detailed published theoretical study of Sr I scattering polarization in 3D HD simulations is $\mu=0.5$ \citep{TrujilloBueno2007}. This polarization map with infinite spectral and high spatial resolution contains patches of polarization as large as 1\%, with most of the signals varying between 0\% and 0.7\%, in the case where horizontally fluctuating microturbulent magnetic fields in the Hanle saturation regime of $B=300$ G in the downflowing intergranules and $B=15$ G in granules at all heights, are considered. In the unmagnetized case, but with a degraded spectral resolution of 25 m\AA \ and spatial resolution corresponding to a 1 m telescope, the signals vary between $-0.08$\% and 0.9\%. Patches of granular size with the above mentioned signal levels should be detectable in our data, but are not directly seen. With a statistical approach we estimated the sizes of the scattering polarization structures to be in the range between about 0.5\arcsec to 1\arcsec. The obtained size is on the order of the patch sizes of about 1\arcsec shown by \citet{TrujilloBueno2007}. However, a more definite conclusion requires that the simulations be degraded to the same spatial resolution and scattered light conditions as the observations. Nevertheless, finding larger polarization signals in the intergranules is in qualitative agreement with \citet{TrujilloBueno2007} and results from a recently submitted paper by \cite{DelPinoAleman2018}. They state that scattering polarization emerges from local fluctuations of the radiation field by plasma inhomogeneities, leading to axial symmetry breaking, even when observed at $\mu=1$. Polarization is therefore predominantly found at the interface of granules and intergranules, with a tendency for stronger polarization in intergranular lanes. Scatter plots provided by \cite{DelPinoAleman2018} show a negative correlation, independent of the $\mu$ value under consideration. To conclude, in this work we have shown that instruments like FSP are now starting to reach the required combination of polarimetric sensitivity and spatio-temporal resolution to provide first observational feedback to theoretical studies of scattering polarization on small spatial scales. We have presented full Stokes filtergraph observations at $\mu=0.6$ in the Sr I 4607.3 \AA \ line and analyzed the images statistically, as the signal-to-noise ratio was not sufficient to directly detect local fluctuations in the solar scattering polarization signals at spatial scales significantly below 1\arcsec. From this analysis we found an anti-correlation between the line core Stokes $Q$/$I$ signals and the continuum intensity. We compared our findings with published observations, which were carried out at $\mu=0.3$ and showed a positive correlation. We additionally compared our result with 3D HD and MHD simulations, where the latter showed a negative correlation independent of the $\mu$ value. | 18 | 8 | 1808.06539 |
1808 | 1808.03400_arXiv.txt | The origin of fast radio bursts (FRBs), bright millisecond radio transients, is still somewhat of a mystery. Several theoretical models expect that the FRB accompanies an optical afterglow (\eg \cite{tot13,kas13FRB}). In order to investigate the origin of FRBs, we perform $gri$-band follow-up observations of \FRB\ (estimated $z \lsim 0.8$) with Subaru/Hyper Suprime-Cam at $8$, $11$, and $14$~days after discovery. The follow-up observation reaches a $50\%$ completeness magnitude of $26.5$~mag for point sources, which is the deepest optical follow-up of FRBs to date. We find $13$ counterpart candidates with variabilities during the observation. We investigate their properties with multicolor and multi-wavelength observations and archival catalogs. Two candidates are excluded by the non-detection of \FRB\ in the other radio feed horns that operated simultaneously to the detection, as well as the inconsistency between the photometric redshift and that derived from the dispersion measure of \FRB. Eight further candidates are consistent with optical variability seen in AGNs. Two more candidates are well fitted with transient templates (Type IIn supernovae), and the final candidate is poorly fitted with all of our transient templates and is located off-center of an extended source. It can only be reproduced with rapid transients with a faint peak and rapid decline and the probability of chance coincidence is $\sim3.6\%$. We also find that none of our candidates are consistent with Type Ia supernovae, which rules out the association of Type Ia supernovae to \FRB\ at $z\leq0.6$ and limits the dispersion measure of the host galaxy to $\lsim300$~pc~cm$^{-3}$ in a Type Ia supernova scenario. | \label{sec:intro} Fast radio bursts (FRBs) are bright millisecond radio transients that were first discovered in a search of archival data of the Parkes Radio Telescope \citep{lor07}. Subsequent searches discovered further FRBs with the Parkes Radio Telescope (\eg \cite{cha16}), the Green Bank Telescope \citep{mas15}, the Arecibo Telescope \citep{spi14}, the Molonglo Observatory Synthesis Telescope \citep{cal17}, and the Australian SKA Pathfinder \citep{ban17}; information on all FRBs is listed in the FRB Catalogue \citep{pet16}.\footnote{ http://frbcat.org/} The defining characteristic of FRBs is a dispersion measure (DM) in excess of what can be explained by the Milky Way. If this excess is attributed to free electrons in the intergalactic medium (IGM), FRBs could thus conceivably be used to probe the so-called ``missing'' baryon and magnetic fields and turbulence in the IGM (\eg \cite{rav16}). The observed rate of FRBs is at least as high as $5\times10^3$ sky$^{-1}$ day$^{-1}$ \citep{bha18}. However, the origin of FRBs is still unknown. There are many theoretical proposals; for example, mergers of double neutron star binaries \citep{tot13}, mergers of double white dwarf binaries \citep{kas13FRB}\footnote{They assume that the emitting region is a portion of the merged white dwarf to reproduce the short duration of FRBs.}, the collapse of rotating supermassive neutron stars to black holes \citep{fal14,zha14frb}, exotic Galactic compact objects \citep{kea12,ban14}, interactions between the supernova shock and magnetosphere of a neutron star \citep{ego09}, compact objects in young supernovae \citep{con16,pir16}, supergiant pulses from extragalactic neutron stars \citep{cor16}, and giant flares from magnetars \citep{tho13,pen15}. Observationally, most FRBs are non-recurrent, with the exception of FRB~121102 \citep{spi14,spi16}. Thanks to its repeatability, radio interferometric observations of its bursts have achieved a subarcsecond localization and identify a faint and persistent optical counterpart \citep{cha17}. Follow-up observations reveal that the host galaxy is an irregular and low-metallicity dwarf galaxy at $z=0.19$ and does not show optical signatures of AGN activity \citep{mar17,ten17} and that the source of FRB~121102 is spatially coincident with a star-forming region \citep{bas17,kok17}. These observations are consistent with the proposal of newly born neutron stars as the origin of FRBs. Unlike FRB~121102 no repeat emission has yet been discovered in the other FRBs despite considerable effort \citep{lor07,rav15,pet15}. Owing to the large single-dish telescopes used to discover FRBs, localization is typically $\sim15$~arcmin, and there are a large number ($>10^4$) of galaxies in the localized region. In order to clarify the origin of FRBs, the first step is a precise localization with telescopes which have better spatial resolution. In scenarios involving coincident optical emission this can be achieved by using wide-field optical telescopes to monitor FRB fields. The SUrvey for Pulsars and Extragalactic Radio Bursts (SUPERB) operates a realtime data analysis pipeline issuing realtime alerts \citep{kea17,bha18}. This enables searches for contemporaneous variability in the radio, or other wavelengths, or indeed in other windows of observation such as neutrinos or gravitational waves. Previously \citet{kea16} reported a variable radio source in the field of FRB~150418, which was thought to be a fading counterpart associated with the FRB, but continued longer-term monitoring revealed a persistent radio source with short timescale variability \citep{wil16,joh17}. The variability and the location are consistent with an active galactic nuclei at the galaxy's center \citep{aki16,bas16} but it is unclear if this is truly associated with the FRB event, or more generally how FRBs and AGN could be associated (see \eg \cite{vie17}). \begin{figure*} \begin{center} \includegraphics[width=16cm]{f1.eps} \end{center} \caption{Three color image on Day~14 of a part of a field followed-up with HSC centered at the central position of the beam 04. The FWHM of beam profile and the localization area adopted in this paper are shown in a green circle with a radius of $7.05$~arcmin and a white circle with a radius of $15$~arcmin, respectively. The locations of 13 final candidates are shown in cyan circles. } \label{fig:image} \end{figure*} After a realtime alert from the SUPERB collaboration, we performed optical imaging observations of \FRB\ detected in beam 04 of the Parkes multi-beam receiver \citep{man01}. This FRB has a DM of $960.4\pm0.5$~pc~cm$^{-3}$ corresponding to an estimated redshift of $\sim0.8$ assuming it lies along an average line of sight through the Universe \citep{bha18}. An optical afterglow is expected by some theoretical models, \eg the merger of double neutron star binaries and double white dwarf binaries. We use Subaru/Hyper Suprime-Cam (HSC, \cite{miy12,miy18hsc}) that is a unique wide-field camera on an 8m-class telescope with a field of view of 1.77~deg$^2$ and a pixel size of $0.17$~arcsec. The HSC has the highest survey power per unit time of any optical telescope and its field of view is 40 times larger than the typical localization of FRBs. Thus it is the most powerful instrument for the follow-up observations of FRB fields in the optical. This paper consists of the following sections. In Section~\ref{sec:obs}, the observations and data analyses are described. In Section~\ref{sec:nature}, we present multicolor light curves of candidates possibly associated with \FRB, and discuss their nature. In Section~\ref{sec:constraint}, we describe constraints on the association between \FRB\ and Type Ia supernova (SN~Ia) from the observations. In Section \ref{sec:conclusion}, a discussion and our conclusions are presented. In this paper, we adopt the AB magnitude system unless otherwise noted and the fiducial cosmology with $H_0=70~{\rm km~s^{-1}~Mpc^{-1}}$, $\Omega_\lambda=0.7$, and $\Omega_{\rm M}=0.3$. | \label{sec:conclusion} We performed optical follow-up observations of \FRB\ using Subaru/HSC on Days~8, 10, and 14 after a realtime alert from the SUPERB collaboration \citep{bha18}. The survey field covers the localization area of \FRB, and the $50\%$ completeness magnitude is $26.5$~mag for point sources, which is the deepest among the optical follow-up observations of FRBs covering the entire localization area. \begin{figure*} \begin{center} \includegraphics[width=16cm]{f9.eps} \end{center} \caption{$g$-, $r$-, and $i$-band difference fluxes of candidates (red: \SNa, \SNc, and \SNd, blue: \SNb, and black: the others). } \label{fig:diffLCs} \end{figure*} After various sifting and screening techniques are applied and subsequent visual inspection, we find $13$ candidates in the localization area of \FRB. The properties of $13$ candidates are summarized in Table~\ref{tab:scores}. Among them, the association of Cand-5 with \FRB\ is excluded by the non-detection in the radio of \FRB\ in the other beams at Parkes. Another 8 candidates are inconsistent with the transient templates and are located at the center of extended objects, and thus could be optical variabilities of AGNs. In particular, Cand-1 and Cand-10 are located at a distance of about twice the FWHM from the radio sources detected with ATCA, and the spectral slopes of the radio sources are consistent with that of the AGN. Although the possibility that one of these 8 candidates and the optical variability of AGN are associated with \FRB\ is not ruled out, it is also possible that all of them are unrelated to \FRB\ and the association between them and \FRB\ can not be investigated from our optical follow-up observations. The photometric redshifts of the host galaxies of these 8 candidates are consistent with the maximum redshift inferred from the DM of \FRB. After considering the agreement of light curves fit with known transient templates, the location of candidates in host galaxies, and photometric redshifts, we focus on $3$ candidates. The final candidate, \SNc, is associated with a galaxy with a photometric redshift higher than the maximum redshift estimated from the DM of \FRB. They are not prominent in $g$-, $r$-, and $i$-band difference fluxes (Figure~\ref{fig:diffLCs}). Two candidates among the $3$ that we deemed to be most interesting are well fitted with transient templates with $Q>10^{-4}$. Their most probable templates are RTs at $z=0.60^{+0.03}_{-0.23}$, SN~IIP at $z=0.20^{+0.03}_{-0.03}$, and SNe~IIn at $z=0.55^{+0.08}_{-0.23}$ for \SNa, and SNe~IIn at $z=0.10^{+0.03}_{-0.03}$ for \SNd. \SNd\ is located at the center of an extended object and thus could be due to the optical variabilities of AGN. \SNb\ is not well fitted with the transient templates and located off-center of its host galaxy. However, by stretching the RT templates, the multicolor light curves of \SNb\ are reproduced with $0.15\leq s \leq0.8$. This suggests that \SNb\ is an RT with a rather faint peak and rapid decline. \SNa\ and \SNb\ could have exploded at the same date as \FRB, although some theoretical models for FRBs do not necessarily require this. However, we can not conclude their association with \FRB. According to a theoretical estimate with a mock catalog of SNe and observed SN rates \citep{nii14frb}, the number of candidates reproduced with SN templates, \ie \SNa, \SNc, and \SNd, is consistent with the total SN rate, including SNe~Ia and CCSNe. Also, the number density of candidates reproduced with the transient templates inside the localization area of \FRB\ is roughly consistent with that outside the localization area of \FRB\ (Appendix~\ref{sec:outside}) and that of SNe detected in a previous study with a time interval of $6$~days \citep{mor08variable}. No candidates are reproduced with the SN~Ia template. Comparing the $50\%$ completeness magnitude with the difference light curve of SN~Ia templates, our observation is sensitive enough to detect SNe~Ia with $\texp=0$ at $z\leq0.6$. According to the DM of \FRB, this leaves room for an SNe~Ia association with \FRB\ only at $z\sim0.6-0.8$. In other words, if an SN~Ia is associated with \FRB, the DM of the host galaxy of \FRB\ needs to be less than $\sim300$~pc~cm$^{-3}$. \SNa\ and \SNb\ can be well fitted as RTs, of which the volumetric rate is $4-7\%$ of the CCSN rate \citep{dro14}. While \SNa\ might be an SN~IIn according to the $Q$ values, the multicolor light curves of \SNb\ can be reproduced only with RTs with a faint peak and rapid decline. The light curve of \SNb\ is well reproduced with the stretched RT templates with $0.15\leq s \leq0.8$ with $Q>10^{-4}$. The most probable templates for \SNb\ include the RT templates with the same explosion date as \FRB. We compute the expected number of RTs which will be detected coincidentally in the localization area with $g$-band differential flux $> 0.2 \upmu$Jy in a six-day interval using the method outlined in \citet{nii14frb}. We utilize the best-fit template for \SNb\ after stretching, the resultant number of coincident RTs in the localization area is as small as $0.038$, and the probability to have this event during the observation is thus $3.6\%$ according to the Poisson distribution. Outside the localization area of \FRB, the number of candidates best-fitted with the RT template is 1. These results suggest that the coincident detection of an RT irrelevant to \FRB\ is relatively unlikely in the localization area. Thus, if \SNb\ is an RT, it may relate to \FRB. The volumetric rates of RTs and FRBs are consistent \citep{dro14,kea15,bha18}. There are two possible mechanisms in the literature for an RT and FRB to be associated; (1) the RT emission from an ultra-stripped Type Ic supernova from a close interacting binary system \citep{suw15,tau15,moriya17,yos17} and the FRB emission from the interaction between supernova shock and magnetosphere of a neutron star \citep{ego09}, and (2) the RT emission from an accretion-induced collapse of the merger remnant of He and CO white dwarfs \citep{bro17} and the FRB emission from the collapse of a strongly magnetized supermassive rotating neutron star to a black hole immediately after the accretion-induced collapse \citep{fal14,zha14frb,moriya16}. However, there is a major caveat that the RT ejecta can be optically thick at radio frequencies immediately after the explosion and can totally absorb the FRB emission \citep{con16,pir16,kas17}. Our observation demonstrates that deep and wide observations detect several unassociated transients in the localization area of FRB. Thus, it is important to establish a method to exclude them. Theortical studies need to more precisely predict light curve evolution to identify the optical counterparts of FRBs. The optical observations give a lower limit on the redshift. This is complementary with the upper limit on redshift of FRBs that can be estimated by the DM of FRBs. We encourage rapid reporting of FRBs, especially those with low DM values, to enable future wide-field optical work aiming at identifying any and all associated emission in this band. \begin{ack} This research has been supported in part by the research grant program of Toyota foundation (D11-R-0830), the natural science grant of the Mitsubishi Foundation, the research grant of the Yamada Science Foundation, World Premier International Research Center Initiative, MEXT, Japan, and by JSPS KAKENHI Grant Numbers JP15H02075, JP15H05440, JP15K05018, JP16H02158, JP17H06362, JP17H06363, JP17K14255, JP18K03692. EP receives funding from the European Research Council under the European Union Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 617199. We thank the LSST Project for making their code available as free software at http://dm.lsstcorp.org. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. \end{ack} \appendix \begin{figure*} \begin{center} \includegraphics[width=16cm]{f10.eps} \end{center} \caption{Comparisons of the difference light curves of the transients outside the localization area of \FRB\ and the best-fit templates. The fluxes are shifted to be zero at the faintest epoch. } \label{fig:LCout} \end{figure*} | 18 | 8 | 1808.03400 |
1808 | 1808.04372_arXiv.txt | We describe the CO Luminosity Density at High-z (COLDz) survey, the first spectral line deep field targeting CO(1--0) emission from galaxies at $z=1.95-2.85$ and CO(2--1) at $z=4.91-6.70$. The main goal of COLDz is to constrain the cosmic density of molecular gas at the peak epoch of cosmic star formation. By targeting both a wide ($\sim$51 arcmin$^2$) and a deep area ($\sim$9 arcmin$^2$), the survey is designed to robustly constrain the bright end and the characteristic luminosity of the CO(1--0) luminosity function. An extensive analysis of the reliability of our line candidates, and new techniques provide detailed completeness and statistical corrections as necessary to determine the best constraints to date on the CO luminosity function. Our blind search for CO(1--0) uniformly selects starbursts and massive Main Sequence galaxies based on their cold molecular gas masses. Our search also detects CO(2--1) line emission from optically dark, dusty star-forming galaxies at $z>5$. We find a range of spatial sizes for the CO-traced gas reservoirs up to $\sim40$ kpc, suggesting that spatially extended cold molecular gas reservoirs may be common in massive, gas-rich galaxies at $z\sim2$. Through CO line stacking, we constrain the gas mass fraction in previously known typical star-forming galaxies at $z=2$--3. The stacked CO detection suggests lower molecular gas mass fractions than expected for massive Main Sequence galaxies by a factor of $\sim3-6$. We find total CO line brightness at $\sim34\,$GHz of $0.45\pm0.2\,\mu$K, which constrains future line intensity mapping and CMB experiments. | Although the process of galaxy assembly through star formation is believed to have reached a peak rate at redshifts of $z=2$--3 (i.e., $\sim$10--11 billion years ago), the fundamental driver of this evolution is still uncertain \citep{MadauDickinson}. In order to understand the physical origin of the cosmic star formation history (i.e., the rate of star formation taking place per unit comoving volume), we need to quantify the mass of cold, dense gas in galaxies as a function of cosmic time, because this gas phase controls star formation \citep{KennicuttEvans}. In particular, the evolution of the cold gas mass distribution can provide strong constraints on models of galaxy formation by simultaneously measuring the gas availability and, through a comparison to the star formation distribution function, the global efficiency of the star formation process (see \citealt{CarilliWalter} for a review). In this work, we carry out the first fully ``blind" deep-field spectral line search for CO(1--0) line emission, arguably the best tracer of the total molecular gas mass at the peak epoch of cosmic star formation, by taking advantage of the greatly improved capabilities of NSF's Karl G. Jansky Very Large Array (VLA). To date, observations of the immediate fuel for star formation, i.e., the cold molecular gas, have mostly been limited to follow-up studies of galaxies that were pre-selected from optical/near-infrared (NIR) deep surveys (and hence based on stellar light) or selected in the sub-millimeter based on dust-obscured star formation as sub-millimeter galaxies (SMGs; for reviews see, e.g., \citealt{Blain2002,Casey14}). % In particular, optical/NIR color-selection techniques (e.g., ``BzK", ``BM/BX"; \citealt{Daddi04,Steidel04}) have explored significant samples of massive, star forming galaxies at $z\sim$1.5 to 2.5 \citep{Daddi08,Daddi10a,Tacconi10,Tacconi13} and the sub-mm selection has been particularly effective in identifying the most highly star-forming galaxies at this epoch for CO follow-up (e.g., \citealt{Bothwell13}). Although such targeted CO studies are fundamental to explore the properties of known galaxy populations, they need to be complemented by blind CO surveys that do not pre-select their targets, which may potentially reveal gas-dominated and/or systems with uncharacteristically low star formation rate missed by other selection techniques. Targeted CO studies have found more massive gas reservoirs at $z\sim2$ compared to local galaxies. Cold molecular gas is therefore believed to be the main driver for the high star formation rates of normal galaxies at these redshifts (e.g., \citealt{Greve2005,Daddi08, Daddi10a,Daddi10b,Tacconi10,Genzel10, Bothwell13}). Recent studies have claimed tentative evidence for an elevated star formation efficiency, i.e., star formation rate generated per unit mass of molecular gas, at $z\sim2$ compared to local galaxies \citep[e.g.,][]{Genzel15, Scoville16, Schinnerer16, Scoville17, Tacconi17}. Such an elevated star formation efficiency could be related to massive, gravitationally unstable gas reservoirs. The interstellar gas content of galaxies therefore appears to be the main driver of the star formation history of the Universe, during the epoch when galaxies formed at least half of their stellar mass content (e.g., \citealt{MadauDickinson}). Although targeted molecular gas studies currently allow to observe larger galaxy samples more efficiently than blind searches, their pre-selection could potentially introduce an unknown systematic bias. Critically, such studies may not uniformly sample the galaxy cold molecular gas mass function. The best way to address such potential biases, and thus, to complement targeted studies, is through deep field blind surveys, in which galaxies are directly selected based on their cold gas content. Although some targeted CO(1--0) deep studies have previously been attempted (most notably \citealt{Aravena12} and \citealt{Rudnick17}), these studies have typically targeted overdense (proto-)cluster environments. Hence, a blind search approach, to sample a representative cosmic volume is needed, in order to assess the statistical significance of such previous studies. CO(1--0) line emission is one of the most direct tracers of the cold, molecular inter-stellar medium (ISM) in galaxies\footnote{In this work, CO always refers to the most abundant isotopologue $^{12}$CO}. Its line luminosity can be used to estimate the cold molecular gas mass by means of a conversion factor ($\alpha_{\rm CO}$; see \citealt{Bolatto_review} for a review). Although other tracers of the cold ISM have been utilized to date, including mid-{\it J} CO lines and the dust continuum emission, these are less direct tracers because they require additional, uncertain conversion factors (e.g., CO excitation corrections and dust-to-gas ratios). Specifically, while the ground state CO(1--0) transition traces the bulk gas reservoir, mid-{\it J} CO lines such as CO(3--2) and higher-{\it J} lines are likely to preferentially trace the fraction of actively star-forming gas. Hence, their brightness requires additional assumptions about line excitation, in order to provide a measurement of the total gas mass. Furthermore, different populations of galaxies may be characterized by significantly different CO excitation conditions (e.g., BzK, SMGs and quasar hosts; \citealt{Daddi10b,Riechers06,Riechers11a,Riechers11b,Ivison_GN19,Bothwell13,CarilliWalter,Narayanan14}), which also show considerable individual scatter (e.g., \citealt{Sharon16}). Long-wavelength dust continuum emission has been suggested to be a measure of the total gas mass, and is utilized to great extent in recent surveys with ALMA to investigate large samples of far-infrared (FIR)-selected galaxies \citep{Eales12,Bourne13,Groves15,Scoville16, Scoville17,ASPECS2}. Nonetheless, there remain substantial uncertainties in the accuracy of the calibration for this method at high redshift especially below the most luminous, most massive sources.\footnote{The dust continuum method to determine gas masses may be affected by the metallicity dependence of the dust-to-gas ratio \citep{Sandstrom13,Berta16}, by trends in dust temperature with redshift (e.g., \citealt{Magdis12}), or with galaxy population (e.g., \citealt{Faisst17}).} Another caveat to using FIR continuum emission instead of CO comes from the finding that the dust emission measured by ALMA may not always trace the bulk of the gas distribution. This is made clear by the small sizes of the dust-emitting regions compared to the star forming regions and the gas as traced by CO emission (e.g., \citealt{Riechers_GN19,Riechers14,Ivison_GN19,Simpson15,Hodge16,Miettinen17,Chen2017}). Disentangling the causes for the observed increased star formation activity at $z\sim2$ is not straightforward, since an increased availability of cold gas may be difficult to distinguish from increased star formation efficiency due to the uncertainty in deriving gas masses, for representative samples of galaxies. Now, thanks to the unprecedented sensitivity and bandwidth of the VLA and the Atacama Large (sub-)Millimeter Array (ALMA), CO deep field studies can be carried out efficiently, and these are ideal to address such potential selection effects. Previous deep field studies, with the Plateau de Bure Interferometer (PdBI; now the NOrthern Extended Millimeter Array, NOEMA) in the HDF-N \citep{Decarli14, Walter14} and ALMA in the HUDF (ALMA SPECtroscopic Survey in the Hubble Ultra-Deep Field Pilot or ASPECS-Pilot, \citealt{ASPECS1, ASPECS2}), have provided the first CO blind searches covering mid-{\it J} transitions such as CO(3--2)\footnote{The ASPECS-Pilot survey simultaneously covered the CO(2--1) line in the redshift range $z\sim$1.0--1.7, the CO(3--2) line at $z\sim$2.0--3.1, and higher-{\it J} CO transitions at higher redshift.}, which are accessible at millimeter wavelengths. These studies have yielded crucial constraints on the molecular gas mass function at $z\sim1$--3, subject to assumptions on the excitation of the CO line ladder to infer the corresponding molecular gas content.\footnote{A key challenge in these studies is the uncertainty in assigning candidate emission lines to the correct CO transition, in cases where the redshift of the observed line candidates is not independently known.} They have found broad agreement with models of the CO luminosity evolution with redshift by finding an elevated molecular gas cosmic density at $z>1$ in comparison to $z\sim0$, but they may suggest a tension with luminosity function models at $z\gtrsim$1 by finding a larger number of CO line candidates than expected \citep{ASPECS2}. In order to more statistically characterize the molecular gas mass function in galaxies at $z=2$--3 and 5--7 than previously possible, while avoiding some of the previous selection biases, we have carried out the COLDz survey\footnote{The COLDz survey data, together with complete candidate lists, and analysis routines may be found online at coldz.astro.cornell.edu.} a blind search for CO(1--0) and CO(2--1) line emission using the fully upgraded VLA\footnote{The recently expanded VLA, with its new Ka-band detectors, the new 3-bit samplers, the simultaneous 8 GHz bandwidth, and its improved sensitivity, for the first time, enables carrying out this survey study.}. The main objective of this survey is to constrain the CO(1--0) luminosity function at $z=2$--3, which provides the most direct census of the cold molecular gas at the peak epoch of cosmic star formation free from excitation bias, and based on a direct selection of the cold gas mass in galaxies. As such, the COLDz survey is highly complementary to millimeter-wave surveys like ASPECS and targeted studies. The CO(1--0) intensity mapping technique explored by \cite{Keating15,Keating16} is complementary to our approach. Intensity mapping offers sensitivity to the aggregate line emission signal from galaxies, but only measures the second raw moment of the luminosity function (therefore not distinguishing between the characteristic luminosity and volume density). While the intensity mapping technique allows to cover significantly larger areas of the sky, it does not directly measure gas properties of individual galaxies, and is therefore complementary to direct searches such as COLDz. In a previous paper (\citealt{Lentati15}; Paper~0) we have described a first, interesting example of the galaxies identified in this survey. In this work (Paper~\rom{1}), we describe the survey, present the blind search line catalog, analyze the results of line stacking, and outline the statistical methods employed to characterize our sample. In Paper~\rom{2}, we present the analysis of the CO luminosity functions and our constraints on the cold gas density of the Universe at $z=2$--7, (Riechers et al., submitted). % In Section 2 of this work, we describe the VLA COLDz observations, the calibration procedure and the methods to mosaic and produce the signal-to-noise cubes. In Section 3, we describe our blind line search through Matched Filtering in 3D. In Section 4, we present our ``secure" and ``candidate" CO line detections in both the deeper (in COSMOS) and wider (in GOODS-N) fields. In Section 5, we utilize stacking of galaxies with previously known spectroscopic redshifts, to provide strong constraints on their CO luminosity. In Section 6, we derive constraints to the total CO line brightness at $\sim$34 GHz. In Section 7, we discuss the implications of our results in the context of previous surveys. We conclude with the implications for future surveys with current and planned instrumentation. A more detailed analysis of the line search methods, the statistical characterization of the candidate sample properties, and upper limits found for additional galaxy samples are presented in the Appendix. In this work we adopt a flat, $\Lambda$CDM cosmology with $H_0=70\,$km s$^{-1}$ Mpc$^{-1}$ and $\Omega_{\rm M}=0.3$ and a Chabrier IMF.% \begin{table*} \caption{COLDz Observations Summary.} \centering \begin{tabular}{ c c c c c c } \hline Field & Pointing&D & D$\rightarrow$DnC &DnC & DnC$\rightarrow$C \\ & &configuration &configuration & configuration& configuration\\ \hline Baseline range (m) &&40--1000&40-2100&40--2100&40--3400\\ \hline COSMOS&1--7&82 hr&{\textemdash}&11 hr&{\textemdash}\\ GOODS-N&1--7&13 hr&{\textemdash}&{\textemdash}&{\textemdash}\\ GOODS-N&6&{\textemdash}&{\textemdash}&3 hr&{\textemdash}\\ GOODS-N&8--14&15 hr&{\textemdash}&{\textemdash}&{\textemdash}\\ GOODS-N&15--21&15 hr&{\textemdash}&{\textemdash}&{\textemdash}\\ GOODS-N&22--28&14 hr&1.4 hr&{\textemdash}&{\textemdash}\\ GOODS-N&29--35&{\textemdash}&3 hr&12 hr&{\textemdash}\\ GOODS-N&36--42&{\textemdash}&{\textemdash}&11 hr&3 hr\\ GOODS-N&43--49&14 hr&{\textemdash}&1.3 hr&{\textemdash}\\ GOODS-N&50--56&10.5 hr&{\textemdash}&3.5 hr&{\textemdash}\\ GOODS-N&57&2 hr&{\textemdash}&{\textemdash}&{\textemdash}\\ \hline \end{tabular} \tablecomments{We list the total, on-source time in different array configurations, for all pointings in each group combined.} \label{obs_table} \end{table*} | 18 | 8 | 1808.04372 |
|
1808 | 1808.03287_arXiv.txt | The upcoming radio interferometer Square Kilometre Array (SKA) is expected to directly detect the redshifted 21-cm signal from the neutral hydrogen present during the Cosmic Dawn. Temperature fluctuations from X-ray heating of the neutral intergalactic medium can dominate the fluctuations in the 21-cm signal from this time. This heating depends on the abundance, clustering, and properties of the X-ray sources present, which remain highly uncertain. We present a suite of three new large-volume, 349\,Mpc a side, fully numerical radiative transfer simulations including QSO-like sources, extending the work previously presented in Ross et al. (2017). The results show that our QSOs have a modest contribution to the heating budget, yet significantly impact the 21-cm signal. Initially, the power spectrum is boosted on large scales by heating from the biased QSO-like sources, before decreasing on all scales. Fluctuations from images of the 21-cm signal with resolutions corresponding to SKA1-Low at the appropriate redshifts are well above the expected noise for deep integrations, indicating that imaging could be feasible for all the X-ray source models considered. The most notable contribution of the QSOs is a dramatic increase in non-Gaussianity of the signal, as measured by the skewness and kurtosis of the 21-cm probability distribution functions. However, in the case of late Lyman-$\alpha$ saturation, this non-Gaussianity could be dramatically decreased particularly when heating occurs earlier. We conclude that increased non-Gaussianity is a promising signature of rare X-ray sources at this time, provided that Lyman-$\alpha$ saturation occurs before heating dominates the 21-cm signal. | \label{intro} The Epoch of Reionization, hereafter EoR, is the cosmological era during which the first luminous sources reionized the Universe. Observations of the high-redshift Lyman-$\alpha$ forest \citep[e.g.][]{McGreer2015,Davies2018,Bosman2018}, an observed decrease in Lyman-$\alpha$ emitting galaxies at high redshifts \citep[e.g.][]{Pentericci2014, Tilvi2014,Barros2017,Mason2018}, and temperature measurements of the high-redshift intergalactic medium \citep[IGM; e.g.][]{Raskutti2012, Bolton2012} indicate reionization ended sometime before $z \approx 5.7$. The start of substantial reionization (i.e. more than 10 per cent of the hydrogen mass) is constrained to be redshift 10 by the measured Thomson optical depth for CMB scattering \citep[e.g.][]{Planck2016}. Other than these constraints on the timing of the EoR, the astrophysics of this era remains extremely uncertain. The most powerful observational probe of this epoch is the redshifted 21-cm signal originating from the hyperfine spin-flip transition of hydrogen. Three experiments are currently attempting to measure the 21-cm signal from the EoR using low-frequency radio interferometry: LOFAR\footnote{\url{http://www.lofar.org/}}, MWA\footnote{\url{http://www.mwatelescope.org/}} and PAPER\footnote{\url{http://eor.berkeley.edu/}}. The LOFAR collaboration has recently set an upper limit to the 21-cm power spectrum from the Epoch of reionization \citep{LOFAR2017} and similar constraints were previously published based on data from GMRT\footnote{\url{http://gmrt.ncra.tifr.res.in/}} \citep{GMRT2011,GMRT2013}. PAPER also placed constraints on the 21-cm power spectrum \citep{Ali2015}, but have since retracted these claims \citep{Ali2018}. The future interferometers HERA\footnote{\url{http://reionization.org/}} and SKA\footnote{\url{https://www.skatelescope.org/}} are expected to be able to detect and possibly image the EoR. The beginning of the EoR, when the first luminous sources start to appear but reionization is not yet fully under way, is referred to as the Cosmic Dawn (CD). During this period, the gas temperature fluctuations in the neutral IGM are likely to be the dominant contributor to 21-cm fluctuations (see Section~\ref{sec:theory} for more details). The neutral IGM can only be heated by X-ray photons as they have long mean free paths and are thus able to travel far from their origin, penetrating deep into the neutral hydrogen regions. In contrast, the UV photons produced by stars have short mean free paths and only heat and ionize very locally. Therefore, the 21-cm signal from these early stages of reionization is expected to be sensitive to the spectra, abundance, and clustering of any X-ray sources present at this time. The Experiment to Detect the Global EoR Signature, EDGES\footnote{\url{http://loco.lab.asu.edu/edges/}}, has recently claimed to have detected an extremely strong absorption signal from the CD \citep{Bowman2018}. If this result is confirmed then additional physics is required to explain the measured signal. The observational difficulties of this experiment and concerns over the foreground modeling \citep{Hill2018} lead us to conclude that further validation from another independent observation is required in order to verify the result. The nature of X-ray sources present in the CD sources remains extremely uncertain. Simulations have suggested that the first generation of stars (Population III stars, referred to as Pop III stars hereafter) could have formed binary systems as early as redshift 30 \citep{Glover2003}. High-mass X-ray binaries, HMXBs, have therefore been suggested as significant contributors to the X-ray emissions \citep[e.g.][]{Xu2014,Jeon2014,Jeon2015}. QSOs are also a likely candidate for early X-ray heating. \citet{Chardin2015} argued that the observation of a large scatter in the Lyman-$\alpha$ opacity in \citet{Becker2015} suggests patchy hydrogen reionization, implying the presence of rare, bright sources. The presence of high-redshift QSOs is also consistent with the gentle slope at the bright-end of the high-redshift UV galaxy luminosity at $z\sim$7 \citep{Bowler2012,Bowler2014,Bowler2015} and the X-ray spectra associated with these galaxies \citep{Stark2015a,Stark2015b, Stark2017,Mainali2017}. An observation of high-redshift, low-luminosity QSOs in \citet{Giallongo2015} has suggested that the low-mass end of the QSO X-ray luminosity functions (QXLF) may be steeper than previously thought. \citet{Grissom2014, Giallongo2015, Chardin2015, Khaire2016} and \citet{Mitra2016} argue that QSOs may even be numerous enough to contribute significantly to reionization itself. Contrarily, \citet[e.g.][]{Onoue2017,Onorbe2017,Qin2017,Hassan2018,Akiyama2018} and \citet{Parsa2018} argue that QSOs are unlikely to contribute significantly to reionization. Multiple theoretical studies have previously investigated the impact of X-ray heating during the CD. Early work on this topic was analytical \citep[e.g.][]{Glover2003,Furlanetto2004} and considered a simple X-ray background. However, most recent works have focused on semi-numerical \citep[see e.g.][]{Santos2010,Mesinger2013, Fialkov2014,Knevitt2014,Ghara2016,Ghara2017,Greig2018,Das2017,Douna2018} and numerical \citep[eg.][]{Xu2014,Ahn2015,Ross2017} modeling. These works consider the dominant contributors of X-rays in the CD to be HXMBs and, therefore, trace the stellar population. There is disagreement on the contribution of HMXBs. For example, \citet{Knevitt2014} find that HMXBs do not contribute significantly to the CD; whereas, \citet{Greig2018} predict that the heating during the CD will be detectable by SKA. These differences stem from the lack of understanding of high redshift HMXBs, and of high redshift sources in general. QSO source models have also been investigated in previous works both using semi-numerical \citep[e.g.][]{Yajima2014,Datta2016,Qin2017,Hassan2018} and numerical \citep[e.g.][]{Baek2010,Kakiichi2017,Semelin2017,Eide2018} methods. The large scale fully numerical simulations run by \citet{Kakiichi2017} and semi-numerical simulations run by \citet{Hassan2018} and \citet{Qin2017} focus on the impact of QSOs during the EoR rather than the CD. \citet{Datta2016} investigate an individual QSO and assume the luminosity to be the same as a the high redshift QSO observation from \citet{Mortlock2011}. They focus primarily on the detectability of an individual QSO source rather than their contribution to reionization and heating process. The luminosities of the QSOs are often calculated by assuming black hole masses are proportional the mass of stars in the galaxy and are accreting at the Eddington limit. For example, \citet{Yajima2014} have considered individual sources in a comparable way to \citet{Datta2016}, but assuming the luminosity of QSOs to be proportional to the mass of the halo. While there has been an observed correlation between the mass of the bulge of galaxies and the masses of their central black holes \citep[e.g.][]{2004Haring,Lasker2016}, it has been known for a long time that this relationship does not extend to the luminosity of the QSO \citep[e.g.][]{Woo2002}. \citet{Baek2010} and \citet{Eide2018} have used this assumption that $L \propto M_{\rm halo}$ in their detailed fully numerical simulations of QSOs during the CD including the radiative transfer ionizing UV photons, X-rays, and Lyman-$\alpha$ photons, albeit with a smaller boxsize ($\sim$ 100~Mpc $h^{-1}$). In this paper, we extend our suite of numerical simulations of the inhomogeneous heating during the CD previously presented in \cite{Ross2017}, hereafter referred to as Paper I, with the addition of different X-ray emitter models. Using the same cosmic density fields and halo lists, we compare the morphology and evolution of the 21-cm signal for these different cases. We also include a Lyman-$\alpha$ background in order to comment on the possible impact of late Lyman-$\alpha$ saturation. Our simulations are sufficiently large to capture the large-scale patchiness of reionization and to make statistically meaningful predictions for future 21-cm observations. The outline of the paper is as follows. In Section~\ref{sec:method}, we present our $N$-body and radiative transfer simulations and describe our different X-ray source models. In Section~\ref{sec:theory}, we summarize the extraction of the 21-cm signatures from our simulations. In Section~\ref{sec:lya}, we describe our semi-numerical radiative transfer of Lyman-$\alpha$ photons. Section~\ref{sec:results} contains our results, primarily comparisons between the different source models. We then conclude in Section~\ref{sec:conclusions}. The cosmological parameters we use throughout this work are ($\Omega_\Lambda$, $\Omega_\mathrm{M}$, $\Omega_\mathrm{b}$, $n$, $\sigma_\mathrm{8}$, $h$) = (0.73, 0.27, 0.044, 0.96, 0.8, 0.7); where the notation has the usual meaning and $h = \mathrm{H_0} / (100 \ \mathrm{km} \ \rm{s}^{-1} \ \mathrm{Mpc}^{-1}) $. These values are consistent with the latest results from WMAP \citep{Komatsu2011} and Plank combined with all other available constraints \citep{Planck2015,Planck2016}. | \label{sec:conclusions} In this paper, we present a suite of large-volume, fully numerical radiative transfer simulations of X-ray heating of the IGM during the CD, extending our previous work in Paper I. We introduced two types of QSO sources, with power-law spectral slopes of -0.8 and -1.6, and compare their impact to the effects of HMXB X-ray sources considered in Paper I, as well as a new case combining QSO and HMXB sources and a fiducial, stars-only simulation. Unlike HMXBs, the QSOs are rare and are assigned randomly to HMACH haloes with luminosities sampled from the high-redshift extrapolation of an empirical QXLF. These luminosities are not proportional to the host halo mass. As the precise nature and properties of these early sources remain uncertain, we have chosen a QXLF that predicts fairly numerous QSOs in order to examine their maximum possible impact. Our simulations show QSO sources may be able to contribute non-trivially to early X-ray heating and also suggest that it is possible to distinguish between soft- and hard-spectra models using the resulting 21-cm signal, particularly via the non-Gaussianity of the signal. These QSO sources contribute many fewer photons to the X-ray heating than HMXBs, so their overall energy contribution is subdominant compared to HMXB sources when both source types are present. On their own, both QSOs models yield a considerably more extended transition of the 21-cm signal from absorption to emission, and spin temperature saturation of the neutral IGM is not reached until reionization itself is well under way. The late temperature saturation in the simulations with only QSOs cause the non-Gaussianity from reionization itself ($z<10$) to be lower than in the case of full saturation of the spin temperature. This effect is more pronounced for the QSOs with softer X-ray spectra. During the CD, heating from QSOs has a more notable impact on the heating fluctuations than on the mean value of $\delta \rm T_b$. When compared to the stellar-only case, the $\delta \rm T_b$ power spectrum from all X-ray models show more power on larger scales and less on smaller scales until around $z\sim16$. After this time, the power spectrum of simulations including HMXBs decreases on all scales as temperature saturation is approached, but the power spectra for the QSO cases experience a further boost on large scales. The rms fluctuations for all X-ray source models are above the expected noise levels for observations with the SKA1-Low core, implying that low resolution tomographic imaging of the CD may be possible. The rare QSOs boost the rms, particularly when they are the only sources of X-ray heating. In this case, the peak value of the fluctuations are $\sim$10~mK higher than in the HMXB cases, and this peak occurs at lower redshift. By far, the clearest signature of the QSOs is found in one-point higher order statistics of the 21-cm signal PDF distribution: skewness and kurtosis. An increase in both quantities can be seen both when QSOs are the sole sources driving X-ray heating and when they are present with HMXBs. These strong non-Gaussianities are driven by the rareness of the QSOs, introducing fluctuations in the signal largely unrelated to the underlying (mostly Gaussian) density field. However, this increase in non-Gaussianity can be partly suppressed by late Lyman-$\alpha$ saturation, so while an extremely non-Gaussian signal from the CD could indicate the presence of QSOs, a more Gaussian signal would not rule them out. In addition to suppressing the non-Gaussianities, the Lyman-$\alpha$ background fluctuations (in all models) produced by late Lyman-$\alpha$ saturation cause an additional peak in $\delta \rm T_b$ fluctuations, as has been found in several previous works \citep[e.g.][]{Santos2008,Baek2010,Ghara2015,Watkinson2015}. The power spectra show that this is due mainly to contribution from larger scales. The peak magnitude of these rms fluctuations driven by the Lyman-$\alpha$ background is $\approx$8~mK, which is well below the expected image noise of 20~mK for imaging with the SKA1-Low core. However, a power spectrum detection of these fluctuations should still be possible. The difference found between our work and that in \citet{Eide2018} is model dependent and is in part due to their seeding algorithm only allowing the formation of black holes in haloes greater than 10$^{10}$M$_\odot$, resulting in a much lower number density of QSOs. This lower density combined with the assumption that QSOs have optically thick, geometrically thin disks (as described in \citet{Shakura1973}) leads to a somewhat more conservative heating prediction than in our models. This is illustrated by our agreement \citet{Yajima2014}, who follow a prescription similar to \citet{Eide2018} but assumes that black holes accrete at their Eddington luminosities. \citet{Datta2016} also predict that their individual, bright QSO would be detectable in 1000~h integrations with SKA1-Low -- which is in agreement with our own predictions. \citet{Datta2016} use observations of the low-redshift QSOs to determine their luminosities, a method more comparable to our own. A key implication of the results presented in this work is that all the X-ray source models we investigated go through phases in which the fluctuations in the 21-cm signal are above the expected noise for observations with the core of SKA1-Low \citep{Koopmans2015}, suggesting that at least part of this epoch could not only be studied with power spectra, but directly imaged. In Paper~I, we found this to be the case for HMXBs, and we can now extend this conclusion to the cases with rare, QSO-like sources. With higher levels of galactic foregrounds and stronger ionospheric effects, imaging around $z\sim 16$ will not be easy, but images of the CD would open the door to a multitude of analysis techniques to extract information from the signal about the astrophysics of the CD. Examples include parameter estimation through deep learning of images \citep[e.g.]{Shimabukuro2017,Gillet2018} and MCMC approaches \citep[e.g.]{Greig2018}, emulators \citep[e.g.]{Kern2017}, the bispectrum \citep[e.g.]{Shimabukuro2016}, and size distributions of features \citep[e.g.][]{Giri2018}. \citet{Ghara2015} and \citet{Baek2010} find power spectra with similar magnitudes to our own. Detailed comparisons to these works are complicated by the fact that \citet{Baek2010} has no subgrid model for unresolved, low-mass sources and \citet{Ghara2015} use a subgrid model very different from the one employed in this work. The subgrid modeling is particularly important for comparisons as lower resolutions of these simulations mean that resolved haloes do not appear until later in the CD. \citet{Pritchard2007} and \citet{Pacucci2014} also find power spectra with comparable magnitudes. The large-scale fluctuations in these works (at $k\approx 0.1$Mpc$^{-1}$) peak at roughly the same time as our models including HMXBs. \citet{Baek2010} and \citet{Watkinson2015} include measures of the power spectra and higher order statistics of the 21-cm signal produced by HMXB sources. The peak skewness values during the CD found from models S4 and S2 in \citet{Baek2010} are in agreement with the ones found in our HMXB model (S4), but are significantly lower than the values found from our simulations including QSOs. The lack of correlation between our QSO luminosities and their host dark matter haloes, along with their rareness are the factors driving this. The difference is far more pronounced in the early Lyman-$\alpha$ saturation case, but still noticeable in the late Lyman-$\alpha$ saturation case. Similarly, the skewness found for all models in \citet{Watkinson2015} have peak values far lower than that of our QSO models (but the case `$\log\zeta_{\rm X}=55$' is in agreement with our HMXB model). The high level of non-Gaussianity produced by QSOs imply that higher order statistics may be a more useful probe than the power spectra to discriminate between certain source models in the CD. In particular, high non-Gaussianity likely indicates the presence of rare sources, such as QSOs. The skewness shows a clear difference between our models including QSOs and our models containing HMXBs, as well as models from other works. Clearly our QSO-like sources introduce a significantly greater amount of non-Gaussianity in the signal. This result further motivates the use of alternative analysis techniques to interpret the signal from the CD to probe for rare X-ray sources. The bispectra of the 21-cm signals from all the X-ray simulations presented here have been extensively studied in \citet{Watkinson2018}. Conversely, investigating the non-Gaussianities during the EoR could be less insightful than previously hoped if late heating occurs. Despite the additional fluctuations introduced to the kinetic temperature of the gas, non-Gaussianties during the EoR are in fact lower in our QSO-only models. This decrease is due to the magnitude of $\delta T_{\rm b}$ from the neutral regions being lower in the late heating case than for the saturated spin temperature case, removing the brightest points from the signal. There are some other potential X-ray sources that may have contributed to the fluctuations in the 21-cm signal in the CD that we have not yet considered, for example supernovae \citep[e.g.][]{Yajima2015}. In addition, there is still a large parameter space associated with our current sources, for example varying the star formation efficiency of haloes and hence the luminosity of our HMXBs. Due to the computational expense of our simulations, we have not yet been able to fully explore the huge parameter space associated with the CD. However, the alternative of exploring the parameter space with fast semi-numerical models may not be sufficient. Ideally, these two approaches should be combined in order to achieve reliable predictions and interpretation of any observational detections. Another limitation of the current work is the modeling of the Lyman-$\alpha$ background. We have included only the two most extreme cases, one where very early sources build up a Lyman-$\alpha$ background before the simulation begins (early Lyman-$\alpha$ saturation) and one where only sources present in our simulation volume contribute to the Lyman-$\alpha$ background (late Lyman-$\alpha$ saturation). However, the most likely scenario is somewhere in between, with earlier sources, such as mini-haloes, contributing a non-negligible Lyman-$\alpha$ flux to the background, but not achieving full Lyman-$\alpha$ saturation. Finally, recent observations suggest that the z$\approx$10 Universe may not be as dust and metal free as previously thought \citep{Chiaki2019,Tamura2019}. Dust impacts the properties and evolution of galaxies, in particular the escape fraction, which could impact our results for this time. Our RT calculations assume hydrogen and helium to be the only elements present and may not be sufficient once enough metal enrichment has occurred. We leave these considerations for future work. Despite these few caveats, the results from our simulations have shown that the 21-cm signal from the CD may not only be statistically detectable with SKA1-Low, but also imageable. Our X-ray source models have distinct power spectra with markedly different the evolution for our difference models. Finally, the high non-Gaussianity driven by X-ray heating illustrates the need to consider statistics beyond the power spectrum when considering this signal, particularly when considering rare X-ray sources. | 18 | 8 | 1808.03287 |
1808 | 1808.06188_arXiv.txt | The detection of stochastic background of gravitational waves (GWs), produced by cosmological phase transitions (PTs), is of fundamental importance because allows to probe the physics related to PT energy scales. Motivated by the decisive role of non-zero quark chemical potential towards understanding physics in the core of neutron stars, quark stars and heavy-ion collisions, in this paper we qualitatively explore the stochastic background of GW spectrum generated by a cosmological source such as high-density QCD first order PT during the early Universe. Specifically, we calculate the frequency peak $f_{peak}$ redshifted at today time and the fractional energy density $\Omega_{gw}h^2$ in light of equation-of-state improved by the finite quark (baryon) chemical potential (we consider an effective three flavor chiral quarks model of QCD). Our calculations reveal a striking increase in $f_{peak}$ and $\Omega_{gw}h^2$ due to the quark chemical potential, which means to improve the chances of detection, in possible future observations (in particular SKA/PTA experiments), of the stochastic background of GWs from QCD first order PT. Even if the improvements could be weak, by updating the sensitivity of relevant detectors in the future, we can still remain hopeful. Concerning the phenomenological contribution of QCD equation-of-state, and in particular the possibility to detect a stochastic GW signal, we further show that the role of the quark chemical potential is model-dependent. This feature allows to discriminate among possible QCD effective models depending on their capability to shed light on the dynamic of QCD-PT through future observations of primordial GWs. In this perspective, the results are indeed encouraging to employ the GWs to study the QCD PT in high density strong interaction matter. \pacs {04.30.-w, 04.30.Db, 25.75.Nq, 12.39.-x} | Electromagnetic radiation (EMR)-based observations, in particular the cosmic microwave background (CMB) radiation emitted 380,000 years after Big Bang, are one of the most important source of our current understanding of the Universe. This window on the early Universe, however, has a limited horizon because, before that time, the Universe was opaque to EMR. In other words, any signals from earlier times can only be observed indirectly via their footprints on the CMB which is a serious restriction in the sense that many important questions in cosmology require information about the events during the first instant (nanoseconds and microseconds) after the Big Bang. Even though there is a wide scope for exploiting the entire electromagnetic spectrum, the above restriction remains in the face of very early Universe. In this respect gravitational waves (GWs) can remove such a limitation and, therefore, could be able to provide a new source of information about the primordial Universe. Because the GWs, like electromagnetic waves, travel at the speed of light owing to their extremely weak interaction with matter, the Universe has always been transparent to them, providing hence a direct view of the very first epochs of the Universe. As a result, the combination of GW observations \cite{ref:ligo1, ref:ligo2} with CMB observations allows to address some puzzle of present cosmology, such as the nature of dark energy and dark matter (see for example \cite{addazi}), early evolution of structures, and so on\footnote{It is interesting to point out that, the physical meaning of GWs, as the vibrations of spacetime predicted by Einstein, was discussed at the Chapel Hill conference \cite{ref:1957}. In this regards, it was understood that GWs are energy carriers passing through the spacetime that affects the position of particles in its path \cite{ref:Bondi1957, ref:Bondi1959}.}. Moreover, the existence of GWs is not only restricted to General Relativity, but indeed they can be found in many modified theories of gravity \cite{Report,Report2,astrop, sergei,Calmet,lambiase1,lambiase2}. Generally, GWs emerge from cosmological and relativistic astrophysical sources. Concerning the astrophysical sources, coalescing binary neutron stars, as demonstrated, are regarded as the most likely GW sources to be seen by VIRGO/LIGO interferometers. Some researches suggest that GWs emitted by the merging of binary neutron stars could yield significant information about the equation-of-state (EoS) of dense matter and the related gravitational theory, see e.g., \cite{Faber,Taniguchi,Dorota,Oechslin,Bejger,felix}. As recently discussed in \cite{Soroush}, GWs produced by binary mergers lead to circular polarization signal generation which may be captured by X-ray polarimetry missions. The detection of GWs with cosmological origins (unlike their astrophysical counterpart have a stochastic and random character) has special significance in the sense that it can be physically relevant for the Universe evolution in the very early stages. Concerning the cosmological origin, there are primordial GWs emerging from some processes as inflation and reheating epochs. Remarkably, these GWs can be tracked and measured via their unique footprint on the CMB. However, during the expansion of the Universe after inflation, and according to the Standard Model of elementary physics, we have to take into account also for phase transitions (PTs) at lower temperatures that can generate GWs: the electro-weak and quantum chromodynamics (QCD) PTs. Despite the fact that there is still no final agreement on the type of these two PTs, it is believed that GWs should be produced in models with enough long duration, i.e. during first order PTs. More technically, in the first order cosmological PT-based GWs, the nucleation of bubbles is due to a series of expansions and encounters with each other, resulting in a major stochastic background of GWs. The eLISA interferometer \cite{ref:elisa}, as a space-based GW detector as well as other operators as PTA \cite{ref:pta2013} and SKA \cite{ref:ska2004} with different sensitivities\footnote{It should be noted that GWs cover a wide range of frequencies that, for identification of each, require particular technology. For instance, relevant frequency of QCD-PT-based stochastic GWs is around $<10^{-5}$HZ. In Refs. \cite{ref:Kumar2017,noi}, frequencies related to other GW sources are discussed.}, are designed to trap stochastic background of GWs arising from electro-weak and QCD PTs, respectively. Note that, similarly to the CMB radiation which is emitted from the last scattering surface, the stochastic background of GWs is produced from distant surfaces of the Universe perimeter, at the PTs epoch \cite{ref:Geller2018}. The PT, that we are considering in this paper as a cosmological source of stochastic GWs, is related to the QCD epoch\footnote{Recall that, in high energy regime, QCD is an asymptotic freedom and perturbative theory while, at low energy, it is strongly-coupled so that a perturbative approach is not useful \cite{ref:Ahmad2018}.}. After a few microseconds from the Big Bang, a PT happened from a mixed phase of quark-gluon plasma (QGP) evolving in hadrons. To achieve a real understanding of QCD PT dynamics, without an appropriate thermodynamics related to a relevant equation-of-state (EoS), is impossible. In this respect to have a proper EoS becomes therefore crucial, especially when the stochastic background of GWs generated by any PT is known. It severely depends on the critical temperature\footnote{In \cite{noi}, it is shown, in the Planck physics extended framework, assuming some natural cutoffs on the length and momentum of particles into QCD thermodynamic, that the stochastic GW background results affected even in the absence of change in the critical temperature.} $T_*$ (in particular here $T_{*(QCD)}\sim$ a few hundred MeV), \cite{ref:Kumar2017,ref:Hajkarim2015,noi}. In \cite{ref:Witten,ref:JH1985}, it has been shown that the quark-hadron PT could result in the formation of some primordial QGP bodies which can, eventually, survive up to now. However, in the absence of the baryon chemical potential, the quark content of such bodies (as quark stars) in the above QCD critical temperature, have limitations and cannot be so large. This is why, incorporating the quark chemical potential (QCP) into EoS, and owing to a high degree of supercooling at around the same QCD critical temperature, the possible formation of bodies with larger quark content can be achieved. In other words, neglecting the chemical potential can only be a good approximation for low-density QCD-PT\footnote{ More precisely, although at end of QCD-PT the ratio of quark density number to photon number density $\eta=\frac{n_q}{n_\gamma}$ may be tiny, of the order of $\simeq10^{-10}-10^{-9}$ (as required by primordial nucleosynthesis), at temperatures above critical temperature (QGP phase) it is order of unity \cite{ref:j2000} and \cite{book:cosmo}. The exact value of the baryon asymmetry $\eta$ is released in two independent way, the measurements of the light element abundances based on the Big Bang Nucleosynthesis (BBN) and the measurement of the CMB temperature anisotropy. This tiny value shows that the entropy of the Universe is dominated by a huge margin by the CMB photons since for every baryon in the Universe there are over 1 billion photons. This means that in QGP phase (the phase above the QCD scale which is expected, via transition to low phase, to generate stochastic GW(s)) we are dealing with a considerable number of baryons. Therefore, regarding the possibility of large quark densities in QGP phase, the approximation of ignoring the QCP cannot be valid and should be corrected by adding the contribution of the finite QCP. As well as, in Ref. \cite{plb2013} it is shown that by taking into account the anisotropy of positively and negatively charged quarks in the early QGP phase, there may have been fluctuations in the chemical potential.}. We note that the properties of high-density QCD ground state (non-zero baryon chemical potential) play a decisive role in understanding physics in the core of the neutron stars and heavy-ion collisions \cite{ref:npb2000}. It is worth noticing that the hypothesis of quark stars have been discussed for the first time by Itoh in \cite{itoh}. Problems related to dense quark matter and related emissions are discussed in \cite{anderson, flowers, hayashi}. However, one of great issues of lattice QCD simulations is the inability to predict such models since the chemical potential effect, when taken into account in the calculations, lead to a complex fermion determinant which is non-physical. Consequently, in the framework of high-density QCD PT, more attention is paid to phenomenological models such as the MIT bag model \cite{ref:mit1974}, and its generalized versions. Given the irrefutable phenomenological role of EoS, it is interesting to revisit the stochastic GW background power spectrum originated from high-density QCD first order cosmological PT. The approach consists in improving reliable EoSs with a finite temperature and a chemical potential. In other words, the chemical potential contributions (that address the possibility of large quark density bodies in the early Universe) provide a suitable test-bed to investigate on the QCD-based stochastic GW background from systems with large densities. This paper is structured as follows. In Sec. \ref{Sec:Eff}, we briefly present a high-density QCD model, the so called chiral quark model with three flavors (up, down and strange) in which, considering QCP, we deal with the improved EoS. In Secs. \ref{Sec:SGW1} and \ref{Sec:SGW2}, we show the positive role of the QCP to the detection of stochastic GW background. In Sec. \ref{Sec:SGW3}, by employing another high-density effective model of QCD, the so called cold QGP with two light quarks, the up and down quarks, we show that the role of QCP to detect the stochastic signal expected in GWs is highly model-dependent. Finally, Sec. \ref{Sec:Disc} is devoted to summary and results. Throughout this work we use natural units (we set the physical constants $c,~\hbar,~k_B$ and $8\pi G/3$ equal to unity). | \label{Sec:Disc} We have explored the implication of high-density QCD first order PT in the production of stochastic GW background. We started our considerations assuming an effective QCD model with three chiral quark flavors (up, down, strange) including finite temperature and chemical potential. In particular, by focusing on two measurable quantities, namely the peak frequency $f_{peak}$ redshifted at today time and the fractional energy density $\Omega_{gw}h^2$, we have revisited the stochastic background of GW spectrum propagated from first order PT to the QCD era. We have assumed a high-density regime with a finite quark chemical potential. It turns out an increasing of the characteristic frequency and the amplitude of stochastic GW signal received today , as the chemical potential increases (Figs. \ref{BC} (right panel) and \ref{sm1}). This can be considered a solid feedback because, in the presence of chemical potential, the chance of measuring the stochastic background of GWs, caused by the QCD-PT, could be a reliable goal in future observations by experiments like the ``Pulsar Timing Array'' (PTA) and the ``Square Kilometer Array'' (SKA). Due to the reinforcing role of quark chemical potential, this signal amplification enhances the possibility of locating the stochastic GWs emerged from QCD-PT into the sensitivity range of SKA/PTA. Even if this possibility is weak at the moment, by updating the sensitivity of the related experiments in the future, we can still remain hopeful. As a final comment, we discuss the possibility that the constructive contribution of the quark chemical potential to detection of stochastic GWs background could be model-independent (i.e. the existence of a chemical potential independent on the model under consideration might imply an amplification of the GWs due to the QCD-PT). To investigate this topic, we have extended our study to cold QGP effective model of QCD first order PT with two light quarks: up, down. Here, despite to the previous result for $f_{peak}$, it is possible to show that $\mu$ increases the amplitude of stochastic GW background $\Omega_{gw}h^{2}$, but falls with respect to the case $\mu=0$ (Figs. \ref{signal} (bottom panel) and \ref{sm2} (left panel)). So, the underlying effective QCD model predicts stochastic GWs with the peak frequency higher, but with amplitude signal weaker than the one corresponding to $\mu=0$. An important point that should be noted is that in contrast with Lattice outputs which addresses crossover PT, here both the effective QCD models, also in absence of the quark chemical potential, result in a first order PT. Therefore, the appearance of the GW signal in these two models for the case $\mu=0$ is not unexpected. Of course, taking into account the finite chemical potential into Lattice simulation, there is also the possibility for first order QCD-PT, see \cite{ref:prd2013} for instance. As a consequence, these feedbacks suggest that the contribution of the quark (baryon) chemical potential to the detection of stochastic GW background is highly model-dependent. The benefit of the model-dependent output of chemical potential is that, by tracking the effective QCD models in light of GW spectrum, future GW observations can fix the dynamics of the QCD-PT. More precisely, the stochastic GW spectrum can be regarded as a criterion for classifying the effective QCD models from a phenomenological point of view. | 18 | 8 | 1808.06188 |
1808 | 1808.04144_arXiv.txt | The near-Sun kinematics of coronal mass ejections (CMEs) determine the severity and arrival time of associated geomagnetic storms. We investigate the relationship between the deprojected speed and kinetic energy of CMEs and magnetic measures of their solar sources, reconnection flux of associated eruptive events and intrinsic flux rope characteristics. Our data covers the period 2010-2014 in solar cycle 24. Using vector magnetograms of source active regions we estimate the size and nonpotentiality. We compute the total magnetic reconnection flux at the source regions of CMEs using the post-eruption arcade method. By forward modeling the CMEs we find their deprojected geometric parameters and constrain their kinematics and magnetic properties. Based on an analysis of this database we report that the correlation between CME speed and their source active region size and global nonpotentiality is weak, but not negligible. We find the near-Sun velocity and kinetic energy of CMEs to be well correlated with the associated magnetic reconnection flux. We establish a statistically significant empirical relationship between the CME speed and reconnection flux that may be utilized for prediction purposes. Furthermore, we find CME kinematics to be related with the axial magnetic field intensity and relative magnetic helicity of their intrinsic flux ropes. The amount of coronal magnetic helicity shed by CMEs is found to be well correlated with their near-Sun speeds. The kinetic energy of CMEs is well correlated with their intrinsic magnetic energy density. Our results constrain processes related to the origin and propagation of CMEs and may lead to better empirical forecasting of their arrival and geoeffectiveness. | \label{sec:intro} A Coronal mass ejection (CME) represents one of the most energetic phenomenon on the Sun, ejecting a massive amount of solar magnetized plasma (order of $10^{12}$ kg) carrying significant energy ($10^{31}-10^{33}$ erg) \citep[e.g.][]{1974JGR....79.4581G,1997cwh..conf..259H,2016GSL.....3....8G},\citep{2017SSRv..212.1159M,Green2018} in to interplanetary space. The origin of CMEs is related to the magnetic field dynamics on the solar photosphere \citep[e.g.][]{2007AAS...210.2402N}. If a CME is directed towards Earth, it may cause major geomagnetic storms depending upon its kinematics, magnetic structure and magnetic field strength at 1 AU \citep[e.g.][]{2009cwse.conf...77G},\citep{Kilpua2017}. When a high-speed interplanetary CME (ICME) with an enhanced southward magnetic field component hits the Earth, it reconnects with the Earth's magnetosphere, enhances the ring current \citep{1998JGR...10317705K} and temporarily decreases the strength of Earth's horizontal magnetic field component. Such solar-induced magnetic storms can result in serious disruptions to satellite operations, electric power grids and communication systems. Understanding the origin of CMEs, their subsequent dynamics and developing forecasting capabilities for their arrival time and severity are therefore important challenges in the domain of solar-terrestrial physics.\par Near-Sun kinematic properties is one of the features of CMEs that can be used to predict the intensity and onset of associated geomagnetic storms \citep{2002GeoRL..29.1287S}. In order to predict the CME arrival time at 1 AU, several empirical and physics based models constrain CME propagation through interplanetary space \citep{2001JGR...10629207G,2013SpWea..11..661G,2003JGRA..108.1445C,2003JGRA..108.1070F},\citep{2013SpWea..11..661G,2013SoPh..285..295V,2015SoPh..290.1775M,2017ApJ...837L..17T,2018ApJ...854..180D}. The models are usually based on the initial speed of CMEs. CMEs originate in closed magnetic field regions on the Sun such as active regions (ARs) \citep{2001ApJ...561..372S} and filament regions \citep{2015ApJ...806....8G}. Several studies have attempted to connect the near-Sun CME speeds and magnetic measures of their source regions \citep{2017SoPh..292...66K,2015GeoRL..42.5702T,2008ApJ...680.1516W,2002ApJ...581..694M}. \citet{2012Ge&Ae..52.1075F} studied the projected speed of 46 halo CMEs and found that the CME speed is well correlated with the average intensity of line-of-sight magnetic fields at CME associated flare onset. A recent study by \citet{GOPALSWAMY2017b} and \citet{2007ApJ...659..758Q} showed that the poloidal magnetic flux of flux rope ICMEs at 1 AU depends on the photospheric magnetic flux underlying the area swept by the flare ribbons or the post eruption arcades on one side of the polarity inversion line (defined as flare reconnection flux). Extension of these studies offer great potential for better constraining the origin and dynamics of CME flux ropes. \par Magnetic reconnection plays an essential role at the early stage of CME dynamics. Both theoretical calculations and numerical simulations show that enhancement of CME mass acceleration is accompanied by an enhancement in the rate of magnetic reconnection at its solar source \citep{2000JGR...105.2375L, 2003ApJ...596.1341C}. Also, an observation by \citet{2004ApJ...604..900Q} revealed a temporal correlation between the reconnection rate inferred from two-ribbon flare observations and associated CME acceleration. Several previous studies attempted to compare the total flux reconnected in the CME associated flares and CME velocity and observed a strong correlation between these parameters \citep{2005ApJ...634L.121Q, 2009A&A...499..893M, GOPALSWAMY2017b}. It is well established that the acceleration phase of CMEs is synchronized with the impulsive phase of associated flares \citep{2001ApJ...559..452Z, 2003ApJ...588L..53G}. \citet{2008ApJ...673L..95T} observed a close relationship between CME acceleration and flare energy release during its impulsive phase. There exists a feedback relationship between flares and associated CMEs through magnetic reconnection that occurs in the current sheet formed below the erupting CME flux rope \citep{2010ApJ...712.1410T, 2008AnGeo..26.3089V, 2016AN....337.1002V}. This reconnection process significantly enhances the mass acceleration of the ejections as well as release energy through the accompanied two-ribbon flares \citep{2000JGR...10523153F,2000JGR...105.2375L}. These studies motivate us to explore the relationship betwen CME kinematics and the magnetic reconnection which causes the CME flux rope eruption. CMEs are typically observed by coronagraphs which occult the photosphere of the Sun and expose the surrounding faint corona. Basic observational properties of CMEs such as their structure, propagation direction, and derived quantities such as velocity, accelerations, and mass are subject to projection effects depending on the location of the CME source region on the solar surface \citep{JGRA:JGRA17179,angeo-23-1033-2005},\citep{2007A&A...469..339V},\citep{2008JGRA..113.1104H}. The coronagraphs of the Sun-Earth Connection Coronal and Heliospheric Investigation \citep[SECCHI,][]{2008SSRv..136...67H} aboard the Solar TErrestrial RElations Observatory (STEREO) spacecrafts A \& B provide simultaneous observations of CMEs from two different viewpoints in space. Applying the forward modeling technique \citep{2006ApJ...652..763T,2009SoPh..256..111T,2011ApJS..194...33T} to CME white-light images observed from different vantage points, one can better reproduce CME morphology and dynamics. Thus deprojected CME parameters can be estimated \citep{2012SoPh..281..167B,2013JGRA..118.6858S,2013SoPh..284...47X}.\par In this paper, we examine the size, nonpotentiality and the flare reconnection flux of CME associated flaring active regions using observations from different instruments on the Solar Dynamic Observatory \citep[SDO,][]{2012SoPh..275....3P} and connect them with CME knematics and flux properties. \citet{GOPALSWAMY2017b} studied about 50 CMEs from solar cycle 23 and their flux rope properties. Here we consider a number of CMEs from cycle 24 using a different flux rope fitting method for multi-view observations and confirm, extend and set better constraints on the relationship between CME properties and its source regions. \par We organize this paper as follows. In Section~2 we describe the procedure of selecting CMEs and their associated solar sources and summarize the method of measuring the deprojected geometric properties of CMEs and the magnetic properties of their solar sources. In Section~3 we examine the relationship between CME kinematics with magnetic measures of their source regions as well as their intrinsic, near-Sun flux rope magnetic properties. We discuss our results in Section~4 and conclude in Section~5 | In this study, we obtain the deprojected physical parameters of flux rope CMEs of solar cycle 24 and calculate their magnetic (azimuthal flux, axial magnetic field intensity, and magnetic helicity) and kinetic parameters (speed and kinetic energy). Next, we measure the magnetic parameters of the associated source ARs and find the dependency of near-Sun CME kinematics on the AR magnetic parameters. We explain the basis of the relationship found between these parameters and also investigate the correspondence between the magnetic and kinetic properties of CMEs. The main conclusions of this study are: \begin{enumerate} \item The area and nonpotentiality of the entire source regions and the speed of associated CMEs are weakly correlated. The reason is probably the small average ratio ($\approx 0.3$) of reconnection flux during eruptions and the total flux in the source ARs. The smaller value of the flux ratio indicates that usually only a fraction of an AR involves an associated eruption. \item The flare reconnection flux is a proxy of the reconnection energy associated with an eruptive event. In our study, we find a good correlation between CME kinematics (speed and kinetic energy) and reconnection flux with $r$= 0.66 and 0.68 in case of CME speed and kinetic energy, respectively. The slope of the regression line fitted to the reconnection flux-CME speed pairs for the events of solar cycle 24 is 0.69 which is in agreement with that derived by \citet{GOPALSWAMY2017b} for the events of solar cycle 23. The regression equation for the combined 81 events of both cycle 23 and 24 can be further used as an empirical model for predicting the near-Sun speed of CMEs. \item The magnetic content of a CME flux rope is well correlated with its velocity and kinetic energy. We find a good correlation between the magnetic pressure of CME and its kinetic energy. This relationship is evident from the fact that the rapid expansion of CME occurs due to the higher magnetic pressure of CME flux rope relative to that of the background magnetic field. \item We find that CME speed increases with the coronal magnetic helicity carried by the CME flux rope. \end{enumerate} | 18 | 8 | 1808.04144 |
1808 | 1808.02886_arXiv.txt | NGC\,6910 is the northern hemisphere open cluster known to be rich in $\beta$\,Cephei-type stars. Using four-season photometry obtained in Bia\l k\'ow (Poland) and Xinglong (China) observatories, we performed variability survey of NGC\,6910. As the result, we found over 100 variable stars in the field of the cluster, including many stars showing variability due to pulsations and binarity. Thanks to the spectroscopic observations, we also detected changes in the profiles of spectral lines of $\beta$\,Cep stars, caused by pulsations. | NGC\,6910 is the young open cluster containing many $\beta$\,Cep-type variables \citep{Zibi2004}. Preliminary results of the variability search based on photometric data obtained during the international observational campaign allowed to detect eight $\beta$\,Cep-type members \citep{Pigu2008, Saes2010}. Interestingly, it turned out that the frequency spectra of these $\beta$\,Cep stars, arranged according to the decreasing brightness (i.e.~mass) showed a progression of frequencies of the excited modes \citep{Pigu2008}. This result raised hope for a successful ensemble asteroseismology in this cluster \citep{Saes2010}. In the present paper, we show preliminary results of the full variability survey of NGC\,6910 based on the part of the data obtained during the international observational campaign in the years 2005 -- 2007 and 2013. The full results will be published elsewhere. | 18 | 8 | 1808.02886 |
|
1808 | 1808.05973_arXiv.txt | {{\kes} is among the Galactic supernova remnants (SNRs) proposed to be physically linked to $\gamma$-ray emission at GeV energies. Although not conclusively, the nature of the $\gamma$-ray photons has been explained by means of hadronic collisions of particles accelerated at the SNR blast wave with target protons in an adjacent molecular clump. We performed an analysis of \emph{Fermi}-Large Area Telescope (LAT) data of about 9 years to assess the origin of the $\gamma$-ray emission. To investigate this matter we also used spectral modelling constraints from the physical properties of the interstellar medium towards the $\gamma$-ray emitting region along with a revised radio continuum spectrum of {\kes} ($\alpha = -0.54 \pm 0.10$, $S\propto\nu^{\alpha}$). We demonstrated that the $\gamma$-ray fluxes in the GeV range can be explained through bremsstrahlung emission from electrons interacting with the surrounding medium. We also consider a model in which the emission is produced by pion-decay after hadronic collisions, and confirmed that this mechanism cannot be excluded.} | Molecular clouds (MCs) house stellar objects at different stages of their evolution, from star-forming regions (SFRs) to the remains of supernovae (SNe). The detection of $\gamma$ rays at GeV and/or TeV energies from the molecular gas can serve to illuminate the high-energy particle production taking place in these objects located within the cloud and even in its vicinity. Indeed, at a first glance the spatial correspondence of a cloud with the $\gamma$-ray emission is susceptible to explain the latter via collisions of accelerated protons, for instance at supernova remnant (SNR) shock fronts, with target protons \citep[and maybe heavier nuclei,][]{banik+17} in the ambient matter. However, the recognition of this mechanism is not always straightforward since leptonic processes can also result in $\gamma$-ray emission via either bremsstrahlung or inverse Compton scattering produced by relativistic electrons. Certainly, the number of $\gamma$-ray emitting sources detected at GeV energies by the \it Fermi \rm Gamma-ray Space Telescope is growing rapidly. More than 3000 sources were reported in the last catalogues presented by \citet{acero+15} and \citet{ackermann+16}. However, only for $\sim$35 of these sources a reliable counterpart originated in the radio emission from SNRs was found. Remarkably, approximately only half of these SNRs are well found in interaction with surrounding molecular gas.\footnote{See \url{http://www.physics.umanitoba.ca/snr/SNRcat/}.} As a counterpart to the GeV emission, several of the \it Fermi \rm sources were also detected at TeV energies\footnote{See \url{http://tevcat.uchicago.edu/}.}, and/or in the radio/X-ray domains \citep[see for instance,][]{castro+13,acero+16}. However, regardless of the existence of a spatially coincident counterpart, the comprehension of the relative contribution of hadronic and leptonic processes responsible for $\gamma$-ray production remains unclear for a large fraction of cases \citep[e.g.][]{tanaka+11,pivato+13, abd18}. Here we deal with the nature of the GeV $\gamma$-ray emission identified towards ($l$, $b$)$\simeq$(\dms{337}{\circ}{8},\dms{0}{\circ}{0}) with the Large Area Telescope (LAT) detector onboard the \emph{Fermi} satellite. The source known as 3FGL~J1838.6$-$4654 in the \emph{Fermi}-LAT source catalogue \citep[3FGL,][]{acero+15} lies in the GeV emitting region surveyed in this work.% \footnote{The source 3FGL~J1838.6$-$4654 is catalogued as FL8Y~J1638.5$-$4654 in the preliminary version of the \emph{Fermi}-LAT 8-year source list, which will be replaced by the forthcoming 4FGL catalogue.} Given the spatial coincidence on the plane of sky, \citet{liu+15} considered natural a link between the GeV emission and the Galactic SNR~{\kes}. Moreover, using the properties of the molecular gas emission derived by \citet{zhang+15} in a restricted $\sim$7$^{\prime}$ $\times$ 4$^{\prime}$ area along the western rim of {\kes}, \citet{liu+15} proposed the hadronic interactions as the most feasible process to explain the production of the $\gamma$-ray emission in the GeV domain. The large-scale structure of the ambient matter in which {\kes} evolves was recently investigated in the companion paper presented by Supan et al. (2018a). As a result, on the basis of molecular and atomic line emission data, respectively from The Mopra Galactic Plane CO Survey \citep{burton+13} and the Southern Galactic Plane Survey \citep[SGPS,][]{mcclure+05}, along with mid-infrared \emph{Spitzer} \citep{churchwell09, carey09} information, the authors reported the discovery of the natal cloud ($\sim$26$^{\prime}$ in size, mass $M$$\sim$10-30~M$_{\odot}$) of the SNR and several star-forming regions around it. Now, in the light of the newly-determined physical conditions of the $\gamma$-ray emitting cloud, together with an updated set of \emph{Fermi}-LAT data and on radio observations, we re-analised the feasibility of hadronic and leptonic models to fit the broadband spectral energy distribution (SED) for the SNR/$\gamma$-ray source system. | This paper is the second in a series focused on the multiwavelength analysis of the counterparts to the unidentified $\gamma$-ray emission detected at GeV energies towards the SNR~{\kes}. Motivated by the new results recently presented in Supan et al. (2018a) revealing the natal molecular cloud of {\kes}, we performed, for the first time, a global assessment of all available data from radio to $\gamma$ rays in order to determine the relative contribution of the hadronic and leptonic processes to the overall spectrum. To do this, we re-analised the \emph{Fermi}-LAT data to study the $\gamma$-ray radiation spatially coincident (in projection) with the recently unveiled large-scale molecular material in the region of the SNR~{\kes}. Using the leptonic models analysed in this work, we demonstrated that if the main contribution to the $\gamma$-ray emission comes from the SNR then, both radio and $\gamma$-ray data can be successfully modelled by synchrotron radiation and bremsstrahlung mechanism, respectively. A leptonic contribution from the inverse Compton emission to explain the production of the emission at GeV energies can be easily excluded. We also modelled the {\Fermi} spectral data by a hadronic scenario considering the molecular, atomic, and ionised interstellar gases and found that \rm hadronic interactions in a region relatively close to {\kes} provide a viable mechanism for explaining the observed $\gamma$-ray emission, which qualitatively agree with the results of \citet{liu+15}. | 18 | 8 | 1808.05973 |
1808 | 1808.05132.txt | The study of the luminosity measurements of the pre-white dwarf PG 1159-035 has established the properties of the rich power spectrum of the detected radiation and, derived thereof, the physical properties of this celestial body. Those of the measurements which are available online are analysed in this work from a different perspective. After the measurements were band-passed, they were split into two parts (of comparable sizes), one yielding the training (learning) set (i.e., the database of embedding vectors and associated predictions), the other the test set. The optimal embedding dimension $m_0=10$ was obtained using Cao's method; this result was confirmed by an analysis of the correlation dimension. Subsequently, the extraction of the maximal Lyapunov exponent $\lambda$ was pursued for embedding dimensions $m$ between $3$ and $12$; results were obtained after removing the prominent undulations of the out-of-sample prediction-error arrays $S (k)$ by fitting a monotonic function to the data. The grand mean of the values, obtained for sufficient embedding dimensions ($10 \leq m \leq 12$), was: $\lambda = (9.2 \pm 1.0 ({\rm stat.}) \pm 2.7 ({\rm syst.})) \cdot 10^{-2}~\Delta \tau^{-1}$, where $\Delta \tau=10$ s is the sampling interval in the measurements. On the basis of this significantly non-zero result, it may be concluded that the physical processes, underlying the variation of the luminosity of PG 1159-035, are non-linear. The aforementioned result for $\lambda$ was obtained using the $L^\infty$-norm distance; a larger, yet not incompatible, result was extracted with the Euclidean ($L^2$-norm) distance.\\ \noindent {\it PACS 2010:} 05.10.-a; 05.45.-a; 05.45.Gg; 45.30.+s; 95.10.Fh | Introduction} When the hydrogen reserves of a star are exhausted, the star collapses until the temperature in its core enables helium to ignite and burn to carbon. To determine the fate of the star, one only needs to know its mass. For stellar masses comparable to the Solar mass ($M_{\astrosun}$), the outer shells of the star evaporate into space (planetary nebula) leaving a relic at the centre, which evolves into a white dwarf. Discovered in 1977 in a project aiming at the identification of ultraviolet-excess stellar sources (Palomar-Green survey) \cite{green1986}, PG 1159-035 is a celestial body in the Constellation of Virgo, which the experts in the domain of Stellar Evolution place in a transitional phase, from the central star of a planetary nebula to a white dwarf. PG 1159-035 contains about $60 \%$ of the solar mass, confined within a radius of about $2.5 \%$ of the solar radius (about $2.7$ times the radius of the Earth), and is a few hundred times more luminous than our Sun. Stellar bodies in this transitional phase are known as `pre-white dwarves'. The variation of the luminosity of the pre-white dwarf PG 1159-035, arising from non-radial gravity-wave ($g$-wave) pulsations, was measured (for the first time to that detail) by the Whole Earth Telescope (WET) in 1989. The members of the Collaboration introduce the WET project as ``a global, interactive network of photometric observers who together provide essentially continuous coverage of a set of prioritised targets.'' \cite{winget1991} The pre-white dwarf PG 1159-035 might have attracted original attention because its ``near-equatorial declination allowed observatories in both hemispheres to participate in the observations.'' The analysis of the measurements, spanning over $229$ effective hours (hr) of data acquisition, revealed $122$ pulsation modes, with periods ranging from $300$ to $1000$ s \cite{winget1991}. Those of us who do not frequently come across Fourier transforms with a resolution of $1~\mu$Hz will undoubtedly be impressed by Fig.~4 of Ref.~\cite{winget1991}. That work set the region of interest in the power spectrum of the detected light (p.~330): ``The peaks of greatest power in the Fourier spectrum are largely confined to the interval between $1000$ and $2600~\mu$Hz, with the dominant power in the narrower interval between $1750$ and $2250~\mu$Hz.'' Reference \cite{winget1991} was also important for another, less obvious reason: it cemented the foundations of the domain of Asteroseismology, as the discipline studying the ``stellar structure and evolution as revealed by global stellar oscillations.'' To provide an idea of what may be learnt from the analysis of such observations, the authors of Ref.~\cite{winget1991} write (about PG 1159-035) in the abstract of their paper: ``We find its mass to be $0.586~M_{\astrosun}$, its rotation period $1.38$ days, its magnetic field less than $6000$ G, its pulsation and rotation axes to be aligned, and its outer layers to be compositionally stratified.'' The entirety of the luminosity measurements of PG 1159-035 (runs between 1979 and 2002) were analysed in a more recent paper \cite{costa2008}, leading to the detection of $76$ additional (i.e., on top of those which had been identified in Ref.~\cite{winget1991}) pulsation modes. As the authors mention in the abstract of their paper, the $122+76=198$ known pulsation modes of PG 1159-035 represent ``the largest number of modes detected in any star besides the Sun.'' Furthermore, Ref.~\cite{costa2008} improved on the accuracy of the physical quantities of PG 1159-035, e.g., on its rotation period ($1.3920 \pm 0.0008$ days), and provided updated estimates for the object's mass ($0.59 \pm 0.02~M_{\astrosun}$) and magnetic field ($<2000$ G). A number of models, aiming at the description of the measurements obtained from PG 1159-035 and from similar stars in terms of the physical processes in the interior of these bodies, may be found in the literature \cite{kawaler1994,garciaberro2006,corsico2006,corsico2008,althaus2008,costakepler2008}. The free parameters of these models include the stellar mass, the effective temperature $T_{\rm eff}$, the surface helium-layer thickness (usually expressed as a fraction of the stellar mass), and the stellar composition. Using such models, knowledge may be gained of the temporal evolution of celestial bodies which have split off from the so-called Post-Asymptotic Giant Branch, a horizontal branch in the Hertzsprung-Russell diagram, characterised by nearly constant luminosity and sharply decreasing temperature. The temporal evolution of these stars follows mass-dependent curves in the ($\lg T_{\rm eff}$,$\lg g$) plane\footnote{Of course, $\lg x \coloneqq \log_{10} x$.}, where $g$ stands for the ratio of the gravitational acceleration at the surface of the star to that at the surface of the Earth. By variation of the free parameters of the aforementioned models, stellar solutions are obtained and allowed to evolve in time. A database of stellar states (snapshots in the evolution of each simulated body) is thus created. After the (time-dependent) predictions for the pulsation spectra are obtained in each of these solutions, the database element, which best resembles the pulsation spectra obtained from the luminosity measurements of a given source, may be identified. Reliable information on the progenitor of the specific object, as well as forecasts for its future, may thus be obtained. References \cite{kawaler1994,garciaberro2006,corsico2006,corsico2008,althaus2008,costakepler2008} look at each such celestial body from the point of view of Physics, i.e., attempting its description in terms of the established principles of Astrophysics and, in particular, of Stellar Evolution. This work looks at the acquired data from a different perspective, investigating the possibility that the data alone could provide an answer on whether the physical processes, generating the observations, are linear or non-linear. Knowledge of the physical system is used as input only in the filtering of the scalar time-series measurements, namely in setting the appropriate band-pass/stop characteristics, as they have been known from Refs.~\cite{winget1991,costa2008}. To the best of my knowledge, this is the first study of the time-series measurements of PG 1159-035 from the perspective of non-linear dynamics. This work uses those of the time-series measurements of PG 1159-035, which may be found (among other data from a variety of scientific domains) in the web site \cite{timeseries} (data set E); henceforth, these measurements will be referred to as `original' (though, in reality, they have been selected from a larger set of data). Reference \cite{timeseries} does not provide information on how the available data has been obtained from the set of measurements acquired in the WET 1989 runs. The software development, relating to this work, is part of a broader and more ambitious programme, aiming at robust analyses of time series via the application of user-selected linear and/or non-linear methods. Free software performing such analyses has been available since a long time, e.g., see Ref.~\cite{hegger2007}. | Discussion and conclusions} The goal of this work was the analysis of the luminosity measurements of the pre-white dwarf PG 1159-035, in fact those of the measurements which found their way to the `Time-series data source Archives: Santa F\'e Time Series Competition' \cite{timeseries}. It is my belief that the set of the experimental data, acquired in the 1989 runs of the Whole Earth Telescope (WET) project, is considerably more extensive. Following the results of Refs.~\cite{winget1991,costa2008}, the seventeen available time series were suitably band-passed using an elliptical filter, whose $13$ recursion coefficients are listed in Table \ref{tab:RecursionCoefficients}. The filtered data was split into two parts of comparable sizes, one yielding the training (learning) set or database, the second the test set. The optimal embedding dimension was determined using Cao's method \cite{cao1997}, see Section \ref{sec:Cao}: it appears that optimal embeddings require a $10$-dimensional space. This choice was confirmed in Section \ref{sec:CorrelDim} by an analysis of the correlation dimension. The extraction of the maximal Lyapunov exponent $\lambda$ was next attempted by fitting a monotonic function (see Eq.~(\ref{eq:EQ010})) to the out-of-sample prediction-error arrays $S (k)$, defined in Eq.~(\ref{eq:EQ009}); the original arrays contain sizeable undulations, hindering the determination of a region in the ($k$,$S (k)$) plane within which a linear relationship (i.e., the signature of a chaotic dynamical system) holds. A modification is proposed in this work in the evaluation of the $S (k)$ arrays, taking account of the distance between the specific embedding vector of the test set and its corresponding partner in the training set: the smaller the distance between these two vectors, the larger the weight assigned to the associated predictions in the determination of the out-of-sample prediction-error arrays $S (k)$, see Eq.~(\ref{eq:EQ009_1}). The data analysis suggests that the maximal Lyapunov exponent $\lambda$, associated with the luminosity measurements of PG 1159-035, is equal to $(9.2 \pm 1.0 ({\rm stat.}) \pm 2.7 ({\rm syst.})) \cdot 10^{-2}~\Delta \tau^{-1}$, where $\Delta \tau$ represents the sampling interval in the measurements ($10$ s). It was found that the extracted $\lambda$ values do not show significant dependence on the embedding dimension for sufficient embeddings ($10 \leq m \leq 12$), see Fig.~\ref{fig:Lyapunov}. The findings of this work suggest that it is very likely that the source of the observations is indeed chaotic. The aforementioned results refer to the use of the $L^\infty$-norm distance. Interestingly, the use of the Euclidean ($L^2$-norm) distance yields a larger, yet not incompatible, result for the maximal Lyapunov exponent. This work is the first step I have taken in analysing the luminosity measurements of the pre-white dwarf PG 1159-035. I would be glad to receive the entirety of the data (1989 runs) from a credible source, e.g., directly from one of the members of the WET Collaboration. The analysis of the data after suitably involving all files in both the training and the test sets is currently under investigation \cite{matsinos2018}. \begin{ack} I acknowledge an e-mail exchange with S.~Hollos. All the figures have been created with MATLAB \textregistered~(The MathWorks, Inc., Natick, Massachusetts, United States). \end{ack} | 18 | 8 | 1808.05132 |
1808 | 1808.04622_arXiv.txt | We present a high-resolution ($R \simeq 20,000$) near-infrared (9,100--13,500~\AA) long-slit spectrum of P Cygni obtained with the newly commissioned WINERED spectrograph in Japan. In the obtained spectrum, we have found that the velocity profiles of the [\ion{Fe}{II}] emission lines are resolved into two peaks at a velocity of $\simeq220$~km~s$^{-1}$ with a moderate dip in between and with additional sub-peaks at $\simeq\pm100$~km~s$^{-1}$. The sub-peak component is confirmed with the long-slit echellogram to originate in the known shell with a radius of $\simeq10^{\prime\prime}$, which was originally created by the outburst in 1600 AD. On the other hand, the $\simeq220$~km~s$^{-1}$ component, which dominates the [\ion{Fe}{II}] flux from P Cygni, is found to be concentrated closer to the central star with an apparent spatial extent of $\simeq3^{\prime\prime}$. The extent is much larger than the compact ($<0^{\prime\prime}.1$) regions traced with hydrogen, helium, and metal permitted lines. The velocity, estimated mass, and dynamical time of the extended emission-line region suggest that the region is an outer part of the stellar wind region. We suggest that the newly-identified emission-line region may trace a reverse shock due to the stellar wind overtaking the outburst shell. | Luminous blue variable (LBV) stars are believed to have evolved from high-mass main-sequence stars and to become eventually Wolf-Rayet stars after various magnitudes of mass-loss (e.g., \citealt{lan94,mey11,smi14} and references therein). Circumstellar nebulae around LBV stars provide essential clues for mass-loss events (e.g., \citealt{naj97}) and evolutionary process of LBV stars (e.g., \citealt{smi11,wei11}). Steady mass-loss events create emission photospheres or shells around stars (e.g., \citealt{lam85}), whereas flash mass-loss events, which are often called ``eruptions'' or ``outbursts'', create emission shells as those seen in P Cygni and $\eta$ Carinae (e.g., \citealt{lam86,hum99,ish03,smihar06}). Thus the structure and kinematics of the LBV nebulae give us important clues about the mass-loss events. Infrared (IR) [\ion{Fe}{II}] lines are a powerful tool for investigating the structure and physical mechanisms of the LBV mass-loss events \citep{smi02}. Bright IR [\ion{Fe}{II}] lines are typically detected toward shock-excited objects or outflowing objects, such as supernova remnants, massive stars, and low-mass young stellar objects (e.g., \citealt{mea00,smi01a,smi02,har04,lee09,shi13}), and are detected in all the observed LBVs with near-IR (NIR) spectroscopy \citep{smi02}. Because the LBV nebulae are optically thin at the IR wavelength region, IR observations are key tools to study the circumstellar nebulae of LBVs (e.g., \citealt{art11,cla11,gva12}). For example, NIR observations of $\eta$ Carinae clearly resolve the emission components from different areas \citep{smi02c,smi06}. \citet{bar94} found a circular nebula around P Cygni with an angular radius of $\sim11^{\prime\prime}$ and an expansion velocity of $140$~km~s$^{-1}$ using the optical [\ion{N}{II}] $\lambda$6584 line. \citet{smihar06} (hereafter SH06) deeply investigated this nebula using the NIR [\ion{Fe}{II}] $\lambda$16440 line, and concluded that this nebula with a shell-like structure with a radius of $\sim8^{\prime\prime}-10^{\prime\prime}$ was ejected by the 1600-AD outburst. Other circumstellar nebulae outside of the 1600-AD outburst shell have also been studied (e.g., \citealt{mea96,mea00}). In addition, the [\ion{Fe}{II}] emission of P Cygni inside the 1600-AD outburst shell has also been investigated and found to be created in the region of $R\gtrsim100R_*$, where $R_*$ is the radius of P Cygni ($=76\pm14\,R_\odot$; \citealt{lam83}), based on the line ratio and/or the velocity width of the optical [\ion{Fe}{II}] emission lines (e.g., \citealt{isr91,sta91,mar97}). \citet{mar00} suggested that the forbidden lines in P Cygni originate at $\simeq100R_*$, where the wind has reached its terminal velocity. However, to our surprise, the upper limit for the radius of the [\ion{Fe}{II}] emission region has not been explicitly constrained. \citet{arc14} shows the [\ion{Fe}{II}] $\lambda16440$ image of P Cygni nebula with high angular resolution by adaptive-optics observations, but the inner structure within $3^{\prime\prime}$ is unclear because they masked the region. Here, we observed P Cygni with a newly developed high-resolution ($R\simeq20,000$) NIR ($9,100$--$13,500$~\AA) echelle ``WINERED'' spectrograph. P Cygni is the nearest LBV star at a distance of 1.7~kpc \citep{naj97} and thus the best target to study mass-loss events in LBVs. The range of the studied wavelengths, 9,100--13,500~\AA, falls between the optical and infrared wavelengths and has been relatively poorly studied in astronomy. However, this ``niche'' wavelength-range is rich in various types of emission lines, yet is contaminated less with background lines than optical wavelengths. In this paper, we first describe the WINERED spectrograph and the observation in Section 2. In Section 3, we show that the velocity profiles of the NIR [\ion{Fe}{II}] lines have a clear ``double-peak'', which have been considered as ``flat-topped'' in the past studies, and constrain the spatial extent of the [\ion{Fe}{II}] emission region. Finally, we discuss the origin of the extended region of the [\ion{Fe}{II}] emission in Section 4. | \subsection{Origin of the [Fe II] ``double-peak'' profile}\label{sec:doublepeak} When an emission line originates from an optically-thin spherically-symmetric shell/flow with a constant velocity, the intensity per unit frequency bin is independent of frequency; as a result, the line shows a ``flat-topped'' profile \citep{app84,emerson,shu}. The [\ion{Fe}{II}] velocity profiles of P Cygni have been treated as flat-topped in literature so far, and thus the [\ion{Fe}{II}] emission region of P Cygni has been considered as a compact and spherically symmetric layer expanding with a constant velocity (e.g., \citealt{sta91,isr91,mar97,mar00,kog07}). However, our observation with high-resolution NIR spectroscopy revealed that the [\ion{Fe}{II}] lines of P Cygni have ``double-peak'' profiles (\S\ref{result}). Moreover, we found that the ``double-peak'' emission region was spatially extended by $4.9\pm0.2\,\mathrm{kAU}$ (\S\ref{sec:spatial}). Is it plausible for the ``double-peak'' profile to originate from the ``extended emission region''? In optical/infrared spectroscopy, when a part of an optically-thin spherically-symmetric shell/flow with a constant velocity is masked by a slit of spectrograph, the intensity at the frequency corresponding to the radial velocity of the masked region becomes faint, and thus a part of ``flat-topped'' velocity profile is scraped off (e.g., Chapter 9 of \citealt{shu}). Therefore, when the emission region is extended wider than the slit width and the extended component with a slow radial velocity is masked, the velocity profile becomes hollow at the centre. Assuming a spherical, homogeneous and isotropic emission region, the model velocity profile can be calculated as a function of a diameter of the region. The blue-dotted line in Fig.\ \ref{fig:fitting} shows the model velocity profile of the emission region with a diameter of $2^{\prime\prime}$, which is slightly larger than the slit width ($1^{\prime\prime}.6$). The expansion velocity of the model profile is set to be $220$~km~s$^{-1}$, and the instrumental resolution is fully taken into account. Residuals seen in the velocity range of $-130$~km~s$^{-1}$ to $+130$~km~s$^{-1}$ (green-dashed) shows another clear double-peak profile, which is obviously a component of the 1600-AD outburst shell. Indeed, the estimated diameter of the ``double-peak'' emission region (as defined with FWHM$=2^{\prime\prime}.9\pm0^{\prime\prime}.1$; see \S\ref{sec:spatial}) is similarly larger than the slit width ($1^{\prime\prime}.6$). The emission region may be regarded as a region with uniform density with a diameter of roughly $2^{\prime\prime}$, but more accurate modeling should await slit-scanning data for acquiring information on radial density distribution. Consequently, the ``double-peak'' velocity profile is expected, as was observed, when the emission region is partially masked with the slit of spectrograph. We must note that some intrinsic ununiformity of the emission region can enhance or skew the spectral features. \begin{figure} \centering \includegraphics[width=\columnwidth,angle=270]{fig2c_fit.eps} \caption{ The observed velocity profile of [\ion{Fe}{II}] $\lambda$12570 (black-solid; same as Fig.\ \ref{fig2}c) and the model one for the ``extended emission region'' (blue-dotted; see the main text for the detail of the model). The green-dashed profile shows the residual component of the model fitting. } \label{fig:fitting} \end{figure} \subsection{Mass of the ``extended emission region''} \label{sec:mass} Constraining the mass is essential to investigate the nature of the emission region. Under the assumption that the ``extended emission region'' is spherically symmetric (\S\ref{sec:spatial}), the total gas mass ($M$) is given by \begin{equation} M=\mu m_\mathrm{H} \frac{n_e}{f_\mathrm{H}}f\frac{4}{3}\pi(R_2^3-R_1^3), \end{equation} where $\mu$ is the mean molecular weight, $m_\mathrm{H}$ is the mass of hydrogen atom, $n_e$ is the number density of electron, $f_\mathrm{H}$ is the hydrogen ionization fraction, $f$ is the filling factor, and $R_2$ and $R_1$ are the outer and inner radii of the emission region, respectively (SH06). The mean molecular weight $\mu$ is assumed to be 2.2. $f_\mathrm{H}$ in the 1600-AD outburst shell is calculated to be 0.86, using the line ratio [\ion{N}{II}]/[\ion{N}{I}] in SH06. In the ``extended emission region'', hydrogen atoms should be almost fully-ionized because they are much closer to the central star than the 1600-AD outburst shell. Therefore, we treated $f_\mathrm{H}$ in the ``extended emission region'' as unity. The outer radius $R_2$ of the ``extended emission region'' is $1^{\prime\prime}.45$. The inner radius $R_1$ must be small, given the spatial profile of the [\ion{Fe}{II}] $\lambda12570$ line (Fig.\ \ref{fig6}c) shows no apparent dip near the central star. Here, we set $R_1=0$. Estimating $f$ in the ``extended emission region'' is difficult because our observation could not spatially resolve its substructure in detail. We assumed that $f$ is similar to that of the 1600-AD outburst shell in SH06, and adopt $f=0.2\pm0.1$. $n_e$ can be calculated based on the ratios of the diagnostic [\ion{Fe}{II}] lines, $\lambda12567/\lambda16435$ and $\lambda15535/\lambda16435$ (SH06; see the second footnote\ for the notations). In Fig.\ 4 of SH06, we read $\lambda15535/\lambda16435$ as 0.16 in the ``extended emission region'' and as 0.1 in the 1600-AD outburst shell. In SH06, $\lambda12567/\lambda16435$ was 1.3 throughout the regions, and thus $\lambda15535/\lambda12567$ is calculated to be 0.12 and 0.08 in the ``extended emission region'' and the 1600-AD outburst shell, respectively. Comparing the $\lambda15535/\lambda12567$ ratios with the values in Fig.\ 3 of \citet{NS88}, we can estimate the respective electron densities to be $n_e=10000\,\mathrm{cm}^{-3}$ in the ``extended emission region'' and $6000\,\mathrm{cm}^{-3}$ in the 1600-AD outburst shell. The $n_e$ value hardly depends on the electron temperature in this range. With all the needed parameters (Table \ref{t1}), we derived the gas mass in the ``extended emission region'' to be $(8\pm4)\times10^{-4}M_\odot$. This value is about 0.5\% of that in the 1600-AD outburst shell, $M=0.16\pm0.08\,M_\odot$. The mass-loss rate with a constant stellar wind of P Cygni is $3\times10^{-5}M_\odot\,\mathrm{yr}^{-1}$ \citep{naj97b,naj97}; accordingly, the ``extended emission region'' contains gas of the constant stellar wind within $30\pm15$ yr. This value is consistent with a dynamical age, $R/\dot{R}=2.45\,\mathrm{kAU}/220$~km~s$^{-1}\sim50\,\mathrm{yr}$, which means that the total mass of this region can be explained by the steady stellar wind. As a result, the ``extended emission region'' is not considered to be a remnant shell of an eruption but a stellar wind region. \begin{table*} \begin{center} \caption{Parameters of the two [\ion{Fe}{II}] emission regions }\label{t1} \begin{threeparttable} \begin{tabular}{llcc} \hline \hline && 1600-AD outburst shell\tnote{$\ast$1} & Extended emission region \\ \hline Mean molecular weight &$\mu$ & \multicolumn{2}{c}{2.2} \\ Number density of electron&$n_e$ (cm$^{-3}$) & 6000 & 10000 \\ Hydrogen ionization fraction &$f_\mathrm{H}$ & 0.86 & 1 \\ Filling factor &$f$ & \multicolumn{2}{c}{$0.2\pm0.1$} \\ Outer radius &$R_2$ (arcsec)& 9.7 & 1.45 \\ Inner radius &$R_1$ (arcsec)& 7.8 & 0 \\ \hline Total gas mass &$M$ & $\simeq 0.16\pm0.08\,M_\odot$ & $\simeq (8\pm4)\times10^{-4}M_\odot$ \\ \hline \end{tabular} \begin{tablenotes}\footnotesize \item[$\ast$1] The values in this column are adopted from SH06. \end{tablenotes} \end{threeparttable} \end{center} \end{table*} \subsection{[Fe II] excitation} \label{sec:nature} The bright IR [\ion{Fe}{II}] emission is detected in all the observed LBVs with NIR spectroscopy \citep{smi02}. For example, \citet{smi06} showed the [\ion{Fe}{II}] $\lambda$16435 spacio-velocity map of $\eta$ Carinae and clearly indicated the two distinct emission regions within the nebulae; one is the thicker skin extended inside of the H$_2$ shell and consistent with the ``Homunculus'', and the other is the inner region and consistent with the ``Little Homunculus'' \citep{ish03,smi05}. The origin of the forbidden lines of LBV nebulae are not completely clear \citep{smi02,smi12}. On one hand, the shocked stellar wind interacted with the ambient medium radiates the forbidden lines: \citet{smi02} reported that the NIR [\ion{Fe}{II}] lines are good probes of shock-excited events such as LBV eruptions. If the ``extended emission region'' of P Cygni is heated by shock, its origin could be an episodic and relatively strong wind that occasionally happens due to stellar fluctuations. On the other hand, the forbidden lines may simply be radiatively excited \citep{smi06}: \citet{smi07b} suggested that, compared with shock heating, radiative heating dominates the energy balance in the Homunculus of $\eta$ Carinae by 2 orders of magnitude. If the ``extended emission region'' of P Cygni is radiatively heated, what we see in the region is a simply steady stellar wind with less number density and then is more extended than the compact stellar wind region traced by other lines. As a result, both scenarios are consistent with the statement that the ``extended emission region'' of P Cygni traces a stellar wind, not an eruption. \subsection{Origin of the ``extended emission region''} The expansion velocity of the ``extended emission region'' ($\sim220$~km~s$^{-1}$) is consistent with the terminal velocity seen in the P Cygni profile (see the vertical lines in Fig.\ \ref{fig2}). This implies that the ``extended emission region'' traces the outer wind after being accelerated and reaching the terminal velocity. The expansion velocity of this region is faster than that of the 1600-AD outburst shell ($\sim140$~km~s$^{-1}$), suggesting that this region overtakes the outer shell, produces a reverse shock, and emits the [\ion{Fe}{II}] emission. A numerical simulation in \citet{dwa98} shows that such a reverse shock emerges in the LBV nebulae (assuming $\eta$ Carinae), and its radius can be several times smaller than the outer shell, like this ``extended emission region''. Consequently, we propose that the ``extended emission region'' traces the reverse shock region due to the stellar wind overtaking inside of the outburst shell. Both the 1600-AD outburst shell region and the ``extended emission region'' show some brightness asymmetry in our data, although we have discussed them with a spherically-symmetric geometry so far. In the upper plot of Fig.\ \ref{fig7}, a bright emission was visible at the northern blueshifted part in the 1600-AD outburst shell\footnote{This feature is also seen in Fig.\ 5 of SH06 though the slit positions were not identical.}. In the lower panel of Fig.\ \ref{fig7}, the blueshifted part of the ``extended emission region'' is found to be brighter than the other areas. Because the 1600-AD outburst shell does not have velocity components at $v>140$~km~s$^{-1}$, this bright spot of the ``extended emission region'' is free from contamination of the shell. As a result, the two regions may share the similar asymmetry although they are spatially separated. This similarity also supports the reverse shock scenario; the denser region in the 1600-AD shell naturally causes stronger emission in the shock as the wind overtakes the inside of the shell. The extended [\ion{Fe}{II}] emission are also observed in the stellar wind region of $\eta$ Carinae. \citet{smi04c} found a UV excess emission region at $0^{\prime\prime}.1-0^{\prime\prime}.6$ from the central star of $\eta$ Carinae, which emanates from the outer parts of the stellar wind region. \citet{hil06} detected a UV [\ion{Fe}{II}] emission line from the UV region, $0^{\prime\prime}.2$ from the central star. This [\ion{Fe}{II}] emission region in $\eta$ Carinae is similar to the ``extended emission region'' in P Cygni; both are spatially-extended around the central star and considered to be the outer parts of the stellar wind region. Moreover, their sizes are not so much different (0.2--1.4~kAU for $\eta$ Carinae and 4.9~kAU for P Cygni), and may scale with the luminosity of the central source. Therefore, such extended [\ion{Fe}{II}] emission regions could be a common structure in LBV nebulae. Structure of the P Cygni nebulae we propose in this paper is as follows. The inner region of the wind ($\lesssim100\,R_*$) is traced by the metal permitted lines ($v=180$~km~s$^{-1}$). The wind is accelerated by the radiation of the central star and reaches the terminal velocity at $\sim300\,R_*$ \citep{lam85}, which is traced by the P Cygni profile of H- and He emission lines ($v=220$~km~s$^{-1}$). The wind velocity exceeds the expansion velocity of the 1600-AD outburst shell ($v=140$~km~s$^{-1}$), so that the reverse shock emerges when the wind overtakes the shell, which produces the [\ion{Fe}{II}] ``extended emission region'' we have found in this paper ($v=220$~km~s$^{-1}$). The radius and total gas mass of the shock region are about 15\% and 0.5\% of those of the 1600-AD outburst shell. A promising way to study details of this newly-found region would be to spatially resolve it (within $3^{\prime\prime}$ from the central star) with adaptive-optics observations of the [\ion{Fe}{II}] lines. | 18 | 8 | 1808.04622 |
1808 | 1808.08060_arXiv.txt | The origin of galactic spiral arms is one of fundamental problems in astrophysics. Based on the local analysis Toomre (1981) proposed the swing amplification mechanism in which the self-gravity forms spiral arms as leading waves of stars rotate to trailing ones due to galactic shear. The structure of spiral arms is characterized by their number and pitch angle. We perform global $N$-body simulations of spiral galaxies to investigate the dependence of the spiral structure on disk parameters and compare the simulation results with the swing amplification model. We find that the spiral structure in the $N$-body simulations agrees well with that predicted by the swing amplification for the wide range of parameters. The pitch angle decreases with increasing the shear rate and is independent of the disk mass fraction. The number of spiral arms decreases with both increasing the shear rate and the disk mass fraction. If the disk mass fraction is fixed, the pitch angle increases with the number of spiral arms. | The formation mechanism of galactic spiral arms in disk galaxies is one of important problems in galactic astronomy. The spiral arms are excited by tidal interactions with nearby companion galaxies \citep[e.g.,][]{Oh2008, Dobbs2010} and by the central stellar bar \citep[e.g.,][]{Buta2005}. However, the spiral arms can also be excited and maintained without external perturbations. One theory to explain the origin of spiral arms in disk galaxies is swing amplification mechanism \citep{Goldreich1965, Julian1966, Toomre1981}. During the rotation, a wave is amplified if Toomre's $Q$ is $1\mbox{\--}2$. In $N$-body simulations of multi-arm spiral galaxies, it is observed that the spiral arms are transient and recurrent \citep[e.g.,][]{Sellwood1984, Sellwood2000, Baba2009, Fujii2011}. This feature can be understood by the swing amplification mechanism. In a differentially rotating disk, if a perturber, such as a giant molecular cloud, exists, a stationary density structure around a perturber forms \citep{Julian1966}. Even without a explicit perturber, the density pattern can be amplified. If the leading wave exists, it rotates to a trailing wave due to the shear. If the self-gravity is sufficiently strong, the rotating wave is amplified during the rotation. These processes are called swing amplification \citep{Goldreich1965, Julian1966, Toomre1981}. The amplified density patterns may correspond to spiral arms observed in the galaxies. In the swing amplification theory, the local and linear approximations were adopted. First, the deviation of stellar orbits from the circular orbit on the disk midplane is assumed to be small compared to the orbital radius. This is local approximation or epicycle approximation \citep{Binney2008}. In addition, the deviation of various quantities, such as the surface density, from the unperturbed state is assumed to be small, that is, the deviation from the circular orbit is small compared to the wavelength. Using this approximation, the hydrodynamic equation or Boltzmann equation in the local coordinate system is linearized \citep{Goldreich1965, Julian1966}. In this respect, this is linear approximation. In the linear theory of swing amplification, a perturber or a seed leading wave is necessary for the growth of the spiral arms. \cite{Donghia2013} performed $N$-body simulations and examined the non-linear effect. Their simulations show that perturbers are not necessary once the spiral arms are developed. The spiral arm itself causes overdense and underdense regions that behave as perturbers and generate another spiral arm. This phenomenon cannot be explained only by the linear theory. \cite{Kumamoto2016} clearly showed that the non-linear interaction between spiral arms forms overdense and underdense regions by the more controlled simulations. However, we cannot still deny the importance of the linear theory of the swing amplification to explain the formation process of the spiral arm from a leading wave or a perturber caused by the non-linear interaction. The linear theory of the swing amplification may explain some aspects of the basic physics of the spiral arm formation. In addition, the short-scale spiral structures in Saturn's ring, so-called self-gravity wakes, are said to be formed by the swing amplification \citep{Salo1995, Michikoshi2015}. The recent $N$-body simulation suggests that self-gravity wakes exists even in a ring around a small body \citep{Michikoshi2017}. This type of structure may be ubiquitous. Therefore, it is important to understand physical mechanism of swing amplification. In the series of our papers, we have investigated the swing amplification mechanism using the local linear theory and the local $N$-body simulations \citep{Michikoshi2014, Michikoshi2016, Michikoshi2016a}. The global $N$-body simulations of the spiral arms show that the pitch angle of the spiral arms decreases with increasing the shear rate \citep{Grand2013}. This tendency is expected from the view of the swing amplification mechanism \citep{Julian1966}. From the local $N$-body simulations and the local linear analyses, we confirmed this trend and obtained the accurate pitch angle formula \citep{Michikoshi2014} (hereafter referred to as Paper I). The proposed pitch angle formula is consistent with other global $N$-body simulations \citep{Grand2013, Baba2015, Fujii2018}. The physical understanding of the dependence of the pitch angle on the shear rate is given based on the phase synchronization of the epicycle motion \citep{Michikoshi2016a} (hereafter referred to as Paper III). It is suggested that the number of spiral arms is inversely proportional to the disk mass fraction \citep{Carlberg1985a}. \cite{Donghia2013} confirmed that the number of spiral arms is determined by the critical wavelength of the gravitational instability. It follows that the inverse relation between the disk mass and the number of spiral arm. \cite{DOnghia2015} adopted more detailed model of disk and halo models and obtained the number of spiral arms formula, which depends on the distance from the galactic center. Recently \cite{Fujii2018} performed global simulations that include a live bulge and dark matter halo. Their results show that a larger shear rate results in a smaller number of spirals. However, the dependence of the number of spiral arms on the shear rate has not been investigated quantitatively. In the previous works, a factor $X$, which is the azimuthal wavelength normalized by the critical wavelength, is assumed to be $1$--$2$. In general, $X$ depends on the shear rate \citep{Athanassoula1984}. \cite{Michikoshi2016} (hereafter referred to as Paper II) obtained the detailed formula of $X$, the pitch angle, the amplification factor, and the number of spiral arms as a function of disk parameters. It is suggested that $X$ increases and the number of spiral arms decreases with increasing the shear rate. This prediction has not yet been confirmed by global simulations. So far the results of the local $N$-body simulations agree well with the local linear analysis of the swing amplification mechanism (Paper I, II). However, in realistic spiral arms, the local approximation is not always valid. Especially, for the grand-design spiral arms, the local approximation would break down. Thus it is important to investigate the spiral structure by global $N$-body simulations. In the present paper we extend local $N$-body simulations to global ones and systematically investigate the dependencies of the number and pitch angle of spiral arms on the disk parameters. The outline of this paper is as follows. In Section \ref{sec:method}, we introduce the model and simulation method. In Section \ref{sec:res}, we give the results of the $N$-body simulations. In Section \ref{sec:dis}, we provide the intuitive explanation of the dependencies of the pitch angle and the number of spiral arms. We summarize our findings in Section \ref{sec:summary}. | \label{sec:dis} We present the intuitive derivation of the pitch angle and number of spiral arms. Except for the numerical coefficient, the pitch angle formula can be obtained from the phase synchronization argument \citep{Michikoshi2016a}. We briefly summarize its derivation. We consider a single leading wave in a rotating frame. Due to the shear, the wave rotates from leading to trailing. When the wave changes from leading to trailing, the stabilizing effect of Coriolis force is reduced. Thus, the particles are pulled towards the wave center by the self-gravity and their epicycle phases are synchronized. Then the wave amplitude becomes the maximum after the half of an epicycle period \citep{Michikoshi2014}. The pitch angle evolves with time as $\tan \theta = 1/(2A t)$ where $t$ is the elapsed time from $\theta = 90^\circ$. Substituting $t = \pi/\kappa$ we obtain the pitch angle as $\tan \theta \simeq \kappa/2\pi A$. This result is consistent with that of the local simulations and the swing amplification $\tan \theta \simeq \kappa/7A$ \citep{Michikoshi2014}. The azimuthal wavelength $\lambda_y$ is given by the pitch angle $\theta$ and the radial wavelength $\lambda_x$, \begin{equation} \lambda_y = \frac{\lambda_x}{\tan \theta}. \end{equation} The radial wavelength is often assumed to be $\lambda_x = \lambda_\mathrm{cr}$, where $\lambda_\mathrm{cr}$ is the critical wavelength of the gravitational instability for the axisymmetric modes \citep{Toomre1964}. Though this relation is not obvious for non-axisymmetric modes, the local linear analyses of the swing amplification and the local $N$-body simulations confirm $\lambda_x \simeq \lambda_\mathrm{cr}$ for $\kappa/\Omega<1.6$ \citep{Michikoshi2016}. Thus, adopting this relation we obtain \begin{equation} \lambda_y = \frac{\lambda_\mathrm{cr}}{\tan \theta} \simeq \frac{28 \pi^2 G \Sigma_\mathrm{d} A}{\kappa^3}. \end{equation} Using the azimuthal wavelength, we calculate the number of spiral arms as \begin{equation} m = \frac{2 \pi r}{\lambda_y} \simeq \frac{\kappa^3 r}{14 \pi G \Sigma_\mathrm{d} A} \sim \frac{\kappa^3}{14 f A \Omega^2}, \end{equation} where we used the approximation $\Omega^2 \simeq \pi G \Sigma_\mathrm{d}/r f$ (Paper II, Appendix \ref{sec:estfac}). For $1.0 < \kappa/\Omega <1.5$, we numerically find that $A \kappa / \Omega^2 $ is almost constant between 0.65 and 0.77. Thus in this parameter range, we can approximate $A \kappa / \Omega^2$ as a constant $0.71$. This approximation can recover the previous result, which is \begin{equation} m \sim 0.1 \frac{\kappa^4}{f \Omega^4}. \end{equation} This expression agrees with that obtained by the swing amplification (equation (\ref{eq:numarm0})) except for the dependence on $Q$. In the above argument we assumed that $\lambda_x \simeq \lambda_\mathrm{cr}$. On the other hand, $\lambda_y$ increases with $\Gamma$ and decreases with increasing $\theta$ since $\theta$ decreases with increasing $\Gamma$. This indicates that $m$ is larger for larger $\theta$, which is consistent with equation (\ref{eq:mtrelation}). We have performed the global $N$-body simulations of disk galaxies in order to compare the spiral structure with those by the swing amplification theory. The mean pitch angle and number of spiral arms were calculated in the disks with various shear rates and mass fractions. We confirmed that the dependencies of the spiral structure on disk parameters agree with those in the swing amplification theory. The pitch angle decreases with increasing the shear rate and is independent of the disk mass fraction. The number of spiral arms decreases with both increasing the shear rate and the disk mass fraction. It follows that the pitch angle tends to increases with the number of spiral arms if the disk mas fraction is fixed. From the swing amplification mechanism only we cannot understand the overall process of the spiral arm formation. The $N$-body simulations show that the spiral arms are transient and recurrent, that is, the spiral arms are formed and destructed continuously. Two questions remain unsolved in this process. One is the origin of seed leading waves. In the realistic galaxies, the swing amplification mechanism requires relatively strong leading waves. The $N$-body simulations show that the overdense or underdense regions forms due to the nonlinear interaction between spiral arms \citep{Donghia2013, Kumamoto2016}. However, its physical mechanism is still unclear. We have to understand the generation mechanism such leading waves. The other is the fate of the amplified spiral arms. The $N$-body simulations show that the amplified arms are finally destructed. The destruction mechanism has not yet been understood completely. \cite{Baba2013} pointed out that the stars in spiral arms escape and the spiral arms damp due to the non-linear wave-particle interaction. It is also suggested that the nonlinear wave-wave interaction generates the leading arms from the swing-amplified arms \citep{Fuchs2005}. The wave-wave interaction may also contribute to damping of the spiral arms. In addition, the gas component of the disk neglected in the present study, may potentially affect the dynamics of spiral arms \citep[e.g.,][]{Bottema2003}. Further study on this effect is necessary. In our $N$-body simulations, we adopt a artificial galactic model and generate the initial condition by simple manner to control the key disk parameters. Our results suggest that a fudge factor in equation (\ref{eq:numarm0}) depends on the galactic model. Thus, it is necessary to determine this factor for more realistic galactic model. In addition, the initial condition of our model is not exactly in an equilibrium. Thus, we adopt the randomizing-azimuthal method for avoiding unnatural structures \citep{McMillan2007, Fujii2011}. It would be better to adopt the more sophisticated method for generating initial conditions \citep{Hernquist1993, Kuijken1995, McMillan2007, Miki2018}. In the future work, we will validate the swing amplification theory base on more realistic model. Numerical computations were carried out on Cray XC30 at Center for Computational Astrophysics, National Astronomical Observatory of Japan. | 18 | 8 | 1808.08060 |
1808 | 1808.01141_arXiv.txt | Approximate gravitational potentials are often used to describe analytically the motion of particles near black holes (BHs), as well as to study the structure of an accretion disk. Such 'pseudo-Newtonian' potentials are used with the flat-metric equations. Here we consider the motion of a free particle near a non-rotating BH in the context of an exact `logarithmic' gravitational potential. We show how the logarithmic potential gives an exact solution for a mechanical problem { and present the relativistic Bernoulli equation for the fluid in the Schwarzschild metric.} | { In the Newton celestial mechanics, a gravitational potential is one of the basic concepts. In the General Relativity (GR) there is generally no such concept as a gravitational potential. In some special cases, however, it is possible to use such a concept, as we show in this work. This gravitational potential is different from what is usually termed as a pseudo-Newtonian potential. } To describe analytically and in a simple way the dynamics of particles near a BH, as well as to study the structure of an accretion disk, approximate approaches are frequently used. For example, it is common to utilize pseudo-Newtonian gravitational potentials in the equations written in the flat ,etric. For a non-rotation BH, the potential by \citet{pacz-wiita1980} is used (hereafter, `PW potential'). For a rotating black hole, \cite{artemova+1996} proposed a formula for a pseudo-Newtonian gravitational force acting on particles near Kerr BH. Here we consider a non-rotating BH and a `logarithmic' gravitational potential. This gravitational potential, together with an allowance for the curvature of the space-time, provide the laws of motion for a free particle, which are identical to those derived in the General Relativity (GR). In Sect.~\ref{s.potentials} the pseudo-Newtonian gravitational potentials are very briefly reviewed. { We introduce the logarithmic potential in Sect.~\ref{s.log_potential}.} In Sect.~\ref{s.solution} we consider the equation of motion of a particle in a curved space-time and derive the conserved value of energy. We obtain the law of motion for the logarithmic potential and consider its consequences in Sect.~\ref{s.velocities}. { The relativistic Bernoulli equation for a stationary fluid around a Schwarschild BH is derived in Sect.~\ref{s.bernoulli}. } | The black hole gravitation causes the curvature of space around it. A logarithmic potential can be introduced to describe the motion of particles in such gravitational landscape. { In contrast with pseudo-Newtonian potentials, which can give only approximate results, the logarithmic potential provides the exact laws of motion. For this,} we consider the logarithmic potential within a different approach, which represents the 3+1 { decomposition} of the Schwarzschild space-time near a black hole. The advantage of such an approach for GR problems is that it allows using the physical concepts analogous to those in the classical physics. In particular, the energy of a particle can be derived from the equation of motion using the logarithmic potential. We show that the derived velocity of a particle, physically measured by a local observer, is correct in the sense that it is identical to that in GR. { The relativistic Bernoulli equation for a fluid in the Schwarzschild metric is obtained.} { The choice of a potential and a method to deal with it depends on a desired accuracy of a problem. For considerations, which are not very precise, one can use the classical Newtonian mechanics and the Paczynski-Wiita's potential. It is not advised to use the logarithmic potential in the framework of the classical mechanics, since it gives less accurate results comparing to those obtained with the Paczynski-Wiita's potential (see discussion at the end of Sect.~\ref{s.velocities}). } { One can also use the potential approach in the framework of classical mechanics to approximate the motion of a particle in the Kerr metric, by using a more sophisticated formula for a potential~\citep[see, for example,][where index $\beta$ is introduced]{kfm_book2008,artemova+1996}. However, the exact consideration of a particle motion in the Kerr metric implies the existence of a gravitomagnetic force, which is analogues to the Lorentz force in the electromagnetic theory and which is not conservative, that is, it cannot be determined by a potential~\citep[see, for example,][equations 3-18 and 3-19abc]{thorne_et1986}. The exact force in the Kerr metric can be written out in the context of problem 1 of paragraph 88~in \citet{landau-lifshitz-e-2-1975} (see equation 3 there). This task could be a subject of another study. } | 18 | 8 | 1808.01141 |
1808 | 1808.05886_arXiv.txt | The recent detection of gravitational waves (GWs) and electromagnetic (EM) waves originating from the same source marks the start of a new multi-messenger era in astronomy. The arrival time difference between the GW and EM signal can be used to constrain differences in their propagation speed, and thus gravitational theories. We study to what extent a non-zero time delay can be explained by gravitational lensing when the line of sight to the source passes near a massive object. For galaxy scale lenses, this delay becomes relevant for GWs with frequencies between $10^{-6}$ and $10^{-9}$ Hz, sourced by super massive binary black-holes. In addition to GWs detectable by Pulsar Timing Arrays (PTAs), we expect to find also a unique and recognizable EM signal. We show that the delay between the GW and EM signal can be of the order of days to months; within reach of future observations. The effect may become important in future multi-messenger astronomy probing of gravitational propagation and interactions. | In September 2015, the first direct observation of GWs was made by the two detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) \citep{Abbott:2016blz}. This observation opened a whole new field of study in astrophysics, and in the last years, research and interest in gravitational waves have increased considerably. As new observatories -- such as VIRGO (already in use) and Advanced VIRGO \citep{Banks:2017}, in Italy, the Japanese groundbased interferometer KAGRA (the KAmioka GRAvitational wave detector) \citep{Aasi:2013wya}, eLISA (the Evolved Laser Interferometer Space Antenna) \citep{Nishizawa:2016eza}, and DECIGO (the DECi-hertz Interferometer Gravitational wave Observatory) \citep{Isoyama:2018rjb, Yagi:2013du} -- are completed and begin operations, they will constitute new powerful instruments to study the universe. With the first combined detection of gravitational and EM waves \citep{2017PhRvL.119p1101A}, a new multi-messenger era has begun in astronomy. In this work, we study the arrival time differences due to gravitational lensing, between GWs and EM signals emitted by a common source at the same time or with known intrinsic time delays. In \cite{Takahashi:2016jom}, two lens configurations -- point mass and singular isothermal sphere (SIS) -- were considered. It was found that the lens imprints a characteristic modulation on the waveform. In particular, if the wavelength of the GW is large compared to the gravitational radius of the lens, it will pass almost unperturbed, and there will be a time delay delay between the GW and EM signal. A time delay between \textit{GW170817} and its EM counterpart is not expected for lenses with $M\gtrsim 10^3 M_\odot$ because of the large GW frequency. Note that if we consider modified gravity theories, GWs may propagate slower than the speed of light and there could be a time delay for this reason. The close to simultaneous detection of \textit{GW170817} and the EM signal has been used to constrain such theories \citep{Lombriser:2016,Creminelli:2017sry,Sakstein:2017xjx,Ezquiaga:2017ekz,Baker:2017hug,Boran:2017}. A pulsar was used for the first indirect observation of GWs when in 1974, the energy loss of the binary system PSR 1913+16 was attributed to the emission of GWs \citep{1975ApJ...195L..51H}. Observations agreed with the theoretical expectation of general relativity to better than 0.1\,\%. A different method involving pulsars being developed, and already in use for some time, to observe GWs with very low frequencies is Pulsar Timing Arrays (PTAs) \citep{1742-6596-610-1-012017, Lee:2011et, 2018MNRAS.477..964K, Huerta:2015, Sesana:2012}. The goal of this work is to compute and understand the feasibility of observing the time delay between EM signals and GWs observed with PTAs, corresponding to wavelengths longer or comparable to the gravitational radius of galaxy lenses. To have a time delay, there has to be a lens -- in our case typically a galaxy with $M\sim10^{11} M_\odot$ -- close enough to the line of sight to the source. The probability that a source at redshift $z\sim1$ is gravitationally lensed by a galaxy is of the order of $10^{-2}-10^{-3}$ \citep{Turner:1984}. In such a case, we find that the time delay will be observable for a large range of sources for next generation observatories. The article is organized as follows: In Section \ref{optics}, we explain why we expect a time delay and discuss the correct use of geometrical and wave optics. The heart of the work is Section \ref{time delay}, where we calculate and give numerical examples of the expected time delays . In Section \ref{Gravitational Wave Detection}, we describe PTAs and update on the latest results. Section \ref{SMBBH} treats the formation and evolution SMBBHs, and their GW and EM emission. The sensitivity needed to observe the time delays are presented in Section \ref{sensitivity} and conclusions are drawn in Section~ \ref{conclusions}. | \label{conclusions} For a gravitationally lensed source, there will be a time delay between GWs and EM signals, if the GW wavelength is much larger than the gravitational radius of the lens, which in turn is much larger than the wavelength of the EM signal. This effect may become an important tool for future multi-messenger astronomy, e.g., to study the propagation speed of gravitational theories \citep{Fan:2017}, and thus gravitational theories. For the first combined observation of GWs with an EM counterpart, \textit{GW170817}, no delay is expected for lenses with $M\gtrsim 10^3 M_\odot$. In this paper, we note that for GWs signals detected with PTAs, a time delay to a possible EM counterpart is expected in cases where the source is lensed by galaxy mass objects. In fact, both GW and EM signals from inspiraling SMBBHs are, in theory, detectable with current technologies, although not yet realized. With future data from SKA, we will be able to measure the gravitational signal, coming from SMBBHs with total mass $M\gtrsim10^8\ M_\odot$, with a $S/N\gtrsim 3$. Together with EM observations from next generation $X$-ray satellites, whose sensitivity needs to be further studied for distant sources, this will allow us to measure time delays of the order of months, expected for a lens mass $M\approx10^{11}\ M_\odot$. Note that the lens mass can be constrained from the EM image positions. A major challenge of these observations is the detection of GWs with high enough sensitivity. We showed that, with a large enough number of pulsars, and with prolonged and precise observations, this will be possible. For close sources, the EM counterpart should be easily detectable, while for sources at redshift $z\approx1$, it is not still clear how well this can be pursued (see chapter \ref{detEMcount}). The fact that the expected EM signals are unique for binary SMBHs systems, opens up for the possibility to recognize and identify these sources, and perform dedicated follow up GW observations. Once the theoretical feasibility of the observations are certified, an open problem is how accurate we can couple the emission of the GW and EM signals in the time domain. We expect a direct correlation between the frequency of the GW and the frequency of EM spectral line modulation. The study of whether observations will allow this to be done with sufficient precision is left for future work. \nocite{*} | 18 | 8 | 1808.05886 |
1808 | 1808.00001_arXiv.txt | We perform an improved cosmic microwave background (CMB) analysis to search for dark matter--proton scattering with a momentum-transfer cross section of the form $\sigma_0v^n$ for $n\!=\!-2$ and $n\!=\!-4$. In particular, we present a new and robust prescription for incorporating the relative bulk velocity between the dark matter and baryon fluids into the standard linear Boltzmann calculation. Using an iterative procedure, we self-consistently include the effects of the bulk velocities in a cosmology in which dark matter interacts with baryons. With this prescription, we derive CMB bounds on the cross section, excluding $\sigma_0 \! > \! 2.3 \! \times\! 10^{-33}~\mathrm{cm}^2$ for $n\!=\!-2$ and $\sigma_0 \! > \! 1.7 \! \times \! 10^{-41}~\mathrm{cm}^2$ for $n\!=\!-4$ at 95\% confidence, for dark matter masses below 10~MeV. Furthermore, we investigate how these constraints change when only a subcomponent of dark matter is interacting. We show that \textit{Planck} limits vanish if $\lesssim \! 0.4\%$ of dark matter is tightly coupled to baryons. We discuss the implications of our results for present and future cosmological observations. | Cosmological observables provide a unique avenue to search for evidence of non-gravitational interactions between dark matter (DM) and the Standard Model particles, and thereby gain insight into the unknown physical nature of DM. In particular, elastic scattering between DM and baryons transfers heat and momentum between the two fluids. The time evolution for the rate of momentum transfer depends on how the interaction cross section scales with the relative particle velocities, and the effects of scattering can be important at different cosmological epochs. If scattering is efficient before recombination, it affects the temperature, polarization, and lensing anisotropies of the cosmic microwave background (CMB), as well as the linear matter power spectrum on small angular scales~\cite{Chen:2002yh,Sigurdson:2004zp,Dvorkin:2013cea,Gluscevic:2017ywp,Boddy:2018kfv,Xu:2018efh}. If scattering is significant in the post-recombination Universe, it can result in anomalous late-time heating or cooling of the baryon gas, altering the 21-cm signal from neutral hydrogen at redshifts prior to the Epoch of Reionization~\cite{Tashiro:2014tsa,Munoz:2015bca,Barkana:2018lgd}. In a $\Lambda$CDM Universe, there is a relative bulk velocity between the cold DM and baryon fluids, which results in supersonic coherent flows of the baryons post recombination~\cite{Tseliakhovich:2010bj}. If DM and baryons interact, but the rate of momentum transfer is low, the drag force between the two fluids may not efficiently dissipate their relative bulk velocity, allowing it to dominate over the thermal particle motions, once the Universe is sufficiently cooled. Furthermore, if the relative bulk velocity is significant prior to recombination, the computation of the Boltzmann equations for the CMB becomes infeasible using standard methods: the equations describing the velocity fluctuations of the fluids become nonlinear, resulting in the coupling of individual Fourier modes. In an attempt to address this issue when computing CMB limits on DM--baryon interactions, previous studies~\cite{Dvorkin:2013cea,Xu:2018efh,Slatyer:2018aqg} used the root-mean-square (RMS) of the relative bulk velocity as a correction to the thermal velocity dispersion, suppressing the rate of momentum transfer, and thus obtaining conservative upper limits on DM--baryon interactions. That approach has two important caveats: the RMS velocity was computed in $\Lambda$CDM, inconsistent with a cosmology that features DM--baryon interactions; and the same RMS velocity was used in the Boltzmann equations for all Fourier modes, neglecting differences in how modes contribute at a given scale. In this work, we develop an improved treatment of the relative bulk velocity and reassess CMB limits on DM--proton scattering. Specifically, we supplement the standard Boltzmann linear calculations with an iterative procedure that self-consistently includes the effects of the relative bulk velocity in a cosmology in which dark matter interacts with baryons. We parameterize the momentum-transfer cross section as $\sigma_\textrm{MT} \! = \! \sigma_0 v^n$, where $v$ is the relative velocity between the scattering particles, and focus on two interaction models for which the relative bulk velocity is expected to have a substantial impact: $n\!=\!-2$ (arising in the case of, \textit{e.g.}, electric or magnetic dipole interactions through light mediators) and $n\!=\!-4$ (from, \textit{e.g.}, Coulomb-like interactions or Yukawa interactions through light mediators). We analyze the latest public CMB data from the \Planck{} 2015 data release~\cite{2016A&A...594A...1P,2016A&A...594A..11P} and find $\sigma_0 \! < \! 2.3 \! \times \! 10^{-33}~\cm^2$ for $n\!=\!-2$ and $\sigma_0 \! < \! 1.7 \! \times \! 10^{-41}~\cm^2$ for $n\!=\!-4$ at the 95\% confidence level (C.L.) for DM masses below $10~\MeV$. We forecast the sensitivity of the next-generation ground-based CMB experiment and find that CMB-Stage 4~\cite{2016arXiv161002743A} could deliver roughly a factor of $\sim\! 3$ improvement (not including a CMB lensing analysis), for a DM mass of $1~\MeV$. Additionally, we report limits on $\sigma_0$ for scenarios in which only a fraction of DM interacts with protons. For very small fractions, large values of $\sigma_0$ are allowed, and there exists a regime in which the DM and baryons are tightly coupled, such that DM behaves as baryons and experiences acoustic oscillations. We find that the constraining power of \textit{Planck} is drastically diminished when less than $0.4\%$ of DM is interacting. The Experiment to Detect the Global Epoch of Reionization Signature (EDGES) recently reported an anomalously large sky-averaged absorption signal~\cite{Bowman:2018yin}, which was attributed to dark matter interactions with baryons~\cite{Barkana:2018lgd}. Our results do not rule out a phenomenological $n\!=\!-4$ interaction invoked to explain the EDGES signal~\cite{Barkana:2018lgd}; however, we do exclude a percent of DM interacting with ions only, at a level consistent with the EDGES signal~\cite{Barkana:2018qrx}. In a separate study, we investigate the regime of subpercent fractions of millicharge-like DM and discuss the implications of our newly-derived CMB limits for the DM interpretation of EDGES~\cite{paper2:inprep}. This paper is structured as follows. In Section~\ref{sec:boltzmann}, we derive the Boltzmann equations that include DM--baryon scattering and present a new treatment of the relative bulk velocity. In Section~\ref{sec:cmb}, we describe and quantify the effects of scattering on the CMB power spectra. In Section~\ref{sec:constraints}, we describe our analysis of \Planck{} 2015 data and present new limits on the interactions with $n\!=\!-2$ and $n\!=\!-4$. We discuss and conclude in Section~\ref{sec:conclusions}. | \label{sec:conclusions} We have conducted a comprehensive study of the impact of scattering between DM and protons on the CMB power spectra. In particular, we adopted a phenomenological approach of parameterizing the momentum-transfer cross section as $\sigma_\textrm{MT} \! = \! \sigma_0 v^n$ (where $v$ is the relative velocity between the scattering particles) and focused on negative powers of velocity dependence that arise in well-motivated simplified models of DM interactions: $n\!=\!-2$ and $n\!=\!-4$. Such interactions are cosmologically important at times close to recombination, unlike the class of models with $n\! \geq\! 0$, for which scattering has the largest impact in the early Universe. We assessed the impact of the relative bulk velocity between the DM and baryon fluids that may arise in the pre-recombination Universe, when the relative bulk velocity surpasses the relative thermal velocity dispersion. A large relative bulk velocity results in nonlinear Boltzmann equations and the mixing of Fourier modes. We presented a new treatment to sidestep these difficulties, while capturing the physics behind mode coupling: we introduce a mode-dependent RMS velocity dispersion as a proxy for the bulk relative velocity, and we incorporated it into the computation of the linear Boltzmann equations in a self-consistent manner appropriate for a cosmology that includes DM--baryon scattering. We analyzed \Planck{} 2015 temperature, polarization, and lensing data to search for evidence of DM--proton scattering. We found that the data are consistent with no interactions and use our results to produce upper limits on the coefficient of the momentum-transfer cross section as function of DM mass, shown in Figure~\ref{fig:exclusion} and provided in Table~\ref{tab:exclusion}. Additionally, we considered the case in which only a small fraction of DM interacts with protons; for a DM mass of $1~\MeV$, we constrained the DM--proton interaction as a function of the fraction in Figure~\ref{fig:exclusion-fraction}. We discussed two regimes of DM--baryon scattering: weak-coupling regime, in which the momentum-transfer rate is inefficient due to Hubble expansion and damps acoustic oscillations on small scales; and a strong-coupling regime, in which DM and baryons are tightly coupled, resulting in DM undergoing acoustic oscillations with the baryons. If all the DM is allowed to interact with baryons, \Planck{} data constrain the interaction to be in the weak-coupling regime. However, if only a fraction of DM interacts with baryons, constraints on the cross section progressively weaken as the fraction decreases. For fractions below $\sim\! 0.4\%$, we find that \Planck{} constraints significantly degrade: the DM and baryons are allowed to be so tightly coupled that DM essentially becomes cosmologically indistinguishable from a small additional amount of baryons. Interestingly, such strongly-coupled dark matter could alleviate the mild tension between CMB and Big Bang Nucleosynthesis (BBN) measurement of the energy density of baryons. Recent BBN measurements of the deuterium abundance yield the values $\Omega_b h^2\!=\!0.02166\!\pm\!0.00015\!\pm\!0.00011$~\cite{Cooke:2017cwo} and $\Omega_b h^2\!=\!0.02174\!\pm\!0.00025$ \cite{Zavarygin:2018dbk}, whereas the latest \Planck{} 2018 data yield $\Omega_b h^2\!=\!0.02237\!\pm\!0.00015$~\cite{Aghanim:2018eyx}. These BBN values for the baryon density are lower than the CMB value by the equivalent of $0.5$\%--$0.6$\% of the DM energy density, and a strongly-coupled DM subcomponent with $f_\chi\!\sim\!0.4$\% could largely account for this discrepancy. This feature is not unique to $n\!=\!-4$; any interaction that tightly couples this subcomponent of DM to baryons around the time of recombination could be interpreted as an additional contribution to baryons. The $n\!=\!-4$ interaction has received a fair amount of recent attention in light of DM interpretation of the EDGES signal~\cite{Barkana:2018lgd}. The initial claim of Ref.~\cite{Barkana:2018lgd} was that a phenomenological $v^{-4}$ interaction could explain the EDGES signal---and our CMB analysis does not rule out such a possibility. However, our results do exclude a percent of millicharge-like DM scattering only with ions at the level needed to explain EDGES~\cite{Barkana:2018qrx}. Finally, we presented a conservative forecast for the next-generation ground-based CMB-Stage 4 experiment, and showed a factor of $\sim\! 3$ improvement over \Planck{} limits on $\sigma_0$ for the $n\!=\!-4$ interaction. Next-generation ground-based CMB surveys optimized for high-multipole science (where the signals of DM scattering may be particularly prominent) thus have a bright future in terms of DM searches with cosmological data. | 18 | 8 | 1808.00001 |
1808 | 1808.05624_arXiv.txt | We analyze the Sun as a source for the indirect detection of dark matter through a search for gamma rays from the solar disk. Capture of dark matter by elastic interactions with the solar nuclei followed by annihilation to long-lived mediators can produce a detectable gamma-ray flux. We search three years of data from the High Altitude Water Cherenkov (HAWC) observatory and find no statistically significant detection of TeV gamma-ray emission from the Sun. Using this, we constrain the spin-dependent elastic scattering cross section of dark matter with protons for dark matter masses above 1 TeV, assuming a sufficiently long-lived mediator. The results complement constraints obtained from Fermi-LAT observations of the Sun and together cover WIMP masses between 4 and $10^6$ GeV. In the optimal scenario, the cross section constraints for mediator decays to gamma rays can be as strong as $\sim10^{-45}$~cm$^{-2}$, which is more than four orders of magnitude stronger than current direct-detection experiments for 1 TeV dark matter mass. The cross-section constraints at higher masses are even better, nearly 7 orders of magnitude better than the current direct-detection constraints for 100 TeV dark matter mass. This demonstration of sensitivity encourages detailed development of theoretical models in light of these powerful new constraints. | 18 | 8 | 1808.05624 |
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1808 | 1808.03329_arXiv.txt | {The detection of abundant \ce{O2} at 1-10\% relative to \ce{H2O} ice in the comae of comets 1P/Halley and 67P/Churyumov-Gerasimenko, motivated attempts to explain the origin of the high \ce{O2} ice abundance. Recent chemical modelling of the outer, colder regions of a protoplanetary disk midplane has shown production of \ce{O2} ice at the same abundance as that measured in the comet.} {A thorough investigation is carried out to constrain the conditions under which \ce{O2} ice could have been produced through kinetic chemistry in the pre-Solar nebula midplane.} {An updated chemical kinetics code is utilised to evolve chemistry under pre-Solar nebula midplane conditions. Four different chemical starting conditions, and the effects of various chemical parameters are tested.} {Using the fiducial network, and for either reset conditions (atomic initial abundances) or atomic oxygen only conditions, the abundance level of \ce{O2} ice measured in the comets can be reproduced at an intermediate time, after 0.1-2 Myr of evolution, depending on ionisation level. When including \ce{O3} chemistry, the abundance of \ce{O2} ice is much lower than the cometary abundance (by several orders of magnitude). \ce{H2O2} and \ce{O3} ices are abundantly produced (at around the level of \ce{O2} ice) in disagreement with their respective abundances or upper limits from observations of comet 67P. Upon closer investigation of the parameter space, and varying parameters for grain-surface chemistry, it is found that for temperatures 15-25 K, densities of $10^{9}-10^{10}$ cm$^{-3}$, and a barrier for quantum tunnelling set to 2 {\AA}, the measured level of \ce{O2} ice can be reproduced with the new chemical network, including an updated binding energy for atomic oxygen (1660K). However, the abundances of \ce{H2O2} and \ce{O3} ices still disagree with the observations. A larger activation energy for the \ce{O + O2 -> O3} reaction ($E_{\rm{act}}$>1000 K) helps to reproduce the non-detection of \ce{O3} ice in the comet, as well as reproducing the observed abundances of \ce{H2O2} and \ce{O2} ices. The only other case where the \ce{O2} ice matches the observed abundance, and \ce{O3} and \ce{H2O2} ice are lower, is the case when starting with an appreciable amount of oxygen locked in \ce{O2}.} {The parameter space investigation revealed a sweet spot for production of \ce{O2} ice at an abundance matching those in 67P and 1P, and \ce{O3} and \ce{H2O2} ices abundances matching those in 67P. This means that there is a radial region in the pre-Solar nebula from 120-150 AU, within which \ce{O2} could have been produced in-situ via ice chemistry on grain surfaces. However, it is apparent that there is a high degree of sensitivity of the chemistry to the assumed chemical parameters (e.g. binding energy, activation barrier width, and quantum tunnelling barrier). Hence, because the more likely scenario starting with a percentage of elemental oxygen locked in \ce{O2} also reproduces the \ce{O2} ice abundance in 67P at early stages, this supports previous suggestions that the cometary \ce{O2} ice could have a primordial origin.} | \label{intro} The detection of abundant molecular oxygen at 1-10\% (average 3.8${\pm 0.85}$\%) relative to \ce{H2O} ice in the coma of comet 67P/Churyumov-Gerasimenko \citep[herinafter 67P:][]{bieler15} came as a surprise, as it was the first detection of \ce{O2} in a comet. This was not expected because \ce{O2} ice has been found to be efficiently converted to \ce{H2O} ice in laboratory studies under interstellar conditions \citep[e.g.][]{ioppolo2008}. Subsequent to this detection, a re-analysis of Comet 1P/Halley data from the \emph{Giotto} mission \citep{rubin2015} indicated a similar \ce{O2}/\ce{H2O} ice ratio (3.8$\pm1.7$\%), suggesting that indeed \ce{O2} ice may be a common ice species in Solar System comets. These detections thus prompted speculation as to the chemical origin of the \ce{O2} ice. \citet{taquet2016} modelled the chemical evolution of material from the pre-stellar core stage to the midplane of the formed protoplanetary disk, and found that \ce{O2} ice can be produced at the early stages and survive the transport to the disk midplane. \citet{mousis2016} found that, if \ce{O2} ice is formed from radiolysis of \ce{H2O} ice through the reaction \ce{2\rm{i}H2O ->[$\gamma$] 2\rm{i}H2 + \rm{i}O2} (where ``i'' denotes a molecule in the ice form), then this likely did not happen during the pre-Solar nebula (PSN) disk phase, but rather in the parent cloud, thus supporting the findings of \citet{taquet2016}. \citet{dulieu2017} performed laboratory experiments to investigate if dismutation of \ce{H2O2} ice (\ce{2iH2O2 -> 2iH2O + iO2}) on the cometary surface could be the origin of the \ce{O2} detection. However, this explanation requires a high initial abundance of \ce{H2O2} ice relative to \ce{H2O} ice (twice the detected abundance of \ce{O2}, or $\sim$7\%), and a high efficiency for the conversion of \ce{H2O2} to \ce{O2} in order to match the low detected level of \ce{H2O2} relative to \ce{O2} of $\sim 6\times 10^{-4}$. \ce{O3} ice, a molecule chemically related to \ce{O2}, \ce{H2O2} and \ce{H2O}, was not detected in the coma of comet 67P, and has an upper limit of $10^{-6}$ with respect to \ce{H2O} ice. It is worth to note here that molecular oxygen is also produced when \ce{CO2} ice is exposed to far-UV radiation \citep[see e.g.][]{martindomenech2015}. However, although this may be viable chemical route to \ce{O2} ice, it does not explain the strong association between the production rates for \ce{H2O} and \ce{O2} seen for comet 67P \citep{bieler15}. On the other hand, experiments investigating chemistry in \ce{CO2} ice irradiated with 5 keV ions (\ce{H+} and \ce{He+}) and electrons \citep{ennis2011,jones2014} favour the production of ozone (\ce{O3}) over molecular oxygen (\ce{O2}). These experiments mimic the conditions that ices are exposed to in the outer Solar System, and upon cosmic ray impact. In \citet{eistrup2016} (hereafter Paper 1), it was found through chemical kinetic modelling of protoplanetary disk midplanes that \ce{O2} ice could be produced to match the measured cometary abundance by 1 Myr, if the chemical starting conditions were purely atomised and the ionisation level was low ($\sim10^{-19}$ s$^{-1}$). Purely atomised starting conditions reflect the assumption that an energetic stellar outburst or accretion heating close to the star could have fully dissociated all volatiles in the midplane, and low ionisation means that the only ionisation source in the midplane is the decay of short-lived radionuclides. This latter scenario assumes that a magnetic field could have shielded the midplane from cosmic rays \citep[as proposed by][]{cleeves13crex}. This finding sparked interest into whether or not the chemical origin of the \ce{O2} ice could be chemical processing of the icy material in the pre-Solar nebular (PSN) disk midplane. Most recently \citet{mousis2018} explored the possibility that turbulent transport of icy grains between the disk midplane and the upper layers of the disk exposed the grains to a stronger cosmic-ray flux thus chemically processing \ce{H2O} ice to produce \ce{O2} ice via radiolysis. They find that on a 10 Myr timescale \ce{O2} ice in the midplane remains underproduced by up to two orders of magnitude relative to the abundances observed in the comets. \citet{eistrup2018} also found that this abundance for \ce{O2} ice be reached on similarly long timescales. Based on the promising results in Paper 1, this work investigates under which conditions in the PSN midplane \ce{O2} ice could have been chemically produced in-situ to reach the observed abundance level in the comets. This work differs from that in \citet{mousis2018} in that a full chemical kinetics network is used that follows the chemical connection between \ce{H2O}, \ce{O2} and related ice species. A disk model more suitable for the PSN is used, and a more thorough investigation of the \ce{O2} kinetic ice chemistry is conducted. Initial chemical abundances, physical conditions, parameters for grain-surface chemistry, as well as the inclusion of \ce{O3} in the chemical network are all tested to see the effect on the \ce{O2} ice production and abundance. | \label{concl} Since the somewhat unexpected detection of abundant \ce{O2} ice in the coma of comet 67P, several studies have attempted to explain the origin of the \ce{O2}. Building on the results from Paper 1, this work has investigated the possibility of in-situ formation of \ce{O2} ice on grains in the midplane of the PSN disk midplane. While a high abundance of \ce{O2} ice, matching that observed in comet 67P, was reproduced outside the \ce{O2} ice in the PSN disk midplane at intermediate evolutionary stages when assuming the initial chemistry to be reset, the same production was not seen after including \ce{O3} ice chemistry into the chemical network. For the fiducial choice of parameters for grain-surface chemistry, and an activation energy of 500 K for the \ce{O + O2 ->O3} reaction on the grains, \ce{O3} ice was in most cases found to be the dominant oxygen-carrier next to \ce{H2O} ice, and \ce{O2} ice was orders of magnitude too low in abundance compared to the abundance observed in comet 67P. In order to test the sensitivity of the production of \ce{O2}, \ce{O3}, and \ce{H2O2} ices to the assumed parameters for grain-surface chemistry, in particular the barrier width for quantum tunnelling $b_{\rm{qt}}$ and the ratio of diffusion-to-binding energy of ice molecules $E_{\rm{diff}}/E_{\rm{bin}}$, a parameter space investigation was conducted. Several temperatures and densities were also tested, and the reset scenario assumed for initial abundances. This led to a sweet-spot set of parameters being revealed: $b_{\rm{qt}}$= 2{\AA}, $E_{\rm{diff}}/E_{\rm{bin}}=0.3-0.5$ $T$=15-25 K and $n=10^{9}-10^{10}$ cm$^{-3}$ which facilitated \ce{O2} reproduction matching the observed level. However, the abundances of \ce{O3} and \ce{H2O2} ices were still in disagreement with the observed values by orders of magnitude. As a last adjustment of the chemistry intended to lower the \ce{O3} ice abundance, the activation energy for production of \ce{O3} ice from the association of O and \ce{O2} ices was increased in order to mitigate possible unknown chemical pathways away from \ce{O3}. For an activation energy of $E_{\rm{act}}= 2000$ K, $E_{\rm{diff}}/E_{\rm{bin}}=0.5$, and the remaining physical and chemical conditions as given above, the abundances of \ce{O2} ice, \ce{H2O2} ice, and the upper limit for \ce{O3} ice in the comet were all reproduced. This matches a formation location in the PSN disk midplane between 120-150 AU, just outside the \ce{O2} iceline. However, this high activation energy for \ce{O3} ice production is not supported by laboratory estimates, and thus more laboratory work is needed to determine potential missing chemical pathways for \ce{O3} ice chemistry. A model starting out with a percentage of elemental oxygen locked in \ce{O2} and thus assuming a primordial origin of \ce{O2}, also reproduced the observed abundance of \ce{O2} ice at early stages of evolution, without increasing $E_{\rm{act}}$ for the O + \ce{O2} reaction. Here, the \ce{O3} and \ce{H2O2} ice abundances were below the \ce{O2} ice abundance, but not matching the observed abundance levels. However, since the observed abundances of all three ices species are only reproduced in this work in the case for a set of rather extreme choices for the chemical parameters, the most plausible explanation for the origin of the cometary \ce{O2} ice remains the primordial one, as originally proposed by \citet{taquet2016}. | 18 | 8 | 1808.03329 |
1808 | 1808.03059_arXiv.txt | {We have obtained the first complete ultraviolet (UV) spectrum of a strong Lyman continuum(LyC) emitter at low redshift -- the compact, low-metallicity, star-forming galaxy \source\ --\ with a Lyman continuum escape fraction of 46\% discovered recently. The Space Telescope Imaging Spectrograph spectrum shows strong \lya\ and \Ciiiuv\ emission, as well as \Oiiiuv. Our observations show that strong LyC emitters can have UV emission lines with a high equivalent width (e.g.\ EW(\Ciii)$=11.7 \pm2.9$ \AA\ rest-frame), although their equivalent widths should be reduced due to the loss of ionizing photons. The intrinsic ionizing photon production efficiency of \source\ is high, $\log(\chioncorr)=25.56$ erg$^{-1}$ Hz, comparable to that of other recently discovered $z \sim 0.3-0.4$ LyC emitters. Combining our measurements and earlier determinations from the literature, we find a trend of increasing \chioncorr\ with increasing \Ciiiuv\ equivalent width, which can be understood by a combination of decreasing stellar population age and metallicity. Simple ionization and density-bounded photoionization models can explain the main observational features including the UV spectrum of \source. } | \label{s_intro} To improve our understanding of galaxies, their ISM, and ionizing properties at high redshift, UV spectra play a fundamental role, especially as this domain is accessible to ground-based telescopes over a very wide redshift range, and observations of the most distant galaxies become feasible with the largest telescopes. Therefore both observational works and studies improving and applying the diagnostic power of rest-UV lines have flourished recently \citep[see eg.][]{Stark2014Ultraviolet-emi,Stark2017Lyalpha-and-C-I,Fevre2017The-VIMOS-Ultra,Maseda2017The-MUSE-Hubble,Jaskot2016Photoionization,Gutkin2016Modelling-the-n,Nakajima2018The-VIMOS-Ultra} At low redshift, there are relatively few UV observations of star-forming galaxies covering the spectral range of $1200-2000$ \AA, which includes for example\ \lya, \Civ, \Heiiuv, O~{\sc iii}] $\lambda\lambda$1660,1666 (hereafter \Oiiiuv), C~{\sc iii}] $\lambda\lambda$1907,1909 (hereafter \Ciiiuv) and other emission lines, although the need for comparison samples has recently been recognized \citep[cf.][]{Rigby2015C-III-Emission-,Berg2016Carbon-and-Oxyg,Senchyna2017Ultraviolet-spe}. Despite this, only approximately 28 sources with \Ciii\ emission line detections from the HST are currently known from these studies. However, and most importantly, none of them is known as a Lyman continuum (LyC) emitter, and follow-up observations in the LyC are too time consuming for these $z \ll 0.3$ sources. Since Lyman continuum emitters are obviously fundamental to understand the sources of cosmic reionization, it is of prime interest to study such sources in terms of their physical properties, interstellar medium (ISM), stellar populations, and so on. Building on the recent success in identifying LyC emitters with HST at $z \sim 0.3$ \citep{Leitherer2016Direct-Detectio,Izotov2016Eight-per-cent-,Izotov2016Detection-of-hi,\paper,Izotov2018Low-redshift-Ly}, we have targeted one of the strongest LyC leakers, the compact $z=0.369$ galaxy \source\ with a LyC escape fraction of 46\% from \cite{\paper} to obtain the first complete HST UV spectrum of a strong LyC emitter. | \label{s_conclude} We have obtained the first complete UV spectrum of a low-redshift galaxy with strong LyC emission, \source, which was recently discovered by \cite{\paper}, and which shows a very high escape fraction of LyC radiation. This galaxy is a low-metallicity ($\oh = 7.65$), low-mass ($\log M_\star \sim 8.2$ \msun), compact star-forming galaxy, which had been selected for its very high ratio of the optical lines \oiiil / \Oii $=11.5$. The observations with STIS on board HST, covering the spectral range $\sim 1200-2200$ \AA\ restframe, show strong \lya\ and \Ciiiuv\ emission, as well as the presence of \Oiiiuv. We find a C/O abundance of $\log({\rm C/O})\sim -0.9$; that is, low, but comparable to other C/O measurements at low metallicity. \source\ shows a very strong \Ciiiuv\ emission line with an equivalent width EW(\Ciii)$=11.7 \pm2.9$ \AA, comparable to some other low-redshift sources of similarly low metallicity (see Fig.\ \ref{fig_c3}). The high EW(\Ciii) shows that {\em strong} LyC emitters do not necessarily have weak \Ciii\ emission, as predicted by some models \citep[cf.][]{Jaskot2016Photoionization}. Simple photoionization models can explain the main observational features and the UV spectrum of \source, but are not able distinguish between no LyC escape and the observed \fesc=$46$ \%. The intrinsic ionizing photon production efficiency of \source\ is $\log(\chioncorr)=25.56$ erg$^{-1}$ Hz, comparable to that of the other recently discovered $z \sim 0.3-0.4$ LyC emitters \citep[see][]{Schaerer2016The-ionizing-ph}, and higher than the canonical value for \chioncorr\ by a factor of approximately two \citep[cf.][]{Robertson2013New-Constraints}. With other data from the literature, we find a trend of increasing \chioncorr\ with increasing \Ciiiuv\ equivalent width (Fig.\ \ref{fig_chion} left), which can be understood by a combination of decreasing stellar population age and metallicity. If confirmed with larger samples, such a relation would be useful for studies of high-$z$ galaxies, which rely on rest-UV spectra. The majority of the $z \sim 0.3-0.4$ leakers discovered with HST/COS observations do not follow the correlation between \chioncorr\ and EW(\Oiii) proposed by \cite{Chevallard2018Physical-proper}. | 18 | 8 | 1808.03059 |
1808 | 1808.01740_arXiv.txt | \centerline{\bf Dedicated to the memory of Stephen Hawking} \vspace{3mm} \noindent This paper presents strong observational evidence of numerous previously unobserved anomalous circular spots, of significantly raised temperature, in the CMB sky. The spots have angular radii between 0.03 and 0.04 radians (i.e. angular diameters between about 3 and 4 degrees). There is a clear cut-off at that size, indicating that each anomalous spot would have originated from a highly energetic point-like source, located at the end of inflation -- or else point-like at the conformally expanded Big Bang, if it is considered that there was no inflationary phase. The significant presence of these anomalous spots, was initially noticed in the Planck 70 GHz satellite data by comparison with 1000 standard simulations, and then confirmed by extending the comparison to 10000 simulations. Such anomalous points were then found at precisely the same locations in the WMAP data, their significance confirmed by comparison with 1000 WMAP simulations. Planck and WMAP have very different noise properties and it seems exceedingly unlikely that the observed presence of anomalous points in the same directions on both maps may come entirely from the noise. Subsequently, further confirmation was found in the Planck data by comparison with 1000 FFP8.1 MC simulations (with $l \leqslant 1500$). The existence of such anomalous regions, resulting from point-like sources at the conformally stretched-out big bang, is a predicted consequence of conformal cyclic cosmology (CCC), these sources being the Hawking points of the theory, resulting from the Hawking radiation from supermassive black holes in a cosmic aeon prior to our own. | 18 | 8 | 1808.01740 |
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1808 | 1808.07399_arXiv.txt | {We present a new Monte Carlo code for Comptonisation in Astrophysics (MoCA). To our knowledge MoCA is the first code that uses a single photon approach in a full special relativity scenario, and including also Klein-Nishina effects as well as polarisation. In this paper we describe in detail how the code works, and show first results from the case of extended coronae in accreting sources Comptonising the accretion disc thermal emission. We explored both a slab and a spherical geometry, to make comparison with public analytical codes more easy. Our spectra are in good agreement with those from analytical codes for low/moderate optical depths, but differ significantly, as expected, for optical depths larger than a few. Klein-Nishina effects become relevant above 100 keV depending on the optical thickness and thermal energy of the corona. We also calculated the polarisation properties for the two geometries, which show that X-ray polarimetry is a very useful tool to discriminate between them. } | Up-scattering of low-energy photons by Inverse Compton on a hot gas of electrons (i.e. Comptonisation) is an important mechanism in astrophysics. In particular, in accreting sources such as X-Ray Binaries (XRBs) and Active Galactic Nuclei (AGN) this mechanism is believed to be responsible for their hard X-ray emission \citep{Sunyaev1980}: soft photons produced by the accretion disc are Comptonised by a corona of hot electrons. The typical Comptonisation spectrum of AGN can be approximated well by a power-law with photon energy index $\Gamma \sim 1.5-2.0$ extending from a few to hundreds keV with an exponential cut-off at high energies (e.g. \cite{Perola2002}, \cite{Dunn2010}). The corona of electrons is characterised by its temperature, $k\,T_e$, its geometry and its density (or optical depth, $\tau$). Thanks to the NuSTAR \citep{Harrison2013} high quality broad-band (3-79 keV) spectra, the coronal properties of AGN have been the subject of several studies in the last years (e.g. \cite{Fabian2015}, \cite{Tortosa2018}, and references therein). The measured cut-off energies, even if with a large scatter and in some cases with only lower limits, cluster to values between 100 and 250 keV, in agreement with previous measurements performed by BeppoSAX (e.g \cite{Perola2002}), INTEGRAL and Swift missions \citep{Molina2013}. Using the approximate relation stating that the observed high-energy cut-off correspond to approximately two to three times the thermal energy of the corona (\cite{Petrucci2000}, \cite{Petrucci2001}) (which has been proved to be accurate for an extended slab geometry but it is often used for coronae of any geometry and size), the extrapolated $k\,T_e$ is of the order of $\sim 50-150$ keV. Furthermore, if the corona is really compact as evidence, mainly from timing arguments \citep[][and reference therein]{Uttley2014}, suggests, these values would put the coronal parameters very close to the boundary for pair production \citep{Fabian2015}. XRBs, on the other hands, do not in general have stable X-ray emission and cycle from a state in which the thermal emission of the disc is dominant over a steep power-law tail at high-energy with typical spectral index $\Gamma \sim 2.5$ (the so-called soft-state) and a state characterised by a strong and flatter power-law emission with a spectral indices and high energy cutoffs similar to those observed in AGN (i.e. $\Gamma \sim 1.5 -2.0$, \cite{Fabian2015}) but often associated with the presence of a jet observed in the radio which correlates non-linearly with the X-ray luminosity (the so-called hard-state) \citep{Fender2001}. One of the most popular interpretations, also supported by the study of the variability of these sources in the two states, is that in the hard state the accretion disc is truncated at some radius and the inner flow is filled by the corona which Comptonises the thermal emission producing the strong power-law emission at high energies and a stable jet is also formed. As the accretion rates increases, the accretion disc extends up to the innermost stable circular orbit (ISCO) and a very small but hot corona produces a much steeper power-law at high energies and the Lorentz factor of the jet rises sharply, before the jet is suppressed in a soft disc-dominated state \citep{Fender2004}. In the last three decades, the Comptonisation problem has been addressed by many authors in different ways and the results of these studies are now often available in the form of \texttt{XSPEC}\footnote{\texttt{XSPEC} is a command-driven, interactive, X-ray spectral-fitting programme. More information can be found at: \url{http://heasarc.gsfc.nasa.gov/xanadu/xspec/}} models which are widely used by astronomers to fit X-ray spectra. Most, if not all, of these \texttt{XSPEC} models have been obtained by analytically or numerically solving the nonlinear radiative transfer equations under certain approximations and/or simplifying assumptions. Different approaches were adopted, from solving the Kompaneets equations in the diffusion regime ($\tau \gg 1$) and in the optically thin regime ($\tau < 1$) and then combining the asymptotic solutions to using iterative procedures to solve the radiative transfer equations for consecutive scattering orders.% The advantage of a semi-analytical approach is its capacity to build a grid of solutions for a large range of coronal parameters in order to fit the data. The comparison made between this approach and the first Monte Carlo simulations \citep{Stern1995} was showing a good agreement in most regimes while offering a much faster method with respect to the computational time needed on the most advanced calculators at that time. However, this approach has several limitations. In particular it is less reliable for specific combinations of coronal parameters and it basically consists in a mono-dimensional description of the radiative process. It is beyond the purposes of this paper to discuss in detail all the semi-analytical methods for solving the Comptonisation problem and we refer the reader to the complete analysis made by \cite{Poutanen1996} who, while presenting their calculations (which led to \texttt{compPS} XSPEC model), also analysed the different approaches and results of their predecessors (e.g. \cite{Titarchuk1995, HuaTitarchuk1995}). In the context of this scenario we developed \texttt{MoCA}: a Monte Carlo code for Comptonisation in Astrophysics. Our code differs from other models because instead of solving radiative transfer equations we followed every photon from the source to the observer using the Monte Carlo method. This approach allows to explore the whole space of parameters characterising the Comptonising medium without any particular limitation. \texttt{MoCA} includes special relativity and all quantum effects such as the Klein-Nishina differential cross-section and scattering angles distribution and the Maxwell-J\"{u}ttner electron distribution. The code is modular and, even if in this paper we discuss only the case of the hot coronae around accreting black holes, it can be easily modified to be applied to different Comptonisation problems in astrophysics. An important feature of \texttt{MoCA} is polarisation: for every photon we register its Stokes parameters, which allows us to calculate the polarisation degree and polarisation angle. This feature is particularly relevant now that the SMEX NASA mission IXPE \citep{Weisskopf2016} has been approved, as onboard it will have the first new generation X-ray polarimeter after 40 years since the last X-ray polarisation measurements. Polarimetry combined to spectroscopical analysis has the potential to infer the geometry of the corona which can help to understand its origin. For this work we have considered two geometries for the corona: a spherical corona and a slab corona. In the first case (if it is very compact) one might expect the corona to be the base of a jet (or an aborted jet) while in the latter scenario it can be originated by perturbations in the disc. This version of the code does not include General Relativity (GR) effects therefore, even if we consider the geometrical effect of a compact corona on the spectrum and polarisation signal, we mostly focus on the case of extended coronae (this allows us to compare with the above mentioned XSPEC models which do not include GR as well and consider only extended coronae). Nonetheless a version of MoCA coupled with a GR ray-tracing code is being developed and will be the subject of a future paper. MoCa is not the first code to deal with Comptonisation (including polarisation) with a Monte Carlo approach. A similar approach was used a few years ago by Schnittman and collaborators \citep{Schnittman2010}. However, to increase the computational efficiency of the calculations they used photon packets that include the entire broad-band spectrum instead of a single photon. For this reason their code works in Thomson regime and the energy exchange is taken into account only by the boost in the reference frame of the rotating corona and then in the reference frame of the electron while the scattering is always elastic. More recently, Beheshtipour and collaborators \citep{Beheshtipour2017} expanded upon the work of Krawczynski \citep{Krawczynski2012} and manage to include proper Klein-Nishina treatment for Comptonisation in their code (among other things such as the contribution of non-thermal electrons in the corona and cyclotron photons in addition to thermal photons as seeds) following the same photon packets approach as in Schnittmann. The paper is organised as follows: a brief description of the code is given in Section 2, with full details in the Appendix. In the following sections we show the results obtained with \texttt{MoCA} when applied to the case of Comptonisation for accreting sources: Section 3 is focussed on spectra while in Section 4 we focus on the polarisation signal. Lastly, in Section 5, we summarise our work. | We have presented \texttt{MoCA}, a Monte Carlo code for Comptonisation in Astrophysics which includes polarisation. To our knowledge \texttt{MoCA} is the first code operating with single photons and including all special relativity and quantum effects. The main disadvantage of this approach is the long computing time, which implies the need to parallelise the code on clusters of computers. The advantage with respect to pure analytical models such as those available in XSPEC is that we can explore the totality of the parameters space for the Comptonising medium (i.e. thermal energy and optical thickness of the corona) without any restriction and this approach will also allow a better understanding of the whole process. We also included all corrections such as Klein-Nishina cross-section and scattering angle distribution. These effects, small below 100 keV, must nonetheless be taken into account when inferring the thermal energy of the corona from observations. In some sources it has been found that coronae can have extremely high energy cut-off \citep[e.g. NGC 5506,][]{Matt2015} and therefore thermal energy, which is inferred by measuring the curvature of NuSTAR spectra at high energy and in this context K-N effects cannot be neglected. From the polarimetric point of view we did not seen any deviation due to K-N effects, but this was to expected as we focussed our attention below 100 keV where these effects are small. However, one can imagine a scenario in which the thermal energy of the corona is few tens of keV and in that case we expect to see a difference both on the spectrum and the polarisation but we defer such investigation to future papers focussed on the exploration of the coronal parameters space. In its actual form the code is fast enough to explore different geometries of the corona with different parameters. Spectra can then be compared with those obtained by NuSTAR to derive coronal parameters, especially in the high optical depth regime where analytical models are not reliable. As already mentioned, much observational evidence points in the direction of compact coronae above or around the compact object. In order to properly treat such coronae, gravitational effects must be taken into account. We have recently included a ray-tracing routine to take into account GR effects: this new version of \texttt{MoCA}, and applications of the code to different astrophysical scenarios, will be discussed in future papers. Nonetheless we have shown the geometrical effect of more compact coronae on the spectra and the polarisation signal: the spectra become softer as the corona shrinks and the polarisation changes dramatically as we approach a more symmetrical shape of the corona. The study we performed will also be useful to quantify the impact of GR effects on compact coronae with respect to a purely geometrical effect. In a few years, when the NASA Imaging X-ray Polarisation Explorer, IXPE, is launched, it will be possible to use our code to simulate the polarisation signal expected in different scenarios and to compare our results with the observation. We show that polarimetry has the potential to discriminate between different geometries of the corona shedding a light on the possible origin of the corona itself. Even integrating the polarisation signal in the next generation X-ray polarimeters energy band the two geometries we considered in this work are expected to produce different signals at any inclinations. We also show that if the photons arising from the disc are initially polarised, the final signal can be very different from the unpolarised seed photons scenario. It will be fundamental to verify the nature of the polarisation expected from the accretion disc by observing a very bright XRB in a clean soft state before observing the polarisation of Comptonised radiation in hard state. \texttt{MoCA} is a Comptonisation code which calculate the scattering-induced polarisation produced by such mechanism. Nonetheless if magnetic fields are present, synchrotron X-ray radiation is expected to be polarised as well. However we show that scattering-induced polarisation is of the order of few \% while synchrotron radiation is expected to be polarised up to several tens \% so the two mechanisms should be clearly distinguishable. \begin{appendix} | 18 | 8 | 1808.07399 |
1808 | 1808.09451_arXiv.txt | We study the influence of stellar metallicity on the fraction of stars with planets (i.e., the occurrence rate of planetary systems) and the average number of planets per star (i.e., the occurrence rate of planets). The former directly reveals the planet formation efficiency, whereas the latter reveals the final product of formation and evolution. We show that these two occurrence rates have different dependences on stellar metallicity. Specifically, the fraction of stars with planets rises gradually with metallicity, from $\sim$25\% to $\sim$36\% for 0.4 dex of [Fe/H] for all \emph{Kepler}-like planets (period $P<400$ days and radius $R_{\rm p}\gtrsim R_\oplus$). The average number of planets per star reaches a plateau (or possibly starts declining) at [Fe/H]$\gtrsim0.1$. This is plausibly caused by the emergence of distant giant planets at high metallicities, given that the close-in small planets and the distant giants preferentially co-exist in the same system. | \label{sec:introduction} Dependence of planet occurrence rate on host star properties provides insights into the formation of planet. The well established planet-metallicity correlation states that metal-rich stars preferentially host giant planets \citep{Santos:2001,Santos:2004,Fischer:2005}. This supports the core accretion model as the primary channel for giant planet formation (\citealt{IdaLin:2004}; but see \citealt{Nayakshin:2017} for an alternative explanation). However, there has been a long debate on whether or not such a correlation extends to smaller (radius $R_{\rm p}<4~R_\oplus$) planets \citep{Sousa:2008,Buchhave:2012,Buchhave:2014,Schlaufman:2015,Wang:2015,Buchhave:2015,Zhu:2016}. Putting aside the overall occurrence rate, several studies indeed have confirmed that small and hot (orbital period $P\lesssim10$ days) planets do appear preferentially around metal-rich stars \citep{Beauge:2013,Adibekyan:2013,Mulders:2016,Dong:2018,Petigura:2018,Wilson:2018}. In studying the dependence on host star properties, one should be cautious about which occurrence rate to use. There are two types of occurrence rates to quantify the popularity of planets: the fraction of stars with planets, which we denote as $\Fp$, and the average number of planets per star, which we denote as $\barnp$. With the known number of stars, the former corresponds to the number of planetary systems and the latter the number of planets. The ratio, $\barnp/\Fp$, gives the average multiplicity, namely the average number of planets per planetary system \citep{Zhu:2018}. Therefore, unless every planetary system contains only one planet, the two occurrence rates would be different. Because the role of stellar properties comes primarily in determining the formation efficiency of planets, the fraction of stars with planets $\Fp$ is more appropriate to use \citep{Zhu:2016}. The average number of planets per star reveals the final product of both planet formation and dynamical evolution, the latter of which can largely modify the number of planets in the system. The problem becomes further complicated, because $\Fp$ is not a quantity that can be easily derived, in particular for transit missions such as \emph{Kepler} \citep{Youdin:2011,Zhu:2018}. For these reasons, previous statistical studies on the metallicity dependence all used the average number of planets per star either explicitly or implicitly \citep{Wang:2015,Buchhave:2015,Mulders:2016,Petigura:2018,Wilson:2018}. Therefore, their results do not necessarily reveal the dependence of the formation efficiency of small planets on stellar metallicity. A recent work by \citet{Zhu:2018} combined the information of transiting planets and their non-transiting companions as inferred from the transit timing variations \citep{Holman:2005,Agol:2005} and constrained the fraction of Sun-like stars with \emph{Kepler}-like planets (periods $P<400$ days and radii $R_{\rm p}\gtrsim R_\oplus$) to be $\eta_{\rm Kepler}=30\pm3\%$. Using the methodology and the terminology of \citet{Zhu:2018}, we come to revisit the metallicity dependence of the small planet population. This paper is organized as follows. In Section~\ref{sec:qualitative} we describe the data used in this work and compare the metallicity distribution of stars with and without planets. In Section~\ref{sec:quantitative} we derive the two occurrence rates ($\Fp$ and $\barnp$) for different metallicity bins. Our results are discussed in Section~\ref{sec:discussion}. \begin{figure}[t] \epsscale{1.2} \plotone{rich_vs_poor.pdf} \caption{Radii and orbital periods of planets found in the LAMOST-\emph{Kepler} sample. Planets are divided into six different categories depending on the host star metallicity and the number of transiting planets found. In particular, ``[Fe/H] poor'' means [Fe/H]$<-0.07$, ``[Fe/H] intermediate'' means $-0.07<$[Fe/H]$<0.10$, and ``[Fe/H] rich'' means [Fe/H]$>0.10$. These boundaries are chosen such that each bin contains the same number of planetary systems. We also over-plot the average detection efficiency curves for three metallicity bins, with solid, dashed, and dotted curves being the 90\%, 50\%, and 10\% efficiency curves, respectively. \label{fig:sample}} \end{figure} \begin{figure} \epsscale{1.1} \plotone{cumulatives.pdf} \caption{Cumulative distribution functions (CDF) of metallicities of stars in different categories. Here small planets are planets with radii $R_{\rm p}<4~R_\oplus$, and large planets are those with $R_{\rm p}>4~R_\oplus$. Stars with planets belonging to multiple categories appear in all those categories, but stars with multiple planets in the same category are only counted once. This figure shows that planet hosts are preferentially metal-rich. There is no difference in metallicities of stars with 1-2 $R_\oplus$ planets and those with 2-4 $R_\oplus$ ones (sometimes called super-Earths and mini-Neptunes, respectively). \label{fig:cdfs}} \end{figure} | \label{sec:discussion} The occurrence rate of giant planets shows strong dependence on stellar metallicity, but previous studies have not agreed on whether this correlation extends to small planets. In this work, we revisit this issue with the help of large and uniform spectroscopic LAMOST survey of the \emph{Kepler} stars. We point out that previous studies have commonly used the occurrence rate of planets, measured as the average number of planets per star $\barnp$, when studying the metallicity dependence (and mass dependence as well). However, this occurrence rate reflects the final outcome of planet formation and evolution, and is therefore not a direct measure of the formation efficiency. The occurrence rate of planetary system, measured as the fraction of stars with planets $\Fp$, reflects more directly the planet formation efficiency. To study the metallicity dependence, one therefore would like to derive $\Fp$ as a function of stellar metallicity. However, because of the difficulty in constraining $\Fp$ precisely with the available data, we use the quantity $\langle g_{1k}+\sum_{j=1}^k g_{jk} \rangle \Fp$ as a \emph{tracer} of $\Fp$. For comparison, we also study the $\barnp$ tracer $g_{11}\barnp$. We derive these two tracers for different stellar metallicities, and find that they do behave differently in particular at high stellar metallicities. Specifically, the $\Fp$ tracer continuously increases as stellar metallicity increases, whereas the $\barnp$ tracer shows a break in its metallicity dependence. We show that these trends hold even if only small planets are included. It is plausible that the correlation between close-in small planets and distant giant planets drives the difference in the two occurrence rates. As \citet{ZhuWu:2018} recently found, \footnote{See also \citet{Bryan:2018} and \citet{Herman:2018}.} about one third of the \emph{Kepler}-like systems have distant cold Jupiters, and this fraction doubles in the high-metallicity ([Fe/H]$>0.1$) systems. The emergence of cold Jupiters at high metallicities can drive dynamical instabilities in systems that are already heavily packed, which reduces the number of planets but not the number of planetary systems \citep[e.g.,][]{Matsumura:2013,Huang:2017,Lai:2017,Pu:2018}. After the exclusion of systems with at least four transiting planets, the break in the metallicity dependence of the $\barnp$ tracer does disappear. The correlation between inner and outer planetary systems can also explain more detailed trends in the metallicity dependence of the occurrence rate $\barnp$. \citet{Petigura:2018} found that the occurrence rate of large planets consistently increases with stellar metallicity, but the occurrence rate of relatively small planets shows different behavior: within orbital period $P\sim10$ days, the occurrence rate consistently increases; beyond that the occurrence rate seems to decrease with metallicity. This, in principle, could also be explained by the correlation between inner small planets and the cold giants, as smaller planets are more likely affected by the cold giants \citep{Lai:2017}. Our work indicates that the formation efficiency of relatively small planets still depends on the stellar metallicity, but this dependence is much weaker than the giant planet-metallicity correlation. Taking the nominal value $\langle g_{1k}+\sum_{j=1}^k g_{jk} \rangle\approx 0.11$, we find that $\Fp$ changes from $25\%$ at [Fe/H]$\approx-0.2$ to $36\%$ at [Fe/H]$\approx+0.2$ and thus by only a factor of 1.4, whereas the giant planet occurrence changes by a factor of $\sim10^{2\Delta{\rm [Fe/H]}}=6.3$. This is also consistent with the qualitative behaviors of the cumulative distributions of metallicities as shown in Figure~\ref{fig:cdfs}. Therefore, although the formation efficiencies of both small and giant planets depend on stellar metallicities, giant planets require more stringent conditions for their formation. | 18 | 8 | 1808.09451 |
1808 | 1808.05952_arXiv.txt | {We use the \textit{Gaia} DR2 distances of about 700 mid-infrared selected young stellar objects in the benchmark giant molecular cloud Orion\,A to infer its 3D shape and orientation. We find that Orion\,A is not the fairly straight filamentary cloud that we see in (2D) projection, but instead a cometary-like cloud oriented toward the Galactic plane, with two distinct components: a denser and enhanced star-forming (bent) Head, and a lower density and star-formation quieter $\sim$75 pc long Tail. The true extent of Orion\,A is not the projected $\sim$40\,pc but $\sim$90\,pc, making it by far the largest molecular cloud in the local neighborhood. Its aspect ratio ($\sim$30:1) and high column-density fraction ($\sim$45\%) make it similar to large-scale Milky Way filaments (``bones''), despite its distance to the galactic mid-plane being an order of magnitude larger than typically found for these structures.} | \label{Intro} \defcitealias{Schlafly2014}{Schlafly et al.} The archetypal giant molecular cloud (GMC) Orion\,A is the most active star-forming region in the local neighborhood, having spawned $\sim$3,000 young stellar objects (YSOs) in the last few million years \citep[e.g.,][]{Megeath2012, Furlan2016, Grossschedl2018}. Some of the most basic observables of the star-formation process, including star-formation rates and history, age spreads, multiplicity, the initial mass function, and protoplanetary disk populations, have been derived for this benchmark region \citep[e.g.,][]{Bally2008,Muench2008}. Previous distance estimates to the Orion Nebula Cluster (ONC), the richest cluster toward the northern end of the cloud, put this object at about \SI{400}{pc} from Earth \citep[e.g.,][]{Sandstrom2007, Menten2007, Hirota2007, Kim2008, Kuhn2018}. Moreover, there has been some evidence that the northern part of the cloud, including the ONC (or ``Head''), is closer than the southern part (or ``Tail'')\footnote{For simplicity we classify the Orion\,A cloud roughly into Head and Tail; the Tail represents the less star-forming part.}, containing L1641 and L1647 \citep{Schlafly2014, Kounkel2017, Kounkel2018}. \begin{table*}[!ht] \begin{center} \small \caption{Distances to sub-regions in Orion\,A from the Literature.} \renewcommand{\arraystretch}{1.2} \begin{tabular}{llll} \hline \hline \multicolumn{1}{c}{Reference} & \multicolumn{1}{c}{Method} & \multicolumn{1}{c}{Region} & \multicolumn{1}{c}{Distance (pc)} \\ & & & \multicolumn{1}{c}{(pc)} \\ \hline \citet{Genzel1981} & proper motion and radial velocity & Orion KL & $480\pm80$ \\ & of H$_2$O masers & & \\ \citet{Hirota2007} & VERA/VLBI & Orion KL & $437\pm19$ \\ \citet{Menten2007} & VLBI & ONC & $414\pm7$ \\ \citet{Sandstrom2007} & VLBI & ONC & $389^{+24}_{-21}$ \\ \citet{Kim2008} & VERA/VLBI & Orion KL & $418\pm6$ \\ \citet{Lombardi2011} & density of foreground stars & Orion\,A & $371\pm10$ \\ \hline \citet{Schlafly2014}\tablefootmark{a} & PanSTARRS optical reddening & $(l/b)$ at $(\SI{208.4}{\degree},\SI{-19.6}{\degree})$ north of the ONC & $418^{+43}_{-34}$ \\ & \citep{Green2014} & $(l/b)$ at $(\SI{209.1}{\degree},\SI{-19.9}{\degree})$ west of the ONC & $478^{+84}_{-59}$ \\ & & $(l/b)$ at $(\SI{209.0}{\degree},\SI{-20.1}{\degree})$ west of the ONC & $416^{+42}_{-36}$ \\ & & $(l/b)$ at $(\SI{209.8}{\degree},\SI{-19.5}{\degree})$ north to L1641-North & $580^{+161}_{-107}$ \\ & & $(l/b)$ at $(\SI{212.2}{\degree},\SI{-18.6}{\degree})$ east to L1641-South & $490^{+27}_{-27}$ \\ & & $(l/b)$ at $(\SI{212.4}{\degree},\SI{-19.9}{\degree})$ west to L1641-South & $517^{+44}_{-38}$ \\ & & $(l/b)$ at $(\SI{214.7}{\degree},\SI{-19.0}{\degree})$ south-east of L1647-South & $497^{+42}_{-36}$ \\ \hline \citet{Kounkel2017}\tablefootmark{a} & VLBI & 15 YSOs near the ONC & $388\pm5$ \\ & & 2 YSOs near L1641-South & $428\pm10$ \\ \hline \citet{Kounkel2018} & {\it Gaia} DR2 of APOGEE-2 sources & ONC & $386\pm3$ \\ & + HR-diagram selection & L1641-South & $417\pm4$\ \\ & & L1647 & $443\pm5$ \\ \hline \citet{Kuhn2018} & {\it Gaia} DR2 of {\it Chandra} X-ray sources & ONC & $403^{+7}_{-6}$ \\ & & north and south to ONC & $\sim395$ \\ \hline \end{tabular} \renewcommand{\arraystretch}{1} \label{tab:literature} \tablefoot{ \tablefoottext{a}{See also Fig.~\ref{fig:scatter_literature}.} } \end{center} \end{table*} To know the true 3D spatial shape and orientation of this giant filamentary structure would allow one not only to determine accurate cloud and YSO masses, luminosities, and separations for this benchmark region, but it would also bring important hints on the formation of GMCs in the disk of the Milky Way. \citet{Schlafly2014} first found an indication of a distance gradient across Orion\,A (see Table~\ref{tab:literature}), using a method based on optical reddening of stars \citep{Green2014} which is not sensitive to regions of high column-density. \citetalias{Schlafly2014} found that the Tail of the cloud is about 70\,pc more distant than the ONC region. \citet{Kounkel2017} conducted 15 VLBI observations toward young stars near the ONC, and two observations toward L1641-South. These observations again suggest an inclination of the cloud away from the plane of the sky, with a difference in distance of about 40\,pc from Head to Tail (until L1641-South). The distances reported in \citet{Schlafly2014} and \citet{Kounkel2017} are presented in Fig.~\ref{fig:scatter_literature} and in Table~\ref{tab:literature}. \citet{Kounkel2018} continued the analysis of this region by using new APOGEE-2 data combined with the newly released {\it Gaia} DR2 catalog \citep{Brown2018}. In this recent paper, they focus on stellar populations and the star-formation history across the whole Orion complex in a high dimensional space using a clustering algorithm. They report a more distant Tail compared to the Head (about 55\,pc distance difference). In this paper we have used the newly released {\it Gaia} DR2 to infer the 3D shape and orientation of Orion\,A. As a proxy to the cloud distance we will use the latest catalog of mid-infrared selected YSOs in this cloud, with ages $\lesssim 3$ Myr, for which a {\it Gaia} DR2 parallax measurement exists. These very young stars lie relatively close to, or are still embedded in the Orion\,A GMC, sharing the same velocity as the cloud \citep{Tobin2009, Hacar2016}, and are thus the best tracer of the cloud's shape. \begin{figure}[!ht] \centering \includegraphics[width=1\linewidth]{Figure1_scatter.pdf} \caption{ {\it Gaia} DR2 $\varpi$ of YSOs with IR-excess in Orion\,A versus $l$ (top, $\sigma_\varpi$ as error-bars), and projected YSO distribution displayed on the {\it Herschel} map (bottom). Red are YSOs that pass the applied selection criteria as discussed in the first two steps in Sect.~\ref{Data}. The blue sources represent the sources lost when the flux-excess-cut is applied. This highlights that nebulae (near the ONC, see map) cause additional $\varpi$ uncertainties, not reflected in $\sigma_\varpi$. The 1D distribution of $\varpi$ for both samples is shown in the histogram on the right. The red and blue middle lines show the median $\varpi$ of the samples. The lower and upper borders (black dashed lines) indicate the applied distance cuts to avoid possible foreground or background contamination when deducing the average distances. The middle gray line shows the distance to the ONC of 414\,pc \citep{Menten2007}, while the gray shaded band represents the 2D projected size of the cloud of about 40\,pc at 414\,pc. } \label{fig:scatter} \end{figure} \begin{figure}[!ht] \centering \includegraphics[width=0.95\linewidth]{Figure2_hist_Gmag.pdf} \caption{Histogram of {\it Gaia} DR2 $G$-band magnitudes. The gray distribution shows all YSOs toward Orion\,A with measured {\it Gaia} DR2 parallaxes. The red and blue distributions show the YSO samples that pass our required selection criteria, while we distinguish sources with (red) and without (blue) flux-excess-cut (see also Fig.~\ref{fig:scatter}).} \label{fig:mag_hist} \end{figure} \begin{figure*}[!ht] \centering \includegraphics[width=0.95\linewidth]{Figure3_mean.pdf} \caption{ Top: Distance estimates ($1/\varpi$) for YSOs in Orion\,A versus $l$ and their average distances per $\Delta l$. YSOs are shown as red dots with error-bars ($\sigma_\varpi/\varpi^2$). Over-plotted are the median (blue diamonds) and mean (orange circles) distances per $\Delta l = \SI{1}{\degree}$ (blue/green vertical lines on the bottom map correspond to the bin boundaries, factor two over-sampled). The 1$\sigma$ and 2$\sigma$ lower and upper percentiles are shown as blue shaded areas. The horizontal gray line represents the \citet{Menten2007} distance to the ONC at $\SI{414}{pc}$ with a range of $\SI{\pm 20}{pc}$ (gray shaded area) corresponding to the projected extent in $l$ of the cloud ($\SI{\sim40}{pc}$ at $\SI{414}{pc}$). Bottom: Distribution of the YSOs in Galactic coordinates projected on the {\it Herschel map}. The displayed area corresponds to the VISTA observed region \citep{Meingast2016}. The dark shades of the gray scale indicate regions of high dust column-density (or high extinction). The distribution of YSOs follows the high density regions of the cloud, shown by their mean($b$) positions per $\Delta l$ (orange squares). } \label{fig:mean} \end{figure*} | \begin{table*}[!ht] \begin{center} \small \caption{Mean positions per Galactic longitude bin ($\Delta l$).} \begin{tabular}{ccccccccc} \hline \hline \multicolumn{1}{c}{$\Delta l$ bin center} & \multicolumn{1}{c}{$\bar{b}_\mathrm{YSOs}$} & \multicolumn{1}{c}{$\bar{d}_\mathrm{YSOs}$} & \multicolumn{1}{c}{$X$} & \multicolumn{1}{c}{$Y$} & \multicolumn{1}{c}{$Z$} & \multicolumn{1}{c}{$X_\mathit{Orion}$} & \multicolumn{1}{c}{$Y_\mathit{Orion}$} & \multicolumn{1}{c}{$Z_\mathit{Orion}$} \\ \multicolumn{1}{c}{(deg)} & \multicolumn{1}{c}{(deg)} & \multicolumn{1}{c}{(pc)} & \multicolumn{1}{c}{(pc)} & \multicolumn{1}{c}{(pc)} & \multicolumn{1}{c}{(pc)} & \multicolumn{1}{c}{(pc)} & \multicolumn{1}{c}{(pc)} & \multicolumn{1}{c}{(pc)} \\ \hline 207.0 & -19.20956 & 371.03 $\pm$ 21.83 & -312.18 & -159.06 & -122.08 & 370.22 & -24.44 & 1.60 \\ 207.5 & -19.15597 & 394.01 $\pm$ 30.83 & -330.14 & -171.86 & -129.29 & 393.35 & -22.72 & 2.13 \\ 208.0 & -19.14714 & 396.69 $\pm$ 20.38 & -330.88 & -175.93 & -130.11 & 396.20 & -19.61 & 2.27 \\ 208.5 & -19.24683 & 391.01 $\pm$ 24.00 & -324.42 & -176.15 & -128.89 & 390.68 & -16.10 & 1.61 \\ 209.0 & -19.41924 & 392.69 $\pm$ 25.02 & -323.92 & -179.55 & -130.56 & 392.48 & -12.93 & 0.48 \\ 209.5 & -19.59683 & 393.22 $\pm$ 21.78 & -322.42 & -182.42 & -131.89 & 393.10 & -9.70 & -0.71 \\ 210.0 & -19.67799 & 390.21 $\pm$ 26.41 & -318.20 & -183.71 & -131.40 & 390.16 & -6.41 & -1.23 \\ 210.5 & -19.59386 & 395.07 $\pm$ 30.41 & -320.69 & -188.90 & -132.49 & 395.06 & -3.25 & -0.65 \\ 211.0 & -19.46612 & 401.18 $\pm$ 30.38 & -324.22 & -194.81 & -133.69 & 401.18 & 0.0 & 0.24 \\ 211.5 & -19.36718 & 409.36 $\pm$ 31.97 & -329.28 & -201.79 & -135.75 & 409.34 & 3.37 & 0.94 \\ 212.0 & -19.15993 & 417.43 $\pm$ 43.81 & -334.39 & -208.95 & -137.00 & 417.37 & 6.88 & 2.46 \\ 212.5 & -19.09259 & 423.31 $\pm$ 45.68 & -337.38 & -214.93 & -138.46 & 423.17 & 10.47 & 2.96 \\ 213.0 & -19.22319 & 435.13 $\pm$ 35.87 & -344.59 & -223.78 & -143.27 & 434.89 & 14.34 & 2.02 \\ 213.5 & -19.53701 & 448.16 $\pm$ 32.40 & -352.20 & -233.12 & -149.87 & 447.79 & 18.42 & -0.42 \\ 214.0 & -19.73136 & 461.17 $\pm$ 39.97 & -359.88 & -242.74 & -155.69 & 460.60 & 22.72 & -2.06 \\ 214.5 & -19.74885 & 467.31 $\pm$ 38.40 & -362.47 & -249.12 & -157.90 & 466.54 & 26.85 & -2.30 \\ \hline \end{tabular} \tablefoot{The mean positions per bin ($\Delta l = \SI{1}{\degree}$, within a Galactic latitude range $\SI{-20.5}{\degree}<b<\SI{-18.1}{\degree}$) correspond to the orange dots in Figs.~\ref{fig:mean}, \ref{fig:xy_stretch}, and \ref{fig:xyz}. The reported mean distances ($\bar{d}_\mathrm{YSOs}$) do not include a systematic global parallax offset. The distance error is the standard deviation of the mean. $XYZ$ are Galactic cartesian coordinates (see also Fig.~\ref{fig:xyz}). $XYZ_\mathrm{Orion}$ are transformed Galactic cartesian coordinates with $X$ pointing toward Orion\,A (see also Fig.~\ref{fig:xy_stretch}).} \label{tab:mean} \end{center} \end{table*} \begin{table*}[!ht] \begin{center} \small \caption{Averaged parallaxes and derived distances to different large-scale sub-regions in Orion\,A.} \begin{tabular}{lcccccc} \hline \hline Region & $l$-Range & Sample & Mean($\varpi$) & Mean($d$) & Median($\varpi$) & Median($d$) \\ & (\si{\degree}) & size & (mas) & (pc) & (mas) & (pc) \\ \hline Orion\,A (all) & 208 -- 215 & 650 & 2.50$\pm$0.20 & 400$\pm$32 & 2.52$\pm$0.10 & 397$\pm$16 \\ Head (ISF) & 208 -- 211 & 483 & 2.55$\pm$0.16 & 393$\pm$25 & 2.54$\pm$0.08 & 393$\pm$13 \\ Tail & 211 -- 215 & 145 & 2.33$\pm$0.24 & 428$\pm$42 & 2.33$\pm$0.17 & 430$\pm$31 \\ Tail-L1641 & 211 -- 214 & 130 & 2.36$\pm$0.23 & 424$\pm$42 & 2.35$\pm$0.17 & 426$\pm$31 \\ Tail-L1647-South & 214 -- 215 & 15 & 2.14$\pm$0.18 & 467$\pm$32 & 2.17$\pm$0.07 & 461$\pm$15 \\ \hline \end{tabular} \tablefoot{The averages per $l$-range are calculated within $\SI{-20.5}{\degree}<b<\SI{-18.1}{\degree}$. The reported parallaxes and distances do not include a systematic global offset. Shown as uncertainties are the standard deviation from the mean and the median absolute deviation. On top of this we expect a systematic error of about 10\,pc.} \label{tab:regions} \end{center} \end{table*} The 3D shape of Orion\,A, now accessible via the {\it Gaia} measurements, informs and enlightens our knowledge on this fundamental star-formation benchmark. The main result from this work is that Orion\,A is longer than previously assumed and has a cometary shape pointing toward the Galactic plane. Also of note, the Head of the cloud appears to be bent in comparison with the Tail (Fig.~\ref{fig:xyz}). Why would this be the case? One important hint is that the star-formation rate in the Head of the cloud is about an order of magnitude higher than in the Tail (Gro\ss scheld et al., in prep.). Taking this into consideration, one can think of at least two scenarios to explain the enhanced star-formation rate and the shape of the Head: 1) cloud-cloud collision and 2) feedback from young stars and supernovae. Recently, \cite{Fukui2018} interpreted the gas velocities in this region as evidence that two clouds collided about 0.1 Myr ago, and are likely responsible for the formation of the massive stars. While we cannot rule out this scenario with the data presented here, we point out that there is evidence for a young population of foreground massive stars \citep[e.g.,~in NGC\,1980, NGC\,1981,][]{Bally2008,Alves2012,Bouy2014} \citep[cf.][]{Fang2017}, that could provide the feedback necessary to bend the Head of the cloud. An investigation on the second scenario is needed and beyond the scope of this work, but it seems plausible that an external event to the Orion\,A cloud could have taken place in the last million years. The 3D shape of the cloud clarifies some previous results. For example, \citet{Meingast2018} found evidence for different dust properties in Orion\,A, when comparing the regions in the Head and the Tail of the cloud. They argued, correctly, that the dust in L1641 might not ``see'' the radiation from the massive stars toward the Head of the cloud, and their properties are then not affected by it. Our result validates this view: the dust grains in L1641 lie substantially in the back of the ONC, which contains the most massive stars in the region, and are hence shielded, or too far from the sources of UV radiation. The deduced length of the Orion\,A filament of 90\,pc makes it similar to the Nessie Classic filament \citep[$\SI{\sim80}{pc}$,][]{Jackson2010}, which is often regarded as a prototypical large-scale filament, or a ``bone" of the Milky Way \citep{Goodman2014}. \citet{Zucker2017} undertook an analysis of the physical properties and kinematics of a sample of 45 large-scale filaments in the literature. They found that these filaments can be distinguished in three broad categories, depending on their aspect ratio and high column-density fraction. Orion\,A has an average aspect ratio of about 30:1 when taking the length of 90\,pc and its average width (FWHM $\sim$3\,pc), and a high-column-density fraction of about 45\%. For the latter we use an A$_K$ threshold of 0.5\,mag, comparable to $1\times10^{22}\mathrm{cm}^{-2}$ in \citet{Zucker2017}. This puts Orion\,A squarely into their category c), which describes highly elongated, high-column-density filaments, or so called "bones" of the Milk Way. The position-angle between Orion\,A and the plane is in agreement with the average position-angles of the bones in their sample, but Orion\,A differs significantly from the known bones regarding its distance from the mid-plane of the Milky Way ($\sim$145\,pc), which is an order of magnitude larger than the median distance between bones and the Galactic plane. This discrepancy calls for a large-scale process to have pushed the cloud this far from the plane. \cite{Franco1986} proposed a scenario for the origin of the Orion complex as the consequence of an impact of a high-velocity cloud with the plane of the Galaxy (from above) that could account for the abnormal distance of Orion below the plane. Nevertheless, the cloud's cometary shape with a star-bursting Head closer to the plane, as shown in this work, seems to be at odds with this scenario. Finally, we point out that the unexpected length of Orion\,A along the line-of-sight affects the observables toward the cloud (masses, luminosities, binary separations) that will need revision. For example, the current cloud and YSO masses toward the Tail can be underestimated by about 30\% to 40\% under the common assumption of a single constant distance to Orion A, while binary separations can be underestimated by about 10\% to 20\%. | 18 | 8 | 1808.05952 |
1808 | 1808.00570_arXiv.txt | Targeting faint polarization patterns arising from Primordial Gravitational Waves in the Cosmic Microwave Background requires excellent observational sensitivity. Optical elements in small aperture experiments such as \bicepthree~and \keckarray~are designed to optimize throughput and minimize losses from transmission, reflection and scattering at millimeter wavelengths. As aperture size increases, cryostat vacuum windows must withstand larger forces from atmospheric pressure and the solution has often led to a thicker window at the expense of larger transmission loss. We have identified a new candidate material for the fabrication of vacuum windows: with a tensile strength two orders of magnitude larger than previously used materials, woven high-modulus polyethylene could allow for dramatically thinner windows, and therefore significantly reduced losses and higher sensitivity. In these proceedings we investigate the suitability of high-modulus polyethylene windows for ground-based CMB experiments, such as current and future receivers in the \bicep/\keckarray~program. This includes characterizing their optical transmission as well as their mechanical behavior under atmospheric pressure. We find that such ultra-thin materials are promising candidates to improve the performance of large-aperture instruments at millimeter wavelengths, and outline a plan for further tests ahead of a possible upcoming field deployment of such a science-grade window. \\ | \label{sec:intro} Many ground-based millimeter-wave receivers, such as those targeting the 2.7~K Cosmic Microwave Background (CMB), are designed around cryogenically cooled detectors and optics. Cryogenic receivers therefore include a vacuum window that separates cold components under vacuum from ambient air. Materials suitable for the fabrication of such windows must withstand the force developed by atmospheric pressure over the large area of the clear optical aperture, and minimize optical loading (transmission loss, reflections and scattering). These specifications lead to conflicting solutions, as strong materials are typically not transparent in-band (Kevlar\textsuperscript{\textregistered}, Dacron\textsuperscript{\textregistered}, carbon fiber, composites), while transparent materials have comparatively low bulk modulus and tensile strength (Polyethylene, Polypropylene, Teflon). CMB experiments so far have found a compromise by using various forms of polyethylene. Zotefoam\textsuperscript{\textregistered}\footnote{http://www.zotefoams.com/} (HD30, PPA30), a Nitrogen-expanded polyethylene closed-cell foam, has been employed for experiments with aperture sizes smaller than $\sim13"$ (e.g. \bicepone~[\citenum{Yoon2006}], \biceptwo~[\citenum{Ogburn2014}], \keckarray~[\citenum{Vieregg2012}], SPT-SZ~[\citenum{Carlstrom2011}], \sptpol~[\citenum{SPTPol2012}], ACBAR~[\citenum{Runyan2003}], PolarBear~[\citenum{Kermish2012}]). Zotefoam\textsuperscript{\textregistered} has been used successfully in stacks up to 5'' thick for windows up to 13'' in diameter. With in-band transmission exceeding $99$\% and low index of refraction $n\sim1$, no anti-reflective (AR) coating is necessary. This made Zotefoam\textsuperscript{\textregistered} an ideal candidate for mm-wave windows. However, scaling to larger diameter and thicker layers has proved too cumbersome. For larger apertures, where the required thickness of Zotefoam\textsuperscript{\textregistered} would become unwieldy, slabs of bulk high-density polyethylene or ultra-high molecular weight polyethylene (HDPE and UHMWPE) have been the default solution (e.g. for \bicepthree~[\citenum{Ahmed2014, Grayson2016}], \abs~[\citenum{Essinger-Hileman2010}], \sptthreeg~[\citenum{Benson2014}], \class~[\citenum{Essinger-Hileman2014}], QUIET~[\citenum{Bischoff2013}], ACT-MBAC~[\citenum{Swetz2011}], ACTPol and AdvACT~[\citenum{Thornton2016}]). The transmission properties of these materials have been studied in the lab (e.g.~[\citenum{Dalessandro2018}]) and their loss is known to scale with the thickness. With an index $n=1.53$, antireflection-coating becomes necessary to minimize reflection losses. \begin{figure} [h!] \begin{center} \begin{tabular}{c} \includegraphics[height=6.2cm,trim=7mm 0mm 15mm 0mm,clip]{HDPE_measured_index_losstan.png} \\ \includegraphics[height=6.2cm, trim = 5mm 0mm 16mm 12mm, clip]{HDPE_loss_vs_freq_thickness.png} \includegraphics[height=6.2cm, trim = 10mm 0mm 0mm 12mm, clip]{HDPE_relative_NET_vs_freq_thickness.png} \end{tabular} \end{center} \caption[example] { \label{fig:NET} \textbf{Top:} Measured HDPE index of refraction and loss tangent from multiple references in~[\citenum{Lamb1996}]. In subsequent figures and calculations, we assume HDPE $n=1.53$ and $\tan\delta = 2\!\times\!10^{-4}$ for frequencies below 300~GHz. \textbf{Bottom Left:} Transmission loss for HDPE windows of 6 different thicknesses (ranging from 0.01" to 1.25") as a function of frequency, calculated assuming a loss tangent for HDPE of $2\!\times\!10^{-4}$. The standard atmospheric observing bands are shown in orange (30-40~GHz), red (100~GHz), green (150~GHz), and blue (220-270~GHz). \textbf{Bottom Right:} Relative Noise-Equivalent Temperature (NET, in $\mu$K$\sqrt{\text{s}}$) or, relative survey time (in seconds), as a function of window thickness, for different observing frequencies corresponding to the color-coded points in the left panel. This figure is generated using the estimated transmission loss from points in the middle panel as input in an NET calculator, assuming all other instrument parameters remain fixed to BICEP3 [\citenum{Ahmed2014,Grayson2016}] values. The NET and survey time shown are relative to an ideal no-window case normalized to 1. The degradation in sensitivity introduced by the window is worse in higher frequency bands. For example, a 1/2"-thick window at 150~GHz would increase the NET by 20\%, or would require a 44\% longer survey time to reach the same noise level. } \end{figure} To achieve ever-increasing sensitivities, CMB experiments depend on a steady increase in optical throughput (more detectors in the focal plane and larger focal planes), which naturally translates into larger optical apertures. The thickness of HDPE/UHMWPE slabs used as vacuum windows must increase accordingly in order to withstand larger forces from atmospheric pressure. Figure~\ref{fig:NET} shows the dependence of transmission loss and relative sensitivity on nominal window thickness, for different observing frequencies assuming the standard bulk polyethylene windows. The Noise-Equivalent-Temperature (NET) is a steep function of window thickness, especially at higher frequencies. Above 100~GHz, even a modest thickness of HDPE significantly affects the sensitivity on the sky, as the window begins to contribute significantly to the total optical loading on the detectors. `Stage 3' CMB experiments are planning receivers with apertures in excess of 60~cm (for example \biceptng's 28" diameter receivers) with several bandpasses up to 270~GHz. Improvements in vacuum window design and fabrication are necessary in order to prevent degradation in sensitivity as observations push to higher frequencies. Since the 1990s, advancements in gel spinning technology have allowed the commercial development of spun UHMWPE fibers known as Dyneema\textsuperscript{\textregistered}\footnote{Dyneema\textsuperscript{\textregistered} is a regisitered trademark of Royal DSM N.V.} or Spectra\textsuperscript{\textregistered}\footnote{Spectra\textsuperscript{\textregistered} is a regisitered trademark of Honeywell International.}. For the rest of this paper, we refer to these fibers as High Modulus Polyethylene (HMPE). Extruding UHMWPE gel through a spinneret at a carefully controlled temperature leads to a high degree of molecular chain alignment (see Figure~\ref{fig:dyneema_photos}). The alignment of the fibers, or crystallinity, yields a quoted tensile modulus and tensile strength approximately 100 times higher than that of the bulk UHMWPE. The tensile strength of HDPE is typically between 20 and 40 MPa while that of HMPE is 1-4 GPa [\citenum{dsm1,dsm2,dsm3,dsm4}]. Thin, fabric-like sheets can be woven from individual fibers and coated to prevent fraying. With a strength-to-weight ratio exceeding that of steel by a factor of approximately 10, industrial applications of HMPE have included radomes, ballistics protection, lightweight link chains and a wide range of technical fabrics. \begin{figure} [bt] \begin{center} \begin{tabular}{c} \includegraphics[height=5.1cm, trim = 0mm 0mm 0mm 0mm, clip]{large_diam_1layer_test6.JPG} \includegraphics[height=5.1cm]{dyneema_closeup.png} \includegraphics[height=5cm, trim = 4mm 0mm 0mm 0mm, clip]{PE_fibers.pdf} \end{tabular} \end{center} \caption[] { \label{fig:dyneema_photos} \textbf{Left:} photos of a prototype HMPE vacuum window with 27'' clear aperture under test on a vacuum chamber. A depth gauge measures the deflection at the center of the window as a function of time. \textbf{Middle:} Closeup photo showing the texture of the woven fabric. \textbf{Right:} Cartoon representation of molecular alignment obtained in high-modulus polyethylene compared to the bulk polyethylene.} \end{figure} Since these HMPE fibers are fabricated from Ultra High Molecular Weight Polyethylene, we expect they might have similar refractive index and loss tangent at millimeter wavelengths as the bulk material. The combination of increased strength and likely suitable optical properties presents the potential of dramatically thinner (and therefore more transparent) vacuum windows. Here we present initial results of an investigation aiming to test the relevant mechanical and optical characteristics of windows made of woven HMPE fabric. An example prototype with 27'' clear aperture is shown under test on a vacuum chamber in Figure~\ref{fig:dyneema_photos}. The woven-like nature of the `raw' HMPE fabric requires further custom processes to laminate it with other plastics to obtain a vacuum tight surface, to prevent fraying, and to transform the woven matrix into an optically homogeneous material. The outline of these proceedings is as follows. In Section~\ref{sec:mechanical} we present tests aiming to validate the high tensile characteristics of the HMPE fibers and to investigate the behavior of prototype windows placed under atmospheric pressure for long periods of time. We have experimented with various fabrication processes and are therefore including results for different samples and prototypes. Throughout these proceedings we use the term `raw Dyneema\textsuperscript{\textregistered}' or `raw HMPE' to refer to the unlaminated woven fabric of high modulus fibers as received from the manufacturer. The samples referred to as `single layer' or `double layers' are made of one or more layers of raw HMPE fabric laminated in between thin layers of LDPE on either side. We are also experimenting with a different form of non-woven HMPE fabric, which we refer to as `CT10', consisting of wider flat-pressed sheets of HMPE laminated together. We note that we are still optimizing the window fabrication process and do not discuss the details here. In Section~\ref{sec:optical} we present results from reflection spectra of HMPE samples that confirm their index of refraction is consistent with that of bulk UHMWPE. Section~\ref{sec:future} describes plans for future work paving the way to a full technology demonstration and eventual field deployment of a large-aperture HMPE window on BICEP3 at the South Pole. Section~\ref{sec:conclusions} summarizes our Conclusions. | \label{sec:conclusions} For experiments with photon-limited detectors, probing the faint polarization patterns in the CMB requires ever-increasing sensitivity and therefore expanding focal plane arrays. The aperture size of CMB telescopes has been growing, driving the need for new technology development. In particular, future large-aperture receivers will have to meet the challenge of fabricating larger optical elements that retain structural integrity without introducing prohibitively large losses. Ultra-thin windows made from woven high modulus fibers of UHMWPE are promising candidates for large-aperture receivers operating at millimeter wavelengths. By providing an order of magnitude reduction in loss from the window, they could lead to a significant reduction in the photon loading from the instrument and therefore an improvement in sensitivity. We have presented the initial mechanical and optical system-level tests that are currently underway in order to vet these new materials for use in CMB receivers. Provided our continued testing of prototypes is successful, we plan to deploy a science-grade multi-layer woven HMPE window on the \bicepthree~receiver in the coming year. We expect that replacing the current 1.25''-thick slab HDPE with a new multi-layer woven HMPE window will improve the sensitivity by 25\%. | 18 | 8 | 1808.00570 |
1808 | 1808.05739_arXiv.txt | The scattering of fast radio bursts (FRBs) by the intergalactic medium (IGM) is explored using cosmological hydrodynamical simulations. We confirm that the scattering by the clumpy IGM has significant line-of-sight variations. We demonstrate that the scattering by the IGM in the voids and walls of the cosmic web is weak, but it can be significantly enhanced by the gas in clusters and filaments. The observed non-monotonic dependence of the FRB widths on the dispersion measures (DM) cannot determine whether the IGM is an important scattering matter or not. The IGM may dominate the scattering of some FRBs, and the host galaxy dominates others. For the former case, the scattering should be primarily caused by the medium in clusters. A mock sample of 500 sources shows that $\tau_{\rm{IGM}} \propto \rm{DM_{IGM}}^{1.6-2.1}$ at $z<1.5$. Assuming that the turbulence follows Kolmogorov scaling, we find that an outer scale of $L_0\sim 5\,$pc is required to make $\tau_{\rm{IGM}} \sim 1-10\,$ms at $\nu=1\, $ GHz. The required $L_0\sim 5\, $pc can alleviate the tension in the timescales of turbulent heating and cooling but is still $\sim 4$ orders of magnitude lower than the presumed injection scale of turbulence in the IGM. The gap is expected to be effectively shortened if the simulation resolution is further increased. The mechanisms that may further reduce the gap are shortly discussed. If future observations can justify the role of the IGM in the broadening of FRBs, it can help to probe the gas in clusters and filaments. | Fast radio bursts (FRBs) are a recently discovered class of millisecond-duration radio transients (e.g., \citealt{Lorimer2007, Thornton2013, Champion2016, Petroff2016}). The dispersion measures (DMs) of observed FRBs range from 176 to a few thousands (the highest value until now is 2596 ${\rm{pc\, cm^{-3}}}$; see \citealt{Bhandari2018}). For most observed events, their DMs are much higher than the expected value because of the medium in the Milky Way, which indicates that FRBs are of extra-galactic origin. It is suggested that the DMs of FRBs are substantially contributed by the intergalactic medium (IGM), which can be used in principle to probe the properties of the IGM(\citealt{Ioka2003, Inoue2004, Deng2014, McQuinn2014}). The broadening of the pulse width because of scattering by the turbulent medium, i.e., $\tau$, is also an important parameter of FRBs. The scattering by the Galaxy is inadequate to explain the broadening of several FRBs at high latitudes. The location of the non-galactic scattering has not been determined because both the host galaxy medium and IGM may play important roles. The host can cause significant broadening that is sufficiently strong to explain the observation (\citealt{Cordes2016}; \citealt{Katz2016}; \citealt{Xu2016}, hereafter XZ16). Meanwhile, the contribution of the IGM is under debate. \citet[hereafter MK13]{Macquart2013} estimated that the broadening contributed by the extended, diffuse IGM at $z<3$ was approximately $\tau_{\rm{IGM}} \la 1 \,$ms at $\nu \sim 300$ MHz. They showed that the intervening halo gas and intra-cluster medium (ICM) along the LOS might be capable of producing $\tau_{\rm{IGM}} \sim 5 \,$ms at $\nu \sim 300$ MHz, but they doubted the probability. Two major concerns were recently raised against the IGM as an important scattering matter: (1) To produce $\tau_{\rm{IGM}} \sim 5 \,$ms at $\nu \sim 300$ MHz, the outer scale of turbulence with the Kolmogorov spectrum must be $\sim 10^{-2}\,$pc, which appears too small compared to the often presumed injection scale ($\geq 100\,$kpc) and is incompatible with the cooling rate of the IGM(\citealt{Luan2014}, XZ16). (2) The non-monotonic dependence of the observed FRB widths on DMs is inconsistent with the expectations for intergalactic scattering(\citealt{Katz2016}). However, \citet{Yao2017} argued that the broadening of observed FRBs tended to increase with the DM contributed by the IGM. In fact, the strength of this tendency may have been weakened by the large lines-of-sight(LOS) variations in the scatter measure (SM) caused by the clumpy IGM (MK13). The anisotropic gravitational collapse makes the initially small-amplitude density fluctuations of cosmic matter form a large scale spatial pattern known as the cosmic web, which consists of clusters, filaments, walls and voids (\citealt{Zeldovich1970, Bond1996}). The density perturbation growth in the late nonlinear stages because of gravitational instability can be described by a turbulence model (\citealt{Shandarin1989}). In addition, the accretion of matter to collapsed objects is highly anisotropic and non-homogenous. The gas accreted into dark matter halos occurs in both hot and cold mode, and contains clumps of various size(\citealt{Dekel2009}). When low mass dark matter halos falling into the gaseous halo of more massive dark matter halos, both thermal and dynamical instabilities, such as the Kelvin-Helmholtz and Rayleigh-Taylor instability, will be triggered and can lead to density fluctuations on scale smaller than the satellite halos(e.g., \citealt{Mayer2006, Abramson2011}). Recent cosmological hydrodynamical simulations without a star formation process found considerable density fluctuations of gas on the resolution scale, i.e., tens of kpc, particularly in clusters and filaments(\citealt{Vazza2010, Zhu2017}). Cosmological hydrodynamical simulations of galaxy formation have shown density and temperature fluctuation on their resolution scale of a few kpc in regions within and outside the dark matter halos (e.g., \citealt{Vogelsberger2012}, \citealt{Nelson2013} ). In this work, we probe the scattering of FRBs by the clumpy IGM using cosmological hydrodynamical simulations and revisit the required outer scales of turbulence that can make the IGM an important contributor to the broadening of FRBs. We present the numerical methodology in Section 2. The DM and SM contributed by the IGM residing in the cosmic web are probed in Section 3. We then probe the scattering of FRBs by the IGM in Section 4. In Section 5, we discuss the required outer scales of turbulence to make the IGM play important roles in the broadening of FRBS. Then we summarize our results in Section 6. | Using cosmological hydrodynamical simulations, we investigate the dispersion and scattering of FRBs caused by the IGM. The mean value of dispersion measure contributed by the IGM as a function of redshift $z$ in our work is in well agreement with the literature(e.g., \citealt{McQuinn2014}). Moreover, we probe the contribution to $\rm{DM}_{\rm{IGM}}$ by the gas residing in various structures of the cosmic web. We find that the gas in clusters contributes approximately $\sim 15\%-20 \%$ of the total dispersion measure caused by the IGM, the gas in filaments contributes $\sim 35-45\%$, and the gas in voids and walls contribute the remaining $\sim 35-45\%$. We confirm that the scattering by the clumpy IGM has significant LOS variations. We show that the scattering of FRBs by the IGM in voids and walls is weak, but the medium in clusters and filaments can enhance the scattering by a factor of 200 in our simulation with the highest resolution. Specifically, the gas in clusters contributes approximately $65-80$\% of the total SM caused by the IGM, while gas in filaments contributes $20-30$\%. We argue that the observed non-monotonic dependence of the widths of FRBs on DMs cannot determine whether the IGM is an important scattering matter of FRBs or not, considering the significant LOS variations, limited number of observed events and mixing contribution to the DMs by the host galaxy and IGM. Under the assumption of turbulence following Kolmogorov scaling, an outer scale of $\sim 5$pc is required to make $\tau_{\rm{IGM}}$ reach $\sim 1-10\,$ms at 1 GHz to explain the observed events with $\tau \geq 1\,$ms. This outer scale can significantly alleviate the tension regarding the timescale of turbulent dissipation and IGM cooling but remains approximately 4 orders of magnitude lower than the currently estimated turbulence injection scale due to structure formation. We find that the estimated effective scattering measure in our simulation is notably sensitive to the simulation resolution. With a higher resolution, stronger density fluctuations can be resolved. The gap in the outer scale of turbulence may be effectively shortened if the simulation resolution can be enhanced. With a mock sample of 500 sources evenly distributed in the redshift range of $0.1<z<1.5$, the dependence of $\tau_{\rm{IGM}}$ on $\rm{DM}_{\rm{IGM}}$ is $\tau_{\rm{IGM}} \propto \rm{DM_{IGM}}^{1.56-2.02}$. The upper value of the scaling index, i.e., 2.02, is determined by the gas in clusters. Factors including feedback from star formation and AGN, and supersonic turbulence may further decrease the gap in the outer scale. Feedback processes can drive the density fluctuations below tens of kpc. The density fluctuation of supersonic turbulence differs from that of subsonic turbulence, which may change the required scales (see XZ16). Meanwhile, effects such as $z_L$ and $D_{\rm{eff}}$ have not been considered, which makes our results for $\tau_{{\rm{IGM}}}$ somewhat overestimated. The selection effect and intrinsic redshift distribution of the FRBs remain unclear. Finally, the contributions from both the IGM and host galaxies may play important roles in the scattering of FRBs. Namely, the IGM in filaments and clusters may dominate the scattering of some FRBs, whereas the host galaxy dominates others. As the number of observed events continues increasing, the dependence of $\tau$ on DM may help to ascertain the relative contributions from the host galaxy and IGM. A more comprehensive investigation will be conducted in the future to cover these factors. | 18 | 8 | 1808.05739 |
1808 | 1808.10226_arXiv.txt | {Diffuse interstellar bands (DIBs) are broad absorption features measured in sightlines probing the diffuse interstellar medium. Although large carbon-bearing molecules have been proposed as the carriers producing DIBs, their identity remains unknown. DIBs make an important contribution to the extinction curve; the sight line to the young massive star-forming region M17 shows anomalous extinction in the sense that the total-to-selective extinction parameter differs significantly from the average Galactic value and may reach values $R_{V} > 4$. Anomalous DIBs have been reported in the sight line towards Herschel~36 ($R_{V} = 5.5$), in the massive star-forming region M8. Higher values of $R_V$ have been associated with a relatively higher fraction of large dust grains in the line of sight.} {Given the high $R_V$ values, we investigate whether the DIBs in sight lines towards young OB stars in M17 show a peculiar behaviour.} {We measure the properties of the most prominent DIBs in M17 and study these as a function of $E(B-V)$ and $R_{V}$. We also analyse the gaseous and dust components contributing to the interstellar extinction.} {The DIB strengths in M17 concur with the observed relations between DIB equivalent width and reddening $E(B-V)$ in Galactic sight lines. For several DIBs we discover a linear relation between the normalised DIB strength EW/$A_{V}$ and $R_{V}^{-1}$. These trends suggest two groups of DIBs: (i) a group of ten moderately strong DIBs that show a sensitivity to changes in $R_{V}$ that is modest and proportional to DIB strength, and (ii) a group of four very strong DIBs that react sensitively and to a similar degree to changes in $R_{V}$, but in a way that does not appear to depend on DIB strength.} {The DIB behaviour as a function of reddening is not peculiar in sight lines to M17. Also, we do not detect anomalous DIB profiles as seen in Herschel~36. DIBs are stronger, per unit visual extinction, in sight lines characterised by a smaller value of $R_{V}$, i.e.\ those sight lines that contain a relatively large fraction of small dust particles. New relations between extinction normalised DIB strengths, EW/$A_V$, and $R_V$ support the idea that DIB carriers and interstellar dust are intimately connected. Furthermore, given the distinct behaviour of two groups of DIBs, different types of carriers do not necessarily relate to the dust grains in a similar way.} | \label{P3:sec:intro} The nature of the carrier(s) of diffuse interstellar bands (DIBs) is one of the oldest mysteries in stellar spectroscopy. Over 400 DIBs have been observed in the optical wavelength range \citep[e.g.][]{2009ApJ...705...32H} and about a dozen DIBs have been detected in the near infrared \citep{2011Natur.479..200G, 2014A&A...569A.117C, 2015ApJ...800..137H}. DIBs are thought to be large carbon-bearing molecules and may represent the largest reservoir of organic material in the Universe \citep{2014IAUS..297....3S}. Laboratory experiments simulating interstellar conditions recently proposed C$_{60}^{+}$ as the carrier of the $\lambda$9577 and $\lambda$9632 DIBs \citep{2015Natur.523..322C}, but the vast majority of the DIBs remains unidentified. For a recent overview of DIBs, see \citet{2014IAUS..297.....C}. DIBs measured in sight lines towards massive star forming regions are reported to behave differently compared to the average Galactic sight line. \citet{1997ApJ...489..698H} noted that the DIBs observed in the direction of M17, over the extinction range of $A_V =$ 3 - 10, show little change in spectral shape nor a significant increase in strength. They suggested that either the DIB features are already saturated at a small value of the visual extinction $A_{V}$, or that the interstellar material local to M17, where the increased extinction is being traced, does not contain the DIB carriers. \citet{2013ApJ...773...41D} and \citet{2013ApJ...773...42O} detected anomalously broad DIBs at $\lambda\lambda$5780.5, 5797.1, and 6613.6 in the sight line to Herschel~36, an O star multiple system associated with the Hourglass nebula in the giant H~{\sc ii} region M8 (Lagoon Nebula). The DIBs show an excess of absorption in the red wing of the profile; excited lines of CH and CH$^{+}$ are detected as well. \citet{2013ApJ...773...42O} interpret this observation as being caused by infrared pumping of rotational levels of relatively small molecules. Sight lines towards massive star forming regions (Orion Trapezium region, Carina, M8) often show a high value of the total-to-selective extinction parameter $R_{V}$ \citep[see e.g.][]{1989ApJ...345..245C, 2007ApJ...663..320F}. The common interpretation is that the value of $R_{V}$ characterises the dust particle size distribution. Sight lines that include relatively many small dust particles display an extinction curve with a small value of $R_{V}$ and produce stronger interstellar absorption at short (UV) wavelengths, and vice versa. Most Galactic sight lines have $R_{V} \sim 3.1 \pm 0.3$ \citep[][]{2007ApJ...663..320F} and we refer to extinction curves with higher or lower values of $R_{V}$ as anomalous. The strongest feature in the extinction curve is the 2175~\AA\ bump; although the carrier of this feature also remains unidentified, it is generally attributed to carbonaceous particles, either in the form of graphite, a mixture of hydrogenated amorphous carbon grains and polycyclyc aromatic hydrocarbons (PAHs), or various aromatic forms of carbon \citep[e.g.][]{1977ApJ...217..425M, 1998ApJ...507L.177M, 2015ApJ...809..120M}. It is believed that the presence and strength of the bump depends on the metallicity of the environment as it appears slightly weaker in the LMC extinction curves, and it is essentially absent in the SMC extinction curve \citep{1998ApJ...500..816G, 1999ApJ...515..128M}. Some sightlines towards the LMC (specifically the LMC\,2 supershell near 30 Dor) and the SMC sight lines have small $R_{V}$ values \citep[$\sim 2.7$,][]{2003ApJ...594..279G}. Remarkably, the one SMC line of sight that exhibits normal strength DIBs (and CH) shows Galactic-type dust extinction and includes the 2175~\AA\ extinction feature \citep{2002ApJ...576L.117E,2006ApJS..165..138W, 2007A&A...470..941C}. Furthermore, Galactic sight lines that are SMC-like show very weak DIBs per unit reddening (\mbox{\citealt{2002ApJ...573..670S}}; \mbox{\citealt{2007A&A...470..941C}}). If the carriers of the DIBs and those of the 2175~\AA\ bump are produced from the same initial dust through the same physical process, or if the DIB carriers originate from the fragmentation of the 2175~\AA\ bump carriers, one would expect them to be related. More recently \citet{2011ApJ...733...91X} studied the relation between DIBs and the 2175~\AA\ bump in detail. They collected 2175~\AA\ bump and DIB strength measurements, from the literature, towards 84 interstellar sightlines for eight DIBs and found no significant correlation between the two. They explain the lack of a correlation by hypothesising that DIB carriers correspond to the smallest, free-flying PAH molecules and ions, while the 2175~\AA\ carriers correspond to the larger or clustered PAHs. In \citet[][hereafter \citetalias{paper1}]{paper1} we studied a sample of young massive (pre-)main-sequence stars in the giant \ion{H}{ii} region M17 located at a distance of $1.98_{-0.12}^{+0.14}$~kpc \citep{2011ApJ...733...25X}. We obtained optical to near-infrared VLT/X-shooter spectra and derived the extinction parameters by modelling the spectral energy distribution. The sight lines are characterised by anomalous extinction ($R_{V}$ in the range 3.3 to 4.6 and $A_{V}$ between 5 and 14~mag). M17 is one of the most luminous star-forming regions in the Galaxy with a luminosity if $3.6\times10^{6}$~L$_\sun$ \citep{2007A&A...462..123P}. It contains about 16 O stars and more than 100 B stars; its age is $\leq 1$~Myr \citep[][\citetalias{paper1}]{1997ApJ...489..698H,2008ApJ...686..310H,2007ApJS..169..353B,2009ApJ...696.1278P}. In this paper we present a detailed analysis of the DIBs in eight sight lines to M17, taking into account the anomalous extinction observed in this region ($R_V > 3.1$). Earlier work hinted at the peculiar behaviour of the DIBs in these sight lines \citep{1997ApJ...489..698H} and we investigate whether the DIB properties are somehow related to the extinction caused by dust. Such a relation may shed new light on the physical and chemical nature of the DIB crriers. The paper is organised as follows: in the next section we briefly describe the data set and reduction procedure, and in Section~\ref{P3:sec:extinction} we characterise the interstellar extinction in the direction of M17, both the gaseous and the dust component. In Section~\ref{P3:sec:DIBs} the DIB properties are presented. Subsequently, we compare the DIB properties to those observed in other Galactic sight lines (Section~\ref{P3:sec:OtherSightlines}). In Section~\ref{P3:sec:DIBvsRv} we address the observed dependence of the DIBs in M17 on the value of $R_{V}$. In Section~\ref{P3:sec:discussion} we discuss the results in the context of the anomalous extinction and the properties of the interstellar dust. In the last section we summarise our conclusions. | \label{P3:sec:discussion} \subsection{Extinction in M17} We calculated the extinction properties of the sight lines towards M17, with overall relatively large $R_V$ values, using different methods; \emph{i)} by dereddening the SED of the stars using Cardelli's extinction law and then fitting it to Kurucz models to find $A_V$ and $R_V$ (from that $E(B-V)=A_V/R_V$). \emph{ii)} Directly by comparing the intrinsic magnitudes to the observed ones, to find $A_V$ and $E(B-V)$ ($R_V=A_V/E(B-V)$). And \emph{iii)} by finding $A_V$ and $E(B-V)$ from the intrinsic and observed magnitudes and calculating $R_V$ as defined by \citet[Eq.~\ref{P3:eq:Rv_fitzpatrick}]{2007ApJ...663..320F}. We observe that the colour excess $E(B-V)$ calculated with Cardelli's extinction law and the SED fitting is systematically higher than using the other two methods. This confirms that this extinction law is not well suited for large values of $R_V$ as already stated in \citet{1989ApJ...345..245C}. We conclude that the best way of obtaining the extinction properties is to use the intrinsic and observed magnitudes and then calculate $R_V$ as shown in Eq.~\ref{P3:eq:Rv_fitzpatrick}, because with this equation it is also possible to take into account the NIR part of the SED. \subsection{Relation of DIBs with E(B-V)} In Fig.~\ref{P3:fig:DIBvsEBV} we show the relation of the DIBs at 5780 and 5797~\AA\ with the colour excess $E(B-V)$ in M17 and compare it with other sight lines published in the literature. $E(B-V)$ for the sight lines in M17 is relatively high compared to other Galactic sight lines; nevertheless, the DIB strength seems to follow the same trend as observed in other reddened sight lines. \citet{2013A&A...551A...5E} reported an anomalous behaviour of the DIB strength in sight lines towards the star forming region RCW\,36. We do not find a similar deviation in the sight lines towards M17. The behaviour reported in RCW\,36 could be due to the way in which the authors calculated $A_V$. They assumed a value of $R_V=3.1$, dereddened the spectrum using Cardelli's extinction law, and then fitted it to Kurucz models. In this paper we show that the value of $E(B-V)$ can be overestimated by as much as 0.5~mag (Fig.~\ref{P3:fig:E_BV_comparison}) when using Cardelli's extinction law. Previous studies have shown that star-forming regions such as M17 and M8 (where Herschel~36 resides) often show high values of $R_V$ \citep[e.g.][]{1989ApJ...345..245C,1997ApJ...489..698H}. Therefore the assumption that $R_V=3.1$ for RCW\,36 probably underestimates its true $R_V$. \subsection{Relation of DIBs with $R_V$} The observed trend of EW(DIB)/$A_V$ with $R_V^{-1}$ for M17 and other sightlines with $R_V \gtrapprox 3.8$ ($R_V^{-1} \lessapprox 0.26$; cf. Figure~\ref{P3:fig:EWAV_vs_Rv}) is reminiscent to what \citet{1989ApJ...345..245C} and \citet{2017ApJ...835..107X} find for the 2175~\AA\ bump, the carrier of which is thought to consist of some (unidentified) carbonaceous material; however, the trend of the bump is weaker than that observed for the DIBs. The slope of the linear relation between EW/$A_V$ and $R_V^{-1}$ (valid for $R_V \gtrsim 3.8$) can be interpreted as a measure of the sensitivity to which variations in the abundance of DIB carriers (per unit visual extinction) are related to variations in the average grain size of interstellar dust. This slope can then be interpreted in the context of either the depletion of the DIB carrier as the dust grains coagulate and grow \citep[see e.g.][EW/$A_V$ decreases while $R_V$ increases]{1980ApJ...235...63J,2009A&A...502..845O} or the production of DIB carriers as the larger grains get destroyed by the increasingly effective UV radiation field \citep[see e.g.][EW/$A_V$ increases and $R_V$ decreases]{1995ApJS..100..187C,2004ASPC..309..347J}. Alternatively, in the hypothesis that some DIB carriers are ionized species, the strengths of DIBs are expected to increase with a stronger effective UV radiation field. If $R_V$ could be regarded as a tracer of the effective UV radiation field, higher values correspond to a lower ionization fraction, hence lower EW/$A_V$. In this context the slope of EW/$A_V$ versus $R_V^{-1}$ would be directly related to the ionization potential of the carrier species. With the current data we can not distinguish between these different scenarios. However, it is possible to identify groups or families of DIB carriers which behave similarly in the transition from the more dense to diffuse ISM (high to low $R_V$). To investigate this we compared the column density of the DIB carriers multiplied by the (unknown) oscillator strength, $Nf$, with the slope d(EW/$A_V$)/d$R_V^{-1}$ (cf. Fig.~\ref{P3:fig:EWAV_vs_Rv}; Table~\ref{P3:tab:fitresults}). This slope can be viewed as a measure of the sensitivity of the DIB carriers to changes in $R_V^{-1}$, hence in grain size distribution or as a measure of the carrier's ionization potential. We will refer to this slope as the DIB-$R_V$ sensitivity. Assuming that the optically-thin approximation holds for the DIBs (no saturation of absorption) we have: \begin{equation} Nf = 1.13 \times 10^{20} \,\frac{\mathrm{EW}}{\lambda^{2}} \end{equation} where $N$ is the column density in ${\rm cm^{-2}}$, $f$ the oscillator strength, EW is the equivalent width (in \AA) and $\lambda$ is the central wavelength of each DIB (in \AA). We show the dependence of the DIB-$R_V$ sensitivity on $Nf\lambda^2$, and $Nf$ in Fig.~\ref{P3:fig:strength_vs_slope}; In both cases a linear fit is shown with a dashed line and the shaded region shows the 2$\sigma$ error to the fit. Additionally we marked the $C_{60}^{+}$ DIBs with green pentagons. First we discuss the results in the context of $R_V$ as a proxy for changes in the grain size distribution. We are able to identify two groups; the first group contains ten moderately strong DIBs, including the two $C_{60}^+$ DIBs, the DIBs presenting a red wing in Herschel~36 (5780, 5797, and 6614), and those at 6196, 6379, 7224, 8620, and 11797~\AA. These DIBs show a modest sensitivity to the change in grain size, and their sensitivity increases about linearly as a function of DIB strength. The second group consists of four strong DIBs (at 4430, 6284, 13176, and 15268~\AA), that are very sensitive to the change in grain size distribution (large d(EW/$A_V$)/d$R_V^{-1}$ slope values), but their DIB-$R_V$ sensitivity does not seem to depend on the DIB strength. In the case of the first group, we postulate that the observed linear increase of the DIB-$R_V$ sensitivity with the amount of DIB carriers, $Nf$, suggests that the increase of the latter is primarily due to an increase in column density and that $f$ is quite similar for this group of DIB carriers. This is because the reverse situation, i.e that a systematic increase of the sensitivity of DIB carriers to changes in $R_V$ is related to a systematic increase of the oscillator strength of the DIB carriers appears much more unlikely. If this is the case, the oscillator strengths of these DIBs could be extracted with reference to the two DIBs at 9577 and 9632~\AA\ assigned to C$_{60}^+$ ($f_{9577}=0.018$ and $f_{9632}=0.015$). The linear dependency of the DIB-$R_V$ sensitivity on the DIB strength implies that the relative production/destruction rate of these DIB carriers is the same for the same change in typical grain size ($R_V$). In other words, for a doubling of the abundance of DIB carriers in the first group, the same change in grain size distribution is required. This may imply a common production/destruction mechanism. The fact that the DIB-$R_V$ sensitivity of the stronger DIBs is independent of their strength suggests the existence of an additional reservoir of DIB carriers unrelated to the dust grains. These carriers would be produced/destructed as the grain size distribution changes as well as via other mechanisms. Alternatively, we consider the scenario where $R_V$ is a proxy of the effective UV radiation field strength and the DIB carriers are large ionised molecules. In this case Fig.~\ref{P3:fig:strength_vs_slope} has to be interpreted differently. Here the slope d(EW/$A_V$)/d$R_V^{-1}$ is an indirect measure of the carrier's ionization potential. The broad DIBs at 15268, 13176, 6284 and 4430~\AA\ have a (similar) strong slope which implies a (similar) low ionization potential. The ionization potential of the carriers of these broad DIBs is then expected to be significantly lower than the ionization potential of 7.58~eV measured for $C_{60}$ (\citealt{DEVRIES1992159}). In the opposite direction, the narrow DIBs at 7224, 5797, 6614, 6196, and 6379~\AA\ which have increasingly shallower slopes should then have increasingly higher ionization potentials. For PAHs the ionisation potential is strongly related to their number of $\pi$-electrons (see Fig.~B.1. in \citealt{2005A&A...432..515R}). We note that in the case that there are several foreground clouds contributing to the extinction in the sightline towards M17, the interpretation of the observed relations is complicated. The hypotheses presented above assume that most of the variation in $A_V$ and $R_V$ arises from the dust and gas in the M17 region. Correcting for a foreground sheet of dust, with $A_V = 2$ and a constant foreground EW(DIB)/$A_V$ contribution projected across the M17 region, would shift all the EW/$A_V$ values vertically. Also, correcting for foreground dust with a nominal $R_V$ = 3.1, will sightly increase the $R_V$ values derived for the local M17 dust, but have little impact on the slope of the relation between EW(DIB)/$A_V$ and $R_V^{-1}$. It could also affect the mean normalised line strengths. The above scenarios and hypotheses can be further tested by examining the relation between EW(DIB)/$A_V$ and $R_V$ for other star forming regions that probe a range of extinction properties and grain size distributions, similar to M17. This will also help to disentangle the impact of foreground dust extinction and to determine possible effects due to measurement uncertainties. \begin{figure*}[ht!] \centering \includegraphics[width=0.9\hsize]{figures/slope_vs_NflAv_NfAv.pdf} \caption{Slope representing the sensitivity of EW/$A_V$ with changes in $R_V^{-1}$ versus mean $A_V$ normalised line strength (left; expressed as $Nf/A_V$) and versus the log of this quantity (right) for all sightlines. The dashed line and the shaded regions represent the linear fit to the group of DIBs with slopes $\lesssim 1000$ and the 2$\sigma$ error bars to the fit. The two $C_{60}^{+}$ DIBs are represented with light green pentagons.} \label{P3:fig:strength_vs_slope} \end{figure*} | 18 | 8 | 1808.10226 |
1808 | 1808.08107_arXiv.txt | It is well known that the tidal deformability of a compact star carries important information about the interior equation-of-state (EOS) of the star. The first gravitational-wave event GW170817 from a binary compact star merger observed by the LIGO/VIRGO detectors have already put limits on the tidal deformability and provided constraints on the ultra-high nuclear density EOS. In view of this ground breaking discovery, we revisit and extend our previous work [Phys. Rev. D {\bf 95}, 101302(R) (2017)] which found that taking the effect of elasticity into account in the calculation of the tidal deformability of compact star models composed of crystalline color-superconducting (CCS) quark matter can break the universal I-Love relation discovered for fluid compact stars. In this paper, we present our formulation in detail and provide more analysis to complement our previous findings. We focus and extend the study of the screening effect on the tidal deformability, which we found previously for hybrid star models, to various theoretical two-layer compact star models. Besides solid quark stars and hybrid stars, we also consider (1) solid quark stars dressed in a thin nuclear matter crust and (2) quark stars with a fluid quark-matter core in the color-flavor-locked phase surrounded by a solid CCS quark matter envelope. We show that the screening effect of these two-layer models in general depends on the thickness of the envelope and the ratio between the density gap and the core density at the core-envelope interface. However, for models with a fluid envelope and a vanishing small density gap, the screening effect remains strong even as the thickness of the envelops tends to zero if the quark matter core has a fairly uniform density. The relevance of our study to GW170817 is also discussed. We find that quark star models which are ruled out by the observation limits on the tidal deformability can be revived if the entire quark star is in a CCS phase instead of a fluid phase, thus adding complication on putting constraints on the quark star EOSs. In contrast, the screening effect causes the tidal deformability of a hybrid star with a CCS quark matter core agrees with that of a corresponding stellar model with a fluid core to within less than 1\% if the core size is less than about 70\% of the stellar radius. The implication is that if a hybrid star EOS model is ruled out by the observation limits on the tidal deformability, the conclusion will hold no matter whether the quark matter is in a fluid or solid state, assuming that a large solid core comparable to the stellar radius is not favored in nature. Our study advocates that the tidal deformability not only provides us information on the EOS, but may also give insights into the multi-layer structure and elastic properties of compact star models composed of CCS quark matter. | Introduction} Compact stars have long been perceived as natural laboratories of matter in extremely high density and low temperature, which cannot be attained on Earth. The uncertainties of the equations of state (EOSs) of matter in such an environment can be constrained through observing the signals from compact stars. Aside from traditional observations of electromagnetic signals, gravitational wave signals from compact stars first come into play last year. On 17 August 2017, the Advanced LIGO and Virgo network made the first successful detection of the gravitational wave signal from a binary compact star system, GW170817 \cite{PhysRevLett.119.161101}. The first analysis of the signal already places upper bounds on the tidal deformability, which is a parameter quantifying the ratio of the induced quadrupole moment of a star to an external tidal field. This parameter, denoted by $\lambda$, is shown to be encoded in the emitted gravitational wave signals as a small correction in the phase of the waveform during the early stage of binary compact star inspirals. The measurability of $\lambda$ with gravitational-wave observations has been studied \cite{2008PhRvD..77b1502F,2012PhRvD..85l3007D,PhysRevLett.111.071101,2013PhRvD..88d4042R,PhysRevLett.112.101101,PhysRevD.89.021303,2015PhRvD..91d3002L,2016PhRvD..93f4082H,2017PhRvD..95j4036L,2017PhRvD..96l1501D,2017PhRvD..96h4060K}. Since this parameter is sensitive to the EOS \cite{2009PhRvD..80h4035D,2010PhRvD..82b4016P}, the gravitational wave signals effectively carries information of the EOS independent of the electromagnetic signals. Indeed, based on the GW170817 signal, work has been done to put constraints on the compact star EOSs (\cite{2018ApJ...852L..29R,PhysRevLett.120.172703,PhysRevD.97.083015,PhysRevD.97.084038,2018ApJ...857L..23R,2018ApJ...852L..25R,2017ApJ...850L..34B,PhysRevLett.120.172702,2018RAA....18...24L,Abbott:2018exr}). With this ground breaking first observation, the prospect of using the tidal deformability to probe the properties of compact stars in the future is very promising. One of the open questions that may be explored with gravitational wave measurements is the properties of quark matter in a cold dense environment. It is generally believed that deconfined quarks may exist inside the core of compact stars, which corresponds to the high density and low temperature region of the QCD phase diagram \cite{1965Ap......1..251I, 1970PThPh..44..291I,1973PhLB...47..365F,1975PhRvL..34.1353C, 1976PhLB...62..241B}. At asymptotically high density, QCD predicts that the up, down and strange quarks in the deconfined quark matter would pair up equally to form standard Cooper pairs based on the BCS mechanism and become color superconducting. This phase of quark matter is called the color-flavor-locked (CFL) phase \cite{1999NuPhB.537..443A}. On the other hand, the phase of quark matter at a relatively lower density within a compact star is uncertain when the strange quark mass ($\sim 150~\text{MeV}$) is comparable to the quark chemical potential ($\sim 400~\text{MeV}$) since perturbative QCD is no longer adequate in this regime. It is proposed that in such conditions quark matter may be in the crystalline color superconducting (CCS) phase \cite{2001afpp.book.2061R,2001PhRvD..63g4016A,2005PhLB..627...89C,2006PhRvD..73k4012M,2006PhRvD..74i4019R,2006PhLB..642..350C}, which is a rigid state of matter expected to have an extremely high shear modulus about 20-1000 times that of nuclear matter in a neutron star crust \cite{2007PhRvD..76g4026M}. The exact transition point between the CFL phase and the CCS phase is highly uncertain and the possibility of such a transition existing within a compact star cannot be ruled out \cite{2014PhRvD..89j3014M,2015ApJ...815...81M}. The possibility of sequential QCD phase transitions within compact stars has also been studied \cite{2017PhRvL.119p1104A}. Moreover, there might be a transition point between the quark matter phase to nuclear matter lying within the density range of a compact star. As a result, several phases of matter with distinct properties could exist within compact stars. For instance, `hybrid stars' containing a quark matter core and a nuclear matter envelope has long been hypothesized to be some of the observed compact stars \cite{1975PhRvL..34.1353C,1976PhLB...62..241B,1976Natur.264..235C,2000PhR...328..237H}. In another scenario where strange matter is the absolute ground state for strong interactions \cite{1984PhRvD..30..272W}, most of the hadronic matter is turned into deconfined quark matter within a compact star. A thin layer of nuclear matter might exist on the top of the quark matter since the compact star attracts normal nuclear matter from the surroundings. The strange quark matter is not in direct contact with the nuclear matter crust due to Coulomb repulsion. As a result, such a model is composed of quark matter dressed in a thin layer of nuclear matter. The two phases of matter are separated by a thin layer of electrons \cite{1986ApJ...310..261A,2015ApJ...815...81M}. While different theoretical possibilities have been proposed, could we tell from observations in what phase(s) deconfined quark matter (if exists) can occur in compact stars? This is certainly a non-trivial question since even the EOS of traditional neutron stars is still an open question. Following the successful measurement of the gravitational wave signal GW170817 from binary compact stars, we can now study the properties of compact stars through a completely new window, in particular using the observation limits on the tidal deformability as mentioned above. It will soon be possible to put constraints on those hypothetical phases within compact stars. In \cite{2017PhRvD..95j1302L}, we propose that the tidal deformability of compact stars may give us a useful probe to solid quark stars due to the extreme rigidity of the CCS phase of quark matter. Penner {\it et al.} \cite{2011PhRvD..84j3006P} first studied the effect of elasticity on the tidal deformability of neutron stars using polytropic models with a thin elastic crust to mimic traditional neutron star models. They conclude that the elasticity of the neutron-star crust causes a tiny reduction of the tidal deformability compared to the fluid counterpart. On the other hand, our previous study \cite{2017PhRvD..95j1302L} reveals that the tidal deformability of a solid quark star can be up to about 60\% smaller than its fluid-star counterpart. This causes a significant deviation in the I-Love relation, which relates the moment of inertia ($I$) and the tidal deformability (sometimes quantified by the tidal Love number \cite{1911spge.book.....L}), of solid quark stars from the universal relation \cite{2013PhRvD..88b3009Y,2013Sci...341..365Y} discovered for fluid compact stars. (see \cite{2017PhR...681....1Y} for a review). As a result, the properties of solid quark stars containing the CCS quark matter can be constrained from the I-Love relation if the independent accurate measurements of $I$ \cite{2005ApJ...629..979L} and tidal deformability \cite{2008PhRvD..77b1502F}, $\lambda$, are available in the future. In this paper, we extend the study to three types of composite compact star models containing the CCS phase quark matter: (1) hybrid stars containing a solid CCS phase quark matter core and a fluid nuclear matter envelope \cite{2008PhRvD..77b3004I,2009PhRvD..79h3007K,2013PhRvD..88l4002L}, (2) dressed quark stars with a solid quark matter core in CCS phase and a thin nuclear matter crust separated by Coulomb force \cite{2015ApJ...815...81M}, (3) two-layer quark stars with a fluid CFL quark matter core and a solid CCS quark matter envelope \cite{2014PhRvD..89j3014M}. These models all contain two layers with distinct elastic properties. We focus on the effect on the tidal deformabilities brought by the rigid CCS phase and the influence on such an effect caused by a layer in different composition. For instance, we have found the so-called `screening effect' in \cite{2017PhRvD..95j1302L}, where the fluid envelope of a hybrid star masks the effect of elasticity of the CCS quark matter core on the tidal deformability so that the value of $\lambda$ for the hybrid star is essentially the same as that of a stellar model with a fluid quark matter core. As mentioned above, the calculation of the tidal deformability of traditional neutron stars with an elastic crust in general relativity (GR) has been formulated by Penner {\it et al.} \cite{2011PhRvD..84j3006P}. We have formulated the problem ourselves and re-derived the set of equations using a different choice of variables comparing to \cite{2011PhRvD..84j3006P} so that the resulting matter equations can be compared directly to those corresponding Newtonian equations (e.g., \cite{2015Icar..248..109B,2015Icar..258..239B}) in elastic layers. We have applied our equations in the previous study \cite{2017PhRvD..95j1302L} and we present the full set of equations and the relevant boundary conditions in this paper. In Sec.~\ref{sec2:level1}, we present the formulation to compute the tidal deformability of two-layer compact stars with a solid component. Section~\ref{sec4:level1} presents our numerical results for various two-layer compact star models. In Sec.~\ref{sec:factors}, we study how the screening effect is affected by the stellar structure and physical parameters. We also briefly discuss the relevance of our work to GW170817 in Sec.~\ref{sec:GW170817}. Finally, we conclude our paper in Sec.~\ref{sec:conclude}. Unless otherwise noted, we use geometric units with $G=c=1$. | \label{sec:conclude} In this paper, we study the tidal deformability of compact star models containing the extremely rigid CCS phase quark matter. We have presented a formulation to determine the tidal deformability of two-layer compact stars with a solid component. Comparing to previous work on this subject (e.g., \cite{2011PhRvD..84j3006P}), our formulation is written in terms of a different set of matter variables so that the resulting equations can be compared directly to their Newtonian counterparts. We have applied our formulation to study four different compact star models: (1) solid quark stars composed entirely of CCS quark matter \cite{2017PhRvD..95j1302L}; (2) hybrid stars with a nuclear matter fluid envelope on top of a CCS quark-matter core \cite{2008PhRvD..77b3004I,2009PhRvD..79h3007K,2013PhRvD..88l4002L}; (3) dressed solid quark stars with a thin nuclear matter solid crust \cite{2015ApJ...815...81M}; and (4) two-layer quark stars with a fluid CFL quark-matter core surrounded by a CCS quark-matter envelope \cite{2014PhRvD..89j3014M}. We focus on the screening effect on the tidal deformability due to the envelope of various two-layer compact star models, which screens off the influence by the elastic or fluid property of the core. Our results show that the screening effect in hybrid stars is strong as long as the size of the solid quark-matter core is less than about 70\% of the stellar radius. For instance, the fractional deviation in the normalized tidal deformability of a hybrid star, with a solid core with radius about half of the stellar radius from the corresponding pure fluid model is below 1\%. On the other hand, the screening effect in dressed solid quark stars with a thin nuclear-matter crust featuring a large density gap at the core-crust interface is very weak. Further analysis in Subsection~\ref{ssec:den_gap} shows that the large density gap is the reason for the weakness of the screening effect. In other words, if the density gap is zero, the screening effect would become so strong that the tidal deformability of the model would deviate a lot from that of a solid quark star with the same background profile. We have also found that the screening effect in two-layer quark star models with a fluid CFL core surrounded by a CCS solid envelope is different from hybrid stars in terms of the dependence on the thickness of the core and envelope. Compared to the case of hybrid stars, the screening effect of two-layer quark stars is more sensitive to the position of transition between the fluid core and solid envelope. Besides, we also investigate how the screening effect in two-layer compact stars is affected by the core size, the density gap at the core-envelope interface and the compactness of the stars. First, we adjust the core size of two-layer models without a density gap at the interface to study its influence on the screening effect. For models with a fluid core and a solid envelope, the screening effect gradually changes with the core size. The screening factor, defined in Sec.~\ref{sec:factors}, reduces from 1 to 0 (no screening) as the core size increases from 0 to the stellar radius. On the contrary, the screening effect of models with a solid core and a fluid envelope show a much weaker dependence on the core size. We also find that for models with a rather uniform density profile, the screening factor remains close to 1 for any core size between 0 and the stellar radius, which indicates strong screening regardless of the core size. For polytropic models with a solid core and a fluid envelope, the screening factor remains close to one for core size less than 0.75 of the stellar radius. We also show that the screening factor of a two-layer incompressible model with a solid core and a thin fluid envelope reduces gradually to 0 as the density gap at the core-envelope interface increases from 0 to 100\% of the core density. This indicates that the density gap at the interface is an important factor to affect the screening effect. It specifically explains the weak screening effect in dressed quark stars. The effect of GR on the screening effect is also studied by varying the compactness of our stellar models. A slight reduction on the screening factor is found on two-layer incompressible models as the compactness increases from the Newtonian limit (i.e., compactness equals 0), to the highly relativistic case (compactness equals 0.44). However, the reduction in screening factor is not significant as long as we are considering the typical range of compactness of around 0.2. Our numerical investigation suggests that the screening effect depends crucially on the detailed stellar structure such as the core size, composition (fluid or solid state) of the core and envelope, and the density gap at the core-envelope interface. Finally, we have demonstrated how quark star models which are ruled out by the observation limits on the tidal deformability obtained from GW170817 \cite{PhysRevD.97.083015} can be revived if the entire quark star is in a CCS phase instead of a fluid phase. This illustrates how the crystalline phase of quark matter might come into play when one tries to use the information on the tidal deformability obtained from gravitational wave observations to put constraints on quark-matter EOS models. Our study also advocates that the tidal deformability not only provides us information on the EOS, but may also give insights into the multi-layer structure and elastic properties of compact star models composed of CCS quark matter. With the expectation that more compact star mergers will be observed in the coming decades, the possibility of using the observed gravitational wave signals to constrain the various models of deconfined quark matter will become very promising. \appendix | 18 | 8 | 1808.08107 |
1808 | 1808.04868_arXiv.txt | Over the last decade there has been mounting evidence that the strength of the Sun's polar magnetic fields during a solar cycle minimum is the best predictor of the amplitude of the next solar cycle. Surface flux transport models can be used to extend these predictions by evolving the Sun's surface magnetic field to obtain an earlier prediction for the strength of the polar fields, and thus the amplitude of the next cycle. In 2016, our Advective Flux Transport (AFT) model was used to do this, producing an early prediction for Solar Cycle 25. At that time, AFT predicted that Cycle 25 will be similar in strength to the Cycle 24, with an uncertainty of about 15\% . AFT also predicted that the polar fields in the southern hemisphere would weaken in late 2016 and into 2017 before recovering. That AFT prediction was based on the magnetic field configuration at the end of January 2016. We now have 2 more years of observations. We examine the accuracy of the 2016 AFT prediction and find that the new observations track well with AFT's predictions for the last two years. We show that the southern relapse did in fact occur, though the timing was off by several months. We propose a possible cause for the southern relapse and discuss the reason for the offset in timing. Finally, we provide an updated AFT prediction for Solar Cycle 25 which includes solar observations through January of 2018. | The appearance of solar activity (sunspots, flares, coronal mass ejections, etc) is cyclic with an average period of about 11 years. Large solar storms, which also vary with the solar activity cycle, produce space weather events that can have devastating impacts on our assets in space, as well as here on Earth (e.g., communications and power grids). Accurate solar cycle predictions are essential for planning of future and current space missions and for minimizing disruptions to the nation's infrastructure. While there are still several different solar cycle prediction techniques \citep{2008Pesnell,2015Hathaway}, one method is emerging as a definitive leader in the field: the amplitude of the Sun's polar magnetic fields at solar cycle minimum \citep [e.g.,][]{2005Svalgaard_etal, 2013MunozJaramillo_etal}. Surface Flux Transport (SFT) models \citep{2005Sheeley,2014Jiang_etalB}, which simulate the evolution of the Sun's magnetic field, provide a way of estimating the amplitude of the polar fields several year prior to solar minimum, thereby extending the range of solar cycle predictions. The Advective Flux Transport (AFT) model is one such SFT model, designed specifically with the intent of being as realistic as possible without the use of free parameters \citep {2014UptonHathawayA, 2014UptonHathawayB, 2015UgarteUrra_etal}. The AFT model was recently used to make an ensemble of 32 predictions for the amplitude of Solar Cycle 25 \citep {2016HathawayUpton} (hereafter referred to as HU16). In this study, 3 model parameters - the convective motion details, active region tilt, and meridional flow profile - were varied in order to also determine the relative uncertainty produced. HU16 found that the polar fields near the end of Cycle 24 would be similar to or slightly smaller than the polar fields near the end of Cycle 23, suggesting Cycle 25 would be similar or somewhat weaker than Cycle 24. After four years of simulation, the variability across the ensemble produced an accumulated uncertainty of about 15 \%. Additionally, all realizations in the HU16 ensemble predicted a relapse in the southern polar field in late 2016 and into 2017. One of the biggest sources of uncertainty in making solar cycle predictions comes from the large scatter inherent in the systematic (Joy's Law) tilt of Active Regions (ARs)\citep{2014Jiang_etalA}. This tilt angle produces an axial dipole moment in newly emerged ARs, which continues to evolve during the lifetime of the AR. Over the course of the solar cycle, the axial dipole moments of the residual ARs are transported to higher latitudes, where they accumulate, causing the reversal and build up of the polar fields. The net global axial dipole at the end of the cycle (i.e., solar cycle minimum), forms the seed that determines the amplitude of the next cycle. \citet{2014Cameron_etal, 2017Nagy_etal} showed that large, highly tilted 'rogue' active regions can have a huge impact on the Sun's axial dipole moment, particularly if they emerge close to the equator. We are now two years closer to solar minimum since our last prediction. At this late stage of the solar cycle, fewer ARs emerge, reducing the likelihood that a 'rogue' active region will emerge. Those that do emerge typically have much weaker flux \citep{2015MunozJaramillo}, emerge closer to the equator (Sp\"orer's Law), and have smaller tilt angles (Joy's Law). The net effect of all of these factors, barring the emergence of a large 'rogue' active region, means that the few ARs that are left to emerge will have very small axial dipole moments and little impact on the polar field strengths. Another effect is that the uncertainly caused by the variability in the tilt is significantly reduced. With the solar cycle minimum only 2-3 years away, this is an optimal time for an updated prediction. In this paper we begin by revisiting the previous Solar Cycle 25 prediction made with the AFT model. We discuss the accuracy of those predictions as compared to the observations that have since occurred. We then provide an updated prediction for Solar Cycle 25. | We have investigated the accuracy of the predictions made by AFT in 2016 (HU2016). We found that those predictions are largely in line with the observations that have occurred since that prediction was made.The biggest discrepancy was found to be the timing of a relapse in the strength of the southern polar field - while the amplitude was correct, the relapse actually occurred about 9 months later. We identified a few active regions that produced leading polarity streams that caused this relapse, with the most significant of these ARs, being NOAA 12192. We found that the offset in the timing of the relapse was due primarily to formation of the polarity inversion line right at the 55\textdegree latitude cutoff. Slight differences in the surface flux transport can significantly change the amount of flux above or below this line, resulting in offsets in the timing of the evolution of the hemispheric polar fields. Despite this offset, the evolution of the axial dipole for the last 2 years was accurately predicted in HU2016. We provided an updated prediction for solar Cycle 25, which incorporated the observations up to Jan 2018. The new prediction gave an axial dipole of +1.56 $\pm 0.05$ G for the start of 2020 and +1.54 $\pm 0.04$ G for start of 2021. This indicated that Cycle 25 will be on the order of 95\% of Cycle 24. Of the predictions that are using the axial dipole as a predictor, AFT is on the lower end of the spectrum. \citep {2017Jiang_Cao} expects the axial dipole at 2020 to be 1.76 $\pm$ 0.68 G, or comparable to Cycle 24. \citep {2017Wang} also expects Cycle 25 to be comparable to Cycle 24. \citep {2016Cameron_etal} predicts that Cycle 25 will be slightly higher than Cycle 24, but acknowledges that the reliability of this prediction is limited by the intrinsic uncertainty. Given the consensus of these predictions with our own results, we are confident that Cycle 25 will indeed be another weak cycle. We note that our new prediction ( +1.56 $\pm 0.05$ G) falls within the uncertainty given in our HU2016 prediction (+1.36 $\pm 0.20$ G). While this demonstrates that AFT can accurately predict the evolution of the axial dipole, within the uncertainty, 4 years in advance of the minimum, the addition of two more years of observations significantly adds to the precision of the AFT solar cycle predictions. At this late stage of the cycle, the uncertainty in AFT's ability to predict the polar fields is very small. We acknowledge that there is additional uncertainty associated with using the axial dipole as a predictor of the amplitude of the next cycle. Compounding this is the fact that, while this trend appears to be linear for cycles stronger than Cycle 24, we do not yet have data to show that this relationship holds for cycles that are weaker than Cycle 24 (see Figure 1 HU2016, which shows Cycle 24 is the smallest cycle used to determine this relationship). Though we do make this assumption in our prediction for the strength of Cycle 25, Cycle 25 will be a test of this assumption. As the saying goes, \textit{only time will tell}, but we await it with open arms. | 18 | 8 | 1808.04868 |
1808 | 1808.08041_arXiv.txt | { Multi-pixel fast silicon detectors represent the enabling technology for the next generation of space-borne experiments devoted to high-resolution spectral-timing studies of low-flux compact cosmic sources. Several imaging detectors based on frame-integration have been developed as focal plane devices for X-ray space-borne missions but, when coupled to large-area concentrator X-ray optics, these detectors are affected by strong pile-up and dead-time effects, thus limiting the time and energy resolution as well as the overall system sensitivity. The current technological gap in the capability to realize pixelated silicon detectors for soft X-rays with fast, photon-by-photon response and nearly Fano-limited energy resolution therefore translates into the unavailability of sparse read-out sensors suitable for high throughput X-ray astronomy applications. In the framework of the ReDSoX Italian collaboration, we developed a new, sparse read-out, pixelated silicon drift detector which operates in the energy range 0.5--15 keV with nearly Fano-limited energy resolution ($\leq$150 eV FWHM @ 6 keV) at room temperature or with moderate cooling ($\sim$0~$^{\circ}$C to +20~$^{\circ}$C). In this paper, we present the design and the laboratory characterization of the first 16-pixel (4$\times$4) drift detector prototype (PixDD), read-out by individual ultra low-noise charge sensitive preamplifiers (SIRIO) and we discuss the future PixDD prototype developments. } | \label{sec:intro} The study of high energy radiation from celestial objects is one of the most powerful diagnostic tools to access and understand the mechanisms underlying the most energetic and violent phenomena in the Universe. The X-ray range (0.5--10 keV) is particularly suitable for this investigation thanks to a mature detector and optics technology. Spectral and timing radiation signatures at these energies offer a direct access to plasma in environments hosting extreme conditions of gravity, density or magnetic field. The need for high sensitivity spectroscopic and timing experiments has inspired in the last years intensive R\&D programs focused on the development of innovative, fast, pixelated detectors. As a matter of fact, when imaging X-rays, the size of the optics point spread function (PSF) is typically in the range of one millimetre or less for the usual focal lengths. In cases where imaging is not the primary scientific goal, the ideal pixel size is as small as required for an oversampling of the PSF, but as large as possible to reduce charge sharing and power consumption by reducing the number of required readout channels. In this energy range, silicon is probably the most suitable detector material, due to its quantum efficiency and advanced manufacturing technology. \begin{figure}[!ht] \centering \includegraphics[height=0.35\textwidth]{Figures/PixDD_pixel.pdf} \includegraphics[height=0.30\textwidth]{Figures/PixDD-3D_cut.pdf} \caption{Simplified single pixel layout (left) and multi-pixel layout (right) of the PixDD detector. See text for details.} \label{fig:pixddlayout} \end{figure} Different large pixel detectors have been proposed as focal plane sensor for X-ray spectral-timing study of astrophysical sources. The widely used Si-PIN detectors show very interesting capabilities in terms of X-ray detection efficiency and sensor effective area. Their performance is however limited by the large anode capacitance (of the order of $10^3$ fF), which makes this kind of sensor not suitable for applications where a nearly Fano-limited energy resolution ($\leq$150 eV FWHM @ 5.9 keV) is required, especially if the experiment is characterized by a high counting rate (i.e. a short peaking time is required) with limited resources for detector cooling (i.e. large parallel noise) and read-out (small pixel size). Similarly, charge coupled devices (CCDs) with large pixel area suffer the same problems, even worsened by the integration of the leakage current between the read-out of two consecutive image frames (usually worked around with deep cooling, typically to temperatures lower than $-70$ $^{\circ}$C). Moreover, since the CCD is an integration-based imaging detector, it is not suitable for photon-by-photon spectral and timing information at high rates (for bright sources, due to pile-up): this is actually a requirement for the astrophysical applications described above. Recently, Depleted p-channel Field Effect Transistors (DePFET \citep{Kemmer1987, Kemmer1990, Lutz2001}) have been developed and several prototypes have been manufactured. DePFET are excellent sensors for both space-borne imaging applications and high resolution X-ray spectroscopy when a frame rate around 10~kHz is required, as implemented for example in the Athena WFI high count rate capable sensor \citep{Meidinger2017}. An approach to a higher frame rate has been studied for the DePFET Sensor with Signal Compression camera (DSSC) at the European XFEL in Hamburg \citep{Porro2012}. Although in these devices all pixels are read out simultaneously at a rate of a few MHz, the high speed read-out requires a high power consumption and heat dissipation, making this scheme less than ideal for space-borne applications. In this paper we present the design, production and laboratory characterization of a state-of-the-art pixelated detector prototype --- PixDD --- based on planar silicon technology. PixDD is aimed at the measurement of X-rays between 0.5 and 15 keV with a nearly "Fano-limited" spectral resolution, a timing resolution of few microseconds and a photon-by-photon fast read-out. The detector system exploits the superior noise characteristics typical of the Silicon Drift Detectors (SDD) and the ultra-low noise performance of a dedicated front-end electronics. The PixDD development builds on the state-of-the-art results achieved in Italy on both SDDs, with the combined design and manufacturing technology of INFN-Trieste and Fondazione Bruno Kessler (FBK, Trento), and the read-out electronics, with the unprecedented noise performance of the SIRIO charge preamplifier \citep{Bertuccio2007,Bertuccio2014} developed at Polytechnic of Milan. This high-performance, pixelated silicon detector ($<$1 mm$^2$/pixel) has been designed aiming to imaging, timing and spectroscopic studies of astrophysical X-ray sources and will enable the development of a large-area detector with immediate application to spaceborne high-energy astrophysics experiments. \begin{figure}[!t] \begin{center} \includegraphics[width=0.80\textwidth]{Figures/pixdd_2_transparent.pdf} \caption{The first PixDD detector prototype. Left: n-side (anode side), Right: p-side (entrance window side).} \label{fig:pixddphoto} \end{center} \end{figure} \begin{figure}[!t] \begin{center} \includegraphics[width=0.80\textwidth]{Figures/PixDD_QE_v3.pdf} \caption{Estimated quantum efficiency of the PixDD detector for back-illumination.} \label{fig:pixddqe} \end{center} \end{figure} | \label{sec:conclusion} \begin{figure}[!t] \centering \includegraphics[width=0.85\textwidth]{Figures/20180105_003_55Fe_RECON.pdf} \caption{ $^{55}$Fe energy spectrum at $\mathrm{+27\,^{\circ}C}$ obtained by summing together single events ($\mathrm{m = 1}$) acquired by CH10 and multiple events ($\mathrm{m \geq 2}$) collected by CH10 and the neighbouring pixels. } \label{fig:55ferecon} \end{figure} In the framework of the RedSoX Italian collaboration, a novel, pixelated, silicon drift detector (PixDD) has been designed and produced to fill the technological gap in the capability of realizing pixel silicon detectors with fast response, which are capable of asynchronously detect and trigger on the individual X-ray photons and can offer a nearly Fano-limited energy resolution and soft X-ray response at room temperature, as required by high throughput X-ray astronomy applications. The whole system, composed of a 16 pixels $\mathrm{500\,\mu m\,\times \,500 \,\mu m}$ wide, has been integrated with ultra low-noise front-end electronics (SIRIO 3.4) and characterized at $\mathrm{+ 27\,^{\circ}C}$ at the INAF-IAPS laboratories, demonstrating outstanding noise figure (single channel $\mathrm{ENC \leq 10\, e^{-}}$ r.m.s.) and spectroscopic capabilities ($\mathrm{\Delta E \leq 150\,eV}$ FWHM at 5.9~keV). The physical and electronic behaviour of the individual pixels have been studied to assess the charge sharing between neighbouring detector cells, resulting in a limited fraction of shared events ($\simeq$16\%) whose contribution to the energy resolution does not undermine the overall detector performance. Further experimental activities have already taken place aimed at the design and production of a large PixDD detector, composed by $\mathrm{16 \times 8}$ pixels with $\mathrm{300 \times 300\,\mu m^2}$ dimensions. The $\mathrm{16 \times 8}$ PixDD will be read-out by a monolithic $16\times 8$ channel ASIC (namely RIGEL) developed by Polytechnic of Milan and University of Pavia and currently in production. The PixDD--RIGEL hybrid will be flip-chip-bonded exploiting the bump bonding technique developed at the Karlsruhe Institute of Technology (KIT) \citep{Caselle2016}. \\ | 18 | 8 | 1808.08041 |
1808 | 1808.08870_arXiv.txt | In the present research, we study the effects of a single giant planet in the dynamical evolution of water-rich embryos and planetesimals, located beyond the snow line of systems around Sun-like stars, in order to determine what kind of terrestrial-like planets could be formed in the habitable zone (hereafter HZ) of these systems. To do this, we carry out $N$-body simulations of planetary accretion, considering that the gas has been already dissipated from the disk and a single giant planet has been formed beyond the snow line of the system, at 3 au. We find that a giant planet with a value of mass between Saturn-mass and Jupiter-mass, represents a limit from which the amount of water-rich embryos that moves inward from beyond the snow line starts to decrease. From this, our research suggests that giant planets more massive than one Jupiter-mass become efficient dynamical barriers to inward-migrating water-rich embryos. Moreover, we infer that the number of these embryos that survive in the HZ significantly decreases for systems that host a giant planet more massive than one Jupiter-mass. This result has important consequences concerning the formation of terrestrial-like planets in the HZ with very high water contents and could provide a selection criteria in the search of potentially habitable exoplanets in systems that host a gaseous giant around solar-type stars. | At the present time, we know that planetary systems are common in the Universe. They could be found around different stars and be composed by all kind of planets with a huge variety of parameters. Up to date, there are 3824 confirmed exoplanets and 2859 planetary systems \texttt{(http://exoplanet.eu/)}, and more objects are waiting to be confirmed. As the years pass, the observational techniques improve and the theoretical models become more refined. In fact, observational studies as \citet{Cumming2008} and \citet{Howard2013}, and theoretical works as \citet{Mordasini2009}, \citet{Ida2013}, and \citet{Ronco2017} have shown the existence of a wide diversity of planetary systems, suggesting that those systems consisting only of rocky planets would seem to be the most common in the Universe. Of particular interest are the terrestrial-like planets located in the so-called ``habitable zone'' (hereafter HZ) of a given system, which is defined as the circumstellar region inside which a planet can retain liquid water on its surface. However, the location of a terrestrial-like planet in the HZ is a necessary condition but not enough to say that such a planet could host life as we know today. In fact, the maintenance of habitable conditions on a planet requires to satisfy other conditions, which are related to the existence of a suitable atmosphere, organic material, the presence of a magnetic field, plate tectonics that replenish the atmosphere of CO2, among others \citep{Martin2006}. Several authors worked with $N$-body simulations in order to describe the possible formation and evolution of a planetary system and the water delivery in the HZ in different dynamical scenarios. In particular, many works focused on the study of planetary systems that host at least one gaseous giant. For example, \citet{Raymond2004} and \citet{Raymond2006} explored the accretion process and dynamics of terrestrial planets around a Sun-like star under the effects of a Jovian planet in the outer disk, while \citet{Mandell2007} studied the formation of Earth-like planets during and after giant planet migration in solar-type stars, considering systems with a single migrating giant planet and other ones with an inner migrating gas giant and an outer non-migrating giant planet. Moreover, \citet{Raymond2011} studied the terrestrial-like planet formation and water delivery in systems with multiple unstable gas giant planets. On the other hand, \citet{Raymond2007} studied the habitable planet formation considering one Jovian-type planet around binary systems. They worked with a Sun-like star as the primary star and took values of 0.5 $\textrm{M}_{\textrm{\sun}}$, 1 $\textrm{M}_{\textrm{\sun}}$, and 1.5 $\textrm{M}_{\textrm{\sun}}$ for the secondary star of the binary system, focusing their attention on the formation of Earth-like planets in the HZ of the primary star. More recently, \citet{Quintana2014} worked with terrestrial planet formation around a Sun-like star considering a massive planet in the system with values of masses between 1 $\textrm{M}_{\textrm{\earth}}$ and 1 $\textrm{M}_{\textrm{jup}}$, while \citet{Izidoro2015} used dynamical simulations to show that gas giant planets act as barriers to the inward migration of super-Earths initially located in distant orbits around a Sun-like star, considering interactions with a gaseous protoplanetary disk in the middle stages of their formation. Lately, \citet{Zain2018} worked with planetary formation and water delivery in the HZ around a Sun-like star considering different scenarios: one with a Jovian-like giant, one with a Saturn-like giant and other ones without giant planets in the system. They found that planets with high amount of water in mass, were formed in the HZ of all their work scenarios. All these works focus their attention in the late stages of terrestrial planet formation, assumed that water was delivered to planets via collisions, considering the condensation of material beyond the snow line, located about 3 \textrm{au}. In the present work, we use $N$-body simulations in order to study the dynamical evolution of systems that host a massive gaseous giant just beyond the snow line around a Sun-like star, when the gas has been already dissipated of the disk. The main goal of our research is to understand how the giant planet of a system affects the formation of the terrestrial ones, in particular those potentially habitable. To do this, we propose different scenarios, considering only one giant planet per system around the snow line, whose mass ranges from 0.5 $\textrm{M}_{\textrm{sat}}$ to 3 $\textrm{M}_{\textrm{jup}}$, where $\textrm{M}_{\textrm{sat}}$ and $\textrm{M}_{\textrm{jup}}$ represent the planetary mass of Saturn and Jupiter, respectively. This work is structured as follows: in Section 2, we describe the model and the numerical method that we used for selecting the initial conditions of our work. In Section 3, we present the $N$-body code and specify the physical and orbital parameters of the bodies that participate of the numerical simulations. In Section 4, we show the HZ model that we used in order to classify the potentially habitable planets. In Section 5, we expose the results obtained from the $N$-body simulations. At the end, we give the conclusions of the present research in Section 6. | In the present work, we analyzed how a single giant planet located around the snow line affects the dynamical evolution of terrestrial-like planets and water delivery in the HZ after the gas dissipation in solar-type star systems. Our study showed a statistical analysis based on results obtained from $N$-body simulations of planetary accretion. In order to analyze the sensitivity of our analysis regarding the mass of giant planets, we carried out $N$-body simulations for six different work scenarios, in which the mass of the giant planet was varied between 0.5 $\textrm{M}_{\textrm{sat}}$ and 3 $\textrm{M}_{\textrm{jup}}$. Our results suggest that a Jupiter-mass planet could represent a limit mass above which the amount of water-rich embryos that moves inward from beyond the snow line starts to decrease. From this, a giant planet more massive than one Jupiter-mass might results to be an efficient dynamical barrier to inward-migrating water-rich embryos. This result has relevant implications concerning the survival of water-rich terrestrial planets in the HZ of a given system. In fact, while the six work scenarios of our research produced planets in the HZ, the percentage of dry (water) worlds that survive in the HZ increases (decreases) as a function of the giant's mass. In this context, a Jupiter-mass planet located around the snow line seems to represent a limit mass above which the number of water worlds in the HZ significantly decreases. In fact, those scenarios that host a perturbing of 2 $\textrm{M}_{\textrm{jup}}$ and 3 $\textrm{M}_{\textrm{jup}}$ around the snow line represent extreme cases, which did not produce water worlds in the HZ in any simulation. It is important to remark that the results previously described should be interpreted in the context of the numerical model used to carry out the $N$-body simulations. In fact, the \textsc{MERCURY} code used in the present study treats all collisions as inelastic mergers, which conserve the total mass and the water content of the interacting bodies. Thus, the masses and water contents of all planets formed in HZ should be interpreted as upper limits. Recent investigations based on hydro dynamical simulations have shown that collisions are not always perfect mergers. In fact, studies such as those developed by \citet{Leinhardt2012} and \citet{Genda2012} analyze the limits of the different collisional regimes and describe the size and velocity distribution of the post-collision bodies. Later, \citet{Chambers2013} used the results of those works to carry out $N$-body simulations of terrestrial planet formation incorporating fragmentation and hit-and-run collisions. In such a work, the author compared those $N$-body simulations with other ones previously developed assuming all collisions as perfect mergers. The general results derived by \citet{Chambers2013} suggested that the final planetary systems produced in the two numerical models were similar. However, the author observed that planets that result in a given system have somewhat smaller masses and eccentricities when a more realistic treatment is included in the model. Recently, \citet{Quintana2016} studied giant impacts on Earth-like planets in the last stage of the evolution of a planetary system, using $N$-body simulations, which included fragmentation and hit-and-run collisions. On the other hand, \citet{Dvorak2015} developed hydrodynamic simulations to infer the amount of water in fragments after a collision for different velocities and impact angles. They found that most of the water is retained by the survivor body for impact angles $\alpha \lse 20^{\circ}$ and velocities $\nu \lse 1.3 \nu_{esc}$, with $\nu_{esc}$ their escape velocity. As a last work, \citet{Mustill2017} explored the effects of implementing a more realistic collision treatment on in-situ formation of planets which radial distances of few tenth of au. Taking those results into account, we consider that is important to include a more realistic treatment of the collisions and the evolution of water in the $N$-body code, in order to refine our percentages of water in the final potentially habitable planets found in all the work scenarios and verify if the dry planets that we found were totally dry or if they could present a small amount of water in mass. One last thing to take into account, is the fact that we fix the snow line in 2.7 au. We are aware of the evolution of the snow line with time and its profile according to a Sun-like star \citep{Ciesla2015}. However, we consider a fix snow line as a good approximation during our integration time and a distance of separation between dry and water rich material at the beginning of our simulations, as it is assumed by different authors such as \citet{Raymond2004}, \citet{Obrien2006}, \citet{Raymond2009}, \citet{Ronco2014}, \citet{Zain2018}, among others, who worked with $N$-body simulations in the last stage of the formation of a planetary system around a solar-mass star, once the gas has been already dissipated from the disk. Even though, we consider that it would be a good experiment to move the snow line inward as \citet{Ciesla2015} in their simulations in order to test the sensitivity of our results with respect to an inner separation between dry and water-rich material. This could have important consequences with respect to the final amount of water in mass of the resulting final planets in the HZ. However, this analysis is out of the scope of this work. We consider that the present work allows us to get a better understanding of the role of giant planets in the formation of terrestrial planets around a Sun-like star. We infer that our results could give a selection criteria for future searches of potentially habitable exoplanets. | 18 | 8 | 1808.08870 |
1808 | 1808.05269_arXiv.txt | Parker's coronal braiding and nanoflaring scenario predicts the development of tangential discontinuities and highly misaligned magnetic field lines, as a consequence of random buffeting of their footpoints due to the action of sub-photospheric convection. The increased stressing of magnetic field lines is thought to become unstable above some critical misalignment angle and to result into local magnetic reconnection events, which is generally referred to as Parker's ``nanoflaring scenario''. In this study we show that the {\sl minimum (magnetic) energy principle} leads to a bifurcation of force-free field solutions for helical twist angles at $|\varphi(t)| = \pi$, which prevents the build-up of arbitrary large free energies and misalignment angles. The minimum energy principle predicts that neighbored magnetic field lines are almost parallel (with misalignment angles of $\Delta \mu \approx 1.6^\circ-1.8^\circ$), and do not reach a critical misalignment angle prone to nanoflaring. Consequently, no nanoflares are expected in the divergence-free and force-free parts of the solar corona, while they are more likely to occur in the chromosphere and transition region. | The sub-photospheric layers of the Sun exhibit vigorous convective motions, which are driven by a negative vertical temperature gradient $dT/dh < 0$ due to the B\'{e}nard-Rayleigh instability (Lorenz 1963). The convective motion of the sub-photospheric fluid is a self-organizing process that creates granules with a characteristic size $\ell \approx 1000$ km and horizontal velocity $v \approx 2$ $\rm km ~ s^{-1}$. It follows that the convective motions have a typical time scale $\tau = \ell / v \approx 500$ s, or 7 minutes, which matches the observed life time of granules. The question now arises how the solar photosphere affects the coronal magnetic field. In Parker's theory for solar coronal heating (Parker 1972, 1983), a coronal loop is perturbed by small-scale, random motions of the photospheric footpoints of the coronal field lines, driven by sub-photospheric convective flows. According to Parker, these motions lead to twisting and braiding of the coronal field lines. As the magnetic field evolves, thin current sheets are formed in the corona, and energy is dissipated by magnetic reconnection. The reconnection is likely to occur in a burst-like manner as a series of ``nanoflares'' (Parker 1988). Parker's magnetic braiding scenario has become the main paradigm for coronal heating in active regions, and the nanoflare heating theory has been widely adopted (see reviews by Cargill 2015; Klimchuk 2015; Aschwanden 2005). However, the response of the coronal magnetic field to random footpoint motions is a complex physical problem, and the implications of Parker's theory are not yet fully understood. Parker (1983, 1988) created several cartoons that depict how the random motion of coronal magnetic field lines (or lines of force) wind around neighbored, less-twisted (or untwisted) field lines (Fig.~1), either for dipolar field lines (Fig.~1a) or in the form of stretched-out flux tubes (Fig.~1b). The winding motion has been aptly called ``coronal loop braiding," although it has never been demonstrated that a braided field can be formed by random motions of the photospheric footpoints. Some cartoons display a single braided field line among a set of untwisted (straight) field lines (Fig.~1c), or a single flux tube surrounded by a set of untwisted (straight) flux tubes (Fig.~1d). The magnetic braiding model predicts that the misalignment angle between a braided field line and a neighboring less-braided field line will increase with time, building up magnetic stress until a reconnection event is triggered, which causes some or all of the magnetic energy to be released. When a coronal loop system is viewed from the side, it generally shows a collection of nearly parallel threads that do not cross each other, and neighboring threads are co-aligned to within a few degrees. The threads are believed to follow the magnetic field ${\bf B} ({\bf r})$, so the direction of ${\bf B}$ in neighboring threads must be co-aligned to within a few degrees. In many cases the average direction of the threads is consistent with that predicted by potential field models. Therefore, the observations provide little evidence for the presence of braided fields with misalignment angles of about 20 degrees relative to the potential field, as predicted by Parker (1983). The observations are consistent with the much simpler geometries rendered in Figure~2, which shows a dipolar flux tube system with slightly twisted (Fig.~2a,b) or a strongly twisted (Fig.~2c,d) flux tubes. In this paper we consider the assumptions of Parker's braiding model and its suitability to explain the observed coronal loops. We argue that the model is not internally consistent because it predicts that thin current sheets will form quickly, but reconnection is assumed to be postponed until the braided field is fully formed. It is not clear that a braided field will form because the timescale for the formation of thin current sheets (a few minutes) is much shorter than the time needed to build up the braided field (hours). We propose an alternative ``solution'' to the Parker problem in which reconnection causes the magnetic field to remain close to a minimum energy state in which the field lines do not deviate strongly from straight lines (also see Rappazzo \& Parker 2013; Rappazzo 2015). According to this scenario, the relative displacements of the footpoint at the two boundary plates in the Parker model are not much larger than the correlation length $\ell$ of the footpoint motions. We also compare the predictions of the minimum energy scenario with results from MHD simulations, and discuss the role of magnetic braiding in coronal heating. We find that quasi-static braiding driven by granule-scale footpoint motions cannot provide enough energy to heat active-region loops to the observed temperatures and densities. | \begin{enumerate} \item{Simplifying the random walk trajectory of a coronal footpoint motion to a circular path (without loss of generality in Parker's model), the force-free magnetic field solution is a helically twisted loop whose footpoint is rotated with a time-dependent rotation angle $\varphi(t)$, and the free energy increases quadratically with the rotation angle, i.e., $\varepsilon_{free}(t) \propto \varphi^2(t)$, which implies that the free (magnetic) energy can grow to arbitrary large values in Parker's scenario.} \item{We employ the minimum energy principle to the footpoint motion of helically twisted loops whenever there is a bifurcation between multiple force-free field solutions. This obeys the principle of the highest statistical likelihood, prevents the build-up of infinite energy, and yields small misalignment angles between adjacent loops, without creating tangential discontinuities or producing nanoflares in the corona.} \item{We estimate the misalignment angles between two adjacent loops (separated by $\Delta r = 1$ Mm, for separation distances of $r=1-10$ Mm, and with twisting by a half turn) and obtain relatively small misalignment angles of $\Delta \mu = 1.6^\circ-1.8^\circ$ between adjacent loops, which confirm the observations of ubiquitous near-parallel loops seen in EUV. The Parker model predicts substantially larger misalignment angles and a threshold value of $\mu_{crit} \ge 20^\circ$ is required for nanoflaring (Parker 1983).} \item{The Parker scenario predicts that the location of nanoflares is distributed throughout the corona, because individual field lines or flux tubes are uniformly twisted along their length (since the non-potential $\alpha$-parameter is constant along each field line). This spatial prediction of nanoflares in the entire corona is not consistent with observations, because all small EUV nanoflares and hard X-ray microflares are found to be localized in the lowest part of the solar atmosphere. Therefore, nanoflares are more likely to occur in the lower atmosphere (in the chromosphere and transition region), where the magnetic field is not force-free.} \end{enumerate} In summary, while Parker's braiding model faces the three major problems of: (i) the (unphysical and unobserved) discontinuity of the magnetic field, (ii) large (unobserved) misalignment angles, and (iii) the (unobserved) location of coronal nanoflares. In contrast, the minimum energy model of helically twisted loops offers: (i) a continuous 3-D magnetic field solution without discontinuities, (ii) small misalignment angles ($\Delta \mu \lapprox 1.6^\circ-1.8^\circ $) that are consistent with observations, and (iii) nanoflare locations in the lower atmosphere (chromosphere to transition region) where EUV nanoflares and hard X-ray microflares are observed indeed. In short, all problems of Parker's braiding and nanoflaring model can be reconciled with the minimum energy principle. | 18 | 8 | 1808.05269 |
1808 | 1808.00485_arXiv.txt | LHS 1140 is a nearby mid-M dwarf known to host a temperate rocky super-Earth (LHS 1140 b) on a 24.737-day orbit. Based on photometric observations by MEarth and Spitzer as well as Doppler spectroscopy from HARPS, we report the discovery of an additional transiting rocky companion (LHS 1140 c) with a mass of 1.81 $\pm$ 0.39 \mearth\ and a radius of 1.282 $\pm$ 0.024 \rearth\ on a tighter, 3.77795-day orbit. We also obtain more precise estimates of the mass and radius of LHS 1140 b to be 6.98 $\pm$ 0.89 \mearth\ and 1.727 $\pm$ 0.032 \rearth. The mean densities of planets b and c are $7.5\pm1.0~\rm{g/cm^3}$ and $4.7\pm1.1~\rm{g/cm^3}$, respectively, both consistent with the Earth's ratio of iron to magnesium silicate. The orbital eccentricities of LHS 1140 b and c are consistent with circular orbits and constrained to be below 0.06 and 0.31, respectively, with 90\% confidence. Because the orbits of the two planets are co-planar and because we know from previous analyses of \emph{Kepler} data that compact systems of small planets orbiting M dwarfs are commonplace, a search for more transiting planets in the LHS 1140 system could be fruitful. LHS 1140 c is one of the few known nearby terrestrial planets whose atmosphere could be studied with the upcoming \emph{James Webb Space Telescope}. | \label{sec:intro} Small planets are very common around M dwarfs \citep{Dressing2013,Bonfils2013,Mulders2015}, with a cumulative occurrence rate of at least 2.5 $\pm$ 0.2 planets per M dwarf \citep{Dressing2015a}. Compared to Sun-like counterparts, such planets are easier to detect due to the smaller sizes and lower masses of the stars, which translate into larger transit depths and Doppler signals. Moreover, the detection and follow-up studies of terrestrial planets in the habitable zone are facilitated by the fact that the same stellar insolation as that received by the Earth is achieved at shorter orbital periods around M dwarfs. The increased frequency and greater depth of transits also renders the atmospheres of these worlds more accessible to transmission and emission spectroscopy, and atmospheric studies are eagerly anticipated with both the upcoming \emph{James Webb Space Telescope} \citep[e.g.][]{Morley2017} and the Extremely Large Ground-based Telescopes \citep[e.g.][]{Rodler2014}. For these reasons, the only terrestrial exoplanets whose atmospheres can be spectroscopically studied in the near-future will be those that orbit nearby mid-to-late M dwarfs. Considering stars with masses less than $0.3 M_{\sun}$ and within 15 parsecs, there are only four such stars known to host transiting planets: GJ 1214 \citep{Charbonneau2009}, GJ 1132 \citep{BertaThompson2015}, TRAPPIST-1 \citep{Gillon2017}, and LHS 1140 \citep{Dittmann2017}. There are also an additional 7 non-transiting systems: Proxima \citep{Anglada-Escude2016}, Ross 128 \citep{Bonfils2018Ross128}, YZ Cet \citep{Astudillo-Defru2017b}, GJ 273 and GJ 3323 \citep{Astudillo-Defru2017a}, Wolf 1061 \citep{Astudillo-Defru2017a,Wright2016}, and Kapteyn's star \citep{Anglada-Escude2014}. The \emph{Kepler dichotomy} refers to the observed excess of stars with single transiting planets compared to the expectations based on geometry and the population of stars with multiple transiting planets \citep{Lissauer2011}. \cite{Ballard2016} studied this effect for M dwarfs, and found they could account for the observed Kepler population if they posited that half of the planetary systems have on average 7 planets with small mutual inclinations, while the other half of planetary systems have only a single close-in planet, or multiple planets with a large range of mutual inclinations. Numerous compact systems of small planets orbiting M dwarfs are known. In fact, \cite{Muirhead2015} found that 21$^{+7}_{-5}$\% of the Kepler M dwarfs host multiple planets with orbital periods less than 10 days. Indeed, of the 11 planetary systems of nearby mid-to-late M dwarfs described in the preceding paragraph, the majority have (or are suspected to have) more than one planet. Our intensive campaign with HARPS to follow-up GJ 1132 recently revealed the presence of at least one additional planet \citep{Bonfils2018}, although it does not appear to transit \citep{Dittmann_1132}. \citet{Dittmann2017} announced the discovery of a terrestrial planet on a 24.7-day orbit in the habitable zone of LHS 1140, with an estimated zero-albedo equilibrium temperature of 230 $\pm$ 20 K. Given the context above, LHS 1140 is a particularly attractive target to search for co-planar planets orbiting interior to the known planet. Therefore, since the discovery of LHS 1140 b, we have intensively monitored this star with MEarth and HARPS in the hope that we would uncover additional transiting planets. A secondary science goal of these observations is to refine the estimate of the density of LHS 1140 b, and hence to address whether the ratio of the iron core to the rocky mantle is consistent with that of the Earth and terrestrial planets generally, given the small spread in abundances of Fe, Mg, and Si among nearby (albeit Sun-like) stars \citep{Bedell2018}. LHS 1140 is a slowly rotating and inactive star, and hence there is no reason to expect that stellar photospheric effects will set a limit to the precision with which the planetary mass may be determined. In this paper, we present a substantially improved estimate for the density of LHS 1140 b, and report the discovery of another small terrestrial planet, LHS 1140 c, on a 3.8-day orbit. This paper is structured as follows. Section \ref{sec:star} summarizes our knowledge of the host star LHS 1140. Section \ref{sec:data} provides an overview of the different instruments and surveys that were used to conduct photometric and spectroscopic monitoring of LHS 1140. Section \ref{sec:discovery} outlines the process that led to the discovery of the new terrestrial companion LHS 1140 c. Subsequently, we performed joint modeling of the two planets to estimate their orbital parameters as described in Section \ref{sec:modeling}. We conclude by discussing the scientific implications of our findings in Section \ref{sec:discussion}. | \label{sec:discussion} \citet{Dittmann2017} first announced the discovery of a transiting super-Earth orbiting the nearby M dwarf LHS 1140. We managed to better constrain the properties of the planet by estimating its mass $m_b = 6.98 \pm 0.89$ \mearth\ and radius $r_b = 1.727 \pm 0.032$ \rearth. These improved values are significantly influenced by the revised stellar mass and radius from more accurate measurements as well as the new parallax value for LHS 1140 from Gaia DR2. Furthermore, we estimate the eccentricity of LHS 1140 b to be below 0.06 with a 90\% confidence, consistent with a circular or an Earth-like orbit. We also see strong evidence of a second terrestrial planet on a $P_c = 3.777950 \pm 0.000005$ day orbit around LHS 1140. In particular, we managed to observe several transits of LHS 1140 c with the ground-based MEarth survey as well as a single transit in April 2018 using the \emph{Spitzer Space Telescope}. The planetary signal was also discovered independently in the radial velocities from the HARPS M~dwarfs survey. Combining photometric and RV data yields a mass estimate of $m_c = 1.81 \pm 0.39$ \mearth\ and a planetary radius of $r_c = 1.282 \pm 0.024$ \rearth. The orbital eccentricity is $e_c < 0.14$ with 80\% confidence and $e_c < 0.31$ with 90\% confidence. Based on our mass and radius estimates for LHS 1140 b and c, we can calculate the mean densities of the two planets: $\rho_b = 7.5 \pm 1.0$ g cm$^{-3}$ and $\rho_c = 4.7 \pm 1.1$ g cm$^{-3}$. We note that the density for planet b decreased from the $\rho_b = 12.5 \pm 3.4$ g cm$^{-3}$ reported by \citet{Dittmann2017}, mostly due to the 21\% increase in the planetary radius. Both planets are consistent with a rocky composition, as can be seen from the mass-radius diagram in Figure \ref{fig:mrrelation} which also illustrates the expected densities for several theoretical bulk compositions \citep{Zeng2016}. The density of LHS 1140 c is also consistent with the findings of \citet{Rogers2015} and \citet{Dressing2015b} who observed that planets with radii below $\sim$1.6 \mearth\ are preferentially rocky (that is, heavy enough to be composed of iron and silicates alone) whereas larger planets tend to have lower densities which implies voluminous layers of volatiles (H/He and astrophysical ices). LHS 1140 b, on the other hand, is consistent with a rocky composition despite having a radius of 1.73 $\pm$ 0.03 \rearth. Therefore, we see further evidence that the transition between planets with and without volatile envelopes is gradual \citep{Rogers2015}. We note that LHS 1140 b falls at the minimum of the occurrence rate versus planet radius recently presented by \citet{Fulton2017}. \begin{figure} \plotone{f8.pdf} \caption{Mass-radius distribution of known nearby small exoplanets orbiting M dwarfs (distances less than 15 pc and host masses less than 0.3 \msun). The solid and the dashed lines show the expected mean densities for various planetary compositions \citep{Zeng2016}. The masses and radii for the TRAPPIST-1 planets were adopted from \citet{Grimm2018}. LHS 1140 b and c are both consistent with a rocky (predominantly iron and magnesium silicates) composition.\label{fig:mrrelation}} \end{figure} We can also estimate the equilibrium black-body temperatures of the two planets by using the stellar temperature and Stefan-Boltzmann law. In particular, we obtain $T_{\rm eq,b}$ = 235 $\pm$ 5 K and $T_{\rm eq,c}$ = 438 $\pm$ 9 K for planets b and c, respectively, assuming a Bond albedo of 0. An Earth-like albedo of 0.3 would yield temperatures of 215 K and 401 K, respectively. The incident fluxes on the two planets compared to Earth are $S_b = 0.503 \pm 0.030$ \searth\ and $S_c = 6.16 \pm 0.37$ \searth. This implies that LHS 1140 c is hot enough to be a Mercury analogue and is likely not habitable in the Earth-based sense. It is also likely to be tidally locked and, barring gravitational perturbations from additional planetary companions, is expected to be in spin-orbit resonance. The outer planet (LHS 1140 b), however, receives half the flux incident on Earth, and could thereby be more accurately characterized as a Super-Mars. Depending on the atmospheric properties, the conservative inner and outer habitable zone limits for LHS 1140 would be 0.07 AU and 0.14 AU, respectively \citep{Kopparapu2013}, placing LHS 1140 b well within the conservative habitable zone. This is mostly consistent with the findings of \citet{Kane2018}, although we place LHS 1140 b deeper within the habitable zone due to our revised values for the orbital semi-major axis as well as the effective stellar temperature. We note that the orbital period ratio of 1:6.55 between the two planets means that they are unlikely to be in direct orbital resonance. Orbital resonances often indicate a history of planetary migration, such as in the four-planet Kepler-223 system \citep{Mills2016} or around TRAPPIST-1 \citep{Tamayo2017}. However, recent simulations suggest that most hot super-Earths like LHS 1140 c are not expected to form in situ \citep{Cossou2014,Ogihara2015}, although resonant chains can also be disrupted by the dispersal of the gaseous disk \citep{Cossou2014}. Nonetheless, the relatively large difference between the orbital periods increases the likelihood of additional unseen companions, especially since many known planetary systems with multiple close-in super-Earths are much more compact. This view is also supported by the \textit{Kepler dichotomy} \citep{Lissauer2011,Ballard2016}. In particular, M dwarfs seem to exhibit either a single transiting planet (explained by a single planet or a multiple-planet system with large mutual orbital inclinations) or a large number of near-coplanar transiting planets \citep{Ballard2016}. The similar orbital inclinations of LHS 1140 b and c (89.89 and 89.92 degrees, respectively) suggest that LHS 1140 might belong to the latter group, with more planets yet to be discovered. Despite the fact that we do not currently see additional significant signals in the photometry and the radial velocities (as illustrated by the GLS periodogram in Figure \ref{fig:periodogram}), we strongly encourage further photometric monitoring as well as high-precision RV follow-up. We also note that LHS 1140 is one of the few nearby systems where the masses and radii of the planets can be determined with a relatively high accuracy, due to our comparatively good knowledge of the stellar parameters. Planets in the LHS 1140 system are also potential targets for atmospheric spectroscopy observations with the \emph{James Webb Space Telescope} (JWST). \citet{Morley2017} modeled the emission and transmission spectra of LHS 1140 b for varying surface pressures and atmospheric compositions, and noted that a 5$\sigma$ detection of transmission spectral features would likely be very challenging, if the atmosphere had a similar mean molecular weight compared to that of the Earth. However, both emission and transmission spectra are sensitive to the molecular composition of the atmosphere, which can strongly depend on temperature; the emission spectra are directly sensitive to temperature as well. Due to its much higher equilibrium temperature and lower surface gravity, LHS 1140 c would be a significantly better candidate for the detection of both emission and transmission spectral features. In particular, the two planets tested by \citet{Morley2017} that have radii and temperatures similar to those of LHS 1140 c - namely TRAPPIST-1 b and GJ 1132 b - would likely require less than a dozen transits or eclipses to detect a Venus-like atmosphere, depending on the Bond albedo and surface pressure. Comparative planetology studies are often challenging due to the fact that planets in different systems evolve in very different stellar environments. Therefore, characterizing the atmospheres of multiple planets in the same planetary system would likely yield a much better understanding of how planets and their surface environments form and develop. | 18 | 8 | 1808.00485 |
1808 | 1808.05605_arXiv.txt | We present new measurements of the flux power-spectrum $P(k)$ of the $z<0.5$ \HI\ Lyman-$\alpha$ forest spanning scales $k \sim 0.001-0.1\, \mathrm{s \, km}^{-1}$. These results were derived from 65 far ultraviolet quasar spectra (resolution $R \sim 18000$) observed with the Cosmic Origin Spectrograph (COS) on board the Hubble Space Telescope. The analysis required careful masking of all contaminating, coincident absorption from \HI\ and metal-line transitions of the Galactic interstellar medium and intervening absorbers as well as proper treatment of the complex COS line-spread function. From the $P(k)$ measurements, we estimate the \HI\ photoionization rate ($\Gamma_{\rm HI}$) in the $z<0.5$ intergalactic medium. Our results confirm most of the previous $\Gamma_{\rm HI}$ estimates. We conclude that previous concerns of a photon underproduction crisis are now resolved by demonstrating that the measured $\Gamma_{\rm HI}$ can be accounted for by ultraviolet emission from quasars alone. In a companion paper, we will present constraints on the thermal state of the $z<0.5$ intergalactic medium from the $P(k)$ measurements presented here. | \label{sec:intro} The intergalactic medium (IGM), being the largest reservoir of the baryons in the Universe, plays an important role in the formation of cosmic structures. The ultraviolet (UV) radiation emanating from this cosmic structure photoionizes and heats the IGM. The trace amount of neutral hydrogen in the highly-ionized IGM imprints a swath of absorption lines on the spectra of background quasars known as the Lyman-$\alpha$ forest. Observations of the Lyman-$\alpha$ forest in a large sample of background quasar sightlines can probe the underlying density fluctuations in the IGM, measure its thermal state, and determine the amplitude of the UV ionizing background. The temperature and density of the photoionized IGM follow a tight power-law relation over two decades in the density, $T(\Delta)=T_0\,\Delta^{\gamma -1}$, where $\Delta=\rho/\bar{\rho}$ is the overdensity, $T_0$ is the temperature at mean density $\Delta=1$, and $\gamma$ is the power-law index. This power-law relation quantifies the thermal state of the IGM \citep{Hui97,Theuns98,McQuinn16}. While a wide variety of statistics have been applied to Lyman-$\alpha$ forest spectra with the goal of measuring its thermal state \citep{Haehnelt98, Schaye99, Theuns00, Zaldarriaga01, McDonald06,Lidz10, Becker11t, Bolton12, Rorai17, Hiss18}, the power spectrum of the transmitted flux is appealing for several reasons: 1) it is sensitive to a broad range of scales, in particular, the small-scales that encode information about the IGM thermal state, 2) it is thus capable of breaking strong parameter degeneracies, 3) systematics due to noise, metal-line contamination, resolution effects, and continuum errors impact it in well-understood ways, and 4) it can be described by a simple multivariate Gaussian likelihood enabling straightforward principled statistical analysis and parameter inference \citep{Irsic17,Walther18a,Walther19}. For these reasons, the power-spectrum has been used to constrain parameters such as the UV ionizing background intensity \citep{Gaikwad17a}, alternate cosmology models with warm and fuzzy dark matter \citep{Viel08,Viel13,Garzilli17,Irsic17}, and cosmological parameters including neutrino masses \citep{McDonald06,Palanque13ps,PD15Neutrino,Yeche17Neutrino,Irsic17t}. There are many measurements of the flux power-spectrum at high redshifts \citep[e.g][]{McDonald00, Croft02, Kim04ps, Palanque13ps, Irsic17,Yeche17Neutrino, Walther18a} where ground-based telescopes with medium or high resolution spectrographs were used to observe the Lyman-$\alpha$ forest redshifted to optical wavelengths. However to date, there are no measurements at low-redshifts $z < 1.6$ \citep[but see][]{Gaikwad17a} where space-based observations are required because the redshifted Lyman-$\alpha$ transition lies in the UV below the atmospheric cutoff. Recently, large surveys \citep[e.g,][]{Tumlinson13, Danforth14, Burchett15, Borthakur15} have gathered a significant amount of Lyman-$\alpha$ forest spectra using the Cosmic Origin Spectrograph (COS) on-board the Hubble Space Telescope (HST) that can be used to measure the Lyman-$\alpha$ forest power-spectrum at low redshifts. The power spectrum at low redshifts is of particular interest since it provides another method for measuring the UV ionizing background, whereas previous work based on fitting the distribution of column densities argued for a `photon underproduction crisis' \citep{Kollmeier14,Wakker15}. Also, it can measure the thermal state of the low redshift IGM where long after the impulsive photoheating from reionization events is complete, theory robustly predicts the IGM should have cooled down to temperatures of $T_0\simeq 5000$ K at $z = 0$ \citep[see e.g][]{McQuinn16, Pheobe16t0}. Constraints on the low-redshift thermal state would thus provide an important check on our theoretical understanding of the IGM and shed light on the degree to which any other processes such as blazar heating, feedback from galaxy formation, or any other exotic physics can inject heat into the IGM. In an earlier study using the Space Telescope Imaging Spectrograph, \citet{Dave01} obtained preliminary evidence that the $T_0$ is indeed about $5000$ K at $z\sim 0$, but they also found that the observed low-$z$ Lyman-$\alpha$ lines are not consistent with pure thermal broadening and may therefore also be broadened by some additional processes such as some type of feedback. Similar issues with line broadening are also reported by \citet{Gaikwad17b,Viel17} and \citet{Nasir17}. We can now revisit these issues with much larger sample. In this paper, we present new measurements of the Lyman-$\alpha$ forest flux power spectrum at $z<0.5$ in five redshift bins. We use high quality Lyman-$\alpha$ forest spectra (S/N per pixel $>10$) observed in 65 background quasars from the sample of \citet{Danforth14}. Combining these power spectrum measurements with state-of-the-art cosmological hydrodynamical simulations run with the Nyx code \citep{Almgren13,Lukic15}, we constrain the intensity of UV background \(\Gamma_\mathrm{HI}\) at $z<0.5$. Our UV background measurements are consistent with recent studies \citep{Shull15, Gaikwad17a, Gaikwad17b,Fumagalli17} which confirm that there is no crisis with UV photon production at $z<0.5$ and that the primary contributors to the UV background are quasars. In a companion paper (Walther et al. in prep.), we will use these power-spectrum measurements to constrain the thermal state of the IGM at $z<0.5$. The paper is organized as follows. In Section 2, we discuss the Lyman-$\alpha$ forest data. In Section 3, we describe our method to compute the power spectrum and present the resulting measurements. In Section 4, we discuss the implications of our power spectrum regarding the UV ionizing background and compare with previous work. In Section 5, we present our conclusions and discuss future directions. Throughout the paper, we adopt a flat $\Lambda$CDM cosmology with parameters $\Omega_m=0.319181$, $\Omega_b h^2 = 0.022312$, $h = 0.670386$, $n_s = 0.96$, and $\sigma_8 = 0.8288$ consistent with \citet{Planck18}. This cosmology is used both for our power spectrum measurements as well as for our cosmological hydrodynamical simulations. All of the distances quoted are comoving. \begin{figure*} \includegraphics[width=\textwidth,height=\textheight,keepaspectratio]{spectra.pdf} \caption{Illustration of our masking procedure. Different panels show random 30 \AA~regions of five quasar spectra with different S/N per pixel as denoted in panels, in decreasing order from top to bottom panel. The red and green dash lines indicate continuum ($y=1$ line) and zero level ($y=0$ line). Magenta curve shows the error in the normalized flux. The shaded regions show our masks. Blue and red ticks indicate the metal absorption from the ISM of the Milky Way and from intervening absorbers, respectively. We also mask geocoronal airglow emissions as shown in middle panel associated with O {\sc i} ($\lambda \sim 1305$ \AA).} \label{fig1} \end{figure*} | We present a new high precision high resolution power spectrum measurement in five different redshift bins at $z<0.5$. For this measurement, we have used high-quality medium resolution Lyman-$\alpha$ forest data from HST/COS from the largest low-$z$ IGM survey published by \citet{Danforth14}. We applied the procedure developed in \citet{Walther18a}, which takes into account masked metal-line absorptions, noise in the data and the finite resolution of the instrument. The data allow us to reliably probe the power spectrum up to small scales $k<0.1$ s km$^{-1}$ and our measurements show the expected thermal cut-off in the power at small scales $k>0.03$ s km$^{-1}$, resulting from pressure smoothing of IGM gas and thermal Doppler broadening of absorption lines. Our power spectrum measurements are provided in Table~\ref{tab2}. We compare these with cosmological hydrodynamical simulations and obtain constraints of the UV background at $z<0.5$. Our measured hydrogen photoionization rates (Table~\ref{tab3}) are consistent with the previous estimates \citep{Shull15,Gaikwad17a,Gaikwad17b,Fumagalli17} and recent UV background models \citep{KS19, Puchwein19}. This suggests that the low-$z$ UV background is dominated by ionizing photons emitted by quasars without requiring any significant contribution from galaxies. The power-spectrum measurements presented here, in principle, can probe the thermal state of the low-$z$ IGM. At low-$z$, theoretical calculations using standard heating and cooling rates show that the IGM loses memory of the previous heating episodes caused by the hydrogen and helium reionization. This makes understanding and predicting the structure of the low-$z$ IGM relatively simple, as it is independent of the physics associated with hydrogen and helium reionization heating, which complicate modeling at higher redshifts ($z \gtrsim 2$). In the absence of any other heating processes, theory predicts that the diffuse low-density photoionized IGM cools down after $z \sim 2$ and asymptotes toward a single temperature-density relation with $\gamma$ close to 1.6 and T$_0 \sim 5000$ K \citep{McQuinn16} at $z=0$. Such a predicted cool-down of the IGM at low-$z$ has not yet been observationally confirmed. Indeed, there are no reliable measurements of the thermal state of the IGM at $z<1.6$ \citep[but see][]{Ricotti00} where the atmospheric cut-off does not allow us to observe Lyman-$\alpha$ forest from ground based telescopes. In a companion paper (Walther et al. in prep.) we will use the power spectrum measurements presented here to jointly constrain the IGM thermal state (T$_0$, $\gamma$) and the UV background ($\Gamma_{\rm H\, I}$). These measurements will help us understand the physics of IGM and address important questions such as whether feedback processes associated with galaxy formation modify the thermal state of the IGM at low-$z$ \citep{Viel17, Nasir17} and/or if there is any room for the existence of non-standard heating processes powered by TeV Blazars \citep{Puchwein12, Lamberts15} or decaying dark matter \citep{Furlanetto06DM_decay,Araya14}. In contrast with the high-$z$ Universe, the much lower opacity of Lyman series absorption arising in the low-$z$ IGM results in dramatically reduced line blanketing, making it relatively straightforward to identify all lines as either resulting from the Lyman-series or metal absorption. This results in a large redshift path length where Lyman series absorption can be studied, data analysis and preparation are simplified, and important systematics from metal-line contamination arising at small-scales \citep[high-$k$; see section 4.1 of][]{Walther18a} are mitigated. Furthermore, our measurements demonstrate that COS resolution is sufficient to obtain high-quality power-spectrum measurements even at the small-scales (high-$k$, $k\sim 0.1\,{\rm s\,km^{-1}}$) required for probing the thermal state of the IGM and demonstrate the important role that HST/UV spectroscopy can play in our understanding of the low-$z$ IGM. We conclude by noting that, owing to the paucity of archival near-UV spectra covering the Lyman-$\alpha$ transition at $0.5<z<1.6$, there are essentially no constraints on the physical state of IGM gas in this redshift interval, representing 5 Gyr of the Universe's history. It is critical that HST UV spectroscopy fill this gap in our understanding of the Universe before HST's mission is complete, otherwise we could remain in the dark for decades. | 18 | 8 | 1808.05605 |
1808 | 1808.02714.txt | We present medium-resolution K-band long-slit spectroscopy of 29 true, likely, possible and candidate Galactic Plane planetary nebulae (PNe) from the UWISH2 survey - many of which have only been recently discovered. These objects are bright in molecular hydrogen (H$_2$) emission, and many have bipolar morphologies. Through the detection of the Br$\gamma$ emission line, which traces ionized hydrogen, we find that the majority of the candidate PNe are indeed likely to be PNe, while 2 of the targets are more likely young stellar objects (YSOs) or pre-planetary nebulae (pPNe). We detect Br$\gamma$ in 13 objects which have no detection in IPHAS or SHS H$\alpha$ surveys. This implies they are potential members of the little-known optically-obscured PN population, hidden from wide-field optical surveys. We use the spatial extent of the H$_2$ 1-0 S(1) and Br$\gamma$ lines to estimate the evolutionary stage of our targets, and find that W-BPNe (bipolar PNe with pinched waist morphologies) are likely to be younger objects, while R-BPNe (bipolar PNe with large ring structures) are more evolved. We use line ratios to trace the excitation mechanism of the H$_2$, and find the 1-0 S(1) / 2-1 S(1) and 1-0 S(1) / Br$\gamma$ ratios are higher for R-BPNe, implying the H$_2$ is thermally excited. However, in W-BPNe, these ratios are lower, and so UV-fluorescence may be contributing to the excitation of H$_2$. | %%%%%%%%%%%%%%%%%%%%%%%% \begin{table*} %%% observations \centering \caption{Observation log and additional information for the 29 targets. Morphologies and sizes in H$_2$ and H$\alpha$ are taken from table A1 of \citet{2018MNRAS.tmp.1499G}. Morphologies make use of the `ERBIAS' classification system \citep{2006MNRAS.373...79P}, and sizes are the major and minor axis dimensions in arcsec. Where no H$\alpha$ morphology is given, the object is not detected in H$\alpha$ emission. PN status comes from the HASH PN database \citep{2016JPhCS.728c2008P}, where `T', `L', `P' and `C' refer to true, likely, possible and candidate PNe - see text for details.} \resizebox{1.0\linewidth}{!}{ \begin{tabular}{lllllllllll} % four columns, alignment for each \hline PN G & Other names & RA & Dec & Integration (s) & Airmass & \multicolumn{2}{c}{H$_2$} & \multicolumn{2}{c}{H$\alpha$} & PN status \\ & & & & & & Morph. & Size & Morph. & Size & \\ \hline 004.7-00.8 & --- & 269.95542 & -25.26527 & 1200 & 1.71 & Bams & 25x12 & --- & --- & C \\ 009.7-00.9 & SSTGLMC G009.7612-00.9575 & 272.71231 & -20.96230 & 1200 & 1.56 & Bs & 18x6 & --- & --- & C \\ 020.7-00.1 & --- & 277.37398 & -10.94099 & 1200 & 1.46 & Bs & 14x9 & A & 15x9 & C \\ 020.8+00.4 & SSTGLMC G020.8543+00.4857 & 276.84922 & -10.50625 & 1200 & 1.34 & B & 2.8x1.2 & --- & --- & C \\ 024.8+00.4 & SSTGLMC G024.8959+00.4586 & 278.76581 & -6.93617 & 1200 & 1.23 & Bs & 14x6 & --- & --- & C \\ 025.9-00.5 & --- & 280.21143 & -6.44546 & 1200 & 1.46 & Ers & 8x5 & --- & --- & C \\ 032.6-01.2 & MPA J1855-0048 & 283.85720 & -0.80638 & 1200 & 1.31 & Bps & 12x5 & E & 10x5 & T \\ 034.8+01.3 & --- & 282.55901 & +2.30305 & 1200 & 1.17 & Bs & 14x7 & --- & --- & C \\ 035.7-01.2 & NVSS 190102+015727 & 285.26293 & +1.95644 & 1200 & 1.17 & Bs & 26x12 & --- & --- & C \\ 036.4+00.1 & GPSR5 36.481+0.155 & 284.34075 & +3.23021 & 1200 & 1.25 & Bps & 12x5 & --- & --- & C \\ 037.4-00.1 & --- & 285.07885 & +3.90133 & 1080 & 1.28 & Er & 6x5 & --- & --- & C \\ 040.4+01.1 & --- & 285.32726 & +7.20967 & 1200 & 1.11 & Bs & 12x4 & --- & --- & C \\ 040.5-00.7 & --- & 287.02679 & +6.41554 & 1200 & 1.24 & Bs & 12x7 & --- & --- & C \\ 042.1+00.4 & --- & 286.67062 & +8.38580 & 1200 & 1.55 & Bs & 9x9 & --- & --- & C \\ 047.1+00.4 & --- & 289.05872 & +12.86745 & 1200 & 1.27 & Brs & 25x14 & S? & --- & C \\ 047.5-00.3 & --- & 289.95370 & +12.76896 & 1200 & 1.24 & Es & 12x8 & --- & --- & C \\ 048.2-00.4 & --- & 290.40474 & +13.37742 & 1200 & 1.47 & Bs & 10x8 & --- & --- & C \\ 050.0-00.7 & --- & 291.57894 & +14.80423 & 1320 & 1.41 & Bs & 12x12 & --- & --- & C \\ 050.5+00.0 & NVSS J192414+153909 & 291.06046 & +15.65315 & 1320 & 1.23 & Bs & 16x5 & S & --- & L \\ 057.9-00.7 & Kn 7 & 295.60822 & +21.75634 & 1080 & 1.33 & Brs & 26x20 & B & 27x30 & T \\ 058.1-00.8 & IPHASX J194301.3+215424 & 295.75604 & +21.90672 & 1320 & 1.61 & Bs & 20x12 & B & 15x12 & L \\ 059.7-00.8 & IPHASX J194633.0+231659 & 296.63714 & +23.28371 & 1440 & 1.17 & Bs & 12x9 & Ea & 13x9 & P \\ 060.5-00.3 & K 3-45 & 296.56513 & +24.18437 & 1200 & 1.93 & Bps & 11x6 & Bs & 11x6 & T \\ 061.8+00.8 & --- & 296.14467 & +25.92826 & 1200 & 1.40 & Bs & 12x13 & B? & 12x12 & C \\ 062.1+00.1 & --- & 297.01712 & +25.81331 & 1200 & 1.71 & Ear & 12x10 & E? & 10x8 & C \\ 062.2+01.1 & --- & 296.15164 & +26.44203 & 1200 & 1.00 & Bs & 16x10 & E? & 11 & C \\ 062.7+00.0 & IPHASX J194940.9+261521 & 297.42017 & +26.25520 & 1200 & 2.20 & Bs & 17x8 & Bps & 13x7 & T \\ 064.1+00.7 & --- & 297.57807 & +27.89812 & 1080 & 1.05 & Bs & 11x4.5 & E? & 2.3x4 & C \\ 064.9+00.7 & --- & 298.03161 & +28.54425 & 1200 & 1.96 & Brs & 10x8 & B? & 10x8.5 & C \\ \hline \end{tabular}} \label{tab:observations} \end{table*} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% A planetary nebula (PN, or PNe plural) is an expanding gaseous shell, formed from the material released during periods of heavy mass loss on the asymptotic giant branch (AGB) phase of stellar evolution \citep{1970AcA....20...47P}. It is the penultimate stage of evolution for a low to intermediate mass star (0.8 $M_{\odot}$ to 8 $M_{\odot}$). The star responsible for the formation of the PN (central star, or CSPN), will move to the left of the Hertzsprung-Russell diagram as its surface temperature increases, until eventually becoming a white dwarf. UV radiation from the CSPN excites and ionizes the gaseous material, creating strong emission lines in the optical and infrared. There are currently over 3000 PNe known in the Milky Way \citep{2016JPhCS.728c2008P}. Many of these were discovered by H$\alpha$ emission surveys, including the SuperCOSMOS H$\alpha$ Survey (SHS; \citeauthor{2005MNRAS.362..689P} \citeyear{2005MNRAS.362..689P}) and INT Photometric H$\alpha$ Survey of the Northern Galactic Plane (IPHAS; \citeauthor{2005MNRAS.362..753D} \citeyear{2005MNRAS.362..753D}). However it is likely that many PNe are yet to be discovered, obscured by dust in the Galactic Plane. It is therefore necessary to switch to infrared observations, which can penetrate the dust and reveal a variety of new objects. Studies such as those of \citet{2011MNRAS.413..514C} and \citet{2012MNRAS.427.3016P} have shown how certain infrared diagnostics can be used in order to successfully separate PNe from possible imposters. The near-IR region is ideal for studying molecular hydrogen (H$_2$) in PNe - something known to us since its first detection by \cite{1976ApJ...209..793T}. Many PNe contain large reservoirs of H$_2$ in and outside the photodissociation region (PDR) \citep{1993IAUS..155..155T}, and it has also been proposed that H$_2$ emission can originate from the ionized region \citep{2011A&A...528A..74A}. However, extended H$_2$ emission can also be detected at large distances from the main nebula site, as shown recently by \citet{2018ApJ...859...92F}. H$_2$ is therefore an excellent tracer of the morphology of PNe, and many studies have been conducted to investigate relationships between morphology and H$_2$ emission. For example, there is strong observational evidence that bipolar PNe (BPNe) have brighter H$_2$ emission - known as Gatley's Rule (\citeauthor{1988ApJ...324..501Z} \citeyear{1988ApJ...324..501Z}; \citeauthor{1994ApJ...421..600K} \citeyear{1994ApJ...421..600K}). However, H$_2$ can also be detected in ellipsoidal or barrel-like PNe \citep{2013MNRAS.429..973M}. Bipolar PNe can be further divided into those showing broad, ring-like features (R-BPNe) and those with narrow waists or compact centres (W-BPNe) \citep{1996iacm.book.....M}. The nature of this divide is uncertain - they may form an evolutionary sequence, or originate from different progenitor populations \citep{2000ApJS..127..125G}. The K-band (2 - 2.4 $\muup$m) is home to a wide range of ro-vibrational lines of H$_2$, including the v = 1-0 S(1) (2.1218~$\muup$m) and 2-1 S(1) (2.2477~$\muup$m) lines. Ratios of these lines can indicate the mechanisms responsible for the excitation of the H$_2$ \citep{1976ApJ...203..132B}. Also in this waveband lie recombination lines of hydrogen and helium. The detection of the Br$\gamma$ H recombination line at 2.1661~$\muup$m signifies that the CSPN has begun to photoionize its environment, however this line can also be produced in shocks. Imaging of this line is a powerful tool for studying the evolution of PNe, especially in the transition from proto-planetary nebulae (pPNe) to PNe \citep{2015MNRAS.447.1080G}. The presence of these emission lines makes the K-band particularly advantageous to study both the molecular and ionized components of PNe. In this work, we present K-band long-slit spectra of a sample of PNe and candidate PNe taken from the recent UWISH2 imaging survey (UKIRT Widefield Infrared Survey for H$_2$) \citep{2011MNRAS.413..480F}. We focus on the mechanisms governing the excitation of H$_2$, and how these relate to the evolutionary stages and morphologies of the targets. Along with spectra, we make use of near-IR H$_2$ and optical H$\alpha$ imaging, and mid-IR colours where available. In Sect.~\ref{sec:sample}, we describe the sample and the available data. Sect.~\ref{sec:observations} outlines our observations, and methods used to reduce the data. In Sect.~\ref{sec:results} we describe the spectra and images of the objects, and discuss the links between morphology, line ratios and evolution in Sect.~\ref{sec:discussion}. Finally, we make our conclusions in Sect.~\ref{sec:conclusions}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | \label{sec:conclusions} In this work, we have presented medium resolution, K-band spectra of a sample of 29 Galactic Plane objects, including 4 true, 2 likely, 1 possible and 22 candidate PNe, taken from the UWISH2 survey. The candidate PNe were selected on the basis of their morphologies, and lack of association with known star-forming regions. Evidence for ionized material, in the form of either Br$\gamma$ emission in our spectra or H$\alpha$ emission in narrow-band surveys, is found in all but 2 of the targets. One of these, PN\,G020.8+00.4, is likely to be a pPN - at an earlier stage of evolution with a central star not yet hot enough to ionize its surrounding environment. PN\,G004.7-00.8 has mid-IR colours indicative of a YSO. 13 of the candidate PNe show no clear H$\alpha$ emission, however we detect Br$\gamma$ emission in their spectra. These objects potentially contribute to the optically-obscured PN population, and their discovery clearly highlights the need for multi-wavelength studies of PNe, to accurately predict the number of PNe in the Milky Way. We have used our spectra to calculate line ratios, which have been used to constrain the mechanisms dominating the excitation of H$_2$. Most of our targets that we believe to be PNe are either R-BPNe (large ring structures) or W-BPNe (pinched waist), while the remaining 3 are considered to be elliptical. In agreement with previous studies, we find the former are predominantly thermally excited, while in the latter, UV fluorescence may have more influence. The link between line ratios and the spatial extent of ionized emission could mean that W-BPNe are younger objects, while the R-BPNe are more evolved, and an evolutionary scheme in which one class evolves into the other is worth further investigation. While long-slit spectroscopy is a useful tool for measuring line ratios with the advantage of spatial information in one dimension, more detailed spatial information can be achieved using integral field spectroscopy (IFS). This would allow excitation mechanisms to be inferred over the entire target, while comparing to the two-dimensional structure of the ionized region. | 18 | 8 | 1808.02714 |
1808 | 1808.07108_arXiv.txt | We present \HI\ spectral line and optical broadband images of the nearby low surface brightness dwarf galaxy KDG\,215. The HI images, acquired with the {Karl G. Jansky Very Large Array (VLA}\footnote{The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.}), reveal a dispersion dominated ISM with only weak signatures of coherent rotation. The HI gas reaches a peak mass surface density of 6 \msun\,pc$^{-2}$ at the location of the peak surface brightness in the optical and the UV. Although KDG\,215 is gas-rich, the H$\alpha$ non-detection implies a very low current massive star formation rate. In order to investigate the recent evolution of this system, we have derived the recent and lifetime star formation histories from archival Hubble Space Telescope images. The recent star formation history shows a peak star formation rate $\sim$1 Gyr ago, followed by a decreasing star formation rate to the present day quiescent state. The cumulative star formation history indicates that a significant fraction of the stellar mass assembly in KDG\,215 has occurred within the last 1.25 Gyr. KDG\,215 is one of only a few known galaxies which demonstrates such a delayed star formation history. While the ancient stellar population (predominantly red giants) is prominent, the look-back time by which 50\% of the mass of all stars ever formed had been created is among the youngest of any known galaxy. | \label{S1} The interplay between the gaseous and stellar components of low mass galaxies is extremely complex. Gas-rich dwarf irregular galaxies (i.e., systems with significant mass reservoirs of neutral hydrogen, HI) often host ongoing massive star formation (SF, as traced by \halpha\ emission, with characteristic timescales of $<$10 Myr) and have significant ultraviolet (UV) emission (tracing SF on longer timescales of 100-200 Myr). The stochastic sampling of the upper portion of the initial mass function is known to be a complicating factor in low mass galaxies \citep{lee09}. While significant progress has been made in understanding how the properties of the resolved stellar populations and the integrated UV luminosities are related \citep{mcquinn15}, it remains very difficult to predict how a certain gas-rich dwarf irregular galaxy converts its available reservoir of gas into stars. \begin{figure*} \epsscale{1.15} \plotone{f1.lowres.eps} \caption{HST color image (a) and CMD (b) of KDG\,215. The CMD reveals a strong red giant branch, a significant population of red supergiants, a weak blue plume, and red clump stars. The more densely populated fainter magnitudes are shown as number density contours for clarity. The TRGB is marked by a red line and shaded red area resulting in a distance D $=$ 5.11$^{+0.33}_{-0.17}$ Mpc.} \label{CMD} \end{figure*} An especially important type of galaxy in this regard is the low surface brightness dwarf. Traditionally defined as having low central surface brightnesses ($\mu_{\rm B}$\,$>$\,23.0 mag arcsecond$^{-2}$), low surface brightness galaxies span all galaxy masses and morphological types \citep[e.g.,][]{mcgaugh94,deblok95}. Many (but not all) low surface brightness galaxies host ongoing massive SF as traced by \halpha\ emission \citep[e.g.,][]{schombert11}. The dwarf members of this class have been extensively studied in the context of the threshold gas mass surface density required for SF \citep[e.g.,][]{vanderhulst93,vanzee97} as well as in the derivation of high resolution rotation curves and the resulting constraints on the dark matter distribution within galaxies \citep[e.g.,][]{deblok01,deblok02}. Nearby low surface brightness dwarf galaxies offer a unique opportunity to study their recent SF on a spatially resolved basis. This allows for the reconstruction of the recent evolutionary pathways that have led to their current low surface brightness state. Gas-rich low surface brightness systems that are quiescent in terms of current massive SF (i.e., are \halpha\ non-detections at meaningful sensitivity levels) are especially interesting, as they offer a glimpse of the conditions in which SF has ceased altogether. Is this ``quenching'' of SF due to the current conditions of the gas? Is it caused by feedback from previous SF? Is the efficiency of the SF process fundamentally different than in more massive systems? Answering these questions provides important empirical constraints on simulations of the evolution of low-mass galaxies \citep[e.g.,][]{hopkins14,onorbe15}. The subject of this work, KDG\,215 (originally cataloged in {Karachentseva 1968}\nocite{karachentseva68}, also known as LEDA\,44055, F575$-$3 from {Schombert \etal\ 1992}\nocite{schombert92}, or D575$-$5 from {Schombert \etal\ 1997}\nocite{schombert97}), is a galaxy that possesses unique characteristics. First, its optical surface brightness is extremely low. Of the more than 175 irregular galaxies studied in \citet{hunter06}, KDG\,215 has the second lowest central surface brightness ($\mu_{\rm V}$\,$=$\,24.69$\pm$0.15 mag arcsecond$^{-2}$). \citet{schombert11} finds a somewhat higher central surface brightness ($\mu_{\rm V}$\,$=$\,23.80 mag arcsecond$^{-2}$). Second, KDG\,215 has a current star formation rate (SFR) of zero. Of the more than 60 low surface brightness galaxies in \citet{schombert11}, KDG\,215 is one of only four \halpha\ non-detections (see also {Karachentsev \& Kaisina 2013}\nocite{karachentsev13}). Third, the source is nearby and has sufficiently deep HST images to allow precision color magnitude diagram (CMD) work. The distance measurement by \citet{karachentsev14} places the object securely in the Local Volume (D $=$ 4.83$\pm$0.34 Mpc). Fourth, the source is gas rich. The HI properties were first measured in \citet{salzer90} and \citet{eder00}, in which the total HI flux integrals were measured to be S$_{\rm HI}$ $=$ 4.48 Jy\,km\,s$^{-1}$ and 4.37 Jy\,km\,s$^{-1}$, respectively. The recently completed ALFALFA catalog \citep{haynes18} revises the total HI flux integral up to S$_{\rm HI}$ $=$ 5.51\,$\pm$\,0.06 Jy\,km\,s$^{-1}$. Finally and most importantly, as we demonstrate in this manuscript, KDG\,215 has a star formation history (SFH) that is extreme compared to that of any other known dwarf galaxy: a significant fraction of the stellar mass has been formed within the last 1.25 Gyr. | 18 | 8 | 1808.07108 |
|
1808 | 1808.05427_arXiv.txt | A robust variational approach is used to investigate the sensitivity of the rotation-vibration spectrum of phosphine (PH$_3$) to a possible cosmological variation of the proton-to-electron mass ratio, $\mu$. Whilst the majority of computed sensitivity coefficients, $T$, involving the low-lying vibrational states acquire the expected values of $T\approx-1$ and $T\approx-1/2$ for rotational and ro-vibrational transitions, respectively, anomalous sensitivities are uncovered for the $A_1\!-\!A_2$ splittings in the $\nu_2/\nu_4$, $\nu_1/\nu_3$ and $2\nu_4^{\ell=0}/2\nu_4^{\ell=2}$ manifolds of PH$_3$. A pronounced Coriolis interaction between these states in conjunction with accidentally degenerate $A_1$ and $A_2$ energy levels produces a series of enhanced sensitivity coefficients. Phosphine is expected to occur in a number of different astrophysical environments and has potential for investigating a drifting constant. Furthermore, the displayed behaviour hints at a wider trend in molecules of $\bm{C}_{3\mathrm{v}}\mathrm{(M)}$ symmetry, thus demonstrating that the splittings induced by higher-order ro-vibrational interactions are well suited for probing $\mu$ in other symmetric top molecules in space, since these low-frequency transitions can be straightforwardly detected by radio telescopes. | Recently, the $J\!=\!2\!-\!1$ rotational transition of phosphine (PH$_3$) was detected in the carbon star envelope IRC +10216~\citep{Agundez}, thus confirming the presence of PH$_3$ in the outflows of evolved stars but more significantly outside of the solar system. The appearance of PH$_3$ has been predicted in numerous other astrophysical environments (see the discussion by \citet{15SoAlTe.PH3} and references therein), and because of prominent `irregularities' displayed by its rotation-vibration spectrum, it is a promising system for investigating the cosmological variability of the proton-to-electron mass ratio, $\mu=m_p/m_e$. Observing PH$_3$ outside of our Galaxy is no easy feat, however, nearby Galactic molecular clouds offer a means to constrain $\mu$ through the so-called chameleon scenario~\citep{Khoury:2004,Brax:2004} as evidenced by studies of ammonia~\citep{Levshakov:2010b,Levshakov:2010a} and methanol~\citep{Dapra2017}. At present, the most robust constraint on a temporal variation of $\mu$ was determined from methanol absorption spectra observed in the lensing galaxy PKS1830$-$211~\citep{Kanekar:2015}. The three measured transitions possessed sensitivity coefficients, $T$, ranging from $-7.4$ to $-1.0$ and resulted in a constraint of $\dot{\mu}/\mu< 2\times 10^{-17}\,$yr$^{-1}$ assuming a linear rate of change. This translates to no change in $\mu$ over the past $\approx 7.5$ billion years and is in agreement with the best laboratory constraint to date, which measured optical transitions in $^{171}$Yb$^+$ ions to derive $\dot{\mu}/\mu= (0.2\pm 1.1)\times 10^{-16}\,$yr$^{-1}$~\citep{Godun:2014} again assuming a linear rate of change. Whilst the use of methanol has led to several astronomical constraints~\citep{Jansen:2011,Levshakov:2011,Bagdonaite:2013b,Bagdonaite:2013a,Thompson:2013,Kanekar:2015}, it is worthwhile identifying other molecular absorbers with notable sensitivities to expand the search for a drifting $\mu$. Due to the small difference between its rotational constants $B$ and $C$, and also because of the strong $x\!-\!y$ Coriolis interaction between the coinciding $\nu_2/\nu_4$, $\nu_1/\nu_3$ and $2\nu_4^{\ell=0}/2\nu_4^{\ell=2}$ states (see Fig.~\ref{fig:one}), phosphine is a potential candidate system for probing $\mu$. Notably, the spectrum of PH$_3$, and presumably other molecules of $\bm{C}_{3\mathrm{v}}\mathrm{(M)}$ symmetry, is special due to the anomalous behaviour of the $A_1\!-\!A_2$ splittings~\citep{Ulenikov}. A large number of spectroscopic studies of PH$_3$ have been reported in the literature (see \citet{Mueller} and references therein) and highly accurate data is available for the majority of its states. Furthermore, a robust theoretical description of this molecule, which we utilize for this work, has been developed over the years~\citep{03YuCaJe.PH3,05YuThJe.PH3,06YuCaTh.PH3, OvThYu08a.PH3,OvThYu08.PH3,13SoYuTe.PH3, 14SoHYu.PH3,15SoAlTe.PH3,16SoTeYu.PH3}, culminating in the construction of a comprehensive rotation-vibration line list applicable for elevated temperatures~\citep{15SoAlTe.PH3}. Model radiative transfer calculations of phosphine excitation in the envelope of IRC +10216~\citep{Agundez,Cernicharo} highlighted the importance of infrared pumping from the ground to the first excited vibrational states, helping explain the presence of strong emission bands in the observed spectra. We therefore find it useful to investigate the sensitivity of the ground, fundamental, and low-lying combination and overtone vibrational states of PH$_3$ (see Fig.~\ref{fig:one}) to a possible space-time variation of $\mu$ using a robust variational approach. The paper is structured as follows: In Sec.~\ref{sec:methods} we describe the variational approach used to compute sensitivity coefficients. The results for the phosphine molecule are presented and discussed in Sec.~\ref{sec:results}. Concluding remarks are given in Sec.~\ref{sec:conc}. \begin{figure} \centering \includegraphics{pattern_PH3_AO_new.pdf} \caption{\label{fig:one}The lowest vibrational energy levels of PH$_3$.} \end{figure} | \label{sec:conc} The sensitivity of the rotation-vibration spectrum of PH$_3$ to a possible variation of $\mu$ has been probed using an accurate variational approach. Calculations utilized the nuclear motion program \textsc{trove} in conjunction with an established empirically refined PES and \textit{ab initio} DMS. The low-lying vibrational states were studied as these play an important role in phosphine excitation in the carbon star envelope IRC +10216. Whilst the majority of computed sensitivity coefficients assumed their expected values, anomalous sensitivities were displayed by the $A_1\!-\!A_2$ splittings in the $\nu_2/\nu_4$, $\nu_1/\nu_3$ and $2\nu_4^{\ell=0}/2\nu_4^{\ell=2}$ manifolds. This behaviour arises due to strong Coriolis interactions between states and may be present in other molecules with $\bm{C}_{3\mathrm{v}}\mathrm{(M)}$ symmetry. The fact that molecules with highly sensitive transitions such as ammonia are already being used in advanced terrestrial experiments~\citep{Bethlem:2016} suggests that PH$_3$ may not be a primary candidate for constraining $\mu$ in laboratory studies. Its merit as a probe for a drifting constant is more likely to be in cosmological settings as it is a relevant astrophysical molecule with a well documented spectrum and a negligible hyperfine splitting~\citep{Mueller}. However, it is hard to comment on the necessary conditions for its detection since its presence and formation are not well understood (see the discussion by \citet{15SoAlTe.PH3} and references therein). Despite this, PH$_3$ as a model system shows that the splittings caused by higher-order rotation-vibration interactions, which are essentially low-frequency transitions that can be measured using radio telescopes, have real potential for investigating a possible variation of $\mu$. | 18 | 8 | 1808.05427 |
1808 | 1808.07939_arXiv.txt | We present the concept of a new Fabry-Perot instrument called BTFI-2, which is based on the design of another Brazilian instrument for the SOAR Telescope, the Brazilian Tunable Filter Imager (BTFI). BTFI-2 is designed to be mounted on the visitor port of the SOAR Adaptive Module (SAM) facility, on the SOAR telescope, at Cerro Pach\'on, Chile. This optical Fabry-Perot instrument will have a field of view of 3~x~3~arcmin, with 0.12~arcsec per pixel and spectral resolutions of 4500 and 12000, at H-alpha, dictated by the two ICOS Fabry-Perot devices available. The instrument will be unique for the study of centers of normal, interacting and active galaxies and the intergalactic medium, whenever spatial resolution over a large area is required. BTFI-2 will combine the best features of two previous instruments, SAM-FP and BTFI: it will use an Electron Multiplication detector for low and fast scanning, it will be built with the possibility of using a new Fabry-Perot etalon which provides a range of resolutions and it will be light enough to work attached to SAM, and hence the output data cubes will be GLAO-corrected. | \label{sec:intro} Numerous integral field spectrographs (IFS) have been deployed on 4 to 8 meter-class telescopes during the last few decades. These instruments are built to deliver 3D spectroscopy by sampling different regions of the sky at the same time using different techniques, principally: (1) lenslet arrays, e.g. TIGER/CFHT\cite{Bacon1995}, OASIS/CFHT and SAURON/WHT\cite{Bacon2001}, OSIRIS/Keck\cite{Larkin2006}. (2) mirror slicers, e.g. SPIFFI/VLT\cite{Eisenhauer2003}, NIFS/Gemini\cite{Hart2003}, GNIRS/Gemini\cite{Allington-Smith2006}, SWIFT\cite{Tecza2006}, SINFONI/VLT\cite{Eisenhauer2003b}, KMOS/VLT\cite{Content2006}, MUSE/VLT\cite{Laurent2010}. (3) fiber bundles, e.g. DensePak/KPNO\cite{Barden1988}, SILFID/CFHT\cite{Vanderriest1988}, INTEGRAL/WHT\cite{Arribas1998}, FLAME-GIRAFFE/VLT (Pasquini, 2003SPIE.4841.1682P) and more recently SAMI/AAO\cite{Croom2012}. These IFS have relatively wide spectral range and intermediate spectral resolution ($\sim$~1000~-~5000), but generally have small field-of-views (FoV). For larger FoV another class of instruments, the imaging spectrometers, are used. The most common types are the Fabry-Perot spectrometers (FPS) and Fourier Transform spectrometers (FTS). For a long time, large FoV scanning FPS have been developed in the optical, e.g. TAURUS\cite{Atherton1982}, CIGALE\cite{Boulesteix1984}, HIFI\cite{Bland1989}, MMTF\cite{Veilleux2010}, SAM-FP\cite{Oliveira2017}, and they have been used with great success, especially for projects which required small wavelength coverage and large FoV, of the order of a few arc-minutes squared. This paper describes one such instrument, the Brazilian Tunable Filter Imager 2 (BTFI-2): a Fabry-Perot imaging spectrometer with high image quality provided by ground-layer adaptive optics (GLAO). This opens a whole new window for scientific exploration in areas such as the study of the physics of nearby galaxies, their kinematics, and their star formation history from pc to kpc scales by taking advantage of the large FoV (3~x~3 arcmin) and high spatial resolution, thanks to the SAM facility\cite{Tokovinin2016}. Galaxies consist of baryons distributed in multiple morphological and kinematic components (bulges, disks, bars, black holes) trapped into the deep potential well of dark matter halos. High resolution spatially resolved spectroscopy on large FoV allows gathering detailed spatial and spectral information to measure numerous physical parameters such as (1) the interaction and feedback between the gas, the stars, the dust and the black holes on galactic (10-100 pc) scales and, (2) mass loss mechanisms in stars, HII regions, planetary nebulae and supernova on smaller (pc) scales for galactic structures. BTFI-2 is a new instrument concept based on the Brazilian Tunable Filter Imager (BTFI, Ref. \citenum{Oliveira2013}), a FPS instrument designed for use with the SOAR Adaptive Module (SAM), at the 4.1~m SOAR Telescope, at Cerro Pach\'on, in Chile. BTFI is now officially decommissioned due to a number of reasons described further on in this paper. Instead, a much simpler instrument called SAM-FP has been used since 2016 to meet the needs of the SOAR community in obtaining spectroscopy with the SAM instrument. SAM-FP yields 3~$\times$~3~arcmin GLAO-corrected data cubes for a variety of studies, as mentioned in \autoref{sec:samfp.and.btfi}. However, SAM-FP is equipped with a normal CCD, and not with a photon counting system like an EMCCD, given that it uses the regular SAM camera called SAMI, which limits the detector power at low flux of the instrument. Standard CCDs still exhibit readout noise of a few electrons per pixel which does not allow short exposures and furthermore fast scanning of elementary FP cycles for which sub-electron readout is requested (see \autoref{sec:performance} for details). The most important gain expected with BTFI-2 will be to get deeper data, thanks to the capability of scanning the data cube with shorter exposure times to averaging sky transmission fluctuations. Our plan for the new instrument BTFI-2 is to re-use part of the optical design and components of BTFI. BTFI-2 will then inherit the good features of both BTFI and SAM-FP: it will be a light instrument attached to the SAM's visitor's port (and therefore it will yield GLAO-corrected images), it will contemplate the use of a novel FPS that may enable a range of spectral resolutions, and it will use EMCCD (which will facilitate scanning and will allow for deeper data cubes to be taken). The unique feature of a FPS system attached to SAM is of course the GLAO-corrected images it delivers, over a FoV of 3$\times$3 arcmin. No other 4-meter class telescope has this capability. BTFI and SAM-FP, the two instruments which can be considered precursors of BTFI-2, are now briefly described in the \autoref{sec:samfp.and.btfi}. Then we we show the top level requirements for the instrument in \autoref{sec:top.level.requirements}. \autoref{sec:optical.design} describes the optical design. \autoref{sec:mechanical-design} describes the instrument's mechanical concept with a brief description of each element. Finally, \autoref{sec:conclusion} closes this work with some future steps and planning. | \label{sec:conclusion} This document shows that BTFI-2 is a feasible project considering the optical elements, optical and mechanical concept, and detectors are all available. Accordingly to the expected performance described, BTFI-2 will expand the limits of Fabry-Perot science that can be done at SOAR with SAM, both by increasing the sensitivity and lowering down the duty cycle loss. We plan to improve the FP control system to reach the 500~ms overhead time using the two loaned etalons. The THALES SESO FP must also fit this requirement. A control system will be developed using the Chimera Observatory Control System\cite{Silva2017}\footnote{\url{https://github.com/astroufsc/chimera}}, a Python Framework developed to manage observatories and astronomical instruments. Finally, the BTFI-2 proposal is aligned to the future of instrumentation in SOAR. An upgrade to SAM is under way to improve the performance of GLAO correction at shorter wavelengths in the visible\cite{Faes2018}. This enhances BTFI-2 to make line-ratio studies and reddening measurements with good angular accuracy at (almost) all visible range over the large FoV provided by SOAR. | 18 | 8 | 1808.07939 |
1808 | 1808.02207_arXiv.txt | We explore the effects of strangeness and $\Delta$ resonance in baryonic matter and compact stars within the relativistic-mean-field (RMF) models. The covariant density functional PKDD is adopted for $N$-$N$ interaction, parameters fixed based on finite hypernuclei and neutron stars are taken for the hyperon-meson couplings, and the universal baryon-meson coupling scheme is adopted for the $\Delta$-meson couplings. In light of the recent observations of GW170817 with the dimensionless combined tidal deformability $197 \leq \bar{\Lambda}\leq 720$, we find it is essential to include the $\Delta$ resonances in compact stars, and small $\Delta$-$\rho$ coupling $g_{\rho \Delta}$ is favored if the mass $2.27{}_{-0.15}^{+0.17}\ M_\odot$ of PSR J2215+5135 is confirmed. | Introduction} The recent observation of gravitational waves from the binary neutron star merger event GW170817 suggests that the merging objects are compact~\cite{LIGO2017_PRL119-161101, LigoVirgo2018_arXiv1805.11581}. Assuming low spin priors, the dimensionless combined tidal deformability $\bar{\Lambda}$ is considered to be less than 720 at 90\% confidence level~\cite{LigoVirgo2018_arXiv1805.11579}, while a lower limit with $\bar{\Lambda}\geq 197$ is obtained based on electromagnetic observations of the transient counterpart AT2017gfo~\cite{Coughlin2018_arXiv1805.09371}. Even though the observations of neutron stars' radii are controversial and depend on specific assumptions, the recent measurements seem to be converging and lie at the lower end of 10-14 km range~\cite{Guillot2013_ApJ772-7, Lattimer2014_EPJA50-40, Ozel2016_ARAA54-401, Li2015_ApJ798-56, Steiner2018_MNRAS476-421, Most2018_PRL120-261103, LigoVirgo2018_arXiv1805.11581}. The combined constraints on the tidal deformability and radii of neutron stars indicate a soft equation of states (EoS), where many covariant density functionals are in jeopardy~\cite{Zhu2018_ApJ862-98, Malik2018_PRC98-035804}. A possible solution to this problem is to introduce new degrees of freedom, e.g., $\Delta$ resonances, hyperons, and deconfined quarks~\cite{Gomes2018_arXiv1806.04763}. As one increases the density of nuclear matter, the inevitable emergence of $\Delta$ isobars, hyperons, and quarks can soften the EoSs significantly and reduce the radius and tidal deformability of the corresponding compact stars, which can be consistent with these recent observations. However, a soft EoS will result in compact stars with too small masses that can not reach two solar mass as observed in pulsars PSR J1614-2230 ($1.928 \pm 0.017\ M_\odot$)~\cite{Demorest2010_Nature467-1081, Fonseca2016_ApJ832-167} and PSR J0348+0432 ($2.01 \pm 0.04\ M_\odot$)~\cite{Antoniadis2013_Science340-1233232}, i.e., the Hyperon Puzzle~\cite{Vidana2015_AIPCP1645-79} or $\Delta$ Puzzle~\cite{Drago2014_PRC90-065809}. Extensive efforts were made to resolve the Hyperon Puzzle~\cite{Weissenborn2012_PRC85-065802, Bednarek2012_AA543-A157, Oertel2015_JPG42-075202, Maslov2015_PLB748-369, Maslov2016_NPA950-64, Takatsuka_EPJA13-213, Vidana2011_EPL94-11002, Yamamoto2013_PRC88-022801, Lonardoni2015_PRL114-092301, Togashi2016_PRC93-035808, Weissenborn2011_ApJ740-L14, Klahn2013_PRD88-085001, Zhao2015_PRD92-054012, Kojo2015_PRD91-045003, Masuda2016_EPJA52-65, Li2015_PRC91-035803, Whittenbury2016_PRC93-035807, Fukushima2016_ApJ817-180, Sun2018_CPC42-25101} and $\Delta$ Puzzle~\cite{Drago2014_PRD89-043014, Cai2015_PRC92-015802, Zhu2016_PRC94-045803, Bai2018_PRD97-023018}. Nevertheless, with the constrained observable tidal deformability of GW170817~\cite{LIGO2017_PRL119-161101, LigoVirgo2018_arXiv1805.11579, Coughlin2018_arXiv1805.09371}, those solutions may be challenged, especially for the latest observation of a more massive PSR J2215+5135 ($2.27{}_{-0.15}^{+0.17}\ M_\odot$)~\cite{Linares2018_ApJ859-54}. To satisfy these stringent observational constraints, we consider the possible existence of both $\Delta$ isobars and hyperons in neutron stars. Since relativistic-mean-field (RMF) models~\cite{Brockmann1977_PLB69-167, Boguta1981_PLB102-93, Mares1989_ZPA333-209, Mares1994_PRC49-2472, Toki1994_PTP92-803, Song2010_IJMPE19-2538, Tanimura2012_PRC85-014306, Wang2013_CTP60-479} have been successfully adopted to describe finite (hyper)nuclei~\cite{Reinhard1989_RPP52-439, Ring1996_PPNP37_193-263, Meng2006_PPNP57-470, Paar2007_RPP70-691, Meng2015_JPG42-093101, Meng2016_RDFNS, Typel1999_NPA656-331, Vretenar1998_PRC57-R1060, Lu2011_PRC84-014328, Hagino2014_arXiv1410.7531, Sun2016_PRC94-064319} and baryonic matter~\cite{Glendenning2000, Ban2004_PRC69-045805, Weber2007_PPNP59-94, Long2012_PRC85-025806, Sun2012_PRC86-014305, Wang2014_PRC90-055801, Fedoseew2015_PRC91-034307, Gao2017_ApJ849-19}, in this work the EoSs of baryonic matter are obtained based on RMF model. More specifically, we adopt the covariant density functional PKDD~\cite{Long2004_PRC69-034319}, while the hyperon-meson couplings are fixed based on our previous investigations on hypernuclei and neutron stars~\cite{Sun2016_PRC94-064319, Sun2018_CPC42-25101, Liu2018_PRC98-024316}. For the $\Delta$-meson couplings, as in Ref.~\cite{Drago2014_PRC90-065809}, we adopt the universal baryon-meson coupling scheme, while a vanishing $\Delta$-$\rho$ coupling is considered as well. It is found that the observational tidal deformability and mass of PSR J2215+5135 can be reproduced only by including $\Delta$ isobars in neutron stars. The paper is organized as follows. In Sec.~\ref{sec:the}, we present the formalism of RMF model for baryonic matter, the choices of baryon-meson couplings, the conditions for obtaining the EoSs of neutron star matter, and the formalism to determine the structures of compact stars. Results and discussions are given in Sec.~\ref{sec:num}. We make a summary in Sec.~\ref{sec:con}. | 18 | 8 | 1808.02207 |
|
1808 | 1808.10762_arXiv.txt | We present comprehensive models of Herbig Ae star, HD\,142666, which aim to simultaneously explain its spectral energy distribution (SED) and near-infrared (NIR) interferometry. Our new sub-milliarcsecond resolution CHARA (CLASSIC and CLIMB) interferometric observations, supplemented with archival shorter baseline data from VLTI/PIONIER and the Keck Interferometer, are modeled using centro-symmetric geometric models and an axisymmetric radiative transfer code. CHARA's $330\,$m baselines enable us to place strong constraints on the viewing geometry, revealing a disk inclined at $58^{\circ}$ from face-on with a $160^{\circ}$ major axis position angle. Disk models imposing vertical hydrostatic equilibrium provide poor fits to the SED. Models accounting for disk scale height inflation, possibly induced by turbulence associated with magneto-rotational instabilities, and invoking grain growth to $\gtrsim1\,\mu$m size in the disk rim are required to simultaneously reproduce the SED and measured visibility profile. However, visibility residuals for our best model fits to the SED indicate the presence of unexplained NIR emission, particularly along the apparent disk minor axis, while closure phase residuals indicate a more centro-symmetric emitting region. In addition, our inferred $58^{\circ}$ disk inclination is inconsistent with a disk-based origin for the UX~Ori-type variability exhibited by HD~142666. Additional complexity, unaccounted for in our models, is clearly present in the NIR-emitting region. We propose the disk is likely inclined toward a more edge-on orientation and/or an optically thick outflow component also contributes to the NIR circumstellar flux. | Circumstellar disks are ubiquitous across all masses of star formation \citep[e.g.][]{Andrews13, Ricci14, Ilee16, Lazareff16, Kraus17}: a consequence of the conservation of angular momentum during gravitational collapse. These disks provide the building materials and the natal environment for planets to form and evolve in. The reprocessing of starlight by dust in the innermost regions of protoplanetary disks produces strong near-infrared (NIR) continuum emission, in excess of that expected from a stellar photosphere. Developments in the field of NIR interferometry during the late 1990s enabled the first spatially-resolved observations of the circumstellar structure of Herbig Ae/Be stars -- the precursors to intermediate-mass stars \citep{Herbig60, Strom72} -- to be obtained. The milliarcsecond (mas) resolution offered by the Infrared Optical Telescope Array (IOTA) and Palomar Testbed Interferometer (PTI) showed that the inner disk regions did not extend down to the stellar surface \citep[e.g][]{Millan99, Akeson00}, in agreement with prior spectral energy distribution (SED) modeling \citep{Hillenbrand92}. As the number of Herbig Ae/Be stars observed with NIR interferometry increased, a relationship between the host star luminosity and the characteristic size of the NIR-emitting region emerged \citep{Monnier02}. The slope of this size-luminosity relationship suggests the NIR-emitting region arises from a dust sublimation rim at a temperature of $\sim1800\,$K \citep{Lazareff16}. Early disk models incorporating a dust sublimation rim used a vertical-wall approximation \citep{Dullemond01, Natta01}. However, the strong viewing angle-dependency to the NIR emission associated with such a model is in conflict with the similar levels of NIR excess observed among Herbig Ae/Be stars over a wide range of disk inclination angles \citep{Natta01, Dominik03}. In addition, the significant closure phase ($\phi_{\rm{CP}}$) signals associated with the strongly asymmetric NIR brightness distribution in vertical rim models was not observed \citep{Monnier06,Kraus09}. Instead, curvature of the inner rim is understood to arise due to the dependence of the dust sublimation temperature and grain cooling efficiency on, for example, the gas density, the size distribution of dust grains, grain growth-induced vertical settling, and the relative abundance of different grain compositions \citep{Isella05, Tannirkulam07, Kama09, McClure13}. The picture was further complicated with the first \emph{sub}-mas NIR observations of Herbig Ae/Be stars, made possible with the $\sim330\,$m baselines of the Center for High Angular Resolution Astronomy (CHARA) Array. Through their observations of \object{MWC 275} and \object{AB Aur}, \citet{Tannirkulam08a} found that the ``bounce'' in the secondary visibility lobe predicted by curved rim models was not observed. Instead, to explain the relatively flat profiles of the observed second visibility lobes, an additional NIR-emitting component interior to the silicate dust sublimation front was required. Further evidence for this has been reported in studies using NIR spectro-interferometry \citep[e.g.][]{Kraus08, Eisner09}, high resolution spectroscopy \citep[e.g.][]{Ilee14}, and photometry \citep[e.g.][]{Fischer11}. The nature of this material remains unclear with plausible suggestions including a hot gas reservoir and/or more refractory grain species \citep{Tannirkulam08b, Eisner09}. Here, we focus on the shape, location and viewing geometry of the circumstellar disk of the Herbig Ae star, \object{HD\,142666} (spectral type A8Ve; \citealt{Meeus98}). The IR excess of \object{HD\,142666} (common aliases include V1026~Sco), first identified by \citet{Walker88}, has previously been studied using NIR and mid-IR (MIR) interferometers with operational baselines $\lesssim100\,$m. The characteristic size of the $H$- and $K$-band-emitting regions observed with the Keck Interferometer (KI), VLTI/AMBER and VLTI/PIONIER (henceforth referred to as AMBER and PIONIER, respectively) are consistent with that expected from dust sublimation ($\sim0.4\,$au at a stellar distance of $150\,$pc; \citealt{Monnier05, Lazareff16}) while the MIR emission observed with VLTI/MIDI is more extended than predicted by typically-adopted temperature gradient models suggesting a narrow, dust-free gap is present within the inner few au of the disk \citep{Schegerer13, Vural14}. However, the usual features indicative of optically thin disk regions or disk cavities are not seen in the SED of \object{HD\,142666} \citep{Dominik03} meaning the disk is not typically considered to be (pre-)transitional. Intermediate disk inclinations for HD\,142666 have been indicated via NIR and MIR interferometry ( $48.6^{\circ}\,^{+2.9}_{-3.6}$, \citealt{Vural14}; $\sim60^{\circ}$, \citealt{Lazareff16}), SED analysis ($\sim55^{\circ}$, \citealt{Dominik03}) and ALMA ($\sim60^{\circ}$, \citealt{Rubinstein18}). VLT/NACO differential imaging and ALMA indicate the disk major axis position angle\footnote{Quoted disk position angles, PA$_{\rm{major}}$, are for the disk major axis, measured east of north.}, PA$_{\rm{major}}$, is oriented along a nearly North-South direction ($\sim180^{\circ}$, \citealt{Garufi17}; $161^{\circ}$, \citealt{Rubinstein18})). We present new, high-resolution NIR interferometric data of \object{HD\,142666} obtained using the CLASSIC two-telescope and CLIMB three-telescope beam combiners of the CHARA Array \citep{Brummelaar13}. Section~\ref{sec:obs} details our CHARA observations and the supplementary, shorter baseline NIR interferometry retrieved from the archives. With its $\sim331\,$m maximum baseline length, our CHARA observations offer us the opportunity to distinguish between different curved rim models to understand the dominant process of rim curvature in the disk of \object{HD\,142666}. Our analysis builds upon that of \citet{Tannirkulam08b} who used the TORUS Monte Carlo radiative transfer code \citep{Harries00} to model the NIR interferometric visibilities of two other Herbig Ae stars -- \object{MWC\,275} and \object{AB\,Aur} (spectral types of A1 and A0, respectively; \citealt{Mora01, Hernandez04}) -- obtained with CHARA/CLASSIC (henceforth referred to as CLASSIC). In addition to considering a later-type Herbig~Ae star, (i) our $(u,v)$-plane coverage is much improved compared to the \citet{Tannirkulam08b} study, (ii) we probe $H$- as well as $K$-band emission, and (iii) with the addition of CHARA/CLIMB (henceforth referred to as CLIMB) data, we use $\phi_{\rm{CP}}$ information to further constrain our modeling. A two-fold approach is used in our analysis. First, we constrain the stellar flux contribution to the NIR flux by fitting stellar atmosphere models to optical photometry and employ centro-symmetric geometric models to constrain the viewing geometry of the NIR-emitting region. We then build on these models using the TORUS Monte Carlo radiative transfer code to explore the physical bases behind the location and shape of the observed inner disk rim. Our modeling approach is outlined in Section~\ref{sec:methodology} while the results of our geometric and radiative transfer analysis are presented in Sections~\ref{sec:geoFitResults} and \ref{sec:RTresults}, respectively. In Section~\ref{sec:discussion}, we discuss our results in the context of grain growth to micron sizes in the inner rim and comment on indirect evidence for further complexity in the NIR-emitting region. | \label{sec:discussion} \subsection{Grain growth in the disk of HD\,142666 and the inner rim location} The results presented in Section~\ref{sec:RTresults} indicate that models in which the inner disk rim is dominated by small ($0.1\,\mu$m) grains are incompatible with the SED and NIR interferometry obtained for \object{HD\,142666}. Instead, models invoking the growth of dust grains to micron sizes provide improved fits to the observations. These results support those of \citet{vanBoekel03} who, in their analysis of the shape and strength of the silicate feature in the \emph{Spitzer} spectrum of \object{HD\,142666}, found strong evidence for growth from $0.1\,\mu$m to $2.0\,\mu$m grains with a mass ratio of 1:1.54 in favour of large grains. As MIR emission arises from the disk surface layers, and larger grains are expected to settle to lower scale heights in the disk \citep{Testi14}, the dominance of micron-sized grains in the disk midplane was anticipated to be even more pronounced. Our results support this idea as the models invoking the presence of larger, micron-sized grains (S:large model with $h_{\rm{0,gas}}=7\,$au and $\beta=1.09$ and THM07 mode with $h_{\rm{0,gas}}=8\,$au and $\beta=1.09$) are able to simultaneously reproduce the NIR portion of the SED, the shape and flux of the \emph{Spitzer} spectrum, and the observed $H$- and $K$-band visibilities. The lower $\chi^{2}_{\rm{r,vis}}$ provided by the S:large model fit to the visibilities compared to the THM07 model (see Table~\ref{tab:chisq}) further suggests that the inner disk rim of \object{HD\,142666} is more consistent with models invoking a gas density-dependent dust sublimation temperature \citep[e.g.][]{Isella05} than those invoking constant dust sublimation temperatures where rim curvature arises due to the relative abundance of different grain sizes (in $r$ and $z$) and their relative cooling efficiencies \citep[e.g.][]{Tannirkulam07}. However, it should be noted that using (i) grains $<1.2\,\mu$m as the larger grains, (ii) a different size for the smaller grains, (iii) a different value for $h_{\rm{0,dust}}$ for the larger grains, and/or (iv) a different silicate sublimation temperature (see Table~\ref{tab:RTmodels}) would all affect the rim shape, location and temperature structure predicted by the THM07 models. The parameters we adopted in our THM07 models were chosen for their consistency with the original \citet{Tannirkulam07} study and a comprehensive evaluation of the impact of these variables is beyond the scope of this paper. However, our use of $1.2\,\mu$m-sized grains as the ``large'' grains should produce inner rim locations close to the lower limit allowed by the \citet{Tannirkulam07} and \citep{Isella05} models. This is because silicate grains larger than $\sim1.3\,\mu$m do not significantly contribute to the dust opacity and thus their inclusion would not make the rim any more compact \citep{Isella05}. Of the parameters explored herein, our best model (the S:large model with $h_{\rm{0,gas}}=7\,$au and $\beta=1.09$) produces a sublimation rim that remains optically thick down to within $0.17\,$au of the star (in the disk midplane). This is broadly consistent with the results of our geometric fitting (Section~\ref{sec:geoFitResults}) in which the characteristic radii of the $H$- and $K$-band-emitting regions were found to be $\sim0.22-0.24\,$au in both the PS+R and PS+SR fits. These inner radii are lower than previously published estimates by \citet{Monnier05} and \citet{Schegerer13} based on short-baseline NIR and MIR visibilities ($\sim0.38-0.39\,$au, accounting for differences in the adopted distance to \object{HD\,142666}) but consistent with those in \citet[][$0.19-0.23\,$au]{Vural14}. However, we note that the adopted stellar parameters (including the stellar flux contribution) are not consistent across these studies nor between these studies and our own. As discussed in \citet{Lazareff16}, the characteristic size of the emitting region and the circumstellar flux contribution are intrinsically linked in the visibility so it is understandable that differences in one parameter will lead to differences in the other when comparing studies. \subsection{Indicators of additional complexity in the NIR-emitting region}\label{sec:disc:geom} Throughout our radiative transfer analysis (Section~\ref{sec:RTresults}), we first required our TORUS models to reproduce the observed SED before assessing the fit to the interferometry. In this way, we assume that the disk in our TORUS models accounts for all the NIR circumstellar flux. If additional NIR-emitting gaseous material exists interior to the sublimation rim \citep{Tannirkulam08a, Tannirkulam08b} and/or a dusty outflow exists \citep{Alexander07, Bans12} -- neither of which are accounted for in our models -- they will also contribute to the observed $H$- and $K$-band flux. Additionally, in our geometric modeling (Section~\ref{sec:geoFitResults}), we assumed all the circumstellar NIR flux could be fit using a Gaussian-smoothed ring model and, from this, estimated a disk major axis position angle and inclination of $160^{\circ}$ and $58^{\circ}$, respectively. While this viewing geometry agrees with previous assessments of the disk inclination ($40-60^{\circ}$ \citealt{Dominik03}, \citealt{Vural14}, \citealt{Lazareff16}, \citealt{Rubinstein18}) and position angle ($\sim140-180^{\circ}$ \citealt{Garufi17}, \citealt{Rubinstein18}), indirect evidence for further model complexity is suggested in the visibility and $\phi_{\rm{CP}}$ residuals. As stated in Section~\ref{sec:largegrains}, while the models invoking grain growth to micron sizes provide a good fit to the visibilities across a wide range of PA$_{\rm{base}}$, the model visibility curves appear under-resolved compared to the data along the apparent disk minor axis. In addition, the significant ($\sim50-100^{\circ}$) $\phi_{\rm{CP}}$ signals predicted by our best-fitting TORUS models are not present in the data, indicating the true brightness distribution is more centro-symmetric. \begin{figure} \centering \includegraphics[width=0.47\textwidth]{twoD_chisqmap_3_new.pdf} \caption{ $\chi^{2}_{\rm{r}}$ map showing the comparative goodness-of-fit provided by the S:large model with $h_{\rm{0,gas}}=7\,$au and $\beta=1.09$ to the $H$- and $K$-band visibilities using disk inclinations, $52^{\circ}\leq i\leq 64^{\circ}$, and position angles, $140^{\circ}\leq$PA$_{\rm{major}}\leq 180^{\circ}$. } \label{fig:pa_inc} \end{figure} Further indirect evidence of additional model complexity is found when considering the UX~Ori-type phenomena displayed by \object{HD~142666} \citep{Meeus98, Zwintz09}. This type of variability is associated with line-of-sight fluctuations in opacity and is typically attributed to circumstellar disk occultation \citep{Grinin91, Natta97} although unsteady accretion \citep{Herbst99} and/or the existence of dusty outflows \citep{Vinkovic07, Tambovtseva08} have been proposed as alternative causes. As the disk- and outflow-based origins require intermediate-to-high disk inclinations for line-of-sight occultations to arise, and the inferred disk inclination of $58^{\circ}$ for \object{HD~142666} is relatively low compared to the $\sim70^{\circ}$ inferred for other UX~Ori stars (VV~Ser, KK~Oph, and UX~Ori itself; \citealt{Pontoppidan07, Kreplin13, Kreplin16}), the photometric variability observed for HD~142666 may suggest that the disk is more inclined. Alternatively, the UX~Ori variability may indicate that azimuthal and temporal variations in disk scale height exist. To investigate whether the residuals in the interferometry fits could be reconciled solely by changing the disk viewing geometry, we explored whether a better fit to the visibilities could be achieved if our best-fit S:large TORUS model ($h_{\rm{0,gas}}=7\,$au and $\beta=1.09$) was observed at differing viewing geometries: $52^{\circ}\leq i\leq 64^{\circ}$ and $140^{\circ}\leq$\,\,PA$_{\rm{major}}\leq180^{\circ}$. The resulting $\chi^{2}_{\rm{r}}$ map is shown in Fig.~\ref{fig:pa_inc}. At the original viewing geometry (PA$_{\rm{major}}=160^{\circ}$ and $i=58^{\circ}$), the model provides $\chi^{2}_{\rm{r}}=14.4$. Over the range of inclinations and position angles probed, the model with $i=58^{\circ}$ and PA$_{\rm{major}}=155^{\circ}$ provides the best fit to the visibilities but the improvement in $\chi^{2}_{\rm{r}}$ is small: $\chi^{2}_{\rm{r,min}}=13.9$. This revised disk viewing geometry unsurprisingly still produces model visibilities which are under-resolved along the apparent disk minor axis and model $\phi_{\rm{CP}}$ signals in excess of those observed. As such, the residuals in our TORUS model fitting cannot be explained simply be changing the viewing geometry and instead point to additional model complexity. The disk models we have explored with TORUS assume azimuthal symmetry: we have not accounted for the possible presence of azimuthal variations of the disk scale height (i.e. disk warps). The disk of \object{HD\,142666} is not strongly flared (Section~\ref{sec:RTresults}; c.f.\ \citealt{Meeus01}) and, as such, disk regions at large distances from the star are unlikely to provide line-of-sight stellar occultations when observed at an inclination of $58^{\circ}$ (see Fig.~\ref{fig:images}). Assuming that optically thick material only exists exterior to the dust rim location predicted by the best-fit S:large TORUS model, a disk inclination of $58^{\circ}$ requires azimuthal scale height increases of around $40\%$ in the inner disk for direct line-of-sight occultation. The periods of minimum brightness observed for \object{HD\,142666} last for a maximum of $\sim2-3\,$days \citep{Zwintz09}. Comparing this to the orbital timescale at the inner disk rim ($18.2\,$days), these scale height variations would be required to extend over a maximum of $\sim10-15\%$ of the disk circumference. Furthermore, as the photometric variability is aperiodic, the scale height variations would have to rise and fall on timescales within the $\sim18.2\,$days orbital period. Taking this all into account, the $58^{\circ}$ disk inclination inferred for \object{HD~142666} appears inconsistent with a disk-based origin for the UX~Ori phenomena. In light of this, and the fact that the visibilities of the best-fit S:large TORUS model appear under-resolved along baseline position angles that probe the disk minor axis, it seems likely that either the disk is inclined at $>58^{\circ}$ or that the UX~Ori phenomena observed for HD~142666 is attributed to an outflow component of variable optical depth which is oriented perpendicular to the disk midplane. In both cases, additional NIR emitting material exterior to the flared disk we have considered here is required. | 18 | 8 | 1808.10762 |
1808 | 1808.04751_arXiv.txt | Virgo is a dynamically young galaxy cluster with substructure in its spatial and kinematic distribution. Here, we simultaneously study the phase-space distribution and the main characteristics of Virgo's galaxies, particularly its most abundant galaxy population -- the early-type dwarfs -- to understand their environmental transformation histories. Aside from known correlations with morphological types -- like the larger average clustercentric distance of late-type galaxies -- we find an intriguing behavior of early types with magnitudes $-17 \geq M_r \geq -18$. They show a large velocity spread and an asymmetric phase-space distribution, similar to the late-type galaxies and different from the early types just one magnitude brighter/fainter. Furthermore, we find a close phase-space aggregation of early-type dwarfs at large clustercentric distance and high relative velocity. Nearly all of them show signatures of disk components and their colors imply stellar ages that are younger than the population average. They are not located closely together but spread azimuthally around the cluster center. We show that this is expected from simulations of an infalling galaxy group that slowly gets dispersed after its first pericentric passage. We thus conclude that these galaxies are recent arrivals, and that the peculiar phase-space distribution of early-type dwarfs is evidence for the ongoing growth of this galaxy population. Studying galaxies based on their phase space correlations is a unique way to compare the properties of recent and older cluster members, and to understand which environment most influenced their present-day characteristics. | \label{sec:intro} The environmental dependence of the morphological distribution of galaxies is well known. Dense environments -- clusters and massive groups of galaxies -- preferentially host early-type galaxies, while late-type galaxies are more likely to exist in low-density environments. This phenomenon has been well studied and quantified for giant ellipticals and spirals \citep{Dressler1980}, and extends to dwarf galaxies as well \citep{Binggeli1987}. Early-type dwarfs are the dominant population (by number) in the centers of massive galaxy clusters \citep{Binggeli1987}. The presence of multiple families of early-type dwarfs has been studied by many groups, starting with \citet{Wirth84,Okamura85,Kormendy89}. While some studies interpret the early-type galaxy population from giants to dwarfs as a continuum of smoothly changing properties with decreasing stellar mass \citep[e.g.][]{GrahamGuzman2003,Chen2010,Glass2011}, early-type dwarfs are not simple scaled-down versions of bright ellipticals and lenticulars. For instance, dwarfs at stellar masses around $10^9 \, \msun$ (absolute magnitudes around $ M_r \approx -17$\,mag), have star formation histories with systematically longer timescales than those of bright early types \citep{Gavazzi2002}. The dwarfs' radial intensity profiles largely have low S\'ersic indices close to exponential, similar to late-type galaxies \citep{BinggeliCameron1991}. In the magnitude-size diagram of galaxies, \citet{Janz2008} showed that early-type dwarfs around $10^9 \, \msun$ depart from a continuous sequence of decreasing S\'ersic index from giants to dwarfs --- instead, they tend towards larger effective radii, where also the late types are found \citep{Janz2014}. Therefore, one possibility of morphologically classifying galaxies is to regard them as two parallel sequences of decreasing stellar mass: the late-type sequence, where spirals are followed by irregulars at the low-mass end, and the early-type sequence, where lenticulars of lower mass have less prominent bulges and are then followed by the bulge-less early-type dwarfs \citep{KormendyBender2012}. Even with the similarities in S\'ersic indices and effective radii trends, early-type galaxies are not simply descendants of late-type galaxies as we know them at present. For instance, the internal dynamics of lenticulars show a lower stellar angular momentum and higher central concentration than that of spiral galaxies of similar masses \citep{Dressler1980,Querejeta2015}. The mere removal of gas by ram pressure and subsequent cessation of star formation from lower-mass spirals cannot explain these differences \citep{Vaghmare2015} --- one possibility to connect spirals and lenticulars in parameter space is the loss of angular momentum through mergers \citep{Querejeta2015}. Likewise, the internal dynamics of cluster early-type dwarfs are systematically different from that of present-day low-mass late types \citep{Rys2014}. Additionally, \citet{SanchezJanssen2012} pointed out that the globular cluster systems of today's low-mass late types are, on average, not as rich as those of the brighter early-type dwarfs. Furthermore, for a sample of low-mass early-type galaxies in isolation, \citet{Janz2017} recently found that they consist of a similar mix of fast and slow rotators as those in clusters \citep{Toloba2015}. The role of these galaxies' environmental histories in affecting their internal dynamics thus remains poorly understood. Galaxies found in different environments today (i.e.\ cluster vs.\ group or cluster core vs.\ outskirts) have experienced a different environmental influence on their evolution for most of their lifetime \citep{Lisker2013}. Even for those galaxies that populate the red sequence of the same galaxy cluster today, the Illustris simulation \citep{Vogelsberger2014,Genel14} shows that their properties depend on their environmental history: low-mass galaxies that entered the main progenitor of the cluster at early epochs are found on the high-metallicity side of the stellar mass-metallicity relation today \citep{Engler2017,Pasquali2018}. The fact that a morphology-density relation has been found even for subtypes of early-type dwarfs \citep{Lisker2007} may be a consequence of a range of different environmental histories among this continuously growing galaxy population. In addition to the gradual build-up of galaxy clusters by accreting field galaxies and smaller groups, occasional accretion events of larger galaxy groups can lead to a noticeable asymmetry and disequilibrium of the spatial and dynamical distributions of cluster galaxies. Given the crossing times of more than one gigayear for clusters as massive as Virgo \citep{deVaucouleurs61,BoselliGavazzi2006}, these new members may still appear as spatially distinct subclumps (like the M49 subcluster, \citealt{Binggeli1987}) and/or phase-space aggregations after several gigayears \citep{Vijayaraghavan15,Rhee2017}, depending on their infall direction and orbit. {On the scale of the stellar halo of Virgo's central galaxy M87, phase-space substructures of globular clusters and planetary nebulae have already proven useful to trace the recent accretion history \citep{Romanowsky2012,Longobardi2015}.} Based on the distribution and motions of its galaxies, Virgo has long been known to be a dynamically young, unrelaxed cluster \citep{Huchra85,Binggeli1987}, although the X-ray intensity peak coincides with M87 \citep{Boehringer1994}. In fact, the Virgo dwarf galaxies populate the region between M87 and M84 with roughly constant number density, i.e.\ their distribution is not peaked at M87 \citep{Binggeli1987}. With M86 most likely falling in from behind \citep[e.g.][]{Zhang2015} and M87 deviating from the mean of the velocity distribution of galaxies, \citet{Binggeli1987} concluded that even the Virgo cluster core is a dynamically young structure. Moreover, using the large number of low-mass galaxies has led to confirming several previously known structures around Virgo \citep{Tully1982} as filaments that likely feed the cluster with newly infalling galaxies \citep{Kim2016}, {similar to the findings of \citet{Adami2009} for the Coma cluster.} Further evidence for Virgo's active assembly comes from the velocity distribution of its early-type dwarfs. \citet{Conselice2001a} found that the high velocity dispersion of early-type dwarfs in Virgo resembled that of late-type galaxies rather than giant ellipticals. Therefore, \citeauthor{Conselice2001a} concluded that the Virgo cluster early-type dwarfs are a population that has been built up through infall into the cluster over time and is not a ``primordial'' cluster population. In addition, at least a fraction of the early-type dwarfs has probably also been shaped by dwarf-dwarf mergers \citep{Paudel2017}. Thus, we know that: the Virgo cluster's non-equilibrium dynamics indicate its active assembly, early-type dwarfs are abundant in Virgo, but we lack a complete understanding of the origin of early-type dwarfs and their environmental histories. It is therefore worthwhile to analyze the spatial and kinematic distribution of the Virgo cluster's galaxy population, especially for the abundant dwarfs, to understand their origin. Furthermore, we need to consider that high and low-mass galaxies have likely been influenced differently by various processes over their evolutionary histories, in different environments and over a range of infall histories, which in turn may have affected their morphological type, color, size, internal dynamics, and other properties. This may have led to luminosity-dependent differences in how early-type and late-type galaxies are distributed in the cluster today. Therefore, to understand the dynamical and environmental origin of early-type dwarfs, we investigate how galaxies in various intervals of absolute magnitude populate observer's phase space, i.e.\ how they are distributed with respect to their distance from the cluster center and their line-of-sight velocity relative to the cluster. In Section 2, we describe the observational dataset that serves as basis for our investigation. Section 3 presents our findings of how galaxies are distributed in phase space and what their properties are. To aid the interpretation of our results, we show predictions from simulations of a group-cluster merger in Section 4. This is followed by a discussion in Section 5 and the conclusions in Section 6. | \label{sec:conclusions} Virgo is an actively accreting cluster, with several groups in various stages of infall. Virgo galaxies' properties reflect its active infall history, and studying the morphologies, colors, and internal dynamics of these galaxies is useful to understand the build-up of the cluster as well as the environmental history of the galaxies. In this paper, we have simultaneously considered the properties of galaxies themselves and their current dynamical state in the cluster within the cluster's phase space. We find that the properties of galaxies -- their luminosities and morphologies -- are correlated with their position in phase space. Overall, late-type galaxies are found at larger clustercentric radii, as expected for recent infallers. We also find that the distribution of late-types is asymmetric in velocity space; this also holds for early-type dwarfs with magnitudes $-17 \geq M_r \geq -18$. Low-mass late types as well as early-type dwarfs with disk signatures therefore cluster in phase-space. This asymmetric distribution and clustering indicates recent and ongoing infall. The overall diversity in the galaxy properties across phase space therefore points to Virgo's current state of active assembly. The intermediate magnitude bin of $-17 \geq M_r \geq -18$, which is around where galaxies transition from giants to dwarfs, has a particularly interesting phase-space distribution of galaxies. Specifically, within a narrow radial and velocity bin near \mbox{$d_{\rm M87}$$\,\approx\,$$1.15$\,Mpc} and \mbox{$v_{\rm rel}$$\,\approx\,$$700$\,km\,s$^{-1}$}, we find an overdensity of early-type dwarfs that nearly all show signatures of disk components and have intermediate to young stellar ages compared to the overall population. They are not spatially clustered, but are azimuthally distributed around the center of the cluster. In comparing that phase-space distribution of galaxies with predictions from a basic model for group infall, we find evidence for a previously unrecognized group infall event that occurred $2-3$\,Gyr in the past in the Virgo cluster. This infall likely took place along our line of sight producing a radially distributed subset of dwarf cluster members that share common kinematics. This is the first detection of this type of kinematic structure {for a previously gravitationally bound group of galaxies, specifically using the dynamics of dwarf galaxies, which are greater in number and therefore provide more robust statistical information than more massive former group members.} The phase-space properties of these galaxies combined with their sizes, colors, and morphologies can help us understand when and how they have been transformed. Gas-poor galaxies that have stopped forming stars, but still retain disk structures, were likely stripped of their gas by ram pressure, but not morphologically transformed by tidal forces or mergers. If these galaxies are found at large clustercentric radii with high relative velocities, then they are likely recent infallers; they must have been stripped of their gas in the prior group environment. Their structure and internal dynamics probably still reflect an earlier epoch of their evolution. Comparing their properties to those of early-type dwarfs in galaxy groups, as well as to those closer to the Virgo core, can thus provide insight as to which environment is most critical for determining the galaxies' structure, dynamics, and stellar population properties. | 18 | 8 | 1808.04751 |
1808 | 1808.04798_arXiv.txt | Disk reverberation mapping of a handful of nearby AGN suggest accretion disk sizes which are a factor few too large for their luminosities, apparently at odds with the standard model. Here, we investigate the likely contribution to the measured delay signature of diffuse continuum emission arising from broad line region gas. We start by constructing spherically symmetric pressure-law BLR models (i.e., $P(r)\propto r^{-s}$) that approximately reproduce the observed emission line fluxes of the strong UV--optical emission-lines in the best-studied source, NGC~5548. We then determine the contribution of the diffuse continuum to the measured continuum flux and inter-band delays, accounting for the observed variability behaviour of the ionizing nuclear continuum. Those pressure-law models that approximately reproduce the observed emission-line luminosities unavoidably produce substantial diffuse continuum emission. This causes a significant contamination of the disk reverberation signature (i.e., wavelength-dependent continuum delays). Qualitatively, the diffuse continuum delay signatures produced by our models resemble that observed for NGC~5548, including the deviation of the lag spectrum above that of a simple power-law in wavelength, short-ward of the Balmer and Paschen jumps. Furthermore, for reasonable estimates of the BLR covering fraction, the delay induced by diffuse continuum emission causes elevated inter-band delays over the entire UV--optical regime; for these pressure-law models, there are no `disk-dominated' wavelength intervals. Thus, the diffuse continuum contribution must be taken into account in order to correctly infer AGN accretion disk sizes based on inter-band continuum delays. | 18 | 8 | 1808.04798 |
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1808 | 1808.03940_arXiv.txt | Important observational results have been recently reported on the angular distributions of cosmic rays at all energies, calling into question the perception of cosmic rays a decade ago. These results together with their in-progress interpretations are summarised in this review paper, covering both large-scale and small-scale anisotropies from TeV energies to the highest ones. While the magnetic field in the Galaxy has long been considered as an external data imprinting a quasi-random walk to particles and thus shaping the angular distributions of Galactic cosmic rays through the induced average density gradient, the information encompassed in the angular distributions in the TeV--PeV energy range appear today as a promising tool to infer some properties of the local magnetic field environments. At the highest energies, the extragalactic origin of the particles has been recently determined observationally. While no discrete source of ultrahigh-energy cosmic rays has been identified so far, the noose is tightening around nearby extragalactic objects, and some prospects are discussed. | The origin of cosmic rays (CRs) remains an enduring question in astrophysics. A time-honoured paradigm is that sources of the bulk of these particles could be supernova remnants in the Galaxy. This is mainly because the intensity of cosmic rays observed on Earth can be produced by making use of $\simeq 10$\% of the energetics of these astrophysical objects~\cite{Zwicky1934}, and because the diffusive shock acceleration has been shown to be a mechanism able to convert kinetic energy of the expanding supernova blast wave into accelerated particles~\cite{Bell1978a,Bell1978b,Blanford1987}. However, alternative scenarios with sources related to transient events connected to the death of short-lived massive stars have also been put forward, such as in~\cite{LoebWaxman2006} for instance. The arrival directions of these particles are highly isotropic. This is expected from the propagation of charged particles in the interstellar medium where the directions of the particle momenta are randomized over time by the effective scattering in the encountered magnetic fields. Despite the scrambling action of these fields, searches for small anisotropy contrasts at large scales have been scrutinised over many decades as reviewed for instance in~\cite{Greisen1962,LinsleyWatson1977,DiSciascio2013}. During the past decade, multiple observatories located in both hemispheres have reported significant observations of large-scale and small-scale anisotropies in the TeV--PeV energy band. These results have challenged the long-standing description of CR propagation in terms of a typical spatial diffusion process from stationary sources located preferentially in the disk of the Galaxy, leading to a dipole moment only in the direction of the CR gradient and with an amplitude steadily increasing with the energy. The current picture is much more complex and elaborate~\cite{AhlersMertsch2016}. Galactic CRs are thought to be retained by the Galactic magnetic field as long as the size of their Larmor orbit diameter is much less than the thickness of the Galactic disk. Since the strength of the magnetic field is of the order of microgauss, Galactic CRs might be confined in the Galactic disk up to energies of $100~Z~$PeV, with $Z$ the charge of the particles. Once particles are not confined anymore, the time they spent in the disk tends to the constant free escape time due to the direct escape from the Galaxy. The observed intensity should then be naturally much stronger towards the disk compared to other directions. Due to their high level of isotropy, CRs with energies in excess of $\simeq 1~$EeV have thus long been thought to be of extragalactic origin. In addition, even in the presence of efficient magnetic field amplification at the supernova remnant shock, accelerating intermediate or even heavy nuclei at EeV energies is very challenging~\cite{Blasi2013}. On the other hand, Hillas pointed out the plausible classes of astrophysical objects in which Fermi acceleration could perform up to 100~EeV or so through the essential requirement that the particle Larmor radius must be smaller than the size scale of the acceleration region~\cite{Hillas1984}. Thanks to the jump in statistics as well as to the improved instrumentation experienced in the past decade with the Pierre Auger Observatory, CRs with energies in excess of $\simeq 8~$EeV have indeed been recently observed to originate from extragalactic galaxies~\cite{AugerScience2017}. The exact sources remain, however, unknown since the first detection of a particle with energy in excess of 100~EeV by Linsley at the Volcano Ranch in 1963~\cite{Linsley1963a}. The intervening magnetic fields in extragalactic space and in the Galaxy are uncertain, although the understanding of the magnetic fields in the Milky Way has developed over many decades and has allowed for quantitatively-constrained models to emerge~\cite{JanssonFarrar2012}. The uncertainties remain however too large to firmly predict the deflections that ultra-high energy cosmic rays (UHECRs) should undergo from each line of sight outside from the Galaxy. The effect of the turbulent component of the field is particularly uncertain~\cite{FarrarSutherland2017}. The expected order of magnitude for the deflections is thought to behave as $\simeq 3^\circ Z(E/100~\mathrm{EeV})^{-1}$. With such an order of magnitude, magnetic deflections could be small enough to allow for mirroring to some extent the distribution of sources in the sky. Moreover, the horizon of the highest energy particles ($\gtrsim 60~$EeV) is limited as compared to that of particles of lower energies, because the thresholds are then reached of interactions with background radiations filling the Universe and leading to large energy losses. This is the ``GZK effect''~\cite{GZK}, which allows that only the foreground sources are expected to populate the observed sky maps at these energies. But the small intensity combined to the potential absence of particles with low electric charge at these energies still prevents such a ``charged-particle astronomy'' with current data. All these topics are addressed in detail in this review under the prism essentially of the results obtained during the last decade. This review is meant to be an introduction to the main analysis techniques as well as to the formalisms needed to interpret the results. In this sense, and to allow an introduction to the latest theoretical advances, many classical results are developed from the first principles by reviewing the main steps to derive them. After introducing the basic quantities of interest to decipher the underlying angular distributions of CRs from ground-based experiment data in~\S~\ref{sec:observations}, the guiding thread of this review is to characterize anisotropies from large to small scales, by presenting the experimental results and their interpretations as a function of energy. Thus, harmonic analysis methods in right ascension, traditionally focused on the first harmonic, are first approached in~\S~\ref{sec:harmonic} and their astrophysical consequences discussed in~\S~\ref{sec:astro}. The 3D reconstruction of the intensity on the sphere and the characterization of the anisotropies in terms of power spectrum are the subject of the next two sections, reviewing the analysis techniques in~\S~\ref{sec:3dreco} and the interpretations in~\S~\ref{sec:highorder}. Finally, \S~\ref{sec:xgal} is devoted to the highest energies, because of the specific techniques, which can in particular involve external information such as catalogs of extragalactic astrophysical objects. | \label{sec:conclusion} During the past decade, important observational results have been reported on the angular distributions of TeV--PeV CRs. While only dipolar excesses were expected, the myriad of reported anisotropies has led to important progresses on the understanding of the propagation regime of low-energy Galactic CRs. Overall, the information encompassed in the angular distributions appear today as a tool allowing a possible probe of the local magnetic field environments. In contrast, the quest for finding UHECR sources is more difficult than expected a decade ago. Recent correlations with nearby extragalactic objets look promising. Future work will profit from the increased statistics and ability to perform anisotropy searches with distinction based on the mass of the primaries as anticipated with the upgraded instrumentation at the Pierre Auger Observatory. However, another jump in statistics appears necessary, keeping similar observable resolutions. | 18 | 8 | 1808.03940 |
1808 | 1808.08055_arXiv.txt | {By analysing a database of 26 years of observations of Jupiter with the Nan\c{c}ay Decameter Array, we unambiguously identify the radio emissions caused by the Ganymede-Jupiter interaction. We study the energetics of these emissions via the distributions of their intensities, duration, and power, and compare them to the energetics of the Io-Jupiter radio emissions. This allows us to demonstrate that the average emitted radio power is proportional to the Poynting flux from the rotating Jupiter's magnetosphere intercepted by the obstacle. We then generalize this result to the radio-magnetic scaling law that appears to apply to all plasma interactions between a magnetized flow and an obstacle, magnetized or not. Extrapolating this scaling law to the parameter range corresponding to hot Jupiters, we predict large radio powers emitted by these objects, that should result in detectable radio flux with new-generation radiotelescopes. Comparing the distributions of the durations of Ganymede-Jupiter and Io-Jupiter emission events also suggests that while the latter results from quasi-permanent Alfv\'en wave excitation by Io, the former likely results from sporadic reconnection between magnetic fields Ganymede and Jupiter, controlled by Jupiter's magnetic field geometry and modulated by its rotation.} | \label{Introduction} Nearly 4000 exoplanets have been discovered in the past two decades (http://exoplanet.eu), but little is known yet on their interior and their rotation. It has been demonstrated that detection of their non-thermal magnetospheric radio emission will provide unique information on their magnetic field (and thus their internal structure), their rotation (directly testing spin-orbit synchronization), their orbit inclination, and the presence of satellites \citep{Hess2011,Zarka2015,Lazio2017}. Solar system exploration has revealed that the magnetospheres of Mercury, Earth, Jupiter, Saturn, Uranus, and Neptune, although resulting from the same basic plasma physics processes, show a remarkable diversity of structure and dynamics \citep{Bagenal2013}. The cyclotron maser instability (CMI) has been identified as the ubiquitous mechanism that produces the dominant high-latitude low-frequency radio emissions from these magnetospheres \citep{Zarka1998}. It is therefore expected that the detection of CMI emissions from star-exoplanet systems will shed light on their plasma interactions and open a new field of comparative exo-magnetospheric physics. Moreover, the existence of a substantial planetary magnetic field seems to favour the planet's capability to host life as it protects the atmosphere against bombardment by cosmic rays, stellar flares, and coronal mass ejections, and limits atmospheric escape \citep{Griessmeier2004,Griessmeier2005}. In our solar system, the most intense radio emission is the decameter-wave radiation emitted by Jupiter's magnetosphere. However, although it is often as bright as solar radio bursts at frequencies below 40 MHz, it is at least $10^{3-4}$ times too weak to be detectable against the statistical fluctuations of the galactic radio background at a distance of several parsecs, even with the largest existing low-frequency radiotelescopes like UTR-2 and LOFAR \citep{Zarka2007}. The central questions conditioning radio searches for exoplanets are as follows. (1) How much can radio emissions be stronger than Jupiter's planetary -- or planet-induced -- emission? (2) How does one select the best targets to observe? In spite of our good understanding of the CMI, there is no simple answer from first principles because the wave growth depends on the detailed distribution of keV electrons in the source and the final radio intensity depends on the source structure and size as well as on the interplay of wave convection with various saturation processes (quasi-linear diffusion, non-linear trapping). Empirical scaling laws were therefore derived for answering the above questions, in which the primary engine of the radio emission is the kinetic or magnetic power input from the solar wind to planetary magnetospheres. Average radio powers emitted by planetary magnetospheres were indeed found to be proportional to both the bulk kinetic energy flux and the magnetic energy (or Poynting) flux from the solar intercepted by the magnetosphere \citep{Zarka2001,Zarka2007}. This double correlation comes from the fact that the kinetic and magnetic energy fluxes carried by the solar wind remain in a constant ratio ($\sim$170) between the Earth and Neptune. Determining which one of the two is the real physical driver of the radio emissions is crucial for selecting observation targets. If it is the kinetic energy flux, we should select exoplanets orbiting massive stars with a large mass-loss rate \citep[e.g.][]{Ogorman2018}. If it is the magnetic energy flux, we should aim at exoplanets orbiting strongly magnetized stars \citep[e.g.][]{Folsom2016,Folsom2018}. In both cases, close-in exoplanets (hot Jupiters) should be interesting targets because both energy fluxes increase with decreasing distance to the star. In order to determine which scaling law applies, the paradigm of solar wind--planet interaction was generalized to the interaction between a magnetized flow and a conductive obstacle (magnetized or not), leading to dissipation of the flow's power (kinetic and magnetic) on the obstacle, a fraction of which goes into electron acceleration and precipitation generating radio emissions \citep{Zarka2017b}. This paradigm can be applied to satellite-Jupiter interactions. Only the Io-Jupiter (hereafter I--J) radio emission is quantitatively documented so far, and it seems compatible with the radio-magnetic scaling law only, rough estimates only being available for the other Jovian moons \citep{Zarka2001,Zarka2007}. Unlike bodies embedded in the solar wind, interaction of Jupiter's magnetosphere with the Jovian moons is dominated by the flow of magnetic energy. This flow proceeds via Alfv\'en wave excitation at Io \citep{Saur2004}, and magnetic reconnection at Ganymede which possesses an intrinsic magnetic field \citep{Kivelson2004}. Here we analyze the database of 26 years of radio observations of Jupiter with the Nan\c{c}ay Decameter Array, built by \citet{Marques2017}. In Sect. 2, we detail the unambiguous detection of Ganymede-Jupiter (hereafter G--J) decameter emission from this database. Over 350 G--J emission events are detected, that constitute the basis for the first quantitative study of their energetics (intensity, duration and power) (Sect. 3), that is then compared to the energetics of I--J emissions. In Sect. 4, we combine the results obtained for I--J and G--J emissions to the scaling laws relating radio powers to incident kinetic or magnetic energy fluxes, and we show that the radio-magnetic scaling law provides a general frame for all radio emissions resulting from a flow--obstacle interaction. Then, we extrapolate this scaling law to the hot Jupiters regime and predict radio powers -- and hence flux densities -- $10^{3-7}$ times stronger than Jupiter's. Finally, in Sect. 5 we discuss emission detectability, relevance and limitations of the radio-magnetic scaling law, and further consequences of our study on the timescales of magnetic reconnection between Ganymede and Jupiter. \begin{figure*}[ht!] \centering \resizebox{.9\hsize}{!}{\includegraphics{ganymede_fig1.pdf}} \caption{Occurrence probabilities of Jovian radio emissions detected over 26 years (1990-2015) with the Nan\c{c}ay Decameter Array, displayed as 2D histograms as a function of planetary rotation (CML = Central Meridian Longitude = sub-observer's longitude) and of the orbital phase of the considered satellite, in $5^\circ\times5^\circ$ bins (interpolation at $1^\circ$ resolution was applied to smooth the display). $(a)$ Occurrence probability of all emissions vs. CML and Io's orbital phase. The regions of high occurrence within letter-labelled white boxes correspond to Io-Jupiter emissions (usually named Io-A, Io-B \dots), whereas vertical bands of emission covering restricted CML ranges at all Io phases correspond to non-Io emissions (auroral or induced by other satellites). Different line styles are used to better distinguish overlapping boxes. $(b)$ Occurrence probability of non-Io emissions vs. CML and Ganymede's orbital phase. Ganymede-Jupiter emissions show up within new regions of enhanced occurrence (white boxes), labelled A to D in reference to the non-Io components in which they have been identified (see Fig. \ref{fig02} for details).} \label{fig01} \end{figure*} | Based on the recent 26-year database of Jupiter observations with the Nan\c{c}ay decameter array built by \citet{Marques2017}, the prominent I-J component was revisited (Figs. \ref{fig01}$a$ and \ref{fig03}$a,c$) and the G-J component was detected unambiguously \citep[Figs. \ref{fig01}$b$ and \ref{fig03}$b,d$, and][]{Zarka2017a}. More than 350 G-J emission events were detected in the interval 1990-2015 (Table 1), making it possible to statistically characterise their duration, intensity, and, therefore, energetics (average power), and compare them to those of I-J emission events. We have found that G-J emissions have typical intensities only $\sim$0.5 dB lower than I-J or non-Io emissions (Fig. \ref{fig04}$a$). This suggests that CMI operates at relatively uniform efficiency around Jupiter, where the various radio components are produced, whatever the origin of the accelerated electrons, leading to similar intensity distributions for all radio components. However, the temporal behaviours of G-J and I-J emissions are very different. G-J emissions are much (7.8 times) less frequent than I-J emissions (Fig. \ref{fig04}$a$), and have a typical duration $\sim$1.25 times longer than that of non-Io (auroral) emissions, but $\sim$1.7 times shorter than that of I-J emissions (Fig. \ref{fig04}$b$). These properties can shed light on the physics of the interaction of Ganymede and Jupiter via magnetic reconnection. Non-Io emission events are believed to be associated with "hot spots" (localized precipitations) along Jupiter's main auroral oval \citep{Bagenal2017}. As CMI emission is strongly anisotropic (beamed in a hollow conical sheet widely open around the magnetic field within the source), Jupiter's rotation carries the beam out of the observer's view in a few tens of minutes. I-J emission being tied to Io's flux tube, the radio beam moves with Io's orbital motion, four times slower than Jupiter's rotation, which explains a duration of I-J events much longer than non-Io ones, assuming that the I-J emission is produced in a quasi-permanent way \citep{Louis2017b}. If the G-J radio emission was permanent, emission events would last even longer due to the slower orbital motion of Ganymede \citep{Louis2017a}. Figure \ref{fig04}$b$ shows that this is not the case, and that G-J emission events are likely controlled by Jupiter's rotation. We propose that the G-J interaction via reconnection is governed by a substorm-like regime of storage and sporadic release of energy controlled by Jupiter's rotation, in contrast with an I-J interaction governed by more steady excitation of Alfv\'en waves. Such waves are also likely produced in the wake of Ganymede, following the last reconnection of Jovian magnetic field lines with Ganymede's magnetosphere, but they do not seem to generate detectable emissions comparable to (and longer than) I-J ones. Our main result is that Ganymede- and Io-induced radio powers are in the same ratio as the magnetic power input that they intercept from the magnetosphere, in spite of the different interactions of these moons with Jupiter's magnetosphere (primarily via Alfv\'en waves for Io and magnetic reconnection for Ganymede). Auroral, Io-induced, and Ganymede-induced radio emissions are all found to fit a radio-magnetic scaling law. Quantitative inclusion of G-J and I-J radio emissions strongly grounds this scaling law, the extrapolation of which allows us to predict strong -- potentially detectable -- radio emissions from hot Jupiters. Recent theoretical works \citep{Nichols2011,Saur2013,Nichols2016} that examined specific cases of flow-obstacle magnetic interaction generally agree with the radio-magnetic law, although their quantitative predictions for exoplanets may differ by one order of magnitude for giant planets, and up to two for Earth-like planets, over a total range $\geq$10 orders of magnitude covered by the scaling law. Figures \ref{fig07}$b,c$ characterise average powers for planets orbiting a solar-type star (i.e. with a solar-like magnetic field of $\sim$1 Gauss). Stronger stellar magnetic fields should lead to stronger radio emissions. Intrinsic variability of radio emission is also superimposed on the average behaviour of Fig. \ref{fig07}$b,c$ and may lead to stronger radio bursts. Radio scintillation can temporarily further increase the received flux density by $>$1 order of magnitude. Overall, detectable emissions levels should exist for at least a fraction of the known hot Jupiters, provided that high enough frequencies are emitted (above a few 10's MHz). Very favourable targets are hot Jupiters orbiting stars more strongly magnetized than the Sun, where radio emission can be excited by the planet interaction with the star's magnetic field in a giant analogue of the I-J or G-J systems (and for which the predicted radio power is also increased). This suggests that radio detection of exoplanets should occur soon provided that enough hot Jupiter targets are monitored, which will be the case with the deep surveys of LOFAR \citep[ongoing,][]{Shimwell2017} and SKA \citep[in preparation,][]{Zarka2015}. | 18 | 8 | 1808.08055 |
1808 | 1808.06612_arXiv.txt | {We predict quantitative mass-loss rates and terminal wind velocities for early-type supergiants and luminous blue variables (LBVs) using a dynamical version of the Monte Carlo radiative transfer method. First, the observed drop in terminal wind velocity around spectral type B1 is confirmed by the Monte Carlo method -- at the correct effective temperature of about 21\,000 K. This drop in wind velocity is much steeper than would be expected from the drop in escape speed for cooler stars. The results may be particularly relevant for slow winds inferred for some High-Mass X-ray binaries. Second, the strength of the mass-loss bi-stability jump is found to be significantly larger than previously assumed. Not only could this make bi-stability braking more efficient in massive star evolution, but a rotationally-induced version of the bi-stability mechanism may now be capable of producing the correct density of outflowing disks around B[e] supergiants, although multi-dimensional modelling including the disk velocity structure is still needed. For LBVs, we find the bi-stability jump to become larger at higher metallicities, but perhaps surprisingly also larger at {\it lower} Eddington parameters. This may have consequences for the role of LBVs in the evolution of massive stars at different metallicities and Cosmic Epochs. Finally, our predicted low wind velocities may be important for explaining the slow outflow speeds of supernova type IIb/IIn progenitors, for which the direct LBV-SN link was first introduced.} | \label{s_intro} Mass loss is an important driver of massive star evolution (Chiosi \& Maeder 1986; Langer 2012). This is thought to occur via stationary stellar winds on \& off the main sequence (Vink \& Gr\"afener 2012; Groh et al. 2014), and possibly also in eruptive mode during Luminous Blue Variable (LBV) events (Shaviv 2000; Smith \& Owocki 2006; Owocki 2015). Although detailed stationary wind models of LBVs have been constructed by Vink \& de Koter (2002) using the Abbott \& Lucy (1985) Monte Carlo radiative transfer approach, the predicted mass-loss rates (\mdot) were semi-empirical in nature, and assumed terminal wind velocities (\vinf). Dynamical modelling has yet to be explored. In this paper, we will employ the dynamically-consistent approach of M\"uller \& Vink (2008) to predict velocity structures and mass-loss rates for a range of OB supergiants and LBV models, as well as their metallicity ($Z$) dependence. Pauldrach \& Puls (1990) first encountered the bi-stability jump in modelling the wind of the LBV P\,Cygni. Lamers et al. (1995) subsequently found observational evidence for the bi-stability jump through a drop in wind velocities by a factor of two for a sample of supergiants around spectral type B1 -- at an effective temperature of about 21\,000 K (see also Crowther et al. 2006). It it was originally assumed that the jump was caused by the optical depth of the Lyman continuum, until Vink et al. (1999) showed that the recombination of the main line-driving element iron (Fe) caused an increased amount of line acceleration from Fe {\sc iii} -- and an increase in the mass-loss rate by a factor of five. As these models were semi-empirical in nature, the drop in terminal wind velocity has yet to be theoretically modeled. The issue of whether the mass-loss rate increases at the bi-stability location, as predicted, or whether it drops instead as suggested by empirical results (Trundle et al. 2004; Crowther et al. 2006; Benaglia et al. 2007; Markova \& Puls 2008; Morford et al. 2016), remains unresolved, and may depend on the question whether the discrepancy may be attributed to macro-clumping, as Petrov et al. (2014) showed that the H$\alpha$ line changes its character completely, from an optically thin to an optically thick line below the bi-stability jump. In the current paper, we present new dynamically consistent mass-loss predictions on both sides of the bi-stability jump, and in turns our that we are indeed able to confirm the observed drop in terminal wind velocities. Moreover, we predict an even {\it stronger} jump in the mass-loss rate by a {\it factor of 10} than the factor of $\sim$5 that we found originally, with relevant consequences for massive star evolution, including the efficiency of bi-stability braking (Vink et al. 2010), the possible formation of B[e] supergiant disks (Lamers \& Pauldrach 1991), the slow winds in High-Mass X-ray binaries (HMXBs), LBVs as supernova SN progenitors (Trundle et al. 2008; Groh \& Vink 2011), and very massive stars (VMS) as the possible origin of observed chemical anti-correlations in globular clusters (Vink 2018). In Sects.~\ref{s_model} we briefly describe the Monte Carlo modelling and physical assumptions. In Sect.~\ref{s_res} mass-loss rates and wind terminal velocities are presented for a canonical 60 \msun\ supergiant across the temperature regime of the bi-stability jump, whilst Sect.\,\ref{s_lbv} describes similar results for LBVs, characterized by a larger Eddington $\Gamma$ parameter. The $Z$ dependence is discussed in Sect.\,\ref{s_lbvz}, before ending with a summary in Sect.~\ref{s_sum}. | \label{s_sum} We presented mass-loss predictions from Monte Carlo radiative transfer models for early-type supergiants and LBVs, and we found that: \begin{itemize} \item{The previously discovered observed drop in terminal wind velocities at spectral type B1 is confirmed by our dynamically consistent supergiant models.} \item{The bi-stability jump in mass-loss rate is stronger than was derived in previous Monte Carlo modelling.} \item{This would imply that within the rotationally induced bi-stability model of Pelupessy et al. (2000) for B[e] supergiants, the expected density contrast between the hotter pole and cooler equator could increase by up to one order of magnitude -- to a factor 100 -- which may be sufficient to account for the disk densities of B[e] supergiants, although the disk velocity structure would still need to be explained}. \item{Our wind predictions may have relevance for the slow wind inferred for the HMXB IGR J17252-3616, or other HMXBs.} \item{The temperature of the bi-stability jump is now at the observed location of 21\,000 K, in agreement with {\sc cmfgen} models. This boosts confidence in the applicability of the modified nebular approximation.} \item{The bi-stability jump is larger at {\it lower} Eddington $\Gamma$ parameter.} \item{The bi-stability jump is larger at higher metallicity.} \end{itemize} | 18 | 8 | 1808.06612 |
1808 | 1808.03393.txt | We study reheating in some one and two field realizations of {\it Fibre Inflation}. We find that reheating begins with a phase of preheating in which long wavelength fluctuation modes are excited. In two field models there is a danger that the parametric amplification of infrared fluctuations in the second scalar field - associated with an entropy mode - might induce an instability of the curvature fluctuations. We show that, at least in the models we consider, the entropy mode has a sufficiently large mass to prevent this instability. Hence, from the point of view of reheating the models we consider are well-behaved. | The reheating phase (see e.g. \cite{ABCM, Karouby} for recent reviews) is an integral part of any successfull inflationary model. The inflationary phase leaves behind a state with an exponentially suppressed density of matter particles \footnote{Warm inflation \cite{Berera} is an exception as in this scenario matter particles are produced continuously and efficiently throughout the inflationary phase, and there is no need for a separate period of reheating.}, and a mechanism is required which transforms the energy trapped in the homogeneous inflaton \footnote{The inflaton is the scalar field whose potential energy drives the inflationary expansion.} condensate to quanta of the regular matter fields. Initially, reheating was studied perturbatively \cite{AFW, DL, Stein}, but this neglects the coherent nature of the inflaton condensate. It was then realized \cite{TB, DK} that the reheating phase may begin with a period of parametric resonance instability called {\it preheating} \cite{KLS1, STB, KLS2} during which the oscillations of the inflaton condensate lead to exponential increase in the number density of long wavelength fluctuations of either the inflaton field itself (``self-resonance'') or of fields which are coupled to the inflaton. The resulting state of matter after preheating has a non-thermal distribution, and hence a second stage of reheating is required in order to obtain full kinetic and chemical equilibrium. The equation of state of matter becomes radiation-dominated even after an efficient preheating period. Since the detailed predictions of any inflationary model for observations depends on the length of the period after inflation before the onset of radiation-domination \footnote{The number of e-foldings before the end of inflation when fluctuations on a given physical scale today exit the Hubble radius and hence the inflationary slow-roll parameters evaluated at that scale depend on the length of the reheating phase before the onset of radiation-domination.} it is important in any inflationary model to study the possible presence of parametric resonance. One might fear that the exponential increase in infrared matter fluctuations during preheating might lead to an exponential increase of the cosmological fluctuations \cite{BKM} \footnote{Note that such a process would not violate causality \cite{FB1} since we are talking about modes which, although must larger than the Hubble radius $H^{-1}$ at the time of reheating, are smaller than the horizon.}. In single matter field models, however, this does not happen since the curvature fluctuations are conserved on super-Hubble scales, as can be shown even beyond perturbation theory (see e.g. \cite{LV, AB}). However, in models in which there are extra light fields in addition to the inflaton, there is the danger than fluctuations in the extra fields will also experience parametric resonance of infrared modes \cite{FB2, BV}. If the fluctuations of these entropy modes are coupled to the curvature fluctuations, then the exponentially amplified entropy fluctuations could induce exponentially enhanced curvature fluctuations - on scales which are measured today, hence destroying the agreement between theory and observations. Toy models in which such a dangerous amplification of entropy modes occurs were studied in \cite{us}. On the other hand, it was shown that a number of string-motivated inflationary models such as D3-D7 brane inflation \cite{D3D7} and axion monodromy inflation \cite{axion} are safe from this potential problem. Fibre inflation \cite{Cicoli} is a popular model of inflation motivated by ideas from string theory \footnote{We are not addressing here the possibility that this model lies in the {\it swampland} \cite{swamp} and it not consistent with principles of superstring theory \cite{Vafa}.}. In this paper we show that in the versions of the scenario which we consider here, reheating begins with a period of preheating \footnote{The possibility of preheating in fibre inflation was also considered in \cite{Antusch}, and the macro reheating properties in \cite{Cabella:2017zsa}.}. On the other hand, we show that the entropy modes are sufficiently heavy such that no efficient resonance of these modes occurs during the phase of preheating. Hence, it appears that from the point of view of reheating constraints, the fibre inflation model is safe. A word on our notation: we use natural units in which the speed of light and Planck's constant are set to $1$. Unless otherwise indicated we work in units in which the Planck mass is also set to $1$. We work in the context of a spatially flat homogeneous and isotropic background cosmology given by the metric %% \begin{equation} \mathrm{d}s^2 \, = \, -\mathrm{d}t^2 + a(t)^2 \mathrm{d}{\bf x}^2 \, , \end{equation} %% where $t$ is physical time, ${\bf x}$ are the comoving spatial coordinates, and $a(t)$ is the cosmological scale factor. The Hubble expansion rate is %% \begin{equation} H(t) \, \equiv \, \frac{{\dot a}}{a} \, . \end{equation} %% There are two coupling constants which appear in string theory. The first is the string coupling constant $g_s$ which measures the strength of the string interactions. The value of $g_s$ is set by the expectation value of the string theory dilaton field. The second coupling constant $\alpha^{`}$ measures the strength of quantum effects. It is given by the square of the string length. | We have studied the reheating phase in fibre inflation, taking the parameters used in \cite{Cicoli}. In this model, there are two relevant ``light'' degrees of freedom. They come from the moduli fields of the model. In a first approximation, we (following \cite{Cicoli}) have focused on the modulus field which taken by itself can lead to inflation. We have shown that the reheating phase in this model begins with a phase of parametric self-resonance during which a not negligible fraction of the inflaton energy is transferred to low momenta quanta of the inflaton. We then considered the effects of the second lightest field. In order for the model to be safe, it is important to check that there is no strong parametric resonance of the fluctuations in this second field. Otherwise, the induced entropy fluctuations might lead to a contribution to curvature fluctuations which would destroy the successful predictions of the model. We have shown that, although the second field is light compared to the string scale, it is sufficiently heavy compared to the Hubble scale at the end of inflation such that super-Hubble entropy fluctuations cannot grow. We have chosen the parameters of fibre inflation suggested in \cite{Cicoli}. It would be interesting to scan a wider parameter space of fibre inflation models and search for regions where there is a parametric instability of the entropy mode. | 18 | 8 | 1808.03393 |
1808 | 1808.08439_arXiv.txt | UV solar irradiance strongly affects the chemical and physical properties of the Earth's atmosphere. UV radiation is also a fundamental input for modeling the habitable zones of stars and the atmospheres of their exo-planets. Unfortunately, measurements of solar irradiance are affected by instrumental degradation and are not available before 1978. For other stars, the situation is worsened by interstellar medium absorption. Therefore, estimates of solar and stellar UV radiation and variability often rely on modeling. Recently, \citet{lovric2017} used SORCE/SOLSTICE data to investigate the variability of a color-index that is a descriptor of the UV radiation that modulates the photochemistry of planets atmospheres. After correcting the SOLSTICE data for residual instrumental effects, the authors found the color-index to be strongly correlated with the Mg II index, a solar activity proxy. In this paper we employ an irradiance reconstruction to synthetize the UV color and Mg II index with the purpose of investigating the physical mechanisms that produce the strong correlation between the color-index and the solar activity. Our reconstruction, which extends back to 1989, reproduces very well the observations, and shows that the two indices can be described by the same linear relation for almost three cycles, thus ruling out an overcompensation of SORCE/SOLTICE data in the analysis of \citet{lovric2017}. We suggest that the strong correlation between the indices results from the UV radiation analyzed originating in the chromosphere, where atmosphere models of quiet and magnetic features present similar temperature and density gradients. | Variations of Total Solar Irradiance (TSI) and Spectral Solar Irradiance (SSI) measured at different temporal scales affect the Earth's chemistry and dynamics, thus affecting the Earth's climate \citep[e.g.][]{matthes2006,gray2010,lockwood2011,ermolli2013,seppala2014,schwander2017, matthes2017}. It is well known that most of these variations are modulated by the magnetic activity, in particular by the appeareance on the solar surface of magnetic structures as plages and sunspots, which, in turn, modify the radiative properties of the solar atmosphere. The principal temporal scale of variability is the 11-year cycle, observed since the 17th century, along which both, the number of active regions and the total and spectral intensity vary. Of particular importance are variations measured at wavelengths shorter than approximately 400 nm, which is mostly absorbed by the high and medium layers of the Earth atmosphere. In particular, solar radiation at wavelengths shorter than 120 nm (Extreme UV) plays an important role in creating the Earth ionosphere. Irradiance variations at these wavelengths are responsible for variations of geomagnetic activity, may create disturbances in radio wave propagations and may modify satellite orbits due to the air-drug increase \citep[e.g.][]{floyd2002}. In the stratosphere, heating is caused by direct absorption of near-UV radiation in the Hartley (200-300 nm) and Huggins (320-360 nm) bands, whereas ozone photo-dissociation peaks in the Hartley continuum, at about 250 nm \citep{haigh1994}. Variations of ozone abundance, in turn, cause further heating which, through the top-down mechanism, changes the atmospheric dynamics, thus affecting the tropospheric circulation patterns \citep[][]{scaife2013,bordi2015,gray2016,matthes2017}. Variations of solar irradiance in the UV have been continuously monitored with various instruments since the launch of NIMBUS-7 in 1978 \citep[see for instance][for a review]{deland2012}, whereas continuous monitoring of the EUV started only in 2002 with the launch of the Thermosphere Ionosphere Mesosphere Energetic and Dynamics (TIMED). Unfortunately, measurements of solar irradiance are known to be affected by long-term instrumental degradation effects, so that while variations obtained with different instruments typically agree when compared on temporal scales of the order of a few solar rotations, large differences are found at the solar cycle and longer temporal scales \citep[e.g.][]{deland2012,ermolli2013,yeo2014}. Such discrepancies hinder estimates of the impact of solar activity on the Earth atmosphere properties and in particular of the ozone production \citep[e.g.][]{merkel2011,dhomse2016,matthes2017}. In order to provide the community with consistent spectra over long temporal scales (decades), and to extend them to times where measurements are not available, TSI and SSI measurements are complemented with independent estimates obtained with semi-empirical approaches \cite[e.g.][]{penza2006,fontenla2011,ermolli2011,yeo2014} and/or through regression analyses with proper activity indices \citep[e.g.][]{dudokdewit2009,bolduc2012,thuillier2012,coddington2016}. In the recent past, studies of solar variability have been also motivated by the necessity of improving our understanding of stellar variability \citep[e.g.][for a recent review]{fabbian2017}, with the aim of characterizing the habitable zones of stars and the atmospheres of their exo-planets. Likewise the Earth's atmosphere, modeling of exoplanets requires as fundamental input the radiation emitted by the host star in the UV and shorter bands \citep[e.g.][]{tian2014,madhusudhan2014,shields2016,omalley2017}. For this reason, large efforts have been dedicated to measure stellar UV and XUV spectra \citep[see][for a recent review]{linsky2017}, with recent particular interest in spectra of K and M dwarfs \citep[e.g.][]{france2016,youngblood2016}, their planets being suitable for spectroscopic biomarker searches \citep[e.g.][]{scalo2007,cowan2015,kaltenegger2017}. In the case of stellar fluxes, measurements in the FUV and shorter wavelengths are strongly hampered by interstellar medium absorption, which is significant even for relatively close stars. Consequently, estimates of spectra at these spectral ranges have to rely on models \citep[e.g.][]{wood2005,youngblood2016, fontenla2016} or proxies \citep[e.g.][]{linsky2013,shkolnik2014,smith2017}. It is important to note that there is no space mission scheduled in the near future aimed at observing stellar spectra in the UV and EUV ranges, so that after the Hubble Space Telescope will cease operations, estimates of spectra at short wavelengths will necessarily rely on the use of models and/or proxies measured at longer spectral ranges. Within this framework, \citet{lovric2017} introduced a spectral color index in the solar UV that is linked to the ratio between the flux integrate over the Far-UV and Middle-UV spectral broad-bands. Such a descriptor can be used to characterize UV stellar emission which modulates the photo-chemistry of molecular species, e.g., oxygen, in the atmospheres of planets \citep[e.g.][]{tian2014}. By using solar irradiance measurements obtained with radiometers aboard the Solar Radiation and Climate Experiment satellite \citep[SORCE,][]{ mcclintock2005} for almost a solar cycle, the authors showed that the color index so defined is linearly correlated with the Bremen Magnesium II index, which is an excellent proxy of the magnetic activity \citep{viereck2004}. Lovirc et a. showed that the correlation coefficient is slightly different for the descending phase of Cycle 23 and the ascending phase of the subsequent cycle. Such difference was ascribed to residual instrumental effects, which, when compensated for, lead to a correlation coefficient constant with time. On the other hand, several solar photospheric and chromospheric indices present a clear asymmetry during different phases of a cycle \citep[namely an hysteresis pattern, e.g.][]{bachmann1994,criscuoli2016,salabert2017}, whereas correlation coefficients between indices may vary from cycle to cycle \citep[e.g.][]{bruevich2014,tapping2017}, so that the question arises whether, and to what extent, the data corrections applied by \citet{lovric2017} might include a physical variation of solar emission. The purposes of this paper are to answer this question and to investigate the physical mechanisms determining the high linear relation between the UV spectral color index and solar activity measured with the Mg II index. To this aim we compare the results of \citet{lovric2017} with synthetic indices obtained with an irradiance reconstruction technique based on the use of semi-empirical atmosphere models and full-disk observations. The paper is organized as follows. In Sec.~\ref{sec:data} we describe the solar irradiance measurements analyzed, we describe the UV color index and briefly summarize the correction procedure applied to the data. In Sec.~\ref{sec:reconstruction} we describe in detail the irradiance reconstruction technique, and the input data and the radiative transfer utilized. Results are presented in Sec.~\ref{sec:result} and discussed in Sec.\~ref{sec:disc}. Finally, our conclusions are drawn in Sec.~\ref{sec:concl}. | \label{sec:concl} Results produced by the solar UV irradiance reconstructions presented in this paper reproduce with an excellent agreement the SORCE/SOLSTICE data trends compensated for instrumental degradation according to the method describe in \citet{lovric2017}. This suggests that the proposed technique does not overcompensate irradiance variations and, at the moment, rules out possible temporal variations of the [FUV-MUV] color - Mg II index relation, at least during the time range analyzed, confirming that the [FUV-MUV] color index strongly correlates with the Mg II index, with the UV color index decreasing as the magnetic activity increases. | 18 | 8 | 1808.08439 |
1808 | 1808.06424_arXiv.txt | We consider single-field inflation in light of string-motivated ``swampland'' conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion $\Delta \phi \lesssim \MP$, in combination with a sufficiently steep potential, $\MP V_\phi/V \gtrsim {\cal O}(1)$. Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the $n_S$-$r$ ``zoo plot" of inflationary models, and find that consistency with the Planck satellite and BICEP2/Keck Array requires $\MP V_\phi/V \lesssim 0.1$ and $-0.02 \lesssim \MP^2 V_{\phi\phi}/V < 0$, in strong tension with swampland conjectures. Extension to non-canonical models such as DBI Inflation does not significantly weaken the bound. | Inflation is a postulated period of quasi-de Sitter expansion in the very early Universe (see e.g. Refs.~\cite{Guth:1979bh,Kazanas:1980tx,Starobinsky:1980te,Guth:1980zm,Linde:1981mu,Sato:1981ds,Mukhanov:1981xt,Izawa:1982cu,Albrecht:1982wi,Linde:1983gd} for early seminal work). Inflation provides an explanation for various problems arising in the standard Big Bang cosmology such as the observed homogeneity, flatness, and lack of relic monopoles. In addition, inflation provides a mechanism for generating the density perturbations whose existence we infer from the observation of temperature anisotropies in the Cosmic Microwave Background Radiation (CMBR)~\cite{Guth:1982ec,Hawking:1982cz, Starobinsky:1982ee,Bardeen:1983qw,Steinhardt:1984jj}: these density perturbations, generated when quantum fluctuations leave the Hubble radius during inflation, later grow under gravitational instability to form the observed cosmic large-scale structure. Among the simplest class of inflationary models are single-field models, wherein a dynamical scalar field (the ``inflaton") evolves under the influence of a nearly-flat potential, leading to an approximately constant expansion rate. It would naturally be desirable to embed inflationary models within well-motivated high-energy UV-complete theories, with the latter possibly including a consistent description of quantum gravity: the behaviour of the inflaton field would then be captured by the effective field theory (EFT) given by the low-energy limit of this UV-complete theory. String theory naturally emerges as a potential candidate for such a UV-complete theory. While the huge landscape of string vacua is believed to lead to consistent EFTs, these are conjectured to be surrounded by a ``swampland" of semi-classical EFTs which do not allow for a consistent theory of quantum gravity~\cite{Vafa:2005ui}. Attempts to establish the conditions under which a given EFT does not lie in the swampland have led to a set of conjectures, such as the the weak-gravity conjecture~\cite{ArkaniHamed:2006dz} and, more recently, a set of additional swampland conjectures~\cite{Ooguri:2006in,Klaewer:2016kiy,Ooguri:2016pdq,Freivogel:2016qwc,Brennan:2017rbf,Obied:2018sgi}. In particular, it has long been noted that, while it is easy to obtain Minkowski and Anti-de Sitter vacua in string theory, the same cannot be said about de Sitter (dS) vacua, stable versions of which are notoriously extremely hard to obtain~\cite{Bena:2014jaa,Kutasov:2015eba,Moritz:2017xto,Danielsson:2018ztv}. This has raised the suspicion that theories featuring dS vacua reside in the swampland, rather than in the landscape~\cite{Dvali:2013eja,Obied:2018sgi}. This observation would obviously have profound implications for inflationary theories. Here, we focus on two swampland conjectures~\cite{Obied:2018sgi} whose cosmological implications were recently studied in Ref.~\cite{Agrawal:2018own}. These two conjectures, which we shall refer to as ${\cal SC}_1$ and ${\cal SC}_2$ respectively, place constraints on the proper range traversed by scalar fields in field space, $\Delta \phi$, as well as on the logarithmic gradient of the scalar field potential $V(\phi)$, \begin{eqnarray} \frac{\vert \Delta \phi \vert}{M_{\rm Pl}} \lesssim \Delta \sim {\cal O}(1)\, \quad \quad \left ( {\cal SC}_1 \right ) \,, \label{sc1}\\ M_{\rm Pl}\frac{\vert V_{\phi} \vert}{V} \gtrsim c \sim {\cal O}(1)\, \quad \quad \left ( {\cal SC}_2 \right ) \,, \label{sc2} \end{eqnarray} where $M_{\rm Pl} \simeq 2.4 \times 10^{18}\,{\rm GeV}$ is the reduced Planck mass, $V_{\phi}$ stands for $dV(\phi)/d\phi$, and $c$ is a positive constant of order unity whose actual value depends on the details of the compactification, but which in many string realizations is typically larger than $\sqrt{2}$ and never smaller than unity~\cite{Obied:2018sgi}. It is not hard to see how ${\cal SC}_2$ represents a hazard for inflationary theories, which typically require $V_{\phi} \ll V$ in order to sustain a sufficiently long period (of at least about 60 e-folds) of quasi-de Sitter expansion. The two swampland conjectures ${\cal SC}_1$ and ${\cal SC}_2$ have received significant attention in the recent literature, and various follow-up works have examined their implications for cosmology (including but not limited to inflation and dark energy) and more generally fundamental physics. For an incomplete list of relevant papers, see e.g. Refs.~\cite{Agrawal:2018own,Andriot:2018wzk,Dvali:2018fqu,Banerjee:2018qey,Achucarro:2018vey,Garg:2018reu,Lehners:2018vgi,Kehagias:2018uem, Dias:2018ngv,Denef:2018etk,Colgain:2018wgk,Roupec:2018mbn,Andriot:2018ept,Matsui:2018bsy,Ben-Dayan:2018mhe,Chiang:2018jdg,Heisenberg:2018yae,Damian:2018tlf,Gu:2018akj,Conlon:2018eyr, Visinelli:2018utg}. Several of these works, in particular, noticed that single-field slow-roll inflation is in tension with criterion ${\cal SC}_2$~\cite{Agrawal:2018own,Achucarro:2018vey,Garg:2018reu,Kehagias:2018uem,Dias:2018ngv}, since the latter places a lower bound on the amplitude of primordial gravitational waves produced during inflation, parametrized by the tensor-to-scalar ratio $r$. It can be easily shown that ${\cal SC}_2$ in Eq.~(\ref{sc2}) implies $r>8c^2$ for single-field slow-roll inflation~\cite{Dias:2018ngv}, and since current constraints from the \textit{Planck} satellite in combination with the BICEP2/Keck Array ground-based small aperture telescopes suggest $r<0.07$ at 95\% confidence level (C.L.)~\cite{Array:2015xqh}, a value of the parameter $c \sim {\cal O}(1)$ would strongly violate such bound. In this note, it is our goal to revisit the status of single-field slow-roll inflation in light of current observational data and the conjectured swampland criteria. However, unlike previous work which especially focused on the tensor-to-scalar ratio $r$, here we also consider the restrictions imposed by the second swampland criterion on the scalar spectral index $n_S$, including the second derivative of the potential. We consider for definiteness models where the potential of the inflaton is concave ($V_{\phi\phi} \equiv d^2V/d\phi^2<0$) rather than convex, since the former are observationally preferred over the latter. This allows us to reach a conclusion on the inconsistency between single-field slow-roll inflation, the swampland conjectures, and observational data, which is stronger than those previously reached focusing only on $r$. In particular, we find that single-field slow-roll inflaton potentials with $c>0.1$ are ruled out at $>95\%$ C.L. under generic assumptions based on string theory. We also consider constraints on the curvature of the potential in light of the more recently proposed ``refined'' swampland criterion \cite{Ooguri:2018wrx}, and place a lower bound $-0.02 \lesssim \MP^2 V_{\phi\phi}/V$, in strong tension with the refined conjecture. We then briefly consider convex potentials, restricting ourselves to the case where the inflaton is of the Dirac-Born-Infeld (DBI) form in order to circumvent tight constraints from overproduction of tensor modes, finding that our conclusions are qualitatively unchanged. The rest of this note is organized as follows. In Sec.~\ref{sec:si}, we briefly review the equations of motion in single-field slow-roll inflation and the definition of the slow-roll parameters. In Sec.~\ref{sec:observables}, we make the connection to the observables, namely the scalar spectral index $n_S$ and the tensor-to-scalar ratio $r$, focusing on concave potentials. In Sec.~\ref{sec:dbi}, we briefly consider the case of convex potentials where the inflaton is of the DBI form, and verify that our conclusions are qualitatively unchanged. Finally, in Sec.~\ref{sec:conclusions} we provide concluding remarks. Our main results are showcased in Fig.~\ref{fig:nsrplane}, where we make connection to the well-known ``zoo plot'' of inflationary models on the $n_S$-$r$ plane~\cite{Dodelson:1997hr}. | \label{sec:conclusions} In this note, we have revisited the status of single-field inflation in light of the swampland conjectures Eqs.~(\ref{sc1},\ref{sc2}). Unlike previous related works~\cite{Agrawal:2018own,Achucarro:2018vey,Garg:2018reu,Kehagias:2018uem,Dias:2018ngv}, we have focused not only on the implications of the swampland conjectures for the allowed values of the tensor-to-scalar ratio $r$, but also for the scalar spectral index $n_S$, under the generic expectation that the swampland conjectures lead to $\epsilon \sim \mathcal{O}(c^2)$ and data favour $\eta < 0$. Our main result is shown in Fig.~\ref{fig:nsrplane}, where we showcase the regions in the $n_S$-$r$ plane allowed by the swampland conjectures for various values of the parameters $c$ and $c'$, and compare these to the regions allowed by current observational data. We clearly see that $c \lesssim {\cal O}(0.1)$ and $c' \lesssim {\cal O}(0.01)$ are required to obtain consistency between the predictions of single-field slow-roll inflation and data, at the cost of violating the string-based expectation that $c, c' \sim {\cal O}(1)$. Extension to DBI models results in a constraint of $c \lesssim 0.37$, still in significant tension with the swampland conjectures. | 18 | 8 | 1808.06424 |
1808 | 1808.01803_arXiv.txt | Interior characterization traditionally relies on individual planetary properties, ignoring correlations between different planets of the same system. \rev{For multi-planetary systems, planetary data are generally correlated. This is because, the differential masses and radii are better constrained than absolute planetary masses and radii. We explore such correlations and data specific to the multiplanetary-system of TRAPPIST-1 and study their value for our understanding of planet interiors.} Furthermore, we demonstrate that the rocky interior of planets in a multi-planetary system can be preferentially probed by studying the most dense planet representing a rocky interior analogue. Our methodology includes a Bayesian inference analysis that uses a Markov chain Monte Carlo scheme. Our interior estimates account for the anticipated variability in the compositions and layer thicknesses of core, mantle, water oceans and ice layers, and a gas envelope. \rev{Our results show that (1) interior estimates significantly depend on available abundance proxies and (2) that the importance of inter-dependent planetary data for interior characterization is comparable to changes in data precision by 30\%.} For the interiors of TRAPPIST-1 planets, we find that possible water mass fractions generally range from 0-25\%. The lack of a clear trend of water budgets with orbital period or planet mass challenges possible formation scenarios. \rev{While our estimates change relatively little with data precision, they critically depend on data accuracy. If planetary masses varied within $\pm$ 24\%, interiors would be consistent with uniform ($\sim$7\%) or an increasing water mass fractions with orbital period ($\sim$2-12\%).} | \sloppy Among all exoplanetary systems known today, the TRAPPIST-1 system harbours the largest number of Earth-sized exoplanets in a single system. It is a tightly-packed system in which at least seven planets orbit an ultra-cool star \citep{gillon2017seven}. The proximity of the planets to their central star, the low stellar mass and stellar luminosity imply temperate conditions for the planets, with equilibrium temperatures ranging from about 160 to 400 K. Although characteristics of the planets remind us of Earth and Venus, the characteristics of star and system architecture seem very exotic compared to our Solar System. How systems like TRAPPIST-1 formed and evolved over time is an open and fascinating question that has motivated plenty of exoplanetary studies. Key to our understanding of the formation and evolution is the knowledge \rev{of the} composition and structure of the planetary interiors. Our ability to characterize planetary interiors depends on available observations and prior information. Prior information are based on laboratory work and theoretical considerations and yield important information, e.g., on the anticipated range of possible interiors. Astrophysical observations provide, e.g., planetary mass and radius, and orbital period. For our study, the observational data on planetary radii and masses are taken from \citet{delrez2018early} and \citet{Grimm2018}, respectively. The observed transit depths constrain ratios of planetary-to-stellar radii $R_{\rm p}/R_\star$ for each planet, while the transit timing variations (TTV) constrain ratios of planetary-to-stellar masses $M_{\rm p}/M_\star$ from gravitational interactions among all seven planets and the star. The planet bulk densities are then calculated from $\rho_{\rm p} = \rho_\star \frac{M_{\rm p}}{M_\star} \frac{R^3_\star}{R^3_{\rm p}}$, given the photometrically well-constrained stellar density $\rho_\star$ \citep{seager2003unique}. There are two important consequences that stem from this: (1) mass and radius for \emph{each} planet are correlated, and (2) planetary masses between the planets as derived by TTV are correlated, and (3) planetary radii between the planets are correlated. The correlation of the masses between all planets is a consequence of the planets being in a full resonance chain with each other. \rev{The correlation of planetary radii is because the differential radii (or differential transit depths) are better constrained than the absolute radii because the latter includes the uncertainty on stellar radii.} Correlation of data can have significant influences on the range of inferred planetary interiors. For an individual planet, the correlation of mass and radius has been taken into account for exoplanet interior characterizations \citep{weiss2016revised, crida2018mass}. However, the correlation of data between different planets of a single system has so far not been taken into account. In the present work, we develop a new resampling scheme that formally accounts for this interdependency of planetary \rev{data}. \rev{We demonstrate how our ability of constraining interiors is affected by data interdependencies using the example of planetary masses. We generally believe that it is important to make thorough use of \emph{all} available information (including the discussed data interdependencies) because observational data are few and expensive. Here, we provide the tool to do so. } Previous characterization studies demonstrated the value of refractory rock-forming element abundances as constraints in addition to planetary mass and radius \citep{sotin2007mass,dorn2015can}. \rev{Unfortunately, the host star is too faint ($V=19$) to measure photospheric abundances of refractory elements with available facilities. Measured elemental abundances in the stellar photosphere may otherwise be used as abundance proxies for the rocky planetary interiors}. Given a multi-planetary system, we can derive an abundance proxy based on the most dense planet of the system, because its interior will be dominantly rocky. TRAPPIST-1~e is the most dense and probably a purely rocky planet, given its high bulk density. Thus planet e may be seen as a rocky interior analogue of all planets in the system. We analyse the possible range of elemental abundances for planet TRAPPIST-1~e given only its mass and radius without abundance constraints. The obtained range of bulk abundances of TRAPPIST-1~e is subsequently used as constraints for the other planets. Alternatively, we also investigate the abundance constraint that was suggested by \citet{unterborn2017constraining}. \rev{We note that preliminary tests including new observations for TRAPPIST-1 that were previously unavailable for the study of \citet{Grimm2018} indicate shifts in planet massses within $\pm$24\% \citet{Demoryconf}. Also, \citet{kane2018impact} indicate changes in planetary radii on the order of +2\%. Therefore, our results and those of \citet{suissa2018trappist} and \citet{unterborn2018updated} should be taken with care. We show how much such systematic shifts could effect our interior estimates (Section \ref{systematics}). Nonetheless, our paper demonstrates how interior characterization for multi-planetary systems has extraordinary advances compared to individual planets. } The structure of our study is as follows. We briefly review previous studies on possible interiors of the TRAPPIST-1 planets (Section \ref{prv}). Then we describe our methodology that involves the new resampling scheme (Section \ref{method}). We demonstrate and discuss our results (Section \ref{results}) in light of possible formation and evolution paths of the planets (Section \ref{discussion}), and provide a summary in the conclusions (Section \ref{conclusion}). | \label{conclusion} The TRAPPIST-1 planets do not follow a single mass-radius trend, but there is some scatter among the bulk densities of planets. Here, we have quantified the origin of this scatter, that is mostly due to different amounts of water, but also to some extent the sizes of rocky interiors and the thicknesses of gas envelopes. Our analysis characterizes the nature of TRAPPIST-1 planet interiors while accounting for all available and relevant data. These include the correlated planetary masses \& radii, and stellar irradiation. In addition, we have tested different abundance constraints: a stellar proxy based on stars of similar metallicities as well as a proxy that is based on the most dense and probably a purely rocky planet of the system: planet e. The latter abundance proxy is unique to multi-planetary systems (see Section \ref{proxi}). Furthermore, there are data specific to multi-planetary systems that have not been considered in previous studies: the interdependency of planet masses between different planets as derived from TTV analysis, and the interdependency of planet radii between different planets as derived from TTV analysis. Here, we have developed a new resampling scheme (Section \ref{sec:resamp}) that allowed us to incorporate the information on interdependent data (Section \ref{interdep}). \rev{The information that we can gain on the interiors by accounting for interdependent planetary data can be important (up to 20\% differences) and even be as important as an improvement in mass and radius precision (Section \ref{sec:data}).} \rev{We highlight that the precision on the differential planetary data are much better than on absolute masses and radii. This is because the latter includes stellar uncertainties, while the former does not. By accounting for the correlations among all seven masses, we formally use the knowledge on the differential masses. For multi-planetatary systems, as demonstrated here for TRAPPIST-1, the use of differential planetary data is important for a thorough interior investigation.} \rev{Systematic biases of data can critically influence interior characterization. Care should be taken with our and all previous interior interpretations that critically depend on planetary masses and densities of TRAPPIST-1. Ongoing observational efforts indicate possible changes in mass accuracies within $\pm$ 24\% \citep{Demoryconf}. In this case, all interiors could be consistent with an increasing water mass fraction with orbital period (within 2-12 \% with respect to 1-$\sigma$ errors) or a uniform water mass fraction of ~7\% (within 1-$\sigma$ errors). This is in contrast with our findings based on the most recent data publications \citep{Grimm2018, delrez2018early} that we summarize below:} \begin{itemize} \item TRAPPIST-1~e can be a super-Mercury type planet with non-Earth-like bulk abundance. This is obvious from the \rev{high bulk density} as determined by \citep{Grimm2018} and was discussed by \citep{suissa2018trappist}. Here, we have quantified the rocky composition of planet e to be characterized by Fe/Si$_{\rm T1e}= 11.2 \pm 5.7$ and Mg/Si$_{\rm T1e} = 5.7 \pm 3.7$. If the rocky composition of planet e was indeed different from the other planets, it could be due to a giant impact that has not only stripped-off parts of the mantle \citep{benz1988} but also removed volatile-rich layers. Such a scenario would explain why planet e is much drier than the other planets. However, this scenario would require an impactor larger than planet e, which does not exist in the system and it remains to be studied if impacts are a reasonable scenario. In this scenario, the interiors predicted for all planets might be well described by \U, with the exception of planet e that is best described by \A. \item Alternatively, TRAPPIST-1~e may not be a super-Mercury type planet. There are two interpretations possible under this premise. \begin{itemize} \item First, it is possible that systematic errors of the TTV analysis due to the limited observation time and yet undetected planets in the system, may bias the planetary masses including planet e. If this is the case, the stellar proxy would be the important constraint to favour rather Earth-like interiors for planet e, dismissing high bulk-density interiors. Consequently, due to the interdependency of planetary data, the information kept in the level of incompatibility of data (in scenario \U using the stellar proxy) propagates to all other planets, yielding better constrained interiors by excluding some interior models. In other words, for all planets there is only a subset of interiors that is in agreement with all available data on all planets, their interdependencies, and the stellar proxy. If this case is true, all interiors are well described by scenario \UCM. \item Second, it is possible that the interiors of TRAPPIST-1 planets cannot be described by Earth-like interiors or the suggested stellar proxy. Instead the purely rocky interior of all planets is directly probed by the most dense planet, planet e, assuming that all rocky interiors have similar ratios of rock-forming elements (Mg, Si, Fe). In this case, all predicted interiors are best described by scenario \A. \end{itemize} \item Differences between estimated interiors are large when comparing different abundance constraints (\U and \A). This demonstrates the need to better understand the relative amounts of refractory, rock-forming elements in dwarf systems, like TRAPPIST-1, which probably also depend on our knowledge of the age of the system. Unfortunately, direct estimates of the photosphere of the faint TRAPPIST-1 are unavailable. Both possible abundance constraints based on stars with similar metallicities (\U) and based on the most dense planet (\A) can be justified. However it is difficult to state a clear preference. \item \rev{The information that is kept in the interdependency of planetary data is a valuable constraint that can significantly effect interior estimates. For example, estimated median water budgets can vary up to 20 \% (compare scenarios \U and \UCM). Accounting for interdependency of planetary data compares with changes in data precision of 30\%. } \item Mass and radius data only carry limited information about planetary interios and additional data types are required to significantly improve interior estimates. For example, the improvement on predicted amounts of water due to more precise data (70\% of nominal data uncertainties) is rather small compared to changes in abundance proxies (\U and \A). \item Our inferred ranges of water contents of 0-25\% are high compared to terrestrial Solar System planets, and are smaller by a factor of two compared to predictions from formation studies \citep{alibert2016formation}. Volatile-rich interiors of planets in dwarf star systems are predicted given that the water ice-line is much closer to the star compared to Solar-like system. \item There is no clear trend of volatile fraction with orbital period. This suggests that either the accreted planetesimals were sufficiently mixed such as to blur otherwise expected increases of water fraction with distance from the star. A corresponding uniform water content is indeed possible within 2-$\sigma$ error bars. Alternatively, migration may have rearranged the planets before they were captured in resonance. \item Possible delivery of volatiles after formation by cometary impacts \citep{kral2018cometary} of few Earth oceans are tiny compared to our predicted water mass fractions. This means that the overall water budgets were accreted during formation. Also, the interior degeneracy is large such that uncertainties of predicted water masses are orders of magnitudes larger than possible late-delivered amounts of volatiles. This implies that the data do not allow to validate late delivery of volatiles. \item The loss of volatiles as predicted by \citep{Bourrier_2017} of several tens of Earth oceans is small compared to the total amount of water that shape the planets, except for planet e. This implies that the ice mass fraction of the bulk accreted material does not significantly exceed 30\%. \rev{If data accuracy changes by up to 20\%, this upper limit could be significantly lower ($\sim$15\%).} \item The uncertainty in our predicted water mass fractions stems from the degeneracy with the size, structure, and composition of the rocky interior, as well as with the characteristics of the overlying gas envelope. The estimated degeneracy will be generally lower if interior models are employed that only allow for limited variability, e.g., mantles of pure MgSiO$_3$ as employed in \citep{unterborn2017constraining}. Similarly, estimated degeneracies will be larger if interior models are used that allow for interiors that are unlikely to exist in nature, e.g., pure iron cores surrounded by gas envelopes as used in \citep{suissa2018trappist}. \end{itemize} \rev{Significant further improvements on our understanding of the TRAPPIST-1 planetary interiors are only expected with higher data accuracy and/or informative data other than those investigated here, that may include better understanding of their specific host star chemistry, spectroscopic constraints on atmospheric composition (e.g., with JWST, Ariel, E-ELT), or constraints on tidal parameters \citep[e.g.,][]{papaloizou2017trappist}.} With our study on TRAPPIST-1, we have explored the data types that are specific to multi-planetary systems. Such data will be relevant for the interior characterization of planets in other systems as well. First, there are correlations between the data of different planets that can carry crucial information for interior characterization. Second, we have demonstrated that it is possible to preferentially probe the rocky interiors of all planets by studying the most dense planet of a multi-planetary system. This study provides new pathways for an improved interior characterization that is specific to multiplanetary systems. | 18 | 8 | 1808.01803 |
1808 | 1808.05207_arXiv.txt | We report on the discovery of a dramatic X-ray spectral variability event observed in a $z\sim 1$ broad line type-1 QSO. The \XMM\, spectrum from the year 2000 is characterized by an unobscured power-law spectrum with photon index of $\Gamma\sim 2$, a column density of $N_{\mathrm{H}}\sim 5\times 10^{20}\,\mathrm{cm^{-2}}$, and no prominent reflection component. Five years later, \Chandra\, captured the source in a heavily-obscured, reflection-dominated state. The observed X-ray spectral variability could be caused by a Compton-thick cloud with $N_{\mathrm{H}}\sim 2\times 10^{24}\,\mathrm{cm^{-2}}$ eclipsing the direct emission of the hot corona, implying an extreme $N_{\mathrm{H}}$ variation never before observed in a type-1 QSO. An alternative scenario is a corona that switched off in between the observations. In addition, both explanations require a significant change of the X-ray luminosity prior to the obscuration or fading of the corona and/or a change of the relative geometry of the source/reflector system. Dramatic X-ray spectral variability of this kind could be quite common in type-1 QSOs, considering the relatively few datasets in which such an event could have been identified. Our analysis implies that there may be a population of type-1 QSOs which are Compton-thick in the X-rays when observed at any given time. | Over the last two decades evidence has emerged for variations of the line of sight (LOS) column density, ($N_{\mathrm{H}}$), in nearby type-2 (obscured) active galactic nuclei (AGN). These are inferred from the shape of the X-ray spectrum, which changes dramatically if a source transitions from a transmission-dominated Compton-thin ($N_{\mathrm{H}}<10^{24}\,\mathrm{cm^{-2}}$) state to a reflection-dominated Compton-thick (CT; $N_{\mathrm{H}}>10^{24}\,\mathrm{cm^{-2}}$) one. Sources showing such a behaviour are sometimes referred to as X-ray ``changing look'' AGN \citep{2003MNRAS.342..422M}. These variations can be explained if at least part of the circumnuclear absorbing medium in type-2 AGN is clumpy \citep[][and references therein]{2002ApJ...571..234R,2010IAUS..267..299R,2012AdAst2012E..17B}, with the spectral changes caused by the transit of a cloud along the line of sight. In the standard unification picture, the obscuring torus should lie out of the LOS to the nucleus of type-1 AGN, so they are not expected to exhibit this behaviour. The heavily reddened type-1 AGN ESO 323-G77 has nonetheless displayed $N_{\mathrm{H}}$ variations from typical columns of $\sim 10^{23}\,\mathrm{cm^{-2}}$ to $1.5\times 10^{24}\,\mathrm{cm^{-2}}$ \citep{2014MNRAS.437.1776M}. The LOS in this source is suspected to graze the dusty torus, however, so that clumps therein could obscure the central engine, while leaving the broad line region visible. In addition, several cases of CT eclipses have been reported by \citet{2010IAUS..267..299R}. Furthermore, the archetypical type-1 AGN NGC 5548 shows strong evidence for fast outflows of ionized material that are likely launched from the accretion disk and can block large amounts of the soft X-ray emission \citep{2014Sci...345...64K}. Type-1 AGN may also present themselves as Compton-thick in X-rays if there is a strong decrease of the nuclear X-ray luminosity, with a distant reflector, such as the pc-scale dusty torus itself, producing a light echo for some time \citep{2003MNRAS.342..422M}. This interpretation has been favoured in the case of the highly variable Seyfert 1 galaxy NGC 4051 \citep{1998MNRAS.301L...1G,1999MNRAS.307L...6U} and the Seyfert 1.9 galaxy NGC 2992 \citep{1996ApJ...458..160W,2000A&A...355..485G}. The current sample of AGN showing transitions between Compton-thin and -thick states is comprised of bright, local objects, for which high-S/N, multi-epoch X-ray observations have been obtained. At the higher redshifts probed by deep X-ray survey fields the situation is complicated by the fact that multiple observations with sufficient S/N are generally not available. Thus, even strong spectral variability of the kind discussed above may remain undetectable. We report here on the discovery of extreme spectral variations of this nature in an otherwise typical broad line type-1 QSO. In the following we assume a $\Lambda$CDM cosmology with $H_{0}=70\,\mathrm{km\,s^{-1} Mpc^{-1}}$, $\Omega_{\mathrm{m}}=0.3,$ and $\Omega_{\Lambda}=0.7$. | \label{sec:discussion} The repeat X-ray spectra of RMID 278 provide strong evidence for this typical $z\sim 1$ type-1 QSO switching from a transmission-dominated to a reflection-dominated state. This dramatic spectral change may be caused by either a nuclear eclipse event or a strong decrease of the corona luminosity, leaving the reflected emission from distant material as the dominant component of the source spectrum. In addition, the strong reflection component detected by \Chandra\, but not by XMM, requires a significant increase of the primary continuum X-ray flux in both scenarios, or a dramatic change in the source geometry. This is further supported by the relatively small decrease of the observed 2-10\,keV flux in between the two epochs. In the ``switched off'' corona scenario, the X-ray reflection most likely comes from distant material, such as the pc-scale dusty torus. Its location can be estimated from the dust sublimation radius. Given the bolometric luminosity of our source, we obtain $R_{\mathrm{sub}}\sim 0.25-0.69$\,pc adopting either the relation fitted to observed K band time-lags \citep{2006ApJ...639...46S} or the theoretical prediction of \citet{1987ApJ...320..537B}. Based on these rough estimates, we would expect to still see a notable reflection echo in the 2005 spectrum, if the central engine switched off sometime between 2001 and 2005. On the other hand the strong increase in the reflection component between 2000 and 2005 would require a sustained and significant increase in the coronal luminosity prior to fading away, or a major change of the geometry of the reflector with respect to the corona in between the observations. The optical light curve (Fig.~\ref{fig:rbandlc}) displays no extreme variability between the X-ray observations, which, together with the optical spectra (Fig.~\ref{fig:mmtvssdss}), implies that the source probably did not undergo major changes in accretion rate or change its (optical) AGN type during this period. Even though AGN variability can be much more extreme in X-rays than in optical, especially on short timescales \citep{2014SSRv..183..453U}, these arguments tend to disfavour the ``switched off'' corona. The alternative hypothesis is that the source is in an X-ray bright, heavily obscured state at the time of the \Chandra\, observations. Within the best-fitting \texttt{clumpy} model interpretation, the event is most probably caused by a dense cloud eclipsing the X-ray corona, resulting in an $N_{\mathrm{H}}$ variation from the completely unobscured regime of $N_{\mathrm{H}}\sim 5\times 10^{20}\,\mathrm{cm^{-2}}$ to the CT regime with $N_{\mathrm{H}}\sim 2\times 10^{24}\,\mathrm{cm^{-2}}$. To the best of our knowledge, such an extreme $N_{\mathrm{H}}$ variation by more than three orders of magnitude has never before been observed in a type-1 QSO. This scenario also requires a large increase in the X-ray luminosity at the time of the \Chandra\, observation. Rather than being a coincidence, it could be that these events are connected. The increase in intrinsic luminosity implied by the X-ray spectrum could bring RMID 278 close to or perhaps even beyond the Eddington limit. Such a luminosity increase could launch a wind of CT clouds, which in turn obscures the hot corona \citep[see e.g.][]{1992ApJ...399L..23P}. However, the available data suggest that this would have been a dramatic and short (timescale few months) ``outburst'', possibly resulting in a ``failed wind'' that lifted CT material for only a short period of time. Due to the large uncertainties of the intrinsic luminosity in the CT solution, the implied luminosity increase should not be overinterpreted though. In any case, irrespective of the favoured interpretation of the observations, the data strongly suggest a dramatic change in the spectral properties of the source, associated to a significant change in the absorber column density, possibly accompanied by further changes in the source luminosity and/or relative geometry of the source/reflector system. How often could these events occur? Based on a statistical analysis of X-ray eclipse events in local Seyfert galaxies monitored with RXTE, \citet{2014MNRAS.439.1403M} estimated the probability for a type-1 AGN to undergo an X-ray eclipse to be $0.6\%^{16.6\%}_{0.3\%}$. They did not detect any CT obscuration in their type-1 AGN sample (c.f. \citealt{2014MNRAS.437.1776M}) inferring an upper limit of $<15.8\%$ for such events. The CT obscuration in RMID 278 was seen for one out of 32 type-1 RM-QSOs with repeat XMM and \Chandra\, spectra. Given this limited data set, we are unable to derive robust constraints on the fraction of the type-1 QSOs undergoing CT eclipses. However, considering that we obtained spectra at just two epochs, and over a single time baseline of $\sim 5$ years, this behaviour could be very common. Comparing with the non-detections of \citet{2014MNRAS.439.1403M} and \citet{2014MNRAS.442.2116T} in nearby type-1 AGN, this could imply an important difference in the obscuration properties of local AGN and the more typical accreting SMBH found in deep X-ray surveys. Large area surveys with spectral timing information are needed to unveil the intrinsic fraction of CT obscuration events among the AGN population. The future surveys performed by SRG/eROSITA \citep{Merloni2012} will provide an unprecedentedly large sample of type-1 AGN with repeated X-ray observations on various timescales, allowing for a thorough statistical study of these extreme variations. | 18 | 8 | 1808.05207 |
1808 | 1808.10718_arXiv.txt | GW170817 was not merely an absolute breakthrough in gravitational wave astrophysics and a first in multi-messenger astronomy. The quality and diversity of the electro-magnetic counterpart emission is staggering on its own as well, including unprecedented kilonova spectra and a broadband off-axis gamma-ray burst afterglow that has progressed along a trajectory of rise and decay and by now has even been measured using very large baseline interferometry. For these proceedings, I will summarize the points for discussion that I presented during the workshop regarding off-axis short gamma-ray bursts and their (un-)successful jets and their emission. Given that developments are currently moving very fast in the field, I also touch on some results that have appeared in the literature following the Vulcano meeting. | The recent joint detection\cite{LIGO2017, Abbott2017} of electro-magnetic (EM) and gravitational wave (GW) emission from merging neutron stars (NS) has been one of the biggest scientific achievements of the past decades, revolutionising astrophysical observations and having far-ranging repercussions for transients high-energy astrophysics. Various predictions for a range of potentially detectable EM counterparts had been made prior to the detection of GW170817 / GRB 170817A, but the actual quality and quantity of the data wildly exceeded expectations: kilonovae had largely remained a theoretical construct up to this point, although the first tentative detections were getting published\cite{Tanvir2013,Berger2013}, while short gamma-ray bursts (sGRBs) and their subsequent afterglow jets were only expected for a subset of NS mergers due to their collimated nature. GRB 170817A of course provided us not just with a close view of a GW source, but also with a kilonova \emph{and} a GRB \emph{and} a long-lasting broadband afterglow. In these proceedings, I discuss in particular how the detection of the afterglow for this source has forced us to update our models for sGRB jets and afterglows. | 18 | 8 | 1808.10718 |
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1808 | 1808.07491_arXiv.txt | Weak lensing shear estimation typically results in per galaxy statistical errors significantly larger than the sought after gravitational signal of only a few percent. These statistical errors are mostly a result of \textit{shape-noise} --- an estimation error due to the diverse (and a-priori unknown) morphology of individual background galaxies. These errors are inversely proportional to the limiting angular resolution at which localized objects, such as galaxy clusters, can be probed with weak lensing shear. In this work we report on our initial attempt to reduce statistical errors in weak lensing shear estimation using a machine learning approach --- training a multi-layered convolutional neural network to directly estimate the shear given an observed background galaxy image. We train, calibrate and evaluate the performance and stability of our estimator using simulated galaxy images designed to mimic the distribution of \textit{HST} observations of lensed background sources in the CLASH galaxy cluster survey. Using the trained estimator, we produce weak lensing shear maps of the cores of 20 galaxy clusters in the CLASH survey, demonstrating an RMS scatter reduced by approximately 26\% when compared to maps produced with a commonly used shape estimator. This is equivalent to a survey speed enhancement of approximately 60\%. However, given the non-transparent nature of the machine learning approach, this result requires further testing and validation. We provide python code to train and test this estimator on both simulated and real galaxy cluster observations. We also provide updated weak lensing catalogues for the 20 CLASH galaxy clusters studied. | In weak lensing, the small gravitational deflection of light in its path from the source to the observer enables the measurement of the intervening mass distribution. Prime examples in which weak lensing is applied are in the measurement of cosmic shear, where the large-scale structure is of interest, and in measurements of galaxy cluster lensing, where the mass distribution is comparably more localized \citep[see][for a review of weak lensing applications]{schneider2006weak}. This weak deflection of light induces a small distortion that maps the source plane coordinates $\vec\theta'$ to the image plane coordinates $\vec\theta$. The distortion $\vec\theta'(\theta)$ may be locally approximated as an affine transformation with a Jacobian \begin{equation} \label{eq:shear} \frac{\partial \vec\theta'}{\partial \vec\theta} = \begin{pmatrix} 1-\kappa-\gamma_1 &-\gamma_2 \\ -\gamma_2 &1-\kappa+\gamma_1 \end{pmatrix} = (1-\kappa) \begin{pmatrix} 1-g_1 &-g_2 \\ -g_2 &1+g_1 \end{pmatrix}, \end{equation} where $\kappa$ is known as the \textit{convergence} and parametrizes the uniform stretching of the image, $\gamma_i$ are the two components of \textit{shear} and $g_i = \gamma_i/(1-\kappa)$ are the $\textit{reduced shear}$. Weak lensing shear estimation is typically concerned with measuring the reduced shear in images of faint, high-redshift galaxies and with deducing the lensing mass distribution from these estimates \citep[see][for a derivation of weak lensing formalism]{bartelmann2001weak}.\\ An ideal estimator of $g_i$ is unable to access the pre-lens galaxy image and therefore has to rely on the (true) probability distribution $P(g_i \lvert x)$ of the shear given galaxy image $x$. Here $x$ represents galaxy image pixel responses as observed, including the effects of galaxy population morphology, lens distortion, point-spread-function (PSF), band throughputs and noise --- only to name a few known observational factors. To date, many shear estimation techniques have been developed and studied and these have been primarily focused on reducing various types of systematic errors (e.g. biases due to PSF correction, noise, or source population variation). For a recent review of shear estimation methods and the different sources of estimation bias see \cite{mandelbaum2015great3} and \cite{massey2012origins}. \\ Less attention has been given to the issue of reducing the statistical errors of the shear estimator that result from the wide variation in galaxy shapes. In cluster lensing, the number of background sources is often very limited. The angular resolution of galaxy cluster weak lensing maps is typically limited by the density of available background sources (on which shear can be estimated) and such maps are often computed by locally averaging the shear estimates of only a few neighbouring galaxies at each point in the field. For a given set of background sources, reducing the statistical error (or RMS scatter) of the shear estimator would therefore directly translate to a linear enhancement of the angular resolution of the map (at a pre-selected level of map noise). In galaxy cluster lensing studies, two shear estimation methods that have been widely used are the \textsc{KSB} method \citep{kaiser1994method} for ground based observations and the \textsc{RRG} method \citep{rhodes2000weak} for space based observations. These estimators essentially measure the two component ellipticity $e$ of the galaxy intensity profile from its weighted quadrupole moments, correcting for the weight profile and PSF in different ways. After calibrating a proper \textit{shear susceptibility factor} $G$ \citep[see][]{rhodes2000weak,leauthaud2007weak}, the calibrated ellipticity $\hat{\epsilon} = e/G$ is used as an unbiased local estimate of the reduced shear $g = \langle \hat{\epsilon} \rangle$. Note that although different definitions of ellipticity exist in the literature, here $\hat{\epsilon}$ has been scaled to match the scale of the reduced shear $g$ defined in equation \ref{eq:shear}. The intrinsic per-component scatter $\sigma_{\hat{\epsilon}}$ of $\hat{\epsilon}$ (at constant $g$), resulting from the natural diversity of galaxy intensity profiles (and not from various measurement errors), is known as \textit{shape-noise} and is generally considered to be a lower-limit of the statistical error that quadrupole moment based shear estimators can reach. The actual value of the shape-noise $\sigma_{\hat{\epsilon}}$ is somewhat dependent on source galaxy population \citep[see][where it is found to be ${\sim}0.25$ and ${\sim}0.30$ at the lower and upper magnitude cuts of a specific space-based survey, respectively]{leauthaud2007weak}.\\ In this work we aim to measure shear with a statistical error lower than $\sigma_{\hat{\epsilon}}$ by using additional morphological information, visible in the source galaxy stamp, beyond its quadrupole moments. The premise of our work is that the apparent structure of galaxies isn't fully described by their ellipticity parameters and that quadrupole-based estimators may therefore be suboptimal with respect to statistical error. Shear estimators that measure higher order intensity moments (above quadrupole) and attempt to model their joint statistics \citep[see e.g.][]{refregier2003shapelets,bernstein2016accurate} could also potentially utilize substructure to achieve this goal, although, to the best of our knowledge, these estimators have not yet demonstrated to do so. The idea that there is additional information to be harnessed for weak lensing measurements beyond the imaged quadrupole moments has been suggested before. Additional observables such as radio polarization were used by \cite{brown2011mapping} to constrain the intrinsic morphological orientation of galaxies. Resolved spectroscopic kinematic maps were used by \cite{blain2002detecting,morales2006technique,huff2013cosmic} and more recently \cite{de2015direct}, to reduce the shape noise in measurements of disk galaxies. Dimensionality reduction techniques of existing multi-band photometric data, when used in addition to quadrupole moment ellipticities, have also been shown to carry some additional information \citep{croft2017prediction,niemi2015weak}. In contrast, in this work, we use only a single optical image as an observable and seek new image features that may be used to infer shear. Our approach to this problem is based on a discriminative machine learning model --- a multi-layered (or \textit{deep}) \textit{convolutional neural network} trained to directly estimate shear (and not ellipticity) from the observed galaxy stamps. This approach relies on the availability of a large dataset of simulated galaxy stamps, having known shear and simulated observational conditions matching those of the galaxy clusters under study. We stress that this requirement is both challenging and crucial for properly training and validating a shear estimator in such a machine learning approach.\\ This paper is structured as follows: In \S\ref{sec:observations} we describe the \textit{Hubble Space Telescope} (\textit{HST}) observations, both of the survey in which we measure shear and of the survey from which we generate simulated training and calibration data for the estimator. In \S\ref{sec:simulations} we describe the steps taken to match the simulations to the galaxy cluster observations and to generate a larger and richer training dataset that would promote certain useful invariance properties of the learnt estimator. In \S\ref{sec:model} we describe the machine learning model used and its training procedure. In \S\ref{sec:performance_sim} we calibrate biases and measure the model performance using simulated data. In \S\ref{sec:clash_analysis} we use the learnt model to measure shear in real images of galaxy clusters, also assessing bias (relative to RRG estimates) and statistical performance on the cluster data. We describe our code and data release in \S\ref{sec:reproducibility} and conclude in \S\ref{sec:discussion}. | \label{sec:discussion} We present a machine learning process that allowed us to train a model to perform weak lensing shear estimation directly from simulated examples. This process includes: Simulating galaxy stamps having known shear and an observational distribution matching that of the target stamps, training a \textit{deep convolutional neural network} on the simulated data to produce a model and an assessment of the model performance on both the simulated data and actual galaxy cluster field observations. This approach is novel in several respects: The model is trained to directly estimate lensing shear and not galaxy shapes, it is not based on hand-crafted features but instead attempts to extract all relevant information from the galaxy observations (in the limits of the model architecture) and it is designed to be invariant to the stamp centroid and background estimates. We dealt with the following challenges that were specific to our approach: Avoiding simulation artefacts which would otherwise deteriorate model generalization to actual observations, enlarging and augmenting the training data to promote wanted invariance properties at the learning phase and enforcing known discrete symmetries of lensing shear at the inference phase. In the observed CLASH fields, an additional challenge was to perform bias calibration and statistical error analysis where the true per-stamp shears are unknown. The results of our learnt estimator appear to be consistent with those of commonly used quadrupole moment estimators and show enhanced statistical performance. We find this to be the case both on the simulations and in the real observations where the reduction in RMS errors, compared to the RRG estimator, is at the level of 26\%. This is equivalent to a relative improvement in survey speed of approximately 60\%. This serves as initial indication that what is commonly referred to as the \textit{shape-noise limit} can likely be overcome, at least to some extent, by using the joint statistics of higher order intensity moments of high-redshift galaxy images (above the second order moment statistics tapped by RRG).\\ These results however require additional testing and validation due to the non-transparent nature of the machine learning approach. Although we have made great efforts to rid our simulations of artefacts, these may still exist in our training and test datasets and could potentially be providing the learnt estimator with clues as to what the simulated shears were --- clues that would not be available in real observations. Additional simulations by independent means would allow us to mostly rule out this possibility. Furthermore, studying the error sensitivity (statistical and systematic) of our estimator to additional distributional factors, such as galaxy morphology \citep[using e.g. the Shapelet decomposition of][at increasing order]{refregier2003shapelets}, S/N levels and PSF parameters, is still required. This would enable us to disentangle the various sources of statistical error (e.g. morphology from Poisson noise) and to control potential systematic biases when applying this learnt estimator to different real observing conditions.\\ Using high dimensional statistics to estimate shear can either be done explicitly, by modelling the conditional distribution (conditioned on shear) of post-shear galaxy images --- this is known as a \textit{generative approach} to machine learning, or implicitly, by learning to fit a function that directly maps post-shear images of galaxies to their true shear, in a statistically consistent and efficient way --- known as a \textit{discriminative approach}. This later approach is the one we eventually followed in this work. This choice requires us to have good simulations at our disposal \citep{rowe2015galsim} but allows us to avoid analytically modelling the action of shear on the pre-sheared galaxy image distribution. Training our model in a way that promotes invariance to certain types of transformations is also simplified by the discriminative approach --- achieving this only requires us to simulate these transformations when preparing the training data.\\ We list the following caveats of our approach: \begin{itemize} \item Our estimator does not presently deal with PSF variation. We believe this does not affect the validity of our statistical error analysis, particularly on the simulated test data, but could in principle be leading to local biases of the estimator within the observed field-of-view in the CLASH data --- possible biases which we have not accounted for. We believe this issue can be overcome by training a model to infer shear given both a galaxy stamp and a local estimate of the PSF, such as those made available by the \textsc{TinyTim} PSF model of the \textit{HST} fields \citep{krist201120}. We defer this issue to future work. \item Assuming a total galaxy number density of $37\,\,\mathrm{arcmin}^{-2}$ \citep[see][]{chang2013effective} we estimate that in the well resolved CLASH data ${\sim}4\%$ should contain blends within a $32\times 32\,\textrm{px}$ stamp, although the vast majority of these blends would be of all-background galaxies. For all-background blends, a similar shear would affect the whole stamp, as is the case in a similar proportion of the stamps in the COSMOS based simulations. In addition, blends including foreground galaxies typically manifest as constant or nearly constant additive background levels within the $32\times 32\,\textrm{px}$ background stamps. As discussed in \S\ref{sec:sensitivity}, our estimator is expected to be robust to this type of blending. Stamps with blends that include relatively small foreground galaxies may introduce some systematic biases which we have not accounted for. Although we do not expect blending to introduce a significant effect in the CLASH observational regime, simulating these foreground-background blends in the training data could allow us to both train the CNN estimator to be robust to blending issues and to assess its sensitivity to blending. We defer this refinement of our simulation process to future work. \item Our simulations are lacking in that we do not match the simulated and observed populations in redshift, but only in magnitude-radius space (see \S\ref{sec:mag_rad_matching}). This choice could in principle be overcome, to a large extent, when deeper observations of in-the-field galaxies become available. This is due to the fact that the higher the S/N of the base dataset used by \textsc{GalSim}, the closer the image rescaling factor ($\alpha$ in \S\ref{sec:sn_tradeoffs}) can be to unity. The availability of deeper observations at the training phase, particularly when provided in the specific band we later wish to measure weak lensing shear in, will also allow us to avoid the band mismatch we opt for in \S\ref{sec:acs_total_images}. \item The reliance of our approach on high-fidelity image simulations adds difficulty to its application. This is similarly the case with conventional simulation-based shear calibration techniques and the potential advantage of data-based calibration \citep[e.g.][]{huff2017metacalibration}. \item When producing the training data for our learnt estimator we performed a set of transformations, or augmentations, in addition to the simulated shear. The choice of augmentations was not particularly tuned to the CLASH dataset which we later ran our estimator on, but these were chosen after we were exposed to the CLASH data. As previously discussed, testing our model on additional simulations as well as on real galaxy cluster observations are needed to further validate our approach. \end{itemize} Our technique was developed and tested in the regime of well-resolved space-based images. This was done with particular aim at galaxy cluster weak lensing measurements. The applicability of this technique to the type of ground-based images used in cosmic shear measurements is currently not known and remains to be studied. It is likely that the lack of visible substructure in the ground-based image regime would lead to little gain for this approach.\\ Finally, we would like to stress the point raised in \S\ref{sec:arch} --- we are currently unaware of any justified strategies to choose an optimal model architecture, model weight optimization scheme and training data augmentation scheme. We would like to encourage the reader to use the code and data released in this work as a basis for future experimentation, hopefully, reaching lower statistical errors and further enhancing resolving power in real galaxy cluster weak lensing observations. | 18 | 8 | 1808.07491 |
1808 | 1808.10468_arXiv.txt | We present spatially resolved analysis of a lensed galaxy, SDSS1958+5950 at $z = 2.225$, from the Cambridge Sloan Survey of Wide Arcs in the Sky (CASSOWARY). We use our new high resolution imaging data to construct a robust lens model for the galaxy group at $z = 0.214$. We employ the updated lens model to combine the Integral Field Spectrographic observations on two highly distorted images of the lensed target. We adopt a forward-modeling approach to deconvolve the effects of point spread function from the combined source-plane reconstruction. The approach is adapted to the lens model magnification and enables a resolution of $\sim$170 pc in the galaxy-source plane. We propose an ongoing merger as the origin of the lensed system on the basis of its source-plane morphology, kinematics and rest-frame emission line ratios. Using our novel technique of adaptive coadded source plane reconstruction, we are able to detect different components in the velocity gradient that were not seen in previous studies of this object, plausibly belonging to different components in the merging system. \textit{} | Spatially resolved studies of high redshift galaxies, particularly in the peak of galaxy formation epoch $1\lesssim z\lesssim 3$ \citep{Madau14} hold the key for understanding the physics of galaxy formation and evolution. The development of Integral Field Spectrographs (IFS) and Adaptive Optics (AO) Imaging techniques in the last decade have revealed the diverse kinematic state of galaxies in this epoch, ranging from rotationally supported clumpy disks to more dispersion dominated systems \citep[see][for a review]{Glazebrook13}. Observationally, AO aided IFS surveys \citep[][]{Forster06, Flores06, Maiolino08, Gnerucci11, Genzel11, Contini12, Forster18} have allowed us to achieve an improved resolution of up to 100 mas ($\sim$ 800 pc at $1\leq z\leq 3$), enabling the sampling of $z \sim$ 1 - 3 galaxies in a few coarse resolution elements. However, in order to understand the physical conditions of H\,{\sc ii }\rm regions and the evolution of ISM properties with redshift, it is imperative to resolve star-forming (SF) regions at high-$z$ in the same manner as we resolve them in the local universe. For example, the physical scales of H\,{\sc ii }\rm regions in the local universe span at least an order of magnitude, from small OB associates ($\sim$ 60 pc), stellar aggregates ($\sim$ 240 pc) to large star complexes ($\sim$ 600 pc), with a decrease in surface brightness from the smallest to the largest scales \citep{Elmegreen06, Gusev14}. Therefore, current high-redshift observations are highly biased towards the H\,{\sc ii }\rm physics on the largest scales. Similar systematic biases also exist in kinematic and metallicity gradient analysis of high-$z$ galaxies \citep[e.g.,][] {Yuan13, Jones13, Yuan17}. The improved spatial resolution provided by IFS observations of gravitationally lensed galaxies \citep[e.g.][]{Jones10a, Livermore12, Wisnioski15, Livermore15, Leethochawalit16, Mason17, Patricio18} has played a pivotal role in probing the star-forming regions with a physical resolution down to a few hundred parsecs in the galaxy-source plane. Magnification factors of strongly lensed systems can easily range between 1 - 10 \citep[e.g.][]{Richard11}, with reasonable lensing uncertainties \citep[][]{Collett15}. In extreme cases of giant arcs around galaxy groups and galaxy clusters, the magnification can reach up to a few $\times$ 10, rendering a physical resolution of less than 100 pc at $z \sim 2$. Therefore, giant distorted arcs are ideal candidates to study the physics of high-redshift SF regions at highest spatial resolution possible \citep[][]{Swinbank06, Jones10a, Yuan12, Bayliss14, Livermore15, Johnson17, Girard18}. While it is the giant arcs that offer the largest magnification, modeling of these arcs is also the most challenging. One of the biggest challenges of studying the giant lensed arcs is the large uncertainty in the lens model. The lensing mass distribution very sensitively controls the accuracy and precision of source-plane reconstructions of these arcs. The current strong lens modeling is unable to match the angular resolution of the imaging data (for e.g. HST $\sim 0.\!\!^{\prime\prime}05$) with a residual RMS of up to a few arcseconds \citep[][]{Limousin07, Lagattuta17, Caminha17}. Line of sight substructures, redshift information of multiple image systems have also been shown to have a significant contribution to the systematics errors arising in strong lens models of lensing clusters \citep{Bayliss14b, Johnson16, Acebron17}. However, even with the use of accurate lens models, simple source reconstructions removing the lens deflection from the observations does not allow us to correctly recover the intrinsic source-plane surface brightness. This is because of the point spread function (PSF) convolving with the data in the image plane. PSF remains in the source plane and varies as a function of the source position. The impact of PSF is even more severe in the vicinity of the critical lines. Thus the resulting source-plane resolution limits us from confidently combining independent reconstructions from different multiple images of the same lensed galaxy. In order to fully utilize the power of lensing and recover the physical properties of galaxy delensed, it is important to simultaneously combine the information from different images. This has been shown before by certain case studies \citep[for e.g][]{Coe10, Jones10b, Jones15} of lensed systems. To easily combine the observations and deal with instrumental PSF, a forward modeling approach is ideal to reconstruct the galaxy on the source plane. The use of forward source modeling techniques has gained increasing popularity in the past decade owing to the fast growing data set of strongly lensed systems. Previous lensing studies \citep{Warren03, Night15, Tess16, Johnson17, Des17} have demonstrated the advantages of these techniques in accurately studying source profiles at scales otherwise unachievable through traditional image inversion methods. However, most of these techniques rely on computationally expensive algorithms to optimize lens model parameters and the extended source simultaneously. In this work, we conduct a detailed study of $z \sim$ 2 lensed galaxy using a unique forward modeling approach to combine all the available data from different multiple images of the lensed target. The approach is computationally fast and exploits the best-fit lensing mass model in rendering the physical properties from the combined source-plane data. We choose one of the brightest targets in The Cambridge Sloan Survey of Wide Arcs in the Sky (CASSOWARY), SDSS1958+5950 (hereafter referred by its survey-ID: cswa128; $z = 2.225$). CASSOWARY survey presented a large sample of about 100 group-scale gravitationally lensed systems at $z \sim 1 - 3$ from the Sloan Digital Sky Survey \citep[SDSS;][]{York00} imaging data \citep{Stark13}. The survey targeted star-forming galaxies ($z \sim 1 - 3$) being lensed by an early-type galaxy (or group) at $z \sim 0.2 - 0.7$. \cite{Leethochawalit16} (hereafter \citetalias{Leethochawalit16}) presented IFU observations of a representative sample of 15 lensed galaxies from the survey. cswa128 is lensed by a galaxy group at $z = 0.214$ and reported to have high [N\,{\sc ii}\rm]/H$\alpha$ at the outer edges, by previous work of (\citetalias{Leethochawalit16}). A lens model based on SDSS imaging data was used to interpret IFU observations on a single lensed arc of this target. In this work, we present high resolution imaging data from the NIRC2 instrument on the Keck I telescope that enables us to build a more complex lens model for this system. We also discuss new spectroscopic observations on another lensed image of the galaxy than previously observed by \citetalias{Leethochawalit16}. We use the updated lens model to reconstruct two images of cswa128 on the source plane. To overcome the challenges posed by the PSF, we test a forward modeling approach to merge the two IFS data reconstructions on the source plane. Using our novel technique, we find that cswa128 is highly evident of a merging system. The paper is organised as follows. In section~\ref{sec:data} we present different observations of the lensed system and an overview of the data reduction process. In section~\ref{sec:lensmodel} we describe the lensing methodology and the new lens model of the galaxy group. In section~\ref{sec:analysis} we detail our technique of coadding different images of the lensed galaxy on the source plane and the resulting source plane properties from the reconstruction. We discuss the overall results and summarize the conclusions under Section~\ref{sec:discussion} of the paper. Throughout this paper we adopt a standard $\Lambda$-CDM cosmology with $\Omega_{m} = 0.3$, $\Omega_{\Lambda} = 0.7$ and h $= 0.7$. All magnitudes are given in the AB system \citep{Oke83}. \begin{figure*} \centering \includegraphics[scale= 0.6,angle=0]{sdss_pointing_name.eps} \includegraphics[scale = 0.6,angle=0]{nirc_pointing.eps} \caption{\textit{\bf Left:} SDSS color composite image of cswa128, lensed galaxy behind a galaxy group at $z = 0.214$ (red: SDSS z' filter, green: SDSS r' filter, blue: SDSS g' filter). The OSIRIS pointings are indicated by two rectangles, each covering a different multiple image of the lensed galaxy at a mean systemic redshift of $z = 2.225$. Yellow rectangle a1 (t$_{exp}$ = 5.4ks) represents OSIRIS field for previous observations by \protect\citetalias{Leethochawalit16} while our new observations are shown by the cyan rectangle a2 (t$_{exp}$ = 5.4ks). \textit{\bf Right:} Our new NIRC2 Kp band imaging data (t$_{exp}$ = 8.4ks) with OSIRIS pointings overlaid on top. The spatial resolution has improved by a factor of 10 with NIRC2 observations. The length of the compass indicates an angular scale of $5. \!\!^{\prime\prime}0$.} \label{fig:fig1} \end{figure*} | \label{sec:discussion} Gravitationally lensed systems offer us the unique opportunity to study galactic dynamics at an unprecedented physical resolution in the source plane. Such a fine spatial resolution will not be achievable even with future instruments such as the NIRSpec aboard JWST or GMTIFS on GMT.\footnote{The spatial sampling of NIRSpec is 100mas, and AO aided GMTIFS will have a spatial resolution of 10-25 mas.\label{footnote:gmt}} Ongoing lensing surveys will increase the sample of lensed galaxies by orders of magnitude \citep[e.g. LSST,][]{Oguri10,Marshall10}. To prepare ourselves for interpreting large samples of lensed galaxies, it is of crucial importance to continue studying individual cases like cswa128 in great detail in order to better understand the systematics of lens models and capture the important physical properties of high-$z$ galaxies that are otherwise unattainable without lensing. \begin{figure*} \centering \includegraphics[scale=0.45,angle=0]{Niiha_blue_soucoadd_cont.eps} \includegraphics[scale=0.45,angle=0]{Niiha_red_soucoadd_cont.eps} \includegraphics[scale=0.45,angle=0]{Met_blue_soucoadd_cont.eps} \includegraphics[scale=0.45,angle=0]{Met_red_soucoadd_cont.eps} \caption{Derived 2D source-plane [N\,{\sc ii}\rm]/H$\alpha$ and metallicity maps for blue and red components of emission. Contours are the same as Figure~\ref{fig:fig4}\label{fig:fig9}.} \end{figure*} For example, the fraction of mergers in star-forming galaxies at $z \sim 1-3$ has long been debated. In this redshift regime, merger fractions show a strong dependence with the classification scheme used to classify merger signatures in high-$z$ observational data \citep[e.g.][]{Hung15, Molina17}. Predictions from high resolution simulations show that current observations significantly underestimate the occurrence of mergers in typical star forming galaxies at $z \ge$1 \citep{Rodrigue15}. Gravitational lensing coupled with high resolution imaging and spectrographic observations have the potential to unambiguously classify a galaxy as a merger or disk dominated as demonstrated in this work. In fact, without gravitational lensing, a galaxy like cswa128 would easily be misclassified as a typical clumpy SF galaxy at $z \sim$ 2. The reliability of source-plane properties of lensed galaxies depends strongly on the accuracy of the lensing mass models used to interpret the high resolution observations. In this work, we use high resolution imaging data to identify additional substructures and therefore construct a more robust map of the lensing potential of the galaxy group in cswa128 at $z = 0.214$. However, in order to fully exploit the potential of these natural gravitational telescopes, it is important to assimilate information from multiple images of the lensed target. Along with a high resolution lens model, we present an adaptive forward modelling approach to combine observational data sets on different instances of the lensed arc. We resolve the structure and kinematics of the lensed target at scales of $\sim$170 pc in the source plane. We are able to detect different velocity components of [N\,{\sc ii}\rm] and H$\alpha$ emission lines using this approach that are not seen in traditional source-plane coadding methods. We propose merger as the most plausible scenario in cswa128 on the basis of following observations: \begin{enumerate} \item {\bf Morphology:} Offset between the clumpy stellar emission compared to the rather extended H$\alpha$ morphology. \item {\bf Kinematics:} Chaotic velocity distribution with a clear double-peaked H$\alpha$ emission possibly representing different components of merger. \item {\bf Chemical gradient:} Flat metallicity gradients derived from [N\,{\sc ii}\rm]/H$\alpha$ emission line ratios. \end{enumerate} The results are consistent with the previous analysis by \cite{Leethochawalit16}. However, with the improved SNR of the emission lines in the source plane, we find more conclusive evidence of an ongoing merger in cswa128. The forward modeling technique presented in this paper has been developed specifically for this lensed target and required considerable manual intervention, especially in the construction of source masks. However, being computationally inexpensive, this approach offers a very quick and effective way of combining the data from multiple images to enhance the SNR of emission line maps in the source plane. In our follow-up work, we extend this forward source modeling approach to a fully automated inversion of extended lensed images in a Bayesian manner. We present an algorithm in {\lenstool} to obtain a discretized surface brightness distribution in the source plane for a fixed mass profile of the lens. We use a pixelized grid and Bayesian MCMC optimization algorithm implemented in {\lenstool} to employ a forward modeling approach to deconvolve PSF effects from the source profile. The algorithm allows higher flexibility than traditional parametric ways of modelling source galaxies thus allowing for unbiased reconstructions of irregular source morphologies. Moreover, this method will be widely applicable in studying a variety of lensed systems that will become available with the future instruments and lensed surveys \citep{Rydberg18, Agnello18}. We thank the comments of the anonymous referee, which helped to improve the paper. This work is based on data obtained at the W. M. Keck Observatory. We are grateful to the Keck Observatory staff for assistance with our observations, especially Randy Campbell and Jason. This research was supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. We thank Richard Ellis for sharing his OSIRIS data. SS thanks useful discussions with Prasun Dutta, GEARS3D and CALENDS group. SS is also thankful to Surya Narayan Sahoo for technical help in formatting some of the figures in the paper. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. | 18 | 8 | 1808.10468 |
1808 | 1808.09673_arXiv.txt | {While several studies have investigated large-scale cluster winds resulting from an intra-cluster interaction of multiple stellar winds, as yet they have not provided details of the bordering flows inside a given cluster. } % {The present work explores the principal structure of the combined flow resulting from the interaction of multiple stellar winds inside stellar clusters. } % {The theory of complex potentials is applied to analytically investigate stagnation points, boundaries between individual outflows, and the hydrodynamic structure of the asymptotic large-scale cluster wind. In a second part, these planar considerations are extended to fully three-dimensional, asymmetric configurations of wind-driving stars. } % {We find (i) that one can distinguish regions in the large-scale cluster wind that are determined by the individual stellar winds, (ii) that there are comparatively narrow outflow channels, and (iii) that the large-scale cluster wind asymptotically approaches spherical symmetry at large distances. } % {The combined flow inside a stellar cluster resulting from the interaction of multiple stellar winds is highly structured. } | According to a generally accepted paradigm, the structures known as superbubbles \citep{Chu-2008, McClure-Griffith-2012, Ambrocio-Cruz-etal-2016} are the result of the interaction of multiple stellar winds within stellar clusters. Individual examples are the central cluster at the Galactic center \citep{Ozernoy-etal-1997}, the Arches cluster \citep{Canto-etal-2000, Raga-etal-2001}, the Carina complex \citep{Gull-2011}, M~17 \citep{Reyes-Iturbide-etal-2009, Mernier-Rauw-2013}, and N~70 \citep{Rodriguez-Gonzalez-etal-2011}. The interest in superbubbles is triggered by the desire to understand their X-ray luminosities \citep[e.g.,][]{Raga-etal-2001}, by their potential contributions to the Galactic cosmic-ray flux \citep[e.g.,][]{Binns-etal-2007,Murphy-etal-2016} via acceleration at multiple shocks \citep{Bykov-2001, Ferrand-Marcowith-2010}, and because they are sources of gamma rays \citep{Cesarsky-Montmerle-1983, Domingo-Santamaria-Torres-2006}. In many cases the resulting large-scale wind outside a stellar cluster is assumed to be a spherically symmetric outflow, similar to that described by the original model of interstellar bubbles by \citet{Castor-etal-1975} and \citet{Weaver-etal-1977}. This assumption is invalid inside a given cluster where the winds of several (probably dominating) O and B stars interact with each other. The mutual interaction of stellar winds has been studied over many years in great detail for the case of binary stars \citep[e.g.,][and references therein]{Kallrath-1991, Pittard-2011, Reitberger-etal-2014, Reitberger_EA:2017}, including their additional interaction with the interstellar medium \citep{Wareing-etal-2007, Banda-Barragan-2016, Banda-Barragan-2018}. Additionally, \citet{Parkin_EA:2014} and \citet{Reitberger-etal-2014}, among others, have studied the effects of orbital motion in binary systems. These studies are neglected here, however, because we consider widely separated ($\sim 1$~pc) stars for which the orbital timescale is much longer ($\sim 10^7$~yrs) than the time taken for the interaction region of the winds to come into equilibrium ($\sim 10^5$~yrs). Compared to the existing body of research on binary winds, the investigations of the simultaneous interaction of multiple stars are still in their infancy. The first quantitative model of a large-scale cluster wind resulting from a more realistic internal flow structure was presented by \citet{Canto-etal-2000}. For numerical purposes, these authors had to assume a symmetric distribution of wind-driving stars inside the cluster. This model was subsequently generalized to a statistically homogeneous \citep{Raga-etal-2001} and to a nonuniform \citep{Rodriguez-Gonzalez-etal-2007} stellar distribution. These hydrodynamical (HD) simulations were later applied to explain the X-ray emission of various clusters (as mentioned above) and further generalized to include stellar winds and a supernova event as well \citep{Rodriguez-Gonzalez-etal-2011}. All of the models employing a nontrivial internal structure of stellar clusters are of numerical nature and do not provide details of the colliding plasma flows inside a given cluster. The present paper intends to fill these modeling gaps. First, we present a simplified two-dimensional (2D) analytical model of the interaction of multiple stellar winds and the resulting large-scale cluster wind. Second, we analyze the principal structure of such multisource wind flow geometries. Third, we discuss the corresponding generalization to explore asymmetric 3D configurations, sometimes resorting to numerical methods. In doing so, we restrict ourselves to stellar clusters where the mutual distances between the dominating wind-driving stars are large enough to justify neglect of any orbital motion. Since the termination shock surfaces of the stars are disjoint, the entire wind interaction region is subsonic and thus, to a good approximation, can be taken as incompressible. As shown by several authors \citep{Arthur-2007,Mackey-etal-2015,Scherer-etal-2016}, at least for isolated astrospheres, the density inside an astropause is so low that it is not affected by cooling. The region between astropause and bow shock is affected, but this is not relevant to our study because there are no bow shocks, but rather flows of the intracluster medium around the astropauses. For these, we assume that this medium is in thermal equilibrium, i.e.,\ that cooling is not effective, and thus it can be neglected as well. | With the present study we addressed the problem of the mutual interaction of multiple winds from stars located within a stellar cluster. While several studies have investigated large-scale cluster winds resulting from an intra-cluster interaction of multiple stellar winds, they have as yet not provided details of the colliding flows inside a given cluster. The present work represents a further step towards a quantification of the principal structure of the combined flow within and near such cluster. To this end we have applied the theory of complex velocity potentials to determine the stagnation points and the separatrices between the individual stellar wind regions originating from a planar arrangement of point sources, as well as the structure of the asymptotic large-scale wind outside the cluster. While in two spatial dimensions the use of complex-valued potentials allows a concise analytical treatment of stream lines using stream functions, the extension to the more realistic 3D case requires recourse to numerical methods (although the general theory of vector-valued nulls may be explored analytically, as has in fact been done by various authors). The main results can be summarized as follows. First, one can distinguish distinct regions in the large-scale cluster wind that are filled with plasma from the individual stars. Second, as a consequence of the strengths and locations of the wind sources, the outflow of a given star when projected onto a sphere does not necessarily result in a singly connected region. The wind of a given star may be forced, partly or fully, into comparatively narrow outflow channels. Third, as expected, one can demonstrate analytically that the large-scale cluster wind asymptotically approaches spherical symmetry at large distances. In conclusion, we state that the combined flow inside a stellar cluster resulting from the interaction of multiple stellar winds is highly structured. This confirms the expectation, and is the motivation to carry out further studies on the basis of (magneto)hydrodynamical simulations. | 18 | 8 | 1808.09673 |
1808 | 1808.10374_arXiv.txt | {} {The shape of low-frequency radio continuum spectra of normal galaxies is not well understood, the key question being the role of physical processes such as thermal absorption in shaping them. In this work we take advantage of the LOFAR Multifrequency Snapshot Sky Survey (MSSS) to investigate such spectra for a large sample of nearby star-forming galaxies.} {Using the measured 150\,MHz flux densities from the LOFAR MSSS survey and literature flux densities at various frequencies we have obtained integrated radio spectra for 106 galaxies characterised by different morphology and star formation rate. The spectra are explained through the use of a three-dimensional model of galaxy radio emission, and radiation transfer dependent on the galaxy viewing angle and absorption processes.} {Our galaxies' spectra are generally flatter at lower compared to higher frequencies: the median spectral index $\alpha_{low}$ measured between $\approx$50\,MHz and 1.5\,GHz is $-0.57\pm0.01$ while the high-frequency one $\alpha_{high}$, calculated between 1.3\,GHz and 5\,GHz, is $-0.77\pm0.03$. As there is no tendency for the highly inclined galaxies to have more flattened low-frequency spectra, we argue that the observed flattening is not due to thermal absorption, contradicting the suggestion of \citet{israel90}. According to our modelled radio maps for M\,51-like galaxies, the free-free absorption effects can be seen only below 30\,MHz and in the global spectra just below 20\,MHz, while in the spectra of starburst galaxies, like M\,82, the flattening due to absorption is instead visible up to higher frequencies of about 150\,MHz. Starbursts are however scarce in the local Universe, in accordance with the weak spectral curvature seen in the galaxies of our sample. Locally, within galactic disks, the absorption effects are distinctly visible in M\,51-like galaxies as spectral flattening around 100-200\,MHz in the face-on objects, and as turnovers in the edge-on ones, while in M\,82-like galaxies there are strong turnovers at frequencies above 700\,MHz, regardless of viewing angle. } {Our modelling of galaxy spectra suggests that the weak spectral flattening observed in the nearby galaxies studied here results principally from synchrotron spectral curvature due to cosmic ray energy losses and propagation effects. We predict much stronger effects of thermal absorption in more distant galaxies with high star formation rates. Some influence exerted by the Milky Way's foreground on the spectra of all external galaxies is also expected at very low frequencies.} | \label{s:intro} The radio emission from normal star-forming galaxies traces the underlying distributions of thermal and relativistic plasmas, cosmic ray (CR) electrons, and magnetic fields, thus providing vital information about the physical processes at work in galaxies. Studying the radio emission at different frequencies via the radio continuum spectra of galaxies allows us to understand radio emission processes and the structure and local properties of the galaxy's interstellar medium (ISM). The shape of radio continuum spectra can be characterised to first order by their power-law spectral index $\alpha$ ($S_\nu \approx \nu^{\alpha}$), the value of which can be related to the various radiation processes responsible for the emission. An optically thin plasma yields $\alpha =-0.1$ for thermal bremsstrahlung radiation, while synchrotron radiation gives $\alpha\approx -0.5$ for freshly accelerated CR electrons injected from supernova remnants into the star-forming disk. These CR electrons can sustain considerable synchrotron and inverse Compton radiation losses, giving rise to steeper spectra, with $\alpha$ also dependent on the structure and strength of the magnetic field and the confinement of CRs \citep{beck13,han17}. The transport of CR electrons away from supernova remnants can take the form of either diffusion, which depends on the magnetic field structure, or advection in a galactic wind \citep{{pohl91},heesen16,{heesen18}}. Therefore, galaxy spectra, particularly the integrated (global) ones, depend on a complex interplay between thermal and nonthermal components, CR electron energy losses, and propagation effects \citep{lisenfeld00}. At low radio frequencies, the spectra of galaxies are expected to be modified by additional mechanisms. For instance, \ion{H}{II} regions become optically thick at low frequencies, which affects not only the propagation of free-free emitted photons but also the transmission of photons generated from synchrotron emission. At low frequencies, relativistic bremsstrahlung and especially ionisation losses can also be much more important than at higher frequencies, in particular in starburst galaxies \citep{murphy09}. Finally synchrotron self-absorption and Razin effects can further suppress the radio emission from regions of dense ISM and produce breaks in the galaxy spectra below 10\,MHz \citep{lacki13}. Our current understanding of low-frequency spectra of galaxies and the | \label{s:conclusions} We compiled a sample of 129 nearby star-forming galaxies from the LOFAR MSSS survey and measured their integrated flux densities at 150\,MHz (Table \ref{t:sample}). Combining them with flux densities at various frequencies from the literature, we constructed global radio spectra for 106 objects. A statistical analysis of the data led us to the following conclusions. \begin{itemize} \item The low-frequency radio-FIR relation resembles the high-frequency one, which confirms (i) the good quality of the MSSS data, (ii) the proper removal of AGN-dominated galaxies from the sample, and (iii) the tight relation between dust emission and the almost pure synchrotron radiation at low radio frequencies. It may also indicate that the effect of thermal absorption in the sample is relatively weak at 150\,MHz. \item In general, the global spectra of galaxies in our sample are statistically flatter at lower frequencies, or equivalently, steeper at higher frequencies (Fig. \ref{f:alfa_hist}). The sample median value of the low-frequency spectral index $\alpha_\mathrm{low}$, measured between $\approx$50\,MHz and 1.5\,GHz, is $-0.57\pm0.01$, which is significantly larger than the corresponding value of the high-frequency spectral index $\alpha_\mathrm{high}=-0.77\pm0.03$, calculated between 1.3\, and 5\,GHz. For each galaxy we estimated the spectral curvature as the difference $\Delta\alpha=\alpha_\mathrm{low}-\alpha_\mathrm{high}$ and found that its median value is $0.18\pm0.02$, indicating a small but statistically significant spectral flattening at low frequencies. \item There is no tendency for highly inclined galaxies to have more flattened low-frequency spectra (Fig. \ref{f:alfadiff_incl}). Hence the observed flattening is not due to thermal absorption, which contradicts the suggestion by \citet{israel90}. We show that the flattening does not depend on galaxy morphology either. \end{itemize} Interpretation of these results and discussion of processes to shape the low-frequency spectra were performed with a numerical model of radio emission involving absorption and projection effects. Our modelling of M\,51-like galaxies, which represent low-SFR objects in the local Universe, suggests that local depressions of emission due to thermal absorption can only be seen in spatially resolved radio maps at frequencies below $\approx$ 30\,MHz. We show that thermal absorption can influence the global spectrum at frequencies only below 20\,MHz. A weak flattening observed in some galaxy spectra above this frequency (cf. Fig. \ref{f:spectra}) can be accounted for by the curvature in the synchrotron spectrum due to for example CR electron energy losses and diffusion of CRs from their regions of acceleration. We also predict a possible influence of the Milky Way foreground gas on external galaxy spectra at frequencies below 10\,MHz. Our modelling of M\,51-like galaxies indicates that local radio spectra of central parts of galaxies may differ much from their global spectra, and may even show turnovers due to thermal absorption in edge-on objects. Such turnovers could appear at frequencies of about 100-200\,MHz (Fig. \ref{f:m51_spectra}) and high-resolution observations are necessary to reveal them. Our models also show that even galaxies with simple, power-law-like global spectra can locally show significantly curved spectra, especially far away from the galactic centres. Therefore, integrated spectra alone cannot be properly interpreted without supplementary data on the properties of the local ISM within the galaxies. Moreover, we modelled galaxies with higher SFRs based on observations of M\,82. Compared to M\,51, the modelled M\,82-like galaxies show much stronger absorption effects irrespective of the galaxy tilt. At 150\,MHz, strong absorption was found mainly along the thin disk, while at 30\,MHz our model predicts a more extensive depression of emission around the galaxy centre (Fig. \ref{f:m82_maps}). Towards low frequencies, the integrated spectra of modelled starbursts first flatten and then slightly increase again at about 10\,MHz due to presence of the synchrotron halo. This could explain why simple modelling based on just one mixed region of thermal and nonthermal gas is not able to reproduce the observed spectra of M\,82. In the modelled local spectra of the central starbursts strong turnovers were found below about 1\,GHz for galaxies viewed edge-on and below about 500\,MHz for galaxies viewed face-on (Fig. \ref{f:m82_spectra}). Therefore one can expect much stronger free-free absorption effects and significant changes in the radio spectra of LIRGs and more distant galaxies with high SFRs. Since starburst galaxies are not frequent in the local Universe we observed mostly weak spectral curvatures in our sample. In this work we primarily discussed the impact of free-free absorption on the low-frequency spectra of galaxies. The forthcoming, more sensitive LoTSS HBA survey \citep{shimwell17}, and particularly the planned LBA survey at $\approx 50$\,MHz, as well as Murchison Widefield Array data covering a wide frequency range \citep[e.g.][]{hurley17} are highly desirable to distinguish between a number of processes shaping the spectra in galaxies at frequencies below 100\,MHz (Sect. \ref{s:intro}) as well as to verify our conjectures. Broad-band polarization observations spanning low and high frequencies would also help to constrain the thermal content of galaxies. | 18 | 8 | 1808.10374 |
1808 | 1808.01754_arXiv.txt | % Using a combined {and consistently analysed } GAMA, G10-COSMOS, and 3D-HST dataset we explore the evolution of the galaxy stellar-mass function over lookback times $t_{\rm L} \in \left[0.2,12.5\right] {\rm h^{-1}_{70} Gyr}$. We use a series of volume limited samples to fit Schechter functions in bins of $\sim\!$constant lookback time and explore the evolution of the best-fit parameters in both single and two-component cases. In all cases, we employ a fitting procedure that is robust to the effects of Eddington bias and sample variance. Surprisingly, when fitting a two-component Schechter function, we find essentially no evidence of temporal evolution in $M^\star$, the two $\alpha$ slope parameters, or the normalisation of the low-mass component. Instead, our fits suggest that the various shape parameters have been exceptionally stable over cosmic time, as has the normalisation of the low-mass component, and that the evolution of the stellar-mass function is well described by a simple build up of the high-mass component over time. When fitting a single component Schechter function, there is an observed evolution in both $M^\star$ and $\alpha$, however this is interpreted as being an artefact. Finally, we find that the evolution of the stellar-mass function, and the observed stellar mass density, can be well described by a simple model of constant growth in the high-mass source density over the last $11 {\rm h^{-1}_{70} Gyr}$. \vspace{0.5in} | \label{sec: intro} % Understanding the redshift evolution of galactic properties is a fundamental method for understanding the growth and evolution of structure over cosmic times. These studies typically explore integrated galaxy parameters such as stellar mass density \ccitep[$\rho_\star$, e.g.][]{Madau2014}, galaxy population morphological parameters such as the early-type fraction \ccitep[e.g.][]{Davidzon2017}, individual galaxy evolution parameters such as star formation rates \ccitep{Driver2017}, environmental parameters such as the galaxy two-point correlation function \ccitep[e.g.][]{Croom2005,Zheng2007} and merger rate \ccitep[e.g. ][]{Bridge2010}, and formation parameters such as the galaxy halo mass function \ccitep[e.g.][]{Moster2010}. All of these parameters encode complex physics about the formation and growth of galaxies over time. The integrated galaxy stellar mass density is of particular interest as it can be directly compared to the integrated cosmic star formation history \ccitep[see ][ for an extensive review of such studies]{Madau2014}. Over the last decade deep near-IR surveys such as the Great Observatories Origins Deep Survey \ccitep[GOODS;][]{Giavalisco2004}, the MUlti-wavelength Survey by Yale-Chile \ccitep[MUSYC;][]{Gawiser2006}, the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey \ccitep[CANDELS;][]{Grogin2011,Koekemoer2011}, the Cosmic Evolution Survey \ccitep[COSMOS;][]{Scoville2007} and the FourStar Galaxy Evolution Survey \ccitep[ZFOURGE;][]{Tomczak2014}, have made studying the properties of high redshift galaxies increasingly accessible to the astronomical community. Meanwhile, large multi-wavelength surveys of the low-redshift universe such as the Galaxy And Mass Assembly \ccitep{Driver2011,Driver2016}, the 2dF Galaxy Redshift Survey \ccitep{Cole2001}, and Sloan Digital Sky Survey \ccitep{Bell2003} have allowed us to explore galaxy properties with high statistical accuracy out to redshifts of $\sim\!0.5$. By combining datasets from these two classes of surveys, we are able to create combined samples that allow us to explore, with high number statistics throughout, the evolution of galactic parameters over a vast redshift range. In this work, we explore the evolution of the shape of the galaxy stellar mass function (GSMF) using a combination of surveys. In Section \ref{sec: data} we describe the dataset used here. In Section \ref{sec: method} we describe the parameterisation of the GSMF and the fitting methods employed. In Section \ref{sec: results} we present the results of our analysis, with a discussion of the implications of our fits in Section \ref{sec: discussion}, and in Section \ref{sec: conclusions} we provide some concluding remarks. Throughout this work we use a concordance cosmological model of $\Omega_{\rm M}=0.3$, $\Omega_{\Gamma}=0.7$, ${\rm H_0}=70\,{\rm km s^{-1} Mpc^{-1}}$ and ${\rm h_{70}} = {\rm H_0}/70 \, {\rm km s^{-1} Mpc^{-1}}$. All masses are derived/quoted using a time-invariant \ccite{Chabrier2003} IMF, \ccite{Bruzual2003} population synthesis models, and a \ccite{Charlot2000} dust model. {\bbf All magnitudes are presented in the AB system}. | \label{sec: conclusions}% In this work we have demonstrated the evolution of \ccite{Schechter1976} function parameters over $12.5\,h_{70}^{-1}\,{\rm Gyr}$ using the combined sample of GAMA, G10-COSMOS, and 3D-HST. Using multiple Schechter function fits, we demonstrate that the single component Schechter function is unlikely to produce reliable fits, even out to a redshift of 5. Conversely, the two-component Schechter shows impressive stability of its fitted parameters over the entire redshift range, providing well constrained parameters at essentially all epochs. We explore the evolution of the mass function further by regressing the various parameters such that we achieve a smooth evolution. Our regressed parameters, in our two-component Schechter fits, show little to no evolution of the $M^\star$, $\alpha_i$, or low-mass $\phi^\star$ parameters over time, and are especially stable over the last $\sim\!11.0\,h_{70}^{-1}\,{\rm Gyr}$. Conversely, the high-mass $\phi^\star$ parameter shows strong evolution over the same period. The stability of most parameters, coupled with the evolution of the high-mass component's normalisation parameter, suggests a picture of galaxy evolution where these two components broadly track different mass-evolution mechanisms; the low-mass systems broadly following secular evolution of galaxies, while high-mass systems are constantly being built up through merger processes. At the highest redshifts, the low mass component exhibits somewhat rapid evolution in its normalisation, starting out as the mass-dominant component of the GSMF until it is overtaken at $\sim\!9\,h_{70}^{-1}\,{\rm Gyr}$, when the growing high-mass component becomes the dominant reservoir of mass. We then test whether the build-up of mass over the last $11\,h_{70}^{-1}\,{\rm Gyr}$ is well described by a constant rate of mass growth, finding that this is indeed the case, and that a simple model of the mass function growth is able to perfectly describe the observed evolution of the stellar mass density parameter over the majority of the evolution history of the universe. Nonetheless, we {recognise that this mass growth function encodes a highly complex array of mass growth/loss/redistribution mechanisms, and that alone may be only used as a guiding observable in future complex mass-assembly studies.} We conclude that upcoming deep and highly complete surveys of group-scale environments, at intermediate to high redshift, will be required in order to determine the mechanisms driving the observed growth of stellar mass. | 18 | 8 | 1808.01754 |
1808 | 1808.04989_arXiv.txt | We present coronal density profiles derived from low-frequency (80--240 MHz) imaging of three type III solar radio bursts observed at the limb by the Murchison Widefield Array (MWA). Each event is associated with a white light streamer at larger heights and is plausibly associated with thin extreme ultraviolet rays at lower heights. Assuming harmonic plasma emission, we find average electron densities of 1.8\e{8} cm\tsp{-3} down to 0.20\e{8} cm\tsp{-3} at heights of 1.3 to \rsolar{1.9}. These values represent $\sim$2.4--5.4$\times$ enhancements over canonical background levels and are comparable to the highest streamer densities obtained from data at other wavelengths. Assuming fundamental emission instead would increase the densities by a factor of 4. High densities inferred from type III source heights can be explained by assuming that the exciting electron beams travel along overdense fibers or by radio propagation effects \edit{that may cause a source to appear at a larger height than the true emission site.} We review the arguments for both scenarios in light of recent results. We compare the extent of the quiescent corona to model predictions to estimate the impact of propagation effects, which we conclude can only partially explain the apparent density enhancements. Finally, we use the time- and frequency-varying source positions to estimate electron beam speeds of between 0.24 and 0.60 c. | % \label{introduction} % Type III solar radio bursts are caused by semi-relativistic electrons streaming through and perturbing the ambient coronal or interplanetary plasma. A recent review is given by \citet{Reid14}. The dominant theory, proposed by \citet{Ginzburg58}, invokes a two-step process beginning with the stimulation of Langmuir waves (plasma oscillations) in the background plasma by an electron beam. A small fraction of the Langmuir wave energy is then converted into electromagnetic radiation at either the local electron plasma frequency ($f_p$) or its harmonic (2$f_p$; see reviews by \citealt{Robinson00,Melrose09}). The emission frequency depends mainly on the ambient electron density ($n_e$) because $f_p \propto \sqrt{n_e}$. This relationship produces the defining feature of type III bursts, a rapid drift from high to low frequencies as the exciter beam travels away from the Sun through decreasing densities \citep{Wild50}. The rate at which the emission frequency drifts ($df/dt$) is therefore related to the electron beam speed, which can be obtained in the radial direction by assuming a density model $n_e(r)$. Many authors have employed this technique for various events with various models, generally finding modest fractions of light speed (0.1--0.4 $c$; e.g. \citealt{Alvarez73,Aschwanden95,Mann99,Melendez99,Krupar15,Kishore17}). Alternatively, the coronal and/or interplanetary density gradient can be inferred by instead assuming a beam speed (e.g. \citealt{Fainberg71,Leblanc98}) or by simply assuming that the beam speed is constant \citep{Cairns09}. While these methods can yield robust estimates for the density gradient, they cannot be converted into an explicit density structure $n_e(r)$ without normalizing the gradient to a specific value at a specific heliocentric distance. This normalization has typically been done using estimates from white light polarized brightness data close to the Sun, \textit{in situ} data in the interplanetary medium, or the observed height of type III burst sources at various frequencies. Densities inferred from type III source heights, particularly at lower frequencies, have frequently conflicted with those obtained from other methods. The earliest spatial measurements found larger source heights than would be expected from fundamental plasma emission, implying density enhancements of an order of magnitude or more \citep{Wild59}. This finding was confirmed by subsequent investigations (e.g. \citealt{Morimoto64,Malitson66}), and along with other arguments, led many authors to | % \label{conclusion} % We presented imaging of three isolated type III bursts observed at the limb on different days using the MWA. Each event is associated with a white light streamer and plausibly associated with EUV rays that exhibit activity around the time of the radio bursts. Assuming harmonic plasma emission, density profiles derived from the source heights imply enhancements of $\sim$2.4--5.4$\times$ over background levels. This corresponds to electron densities of 1.8\e{8} cm\tsp{-3} (240 MHz) down to 0.20\e{8} cm\tsp{-3} (80 MHz) at average heights of 1.3 to \rsolar{1.9}. These values are consistent with the highest streamer densities inferred from other wavelengths and with the large radio source heights found using older instruments. The densities are also consistent with recent type III results at higher and lower frequencies, which combined are well-fit by a $C(r - 1)^{-2}$ gradient. By comparing the extent of the radio limb to model predictions, we estimated that \edit{radio propagation effects, principally the ducting-like effect of random scattering by high density fibers,} may be responsible for 0.06--0.30\rsolar{} of our apparent source heights. This shift brings the results from 2 of our 3 events to within a standard range of background densities. We therefore conclude that propagation effects can partially explain the apparent density enhancements but that beams moving along overdense structures cannot be ruled out. We also used the imaging data to estimate electron beam speeds of 0.24--0.60 c. \begin{acks} Support for this work was provided by the Australian Government through an Endeavour Postgraduate Scholarship. We thank Stephen White and Don Melrose for helpful discussions \edit{and the anonymous referee for their constructive comments}. This scientific work makes use of the Murchison Radio-astronomy Observatory (MRO), operated by the Commonwealth Scientific and Industrial Research Organisation (CSIRO). We acknowledge the Wajarri Yamatji people as the traditional owners of the Observatory site. Support for the operation of the MWA is provided by the Australian Government's National Collaborative Research Infrastructure Strategy (NCRIS), under a contract to Curtin University administered by Astronomy Australia Limited. We acknowledge the Pawsey Supercomputing Centre, which is supported by the Western Australian and Australian Governments. The SDO is a National Aeronautics and Space Administration (NASA) satellite, and we acknowledge the AIA science team for providing open access to data and software. The SOHO/LASCO data used here are produced by a consortium of the Naval Research Laboratory (USA), Max-Planck-Institut fuer Aeronomie (Germany), Laboratoire d'Astronomie (France), and the University of Birmingham (UK). SOHO is a project of international cooperation between ESA and NASA. This research has also made use of NASA's Astrophysics Data System (ADS), along with JHelioviewer \citep{Muller17} and the Virtual Solar Observatory (VSO, \citealt{Hill09}). \end{acks} | 18 | 8 | 1808.04989 |
1808 | 1808.06174_arXiv.txt | We used the light curve code XRBinary to model the quiescent K2 light curves of three low-inclination cataclysmic variables (CVs): 1RXS\,J0632+2536 (J0632+2536), RZ\,Leo, TW\,Vir and the pre-CV WD\,1144+011. Optimized light curve models were obtained using a nonlinear fitting code NMfit and visualized by Phoebe 2.0. The disk model of J0632+2536 shows that one hotspot at the edge of the disk is enough to describe its light curve, while the other two dwarf nova (DN): RZ\,Leo and TW\,Vir require two hotspots. A typical pre-CV model with a weak irradiation effect for WD\,1144+011 can explain its single-hump modulation, and the newly observed spectrum confirms its previous classification. The synthetic analyses for the DN clearly indicate that phase zero of the double-hump modulations occurs around the secondary minimum and the primary hump is mainly caused by the hotspot at the edge of the disk. The quiescent disk has a flat temperature distribution with a power index of $\sim0.11$. The disk model of RZ\,Leo implies a truncated disk, supporting its previously speculated classification as an intermediate polar (IP). Except for the IP model of RZ\,Leo, which lacks a component related to the inferred accretion curtain, the models of J0632+2536, TW\,Vir and WD\,1144+011 are consistent with results from the Gaia mission. The derived masses and radii of the secondaries of the three DN are consistent with the semi-empirical relations for CV donor stars, while their effective temperatures are higher than the predictions. Irradiation of the donor stars is investigated to explain this discrepancy. | Dwarf novae (hereafter DN) are a subtype of primarily non-magnetic cataclysmic variables (hereafter CVs), in which a white dwarf primary accretes matters from a Roche-lobe filling late-type star via the inner (L1) Lagrange point \citep{war03}. An accretion disk can extend to the white dwarf surface via viscous processes between adjacent accretion annuli (e.g., friction and shear) due to a weak magnetic field of the white dwarf in DN (B$<$10$^{6}$\,G). Systems in which the magnetic field of the white dwarf is large enough (10$^{6}<B\leqslant$\,10$^{7}$\,G) such that the accretion disk is disrupted inside the white dwarf magnetosphere and material begins to follow the magnetic field lines are called Intermediate Polars (hereafter IPs). In the following, we assume that the disk outside of the magnetosphere in an IP is equivalent in structure to the disk in a regular non-magnetic DN. The interaction between the ballistic stream leaving the L1 point and the accretion disk forms a region of energy release at the edge of the disk called a hotspot. The combination of an accretion disk and a hotspot (hereafter just called the disk model) has been used as the typical accretion model for CVs \citep[e.g.][]{sma70,war03} and has been quite successful in describing the asymmetrical eclipse profile of several high-inclination CVs during quiescence \citep[e.g.][]{bru96,woo86}. This model can also be used to explain a symmetrical CV eclipse profiles during outburst \citep[e.g.][]{kat03,bak15}, which is caused by the significant flux increase of the disk (i.e., the luminous accretion disk almost overwhelms the relatively faint white dwarf and hotspot). Several high-inclination CVs in quiescence have been comprehensively studied using this disk model \citep[e.g.][]{coo84,bai91,mca15}. By detecting variations in the mid-eclipse times, substellar objects have been suggested to exist in several DN (e.g., V2051\,Oph \citep{qia15} and EM\,Cyg \citep{dai10a}). In addition, many synthetic light curve analysis methods (e.g., BINSYN program \citep{lin12}, Eclipsing Light Curve Code \citep{oro00} and the cool-disk model \citep{khr11}) have been developed to analyze CV eclipse light curves. The irregular eclipse light curves of quiescent CVs are composed of the occultations of multiple components including the white dwarf, the accretion disk and hotspots \citep[e.g.][]{sma94,fel04,lit14,mca15}. High-inclination CVs only show a single eclipse in one orbit (i.e., the secondary eclipse of the red dwarf is invisible \cite[e.g.][]{krz65,bai88}), since the red dwarf in a CV system is usually regarded to be a very faint component compared with the accretion disk and the white dwarf. This ``single-eclipse" feature implies that CV eclipse light curves cannot reveal full information about the red dwarf companion. Due to the complexity of the quiescent CV eclipse light curves, high time resolution is necessary to decompose all components. However, over 70\% of CVs with short orbital periods ($<$\,3\,hr) are fainter than 17\,mag in quiescence based on the updated CV catalogue (RKcat Edition 7.24 first published in \cite{rk724}). Therefore, the majority of CVs have only low time-resolution photometry comprised of blended flux from many components, which makes modelling these systems difficult. For example, recent discussions concerning two new-found CVs with deep eclipses carried out by \cite{kju15} and \cite{ken16} clearly indicated that the model light curves cannot perfectly fit the observed eclipsing light curves during ingress and outside of eclipse. Assuming a deep eclipse is a common feature of CVs with orbital inclination higher than 80$^{\circ}$, the fraction of low-inclination CVs can be simply estimated to be around 90\%. To determine a general model independent of inclination, it is necessary to consider low-inclination CVs. The unprecedented light curves from the Kepler K2 mission \citep{how14}, with nearly continuous photometric coverage for 1-3 months at different pointings (Campaigns) along the ecliptic provide an excellent database to study quiescent CV light curves. K2 Campaign 0 (K2-C0) was an engineering test in the early stage of the K2 program and only covered $\sim$\,35 days since the spacecraft was not in fine point during the beginning of the campaign, while K2 Campaign 1 (K2-C1) covered a complete period of 80 days. We focus in this paper on the phased light curves of four systems: 1RXS\,J0632+2536 (hereafter J0632+2536) and TW\,Vir which are both DN, RZ\,Leo which is an unusual IP that also has displayed DN outbursts, making it one of the few systems to be both a magnetic system and a DN, and WD\,1144+011 which is a pre-CV (meaning the secondary is likely not filling its Roche lobe). J0632+2536 was observed in K2-C0, while TW\,Vir, RZ\,Leo and WD\,1144+011 were observed in K2-C1. The phased light curves are investigated in detail using the synthesis methods XRBinary and NMfit described in Section 3. Due to the lack of any eclipse feature, all four objects are likely low-inclination systems. The preset model parameters are discussed in Sections 4 and 5. The details of the white dwarf accretion structure during quiescence and the physical parameters of the stars in each system are further discussed and visualized in Section 6. | \subsection{Synthetic codes} Based on the light curve synthesis code XRBinary derived by E.L. Robinson, NMfit was developed to analyze the light curves of the four low-inclination systems: J0632+2536, RZ\,Leo, TW\,Vir and WD\,1144+011. All parameters of the best-fitting models and their uncertainties are estimated by NMfit. Additionally, Phoebe 2.0 was used to visualize the configuration of each system using each systems best-fitting parameters. Since phase zero is hard to identify in any low-inclination CV system with a double-hump modulation due to the lack of a significant eclipse feature, we tested models which had phase zero located at either the primary or secondary minimum, and chose the model which matched the observed light curve best. Except for WD\,1144+011 which had a single maximum in its phased orbital light curve, the derived CV models of the other three DN indicate that phase zero should be placed at the secondary minimum. \subsection{Physical Models} For J0632+2536 and TW\,Vir, the best-fit disk models show that the primary hump is mostly due to the hotspot at the edge of the disk, a key indicator of mass transfer via the L1 point. Another hotspot on the disk surface can explain the phase difference between the two humps of the double-hump modulations. For WD\,1144+011, the bright ``starspot" representing irradiation of the secondary star is responsible for the modulation seen in the optical light curve. The lack of an accretion curtain in the disk model of RZ\,Leo implies that this model may not be appropriate for a comparison with the measured distance by Gaia. The derived physical models of the other three binary systems are consistent with the results from Gaia DR2. The flat power law index of the disk found in all three DN models ($\xi\sim$\,-0.11) is similar to previous observations \citep[e.g.][]{woo86,woo89,rut16} and supports the theory that a quiescent CV disk deviates from the temperature distribution of a typical steady-state disk. A low-luminosity accretion disk model of RZ\,Leo derived from its K2 light curve further confirms that RZ\,Leo is an IP system with two hotspots on a truncated disk. One of the hotspots on the disk surface contributes a significant fraction of the disk luminosity ($>97\%$ of L$_{d}$), and is located at the inner edge rather than the outer edge of the disk. This may be evidence of an impact region between an inward and overflowing stream and the magnetosphere of the magnetic white dwarf. Compared with RZ\,Leo, the small hotspot of J0632+2536 and two hotspots of TW\,Vir covering large phase ranges are only small contributors to the disk luminosity. Our spectrum of WD\,1144+011 with a relatively flat continuum and H$_{\alpha}$ emission supports its previous classification as a DA+dMe system \citep{ber92}. We note that WD\,1144+011 shows different flux levels in the continuum and emission lines. The model light curve based on the asymmetrical single-hump modulation requires an extra light source (i.e., a weak irradiation region of the secondary rather than a large hotspot at the edge of the disk) to explain the modulation of WD\,1144+011. \subsection{The Secondaries} The estimated $\dot{M}_{rd}$ for all four objects are within a range of $10^{-9}\sim10^{-12}\,M_{\odot}$/year. Except for the pre-CV WD\,1144+011 which contains an oversized secondary, the other three DN have secondaries in thermal equilibrium with masses and radii conforming to the semi-empirical CV donor sequence \citep{kni06,kni11} and MK spectral classes \citep{cox00}. The derived effective temperatures of all three DN are significantly higher than predicted. Hence a DN system containing a substantially hotter secondary may be a common feature rather than a peculiarity. This can be attributed to irradiation of the secondary, since T$_{rd}$ calculated from L$_{rd}$ is an average parameter which can be increased by irradiation. Compared with T$_{eff}$ listed in the Gaia catalog, the lower T$_{rd}$ of the two DN J0632+2536 and TW\,Vir may due to contamination from a hot white dwarf and disk. This is further supported by the T$_{rd}$ of the pre-CV WD1144+011, which is almost consistent with the Gaia T$_{eff}$. It should also be noted that the Gaia temperatures are determined from three broad bandpasses \citep{and18} and the DR2 releases notes urge caution in using them \footnote{\url{https://gea.esac.esa.int/archive/documentation/GDR2/pdf/GaiaDR2_documentation_1.0.pdf}}. Although the double-hump modulation of J0632+2536 can be explained by the partial occultation of the irradiation region on the surface of the secondary due to a large disk and a moderate orbital inclination, investigation of irradiation in the other two DN implies that the effect of irradiation in a CV system is complicated and blended with other modulations. The flux contribution from the secondary of TW\,Vir is the lowest (i.e., L$_{rd}<L_{wd}+L_{d}$) among all four objects. Weak irradiation may exist in the DN TW\,Vir and the pre-CV WD\,1144+011. The former can be further tested by additional light curves obtained when the double-hump variation is evident, while the latter can be further checked by taking a time series of spectra over the course of the complete orbital period of 9.81\,hr. | 18 | 8 | 1808.06174 |
1808 | 1808.08958_arXiv.txt | The Tayler instability (TI) is a non-axisymmetric linear instability of an axisymmetric toroidal magnetic field in magnetohydrostatic equilibrium (MHSE). In a differentially rotating radiative region of a star, the TI could drive the Tayler-Spruit dynamo, which generates magnetic fields that can significantly impact stellar structure and evolution. Heuristic prescriptions disagree on the efficacy of the dynamo, and numerical simulations have yet to definitively agree upon its existence. Criteria for the TI to develop were derived using fully-compressible magneto-hydrodynamics, while numerical simulations of dynamical processes in stars frequently use an anelastic approximation. This motivates us to derive new anelastic Tayler instability criteria. We find that some MHSE configurations unstable in the fully-compressible case, become stable in the anelastic case. We find and characterize the unstable modes of a simple family of cylindrical MHSE configurations using numerical calculations, and discuss the implications for fully non-linear anelastic simulations. | \label{sec:intro} The Tayler instability \citep[TI;][]{Tayler_1973, Markey_Tayler_1973, Markey_Tayler_1974, Acheson_1978, Pitts_Tayler_1985} is a local non-axisymmetric linear instability of an axisymmetric toroidal magnetic field in magnetohydrostatic equilibrium (MHSE). \citet{Spruit_1999} has argued that this instability is particularly important because it can manifest when other instabilities are suppressed by thermal stratification. Growth rates are on the order of the global Alfv\'{e}n-wave crossing time, which is generally short compared to other stellar time scales, even for weak magnetic fields. These two qualities make the TI the most relevant magnetic instability of a toroidal magnetic field in MHSE, at least in a non-rotating star. The TI has been proposed as a mechanism for significantly affecting a stars' % structure and rotational evolution. \cite{Auriere_2007} proposed the TI as a mechanism for explaining the observed dichotomy in the surface magnetic field strengths of intermediate-mass stars. In stars with a relatively weak poloidal field, differential rotation generates a toroidal field unstable to the TI, transforming the field components from low-order to high-order, and yielding disk-average surface fields that may fall below observational detection thresholds. Conversely, in stars with a relatively strong poloidal field, differential rotation decays before generating a toroidal field unstable to the TI, preserving the field components, and yielding low order surface fields seen in Ap/Bp stars. \citet{Spruit_2002} proposed the TI as one half of a dynamo that could be a significant mechanism of angular momentum transport inside the radiative regions of stars. A toroidal field unstable to the TI generates a radial field displacement which is then rewound by differential rotation back into a toroidal field, creating a dynamo loop. The magnetic torque generated by this Tayler-Spruit dynamo could be a missing link in stellar evolution theory, where there is currently a discrepancy between the modeled and observed rotation rates of red giant cores, and of stellar remnants. \citet{Cantiello_etal_2014} showed that the heuristic prescription for the Tayler-Spruit dynamo implemented in the stellar evolution code Modules for Experiments in Stellar Astrophysics \citep[MESA;][]{Paxton_etal_2013,Paxton_etal_2015,Paxton_etal_2018} increases angular momentum transport during red giant branch evolution. The results cannot fully explain the slow core rotation rates of red giant branch stars as observed by \textit{Kepler}, but the models with the dynamo are in better agreement with observations than the models without. Recently \cite{Fuller_2019} demonstrated that a revised prescription implemented into MESA could largely reproduce observed rotation rates. \citet{Maeder_2003, Maeder_2004, Maeder_2005} showed that a heuristic prescription for the Tayler-Spruit dynamo, as implemented in the Geneva stellar evolution code \citep{Meynet_2005}, can have a significant effect on the main-sequence evolution of massive stars. The dynamo imposes near solid-body rotation that enhances meridional circulation and efficient mixing, resulting in larger convective cores, longer main-sequence life times, enriched surface abundances of nucleosynthesized elements, and elevated stellar luminosities. \citet{Song_2016, Song_2018} demonstrated that for massive stars in binary systems, spun up through tidal interactions, dynamo-induced solid body rotation can lead to similar outcomes. Despite the potential significance of the Tayler-Spruit dynamo in stellar structure and evolution, the existence and nature of the dynamo is currently debated through both analytical and numerical calculations. Analytically, various heuristic prescriptions have been developed to predict the magnitude of the magnetic torque \citep{Spruit_1999, Spruit_2002, Maeder_2003, Maeder_2004, Heger_etal_2005, Braithwaite_2006a, Denissenkov_Pinsonneault_2007}. Numerically, non-linear MHD simulations have been unable to agree whether the dynamo actually operates as envisaged \citep{Braithwaite_2006, Zahn_etal_2007}. In light of the potential importance of the Tayler-Spruit dynamo for stars, the disagreement between the analytical predictions and the numerical results is unsettling. The discrepancy motivates us to look at the basic assumptions used in the original TI critera and in the non-linear MHD simulations investigating the Tayler-Spruit dynamo. \cite{Tayler_1973} developed criteria for the TI using fully-compressible ideal MHD, while numerical MHD simulations of stellar interiors frequently use anelastic MHD (eg. \cite{Brown_etal_2012}), an approximation that filters out sound waves, which are very short-period relative to stellar timescales and are therefore prohibitively expensive to compute. The goal of this paper is to re-examine the TI in the anelastic approximation. We derive new anelastic TI (anTI) stability criteria and apply them to a family of simple MHSE models to determine which are subject to the instability. We verify our results numerically using a modified version of the \gyre\ stellar oscillation code \citep{Townsend_Teitler_2013}, which solves a system of linearized anelastic MHD equations to calculate growth rates and eigenfunctions of unstable modes. We conclude that the anelastic case is more restrictive, but that the TI should be present in anelastic MHD simulations if the models used are unstable under the anTI criteria. The paper is structured as follows. In Section~\ref{sec:energy_principle} we given an overview of the energy principle --- the method used to develop the instability criteria. In Section~\ref{sec:compressible_vs_lbr_mhd} we introduce the fully-compressible MHD equations and the Lantz-Braginsky-Roberts (LBR) anelastic approximation for MHD, a form that is valid in the isothermal atmosphere we assume in our later analysis. In Section~\ref{sec:instability_analysis} we summarize the original TI stability criteria derived from the energy principle, and derive the new anTI criteria. In Section~\ref{sec:instability_calcs} we compare the original and anTI criteria to \gyre's numerically calculated growth rates and eigenfunctions for unstable modes in our models, showing that the anTI criteria are correct in anelastic MHD. In Section~\ref{sec:conclusion} we conclude with considerations for future analytical and numerical work. | \label{sec:conclusion} The TI is of interest in the radiative regions of stars because, with differential rotation, it may contribute to forming and maintaining a magnetic field dynamo that could significantly affect the stars' structure and evolution. However, attempts to heuristically derive and numerically simulate the growth and saturation of the TI in stellar models have led to indeterminate results. The TI criteria were derived using fully compressible MHD, but simulations of fluid dynamics in stellar interiors frequently use some version of the anelastic or pseudo-incompressible approximations, which suppress acoustic waves with much shorter periods than stellar timescales. The goal of this paper was not to address the problem of whether the dynamo exists, but to narrow the gap between fully-compressible linear theory and anelastic non-linear simulations of the TI. We undertook this by modifying the classic MHD energy principle \citep{Bernstein_etal_1958} according to LBR anelastic MHD, which --- based on the work of \cite{Brown_etal_2012} --- we regard as the most promising of several anelastic schemes. We derived a version of the MHD energy principle that yields stability criteria (equations~\ref{eq:coeff_lbr} and~\ref{eq:stab_lbr}) in excellent agreement with solutions of the eigenvalue problem calculated using the \gyre\ code. Our test configuration was a family of cylindrically symmetric magnetohydrostatic equilibria with a toroidal background magnetic field and gravity supplied by a line mass (Section~\ref{ssec:instability_calcs_model}). Our results show that the instability still exists in LBR anelastic MHD, but in a more restricted part of parameter space than the fully-compressible case. This is because the energy principle is based on minimizing the potential energy of the system, and anelasticity introduces a constraint which precludes full minimization. However, we conclude that the instability should manifest in anelastic LBR MHD simulations if the models used are unstable under the anTI criteria. We found that the amplitude of the displacement in the horizontal direction is greater than the displacement in the radial direction, as predicted by \cite{Spruit_2002}. We also found that the largest growth rates calculated by \gyre\ are somewhat smaller than predicted for slow rotators by \cite{Spruit_2002}. We are limited in addressing discrepancies between our calculations and heuristic predictions of the saturated state because our analysis and numerical calculations are in the linear regime and lack rotation or dissipative effects, both of which are key ingredients in the proposed instability-driven dynamo \citep{Spruit_2002}. We are unable to predict the non-linear growth rate and amplitude of the instabilities without taking those physical effects into consideration. That is beyond the scope of this work, but it is an open question for future work. Our family of cylindrical models can be implemented in anelastic MHD simulations. Such simulations could verify the linear analysis and calculations that we performed, and determine how non-linear effects impact the growth rate and amplitude of the instability. Choosing models that are unstable under the anTI criteria, and including differential rotation, anelastic MHD simulations could more accurately test the the Tayler-Spruit dynamo and its significance as a mechanism for angular momentum transport in stellar evolution. | 18 | 8 | 1808.08958 |
1808 | 1808.01879_arXiv.txt | If the symmetry breaking leading to the origin of the axion dark matter field occurs after the end of inflation and is never restored, then overdensities in the axion field collapse to form dense objects known in the literature as axion miniclusters. The estimates of the typical minicluster mass and radius strongly depend on the details of the cosmology at which the onset of axion oscillations begin. In this work we study the properties and phenomenology of miniclusters in alternative cosmological histories and find that they can change by many orders of magnitude. Our findings have direct implications on current and future experimental searches and, in the case of discovery, could be used to learn something about the universe expansion prior to Big-Bang-Nucleosynthesis. | The nature of the cold dark matter (CDM) remains unknown to date despite the growth of evidence in support of its existence coming, on top of the original motivations~\cite{1976AJ.....81..687R, 1976AJ.....81..719R}, from gravitational lensing~\cite{Trimble:1987}, the cosmic microwave background radiation (CMBR)~\cite{Ade:2015xua, Aghanim:2018eyx}, also in combination with Lyman-$\alpha$ and weak lensing~\cite{Lesgourgues:2007te}, the hierarchical structure formation of the observable universe~\cite{Springel:2005nw}, the formation and evolution of galaxies~\cite{Davis:1985rj, Efstathiou:1985re, Springel:2006vs}, galactic collisions~\cite{Clowe:2003tk, Markevitch:2003at}, and a plethora of other observational techniques. Among the many hypothetical particles that could compose the CDM is the quantum chromodynamics (QCD) axion~\cite{Weinberg:1977ma, Wilczek:1977pj}. The axion is the pseudo-Goldstone boson arising in the spontaneous breaking of a U(1) symmetry first introduced by Peccei and Quinn (PQ~\cite{Peccei:1977hh, Peccei:1977ur}) to address the strong-CP problem~\cite{Belavin:1975fg, tHooft:1976rip, Jackiw:1976pf, Callan:1976je}. The fact that axions could solve two distinct problems in physics makes its search particularly appealing. If the axion field exists, it has a very small mass and faint couplings to ordinary particles. Both happen to be suppressed by a new energy scale, the axion decay constant $f_A$, which corresponds approximately to the scale of PQ symmetry breaking and which is constrained by axion phenomenology to be $f_A\gtrsim 10^7\,$GeV. In particular, the scale $f_A^{-1}$ sets the axion coupling to two photons, which opens the possibility for axion electrodynamics~\cite{Wilczek:1987mv, Krasnikov:1996bm, Li:2009tca, visinelli:2013fia, Tercas:2018gxv, Visinelli:2018zif} and promising laboratory detection methods~\cite{Stern:2016bbw, Raggi:2014zpa, Majorovits:2016yvk, Kahn:2016aff, Alesini:2017ifp, Alesini:2019nzq}. In the literature, mixed dark matter models in which the axion makes up a fraction of the dark matter while the rest is in the form of weakly interacting massive particles (WIMPs) have also been considered~\cite{Bae:2014efa, Bae:2015rra, Baum:2016oow}. See Refs.~\cite{Raffelt:1995ym, Raffelt:2006rj, Sikivie:2006ni, Kim:2008hd, Wantz:2009it, Kawasaki:2013ae, Marsh:2015xka,Kim:2017yqo} for reviews of the QCD axion. The history and the properties of the present axion field strongly depend on the moment at which the breaking of the PQ symmetry occurs with respect to inflation~\cite{Linde:1987bx, Linde:1991km, Turner:1991, Wilczek:2004cr, Tegmark:2005dy, Hertzberg:2008wr, Freivogel:2008qc, Mack:2009hv, Visinelli:2009zm, Acharya:2010zx, Ballesteros:2016xej, Hoof:2018ieb, Tenkanen:2019xzn}. If the PQ symmetry breaking occurs after inflation, a fraction of the total axions component is expected to organize into gravitationally bound structures known as axion ``miniclusters''~\cite{Hogan:1988mp, Kolb:1993zz, Kolb:1993hw, Kolb:1994fi, Sakharov:1996xg}, prompted by the inhomogeneities of the axion field in this scenario. Axion miniclusters are compact objects with a density of various orders of magnitude higher than the present local CDM density. Inside axion miniclusters another type of exotic structure, an axion star~\cite{Kaup:1968zz, Ruffini:1969qy, Das_1963, Feinblum:1968nwc, Teixeira:1975ad, Colpi:1986ye, Seidel:1991zh, Tkachev:1991ka, Chavanis:2011, Braaten:2015eeu, Eby:2015hyx, Eby:2016cnq, Levkov:2016rkk, Helfer:2016ljl, Braaten:2016dlp, Braaten:2016kzc, Bai:2016wpg, Eby:2017xaw, Desjacques:2017fmf, Visinelli:2017ooc, Chavanis:2017loo, Krippendorf:2018tei, Eggemeier:2019jsu}, could possibly form. It has been argued that the first miniclusters that ever come into place have a characteristic size of the order of $\sim 10^{-12}$ solar masses. This scale is much smaller than the smallest clump that WIMPs would assemble into in the standard cosmology, because of their much longer free-streaming length~\footnote{See Ref.~\cite{Gelmini:2008sh} for the effect of a non-standard cosmology on the free-streaming length of WIMPs.}. Therefore, detecting these clumps provides a unique discrimination signature among CDM candidates. As structure formation evolves, axion miniclusters are expected to hierarchically assemble into dark matter halos of galactic size, forming minicluster halos. This claim has yet to be addressed numerically, as well as the possibility that miniclusters might have not survived tidal disruption. Some studies suggest that miniclusters survive hierarchical structure formation to date~\cite{Zurek:2006sy, Tinyakov:2015cgg, Hardy:2016mns, Dokuchaev2017}, claiming that it is possible to constrain the fraction of dark matter in halos using micro-lensing data~\cite{Fairbairn:2017dmf, Fairbairn:2017sil} and femto-lensing in the future~\cite{Katz:2018zrn} (see also \cite{Inomata:2017vxo}). Semi-analytic results on the mass function of axion miniclusters are available today~\cite{Enander:2017ogx}, with refined numerical work recently reported~\cite{Vaquero:2018tib, Eggemeier:2019khm}. Today, the standard axion miniclusters would be gravitationally bound clumps of axions with masses of the order of the largest asteroids like Vesta or Pallas, and of size comparable to an astronomical unit. Miniclusters could suffer tidal disruption by stars, with the value of bound axions diminishing with respect to its early universe estimate. It is usually expected that a sizeable fraction of the galactic DM axions is bound into minicluster structures, the remaining part forming a relatively homogeneous halo. Despite the large number of clumps expected, the Earth would encounter only a few such objects every galactic year (!). On the other hand, if the fraction of axions bound into miniclusters is close to unity, the direct detection of axions in microwave cavity searches could be severely affected. A negative search by a cavity experiment could be an indication that axions are mostly organised into clumped structures like miniclusters. Since axion detection is sensitive to the local CDM energy density, a clumpy axion distribution would lead to spikes in the axion detection spectrum and be relevant for a direct detection technique. The interest in all of the upcoming axion detectors then lies in the present phase-space distribution of the axion CDM, which is not expected to be homogeneous even at the interstellar scale. A reliable detection must take into account the possibility of a inhomogeneous CDM distribution either in space (axion miniclusters and stars) or in momentum (low-dispersion filaments from tidal stripping). Moreover, if the axion is discovered by a haloscope experiment like ADMX, HAYSTAC or CULTASK, the energy spectrum will be immediately measured and could be used to do galactic astronomy~\cite{OHare:2017yze}. The spectrum and its variation in time (daily and anual modulations) can be used to identify substructure in the axion DM distribution like tidal streams from dwarf-galaxies~\cite{Vogelsberger:2010gd} or even from axion miniclusters themselves, obtaining their main properties with precision~\cite{OHare:2017yze}. With these techniques, astronomical quantities like the solar peculiar velocity could be measured even better than with ordinary astronomy. Several variations of the haloscope concept allow to measure the axion velocity distribution by enabling directional detection~\cite{Irastorza:2012jq, Irastorza:2018dyq, Knirck:2018knd}, increasing the precision and decreasing the required measurement time. Understanding the fraction of axions bound in miniclusters and of the axion phase-space will maximise the outcome of the various experiments that will start looking for axion CDM in the near future. The rough properties of axion miniclusters described above have been studied only under the assumption that the universe is radiation-dominated when axions become non-relativistic. This is certainly a simple and minimal assumption but also one that does not need to be necessarily correct. We know with some certainty that the universe expansion must be radiation-dominated after and around neutrino decoupling (temperatures of $T\lesssim 5\,$MeV) not to alter the successful predictions of radiation-dominated Big-Bang Nucleosynthesis (BBN)~\cite{Kawasaki:1999na, Kawasaki:2000en, Hannestad:2004px, Ichikawa:2005vw, DeBernardis:2008zz}, but we have no direct evidence of the expansion rate of the universe at earlier times (higher temperatures). Most importantly, if axions are to be a dominant contribution to the CDM they become CDM at temperatures $\sim\,$GeV, precisely when we cannot ascertain the crucial assumption of radiation domination. In this paper we want to drop entirely this assumption and study the properties of axion miniclusters in different non-standard cosmologies (NSCs) before BBN. The mass and the radius of a minicluster depend crucially on the size of the causal horizon at the time when axions become non-relativistic, which in alternative cosmologies might differ by various orders of magnitude with respect to the standard scenario. In order to focus the discussion on the novel aspects, we assume that axions make up the totality of the cold dark matter observed and that essentially all axions fall into miniclusters. Our results, summarised in \mbox{Table~\ref{table_parameters}} are quite spectacular! In fact, the typical minicluster mass and radius can change by many orders of magnitude with respect to the predictions achieved in the standard cosmology. Most importantly, the time and duration of encounters with the Earth can be largely enhanced or suppressed, opening many possibilities for the direct detection of axion dark matter. Previous works have already studied how the axion mass for which the axion explains the totality of the observed CDM is modified in several NSCs~\cite{Visinelli:2009kt, Visinelli:2017imh, Ramberg:2019dgi} but the changes to the properties of miniclusters are presented here for the first time. Moreover, regarding the treatment of NSCs and the axion DM mass, we improve over previous results by computing the non-standard cosmologies numerically including the recent detailed input from lattice QCD (equation of state and axion mass)~\cite{Borsanyi:2016ksw} and presenting simple analytical comparisons with the standard radiation dominated case. Note that, in addition to the cold axion population, a modified cosmology would alter the yield of thermally produced axions~\cite{Grin:2007yg}, as well as of any other light particle such as neutrinos~\cite{Giudice:2000dp, Giudice:2001ep}; however, since for the range of masses considered in this work, $m_A \lesssim 10\,$meV, the thermal population is a sub-dominant component to the total energy density, we do not discuss this contribution further. This paper is organised as follows. Sec.~\ref{axion_review} is a brief review of the production of cosmological axions. In Sec.~\ref{cosmological_modified} we set the stage for the non-standard cosmological models of interest and we review their impact on the DM axion mass. Sec.~\ref{miniclusters_analytic} presents our results on the properties of axion miniclusters and their phenomenology. Final remarks and conclusions are drawn in Sec.~\ref{Discussion and conclusions}. | \label{Discussion and conclusions} In this paper, we have discussed the properties of axion miniclusters emerging in different cosmological scenarios before Big Bang Nucleosynthesis (BBN) took place. In particular, we have considered different scenarios in which the cosmology before BBN was governed by either i) a matter component, ii) a fast-rolling field $\phi$ leading to a Kination period, or iii) a decaying Kination field $\phi$. Using assumptions commonly made in the literature, we have obtained the mass and size of the minicluster, as well as the enhancement in axion density over the local CDM background, in different cosmological setups. We have sketched the results for the relative quantities describing miniclusters in more detail in \mbox{Fig.~\ref{fig:miniclustermassradius}} as a function of the temperature $\TRH$ at which the modified cosmology transitions to the standard radiation-dominated scenario. In the Figure, we show the mass of the minicluster in the case whether the early cosmological scenario is standard (black lines), matter-dominated (red lines), Kination without (blue lines) and with the decay of the $\phi$ field (green lines). Solid and dashed lines assume $\at=10$ or $\at = 1$, respectively. In order to produce the figure, we fix the relic abundance to the present CDM abundance, so that for each value of $\TRH$ the axion mass is given by Eq.~\eqref{mmm}. We have cut the plots at the value of $\TRH$ for which the axion mass exceeds the bound from the astrophysical considerations or the minimum reheating temperature. In \mbox{Fig.~\ref{fig:miniclustermassradius}}, the right vertical axis gives the size of the minicluster, obtained using the fact that the minicluster density is constant, see \mbox{Eq.~\eqref{size_minicluster}}. For $\TRH \leq T_1^{\rm std}$, the mass and the size are steadily smaller than the standard value for Kination cosmologies, while it is higher than what obtained in the standard scenario for the matter-dominated model. In more details, miniclusters in the MD cosmology can have a mass is up to two orders of magnitude larger than standard (radius up to $\sim 5$ larger), while in the Kination and KD scenarios the mass can be up to a factor $10^9$ smaller than standard (with a radius up to $10^3$ times smaller). The miniclusters obtained when considering the Kination or the KD cosmologies are lighter and more compact, thus making it more frequent for the Earth to come into the vicinity of these objects. As we obtained in \mbox{Fig.~\ref{fig:massCDM}}, when $\TRH \geq T_1^{\rm std}$ the axion field starts to oscillate in the standard scenario and we recover the standard results. When we assume that all of the DM is in the form of axions, the typical minicluster density is set by the DM density at matter-radiation equality, $M_c/R_c^3\sim \rho_{\rm eq}$, and does not depend on the early cosmology within our simplified picture. The minicluster mass and radius however can be very different from standard cosmology as they are set by the size of the horizon when the axion field begins to oscillate and becomes non-relativistic. The astrophysical quantities of relevance for detection tend to depend on different combinations of $M_c$ and $R_c$ and can be very different from the standard scenario: the velocity dispersion $\delta v \propto \sqrt{M_c/R_c}$, the time between encounters with the Earth $T_{\rm btw} \propto M_c/R_c^2$ and the duration of an encounter $\Delta t_{\rm enc} \propto R_c$ are different in non-standard cosmologies for different values of the reheating temperature. In \mbox{Fig.~\ref{fig:miniclusterencounter}} (Top panel) we show the typical duration of a minicluster encounter with the Earth (left vertical axis) and the expected time interval between two consecutive encounters (right vertical axis) as a function of $\TRH$, as well as the velocity dispersion squared (Bottom panel) for the cosmological model studied. For $\TRH \leq T_1^{\rm std}$, both modified cosmologies show detection advantages and disadvantages compared to the standard result. If the axion starts oscillating in a Kination model, the encounter would only last up to a few minutes owing to the small size of the minicluster itself; on the other hand, the frequency of encounter in the Kination cosmology can be enhanced by an $O(10^3)$ factor with respect to the standard case, with the encounters possibly being as frequent as one per a few years. On the contrary, for an axion field that begins to oscillate in a matter-dominated scenario, the encounter would last up to $\approx 50$ days, although one such encounter during a Galactic year would be much more rare. For an axion minicluster forming in the standard cosmology, the velocity dispersion is small enough so that the coherence time of the axion field is much longer than the duration of a minicluster encounter with the Earth. In any modified cosmology we study, the coherence time modifies but not as much as to invalidate the previous statement. We discuss the dependence of the solution on $\at$ spanning through various orders of magnitude, since at presence the effective value of this quantity is uncertain. In \mbox{Fig.~\ref{fig:miniclustermass}} we report the density plot showing the mass of the axion minicluster, in units of $\MS$, depending on both $\TRH$ and $\at$. Again, the largest variations in mass are shown for the Kination models, for which the mass of the minicluster ranges between $10^{-22}$ to $10^{-8}$ solar masses over the allowed range. The range over which the mass of the minicluster varies is much more contained in the standard cosmology, for which $M_c \sim 10^{-11}\,\MS$, and in the MD cosmology for which $M_c$ varies by just two orders of magnitude around the standard value. The white region marks the area where the axion mass is excluded by astrophysical considerations. The dot-dashed line marks the region where $\TRH < T_1^{\rm std}$, where the modified cosmology takes place to the left of the dot-dashed line, and the region $\TRH > T_1^{\rm std}$ where the axion field starts to oscillate in the standard radiation-dominated cosmology, for which $M_c$ is given by the value in the standard cosmological scenario. Overall, the actual value of $\at$ does not change much the general picture. \begin{figure*}[h!] \includegraphics[width=\textwidth]{PlotMass.pdf} \caption{Density plot showing the mass of an axion minicluster, depending on the values of the reheat temperature and the parameter $\at$, for different cosmological models before nucleosynthesis. Top left: Standard scenario. Top right: Low-reheat temperature scenario. Bottom left: Kination scenario. Bottom right: Kination scenario with a decaying $\phi$ field. The dot-dashed line marks the region where the axion field starts to oscillate in the standard scenario (right side) or in the modified scenario (left side).} \label{fig:miniclustermass} \end{figure*} One might question whether an early matter stage, as the one the universe experiences in the MD cosmology, leads to a pre-BBN growth of the structures since adiabatic perturbations in the modulus field entering horizon in such a modified cosmology would grow linearly with the scale factor. This has been considered for CDM seeds in MD models in Refs.~\cite{Erickcek:2011us, Erickcek:2015bda}, and in Kination models in Refs.~\cite{Redmond:2017tja, Redmond:2018xty}. Perturbations in the axion dark matter fluid would be dragged into such primordial perturbations and possibly lead to an early growth. However, such model would be depending on the initial power spectrum of the perturbations in the new field. We have partly addressed this issue in Sec.~\ref{Structure formation during the NSC period} where we have shown that perturbations in the energy density of the axion grow linearly with time only in a MD cosmology, while in Kination the growth is suppressed. This behaviour is peculiar to axion CDM and differs from the WIMP scenario studied in Refs.~\cite{Redmond:2017tja, Redmond:2018xty}. We have been able to estimate the largest mass that could grow into a minicluster in the MD model due to the large fluctuations in the massive scalar field governing the expansion rate in the NSC $\delta_\phi$, by demanding that fluctuations are not so large as to produce an excessive number of primordial black holes. We have found that the radius of the axion minicluster could be enhanced by a factor up to $\sim 30$, corresponding to an enhancement $\sim 30^3 \approx \mathcal{O}\(10^4\)$ in mass with respect to the case in which fluctuations are suppressed $\delta_\phi \simeq 0$. In this scenario, miniclusters would then attain a mass $M_c \sim 10^{-6}\,M_{\odot}$ which is of the same order of magnitude as the mass of the first halos that form in WIMP models from collisional damping and free-streaming that erase density perturbations within that scale\footnote{Depending on WIMP-lepton scattering cross-section, the value of the free-streaming length can also vary by orders of magnitude. The WIMP free-streaming length in a NSC has been estimated in Ref.~\cite{Visinelli:2015eka}.}. We leave further details on the important and interesting issue of an early growth of perturbations to a subsequent work A further aspect which is worth discussing is the eventual survival of axion minicluster from tidal stripping. Here, we have dealt with these computations in Sec.~\ref{Minicluster streams} following closely the treatment in Ref.~\cite{Tinyakov:2015cgg} and the paper therein in which the issue has been addressed for miniclusters in the standard cosmology. As for any dark matter micro-halo~\cite{Goerdt:2006hp, Schneider:2010jr}, the disruption probability after one passage of an axion minicluster through the Galactic disc is given in \mbox{Eq.~\eqref{eq:disruption_probability}}, which we have shown to be independent on the details of the NSC at the lowest order of the approximation. This result holds because the disruption probability is approximately $p_{\rm disr} \propto \sqrt{1/\rho_c} \approx {\rm const}$. In the simplest model we have discussed, the probability of disruption is then independent on the details of the cosmology and on the details of the physics of the axion. The result $p_s \ll 1$, valid in the standard scenario, is then expected to hold also in modified cosmological histories. We then expect a sizeable fraction of the dark matter axions to be bound into miniclusters even in modified cosmologies, since tidal stripping does not seem to provide a mechanism of disruption of these sub-structures. In any case, we have computed the contribution from the tidal stripping ox axion miniclusters to the local energy density in the form of axion streams, by extending the results discussed in Ref.~\cite{Tinyakov:2015cgg} to a NSC scenario. As we show in \mbox{Fig.~\ref{fig:plotstream}}, the number of encounters $N(A)$ with an axion stream for a given enhancement $A$ is expected to be sensibly larger than in the standard scenario for the early Kination and KD cosmologies. In particular, a number of encounters of the order of $N \sim 10^2$ to $10^3$ are expected even for an enhancement $A \sim 10$ of the local axion density. For these reasons, we believe it is worth readapting the existing experimental strategies of detecting axion DM to take into account this broad range of minicluster masses and radii shown in \mbox{Fig.~\ref{fig:miniclustermassradius}}. In the event of a discovery, the minicluster size distribution could be a window to the cosmology in the still unexplored era prior to big-bang-nucleosynthesis. {\bf Note added:} During the completion of the present work, Ref.~\cite{Nelson:2018via} appeared, with their results for an early matter-dominated epoch overlapping with our work. | 18 | 8 | 1808.01879 |
1808 | 1808.03617_arXiv.txt | XMASS-I is a single-phase liquid xenon detector whose purpose is direct detection of dark matter. To achieve the low background requirements necessary in the detector, a new model of photomultiplier tubes (PMTs), R10789, with a hexagonal window was developed based on the R8778 PMT used in the XMASS prototype detector. We screened the numerous component materials for their radioactivity. During development, the largest contributions to the reduction of radioactivity came from the stem and the dynode support. The glass stem was exchanged to the Kovar alloy one and the ceramic support were changed to the quartz one. R10789 is the first model of Hamamatsu Photonics K. K. that adopted these materials for low background purposes and provided a groundbreaking step for further reductions of radioactivity in PMTs. Measurements with germanium detectors showed 1.2$\pm$0.3 mBq/PMT of $^{226}$Ra, less than 0.78 mBq/PMT of $^{228}$Ra, 9.1$\pm$2.2 mBq/PMT of $^{40}$K, and 2.8$\pm$0.2 mBq/PMT of $^{60}$Co. In this paper, the radioactive details of the developed R10789 are described together with our screening methods and the components of the PMT. | \label{sec:intro} Direct detection of dark matter is one of the major scientific challenges in modern astroparticle physics. Based on the proposal \cite{org-xmass}, a single-phase liquid xenon (LXe) detector, XMASS-I was constructed \cite{bibXMASSDetector}. Since the dark matter signal is expected to be rare, dark matter searches require low background detectors. XMASS-I is designed for dark matter and for other many rare event searches. For a spin-independent WIMP-nucleon cross section, it is designed to search as low as $10^{-45}$ cm$^{2}$ for a WIMP mass of 100 GeV/$c^{2}$. To realize this sensitivity, the background level in the fiducial volume is required to be ~$10^{-4}$/day/kg/keV for deposited energies below 100 keV. Background originating from radioactive impurities in detector materials is one of the most serious problems in a low background experiment. It is crucial to prepare materials of sufficiently low radioactivity before detector construction. The dominant source of radioactivity in the XMASS prototype detector \cite{prototype} was the Hamamatsu R8778 photomultiplier tubes (PMTs). Though R8778 was a model developed for the XMASS prototype detector and its radioactivity was much lower than that of standard PMTs, an order of magnitude reduction of radioactivity was necessary to meet the background required for the XMASS-I detector. Therefore we developed a new model of low radioactivity PMT, R10789, based on R8778. In order to lower the background, we screened numerous candidate materials for their radioactivity. In this paper we describe the development target in Section \ref{sec:target}, the screening methods in Section \ref{sec:method} and the components of the PMT in Section \ref{sec:material}. The radioactivity in the final product of R10789 is presented in Section \ref{sec:result}. The development summary is described in Section \ref{sec:summary}, along with a discussion outlining the largest component contributions to the radioactivity, this is necessary to attain further reductions in future developments. The conclusion is written in Section \ref{sec:conclusion}. | \label{sec:conclusion} We succeeded in developing the new low background PMT, R10789, which satisfies the requirements of the XMASS-I detector. It achieved large reduction factor of 8, 4, 1.7 and more than 10 from PMT R8778 for $^{226}$Ra, $^{228}$Ra, $^{60}$Co, and $^{40}$K, respectively. These facts prove that it can be utilized in various low background experiments. The largest contributions to the reduction were obtained by exchanging two items, the stem glass with Kovar alloy and the ceramic dynode support with quartz. This is the first model of Hamamatsu Photonics K. K. PMTs that adopted these materials for low background purposes and provided a groundbreaking step for further improvements of radioactivity in PMTs. | 18 | 8 | 1808.03617 |
1808 | 1808.08219_arXiv.txt | It has been postulated that Fuzzy Dark Matter (FDM) could be a viable alternative to Cold Dark Matter (CDM). FDM is comprised of ultralight bosons which exist as a Bose-Einstein condensate. Due to the very low mass of FDM, the de Broglie wavelength of these bosons are of the order of \kpc and the quantum effects manifest at those scales. Hence, unlike CDM, FDM experiences quantum pressure along with gravitational attraction. In this work, we investigate the gravitational collapse of a spherically symmetric FDM overdensity. We assume a power law density profile for an overdense region of FDM and derive an expression for the temporal evolution of a spherical shell in the non-interacting limit and use it to derive an expression for average overdensity contained in the spherical shell in an Einstein--de Sitter universe. Further, we numerically extend the analysis to the case of interacting bosons. Finally, we discuss the virialization of such an overdense region of non-interacting FDM and derive an expression for overdensity in the linear and the full theory. We compare our results with those obtained in the case of CDM and conclude with a discussion of the results. | \label{sec:introduction} Standard model of cosmology, namely the $\Lambda$CDM model has been a grand success \cite{Aghanim:2018eyx}. However this success also poses some serious questions. Of them a chief concern is regarding the nature of dark matter. Despite the success of Cold Dark Matter(CDM) at large scales, it has met with some problems at scales less than $10$ \kpc (for a recent review, see, for instance, \cite{Bullock:2017xww}). CDM predicts \cite{Navarro:1996gj} that the halos have a cusp in the density profile at its center. However, observations \cite{deBlok:2001hbg, deBlok:2005qh, Oh:2008ww} of low surface brightness galaxies and dwarf galaxies indicate that the density profile at the center of halos are shallower or in other words has a core (for a review, see, for instance, \cite{2010AdAst2010E...5D}). Furthermore, simulations of CDM over predicts the number of dwarf galaxies in the local group by an order of magnitude \cite{Klypin:1999uc}. Of these two difficulties faced by CDM, it has been suggested that, the latter may be alleviated to an extent by taking in to account the effects due to baryons (for a recent work, see, for instance, \cite{2018arXiv180604143G}). However, the dust is yet to settle. \par In order to overcome the small scale issues of CDM, several alternatives to CDM has been suggested. One such alternative is Warm Dark Matter (WDM) (see, for instance, \cite{2001MPLA...16.1795J}). In this model, the dark matter particles possess a thermal velocity which causes them to free stream. This free streaming suppresses the formation of small scale structures thus solving the over abundance of dwarf galaxies and the core-cusp problem \cite{Colin:2007bk, SommerLarsen:1999jx}. However, the free streaming may also lead to certain imprints at large scale which can only be fixed by fine-tuning the parameters\cite{Narayanan:2000tp}. Another variant of CDM is the collisional dark matter (for a recent review, see, for instance, \cite{Salucci:2017cet}). It has been shown that the presence of collisions flattens the core and destroys the dwarf galaxies \cite{Spergel:1999mh}. However, an excess amount of collisions could also lead to the formation of singular core \cite{Yoshida:2000bx}. \par Another proposal, which we will concern ourselves with in this article, is that the dark matter is composed of ultralight bosons \cite{PhysRevLett.85.1158}. A popular candidate of such an ultralight bosonic dark matter, known commonly as Fuzzy Dark Matter (FDM), is axion of mass $m \sim 10^{-22} - 10^{-21}$ eV (for reviews on axion cosmology, see \cite{Sikivie:2006ni, Marsh:2015xka}). All large scale properties of FDM is similar to that of CDM. However, at small scales quantum properties of FDM affects the formation of structure. Due to the small mass of FDM, the de Broglie wavelength is of order of \kpc. The de Broglie wavelength manifests itself as a Jeans length below which the quantum pressure due to the uncertainty principle acts against gravity. Thus, below the de Broglie wavelength, the pressure suppresses the formation of structure and flattens the density profile\cite{PhysRevLett.64.1084, Sin:1992bg, Sahni:1999qe, PhysRevLett.85.1158}. The implications of FDM model to structure formation has been investigated (see, for instance, \cite{Marsh:2013ywa, Hui:2016ltb}). Most of the current searches of dark matter are not designed to detect FDM and hence the negative results do not constrain it. However, experiments have been proposed which are likely to detect FDM \cite{Arvanitaki:2009fg, Kim:2015yna, Graham:2013gfa, Stadnik:2014tta, Stadnik:2015kia, Abel:2017rtm, Hees:2018fpg}. \par In the FDM model, the ultralight bosons form a Bose-Einstein Condensate (BEC) at a very early time. In a BEC all the dark matter particles occupy the ground state and hence is described by a coherent wave function. The evolution of such a system is described by the Schr{\"o}dinger equation together with an equation governing gravity. The exact dynamics of structure formation can only be explored using numerical simulations \cite{Woo:2008nn, Schive:2014dra, Nori:2018hud, Veltmaat:2018dfz}. High-resolution numerical simulations \cite{Schive:2014dra} show that the halo centers have a solitonic core with the outer profile similar to NFW \cite{Navarro:1996gj}. Even though numerical simulations are required to have a complete understanding of the structure formation, analytical approximations often give useful insights. In this spirit, there has been analytical investigations of the steady state of a spherically symmetric Newtonian self-gravitating BEC \cite{PhysRev.187.1767, Boehmer:2007um, 2011PhRvD..84d3531C, 2011PhRvD..84d3532C, Chavanis:2011cz, Harko:2014vya, Chavanis:2016dab}. In these studies, the nature of the virialized halo has been investigated, either assuming that the system is in hydrostatic equilibrium or by using virial theorem. For some other approaches to the study of collapse of axionic scalar field or formation of structure from axions, see, for instance, \cite{deFreitas:2015dwa, Eby:2016cnq, Schiappacasse:2017ham, 1985MNRAS.215..575K, 1994PAN....57..485S, Sakharov:1996xg, Khlopov:1998uj}. In this work, following the footsteps of an earlier work on CDM \cite{1972ApJ...176....1G}, we would like to study the gravitational collapse of a spherically overdense region of FDM. Firstly, assuming a spherically symmetric power law density profile, we will analytically investigate the time evolution of a spherical shell of FDM comprising of non-interacting bosons. We will use the analytical solutions for radius of the shell to arrive at an expression for overdensity and study it in the linear regime. Secondly, we will extend the analysis numerically to the case of interacting bosons, and study the evolution of a spherical shell and its dependence on the strength of interactions. Finally, we will use virial theorem for non-interacting FDM to compute the critical overdensity at which the spherically overdense region would collapse in to a halo. \par The rest of the paper is organized as follows. In the next section we will describe the Gross-Pitaevskii-Poisson system that governs a BEC evolving under the effect of gravity. We describe how such a system can be expressed as hydrodynamic equations, namely the continuity, Euler and Poisson equations. From the hydrodynamic equations, we derive the equation of motion of a spherical shell containing an overdense region of FDM. In section III, assuming a density profile for the overdense region, we analytically and numerically solve for the equation of motion of the spherical shell to calculate the evolution of the shell with time and use the analytical expression to compute the expression for averaged overdensity contained in the spherical shell as a function of time. We further compute the evolution of the shell, numerically, for the case of interacting bosons. In section IV, we use virial theorem to compute the critical overdensity at which the overdense region will collapse in to a halo. We conclude the paper in section V with a discussion of the results. \par We shall work with the units where $c\,=\,1$. | FDM is a compelling model for dark matter. The quantum nature of FDM which gets manifested at kilo parsec scales is capable of resolving the small scale issues that has been ailing CDM. FDM halo can be described as a self-gravitating BEC and hence is governed by the GPP equations (\ref{eqn:GPP}). Numerical simulations \cite{Schive:2014dra} indicate that at large scales the structure formed in FDM is similar to that in CDM. High resolution simulations \cite{Schive:2014dra} show the existence of standing waves of dark matter which evolves in to solitonic cores at the center of the halo. As they accrete more matter, the solitonic core grows and are surrounded by virialized halos with fine-scale, large-amplitude fringes. The surrounding halos are supported against gravity by quantum and turbulent pressure and hence fluctuates in density and velocity. \par With the goal of gaining analytical insights in to the evolution of an FDM halo, we investigated the gravitational collapse of a spherical shell containing an overdense region of FDM. We studied the system in its hydrodynamical form, \ie as a fluid with density $\rho$ and velocity $\vu$ evolving under the effect of opposing forces of Newtonian gravity and quantum pressure. In an expanding universe, we computed the equation of motion governing a spherical shell Eq. (\ref{eqn:R-general}). Assuming a spherically symmetric power law profile Eq. (\ref{eqn:pl-profile}) for the overdense region, we derived an expression for the time evolution of the spherical shell Eqs. (\ref{eqn:sol-Lt}) for the case of non-interacting bosons. The correctness of the analytical solution was further established by comparing it with numerical solution. Using the analytical expressions, we arrived at an expression for the averaged overdensity enclosed by the spherical shell Eq. (\ref{eqn:overdensity}). Further, we numerically evaluated the evolution of a shell in the presence of interaction and compared it with the analytical expressions evaluated for the case of non-interacting bosons. \par We find that, as in the case of CDM, in the beginning, the spherical shell of FDM enclosing the overdense region expands along with the Hubble flow and eventually turns around and begin to collapse. However, contrary to the case of CDM, due to the existence of quantum pressure, the FDM spherical shell eventually gets repelled and starts expanding again. A similar behaviour can be seen by looking at the expression of overdensity as well. We can see from Eq. (\ref{eqn:overdensity}) that the overdensity remains finite and fluctuates with time. The expression for overdensity also has the nice feature that it reproduces the CDM result in the $\hbar/m \rightarrow 0$ limit. We further studied the initial linear evolution of the overdensity. It was found that, in this model, for an overdensity, a valid small $\vartheta$ limit exists only in the $e\rightarrow 1$ limit. In the presence of interactions, the force due to interaction works along with the quantum pressure if the interaction is repulsive while acts against quantum pressure if it is attractive. We found that, for the parameters of interest, the spherical shell would oscillate in the case of attractive interaction, only if $|a_s| << \bar{a}_s$. On the other hand, for repulsive interaction, the shell would oscillate with a larger maximum and minimum radius for larger values of $a_s$. We also found that, for the parameters that we have considered, which correspond to the numbers arrived for a dwarf spheroidal \cite{Schive:2014dra}, the analytical expression for the shell is a good approximation at large to medium scales. \par As the shell contracts, it will interact with inner shells and the dynamics of the shell would be more complicated than the one captured by Eq. (\ref{eqn:sol-Lt}). In reality, as was shown in \cite{Schive:2014dra}, the spherical overdense region would eventually virialize to form a halo. Hence, the solutions discussed above, though captures some of the effects of various forces at play, will not be valid through out the evolution. However, we can investigate beyond the validity of the solutions Eq. (\ref{eqn:sol-Lt}), by making use of virial theorem. In section \ref{sec:virialization}, we used the virial theorem to compute the overdensity after virialization in the linear and in the full theory (see Table \ref{table:1}). In this model, as in the case of CDM \cite{paddylss1993}, we find the critical density at which the overdensity virializes to a halo to be $\bar\delta_c\,\simeq1.69/e^{2/3}\,\simeq\,1.69$. Finally, from the simulations performed for Fornax dwarf spheroidal, see Fig. \ref{fig:1}, our computations shows that the virialized halo would have a radius of $L_{vir}\, \simeq\, L_{max}/2\, =\, .95\,\pc$. \par We shall conclude this article by discussing some of the subtleties involved in the calculation and some interesting aspects that need to be further investigated. First of all, even though this study was motivated by the possibility of FDM being a viable dark matter candidate, the analytical calculations performed in this paper hold for any non-interacting BEC collapsing under the effect of gravity. Secondly, in the case of CDM, as the shell is contracting it will cross the shells which is expanding after their first in fall. In the case of FDM, however, when two shells come close to each other there will be repulsion due to the quantum pressure and hence the dynamics near shell crossing would be more involved than in CDM. Finally, in this work we have used the hydrodynamic description to model the system. It is not clear how well the hydrodynamic description captures the physics underlying the GPP equations (see, for instance, \cite{Uhlemann:2014npa, Kopp:2017hbb, Mocz:2018ium}). Hence, it would be interesting to investigate the regime close to the ``shell crossing'' in more detail. | 18 | 8 | 1808.08219 |
1808 | 1808.01702_arXiv.txt | We present results of the $^{12}$CO (1--0) mosaic observations of the nearby barred-spiral galaxy M83 obtained with the Atacama Large Millimeter/submillimeter Array (ALMA). The total flux is recovered by combining the ALMA data with single-dish data obtained using the Nobeyama 45-m telescope. The combined map covers a $\sim$13 kpc$^{2}$ field that includes the galactic center, eastern bar, and spiral arm with a resolution of \timeform{2''.03} $\times$ \timeform{1''.15} ($\sim45$ pc $\times$ $\sim25$ pc). With a resolution comparable to typical sizes of giant molecular clouds (GMCs), the CO distribution in the bar and arm is resolved into many clumpy peaks that form ridge-like structures. Remarkably, in the eastern arm, the CO peaks form two arc-shaped ridges that run along the arm and exhibit a distinct difference in the activity of star formation: the one on the leading side has numerous H\emissiontype{II} regions associated with it, whereas the other one on the trailing side has only a few. \par To see whether GMCs form stars with uniform star formation efficiency (SFE) per free-fall time ($\SFEff$), GMCs are identified from the data cube and then cross-matched with the catalog of $\HII$ regions to estimate the star formation rate for each of them. 179 GMCs with a median mass of 1.6 $\times$ 10$^{6}$ $\Msun$ are identified. The mass-weighted average $\SFEff$ of the GMCs is $\sim$9.4 $\times$ 10$^{-3}$, which is in agreement with models of turbulence regulated star formation. Meanwhile, we find that $\SFEff$ is not universal within the mapped region. In particular, one of the arm ridges shows a high $\SFEff$ with a mass-weighted value of $\sim2.7$ $\times$ 10$^{-2}$, which is higher by more than a factor of 5 compared to the inter-arm regions. This large regional variation in $\SFEff$ favors the recent interpretation that GMCs do not form stars at a constant rate within their lifetime. | As most star formation takes place in giant molecular clouds (GMCs) and as star formation is one of the fundamental processes that drives the evolution of galaxies, it is essential to understand the processes that determine the star formation efficiency (SFE) in GMCs. \par Molecular clouds with sizes of 20--100 pc and masses of 10$^{4-6}$ $\Msun$ are often classified as GMCs (e.g., \cite{Sanders1985}; \cite{Solomon1987Larson}). Motions inside GMCs are turbulent with resultant CO linewidths of several kilometers per second, which are 'supersonic' for typical temperatures in GMCs ($\sim$10 K). Although early studies proposed that the turbulent linewidth could be a manifestation of the gravitational collapse of GMCs (e.g., \cite{GoldreichKwan1974}), in most places GMCs are assumed to be supported by turbulent pressure and magnetic fields against their self-gravity, and kept in near-virial equilibrium (e.g., \cite{Larson1981}; \cite{Solomon1987Larson}). The observed balance between the virial mass and the cloud mass derived with a reasonable assumption regrading the CO-to-H$_2$ conversion factor, also known as Larson's second law, has been considered as one of the important manifestations of the nature of GMC that is close to the virial equilibrium. \par In the Milky Way (MW), GMCs form stars with a low efficiency in the sense that only 1\% of the GMC mass is converted into stars per free-fall time (\cite{ZuckermanEvans1974}; \cite{Krumholz2005TurbulenceSF}). The low SFE was one of the earliest grounds for assuming that GMCs are in a state of near equilibrium rather than in a state of gravitational collapse because it was argued that if GMCs are in a state of collapse, more stars should be produced within a free-fall time. The recognition of the low efficiency led to another discussion on the idea that some mechanisms should be regulating the star formation rate (SFR) in GMCs. \par In discussing mechanisms that regulate the SFE in GMCs, it is common practice to adopt a parameter called {\it star formation efficiency per free-fall time} ($\SFEff$). The parameter is defined as $\SFEff$ $\equiv$ $\TauFF\mathrm{SFR}/\Mmol$, where $\Mmol$ and $\TauFF$ are the mass and free-fall time of a cloud, respectively. As far as GMCs are concerned, the average value of $\SFEff$ is claimed to be uniform, approximately 0.01, in many galaxies, including the MW (\cite{Krumholz2012UniversalSF}). \par Turbulence is one of the mechanisms considered responsible for regulating $\SFEff$. Turbulence could regulate star formation in a GMC by forming a small volume of high-density regions within it while keeping the bulk of the GMC in near virial balance (e.g., \cite{MacLow2004}). Attempts have been made to construct theoretical descriptions that quantitatively reproduce an $\SFEff$ of $\sim$0.01 in a steady state (e.g., \cite{Krumholz2005TurbulenceSF}; \cite{Federrath2015}). The efforts trying to achieve $\SFEff$ $\sim$0.01 in a steady state implies that GMCs are approximated as long-lived entities that form stars with constant efficiency. \par However, although the model of turbulence regulated star formation succeeded in explaining the low average value of $\SFEff$ to a certain degree (\cite{Federrath2015}), some studies imply that the assumption of quasi-steady virialized GMCs could be oversimplifying the nature of GMCs. First, the lifetime of GMCs has been estimated to be 15--40 Myr, which is only a few $\TauFF$, by several studies; the GMC lifetime is suggested to be effectively limited by the disrupting roles of OB stars (\cite{BlitzShu1980}; \cite{Kawamura2009LMC}; \cite{Murray2011SFE}; \cite{Miura2012M33}) or large-scale shearing motions in inter-arm regions \citep{Meidt2015Lifetime}. If this is true, then GMCs do not necessarily have to be long-lived entities that are kept in near virial balance. Second, Larson's second law alone does not completely rule out the possibility that GMCs are collapsing because even if a GMC is in a state of free-fall, the CO linewidth increases by only a factor of $\sqrt{2}$ compared to a GMC in virial balance (\cite{Larson1981}). The difference is subtle and within the inevitable observational uncertainties. If GMCs are not long-lived as suggested by the first argument, they are allowed to be at least partially collapsing as was argued by \citet{GoldreichKwan1974} (see \cite{BallesterosParedes2011A}). \par Further, recent studies point out that there is a wide spread, larger than two orders of magnitude, in $\SFEff$ observed for Galactic GMCs (\cite{Murray2011SFE}; \cite{Lee2016DynamicSF}; see also \cite{Mooney1988}). Those authors argued that the large scatter in $\SFEff$ is hard explain by the models of turbulence-regulated star formation, which predict a weak dependence of $\SFEff$ on the properties of GMCs. Instead, they proposed that $\SFEff$ should be a time-dependent variable that dynamically increases during the lifetime of GMCs, although the effects of observational bias mist be carefully examined (\cite{Feldmann2011}). \par Accepting that there is a wide scatter in $\SFEff$, it is natural to think of its spatial distribution within a galaxy. If $\SFEff$ indeed increases dynamically during the lifetime of GMCs, there should be a variation in the observed $\SFEff$ across spiral arms because spiral arms have at least moderate impact in organizing the build-up and disruption of massive GMCs (\cite{Egusa2011M51}; \cite{Hirota2011IC342}; \cite{Colombo2014Env}). On the other hand, if $\SFEff$ is stable, then the distribution of $\SFEff$ observed should not exhibit strong spatial variations. Therefore, the investigation of the spatial distribution of $\SFEff$ in galaxies should provide a clue to understand how the rate of star formation is regulated in GMCs, a discussion that is closely connected with the nature of a GMC itself. \par M83 is an ideal target to investigate $\SFEff$ in GMCs because it is one of the nearest (4.5 Mpc, \cite{Thim2003M83Distance}) spiral galaxies that is seen face-on and hosts prominent galactic structures, namely a bar and spiral arms. Metallicities in M83 are comparable to or even higher than in the MW \citep{Bresolin2016M83}, thus CO lines are effective in tracing molecular clouds. Other basic parameters of M83 are listed in table \ref{TableGalaxyParameters}. As this galaxy contains a large amount of molecular gas (3.2 $\times$ 10$^9$ $\Msun$, \cite{Crosthwaite2002M83}), numerous observational studies were made with both single-dish telescopes and interferometers (see references listed in \cite{Hirota2014}). However, due to its low declination, interferometric observations made previous to the arrival of the Atacama Large Millimeter/submillimeter Array (ALMA) suffered from limited $u$-$v$ samplings, and the spatial resolutions achieved were insufficient to resolve individual GMCs. Recently, \citet{Freeman2017} investigated the properties of GMCs in M83 using the ALMA data, but the data used lacked sensitivity to the total flux. \par We present the results of $^{12}$CO (1--0) mosaic observations of M83 taken with the ALMA. The interferometric data are combined with data taken with the Nobeyama 45-m telescope to recover the total flux. Target fields of the observations are selected so that a variety of galactic structures are covered, including the bar, the spiral arm, inter-arm regions, and the galactic center. We examine the observational properties of GMC including $\SFEff$ over galactic structures to see whether or not systematic variation in $\SFEff$ exists. \par We describe the CO observations in section 2 and present the CO distribution in section 3. In section 4, we identify GMCs from the obtained CO data cube and examine their basic properties. Scaling relations of the properties of the identified GMCs and their mass functions are also examined. In section 5, by cross-matching the identified GMCs with $\HII$ regions, we derive $\SFEff$ for each GMC. In section 6, discussions are made to interpreting the meaning of the observed variation in $\SFEff$ and also to see in which regions feedback from massive stars is large enough to disrupt GMCs. In section 7, we present a summary. \par \begin{table} [htbp] \caption{Adopted parameters of M83} \begin{center} \small \begin{tabular} {lr} \hline\hline Parameter& Value\\ \hline Morph. \footnotemark[1]& SAB(s)c \\ Center position (J2000)\footnotemark[2]& \timeform{13h 37m 00s.72}\\ & $-$\timeform{29D 51' 57''.2}\\ Position angle$^{}$\footnotemark[3]& \timeform{225D}\\ Inclination angle$^{}$\footnotemark[3]& \timeform{24D}\\ Systemic velocity (LSR)\footnotemark[4]& 514 km\ s$^{-1}$\\ Distance\footnotemark[5]& 4.5 $\pm$ 0.3 Mpc\\ Linear scale & \timeform{1''} $\sim$ 22pc\\ SFR \footnotemark[6] & 3.0 $\MsunPerYear$ \\ HI mass \footnotemark[7] & 7.9$\times$10$^9$ M$_{\odot}$\\ H$_2$ mass \footnotemark[8] & 3.2$\times$10$^9$ M$_{\odot}$\\ E(B-V)\footnotemark[9] & 0.070 \\ \hline \end{tabular} \end{center} \label{TableGalaxyParameters} \begin{tabnote} \footnotemark[1] {\citet{deVaucouleurs1991RC3}.} \footnotemark[2] {\citet{Thatte2000}.} \footnotemark[3] {\citet{Comte1981M83Parameters}.} \footnotemark[4] {\citet{Kuno2007Atlas}.} \footnotemark[5] {\citet{Thim2003M83Distance}.} \footnotemark[6] {\citet{Jarrett2013WISE}, adjusted to a distance of 4.5 Mpc.} \footnotemark[7] {\citet{Heald2016M83}, adjusted to a distance of 4.5 Mpc.} \footnotemark[8] {\citet{Crosthwaite2002M83}, adjusted to a distance of 4.5 Mpc.} \footnotemark[9] {\citet{Schlegel1998DustMap}.} \end{tabnote} \end{table} | \label{SecDiscussion} \subsection{Is there intrinsic environmental variation of the SFE?} \label{SubsecConstantSFEffOrNot} In the previous subsection, we find that there are approximately three orders of magnitude peak-to-peak spread in the values of observationally derived $\SFEff$. Not only is the scatter of the distribution large, but there are also regional variations in $\SFEff$. In particular, the two ridges within the arm exhibited a clear difference from each other concerning the distribution of $\SFEff$. Before discussing the meaning of the regional variation in $\SFEff$, we first discuss possibilities that the large scatter and regional variations in $\SFEff$ are actually caused by observational effects that produce 'apparent' variations in $\SFEff$ even if $\SFEff$ is intrinsically a constant parameter. We consider three mechanisms here: (1) stochastic sampling of the stellar IMF, (2) uncertainty of stellar ages that affects the SFR calibration factor, and (3) mass consumption of GMCs due to stellar feedback. \par \begin{figure*} [] \begin{center} \FigureFile(158mm,158mm){p17.pdf} \caption{(a-h) Observationally derived 'apparent' value of $\SFEff$ as a function of cloud mass for the GMCs plotted for each regional mask. The dotted red line in each plot indicates the nominal limit for the detection, obtained by assuming a constant SFR of 3.5 $\times$ 10$^{-4}$ $\MsunPerYear$ and a free-fall time of $\TauFF$ = 6.7 Myr. (i) Curves that show the evolution of $\SFEff$ for model GMCs calculated with the toy model of \cite{Feldmann2011}. The left and right curves indicate the evolution of model GMCs with initial masses of 10$^6$ and 10$^7$ $\Msun$, respectively. The intrinsic value efficiency, $\SFEffi$, is fixed as 0.01. The feedback parameter is chosen such that the stellar feedback limits the lifetime of model clouds to 20 Myr. Squares indicate the time steps for 10\$, 30\$, 50\$, 70\$, and 90\$ of the lifetime of model GMCs. Gray shaded area in each plot indicates the range of $\SFEff$ covered by model GMCs within 10\% and 90\% of their lifetimes. } \label{FigSFEfftoM} \end{center} \end{figure*} \subsubsection{Sampling effect of the stellar IMF} If a cluster that illuminates an $\HII$ region contains a small number of stars, ionizing stars are likely less populated due to the stochastic sampling of the stellar IMF. This sampling effect will lead to an underestimation of the SFR for small $\HII$ regions. One might suspect this sampling effect could be responsible for the apparent variation in $\SFEff$, especially for the GMCs in inter-arm regions that exhibited an $\SFEff$ value that is systematically lower than the global mean of 0.01. However, the variation in $\SFEff$ seen in the previous subsection was revealed with a conservative upper limit on the SFR of 3.5 $\times$ 10$^{-4}$ $\MsunPerYear$. If this level of the SFR continues for 3--4 Myr, which is the nominal lifetime of ionizing stars, approximately 1100--1400 $\Msun$ of stellar mass is produced. On the other hand, $\sim$1000 $\Msun$ of stellar mass is enough to avoid the severe effect of stochasticity of the stellar IMF sampling: for example, \citet{Calzetti2010} examined the $\HAlpha$ luminosity per stellar mass for clusters and indicated that the cluster-to-cluster variation is a factor of 2 for $\sim$1000 $\Msun$ clusters. Thus, as long as the sampling effect of the stellar IMF alone is taken into account, the possible amount of the scatter for the apparent value of $\SFEff$ is at most a factor of 2 and is insufficient to explain the observed variation in $\SFEff$. \subsubsection{Uncertainty of stellar ages} As stated in \S\ref{SubsecHaToSFR}, the uncertainty of the star formation history for individual $\HII$ regions should make the SFR calibration factor, which relates the SFR and $\HAlpha$ luminosity, somewhat uncertain. We consider here whether the observed regional variation in $\SFEff$ could be explained by variations in the SFR calibration factor. \par If stars in a cluster powering an $\HII$ region are formed instantaneously, the production rate of Lyman photons from the cluster decay quickly after 3--4 Myr because of the deaths of massive stars (e.g., Fig. 22 of \cite{Scoville2001M51}; Fig. 1 of \cite{Murray2011SFE}). The strong time evolution of the Lyman continuum production rate implies there should be a time evolution of the SFR calibration factor. To see the degree of the time variation of the SFR calibration factor, we here perform a simple calculation using Starburst99. We assume the stellar IMF of \citet{Kroupa2001}, solar metallicity, and the burst mode of star formation, which produces all the stars in a cluster at the same time. From the calculated results, we find that the $\HAlpha$ luminosity per stellar mass is almost constant for the first 2 Myr, and then starts to decline due to the deaths of the ionizing stars, being about 50\%, 20\%, and 10\% of the initial value at approximately 3.5, 4.5, and 5 Myr, respectively. \par The average value of $\SFEff$ in the arm region ($\sim$0.015) is approximately a factor of 3--5 larger than in the inter-arm regions ($\sim$0.0046 and $\sim$0.0027). As far as the burst mode of star formation in clusters is concerned, the only way to produce this amount of variation in $\SFEff$ by just changing the SFR calibration factor is to assume that the $\HII$ regions in the inter-arm are preferentially older than those in the arm regions by a few Myr. Referring to the values obtained with the Starburst99 calculation, if the $\HII$ regions in the arm region are younger than 2 Myr and the ones in the inter-arm regions are older than 4 Myr, it is possible to produce a factor of 3--5 variation in the apparent distribution of $\SFEff$. However, considering the global galactic dynamics, the dwelling time of GMC in the inter-arm region should be a few to several tens of Myr for the galactocentric radii considered here (figure 17 in \cite{Hirota2014}). The dwelling time is much longer than the time for the $\HAlpha$ luminosity of an $\HII$ region to decay. Thus, the existence of $\HII$ regions in the inter-arm regions means that at least some of them are formed in situ. Therefore, it is difficult to consider a process that produces just a few Myr difference in the age distributions of $\HII$ regions across the spiral arm and it is unlikely that the observed variation in $\SFEff$ is simply due to the uncertainty of the star formation history. \par The conclusion arrived at here will not change even if a cluster was created through several events of star formation that occurred over a few Myr (e.g., \cite{Venuti2018}). If a cluster that powers an $\HII$ region was formed in a single instantaneous event, then the lifetime of the $\HII$ region is approximately 5 Myr, as we have seen above. If a cluster was formed through several events spread over a few Myr, then the lifetime of the $\HII$ region is lengthened by a few Myr. However, even if the extra few Myr has to be added to 5 Myr, the lifetime of $\HII$ regions is still likely below 10 Myr and well below the dwelling time in the inter-arm region. \subsubsection{Rapid mass consumption of GMCs within the averaging time for the derivation of SFR} The $\HAlpha$ emission from an $\HII$ region that is used to trace its SFR quickly decays after approximately 4 Myr, because of the deaths of massive stars. Therefore, the SFR derived from the $\HAlpha$ luminosity of an $\HII$ region is essentially a time-averaged value with an averaging window length of approximately 4 Myr (e.g., \cite{Murray2011SFE}). On the other hand, once massive stars are formed inside a GMC, they are considered to be capable of ionizing and disrupting a significant portion of the parental GMC within a timescale of a few tens of Myr (e.g., \cite{Whitworth1979CloudDisruption}; \cite{WilliamsMcKee1997}), which is comparable with the estimated GMC lifetimes (15--40 Myr; \cite{Kawamura2009LMC}; \cite{Murray2011SFE}; \cite{Miura2012M33}). The suggested timescale for cloud destruction is only a few times longer than the averaging window length of $\sim$4 Myr for the derivation of the SFR. Therefore, a GMC associated with the $\HII$ regions could have lost a non-negligible fraction of its mass due to the stellar feedback within the averaging duration. If this is the case, then the $\SFEff$ derived from the observed SFR and cloud mass should be biased upward. \paragraph{Cloud mass evolution model} \par To investigate the impact of this time evolution effect, we employ a toy model introduced by \citet{Feldmann2011}, which solves a differential equation of mass evolution for a GMC: \begin{equation} \frac{d{\Mmol}}{dt} = SFR(t) - \alpha_{\mathrm{fb}} M_{\mathrm{*}}(t), \end{equation} where $SFR(t)$ is the SFR for a GMC, $M_{\mathrm{*}}(t)$ is a the stellar mass associated with the GMC, and $\alpha_{\mathrm{fb}}$ is the feedback parameter. SFR is further expressed as \begin{equation} SFR(t) = -{\SFEffi}\frac{{\Mmol(t)}}{\TauFF}, \end{equation} where $\SFEffi$ is the {\it intrinsic} star formation efficiency per free-fall time. We use the notation $\SFEffi$ to distinguish it from the observationally derived, $\SFEff$. The stellar mass is obtained simply by integrating $SFR(t)$: \begin{equation} M_{\mathrm{*}}(t) = \int_{0}^{t'}|SFR(t)| dt'. \end{equation} Solving these equations, $\Mmol$ and $M_\mathrm{*}$ are described as a function of time. \par The observationally derived SFR just traces the stellar mass that is formed within a fixed time window. Denoting the observed apparent value of the SFR as $\mathrm{SFR}_{a}$, it can be derived as \begin{equation} \mathrm{SFR}_{a}(t) = \frac{\int_{max(t - \tAVG,\ 0)}^{t} M_\mathrm{*}(t') dt'}{\tAVG}, \end{equation} where $\tAVG$ is the time window traced by the SFR tracer. As we use the $\HAlpha$ emission as a tracer of the SFR, we fix $\tAVG$ as 4 Myr. If a cloud is younger than $\tAVG$, then $\mathrm{SFR}_{a}$ for the cloud underestimates the actual SFR because of the fixed averaging window used in the denominator. Using the computed $\mathrm{SFR}_{a}(t)$, $\SFEff$ for a model cloud can be described as \begin{equation} \SFEffa(t) = \frac{\mathrm{SFR}_{a}(t)}{\Mmol(t)} \TauFF. \end{equation} \par We adopt $\TauFF=6.7$ Myr and $\SFEffi=0.01$ as representative values for the GMCs in M83. Although the actual value of $\alpha_{\mathrm{fb}}$ is not unknown, we can derive it by assuming the lifetime of GMC because with the preceding equation, the lifetime of a model cloud is given as $\sim0.5\pi / \sqrt{\alpha_{\mathrm{fb}} \SFEffi / \TauFF}$ \citep{Feldmann2011}. The estimated value of the GMC lifetime varies between 15 to 40 Myr (e.g., \cite{Kawamura2009LMC}; \cite{Murray2011SFE}; \cite{Miura2012M33}). To check the maximum influence the feedback can exert, we here adopt the smallest value of 15 Myr: $\alpha_{\mathrm{fb}}$ is derived as 7.3 Myr$^{-1}$. \par Figure \ref{FigSFEfftoM} plots the observed $\SFEff$ as a function of the cloud mass for each region (a--h). In addition, figure \ref{FigSFEfftoM}(i) shows the evolutionary tracks for model clouds with initial masses of 10$^6$ and 10$^7$ $\Msun$, respectively. Along each of the two tracks, the squares indicate the time steps for 10\%, 30\%, 50\%, 70\%, and 90\% of the lifetime of the model GMC, from the bottom to the top. \par Initially, the model clouds move up almost straight on the plot as $\SFEffa$ increases, which is driven by the rapid growth of the observed SFR. This rapid growth of the observed SFR is due to the underestimation of the observed SFR when the cloud's age is lower than $\tAVG$, as stated above. Even after the initial rapid growth of $\SFEffa$, it continues to rise because the decrease in the cloud mass is always faster than the SFR decreases due to the averaging time imposed in the derivation of the SFR. \par With the adopted parameters, the range of the values for $\SFEffa$ is predicted to be within approximately 0.0038--0.024 for the 80\% of the GMC lifetime, which is approximately equivalent to a $\pm$0.4 dex variation. The calculated range is indicated as the shaded area in figure \ref{FigSFEfftoM} to aid comparison with the actual $\SFEff$ of the GMCs in M83. We note that this range is obtained by adopting the shortest estimate of the GMC lifetime available. If a longer GMC lifetime is assumed, then the range covered by $\SFEffa$ becomes narrower. For example, if the assumed lifetime is 30 Myr, the variation is approximately $\pm$0.2 dex. \paragraph{Comparison with the observed distribution of $\SFEff$} \par Up to now, we have seen that the evolutionary effect of a cloud might cause a variation in the apparent efficiency, $\SFEffa$, even if the intrinsic efficiency is fixed as $\SFEffi=0.01$. The predicted amount of the variation in $\SFEffa$ is up to approximately $\pm$0.4 dex over 80\% of the cloud lifetime, assuming the most intense role of the stellar feedback. Therefore, if the observed variation in $\SFEff$ is over the predicted range of $\SFEffa$ obtained by assuming a fixed value of $\SFEffi$, then $\SFEffi$ is suggested to be nonuniform. \par Comparing the observed $\SFEff$ of GMCs with the predicted range of $\SFEffa$ in figure \ref{FigSFEfftoM}, we see that many GMCs deviate from the predicted $\pm$0.4 dex range of variations and also see signs of regional variations in the efficiency of star formation. For example, in the inter-arm regions, most of the GMCs, especially GMCs more massive than 10$^6$ $\Msun$ are located below the lower end of the predicted range that corresponds to the 10\% of the model GMC lifetime. Thus, if $\SFEffi$ is to be fixed as 0.01, then most of the GMCs in the inter-arm regions have to be in the very young stage of cloud evolution, younger than 10\% of the assumed cloud lifetime. However, this appears implausible, because the dwelling time in the inter-arm regions observed here should be several tens of Myr, taking into consideration galactic dynamics (see figure 17 in \cite{Hirota2014}). Therefore, the intrinsic efficiency, $\SFEffi$, should be significantly lower than the global average of 0.01 in the inter-arm regions. \par Another sign of regional variation in $\SFEff$ can be seen in the primary arm ridge, where a non-negligible number of GMCs exhibit an $\SFEff$ higher than the predicted range for it. Applying the argument same as for the inter-arm regions, the upward deviation of the observed $\SFEff$ in the primary arm ridge suggests that GMCs form stars with an $\SFEffi$ that is higher than 0.01. \par Here, we have seen that the range of observed variation in $\SFEff$ is larger than its allowed range of variation with a fixed value of $\SFEffi$. We also have seen regional variations in the distributions of $\SFEff$ which suggests variation in $\SFEffi$. Therefore, we conclude that the observed variation in $\SFEff$ is not just an artifact caused by the rapid mass consumption of GMCs due to the stellar feedback. \par \subsection{Impact of stellar feedback in limiting the lifetime of GMCs} \label{SectionFeedback} \begin{figure} [] \begin{center} \FigureFile(88mm,88mm){p18.pdf} \caption{ Histogram of the ratio of the outward force, which is a combination of radiation and gas pressure forces , to the self-gravity of GMC, $\Qfb$, for each region. In each plot, the solid histogram shows the number distribution of the GMCs that have associated $\HII$ regions. The dashed histogram in each plot includes both GMCs with and without associated $\HII$ regions. Dotted and dashed vertical lines in each plot indicate $\Qfb$=1 and median value of $\Qfb$ for the samples. } \label {FigFradOverFgravHistogram} \end{center} \end{figure} As we have seen in \S\ref{SubsecMassSpectrum}, the GMC mass function in the primary arm exhibited a steeper slope ($\sim-1.8$) compared to those in the other regions. Disruption of GMCs due to the role of stellar feedback was argued as a possible mechanism for the steeper slope of the GMC function in the primary arm ridge. To check the validity of the argument made in \S\ref{SubsecMassSpectrum}, we examine the impact of stellar feedback in this subsection. \par Stellar feedback takes place in various forms, such as momentum input by radiation pressure, gas pressure, stellar winds, and photo-ionization and photo-dissociation due to UV and FUV radiation. At the scale of 10--100 pc which is relevant to GMCs, the radiation pressure and gas pressure associated with warm ionized gas are considered to play dominant roles in removing gas material from host GMC (e.g., \cite{Matzner2002}; \cite{Lopez2011}; \cite{Murray2011SFE}). Here, we compare the outward force exerted by radiation pressure ($\Frad$) and ionized gas pressure ($\Fgas$) against the inward force of gravity for each GMC to see if stellar feedback is indeed strong enough to destroy the GMCs in M83. \par The force due to the radiation pressure from an $\HII$ region is calculated as \begin{equation} \Frad = L_{\mathrm{bol}}/c, \end{equation} where $L_{\mathrm{bol}}$ is the bolometric luminosity of an $\HII$ region and $c$ is the speed of light. The derivation of $L_{\mathrm{bol}}$ for a GMC is made by converting back the SFR of the GMC (derived in \S\ref{SubsecCrossMatch}) into the extinction-corrected $\HAlpha$ luminosity using equation (\ref{EqSFRCalibration}), and then applying a bolometric-to-$\HAlpha$ luminosity ratio is calculated using Starburst99. The parameters used for the calculation are taken to be as same as those used in \citet{Calzetti2007} to maintain consistency with the SFR calibration described in \S\ref{SubsecHaToSFR}. We must note that the equation only considers the direct radiation emitted by massive stars. In reality, emission absorbed by dust and re-emitted in infrared would boost the radiation pressure. We omit this dust-processed emission from the calculation of radiation pressure for the following two reasons. First, the dust-processed emission is not the most dominant source of the pressure for normal HII regions in a galactic disk (\cite{Lopez2011}; \cite{Lopez2014Feedback}). Second, the calculation of the dust-processed emission requires computations of dust opacity that are far from trivial. As the dust-processed radiation should have a non-negligible impact in the central region, it should be noted that the outward pressure estimated in this subsection is likely to be an underestimate for the central region. \par The force due to the pressure associated with warm ionized gas around an $\HII$ region is calculated as \begin{equation} \Fgas = 4\pi \RHII^2 (2 n_{e} k \THII), \end{equation} where $\RHII$ is the radius of the $\HII$ region, $n_{e}$ is the electron number density, $k$ is the Boltzmann constant, and $\THII$ is the ionized gas temperature. We assume constant temperature of $\THII$ = 10$^4$ $K$. The number density of electrons is estimated as $n_{e} = \sqrt{3 \QLyc / (4 \pi \RHII^3 \alphaRec)}$, where $\QLyc$ is the Lyman continuum production rate and $\alphaRec$ is the recombination coefficient. By assuming Case B recombination, $\QLyc$ is derived from the $\HAlpha$ luminosity for each $\HII$ region. \par The force of gravity for a GMC is calculated as \begin{equation} F_{\mathrm{grav}} = G \frac{{\Mmol}^2}{{R}^2}. \end{equation} Figure \ref{FigFradOverFgravHistogram} shows the distribution of the ratio of the outward force to the inward force, which is $\Qfb$. The radiation and gas pressure, $\Frad$ and $\Fgas$, calculated for each $\HII$ region is divided among the associated GMCs using the same method adopted for the SFR (\S\ref{SubsecCrossMatch}). The median value of $\Qfb$ in the primary arm ridge is close to or above unity, suggesting that many GMCs in this region are certainly being disrupted by stellar feedback. On the other hand, $\Qfb$ is mostly below 1 in other regions. We again note that for the central region, $\Qfb$ is highly uncertain due to the omission of dust-processed radiation, and thus we do not discuss the central region here. As far as subregions in the disk of M83 are concerned, stellar feedback is most efficiently disrupting GMCs in the primary arm. This effectiveness of stellar feedback in the primary arm ridge is in agreement with the expectation that stellar feedback is responsible for forming the steeper slope of the mass function in this region. \par As a by-product of the analysis made here, an approximate estimate of the lifetime of the GMCs can be made. First, we assume that GMCs evolve from a quiescent state in which they form a small amount of stars---and thus $\Qfb$ $<$ 1---to an active state in which they form many massive stars---and thus $\Qfb$ $>1$. For the active GMCs with $\Qfb$ $>$ 1, it would be natural to assume further that they are about to be disrupted by the stellar feedback and thus the average remaining lifetime for them is comparable to the nominal lifetime of massive stars. If stellar feedback is the only process that limits the lifetime of GMCs, then it is possible to gauge their lifetime from the number ratio of GMCs with $\Qfb$ above and below 1. Applying a similar method, the lifetime of a GMC is estimated to be 15--40 Myr in the MW (\cite{WilliamsMcKee1997}; \cite{Murray2011SFE}), Large Magellanic Clouds \citep{Kawamura2009LMC} and M33 \citep{Miura2012M33}. For the GMCs in M83, 37 out of 179 are found to have $\Qfb$ greater than 1. Taking that average lifetime of massive stars as 4 Myr, the average lifetime of a GMC is estimated to be $\sim20$ Myr ($= 179 / 37 \times 4$ Myr), which is not far from the estimation made for other galaxies. However, this estimation has to be treated with great care because it is merely an averaged value found in the limited area presented here, and it also does not take into consideration the role of shear that might be responsible for disrupting GMCs in the inter-arm regions \citep{Meidt2015Lifetime}. \subsection{Implications of the spatial variation in SFE} \label{SubsecImplications} The cloud-scale examination of $\SFEff$ made in \S\ref{SubsecSFEff} indicated the following three points: (1) mass-weighted mean value of $\SFEff$ is $\sim$0.93\% , which is in agreement with the average values found in other systems (e.g., \cite{Krumholz2012UniversalSF}); (2) however there is a large scatter in $\SFEff$ with a MAD of $\sim$0.6 dex and peak-to-peak variation of approximately three orders of magnitude; and (3) there is a regional variation in $\SFEff$. The most prominent characteristic of the regional variation in $\SFEff$ is the high median $\SFEff$ in the primary arm ridge ($\sim$0.027), compared to the inter-arm regions (4.6 $\times$ 10$^{-3}$ and 2.7 $\times$ $10^{-3}$) and the secondary arm ridge ($\sim$3.9 $\times$ 10$^{-3}$). In this subsection, we discuss the implications of these findings. \par There is a group of theories that focus on the roles of turbulence in regulating star formation, and aim to provide a quantitative description which produces $\SFEff$ $\simeq$ 0.01 in a steady state (e.g., \cite{Krumholz2005TurbulenceSF}; \cite{Federrath2015}). The goal of achieving $\SFEff$ $\simeq$ 0.01 in a steady state implies that GMCs are approximated as long-lived entities that form stars with a stable efficiency. The first point, the mass-weighted mean of $\SFEff$ being approximated 0.01, agree with the expectation of the turbulence-regulated model. However, the second point, the large scatter in the apparent distribution of $\SFEff$ does not agree with the assumption of stable efficiency in GMCs. \par Although the turbulence-regulated model of star formation is well applied to some studies made with mostly coarse resolutions that sample several clouds per beam (e.g., \cite{Krumholz2012UniversalSF}), it has been argued that the cloud-scale distribution of $\SFEff$ show some deviations from the expectation of turbulence-regulated models (\cite{Murray2011SFE}; \cite{Lee2016DynamicSF}). In particular, \citet{Lee2016DynamicSF} observed a large scatter in $\SFEff$ in Galactic GMCs, and they argued that it is difficult to explain the large scatter in $\SFEff$ with the models of turbulence-regulated star formation, including \citet{Krumholz2005TurbulenceSF}, \citet{PadoanNordlun2011} and \citet{HennenbelleChabrier2011}. Instead, they claimed that $\SFEff$ should be a time-dependent variable that dynamically increases during the lifetime of GMCs; at the later phase of their lifetime, GMCs produce stars with high $\SFEff$ and are disrupted by stellar feedback. \par The spread in $\SFEff$ observed in M83 is similarly huge as the one observed in Galactic GMCs by \citet{Lee2016DynamicSF}, and therefore the idea that $\SFEff$ increases with time might also hold in M83. The $\SFEff$ observed in Galactic GMCs by \citet{Lee2016DynamicSF} is characterized by a median and scatter about the median of $\sim$1.8\% and 0.91 dex, respectively. The scatter of 0.91 dex is comparable with the MAD of $\sim$0.6 dex observed in M83.\footnote{If the distribution in figure \ref{FigSFEffHistogram}(a) is approximated as a Gaussian, a MAD of 0.6 dex corresponds to a scatter of $\sim$0.9 dex} We note that the median $\SFEff$ of $\sim$1.8\% obtained by \citet{Lee2016DynamicSF} is higher than the one obtained here in M83 (0.3\%), but it is likely due to the fact that \citet{Lee2016DynamicSF} has selected GMCs with active star formation. It is also noteworthy that \citet{Leroy2017M51SFEff} also found the median value of $\SFEff$ in M51 to be $\sim$0.3\% with a resolution of 370 pc. \par If the notion that $\SFEff$ increases with time during the lifetime of a GMC is correct, then the regional variations of $\SFEff$ (the third point) may suggest that large-scale galactic structures exert an influence in organizing the life cycle of GMCs. The GMCs in the primary arm ridge exhibit a higher $\SFEff$ compared to the inter-arm GMCs. If $\SFEff$ increases over the lifetimes of GMCs, the GMCs in the primary arm ridge should be at a late stage of their evolution, producing stars with increased $\SFEff$, while GMCs in the inter-arm regions are at an early stage with low $\SFEff$. The idea that GMCs in the primary arm ridge are at a late stage of their evolution is in agreement with the analysis made in \S\ref{SectionFeedback}, which suggested that the GMCs in the primary arm ridge are about to be disrupted by stellar feedback (\S\ref{SectionFeedback}). \par The discussion so far can be summarized as follows: $\SFEff$ increases with time during the lifetime of a GMC and galactic structures have a certain role in organizing the lifetimes of GMCs. This scenario is in agreement with the suggestion that spiral arms can organize the buildup of massive GMCs (\cite{Egusa2011M51}; \cite{Colombo2014Env}). A concern is the timescale of traversal across inter-arm regions which can be a factor of few longer than the suggested lifetime of GMCs, which is 15--40 Myr. If all GMCs have the same lifetime and also increased $\SFEff$ in the same way, then at least a few GMCs in the inter-arm should exhibit $\SFEff$ values as high as those in the primary arm ridge. However, the inter-arm GMCs do not exhibit such a high $\SFEff$. Therefore, to explain the observed $\SFEff$, a mechanism that obstructs the evolution of GMCs in the inter-arm regions would be required. The large-scale shear that acts to disrupt clouds \citep{Meidt2015Lifetime} might be a candidate mechanism. If there exists a mechanism that disrupts GMCs in the inter-arm before increasing $\SFEff$, the lifetime of GMCs in the arm and inter-arm could be different from each other. Complete mapping of a galaxy in CO and reliable star formation tracers will be required to fully reveal the life cycle of GMCs. Results of the mosaic $^{12}$CO (1--0) observations of the nearby barred galaxy M83 carried out with ALMA are presented. The interferometric data are combined with the data obtained with the Nobeyama 45-m telescope to recover the total flux. The mosaic observations cover a $\sim$13 kpc$^2$ region that includes the galactic center, eastern bar and spiral arm with a spatial resolution of \timeform{2''.03} $\times$ \timeform{1''.15} (44.3 pc $\times$ 25.1 pc), which is comparable to the typical sizes of GMCs. The velocity resolution is $\sim$2.5 $\kmPerS$. \begin{itemize} \item{ With the GMC scale resolution, galactic structures including the spiral arm and the bar are resolved into narrow structures. The bar appears as a continuous molecular ridge with a surface density as high as 200--800 $\MsunPerSqPC$, which exceeds the surface density of typical Galactic GMCs. The spiral arm is resolved into two ridges, or chains of molecular clouds, that run parallel to each other. The one at the leading side, referred to as primary arm ridge, is associated with numerous bright $\HII$ regions while the other one at the trailing side, referred to as secondary arm ridge, appears to be more quiescent. Spurs are found at the leading side of the primary arm ridge and the bar. } \item{The distribution of the massive star-forming regions exhibits a higher degree of concentration, compared to that of CO emission. Most of the $\HII$ regions are concentrated in particular regions, including the primary arm ridge and the bar, which suggests a spatial variation in the SFE. } \item{ We identify 179 GMCs from the CO data using the {\it astrodendro} software package. When making the cloud identification, the data cube is smoothed in the spatial directions to a resolution of \timeform{2.1''} ($\sim$46 pc). Assuming the Galactic CO-to-H$_2$ conversion factor, the median value of the cloud mass is found to be 1.6 $\times$ 10$^6$ $\Msun$. The virial mass and CO luminosity are well correlated to each other, and the median value of the virial parameter for all the identified GMCs is found to be $\sim$1.4, suggesting that most of the GMCs are strongly influenced by their self-gravity. The GMCs in the arm exhibited lower virial parameters with the median value of $\sim$1.0. } \item{ The mass spectrum for all the identified GMCs are fitted with a truncated power law with a slope of -1.58 $\pm$ 0.1, which is close to that of the Galactic GMCs. The fitting is also performed for GMCs in each subregion, and the steepest slope is found in the primary arm ridge (-1.8). We suggest that GMCs in the primary arm ridge are disrupted due to stellar feedback. } \item{ The identified GMCs are cross-matched with the catalog of $\HII$ regions to estimate the SFR for each GMC. As the star formation history for individual $\HII$ regions is not constrained, there should be a factor-of-2 uncertainty in the calibration of the SFR. Despite this weakness, the overall statistical distribution of the SFE for the GMCs in M83 are found to be in agreement with that of Galactic clouds. The median SFE is $\sim$0.5 Gyr$^{-1}$ and the scatter is as large with a peak to peak variation of approximately two orders of magnitude. } \item{ The mass-weighted mean of $\SFEff$ is $\sim$9.4 $\times$ 10$^{-3}$, which is in agreement with the expectations of turbulence regulated star formation models. However, its scatter is as large as $\sim$0.7 dex in MAD, which cannot be explained by a cloud evolution model with a constant $\SFEff$. In addition, a regional variation in $\SFEff$ is also observed. The median value of $\SFEff$ is highest in the primary arm ridge ($\sim$0.027) while it is more than a factor of 5 lower in the inter-arm regions and in the secondary arm ridge. The large spread and significant spatial variation observed in $\SFEff$ support the idea that $\SFEff$ is not a steady time-invariant variable, but is a dynamic variable that increases as GMCs evolve. In particular, the GMCs in the primary arm ridges are suggested to be reaching the last stage of their evolution with elevated $\SFEff$, because the feedback from massive stars appears to be large enough to disrupt them. } \end{itemize} | 18 | 8 | 1808.01702 |
1808 | 1808.04824.txt | { Exoplanetary atmospheric retrieval refers to the inference of atmospheric properties of an exoplanet given an observed spectrum. The atmospheric properties include the chemical compositions, temperature profiles, clouds/hazes, and energy circulation. These properties, in turn, can provide key insights into the atmospheric physicochemical processes of exoplanets as well as their formation mechanisms. Major advancements in atmospheric retrieval have been made in the last decade, thanks to a combination of state-of-the-art spectroscopic observations and advanced atmospheric modeling and statistical inference methods. These developments have already resulted in key constraints on the atmospheric H$_2$O abundances, temperature profiles, and other properties for several exoplanets. Upcoming facilities such as the JWST will further advance this area. The present chapter is a pedagogical review of this exciting frontier of exoplanetary science. The principles of atmospheric retrievals of exoplanets are discussed in detail, including parametric models and statistical inference methods, along with a review of key results in the field. Some of the main challenges in retrievals with current observations are discussed along with new directions and the future landscape.} | \label{sec:intro} A spectrum of an exoplanet provides a window into its atmosphere. A spectrum encodes information regarding the various interconnected physicochemical processes and properties of the atmosphere which are revealed through their influence on the radiation emerging through the atmosphere before reaching the observer. These properties include the chemical composition, temperature structure, atmospheric circulation, clouds/hazes, all of which leave their imprints on the spectrum. Given an observed spectrum, the challenge is to disentangle these various components. This is the goal of `atmospheric retrieval' -- to retrieve the atmospheric properties of an exoplanet from an observed spectrum. The retrieved properties can in turn provide insights into the various atmospheric physical and chemical processes as well as into their formation history. While the introduction of atmospheric retrieval methods to exoplanetary science is a relatively recent and independent development \citep{madhu2009,madhu2011a}, alternate techniques have been in wide usage in the context of Earth-based remote sensing \citep{rodgers2000} and retrievals of solar system planets \citep{irwin2008}. What differentiates exoplanetary atmospheric retrieval from solar system applications is the uniquely challenging nature of observing exoplanetary atmospheres. Firstly, unlike solar system planets, observed exoplanetary spectra are inherently disk-averaged over the spatially unresolved planet. Secondly, given their astronomical origins well beyond the solar system, exoplanetary spectra are naturally substantially fainter, and hence of much lower signal-to-noise (SNR), compared to solar-system objects. Thirdly, any complementary in situ measurements or a priori knowledge possible in the solar system are unavailable for exoplanetary atmospheres. Finally, the parameter space of exoplanetary atmospheres is substantially wider than that of solar system planets. For example, while the equilibrium temperatures of most solar system planets lie below 300 K those of exoplanets extend up to $\sim$3000 K. Similarly large ranges are natural in all other atmospheric parameters and processes - gravities, chemical compositions, circulation patterns, degree and type of insolation, etc, implying enormous complexity and diversity in exoplanetary atmospheres far beyond those experienced in the solar system. The combination of these various factors make exoplanetary atmospheres enormously more challenging to study compared to those of solar system objects, and necessitate substantially more robust techniques for atmospheric modeling and retrieval to make the best use of the limited spectral data available. The origins of atmospheric retrieval techniques for exoplanets were motivated by the `degeneracy problem' faced by early atmospheric observations. Initial molecular detections were claimed based on few channels of infrared photometry or low-resolution spectrophotometry with low SNR \citep[e.g.][albeit some of these datasets have since been revised substantially]{barman2007,tinetti2007,grillmair2008,swain2008a}, such that the spectral features were rarely discernible to the eye. Similarly, temperature inversions were claimed in hot Jupiters based on broadband photometric observations \citep[e.g][]{knutson2008,knutson2009,burrows2007,burrows2008}. These inferences were made using a limited set of forward models containing the putative molecules and assumed temperature profiles that qualitatively matched the data. While the number of free parameters in the forward models typically far exceeded the number of data points then available, the number of models compared against the data were rather limited. This approach left vast areas of parameter space unexplored and degeneracies between various model parameters unknown, thereby providing little statistical basis to the claimed detections. The desire to provide a statistically robust framework to derive atmospheric properties of exoplanets from such low resolution data gave birth to the idea of atmospheric retrieval for exoplanets \citep{madhu2009}. Atmospheric retrieval techniques have since advanced greatly in tandem with parallel advancements in atmospheric observations of exoplanets. In the present chapter we present a pedagogical review of exoplanetary atmospheric retrieval. We first present an overview of the key principles of atmospheric retrieval. We then discuss two primary components of retrieval methods, namely, parametric forward models and statistical inference methods. We then discuss key results in the field from retrievals of state-of-the-art observations. We conclude with a discussion of key issues in this area and the future landscape. \begin{figure*}[t] \centering \includegraphics[width=\textwidth]{retrieval_schematic.png} \caption{Schematic of atmospheric retrieval. Given an observed spectrum and a parametric model of a planetary atmosphere, a parameter estimation method is used to derive the model parameters. The components of a typical atmospheric model are shown on the right. The free parameters typically correspond to the pressure-temperature (P-T) profile and the composition, including the chemical abundances and cloud/haze properties, depending on the datasets. The statistical inference and parameter estimation methods used in contemporary retrieval codes typically allow computation of full posterior probability density functions (PDFs) of the model parameters given a data set, a typical output shown in Fig.~\ref{fig:retrieval}. These PDFs can also be used to compute PDFs of derived quantities such as elemental abundance ratios from those of molecular abundances. In recent advancements retrieval codes are also being coupled with self-consistent equilibrium models to place constraints on departures from radiative-convective and chemical equilibria \citep{gandhi2018}.} \label{fig:schematic} \end{figure*} \begin{figure*}[t] \centering \includegraphics[width=\textwidth]{fig2_Atmospheric_Retrieval.png} \caption{ Example of atmospheric retrieval for a transmission spectrum of the hot Jupiter HD 209458b. The left panel shows an observed spectrum in green along with the model fit and significance contours in purple. The right panel shows the posterior probability distributions of the retrieved compositions and the retrieved pressure-temperature profile.} \label{fig:retrieval} \end{figure*} | 18 | 8 | 1808.04824 |
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1808 | 1808.03531_arXiv.txt | The existence of diffuse Galactic neutrino production is expected from cosmic ray interactions with Galactic gas and radiation fields. Thus, neutrinos are a unique messenger offering the opportunity to test the products of Galactic cosmic ray interactions up to energies of hundreds of \unit{TeV}. Here we present a search for this production using ten years of ANTARES track and shower data, as well as seven years of IceCube track data. The data are combined into a joint likelihood test for neutrino emission according to the KRA$_\gamma$ model assuming a \unit[5]{PeV} per nucleon Galactic cosmic ray cutoff. No significant excess is found. As a consequence, the limits presented in this work start constraining the model parameter space for Galactic cosmic ray production and transport. | A diffuse Galactic neutrino emission is expected from cosmic ray (CR) interactions with interstellar gas and radiation fields. These interactions are also the dominant production mechanism of the diffuse high-energy $\gamma$-rays in the Galactic plane, which have been measured by the \Fermi-Large Area Telescope (\Fermi-LAT)~\citep{FermiTemplate}. In the GALPROP-based \citep{GALPROPWebRun} conventional model of Galactic diffuse $\gamma$-ray production CRs are accelerated in a distribution of sources such as supernova remnants. They propagate diffusively in the interstellar medium producing $\gamma$-rays and neutrinos via interactions with the interstellar radiation field and interstellar gas. The interstellar radiation field is weakly constrained by \Fermi-LAT $\gamma$-ray data and interstellar gas is constrained by both \Fermi-LAT $\gamma$-ray data and radio measurements of CO and HI line intensities. The CR population model itself is normalised to local measurements taken at Earth. The GALPROP model parameters are tuned to achieve optimal agreement between \Fermi-LAT~\citep{FermiTemplate} data and the direction-dependent prediction given by integrating expected $\gamma$-ray yields along the line of sight from Earth. The neutral pion decay component estimated by the conventional model should be accompanied by a neutrino flux from charged pion decay. \begin{figure} \centering \includegraphics[width=0.45\textwidth]{Flux_5PeV.pdf} \caption{\label{fig:ModelFlux}Neutrino flux per unit of solid angle of the KRA$_\gamma^{5}$ model~\citep{KRAgamma}, shown as a function of direction in equatorial coordinates (Hammer projection).} \end{figure} The conventional model, however, under-predicts the $\gamma$-ray flux above \unit[10]{GeV} in the inner Galaxy~\citep{FermiTemplate}. The KRA$_\gamma$ models~\citep{KRAgamma, KRAgamma2, KRAgamma3} address this issue using a radially-dependent model for the CR diffusion coefficient and the advective wind. The primary CR spectrum assumed within the KRA$_\gamma$ models has an exponential cutoff at a certain energy. In order to bracket measurements by KASCADE~\citep{KASCADE} and KASCADE-Grande~\citep{KASCADEgrande}, respectively in the [\unit[100]{TeV}, \unit[100]{PeV}] and [\unit[10]{PeV}, \unit[2000]{PeV}] energy ranges, while maintaining agreement with proton and helium measurements by CREAM~\citep{CREAM_pHe}, cutoffs at 5 and \unit[50]{PeV} per nucleon are considered. The resulting models are referred to as KRA$_\gamma^{5}$ and KRA$_\gamma^{50}$, respectively. The direction dependence of the energy-integrated KRA$_\gamma^{5}$ neutrino flux prediction is shown in Figure~\ref{fig:ModelFlux}. Compared to the conventional model of the Galactic diffuse emission, the KRA$_\gamma$ models predict modified spectra and enhanced overall $\gamma$-ray and neutrino fluxes in the southern sky, especially in the central ridge where a hardening of the CR spectra is reproduced. Hence, neutrinos offer a unique opportunity to independently test the model assumptions of Galactic CR production and transport, accessing energies far beyond the reach of current $\gamma$-ray experiments. The KRA$_\gamma$ predictions have already been tested separately with ANTARES~\citep{GalPlane_ANT} and IceCube~\citep{GalPlane_IC} data. ANTARES and IceCube achieved sensitivities of $1.05\times\Phi_{\text{KRA}_\gamma^{50}}$ and $0.79\times\Phi_{\text{KRA}_\gamma^{50}}$, respectively; both analyses obtained 90\% confidence level (CL) upper limits of $1.2\times\Phi_{\text{KRA}_\gamma^{50}}$. ANTARES additionally examined the \unit[5]{PeV} cutoff model, obtaining a sensitivity of $1.4\times\Phi_{\text{KRA}_\gamma^{5}}$ and an upper limit of $1.1\times\Phi_{\text{KRA}_\gamma^{5}}$ due to an under-fluctuation of the fitted signal flux in the track channel. This paper presents a combination of these two maximum-likelihood analyses exploiting the advantageous field of view of ANTARES as well as the high statistics of IceCube. | This analysis combines seven years of IceCube tracks and ten years of ANTARES tracks and showers using a likelihood ratio test. The results are summarized in Table~\ref{table:results}. Systematic uncertainties on the ANTARES detection efficiency (due to the uncertainty on the acceptance of the ANTARES PMTs) are included in the analysis as in the paper by~\citet{GalPlane_ANT}. As described by~\citet{IC_PS_7yrs}, systematic uncertainties in the modeling of the Antarctic ice and the optical module efficiency lead to an uncertainty on the IceCube detection efficiency of at most 11\% which is not included here. \begin{table*} \centering \caption{\label{table:results}Sensitivities and results of the analysis on the KRA$_\gamma$ models with the 5 and \unit[50]{PeV} cutoffs.} \begin{tabular}{ c c c c c c c}\toprule \multirow{2}{*}{Energy cutoff} & \multicolumn{3}{c}{Sensitivity $[\Phi_{\textrm{KRA}_\gamma}]$} & Fitted flux & $\it{p}$-value & UL at 90\% CL \\\cmidrule(rl){2-4} & Combined & ANTARES & IceCube & $[\Phi_{\textrm{KRA}_\gamma}]$ & [\%] & $[\Phi_{\textrm{KRA}_\gamma}]$ \\\midrule \unit[5]{PeV} & $0.81$ & $1.21$ & $1.14$ & $0.47$ & $29$ & $1.19$ \\ \unit[50]{PeV} & $0.57$ & $0.94$ & $0.82$ & $0.37$ & $26$ & $0.90$ \\\bottomrule \end{tabular} \end{table*} The maximum-likelihood estimate yields a non-zero diffuse Galactic neutrino flux for both models with a p-value of 29\% for KRA$_\gamma^{5}$ and 26\% for KRA$_\gamma^{50}$. Since neither of these results is statistically significant, we place upper-limits on both model normalizations. The KRA$_\gamma^{50}$ model is constrained at the 90\% confidence level (with an upper limit of $0.9\times \Phi_{\textrm{KRA}_\gamma^{50}}$), while the KRA$_\gamma^5$ model is not yet constrained by our analysis. This was expected as the \unit[50]{PeV} cutoff represents an extreme tuning of the acceleration parameters for the Galactic CRs, while the \unit[5]{PeV} cutoff in light CR can be considered a more reliable case for the Galactic accelerators. \begin{figure} \centering \includegraphics[width=0.45\textwidth]{Combined_UL.pdf} \caption{Combined upper limits (UL) at 90\% confidence level (blue lines) on the three-flavor neutrino flux of the KRA$_\gamma$ model with the 5 and \unit[50]{PeV} cutoffs (black lines). The boxes represent the diffuse astrophysical neutrino fluxes measured by IceCube using an isotropic flux template with starting events (yellow) and upgoing tracks (green).}\label{fig:UL} \end{figure} Figure~\ref{fig:UL} represents the combined upper limits in comparison to the all-flavor full sky energy spectrum of the KRA$_\gamma$ models as well as the previous IceCube and ANTARES upper limits. The present upper limit on the \unit[5]{PeV} model is higher than the previously published upper limit for ANTARES alone although the sensitivity is much better. This is due to the overfluctuation observed in the IceCube data sample as well as the difference in the definition of the test statistic. In the ANTARES standalone analysis it was the sum of the shower and track test statistics, computed independently, instead of computing one test statistic from the combined log-likelihood ratio curve (equation~\ref{eq:ts_comb}). The results presented here provide for the first time a combined constraint on diffuse Galactic neutrino emission by IceCube and ANTARES. The limit on the KRA$_\gamma$ model with \unit[50]{PeV} cutoff extends the energy range of the constraint on the model from \unit[10]{GeV} with \Fermi-LAT up to hundreds of TeV. Based on the limit on the KRA$_\gamma^{5}$-model, this analysis limits the total flux contribution of diffuse Galactic neutrino emission to the total astrophysical signal reported by \citet{IC_CombinedFlux} to 8.5\%. In the future, the sensitivity of this analysis can be further improved by including IceCube showers \citep{MESC}. This will allow for a powerful test of the KRA$_\gamma^5$ model, thereby constraining the diffusion mechanisms, the maximal energy injected by supernova remnants and the Galactic gas distributions considered in the model. | 18 | 8 | 1808.03531 |
1808 | 1808.03688_arXiv.txt | Coronal jets and bright points occur prolifically in predominantly unipolar magnetic regions, such as coronal holes, where they appear above minority-polarity intrusions. Intermittent low-level reconnection and explosive, high-energy-release reconnection above these intrusions are thought to generate bright points and jets, respectively. The magnetic field above the intrusions possesses a spine-fan topology with a coronal null point. The movement of magnetic flux by surface convection adds free energy to this field, forming current sheets and inducing reconnection. We conducted three-dimensional magnetohydrodynamic simulations of moving magnetic elements as a model for coronal jets and bright points. A single minority-polarity concentration was subjected to three different experiments: a large-scale surface flow that sheared part of the separatrix surface only; a large-scale surface flow that also sheared part of the polarity inversion line surrounding the minority flux; and the latter flow setup plus a ``fly-by'' of a majority-polarity concentration past the moving minority-polarity element. We found that different bright-point morphologies, from simple loops to sigmoids, were created. When only the field near the separatrix was sheared, steady interchange reconnection modulated by quasi-periodic, low-intensity bursts of reconnection occurred, suggestive of a bright point with periodically varying intensity. When the field near the PIL was strongly sheared, on the other hand, filament channels repeatedly formed and erupted via the breakout mechanism, explosively increasing the interchange reconnection and generating non-helical jets. The fly-by produced even more energetic and explosive jets. Our results explain several key aspects of coronal-hole bright points and jets, and the relationships between them. | Small brightenings and impulsive flows are found throughout the ``quiet" solar corona, in association with photospheric magnetic-field concentrations and parasitic-polarity intrusions. These features are most visible as bright points and jets in coronal holes (CHs), where the background magnetic field is largely unipolar and open and the ambient plasma is dark in EUV and X-ray wavelengths. Coronal bright points are seen as enhanced EUV and X-ray emission from small regions with diameters on the order of 10-50 arcsec, and lifetimes of 3-60 hr in EUV \citep{Zhang2001,Mou2016} and up to $8$ hr in X-rays \citep{Golub1974}. A puzzling feature of most bright points is that their intensity varies periodically, with periods ranging from a few minutes up to a couple of hours \citep{Kariyappa2008,Tian2008}. Their internal morphology appears to be similar in coronal holes and quiet Sun \citep{Habbal1990,Galsgaard2017}: bright points can contain a sigmoid \citep[e.g.,][]{Brown2001}, a few parallel loops \citep{Zhang2012}, or an anemone \citep[e.g.,][]{Shibata1994}. In many cases, bright points are associated with moving magnetic elements (MMEs), sometimes with opposite-polarity concentrations separating from each other due to flux emergence, at other times converging toward each other to coalesce and cancel \citep{Webb1993,Mou2016}. These associations with interactions between opposite-polarity magnetic fields have led to broad acceptance that bright points ultimately derive their energy from magnetic reconnection and the ensuing acceleration and heating of the entrained plasma. Long-lived bright points are frequently observed to produce coronal jets: impulsive, collimated flows of dense, hot plasma, which are launched low in the atmosphere and are guided along the ambient coronal magnetic field \citep{Shimojo1996,Nistico2009,Raouafi2016}. Jets have much shorter lifetimes (a few minutes) than bright points \citep{Savcheva2007}, so an individual bright point can produce multiple jets over its lifetime. Some jets extend so far into the corona that they can be observed in scattered white light in the inner heliosphere \citep[e.g.,][]{Wang1998}, thus contributing mass, momentum, and distinct structures to the solar wind. High-resolution observations have revealed that many, if not most, jets contain miniature filaments (cool plasma) and/or sigmoids (hot plasma) that erupt to generate the jet \citep[e.g.,][]{Innes2009,Raouafi2010,Shen2012,Hong2014,Hong2016,Sterling2015,Sterling2016,Kumar2018}. Typically, though not always, these jets have a strong helical flow component. A relationship between bright points, jets, and the diffuse, persistent columns known as coronal plumes has long been suspected, but has proven difficult to verify and explain. Thus far the strongest connection appears to be the existence of tiny ``jetlets" observed within some plumes \citep{Raouafi2008,Raouafi2014}, but it is unclear whether all plumes are composed of many such impulsive events or whether a different mechanism (e.g., weak, quasi-steady null-point reconnection) is responsible for the enhanced density and flows of plumes. On close inspection, CH jet sources and anemone-type bright points \citep[e.g.,][]{Galsgaard2017} match the magnetic topology of an embedded bipole: a three-dimensional (3D) coronal magnetic null point, with associated inner and outer spine lines and a fan separatrix surface \citep{Antiochos1990,Lau1990}. The photospheric manifestation of this configuration is a minority-polarity intrusion within the majority-polarity magnetic field. The fan surface separates the closed magnetic flux beneath the null point from the globally open flux above and away from the null point. Relative motions of the two flux systems can readily distort the null to form a current sheet there \citep{Antiochos1996}, setting the stage for interchange reconnection between open and closed field lines and associated plasma flows and heating. It is broadly accepted that coronal jets are driven by the onset of explosive magnetic reconnection, while {some observational studies have speculated that} more gradual reconnection in the same magnetic structure could explain a long-duration bright point \citep[e.g.,][]{Doschek2010,Pucci2012,Zhang2012}. In previous work, we and our colleagues have investigated the generation of CH jets within the embedded-bipole model and its null-point topology. The essential feature needed to generate an explosive jet in this model is to store a substantial amount of magnetic free energy within the low-lying closed flux. In configurations with a nearly uniform majority-polarity background field, twisting the internal closed flux by imposing slow, quasi-circular surface flows eventually leads to onset of a kink-like instability. Strong feedback between the ideal triggering mechanism and rapid reconnection through the null-point current sheet releases much of the stored free energy and generates a helical, Alfv\'enic jet \citep{Pariat2009,Pariat2010,Pariat2015,Pariat2016,Wyper2016,Wyper2016b,Karpen2017}. In more recent work, we investigated cases that have a strong majority-polarity concentration adjacent to the minority-polarity intrusion. In that case, a filament channel of strongly sheared, low-lying magnetic flux forms at the polarity inversion line (PIL) between the two concentrations. Reconnection above the PIL forms a flux rope that can support a mini-filament, which rises slowly and eventually erupts as a jet through reconnection between the flux rope and the external field \citep{Wyper2017,Wyper2018}. The underlying mechanism is an exact analogue to the breakout model that explains fast coronal mass ejections \citep{Antiochos1998,Antiochos1999}. Our preceding jet modelling assumed photospheric rotational motions that were strictly internal to the closed-field region. Consequently, we obtained two types of reconnection-driven outflows: weak intermittent plasma releases, and energetic helical jets accompanied by transient bright points beneath the {domed separatrix}. In this paper, we study the activity driven by larger-scale, linear footpoint motions that transport the minority-polarity intrusion across the solar surface, as occurs with {MMEs} in coronal holes. Specifically, we consider the scenario when this motion subjects the closed field beneath the separatrix to a broad {shear.} We have investigated three configurations of increasing complexity and activity. In the first, the minority-polarity flux was moved quite uniformly, but part of the surrounding majority-polarity background flux was left behind due to a gradient in the imposed surface flow. The separatrix was distorted by this shear flow, inducing the development of currents and low-intensity reconnection at the null point. We show that the reconnection process has a natural periodicity, reminiscent of a bright point with quasi-periodic intensity fluctuations. In the second configuration, the minority-polarity patch was placed closer to the gradient in the imposed photospheric flow, so that the flux was substantially sheared and the surrounding PIL was strongly distorted. This case exhibited elevated reconnection and explosive jetting. It transitioned between long-duration, low-intensity bright point-like reconnection and {short-duration, high-intensity jet-like} reconnection and back again. Third, we added a concentration of majority-polarity flux to the second configuration, then advected the minority- and new majority-polarity concentrations past one another. This ``fly-by'' configuration produced still more energetic and explosive activity as the MMEs first connected to, then disconnected from, each other as they passed. In \S\S \ref{sec:setup} and \ref{sec:diagnostics}, we describe the simulation setup and the diagnostics used to interpret the results. The simulations and our analyses are presented in \S \ref{sec:results}. We demonstrate good quantitative agreement between our results and observations, and discuss the implications of our work for natural links between bright points, CH jets, and plumes, in \S \ref{sec:discussion}. In \S \ref{sec:summary} we briefly list the major conclusions of this work. | We conducted several numerical experiments to understand better the nature of coronal bright points and jets driven by moving magnetic elements. Our simulations differ from most previous bright-point models { \citep[e.g.,][]{Priest1994,Parnell1994,Longcope1998,Galsgaard2000} in that we consider an open ambient field. We can compare our simulations quantitatively to observations by adopting typical values for length scale, field strength, and plasma density as described in \S \ref{sec:setup}. Taking $L_{s}$ = $2.5 \times 10^8$\,cm, $B_{s}$ = 2.5\,G, and $\rho_{s}$ = $4 \times 10^{-16}$\,g cm$^{-3}$ yields $V_{s}$ = $1250$\,km s$^{-1}$, $t_{s}$ = 2\,s, and $E_{s}$ = $9.8 \times 10^{25}$ erg. The width of the separatrix then becomes {$\approx 7 \times L_{s} = 17.5$} Mm and the null initially sits at a height of {$\approx 2.7\times L_{s} = 6.75$ Mm}. Similar values were found by \citet{Zhang2012} in potential field extrapolations above two bright points. The background plasma temperature becomes $T \approx 0.94$ MK and the driving speed translates to $25$ km\,s$^{-1}$ and $12.5$ km\,s$^{-1}$ for the fast and slow speeds, respectively. The minority polarity (now with a peak field strength of $62.5$ G and magnetic flux of {$\approx 8.7\times 10^{18}$\,Mx}) is moved a distance of $12 \times L_{s} = 30$\,Mm in each simulation, comparable to the diameter of a supergranule. } In Configuration 1S the field close to the separatrix was sheared, producing steady interchange reconnection modulated by quasi-periodic reconnection bursts. {We can roughly estimate the free energy release rate of the steady component from the energy injected before the onset of reconnection {in the first $200$ time units} of the simulation. By $t=200$ around $2$ units of free magnetic energy are injected into the closed field, Fig. \ref{fig:energies}(a). Accounting for the ramp up of the driver and scaling the values this corresponds to an energy injection rate of $\approx 5.6\times 10^{23}$\,erg\,s$^{-1}$ at the maximum driving speed. During the quasi-steady phase this injection is balanced by losses to numerical diffusion, and equates to roughly the free energy available for heating the plasma. Even after accounting for the unrealistically fast driving speed (see below), this energy release rate compares well with the observed values of $10^{23}-10^{24}$\,erg\,s$^{-1}$ for bright points \citep{Golub1974,Priest1994}.} The energy released by the bursts was a small fraction of the stored free magnetic energy -- $\approx 0.5 \times E_{s} = 4.9\times 10^{25}$ erg occurring {with a period of} $\approx 240 \times t_{s} = 8$ min -- whilst the outflow speeds reached typical values of $\approx 0.05 \times V_{s} \approx 60$ km\,s$^{-1}$ along the outer spine. {The energy released in each burst corresponds to $\approx 18\%$ of the energy released over the same period by the steady component.} Many bright points exhibit quasi-periodic intensity increases, with periods ranging from a few minutes to a couple of hours \citep{Kariyappa2008,Tian2008,Zhang2012}. Our results demonstrate that some of this periodicity can be explained by the natural modulation of the interchange reconnection that occurs as minority-polarity elements are moved by surface motions. The predicted outflow speeds, and certainly the periods of the reconnection cycles, are likely too fast because the driving speed ($12.5$ km\,s$^{-1}$) employed in our simulations is too high. However, Configuration 1F demonstrated that the cycle period is mainly set by the displacement of the minority polarity. We speculate that, at more typical photospheric speeds \citep[$\approx 1.5$ km\,s$^{-1}$, e.g.,][]{Brandt1988}, the reconnection cycle period would increase by a factor of $12.5/1.5 \times 8$\,min $\approx 67$\,min, corresponding to the longest observed oscillations in brightness. Without a full treatment of the thermodynamics, however, it is not clear whether the repetitive, low-intensity reconnection jets in this case would be observable. In Configurations 2 and 3 we showed that filament channels periodically formed and erupted as jets when the field near the PIL is strongly sheared. The jets liberated $\approx 3 \times E_{s} = 2.9 \times 10^{26}$ erg of free magnetic energy, had speeds of $\approx 0.15\times Vs \approx 190$ km\,s$^{-1}$ and durations of $\approx 90\times t_{s} = 2.5$ min. These energies, velocities, and lifetimes are at the lower end of the ranges observed for coronal-hole jets \citep{Shibata1992,Savcheva2007}. Note, however, that our model would predict larger, more energetic jets with different choices for $B_{s}$ and $L_{s}$. Although only two main jets were produced in each simulation, we expect that further shearing and deposition of energy would continue the cycle. The time between the two jets was comparable to (Configuration 2 $\approx 200\times t_{s}$) or faster than (Configuration 3 $\approx 100\times t_{s}$) the time between the reconnection bursts when only the separatrix was strongly sheared. {However, this was using the faster ($25$\,km\,s$^{-1}$) surface driving speed.} Similarly, we then expect that the time between jets would be roughly a factor of {$25/1.5$ greater, $70$-$140$ min}, for typical solar surface flow speeds. Periodic jets associated with bright point flashes with similar periods were described in \citet{Zhang2012}. {The periodic bursty dynamics in our simulations follow from the repeated release of energy stored in the closed-field region. Before each burst or jet, the free magnetic energy is built up through an interplay between ideal surface motions shearing the closed field (storing energy) and reconnection opening sheared and closing unsheared field lines (releasing energy). By analysing simulations at different driving speeds we found that the timescale for this storage and release is set primarily by the distance the structures are driven, rather than the driving speed itself. This is true provided that the driving motions are slow compared to the coronal Alfv\'{e}n speed, as occurs on the Sun. Generally speaking, each burst occurs once a threshold of energy storage is reached. The threshold itself is particular to the setup being considered. Once beyond the threshold, some of the energy stored in the closed field is released impulsively over a short time compared with the time for the energy to be stored. The rapid release of energy points to a strong coupling between ideal and non-ideal effects, producing the sharp increase in reconnection rates measured during the bursts and jets. Therefore, ideal and non-ideal effects are present in {\it{both}} the energy buildup phase and the energy release phase. However, it is their coupling in the release phase that leads to the rapid energy releases and bursty dynamics we observe. Such coupling is a general feature of explosive energy release in the corona. It is manifest in these simulations by the upward expansion and ultimate explosive reconnection of the filament channel in the case of jets (configurations 2 and 3), and the similar expansion of the folded field lines and burst of reconnection as they are reconnected in configuration 1. Once a burst or jet occurs each system returns to slowly rebuilding the stored energy via the interplay of storage via ideal shearing and release via relatively slow reconnection around the null.} In our simulations, the loops of recently reconnected field lines beneath the separatrix are expected to form relatively long-lived bright-point structures. Because our simulations used a simple treatment for the plasma thermodynamics, we cannot directly synthesise observables. However, we obtained a rough estimate of the expected bright-point emission structure in each configuration by using the proxy introduced by \citet{Cheung2012}, whereby the square of the current is averaged along field lines before being integrated along the line of sight to create the image. This procedure picks out current-carrying coronal loops and gives a reasonable comparison to observations in EUV, for example. In Configuration 1, the relatively unstructured bright point was formed by the recently reconnected loops along one side of the minority polarity (Fig. \ref{fig:los}(a)). In Configuration 2, the main filament channel was localised to the right PIL, producing a bright point with more complex internal structure than Configuration 1 (Fig. \ref{fig:los}(b)). An additional filament channel appeared to the left of the trailing minority-polarity tail at this time, just before the onset of the second eruption. In Configuration 3, a clear sigmoid structure formed between the first and second jet when the filament channel was squeezed between the two passing magnetic elements (Fig. \ref{fig:los}(c)). The uneven magnetic pressure from the element nearest each end of the filament channel distorted the currents into a sigmoid \citep[e.g.,][]{DeVore2000}. Therefore, we have shown that different coronal bright-point morphologies can be realised by altering the way in which the separatrix is sheared and the strength of the flux that passes the minority polarity. The localisation of the bright points to one region beneath the separatrix in some events \citep{Galsgaard2017} may be explained by the results of Configuration 1. On the other hand, bright points with more complex structure and sigmoids \citep[e.g.,][]{Brown2001,Zhang2012} are more consistent with Configurations 2 and 3. Our modelling also reveals a natural link between bright points and energetic jets. Surprisingly, even when the shear profile was relatively broad, interchange reconnection at the null stripped the shear/helicity from the outer closed field lines to form a localised filament channel adjacent to the PIL. This mechanism is {similar to} the helicity condensation mechanism \citep{Antiochos2013}, whereby volume-filling reconnections drive magnetic shear/twist towards the boundaries where it collects (PILs) or is removed (separatrices). In our case, the boundary (the separatrix) moves in and out to remove the shear adjacent to it. Consequently, the reach of the mechanism is much more limited, ultimately removing most of the helicity through filament-channel eruption and jet formation. During each eruption, the quasi-steady slow reconnection at the null explosively accelerates for a short time, then resumes a slow rate. Interestingly, the jets have little noticeable rotation, which we attribute to the relatively small flux/energy of the filaments compared with the overall flux/energy of the closed-field region. Together with our previous results \citep{Wyper2017,Wyper2018}, this demonstrates that, depending upon the size and energy of the filament channel, both straight and helical jets can be created by the breakout-jet mechanism and thus can be driven by mini-filament eruptions. Finally, our results are applicable to other jet- and bright-point-like phenomena involving null points above moving minority-polarity intrusions. At smaller scales, EUV bursts in the chromosphere and transition region exhibit similar features. Recently, \citet{Chitta2017} identified a moving minority-polarity feature in the moat flow from a sunspot that was sheared by surface flows, and attributed the associated EUV brightening to reconnection driven by the shearing. Our results support their conclusions. At yet smaller scales, continually moving and cancelling minority magnetic elements are associated with tiny jetlets and plume transient bright points observed at the base of plumes \citep{Raouafi2014}. \citet{Raouafi2014} suggested that the collective action of this energy release helps to power and sustain the plumes. Our results might explain the origin of these plume transient bright points and jetlets. Additionally, the compressive and Alfv\'{e}n waves launched by the periodic outflows and homologous jets in our simulations may account for the quasi-periodic waves observed within plumes \citep[e.g.,][]{DeForest1998,Ofman1999,Thurgood2014}. In this work, we studied minority-polarity moving magnetic elements in an open background field as a model for coronal bright points and jets. Our main results are as follows: \begin{itemize} \item All our simulations exhibited the evolution generic to models with the embedded-bipole topology: free energy build up due to ideal stressing by photospheric motions followed by energy release by reconnection at the null and separatrices. The ideal stressing is always very slow, but the reconnection dynamics vary greatly depending on where the free energy builds up, in particular, how close to the separatrix. For example, if the stressing occurs such that only flux very near the separatrix becomes stressed, then the reconnection becomes essentially steady \citep[e.g.][]{Edmondson2010}. On the other hand, if the stress is concentrated far from the separatrix near the PIL, then the evolution must become explosive in order to release this free energy \citep[e.g.,][]{Wyper2017}. \item Different bright-point morphologies, from simple loops to sigmoids, can be realised by a combination of the surface shear pattern and the strength and distribution of the flux passing the minority polarity. \item Steady interchange reconnection driven by the surface motions is modulated by quasi-periodic, low-intensity reconnection bursts that we speculate would correspond to a quasi-periodic brightening of the newly reconnected bright-point loops. Each burst occurs after the minority polarity has been advected roughly its length across the surface. \item If the surface motions strongly shear the field near the PIL, a filament channel forms. The bright point produces a jet when the filament channel erupts via the breakout mechanism before returning to long-duration, lower intensity bright point energy release. \item Additional bursts of reconnection are driven when strong concentrations of the majority polarity pass by the minority polarity, connecting to and then disconnecting from it. \end{itemize} Our results explain several key aspects of observed coronal bright points and jets, and how the two are related. The results aid in further disentangling the complex behaviour of such events, which also might contribute to the formation and maintenance of coronal plumes. Many potential extensions of this work should be considered, for instance, the role of the background field inclination angle and the implications of including a more realistic treatment of the atmosphere and coronal energy transport processes. Such extensions are left to future work. | 18 | 8 | 1808.03688 |
1808 | 1808.04257_arXiv.txt | The ESPRESSO instrument, to be commissioned in the next months at the ESO VLT, is bound to became a landmark in the field of high-resolution optical spectroscopy, both for its ground-breaking science objectives (search for Earth-like exoplanets; measure of a possible variation of fundamental constants) and for its novel approach to data treatment. For the first time for an ESO instrument, scientific information will be extracted in real time by a dedicated Data Analysis Software (DAS), which includes several interactive workflows to handle the typical analysis cases in stellar and QSO spectroscopy. Data analysis tools in the oncoming ELT era will face very demanding requirements from compelling science case, such as the Sandage Test: the need of handling larger data sizes with a higher degree of accuracy, and the possibility to compare observations and simulated data on the fly. To this purpose, we are currently porting the solutions developed for ESPRESSO to a wider framework, integrating the algorithms within a full-fledged set of Python modules. The project, named ``Astrocook'', is aimed to provide a set of high-level, instrument-agnostic procedures to automatically extract physical information from the data. | Astronomical spectroscopy is rapidly evolving into a precision science. The possibility to acquire visible spectra of distant objects -- such as medium-to-high-redshift QSOs % at high resolution and with a wavelength accuracy below 1$\,\mathrm{m\,s^{-1}}$ is opening exciting opportunities in % the field fundamental physics, e.g.~the possibility to determine a variation of the fundamental constants \citep{2017RPPh...80l6902M}, or to measure the accelerated expansion of the universe from a redshift drift of distant sources \citep{1962ApJ...136..319S,2008MNRAS.386.1192L}. Several instruments are being conceived and realized to meet unprecedented requirements in terms of stability and repeatability of the observations; one is ESPRESSO \citep{2013Msngr.153....6P}, a ultra-stable spectrograph for the ESO Very Large Telescope (VLT), which was intended since its inception as a precursor of the future high-resolution spectrograph \citep{2014SPIE.9147E..23Z} for the ESO Extremely Large Telescope (ELT). ESPRESSO is the first ESO instrument to be equipped with a dedicated Data Analysis Software or DAS \citep{2012SPIE.8448E..1OD,2015ASPC..495..289C,2016SPIE.9913E..3RD}, which is included in the instrument package together with the Data Reduction Software or DRS. This article describes the lessons learned in developing the ESPRESSO DAS, and presents first implementation of the new ``Astrocook'' Python package, which is meant to pave the way towards the next generation of data processing systems \citep{2016SPIE.9910E..2FC}. \articlefigure{O4-5_f1}{cont}{A portion of the Lyman-$\alpha$ forest of QSO J0515-4410 (black line: flux density; red line: error on flux density) as fitted by the Astrocook package. Information obtained from automated Voigt-profile fitting (green line) of the detected lines (red crosses) is used to locally adjust the guess continuum (dotted blue line); the final continuum is determined by smoothing the result after iteration (blue line).} | 18 | 8 | 1808.04257 |
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1808 | 1808.04899_arXiv.txt | {We present a study of the \oiii/\oii\ ratios of star-forming galaxies drawn from Multi-Unit Spectroscopic Explorer (MUSE) data spanning a redshift range $0.28 < z < 0.85$. Recently discovered Lyman continuum (LyC) emitters have extremely high oxygen line ratios: \oiiil/\oiill $> 4$. Here we aim to understand the properties and the occurrences of galaxies with such high line ratios. Combining data from several MUSE Guaranteed Time Observing (GTO) programmes, we select a population of star-forming galaxies with bright emission lines, from which we draw 406 galaxies for our analysis based on their position in the $z-$ dependent star formation rate (\SFR ) - stellar mass (\Mstar ) plane. Out of this sample 15 are identified as extreme oxygen emitters based on their \oiii/\oii\ ratios (3.7$\%$) and 104 galaxies have \oiii/\oii\ > 1 (26$\%$). Our analysis shows no significant correlation between \Mstar , \SFR,\ and the distance from the \SFR\ - \Mstar\ relation with \oiii/\oii . We find a decrease in the fraction of galaxies with \oiii/\oii\ > 1 with increasing \Mstar , however, this is most likely a result of the relationship between \oiii/\oii\ and metallicity, rather than between \oiii/\oii\ and \Mstar . We draw a comparison sample of local analogues with $<z> \approx 0.03$ from the Sloan Digital Sky Survey, and find similar incidence rates for this sample. In order to investigate the evolution in the fraction of high \oiii/\oii\ emitters with redshift, we bin the sample into three redshift subsamples of equal number, but find no evidence for a dependence on redshift. Furthermore, we compare the observed line ratios with those predicted by nebular models with no LyC escape and find that most of the extreme oxygen emitters can be reproduced by low metallicity models. The remaining galaxies are likely LyC emitter candidates. Finally, based on a comparison between electron temperature estimates from the \oiiia/\oiiil\ ratio of the extreme oxygen emitters and nebular models, we argue that the galaxies with the most extreme \oiii/\oii\ ratios have young light-weighted ages. } | \label{s_intro} Extreme oxygen line ratios (\ott\ $\equiv$ \oiiil/\oiil $>4$) were proposed recently as a potential tracer of the escape of ionising radiation from galaxies through density-bounded \hii\ regions \citep{Jaskot13, Nakajima14}. The idea is the following: if a galaxy is leaking ionising photons through a density-bounded region, the ratio of \ott\ can be high if the \hii\ region that we observe is truncated, for example if (part of) the \oii\ region is missing. We see deeper into the ionised region and the external layer of \oii\ is either nonexistent or thinner than in the classical ionisation-bounded scenario. Given their high \ott\ ratios, \citet{Jaskot13} discuss the possibility of LyC escape from "Green Pea" (GP) galaxies, a population of extremely compact, strongly star-forming galaxies in the local Universe \citep{Cardamone09, Izotov11, 2016ApJ...820..130Y}. \citet{Nakajima14} and \citet{Nakajima16} compare \ott\ ratios of different types of high-redshift galaxies, Lyman Break Galaxies (LBGs), and Lyman Alpha Emitters (LAEs) with GPs and Sloan Digital Sky Survey (SDSS) galaxies: high-redshift galaxies have on average higher \ott\ ratios than SDSS galaxies, but comparable to GPs. Furthermore, the observed \ott\ ratios of LAEs are larger than those of LBGs. Along the same line, GPs are also strong LAEs \citep{Henry15, 2016ApJ...820..130Y, 2017A&A...597A..13V, 2017ApJ...838....4Y}, which is very unusual for galaxies in the local Universe \citep{Hayes11, Wold14}. While the \ott\ ratio of galaxies that are leaking ionising photons may be enhanced compared to those with a LyC escape fraction, \fesclyc , equal to zero, there are other situations that can lead to high \ott\ ratios. For example, the \ott\ ratio depends on metallicity: low stellar and nebular metallicities lead to higher \ott\ ratios \citep{Jaskot13}. A harder ionising spectrum will also induce higher \ott\ ratios, as investigated in for example \citet{Pellegrini12}, as well as a higher ionisation parameter (e.g. \citealt{Stasinska15}). Furthermore, shocks could also explain these ratios, as studied in detail in \citet{Stasinska15}. Despite intensive searches for LyC emission from galaxies, only a few LyC leakers have been identified over the last decades in the local Universe \citep{Bergvall06, Leitet13, Borthakur14, Leitherer16}, but most searches resulted in non-detections or upper limits \citep{Siana15, Mostardi15, Grazian16, Rutkowski16, Rutkowski17}. The discovery of the link between LyC emission and \ott,\ however, turned the tide, as demonstrated by for example \citet{Izotov16a,Izotov16b, 2018MNRAS.474.4514I, 2018MNRAS.tmp.1318I}. For their studies, LyC emission was detected for all eleven galaxies at $z \approx 0.3$ that were selected by their extreme \ott\ ratios (\ott\ > 4), among other criteria such as brightness, compactness, and strong \hb\ equivalent widths. Furthermore, a correlation between \ott\ and the escape of ionising photons was found, although the scatter of \fesclyc\ is large \citep{2018MNRAS.tmp.1318I}. At high redshift ($z \approx 3$), four galaxies with high escape fractions ($> 50$\%) have been reported \citep{Vanzella15, 2016A&A...585A..51D, Shapley16, Bian17, 2018MNRAS.476L..15V}, which were selected by similar criteria. Additionally, the recent results from the Lyman Continuum Escape Survey \citep{2018arXiv180601741F} reveal an average escape fraction of $\sim20\%$ for galaxies at $z\approx3$ with strong \oiii\ emission, and a weak correlation between \fesclyc and the \oiii\ equivalent width for $\sim20$ galaxies with directly detected LyC emission. Although the combination of these selection criteria has resulted in relatively few galaxies with confirmed LyC emission yet, the detection of extreme \ott\ emission from a local low-mass GP analogue \citep{2017ApJ...845..165M} might, however, suggest that low-mass extreme \ott\ emitters, and thus possible low-mass LyC emitters, are more common than the bright GP samples suggest. A statistical study of the \ott\ ratios of emission-line selected galaxies over a broad range of stellar masses has, however, not been performed so far. The unique capabilities of the Multi-Unit Spectroscopic Explorer (MUSE) \citep{2010SPIE.7735E..08B} allow us to study the properties of galaxies with extreme \ott\ ratios and how common they are in emission-line selected samples. For this study we combine four MUSE Guaranteed Time Observing (GTO) surveys and collect a sample of mainly emission-line detected galaxies with a high specific star formation rate and stellar masses between $\sim10^6$ and $\sim10^{10}$, from which we compute the distribution of \ott\ ratios in a blind survey of star-forming galaxies. We will here present the properties and occurrences of extreme oxygen emitters spanning the redshift range 0.28 < z < 0.85, where both lines are in the MUSE spectral range, in the largest statistical sample of emission-line detected galaxies in three-dimensional spectral data. This article is organised as follows: in Sect.~\ref{s_data} we describe the data from different programmes that we used for this study; in Sect.~\ref{s_sample} we describe the sample selection; in Sect.~\ref{s_results} we investigate the occurrence of high \ott\ ratios and study potential correlations with stellar mass ( \Mstar ), star formation rate (\SFR ), and the metallicity indicator \rtt\ line ratio; in Sect.~\ref{s_discussion} we study the incidence rate of galaxies with high \ott\ ratios as a function of \Mstar\ and $z$, and we also discuss how our results compare to nebular models with no escape of ionising photons. We end with a discussion on the most extreme oxygen emitters. Throughout this paper we adopt a cosmology with $H_0$ = 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_m$ = 0.3 and $\Omega_\Lambda$ = 0.7. | We constructed a sample of emission-line galaxies in the redshift range $0.28 < z < 0.85$ that are detected in data from four MUSE GTO surveys. The galaxies are selected based on their position in the \SFR\ - \Mstar\ plane in a way that we only included galaxies that are above the redshift-dependent SFMS from \citet{Boogaardetal}. In this regime we expect the sample to be independent of selection effects. Our final sample consists of 406 galaxies, of which 104 (26$\%$) have a high \ott\ ratio (\ott\ > 1) and 15 galaxies are extreme emitters with \ott > 4 (3.7$\%$). We studied the \ott\ ratio as a function of the position in the (redshift-corrected) \SFR\ versus \Mstar\ diagram, as a function of stellar mass \Mstar , \SFR , and metallicity indicator \rtt . We then studied the incidence rate of galaxies with high oxygen ratios, which is defined by either a fixed threshold, \ott\ > 1, or by a metallicity-dependent threshold as a function of \Mstar\ and redshift. The main conclusions of this study are: \begin{itemize} \item Galaxies with a high oxygen ratio are more common at lower masses (\Mstar\ < 9) and above the SFMS. There is no clear correlation between distance from the SFMS and the \ott\ ratio for galaxies in our final sample that are above the SFMS (Fig. \ref{fig:main_sequence}). \\ \item We find no correlation between \ott\ ratio and \Mstar , although the median values in \ott\ bins seems to be anti-correlated (Fig. \ref{fig:m_o32}).\\ \item We observe the same trend between the median values of \ott\ and \SFR , but again no significant correlation for individual galaxies. The \SFR\ of most of our extreme emitters is two to three orders of magnitude smaller than those of confirmed leakers (Fig. \ref{fig:sfr_o32}).\\ \item The fraction of galaxies with high \ott\ ratios is independent of stellar mass when we use a metallicity-dependent \ott\ threshold (Fig. \ref{fig:f_logM_Zcorr}).\\ \item We find no significant correlation between the fraction of high \ott\ emitters and redshift, suggesting that there is no redshift evolution of the number of high \ott\ in the redshift range $0.28 < z < 0.85$ (Figs. \ref{fig:f_logM_Zcorr_zdep} and \ref{fig:fraction_time}). \\ \item Comparing \ott\ and \rtt\ of our galaxies with those of nebular models with no escape of ionising photons, we find that some of the high oxygen emitters can be reproduced by models with a high ionisation parameter ($\log U \approx -2$), a very low stellar and nebular metallicity (smaller than $\sim 1/3$ \Zsun), or a combination of both. However, our extreme emitters are in the same regime as the confirmed leakers from \citet{Izotov16a, Izotov16b, 2018MNRAS.474.4514I} and we therefore cannot exclude the escape of ionising photons from these galaxies. The \ott\ ratio of our most extreme oxygen emitter can only be explained by models with very high ionisation parameter ($\log U > -2$), from which we conclude that this galaxy may be a LyC leaker candidate (Fig. \ref{fig:r23_discussion}). \\ \item For galaxies with a significant \oiiia\ detection, we derived the \oiiia/\oiiil\ ratio and the electron temperature and find that these values are similar to or larger than those predicted by nebular models with extremely low metallicity, high ionisation parameters, and constant \SFR\ at $t = 3 \times 10^8$ years. From this we conclude that a part of the extreme \ott\ emitters may have light-weighted ages of $t < 3 \times 10^8$ years (Fig. \ref{fig:te}). \\ \end{itemize} \label{s_conclusions} | 18 | 8 | 1808.04899 |
1808 | 1808.07853_arXiv.txt | The InfraRed Imaging Spectrograph (IRIS) is a first-light instrument for the Thirty Meter Telescope (TMT). It combines a diffraction limited imager and an integral field spectrograph. This paper focuses on the electrical system of IRIS. With an instrument of the size and complexity of IRIS we face several electrical challenges. Many of the major controllers must be located directly on the cryostat to reduce cable lengths, and others require multiple bulkheads and must pass through a large cable wrap. Cooling and vibration due to the rotation of the instrument are also major challenges. We will present our selection of cables and connectors for both room temperature and cryogenic environments, packaging in the various cabinets and enclosures, and techniques for complex bulkheads including for large detectors at the cryostat wall. | \label{sec:intro} % The InfraRed Imaging Spectrograph (IRIS\cite{Larkin18}) is a first-generation instrument for the Thirty Meter Telescope (TMT\cite{Sanders13}). A combination of the On-Instrument Wave Front Sensor (OIWFS\cite{Dunn14}) and the TMT adaptive optics system NFIRAOS\cite{Herriot14} will allow IRIS to reach the diffraction limit of TMT at wavelengths longer than 1 micron. IRIS combines an imager and an integral field spectrograph operating between 0.8 to 2.5 microns. The imager is composed of four 4K by 4K Teledyne detectors (Hawaii 4RG) with 4 mas pixels and a combined 34 x 34 $\text{arcsec}^2$ field of view. The integral field spectrograph takes $\sim10,000$ spectra simultaneously with spectral resolution $R\sim4000\ \text{to}\ R\sim8000$ on four spatial scales from 4 mas to 50 mas with fields of view of 0.46 x 0.51 $\text{arcsec}^{2}$ to 2.2 x 4.6 $\text{arcsec}^{2}$ respectively. The science applications of IRIS span from our own Solar System to the most distant galaxies in the Universe. \begin{figure} [ht] \begin{center} \begin{tabular}{c} % \includegraphics[width=15cm]{IRISOverview} \end{tabular} \end{center} \caption[cryostat] { \label{fig:cryostat} IRIS is mounted to the underbelly of TMT’s AO system NFIRAOS by the IRIS support structure. After exiting NFIRAOS, light passes through the On Instrument Wave Front Sensor (OIWFS), which allows for tip-tilt, focus, and plate scale corrections, and finally through a window into the science cryostat, which has both an imaging and integral field spectrometer mode. The cable wrap sits below the cryostat on the nasmyth platform, and connects to the nasmyth cabinets (not shown here). The current design also includes a bulkhead around the bottom rim of the cryostat (not shown here) which acts as a cable break for easier installation of the instrument. Also not shown here are the detector control boxes (see Fig.~\ref{fig:leach}) which will be mounted on the sides of the cryostat.} \end{figure} \begin{figure} [hb] \begin{center} \begin{tabular}{c} % \includegraphics[width=6cm]{LeachBox} \end{tabular} \end{center} \caption[leach] { \label{fig:leach} An example of an ARC box; similar enclosures will be attached to the side of the science cryostat and will house detector control electronics.} \end{figure} \begin{figure} [hb] \begin{center} \begin{tabular}{c} % \includegraphics[width=15cm]{IRIS_macro_2_forSPIE} \end{tabular} \end{center} \caption[over] { \label{fig:over} A high-level schematic diagram of Fig.~\ref{fig:cryostat} showing the large number of cable connections required to control IRIS, as well as their paths from the nasmyth cabinets to the cryostat, rotator, or OIWFS.} \end{figure} \begin{figure} [ht] \begin{center} \begin{tabular}{c} % \includegraphics[width=15cm]{Cable_Break} \end{tabular} \end{center} \caption[cable] { \label{fig:cable} The average cable goes through 5-6 cable breaks on its way from the electronics cabinet, through the cable wrap, and into the science cryostat. Cables will be labeled for ease of organization and installation. For example, all cables between the cryostat wall and cold shield will have ``d" in their designation, cables going through the cable wrap will have ``b" in their designation, etc.} \end{figure} IRIS is a large cryogenic cylinder 2 meters in diameter, 3.1 meters in height, with a total mounted mass of $\sim5400$ kg. It is suspended from underside of TMT's adaptive optics system NFIRAOS. IRIS will spin about its vertical axis to correct for field rotation. Most IRIS control electronics will be housed in a climate-controlled cabinet (called the nasmyth cabinet) on a platform below IRIS. Cables exit the nasmyth cabinet and go through a cable wrap, then up to a bulkhead attached to the underside of the cryostat. From there, the cables penetrate IRIS via multiple bulkheads on the sides of the cryostat (see Fig.~\ref{fig:cryostat}). Detector controllers are mounted on the sides of the cryostat in $\text{CO}_2$ gas cooled enclosures. In section \ref{sec:Arch}, we discuss some of the architectural challenges of IRIS with regards to the electronics system, section \ref{sec:hard} briefly discusses the nasmyth cabinets as well as connectors and cables we plan to use, and section \ref{sec:future} discusses some of the actions we plan to take in the near future. | 18 | 8 | 1808.07853 |
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1808 | 1808.02192_arXiv.txt | Temporal photometric variations at near infrared to submillimeter wavelengths have been found in low-mass young stellar objects. These phenomena are generally interpreted as accretion events of star-disk systems with varying accretion rates. There is growing evidence suggesting that similar luminosity flaring also occurs in high-mass star/cluster-forming regions. We report in this Letter the rise and fall of the 900 ${\mu}$m continuum emission and the newly found 349.1 GHz methanol maser emission in the massive star forming region S255IR~SMA1 observed with the Submillimeter Array and the Atacama Large Millimeter/submillimeter Array. The level of flux variation at a factor of $\sim$ 2 at the submillimeter band and the relatively short 2-year duration of this burst suggest that the event is probably similar to those milder and more frequent minor bursts seen in 3D numerical simulations. | \label{sec:intro} Temporal photometric variations associated with young low-mass stars of Class I or II, such as those FU Orion-type (FUor) and EX Lup-type (EXor) events, have been observed in the optical to mid-infrared (MIR) wavelengths \citep{Audard14}. Accompanied by spectroscopic signatures of hot disks and winds, these phenomena are generally interpreted as accretion events of star-disk systems with elevated rates --- instead of falling through steady flows to the central stars, circumstellar material fragments and accretes sporadically due to instabilities developed in the disks. Supplementary evidence includes the semi-periodic ejection events seen in the Herbig-Haro (HH) objects associated with low-mass young stellar objects (YSOs). It is conceivable that at an earlier, more embedded (Class 0/I) evolutionary stage, YSOs may subjected to similar episodic accretion events. Due to envelope obscuration, however, such phenomenon may not be visible in the optical or infrared (IR) but possibly detectable at longer (far-infrared (FIR) to millimeter) wavelengths \citep{Johnstone13}. Indeed, HOPS~383, a Class 0 protostar, was the very first example reported with a brightening event not only in the MIR but also in the submillimeter bands \citep{Safron15}. Furthermore, recent submillimeter observations of YSOs in nearby molecular clouds successfully revealed for the first time through a monitoring program a luminosity flaring event toward a Class I YSO in the Serpens cloud \citep{Yoo17}. Molecular line imaging experiments, probing the thermal history of envelopes around embedded YSOs, also provided indirect indications of luminosity flarings \citep{Jorgensen13}. Does a similar luminosity variation phenomenon occur in the massive star formation process? There now appears to be growing evidence pointing to a positive answer. For example, the massive star-cluster-forming region S255 was first detected with methanol maser flares \citep{Fujisawa15}. Subsequent observations in the near infrared (NIR) witnessed brightening of not only the NIR continuum but also atomic and molecular lines \citep{Caratti17}. NGC 6334(I), another massive star-cluster-forming site, also got spotted with an increase of its submillimeter continuum \citep{Hunter17}. Follow-up observations confirm the emergence of new methanol masers as a result of the luminosity burst \citep{Hunter18}. S255IR is a massive cluster formation region with a bolometric luminosity of several 10$^{4}$ L$_\odot$ at a distance of 1.78$^{+0.12}_{-0.11}$ kpc \citep{Burns16}. NIR imaging revealed a cluster of YSOs associated with the molecular gas ridge sandwiched by two nearby H{\small II} regions \citep{Ojha11}. Submillimeter continuum observations indicated an overall molecular gas of around 300---400 M$_\odot$ in this region, and disclosed at higher angular resolution several dense clumps residing in the complex \citep{Wang11, Zinchenko12, Zinchenko15}. In particular, the dominant source, S255IR~SMA1, coinciding with the NIR source S255IR~NIRS3, is associated with a prominent molecular bipolar outflow and a rotating disk-like structure \citep{Zinchenko12, Zinchenko15}. The putative disk, perpendicular to the outflow in its orientation, probably is viewed closely edge-on \citep{Boley13}. Based on its luminosity and the maser kinematics, the mass of the central YSO is estimated to be $\sim$ 20~M$_\odot$ \citep{Zinchenko15}. This region gained appreciable attention for its flaring signatures in 6.7 GHz methanol maser, NIR, and radio continuum \citep{Fujisawa15, Stecklum16, Caratti17, Cesaroni18} Meanwhile, \cite{Zinchenko17} reported a newly identified submillimeter methanol maser, likely associated with this flare event, too. | \label{sec:discussion} \subsection{A submillimeter flare, a manifestation of a luminosity burst} As illustrated in the Section~\ref{sec:results}, the comparison between our SMA and ALMA observations indicated a factor of 2 increase in both the intensity and flux density of 900 ${\mu}$m continuum toward SMA1 in early 2016. ALMA observations further witnessed, for the first time, the waning of this continuum emission as well as CH$_3$OH maser in mid 2017. No matter whether the dust continuum emission is optically thick or thin, its brightness and flux density variation is reflecting a dust temperature change, unless there is a dramatic modification in dust column density and/or opacity throughout the region. While an increase in luminosity may lead to enhanced sublimation of dust grains in the close vicinity ($\gtrsim$ 10 au) of the central star and alter the heating timescale, the bulk dust properties likely remain similar \citep{Hunter17}. The dust temperature elevated by a factor of $\sim$ 2 in early 2016, thus suggests an overall bolometric luminosity increase by a factor of about 16 in S255IR~SMA1 as total emission of the dust envelope scales with temperature to the 4th power \citep{Hunter17}. For the short cooling timescale (of a few hundred seconds) of dust estimated from its heat capacity \citep{Johnstone13} and cooling rate \citep{Glover12}, the 88\% dimming submillimeter continuum in 2016---2017, correspondingly a decreasing of dust temperature by 40\%, also plausibly reflects and a reduced radiation field, as well as a factor of $\sim$ 8 decrease in its luminosity. Indeed, we witnessed fading (methanol) maser intensity along the same line of sight, most likely due to this reduction in seed radiation. By investigating the NIR to submillimeter spectral energy distribution (SED) taken at the pre-burst phase and at 2016 February, \cite{Caratti17} unveiled a boost dominantly in the FIR at around 30---100 ${\mu}$m. The bolometric luminosity of S255IR~SMA1/NIRS3 grew from $3\times 10^4$~L$_\odot$ to $1.6 \times 10^5$~L$_\odot$, a factor of $\sim$ 5.5 increase. This boost factor appears to be smaller than what we derived. Given that their FIR data are taken at angular resolutions coarser than 6\farcs0, the inclusion of SMA2 and the surrounding material within those SED measurements probably resulted in lowering the boost factor. Furthermore, our luminosity estimation has a strong (fourth power) dependence on the dust temperature; a 10\% uncertainty in the flux density, hence temperature measurement could lead to 40\% uncertainty in the derived luminosity, which may partly mitigate the differences in the boost factors. \subsection{The sequence of events} Based on the propagation of the light echo, \citet{Caratti17} hypothesized that the S255IR~SMA1 burst event occurred in mid-June of 2015. This appears consistent with the first report of 6.7 GHz methanol maser flaring seen from early July of 2015 as reported by \citet{Fujisawa15}. Direct NIR imaging in 2016 April disclosed brightening of the region as compared to the pre-burst image taken in 2009 \citep{Caratti17}. The extended $K_s$-band emission is the reprocessed light from hot dust presumably heated by the central star and escaped from the outflow cavity. Our ALMA image taken in 2016 April, meanwhile, also exhibits boosted submillimeter intensity toward SMA1 as compared to that of 2010. This emission presumably originates from the dusty disk and/or envelope, which remains optically thick to NIR and processes the radiation to longer wavelengths. Based on their Karl G. Jansky Very Large Array (VLA) monitoring observations, \citet{Cesaroni18} further reported exponential flux flaring in the radio continuum between 6 and 45 GHz associated with SMA1 from 2016 July to 2017 February. This rising radio emission was interpreted as the radio jet breakout. Our 2017 July observation of both dust continuum and methanol maser subsequently indicates the dimming of this burst and marks the burst duration at around two years. \subsection{Origin of the luminosity burst} The fact that the submillimeter continuum emission brightened up and dimmed down in conjunction with Class II methanol maser activities in S255IR~SMA1 is suggestive of variation in the IR radiation field and supports the notion of a disk-mediated accretion-related event as suggested by \citet{Caratti17}. Indeed, on the large (10,000 au) scale, several lines of evidence point to the existence of a rotating structure associated with S255IR~SMA1. \citet{Wang11} and \citet{Zinchenko12} demonstrated a velocity gradient perpendicular to the bipolar outflow in several molecular tracers, including CH$_3$CN, HCOOCH$_3$, C$^{18}$O, and CH$_3$OH. While the angular resolution was not sufficient for a firm conclusion, the kinematic signatures of CH$_3$OH emission, including position-velocity diagram and velocity dispersion map, were both indicative of spin-up toward the inner region, reminiscent of Keplerian rotation \citep{Zinchenko15}. MIR imaging by \cite{Boley13} resolved an elongated dusty structure on a 1000 au scale perpendicular also to the bipolar outflow, possibly representing the putative circumstellar disk around S255IR~SMA1. \cite{Caratti17} further reasoned that the accretion burst is disk-mediated based on the observed emission lines, such as H$_2$, Br$\gamma$, as well as CO band-heads, He \small{I}, and Na \small{I}, typically seen as signatures of enhanced accretion, wind, and hot disks in low-mass YSOs. The compact 900 ${\mu}$m continuum excess region seen in Figure~\ref{fig:f3}(c) is likely associated with this structure. Variable accretion is not uncommon in 3D numerical radiation hydrodynamic simulations of (low-mass and primordial) star formation \citep[e.g.][]{Vorobyov15,Hosokawa16}. Asymmetric features like spirals form in the circumstellar disk, which leads to fluctuating accretion rates. Moreover, \citet{Meyer17} suggested the universal sporadic and variable nature of gaseous material accreting from the circumstellar disks to massive YSOs as in their low-mass counterparts. In their investigations of the collapse of 100 M$_{\odot}$ pre-stellar cores, clumps of molecular gas spiraling from a few hundred au in the disk down to a few tens au from the central massive YSO and episodically accretes onto the star. In one particular case, the accretion rates and accompanying luminosity have major jumps up by nearly two orders of magnitudes for 10 years scale, while small variations in accretion rate and luminosity take place frequently. Such a disk fragmentation scenario was invoked as a possible cause leading to the quadruple luminosity burst seen toward NGC 6334(I) \citep{Hunter17}. For the low-mass star case, bursts of FUors and EXors are categorized with different characteristics. While FUor bursts typically arise with increases in mass accretion by several thousand folds and persist for years to decades, EXor bursts have enhanced mass accretion by factors of tens to hundreds and last for just months to years \citep{Hartmann16}. Considering the relative mild magnitude and the short duration of the flare of S255IR~SMA1, its temporal behavior resembles the milder and more frequent burst events, in analog to those seen in the EXors for low-mass YSOs. That being said, in an absolute sense, the scale of energy released by massive YSO events like this one in S255IR~SMA1 or the burst seen in NGC 6334(I) \citep{Hunter17} is dramatically different from the low-mass YSO cases. The luminosity of S255IR~SMA1 at its burst stage, reaching $10^5 L_{\odot}$, corresponds to a mass accretion rate of several times 10$^{-3}$ M$_\odot$ \citep{Caratti17}. This is far more significant when compared with even the FUor bursts. Based on the multiple scale outflows observed toward S255IR~SMA1, \cite{Burns16} conjectured an episodic accretion history over the last few thousand-year timescale. The most recent methanol maser and IR flare combined with our ALMA observations revealing the brightening and dimming signatures in submillimeter continuum further pointed out to an ongoing accretion burst. Monitoring observations of S255IR~SMA1 in its continuum emission shall further constrain the full duration and degree of this latest burst. Meanwhile, supplementary molecular line observation could gauge the gas temperature, which should be subsequently warmed and cooled along the event, although the expected larger thermal time constant may imply a longer time lag and/or perhaps a milder strength in the gas temperature variation \citep{Johnstone13}. Finally, high-angular-resolution imaging is essential for resolving the disk structure and revealing the burst nature of S255IR~SMA1. \begin{deluxetable*}{lcccc} \tablecaption{Observing Parameters and SMA1 Measurements\label{tab:obssetup}} \tablewidth{0pt} \tablehead{ \colhead{Array} & \colhead{SMA} & \multicolumn3c{ALMA} \\ \cline{3-5} } \startdata Observation date & 2010 Dec 15 & 2016 Apr 21 & 2016 Sep 09 & 2017 Jul 20 \\ Configuration & Compact & C36-2/3 & C36(5)/6 [=C40-6] & C40-5 \\ On-source time (minutes)& 135 & 43 & 86 & 43 \\ Antenna number & 8 & 42 & 39 & 43 \\ Minimum projected baseline (m) & 9.1 & 12.1 & 12.0 & 14.6 \\ Maximum projected baseline (m) & 77 & 562 & 2811 & 3041 \\ Continuum (imaging) freq. (GHz) & 343.0 & 335.4 & 335.4 & 335.4 \\ Continuum bandwidth (GHz) & 2 & 1.875 & 1.875 & 1.875 \\ \cline{1-5} SMA1 900 ${\mu}$m continuum & & & & \\ peak brightness (Jy beam$^{-1}$) & 0.50\tablenotemark{a} & 1.1\tablenotemark{a} & 0.24\tablenotemark{b} & 0.14\tablenotemark{b} \\ flux density (Jy) & 0.73\tablenotemark{c} & 1.4\tablenotemark{c} & 0.64\tablenotemark{d} & 0.41\tablenotemark{d} \\ \cline{1-5} SMA1 CH$_3$OH $14_1-14_0 A^{-+}$ maser & & & & \\ peak brightness (Jy/beam) & & 5.9\tablenotemark{e} & 5.9\tablenotemark{e} & 3.6\tablenotemark{e} \\ \enddata \tablenotetext{a}{For a 2\farcs3 $\times$ 1\farcs9 beam with a position angle -73$^{\circ}$} \tablenotetext{b}{For a 0\farcs14 $\times$ 0\farcs14 beam} \tablenotetext{c}{For a 4\farcs0 aperture} \tablenotetext{d}{For a 0\farcs5 aperture} \tablenotetext{e}{For a 0\farcs14 $\times$ 0\farcs14 beam} \end{deluxetable*} \begin{figure*} \includegraphics[width=18cm]{plotf1.pdf} \caption{ \label{fig:f1} 900 ${\mu}$m continuum image of S255IR (a) observed in 2010 December by SMA at an angular resolution of $\sim$ 2\farcs0. Contour levels are at 3, 5, 7, and 9 $\times$ 46~mJy/beam. (b) Observed in 2016 April by ALMA at an angular resolution of $\sim$ 0\farcs6. The positions of SMA1--3 are marked by white crosses. (c) Made through mock SMA observations using panel (b) as the sky model. (d) The difference map made by first scaling panel (a) by 1.2 and subtracting that from panel (c). Contour levels in (c) and (d) are the same as (a), so does the false color scheme. } \end{figure*} \begin{figure*} \includegraphics[width=18cm]{plotf2.pdf} \caption{ \label{fig:f2} Visibility amplitudes of the 335 GHz continuum plotted against the $uv$-distance in meters. Red, blue, and gray points represent data taken with ALMA in 2016 April, 2016 September, and 2017 July, respectively.} \end{figure*} \begin{figure*} \includegraphics[width=18cm]{plotf3.pdf} \caption{ \label{fig:f3} 900 ${\mu}$m continuum image of S255IR (a) observed in 2016 September by ALMA in false color at an angular resolution of 0\farcs14. (b) Observed in 2017 July by ALMA at an angular resolution of 0\farcs14. The contour and labels are the same as those in (a). (c) The difference map made by subtracting panel (b) from panel (a). The contour at 5-$\sigma$ level marks the boundary of regions with significant emission and SMA1--3 are labeled in panel (a)--(c). } \end{figure*} \begin{figure*} \includegraphics[width=18cm]{plotf4.pdf} \caption{ \label{fig:f4} (a) Integrated intensity map of the 349.1 GHz CH$_3$OH $14_1-14_0 A^{-+}$ maser emission observed by ALMA in 2016 September. An inset in the panel displays the CH$_3$OH spectra at its peak position. (b) The integrated intensity map of the same maser emission observed by ALMA in 2017 July. An inset, same as in panel (a), displays the peak position spectra. (c) The difference CH$_3$OH maser map made by subtracting panel (b) from (a). The contour delineates the region with excess 900 ${\mu}$m continuum emission shown in Figure~\ref{fig:f3}(c). } \end{figure*} S.Y.L. acknowledges the support by the Minister of Science and Technology of Taiwan (MOST 106-2119-M-001-013). I.Z.'s research was supported by the Russian Science Foundation (grant No. 17-12-01256). This Letter makes use of the following ALMA data: ADS/JAO.ALMA \#2015.1.00500.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MoST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. | 18 | 8 | 1808.02192 |
1808 | 1808.00474_arXiv.txt | The \emph{Gaia} mission will provide precise astrometry for an unprecedented number of white dwarfs (WDs), encoding information on stellar evolution, Type Ia supernovae progenitor scenarios, and the star formation and dynamical history of the Milky Way. With such a large data set, it is possible to infer properties of the WD population using only astrometric and photometric information. We demonstrate a framework to accomplish this using a mock data set with SDSS \emph{ugriz} photometry and \emph{Gaia} astrometric information. Our technique utilises a Bayesian hierarchical model for inferring properties of a WD population while also taking into account all observational errors of individual objects, as well as selection and incompleteness effects. We demonstrate that photometry alone can constrain the WD population's distributions of temperature, surface gravity and phenomenological type, and that astrometric information significantly improves determination of the WD surface gravity distribution. We also discuss the possibility of identifying unresolved binary WDs using only photometric and astrometric information. | White dwarfs (WDs) are the remnants of stars with initial masses $\lesssim8\mbox{--}10$~M$_\odot$ \citep{1996ApJ...460..489R,2009MNRAS.395.1409S}. The local WD population carries information about the Galaxy's star formation and dynamical history, and constrains models of stellar evolution \citep{1987ApJ...315L..77W,2016NewAR..72....1G,2018arXiv180505849E}. The Sloan Digital Sky Survey (SDSS) catalogued ${\sim}29,000$ spectroscopically confirmed WDs \citep{2013ApJS..204....5K,2015MNRAS.446.4078K}. A fundamental difficulty in studying WDs is that their mass is degenerate with distance. This degeneracy can be broken with high quality spectrometry and accurate atmospheric models. The \emph{Gaia} mission, which recently published its second data release (DR2), is expected to increase the number of known WDs by approximately an order of magnitude \citep{Jordan:2006jg,2014A&A...565A..11C}; \cite{2018MNRAS.tmp.1537K} and \cite{2018arXiv180703315G} have recently published WD catalogues, the latter containing 260,000 high-confidence WDs. \emph{Gaia} also provides astrometric information for local neighborhood WDs. For comparison, the astrometric mission \emph{Hipparcos} had a limiting apparent magnitude of $V \sim 12.4$ \citep{1997A&A...323L..49P}, while \emph{Gaia} will see objects as faint as $G \sim 21$ (with this limit, a WD with a mass of 0.6 M$_\odot$ and effective temperature of 8,000 K is seen to ${\sim}400$ pc, assuming no dust extinction). In a model of the WD population, it is physically meaningful to divide the total population into WD sub-populations. WDs form a family of atmospheric types, where the main classification is between DA and DB, depending on if the envelope is hydrogen- or helium-dominated \citep{Tremblay:2007hq,2011ApJ...737...28B,2015A&A...583A..86K}. DA and DB stars can be identified with accurate photometry, as demonstrated by \cite{Mortlock:2008gf}. The halo WD population is kinematically warmer and older than the disk WD population, such that inferring and comparing properties of these sub-populations can yield information on the star formation and kinematic history of our Galaxy \citep{1998ApJ...503..239I,2016MNRAS.463.2453D}. The sub-population of binary WD systems holds information about stellar evolution \citep{Postnov:2014tza} and Type Ia supernovae progenitor scenarios \citep{Livio:2018rue}, but unresolved binaries are very difficult to identify even with high-quality spectroscopy. With the enormous size of the \emph{Gaia} data set, there is great potential for inferring properties of the WD population using photometry and astrometry, rather than the smaller data set of spectroscopically observed WDs. In this work we demonstrate how to infer properties of the WD population in the solar neighborhood, using SDSS \emph{ugriz} photometry and \emph{Gaia} astrometry. We generate a mock data sample of WDs from a population model of temperature, surface gravity, and spatial number density distribution, of DA and DB atmospheric types. All sample objects have photometry and parallax information with observational errors expected from SDSS and \emph{Gaia}, and sample construction selection effects are taken into account. We also discuss the possibility of identifying binary WD systems and demonstrate how to do so using photometric and astrometric information alone. This paper is organized as follows. We outline our model for the WD population and the observational data that we consider, in Sec.~\ref{sec:model} and Sec.~\ref{sec:data} respectively. We present out method of statistical inference in Sec.~\ref{sec:method}. followed by Sec.~\ref{sec:mock}, where we generate a mock data catalogue and infer the model parameters from that data. We discuss possible extensions to the WD model in Sec.~\ref{sec:subpopulations}, such as differentiating between disk and halo sub-populations, as well as the possibility of identifying unresolved double-degenerate binary WD systems. Finally, in Sec.~\ref{sec:discussion} we present our conclusions. | \label{sec:discussion} In this paper, we demonstrate how to infer properties of the local WD population using only astrometric and photometric information, in the framework of a Bayesian hierarchical model. In our mock sample, we have limited ourselves to a total number of 10,000 WDs and a simple population model, in order to demonstrate the statistical method. The catalogue of WDs in a \emph{Gaia} and SDSS cross-matched sample is expected to be around an order of magnitude larger, enabling us to fit a significantly more complicated model. The model could be extended with more complex distributions of effective temperature, surface gravity, and type, and by including sub-populations as discussed in Sec.~\ref{sec:subpopulations}. With a kinematic model, proper motion information would be very informative, especially in terms of differentiating between disk and halo WDs. When working with real data, there are complications that are not included here but would be straightforward to implement within this framework. Most WD seen by \emph{Gaia} and SDSS are very close to the Sun and almost unaffected by dust. However, hotter and more luminous WDs are seen to further distance and subject to dust reddening and extinction. With a good dust map, selection effects and photometric reddening for such objects can be accounted for. Also not included in this work are incompleteness effects, which are severe for WDs in \emph{Gaia} DR2. This will improve significantly with future data releases, but will still be crucial to account for. \emph{Gaia} parallax measurements provide robust identification of WDs, enabling the construction of volume-limited samples, and breaks the degeneracy between distance and size. It is possible to differentiate sub-populations of WDs using this method, such as a population of binary WD systems. Our statistical model fully and correctly accounts for selection effects and observational uncertainties, permitting the construction of a large data sample, without the need to exclude objects with low signal-to-noise or missing parallax information. | 18 | 8 | 1808.00474 |
1808 | 1808.07062_arXiv.txt | {Many algorithms to solve Kepler's equations require the evaluation of trigonometric or root functions.}{We present an algorithm to compute the eccentric anomaly and even its cosine and sine terms without usage of other transcendental functions at run-time. With slight modifications it is also applicable for the hyperbolic case.}{Based on the idea of CORDIC, our method requires only additions and multiplications and a short table. The table is independent of eccentricity and can be hardcoded. Its length depends on the desired precision.}{The code is short. The convergence is linear for all mean anomalies and eccentricities $e$ (including $e=1$). As a stand-alone algorithm, single and double precision is obtained with 29 and 55 iterations, respectively. Half or two-thirds of the iterations can be saved in combination with Newton's or Halley's method at the cost of one division.}{} \author{M.~Zechmeister\inst{1}} \institute{Institut f\"ur Astrophysik, Georg-August-Universit\"at, Friedrich-Hund-Platz 1, 37077 G\"ottingen, Germany\\ \email{[email protected]}} | Kepler's equation relates the mean anomaly $M$ and the eccentric anomaly $E$ in orbits with eccentricity $e$. For elliptic orbits it is given by \begin{equation} E-e\sin E=M(E).\label{eq:KE} \end{equation} The function is illustrated for eccentricities 0, 0.1, 0.5, 0.9, and~1 in Fig.~\ref{fig:KE}. It is straightforward to compute $M(E)$. But in practice $M$ is usually given and the inverse function $E(M)$ must be solved. The innumerable publications about the solution of Kepler's equation \citep{1993sket.book.....C} highlight its importance in many fields of astrophysics (e.g. exoplanet search, planet formation, and star cluster evolution), astrodynamics, and trajectory optimisation. N-body hybrid algorithms also make use of this analytic solution of the two-body problem \citep{1991AJ....102.1528W}. Nowadays, computers can solve Eq.~(\ref{eq:KE}) quickly. But the speed increase is counterbalanced by large data sets, simulations, and extensive data analysis (e.g. with Markov chain Monte Carlo). This explains ongoing efforts to accelerate the computation with software and hardware, for example by parallelising and use of graphic processing units (GPUs; \citealp{2009NewA...14..406F}). The Newton-Raphson iteration is a common method to solve Eq.~(\ref{eq:KE}) and employs the derivative $E'$. In each step $n$ the solution is refined by \begin{equation} E_{n+1}=E_{n}+E'(M_{n})(M-M_{n})=E_{n}-\frac{E_{n}-e\sin E_{n}-M}{1-e\cos E_{n}}.\label{eq:Newton} \end{equation} A simple starting estimate might be $E_{0}=M+0.85e$ \citep{1987CeMec..40..303D}. Each iteration comes at the cost of evaluating one cosine and one sine function. Hence one tries to minimise the number of iterations. This can be done with a better starting estimate. For example, \citet{1995CeMDA..63..101M} provides a starting estimate better than $10^{-4}$ by inversion of a cubic polynomial which however requires also transcendental functions (four roots). \citet{BOYD200712} further polynomialise Kepler\textquoteright s equation through Chebyshev polynomial expansion of the sine term and yielded with root finding methods a maximum error of $10^{-10}$ after inversion of a fifteen-degree polynomial. Another possibility to reduce the iteration is to use higher order corrections. For instance Pad\'{e} approximation of order {[}1/1{]} leads to Halley's method. Pre-computed tables can be an alternative way for fast computation of $E$. \citet{1997CeMDA..66..309F} used a table equally spaced in $E$ to accelerate a discretised Newton method, while \citet{2006CeMDA..96...49F} proposed an equal spacing in $M$, that is, a direct lookup table which must be $e$-dependent and therefore two-dimensional. Both tables can become very large depending on the desired accuracy. So the solution of the transcendental Eq.~(\ref{eq:KE}) often comes back to other transcendental equations which themselves need to be solved in each iteration. This poses questions as to how those often built-in functions are solved and whether there is a way to apply a similar, more direct algorithm to Kepler's equation. The implementation details of those built-in functions are hardware and software dependent. But sine and cosine are often computed with Taylor expansion. After range reduction and folding into an interval around zero, Taylor expansion is here quite efficient yielding $10^{-16}$ with 17th degree at $\frac{\pi}{4}$. Kepler's equation can also be Taylor expanded \citep{1968NASTN4460.....S} but that is less efficient, in particular for $e=1$ and around $M=0$ where the derivative becomes infinite. Similarly, root or arcsine functions are other examples where the convergence of the Taylor expansion is slow. For root-like functions, one again applies Newton-Raphson or bisection methods. The arcsine can be computed as $\arcsin(x)=\arctan(\frac{x}{\sqrt{1-x^{2}}})$ where Taylor expansion of the arctangent function is efficient and one root evaluation is needed. An interesting alternative method to compute trigonometric functions is the Coordinate Rotation Digital Computer (CORDIC) algorithm which was developed by \citet{volder1959cordic} for real-time computation of sine and cosine functions and which for instance found application in pocket calculators. CORDIC can compute those trigonometric and other elementary functions in a simple and efficient way. In this work we study whether and how the CORDIC algorithm can be applied to Kepler's equation. \begin{figure} \begin{centering} \includegraphics[width=1\linewidth]{Fig/ke} \par\end{centering} \caption{\label{fig:KE}Kepler's equation for five different eccentricities.} \end{figure} | We show that the eccentric anomaly $E$ from Kepler's equation can be computed by a CORDIC-like approach and is an interesting alternative to other existing tools. The start vector $E_{0}=0^{\circ}$ and its Cartesian representation ($\cos E_{0}=1$ and $\sin E_{0}=0$) are rotated using a set of basis angles. The basis angles $\alpha_{n}$ and its trigonometric function values can be pre-computed and stored in an auxiliary table. Since the table is short and independent of $e$, it can be also hard-coded. Our method provides $E$, $\sin E$, and $\cos E$ without calling any transcendental function at run-time. The precision is adjustable via the number of iterations. For instance, single precision is obtained with $n=29$ iterations. Using double precision arithmetic, we found the accuracy is limited to $\sim10^{-15}\sqrt{\frac{2}{1-e}}$ in the extreme corner ($M=0$, $e=1$). For accuracy and speed we re\-commend the one-sided algorithm described in Sect.~\ref{subsec:min-base}. Our method is very flexible. As a stand-alone method it can provide high accuracy, but it can be also serve start value for other refinement routines and coupled with Newton's and Halley's method. In this context we proposed in Sects.~\ref{subsec:CORDIC-Newton} and \ref{subsec:CORDIC-Halley} to propagate cosine and sine terms simultaneously using small angle approximations in the trigonometric addition theorems and derived the limits when they can be applied without accuracy loss. Though the number of iterations appears relatively large, the computational load per iteration is small. Indeed, a with simple software implementation we find a performance that is good competition for Newton's method. However, CORDIC algorithms utilise their full potential when implemented in hardware, that is, directly as a digital circuit. So-called field programmable gate arrays (FGPA) might be a possibility to install our algorithm closer to machine layout. Indeed, hardware oriented approaches can be very successful. This was shown by the GRAvity PipelinE (GRAPE) project \citep{1999Sci...283..501H}, which tackled N-body problems. By implementing Newtonian pair-wise forces efficiently in hardware, it demonstrated a huge performance boost and solved new astrodynamical problems \citep{2003IAUS..208....1S}. Though we could not completely transfer the original CORDIC algorithm to Kepler's equation, it might benefit from ongoing developments and improvement of CORDIC algorithms which is still an active field. In the light of CORDIC, solving Kepler's equations appears almost as simple as computing a sine function. | 18 | 8 | 1808.07062 |
1808 | 1808.09763_arXiv.txt | Kinetic Alfv\'{e}n waves (KAWs) are the short-wavelength extension of the MHD Alfv\'{e}n-wave branch in the case of highly-oblique propagation with respect to the background magnetic field. Observations of space plasma show that small-scale turbulence is mainly KAW-like. We apply two theoretical approaches, collisional two-fluid theory and collisionless linear kinetic theory, to obtain predictions for the KAW polarizations depending on $\beta_\mathrm{p}$ (the ratio of the proton thermal pressure to the magnetic pressure) at the ion gyroscale in terms of fluctuations in density, bulk velocity, and pressure. We perform a wavelet analysis of MMS magnetosheath measurements and compare the observations with both theories. We find that the two-fluid theory predicts the observations better than kinetic theory, suggesting that the small-scale KAW-like fluctuations exhibit a fluid-like behavior in the magnetosheath although the plasma is weakly collisional. We also present predictions for the KAW polarizations in the inner heliosphere that are testable with Parker Solar Probe and Solar Orbiter. | \label{sec:intro} Standard single-fluid magnetohydrodynamics (MHD) contains four linear modes in a collisional plasma: the Alfv\'{e}n wave, the fast-magnetosonic wave, the slow-magnetosonic wave, and the entropy mode. The polarization and dispersion relations identify their counterparts in collisionless kinetic theory \citep{Stix1992book, Gary1993book}. Due to the collisionless nature of the solar wind, kinetic models have been expected to describe these fluctuations more accurately than MHD. However, \cite{Verscharen2017ApJ} compare theoretical predictions for wave polarization properties from both MHD theory and kinetic theory with observations of compressive fluctuations in the solar wind and find that the predictions from linear MHD agree better with the observations than the predictions from kinetic theory for slow modes at large scales. The comparison between the fluid-like and the kinetic behavior of collisionless plasmas is of great importance for our fundamental understanding of plasma turbulence. In this context, we define a fluid-like mode as a plasma mode that follows the predictions from fluid equations with adiabatic and isotropic pressure closure. The magnetic fluctuations in the inertial range of solar wind turbulence exhibit Alfv\'{e}nic correlations \citep{Belcher1971JGR} and a scale-dependent anisotropy with $k_{\perp}\gg k_{\parallel}$ \citep{Horbury2008PhRvL, Wicks2010MNRAS, Chen2011MNRAS, Chen2012ApJ, He2013ApJ, Yan2016ApJL}, where $k_{\perp}$ is the perpendicular wavenumber and $k_{\parallel}$ is the parallel wavenumber with respect to the background magnetic field. Kinetic Alfv\'{e}n waves (KAWs) are the short-wavelength extension of the Alfv\'{e}n-wave branch in the case of highly-oblique propagation with respect to the background magnetic field. Therefore, it is thought that the cascade continues into the KAW-like regime for $k_{\perp}\rho_\mathrm{p} \gtrsim 1$, where $\rho_\mathrm{p}=v_\mathrm{th}/\omega_{\mathrm{cp}}$ is the ion gyroscale, $v_\mathrm{th} $ is the perpendicular thermal speed, $\omega_{c\mathrm{p}}=q_\mathrm{p}B_0/m_\mathrm{p}c$ is the proton gyrofrequency, $q_\mathrm{p}$ is the proton electric charge, $m_\mathrm{p}$ is the proton mass, $B_0$ is the magnitude of the background magnetic field, and $c$ is the speed of light. A growing body of evidence corroborates the presence of kinetic Alfv\'{e}n turbulence in the solar wind \citep{Chandran2009ApJ, Sahraoui2010PhRvL, Chen2010PhRvL, He2011ApJ, Salem2012ApJ, Chen2013PhRvL}. Likewise, observations of small-scale fluctuations in the magnetosheath also suggest the presence of KAW-like turbulence \citep{Chen2017PhRvL, Breuillard2018ApJ}. We extend Verscharen et al.'s (\citeyear{Verscharen2017ApJ}) study to examine KAW-like fluctuations at small scales. In Section \ref{sec:Theory}, we present predictions for fluctuations in the first three velocity moments associated with KAWs from both collisional two-fluid theory and collisionless linear kinetic theory. In Section \ref{sec:Data Analysis}, we describe our analysis of MMS magnetosheath measurements. We compare observations with our predictions in Section \ref{sec:Results}. In Section \ref{Discussion and Conclusions}, we discuss our results and present our conclusions. We present predictions for solar-wind measurements with Parker Solar Probe and Solar Orbiter in the Appendix. | \label{Discussion and Conclusions} The behavior of KAWs departs from the behavior of Alfv\'{e}n waves mainly due to two effects. The ion motion is affected by compression and introduces a polarization-drift term in the equation of motion. Furthermore, the parallel component of the electric field is non-zero and electrons move in the field-parallel direction to neutralize the ion density perturbations. We derive predictions for the proton polarization of KAWs using collisional two-fluid theory and collisionless kinetic theory. In the linear kinetic theory, the fluctuations are represented by fluctuations in the distribution function, $\delta f_s$ so that all moments are included and generally non-zero. Our two-fluid theory, on the other hand, assumes an adiabatic and isotropic closure for the moment hierarchy, i.e., there are no fluctuations in heat flux and the pressure tensor is isotropic. Apart from these differences, fluid and kinetic theory are equivalent. Measurements with even higher velocity-space resolution may be capable of showing the heat-flux suppression in the future. Both theories predict similar behaviors for density and pressure fluctuations, but the parallel and perpendicular velocity fluctuations show clear differences: these fluctuations are greater in two-fluid theory than in kinetic theory. Due to the noise in the velocity observation, we cannot rule out the possibility that fluctuations with very small amplitude exhibit a behavior consistent with kinetic theory. However, our comparison of fluctuations in the magnetosheath above the noise level with our theoretical predictions shows that KAW turbulence behaves fluid-like at ion scales, suggesting that some of the fluid-like behavior found by \cite{Verscharen2017ApJ} extends to the ion-scale fluctuations. We note that relaxing our assumption of temperature isotropy may improve the agreement between our theory and observations. In addition, a study based on a superposition of KAW turbulence with other modes at small scales may modify our results since our present method does not distinguish the contributions from different wave types than KAWs. A comparison with alternative approximations to the dispersion relation \citep{Hunana2013ApJ, Sulem2015JPlPh, Told2016NJPh} may give further insight into the physics of the observed modes. However, these extensions are beyond the scope of this work. Our finding of fluid-like behavior in KAW turbulence suggests that some yet unknown mechanism creates conditions similar to the adiabatic and isotropic closure applied in our two-fluid theory, even at small scales and under collisionless conditions. Anti-phase-mixing \citep{Schekochihin2016JPP} is a potential explanation for this fluid-like behavior. In the turbulent background, nonlinear interactions between fluctuations at different scales can trigger stochastic plasma echoes \citep{Gould1967PRL, Schekochihin2016JPP} that may inhibit the transfer of power to higher moments of the velocity distribution. \cite{Parker2017PoP} and \cite{Meyrand2018arxiv} found that energy transfer from large to small velocity-space scales nearly cancels due to “anti-phase-mixing” excited by a stochastic plasma echo. This process leads to an effective low-moment closure, even under collisionless conditions. In KAWs with larger amplitude, the nonlinear trapping of electrons may contribute to the saturation of damping and a more fluid-like behavior \citep{Gershman2017NatureC}.% Alternatively, wave-particle interactions can suppress fluctuations in higher moments of the velocity distribution. \cite{Verscharen2016ApJ} find that microinstabilities generate fluctuations that scatter protons and thus reduce the anisotropy of the pressure tensor. Wave-particle interactions may then play the role of particle-particle collisions in suppressing fluctuations in higher moments and closing the moment hierarchy at low order. Our finding of the fluid-like behavior of KAW turbulence at scales down to the proton inertial length supports the use of fluid models when studying large- and small-scale fluctuations. This discovery will be beneficial to astrophysical modeling since fluid computations are much faster than kinetic computations. More fundamentally, it is of great importance to determine the physics processes that lead to this fluid-like behavior of an otherwise collisionless plasma. | 18 | 8 | 1808.09763 |
1808 | 1808.05910_arXiv.txt | The idea of dark matter in the form of primordial black holes has seen a recent revival triggered by the LIGO detection of gravitational waves from binary black hole mergers. In this context, it has been argued that a large initial clustering of primordial black holes can help alleviate the strong constraints on this scenario. In this work, we show that on the contrary, with large initial clustering the problem is exacerbated and constraints on primordial black hole dark matter become overwhelmingly strong. | % Soon after realising that black holes (BHs) could form in the early radiation-dominated universe \cite{1967SvA....10..602Z,Hawking:1971ei,Carr:1974nx} from the gravitational collapse of large % density fluctuations, it was pointed out that such objects may even contribute appreciably to the total matter density \cite{1975Natur.253..251C}. An obvious question is therefore whether these primordial black holes (PBHs) could explain {\it all} of the cosmologically observed dark matter (DM), see Refs.~\cite{Carr:2016drx,Sasaki:2018dmp} for recent reviews. This idea has seen greatly renewed interest \cite{Bird:2016dcv,Clesse:2016vqa,Sasaki:2016jop,Carr:2017jsz,Wang:2016ana} after the discovery of binary mergers by the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) \cite{Abbott:2016blz,Abbott:2016nmj,TheLIGOScientific:2016pea,Abbott:2017vtc}, proving the existence of $\mathcal{O}(10M_\odot)$ BHs with so far unclear origin. Constraints on the allowed DM fraction $f_\mathrm{PBH}$ of PBHs derive from a large number of observations and have been explored for a vast range of mass scales, see Refs.~\cite{Carr:2016drx,Carr:2017jsz,Sasaki:2018dmp} for an overview. While there seems to be a broad consensus that $f_\mathrm{PBH}\sim1$ is essentially excluded for black hole masses $m_\text{PBH} \gtrsim 10^{-10}~M_\odot$ when assuming a homogeneously distributed population of PBHs with a single mass, this general picture changes when either of these conditions is not met. Intriguingly, this also opens the window of PBH masses consistent with the LIGO observations by circumventing the stringent constraints from microlensing and from the cosmic microwave background (CMB)~\cite{Garcia-Bellido:2017xvr} (see however~\cite{Zumalacarregui:2017qqd,Garcia-Bellido:2017imq}). Clustered PBH distributions have been argued to arise generically in Refs.~\cite{Chisholm:2005vm,Chisholm:2011kn}, possibly explaining the existence of super-massive BHs~\cite{Dokuchaev:2004kr,Dokuchaev:2007mf}. Only recently it was realized that significant clustering is in fact {\it not} expected for Gaussian primordial fluctuations~\cite{Ali-Haimoud:2018dau,Desjacques:2018wuu}, as predicted by vanilla models of cosmic inflation. However, highly clustered PBH distributions could still plausibly arise, e.g., in the presence of sizeable primordial non-Gaussianities~\cite{Young:2014oea} or from the collapse of domain walls~\cite{Belotsky:2018wph}. In this work we choose to be agnostic about the possible origin of large PBH clustering. Instead we demonstrate that in such a situation $f_\text{PBH} \sim 1$ is in fact still excluded over a wide mass-range, thereby closing this possibly last loop-hole for all DM consisting of PBHs with masses larger than $10^{-10} M_\odot$. The initial clustering of PBHs is indeed a key parameter to understanding the phenomenology of PBH DM, affecting merger rates~\cite{Raidal:2017mfl,Ballesteros:2018swv}, the subsequent structure formation~\cite{Carr:2018rid}, and the interpretation of observational bounds~\cite{Garcia-Bellido:2017xvr}. Here we take a pragmatic and phenomenological approach by parametrising the clustering as a constant, free parameter on the scales of interest. We point out that, for the large PBH clustering discussed in the literature, the expected merger rates easily exceed one per binary and Hubble time. We demonstrate that multiple subsequent mergers severely constrain PBH DM as a possible explanation of the LIGO events because of {\it i)} the expected (as compared to observed) merger rate, {\it ii)} the impact of the additional radiation component in gravitational waves (GWs) on both CMB and large-scale structure observations, and {\it iii)} a present-day stochastic GW background (SGWB) exceeding the sensitivities of current ground- (or future space-) based observatories. This article is organised as follows. We start by describing the GW spectrum and energy density from cosmological PBH mergers, before discussing how the merger rate critically depends on the initial PBH clustering. We then introduce a cascading merger scenario to capture the effects of large clustering, and hence high merger rates. We derive the resulting contributions to the stochastic GW background and the relativistic energy density in GWs, using the cosmological parameters from Ref.~\cite{Aghanim:2018eyx} whenever relevant. Along with the actual event rate observed by LIGO, we use this to place constraints on $f_\mathrm{PBH}$. We discuss the influence of a deviation from the assumptions used in calculating the constraints and show that this does not qualitatively change our results. | % If PBHs are not homogeneously distributed in the Universe but highly clustered, existing bounds on their abundance must be re-interpreted. Here we have demonstrated that the resulting limits % are not weakened, as claimed previously, but instead strengthened because subsequent merger steps would dominate the SGWB. Taking into account constraints from cosmology and direct GW searches, we find that for $\delta_\text{dc,0} > 10^4$ the case of pure PBH DM is firmly excluded in the entire range of initial PBH masses between $10^{-5} \, M_\odot$ and $100 \, M_\odot$. For slightly less conservative assumptions about the decrease of $\delta_\text{dc}$ in subsequent merger steps, this even holds for much smaller initial density contrasts. We note that outside this mass range bounds are also very strong~\cite{Carr:2017jsz}, which essentially left this interval as one out of only two realistic options for explaining all DM in terms of PBHs (the second one arises for much lighter PBHs of $10^{-16} \lesssim m_\text{PBH}/M_\odot \lesssim10^{-11}$ \cite{Niikura:2017zjd}). \bigskip \paragraph*{Note added.---} After this work was finished,~\cite{Raidal:2018bbj} appeared as a preprint and reopened the question of the stability of PBH binary systems with respect to perturbations by nearby PBHs, which could in particular influence the merger rates entering our results. A detailed analysis of this effect in the context of multiple mergers, which most likely requires $N$-body simulations, is still to be performed. \bigskip \vfill \paragraph*{Acknowledgements.---}% We thank Thomas Konstandin for useful comments on the manuscript, Florian K\" uhnel and Hardi Veerm\"ae for relevant discussions and Cole Miller for encouraging us to spell out why the gravitational wave recoil does not significantly affect our analysis. We would also like to thank the anonymous referees for pertinent comments. This work is supported by the German Science Foundation (DFG) under the Collaborative Research Center (SFB) 676 Particles, Strings and the Early Universe as well as the ERC Starting Grant `NewAve' (638528). TB wishes to thank McGill university, where part of this manuscript was completed, for support and hospitality. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science. \newpage | 18 | 8 | 1808.05910 |
1808 | 1808.09625_arXiv.txt | Within the framework of non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order (radial order $n_\mathrm{r}<5$) p modes. The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most of high-order ($n_\mathrm{r}>5$) p modes of all low-temperature stars become unstable. Fortunately, within a wide range of the anisotropic parameter $c_3$, stellar pulsation stability is not sensitive to the specific value of $c_3$. Therefore it is safe to say that calibration errors of the convective parameter $c_3$ do not cause any uncertainty in the calculation of stellar pulsation stability. | \label{sect:intro} Radiation and convection are the two main mechanisms of energy transport in stellar interiors. In low-temperature late-type stars, convection, instead of radiation, becomes the dominant energy transport mechanism. Convection causes transport and exchange of energy, momentum, and material inside stars, and therefore has important influence on stellar structure, evolution and pulsation stability. Non-locality and anisotropy are two most important properties of stellar convection. There has been much research and discussion regarding the effect of non-local convection \citep{XDC1998a, XDC1998b, XD2013}, while the effect of turbulent anisotropy on stellar pulsation stability is less studied. The purpose of this work is to provide an in-depth study and analysis about this problem. In Section \ref{sect:anisotropy} we give a brief introduction of our theoretical treatment of turbulent anisotropy. The dependence of stellar pulsation stability on the anisotropic parameter $c_3$ is discussed in Section \ref{sect:dependence} by means of numerical methods. The results are summarised in Section \ref{sect:conclusions}. | \label{sect:conclusions} In this work we have studied in detail the dependence of pulsation stability of $\delta$ Scuti/$\gamma$ Doradus stars on the anisotropic parameter $c_3$ of turbulent convection. The results show that: \begin{enumerate} \item Turbulent anisotropy has virtually no influence on pulsation stability of g modes and low-order ($n_\mathrm{r}<5$) p modes. In a wide range of the anisotropic parameter $c_3$ ($1 \lesssim c_3 \lesssim 16$), pulsation stability of g and low-order p modes hardly depends on $c_3$. Therefore we are confident to say that, calibration errors of $c_3$ have no substantial effect on pulsation stability of $\delta$ Scuti/$\gamma$ Doradus stars. \item The effect of turbulent anisotropy on pulsation stability of high-order ($n_\mathrm{r} \gtrsim 5$) p modes is non-negligible. Most of high-order p modes of all low-temperature red stars become unstable if turbulent anisotropy is ignored, and the red edge of the $\delta$ Scuti instability strip cannot be modelled theoretically. \end{enumerate} Our non-local and anisotropic model and 3D hydrodynamical simulations show good agreement in the deep convection zone, but have notable difference near the boundary and in the overshooting zone. However, anisotropy has no substantial influence on pulsation stability of g modes and low-order p modes, and the overshooting zone contributes little to mode inertia. Therefore, at least for g modes and low-order p modes, the uncertainty of turbulent anisotropy $\overline{u'^2_\mathrm{h}}/\overline{u'^2_\mathrm{r}}$ in the overshooting zone in static models has no substantial influence on pulsation stability. | 18 | 8 | 1808.09625 |
1808 | 1808.08235_arXiv.txt | Strong gravitational lensing can provide accurate measurements of the stellar mass-to-light ratio $\Upsilon$ in low-redshift ($z$\,$\la$\,0.05) early-type galaxies, and hence probe for possible variations in the stellar initial mass function (IMF). However, true multiple imaging lens systems are rare, hindering the construction of large nearby lens samples. Here, we present a method to derive upper limits on $\Upsilon$ in galaxies with single close-projected background sources, where no counter-image is detected, down to some relative flux limit. We present a proof-of-principle application to three galaxies with integral field observations from different instruments. In our first case study, only a weak constraint on $\Upsilon$ is obtained. In the second, the absence of a detectable counter-image excludes stellar masses higher than expected for a Salpeter IMF. In the third system, the current observations do not yield a useful limit, but our analysis indicates that deeper observations should reveal a counter-image if the stellar mass is any larger than expected for a Milky Way IMF. We discuss how our method can help enlarge the current samples of low-$z$ galaxies with lensing constraints, both by adding upper limits on $\Upsilon$ and by guiding follow-up of promising single-image systems in search of fainter counter-images. | Strong gravitational lensing can be exploited on galaxy scales to provide robust measurements of total projected mass within a characteristic aperture, with uncertainties of only a few per cent \citetext{e.g. \citealt{2010ARA&A..48...87T}}. If the relative contributions of dark matter and stars can be estimated, e.g. using additional information from stellar dynamics, then the stellar mass-to-light ratio $\Upsilon$ can be determined, which in turn constrains the stellar initial mass function (IMF). Applications of this method to lenses at redshift $z$\,=\,0.2 provided some of the first evidence for `heavy' IMFs in elliptical galaxies \citep{2010ApJ...709.1195T}, with a factor of $\sim$2 mass excess, compared to Milky-Way-like IMFs, for the most massive objects (velocity dispersions $\sigma$\,$\ga$\,300\,km\,s$^{-1}$). In recent work, we have developed the use of lenses at lower redshifts ($z$\,\la\,0.05) as an especially robust probe of the IMF, minimising the uncertainties associated with the dark-matter component \citep*{2013MNRAS.434.1964S}. This advantage arises because the critical surface density $\Sigma_{\rm cr}$ (in M$_\odot$\,pc$^{-2}$) scales inversely with the lens distance (assuming distant sources), so that low-redshift lensing can occur only in the high density central parts of galaxies, where stars dominate the total mass. In this case, the stellar mass-to-light ratio $\Upsilon$ can be estimated from a `pure' lensing analysis, without using any dynamical information. From four systems studied in detail to date, with $\sigma$\,$\approx$\,300\,km\,s$^{-1}$, \cite{2018MNRAS.478.1595C} concluded that $\Upsilon$ is on average only 9$\pm$8 per cent heavier than expected from a \cite{2001MNRAS.322..231K} IMF. This result differs strikingly from the distant lensing analysis, and is also in tension with results from pure stellar dynamics \citep{2013MNRAS.432.1862C} and spectroscopic limits on low-mass stars \citep{2012ApJ...760...71C}. As the small sample size in \cite{2018MNRAS.478.1595C} suggests, identifying nearby lenses is challenging. The number of potential lenses is limited by the small volume available at low redshift, and the intrinsic rarity of high-mass galaxies. The number of nearby galaxies with {\it bright} lensed background objects, recognisable as such from broad-band imaging, is prohibitively small. Instead, we have developed a strategy using integral field unit (IFU) spectroscopy to detect multiply-imaged line-emission from faint sources behind selected nearby galaxies. Our method was first applied in the SNELLS (SINFONI Nearby Elliptical Lens Locator Survey) programme \citep*{2015MNRAS.449.3441S}, and later adapted to optical data from MUSE (Multi-Unit Spectroscopic Explorer) \citep{2018MNRAS.478.1595C}, leading to the sample of four multiple-imaging lenses described above, as well as a number of close-projected background emitters without any identifiable lensed counter-image. The new generation of multi-IFU galaxy surveys offers a promising new route to augmenting the nearby lens sample. The ongoing SAMI (Sydney-AAO Multi-object Integral field spectrograph) survey \citep{2015MNRAS.447.2857B} and SDSS-IV MaNGA (Mapping Nearby Galaxies at Apache Point) \citep{2015ApJ...798....7B} are observing thousands of low-redshift galaxies, including hundreds which are massive enough potentially to act as strong lenses. \cite{2018MNRAS.477..195T} recently identified 40 background emission-line sources behind MaNGA target galaxies. In most of these systems, only a single image of the background source is detected in the MaNGA data-cube\footnote{Talbot et al. report multiple imaging for nine background emitters based on pseudo-narrow-band images from the pipeline datacubes. We have independently analysed the data for these systems, using the method of \cite{2017MNRAS.464L..46S}, which was developed to avoid artifacts near galaxy centres caused by the cube reconstruction process. With this analysis, only two of the Talbot et al. systems show possible evidence for multiple imaging: SDSSJ170124.01+372258.09 \citep[as reported in][]{2017MNRAS.464L..46S} and SDSSJ143607.49+494313.22, both at $z_{\rm lens}$\,$\sim$\,0.12.}, but future follow-up observations could detect counter-images to establish more of these systems as low-redshift lenses. In this paper, motivated by the difficulty of finding multiple-imaging lenses at low redshift, we consider whether useful lensing information can be inferred in the cases noted above where only a {\it single} (and unresolved) image of a background source is detected in close projection. As a crude argument (neglecting detection thresholds, external shear, ellipticity, etc), consider a background emitter observed at a projected separation $r_{\rm em}$ from the lens candidate. Lensed counter-images should be formed for any image projected within twice the Einstein radius, $R_{\rm Ein}$. Hence if {\it no} counter-image is present, 0.5\,$r_{\rm em}$ must be larger than the Einstein radius, and therefore enclose a mean surface density which is smaller than the critical value, i.e. $\langle\Sigma\rangle_{0.5 r_{\rm em}}$\,$<$\,$\Sigma_{\rm cr}$. The critical surface density $\Sigma_{\rm cr}$ depends only on the foreground and background redshifts, which are known (in the case of IFU lens searches). Hence if the lensing mass is dominated by stars, so that a mass-follows-light model is applicable, this calculation yields an upper limit to the stellar mass-to-light ratio $\Upsilon$. An alternative, pixel-based, method for exploiting singly-imaged systems was described by \cite{2015ApJ...803...71S}, and applied to mainly more distant galaxies from the SLACS (Sloan Lens Advanced Camera for Surveys) project. As we discuss later in this paper, while Shu et al.'s goals are similar to ours, their implementation is quite different, and not well-suited to the systems discussed here, where the lensed images are unresolved. The remainder of this paper expands on the simplified argument above, taking into account some of the complicating factors already noted. In Section~\ref{sec:meth} we present a more general treatment of a circular `toy model', illustrating the effect of a finite detection threshold, such that only sufficiently bright counter-images are detectable, and the impact of the unknown external contributions to the lensing deflections, modelled as a quadrupole shear. In Section~\ref{sec:applic}, we illustrate the method with application to three observed galaxies (accounting now also for the lens ellipticity), drawn from different data sources, which exemplify the range of results that can be obtained. We show that in favourable cases, useful upper limits to $\Upsilon$ can be obtained, which in principle provide further information on the IMF mass excess factor in elliptical galaxies. In other cases, our method provides a framework to guide future observations, with the goal of either establishing new multiply-imaged systems or else placing tighter upper limits on $\Upsilon$ from single images. Section~\ref{sec:disc} summarizes the results and discusses the prospects for using `upper-limit lensing' to derive statistical results for larger samples from current and future surveys. Where necessary, we adopt a cosmology with parameters ($h$, $\Omega_{\rm M}$, $\Omega_{\Lambda}$)\,=\,(0.696, 0.286, 0.714) \citep{2014ApJ...794..135B}. If we had instead adopted the \cite{2016A&A...594A..13P} parameters, with $h$\,=\,0.678, all determinations of $\Upsilon$ would be reduced by 2.5 percent. \begin{figure} \includegraphics[width=82mm,angle=270]{unlens_circ.eps} \vskip -1mm \caption{Upper-limit lensing constraints on the mass-to-light ratio, for the toy-model case in Section~\ref{sec:meth}. Here, the mass profile is a circular $R^{1/4}$-law profile, and we assume one image of the background galaxy (the `test image') has been detected at a projected separation half of the effective radius. Green, red and blue lines show the fraction of {\it intrinsically} single-, double- and quadruple-image configurations, for fixed observed location of the `test image', as a function of the stellar mass-to-light ratio $\Upsilon$. The heavy grey line shows the probability of {\it not} observing any lensed counter-image, to a flux limit of one quarter that of the test image, i.e. $f_{\rm lim}$\,=\,0.25. The difference between green and grey lines is attributable to multiple image systems (mainly doubles) with counter-images falling below this limit. The green vertical bars show the values of $\Upsilon$ selected in Figure~\ref{fig:configs}, corresponding to different regimes in typical multiplicity. The horizontal scaling is arbitrary for this synthetic example, but set to be similar to the observed cases shown in subsequent figures. Below, we indicate the range in $\Upsilon$ spanned by old-metal-rich populations with a Milky-Way-like IMF, a Salpeter IMF ($\times$1.55 higher in $\Upsilon$), and a `heavy' IMF ($\times$2 higher).} \label{fig:unlens_circ} \end{figure} \begin{figure*} \includegraphics[width=170mm,angle=270]{configs3.eps} \caption{Example image configurations for the circular toy-model case. The fixed `test image' position (representing the detected image of the background galaxy) is at half the effective radius of the mass distribution, and indicated by the blue circle with cross hairs. Lensed counter-images are shown by other blue points, with size proportional to their magnification, relative to the test image. The orange and cyan lines show lensing caustic and critical curves, respectively; the red cross indicates the undeflected source position. Each row shows five cases for a given value of $\Upsilon$ (these values are indicated in Figure~\ref{fig:unlens_circ}). The shear amplitude $\gamma$ and orientation $\theta$ are randomly drawn, to illustrate the scatter introduced by these unknown parameters. In each panel we note the {\it intrinsic} multiplicity (ignoring `central', i.e. Fermat-maximum, images), and also the number of {\it detectable} counter-images, defined as having $>$25\% the flux of the test image.} \label{fig:configs} \end{figure*} \begin{table*} \caption{ Relevant parameters of the systems analysed in Section~\ref{sec:applic}. The velocity dispersion $\sigma_{\rm 6dF/SDSS}$ is from \protect\cite{2014MNRAS.443.1231C} or \protect\cite{2009ApJS..182..543A}. } \label{tab:snells} \begin{tabular}{lcccl} \hline Short ID & SNL-4 & PGC007748 & J0728+4005 & \\ \hline 2MASS ID (2MASX...) & J04431291--1542101 & J02021739-0107405 & J07281702+4005025 & \\ IFU data source & SNELLS & MUSE & MaNGA \\ \hline $z_{\rm lens}$ & 0.037 & 0.043 & 0.050 \\ $z_{\rm src}$ & 1.38 & 0.830 & 0.954 & \\ $\sigma_{\rm 6dF/SDSS}$ & 304$\pm$16 & 254$\pm$6 & 268$\pm$6 & km\,s$^{-1}$ \\ \hline $R_{\rm eff}$ & 3.8 & 11.6 & 5.4 & effective radius (arcsec)\\ PA & --52.8 & +72.8 & +69.6 & deg E of N\\ $e$ & 0.38 & 0.20 & 0.21 & ellipticity 1--$b/a$\\ \hline $L_{\rm ap}$ & 17.6 & 18.9 & 20.6 & $K$-band; $R_{\rm ap}$\,=\,5$\arcsec$ ($10^{10}$\,$L_\odot$)\\ \hline $D_A$ & 152.6 & 175.9 & 201.4 & ang. size distance of lens (Mpc) \\ $\Sigma_{\rm cr}$ & 11.34 & 10.09 & 8.778 & crit. surf. density ($10^3$\,$M_\odot$\,pc$^{-2}$) \\ \hline $r_{\rm em}$ & 4.25 & 3.64 & 3.16 & emitter separation (arcsec)\\ PA$_{\rm em}$ & --36.0 & --77.6 & --53.2 & emitter angle (deg E of N) \\ $f_{\rm lim}$ & 0.4 & 0.08 & 0.4 & relative flux limit for counter-image \\ \hline \end{tabular} \end{table*} | \label{sec:disc} We have described a new method to derive limits on the stellar mass-to-light ratios in galaxies with single close-projected background sources, and presented a proof-of-principle application to three galaxies from different IFU data sources. Our approach is most suitable for application to IFU observations of massive field galaxies, because in this case: {\it (a)} the redshifts of both the foreground and background galaxy are known, and hence so is the critical density for lensing, $\Sigma_{\rm cr}$; {\it (b)} the lensing convergence $\kappa$\,=\,$\Sigma/\Sigma_{\rm cr}$ is likely to be dominated by the stellar mass of the foreground galaxy, and hence is known from observations except for a factor representing the stellar mass-to-light ratio, $\Upsilon$; and {\it (c)} the IFU allows for fairly unambiguous identification of faint counter-images, even close to the centre of the target galaxy, through the spectral contrast advantage of narrow emission lines. We note here that \cite{2015ApJ...803...71S} have previously described an analysis of SLACS `grade-C' systems, i.e. those with no identifiable counter-images, with the aim of deriving constraints from singly-imaged background sources. Their method is based on pixel-based fitting to residual (lens-subtracted) images, assuming a Sersic-profile source, with the lens treated as a singular isothermal ellipse, parametrized by the normalisation $b_{\rm SIE}$. This approach can be effective where the background image shows distinct curvature around the foreground galaxy, which can be unambiguously attributed to lensing (e.g. SDSSJ0847+2925, SDSSJ1446+4943 from their figures A1--A2). In other cases, however, the pixelized method may be susceptible to over-fitting of the intrinsic source structure, or residuals from subtracting the foreground galaxy. For example, in around half of their grade-C systems (e.g. SDSSJ1039+1555, SDSS0818+5410), the residual image shows a single source without obvious distortions suggestive of lensing, yet the Shu et al. analysis surprisingly still recovers $b_{\rm SIE}$ with a few per cent precision. The origin of the tight constraint, especially the lower bound, is unclear in these cases. By comparison, our `point image' method, using only an estimated upper limit on the counter-image flux, is more conservative but probably more robust. In any case, the unresolved images in our example cases are not suitable for pixel-based fitting methods. The results of Section~\ref{sec:applic} are intended to demonstrate the potential of the upper-limit lensing method, rather than to be interpreted as firm limits on the IMF in massive galaxies. In particular, we have not attempted here to determine the `correct' reference mass-to-light ratio for each galaxy. The three examples show the variety of results which can be obtained. In SNL-4, the constraint is currently weak, and can only be tightened with much deeper observations, due to the faintness of the observed source and the alignment of the background galaxy with the major axis of the lens. For PGC007748, a useful (though not very restrictive) limit on the IMF is already possible: the dynamical $\alpha$-versus-$\sigma$ relation of \cite{2013MNRAS.432.1862C} predicts $\alpha$\,$=$\,1.5$\pm$0.3 at the velocity dispersion of this galaxy (254\,km\,s$^{-1}$); hence our limit of $\alpha$\,$\la$\,1.4 (if the stellar population is old) places PGC007748 below the mean of this relation. Finally in J0728+4005, the existing MaNGA data do not provide a useful constraint, but realistic future observations should establish a firm limit on the IMF in this object, since a detectable counter-image should be present over a wide range of $\Upsilon$. Conversely, failure to detect a counter-image in deeper data would imply $\alpha$\,$\la$\,1.0, which would be $\sim$2$\sigma$ below the Cappellari et al. trend at this velocity dispersion. These results lead to two related applications for the upper-limit lensing approach described here. First, and most obviously, exploiting singly-imaged background sources promises to increase the sample of low-redshift galaxies amenable to lensing constraints on $\alpha$. In particular, while large IFU galaxy surveys like SAMI and MaNGA should generate a few new multiple-image lens systems \citep{2017MNRAS.464L..46S,2018MNRAS.477..195T}, the number of singly-imaged close-projected emitters will be much larger. In principle, the inclusion of upper limits can provide additional information on the intrinsic distribution of $\alpha$, e.g. using survival statistics methods \citep{1985ApJ...293..192F}. Indeed, including constraints from singly-imaged systems is {\it essential} to avoid a `lensing bias' which would otherwise favour higher $\alpha$ galaxies at a given separation. \cite{2015ApJ...803...71S} make a similar point with regard to their derivation of the total mass profile slopes from SLACS. The second application of our method is as a framework to guide follow-up observations of systems with close projected background sources, with the aim of either {\it (a)} recovering a faint counter-image, to establish a new lens system, or {\it (b)} attaining more stringent upper-limit lensing constraints, by pushing $U(\Upsilon)$ closer to the fraction of intrinsically-single sources. This is exemplified by the case of J0728+4005. Figure~\ref{fig:pred} shows the positions of the counter-images predicted from the model grid for this galaxy, colour-coded by $\Upsilon$, and the suggested arrangement of three GMOS IFU fields, as used in our $f_{\rm lim}$\,=\,0.1 calculation in Figure~\ref{fig:unlens_m}. Taken together, these strategies offer a promising route to speed up the hitherto laborious task of enlarging the sample of low-redshift lenses, with the aim of deriving secure and robust limits on variation in the IMF mass excess factor in massive early-type galaxies. In future work, we will present a combined analysis of multiple- and single-image systems from ongoing observational programmes, including a more rigorous treatment of the conversion between $\Upsilon$ and $\alpha$. \begin{figure} \includegraphics[width=80mm,angle=270]{pred.eps} \vskip 2mm \caption{Predicted counter-image locations from the lensing model grid, as a function of the stellar mass-to-light ratio, $\Upsilon$, for a deep observation of J0728+4005, with $f_{\rm lim}$\,=\,0.1 (see Figure~\ref{fig:unlens_m}). The `test image' (the position of the detected image of the background emitter) is shown by the black cross. The 5$\times$7\,arcsec$^2$ rectangles indicate hypothetical future Gemini/GMOS IFU observations motivated by our analysis.} \label{fig:pred} \end{figure} | 18 | 8 | 1808.08235 |
1808 | 1808.04531_arXiv.txt | The occurence rate of tidal disruption events (TDEs) by survey missions depend on the black hole mass function of the galaxies, properties of the stellar cusp and mass of the central black hole. Using a power law density profile with Kroupa mass function, we solve the steady state Fokker-Planck to calculate the theoretical capture rate of stars by the black hole. Using a steady accretion model, the Schechter black hole mass function (BHMF) and the cosmological parameters, we calculate the detection rate of TDEs for various surveys which is then fit with the observed TDE rates to extract the Schechter parameters. The rate tension between observation ($\sim 10^{-5}~{\rm yr^{-1}}$) and theory ($\sim 10^{-4}~{\rm yr^{-1}}$) for individual galaxies is explained by the statistical average over the BHMF. | A star orbiting close to the black hole such that the black hole's tidal gravity exceeds the star's self-gravity is tidally disrupted at the pericenter $r_p \leq r_t$, where $r_{t}= (M_{\bullet}/M_{\star})^{1/3} R_{\star}$ is the tidal radius and is called as tidal disruption events (TDEs) [Rees 1998]. The physical parameters crucial for the study of TDEs are the black hole (BH) mass $M_{\bullet}$, specific orbital energy $E$ and angular momentum $J$, star mass $M_{\star}$ and radius $R_{\star}$. For a stellar density $\rho(r) \propto r^{-\gamma}$ in the galactic center and the mass function $\xi(m)$ given by \cite[Kroupa (2001)]{Kroupa_2001}, \cite[Mageshwaran \& Mangalam (2015)]{Mageshwaran_2015} (hereafter MM15) solved the steady state Fokker-Planck equation (\cite[Merritt 2013]{Merritt_2013}) to obtain the capture rate $\dot{N}_t \propto M_{\bullet}^{-0.3}$. We use TDEs as a probe to derive the BHMF from observed detection rate for various surveys. \cite[Milosavljevi{\'c} \etal\ (2006)]{Milosa_2006} have showed that TDEs makes a negligible contribution at the higher end of luminosity functions. \cite[Stone \& Metzger (2016)]{Stone_2016} using the Schechter luminosity function showed that the volumetric rate of TDE detection is sensitive to the occupation fraction of low-mass black holes. \cite[Van Velzen (2018)]{Velzen_2018} using optical/UV selected TDEs and forward modeling showed that luminosity function $\propto L^{-2.5}$. \vspace{-0.5cm} | 18 | 8 | 1808.04531 |
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1808 | 1808.01778_arXiv.txt | Using an axisymmetric numerical code, we perform an extensive study of the magnetic field configurations in non-rotating neutron stars, varying the mass, magnetic field strength and the equation of state. We find that the monopolar (spherically symmetric) part of the norm of the magnetic field can be described by a single profile, that we fit by a simple eighth-order polynomial, as a function of the star's radius. This new generic profile applies remarkably well to all magnetized neutron star configurations built on hadronic equations of state. We then apply this profile to build magnetized neutron stars in spherical symmetry, using a modified Tolman-Oppenheimer-Volkov (TOV) system of equations. This new formalism produces slightly better results in terms of mass-radius diagrams than previous attempts to add magnetic terms to these equations. However, we show that such approaches are less accurate than usual, non-magnetized TOV models, and that consistent models must depart from spherical symmetry. Thus, our ``universal'' magnetic field profile is intended to serve as a tool for nuclear physicists to obtain estimates of magnetic field inside neutron stars, as a function of radial depth, in order to deduce its influence on composition and related properties. It possesses the advantage of being based on magnetic field distributions from realistic self-consistent computations, which are solutions of Maxwell's equations. | \label{s:intro} The macroscopic structure and observable astrophysical properties of neutron stars depend crucially on its internal composition and thus the properties of dense matter. The Equation of State (EoS) determines global quantities such as observed mass and radius. Transport properties such as thermal conductivity and bulk viscosity have an effect on cooling observations as well as emission of gravitational waves. As we enter an era of multi-messenger astronomy, it is crucial to construct consistent microscopic and macroscopic models in order to correctly interpret astrophysical observations. There are a large number of astrophysical observations, \textit{e.g.} soft-gamma repeaters (SGR) or anomalous X-ray pulsars (AXP), that indicate the existence of ultra-magnetized neutron stars or magnetars~\cite{kaspi-17}. While such observations only probe the surface magnetic field, there is no way to measure directly the maximum magnetic field in the interior. Using the simple virial theorem, one may estimate the maximum interior magnetic field to be as high as $10^{18}$~G. If such large fields exist in the interior, they may strongly affect the energy of the charged particles by confining their motion to quantized Landau levels and consequently modify the particle population, transport properties as well as the global structure \cite{avancini-18, tolos-17, franzon-16b, franzon-16, gomes-18, gomes-17b, gomes-17, gomes-14, gomes-13, dexheimer-12, dexheimer-14, wei-17b, wei-17}. However, it is necessary to know the magnetic field amplitude at a given location in the star, \textit{i.e.} a magnetic field distribution, in order to determine its effect on the internal composition and EoS. The ideal way to tackle that problem would of course be to self-consistently solve the neutron star structure equations endowed with a magnetic field, \textit{i.e.} combined Einstein, Maxwell and equilibrium equations, together with a magnetic field dependent EoS, as done by Chatterjee et al.~\cite{chatterjee-15}. This solution is complicated by the fact that in presence of a magnetic field, the neutron star structure strongly deviates from spherical symmetry and the spherically symmetric Tolman-Oppenheimer-Volkov (TOV) equations are no longer applicable for obtaining the macroscopic structure of a the neutron star \cite{bocquet-95,chatterjee-15, dexheimer-17c}. For small magnetic fields, perturbative solutions have been developed~\cite{konno-99}, but can no longer be applied for field strengths which might influence matter properties. There have been several attempts to determine neutron star structure assuming an \textit{ad hoc} profile of the magnetic field, without solving Maxwell's equations, within the TOV system (see \textit{e.g.}~\cite{casali-14, sotani-17, chu-18}). To that end, many authors employ the parameterization introduced twenty years ago by Bandyopadhyay et al. \cite{bandyopadhyay-97}, where the variation of the magnetic field norm $B$ with baryon number density $n_B$ from the centre $B_c$ to the surface $B_s$ of the star is given by the form \begin{equation} B (n_B/n_0) = B_s + B_c [1 - \exp( - \beta (n_B/n_0)^{\gamma})]~, \label{eq:bprofile1} \end{equation} with two parameters $\beta$ and $\gamma$, chosen to obtain the desired values of the maximum field at the centre and at the surface. This is an arbitrary profile, which possesses the same symmetries as the baryon density distribution in the star. Parameters $\left( \beta, \gamma \right)$ are chosen such that the surface field is consistent with observations and the maximum field prevailing at the center conforms to the virial theorem. Lopes and Menezes \cite{lopes-15} later introduced a variable magnetic field, which depends on the energy density rather than on the baryon number density: \begin{equation} B = B_c \left( \frac{\epsilon_M}{\epsilon_0} \right)^{\gamma} + B_s~, \label{eq:bprofile2} \end{equation} where $\epsilon_M$ is the energy-density of the matter alone, $\epsilon_0$ is the central energy density of the maximum mass non-magnetic neutron star and a parameter $\gamma> 0$, arguing that this formalism reduces the number of free parameters from two to one. The authors put forward as additional motivation the fact that it is the energy density and not the number density that is relevant in TOV equations for structure calculations. To account for anisotropy in the shear stress tensor, they applied the above field profile in a formalism~\cite{bednarek-03}, where the different elements containing the pressure are ``averaged'', leading to shear stress tensor of the form diag($B^2/24\pi, B^2/24\pi, B^2/24\pi$) \cite{dexheimer-12, menezes-16}. Nevertheless, this approach within the TOV system is still spherically symmetric and the parameter $\gamma$ not related to any experimental or observational constraint. There have also been suggestions of the magnetic field profile being a function of the baryon chemical potential \cite{dexheimer-12} as: \begin{equation} B(\mu_B) = B_s + B_c \left[ 1-\exp(b \frac{(\mu_B-938)^a}{938} ) \right]~, \end{equation} with $a=2.5$, $b=-4.08 \times 10^{-4}$ and $\mu_B$ given in MeV. In contrast to the profiles in Eqs.~(\ref{eq:bprofile1},\ref{eq:bprofile2}), such a formula avoids that a phase transition induces a discontinuity in the effective magnetic field. However, it was subsequently pointed out by Menezes and Alloy \cite{menezes-16b} that any of the above \textit{ad hoc} formulations for magnetic field profiles are physically incorrect since they do not satisfy Maxwell's equations. In particular, it is obvious that assuming such a magnetic field profile in a spherically symmetric star implies a purely monopolar magnetic vector field distribution, which is incorrect. The inconsistency of this type of approach can be seen, too, by inspecting the most general solution of the equations of hydrostatic equilibrium in general relativity for a spherically symmetric star. In Schwarzschild coordinates, $\left(\bar{t}, \bar{r}, \bar{\theta}, \bar{\varphi} \right)$, the line element reads: \begin{equation} \label{e:def_Schwarzschild} {\rm d}s^2 = -e^{-2\Phi}\, {\rm d}\bar{t}^2 + \left( 1 - \frac{2Gm}{\bar{r}} \right)^{-1}\hspace{-1em} {\rm d}\bar{r}^2 + \bar{r}^2 \left( {\rm d}\bar{\theta}^2 + \sin^2\bar{\theta} {\rm d}\bar{\varphi}^2 \right), \end{equation} where $m(\bar r)$ and $\Phi(\bar r)$ are the two relativistic gravitational potentials defining the metric (at the Newtonian limit, $m$ represents the total mass enclosed in the sphere of radius $\bar r$, and $\Phi / c^2$ becomes the Newtonian gravitational potential). The resulting coupled system of equations for the star's structure has been derived by Bowers and Liang~\cite{bowers-74} and reads \begin{eqnarray} \frac{dm}{d\bar r} &=& 4\pi \bar r^2 \varepsilon \nonumber\\ \frac{d\Phi}{d\bar r} &=& \left( 1 - \frac{2Gm}{\bar rc^2} \right)^{-1} \left( \frac{Gm}{\bar r^2} + 4\pi G\frac{p_r}{c^2}\bar r \right) \nonumber\\ \frac{dp_r}{d\bar r} &=& -\left(\varepsilon + \frac{p_r}{c^2} \right) \frac{d\Phi}{d\bar r} + \frac{2}{\bar r} (p_\perp - p_r) ~, \label{eq:bowers} \end{eqnarray} with an energy-momentum tensor of the form $T^{\mu\nu} = \mathrm{diag}(\varepsilon, p_r, p_\perp,p_\perp)$, where $p_r$ and $p_{\perp}$ are the radial and tangential pressure components. This is the most general energy-momentum tensor one can use assuming spherical symmetry and it goes beyond the perfect-fluid model, for which $p_r = p_\perp$. One may be tempted to cast a general electromagnetic energy-momentum tensor assuming a perfect conductor and isotropic matter, and for a magnetic field pointing in $z$-direction (see \textit{e.g.}~\cite{chatterjee-15}) into this form. However, in the case of the electromagnetic energy-momentum tensor $T^{\theta\theta} \neq T^{\phi\phi}$ (look at Eqs.~(23d)-(23e) of~\cite{chatterjee-15}), in clear contradiction with the assumption of Bowers and Liang~(\ref{eq:bowers}) in spherical symmetry. Another problem arises from the fact that $\lim_{r\to 0} (T^{rr} - T^{\theta\theta}) \not= 0$ and thus, the last term in Eq.~(\ref{eq:bowers}) diverges at the origin (from the first line in this equation, one sees that the quantity $m(\bar r)\sim \bar r^3$ and therefore $m/\bar r^2$ does not diverge). This discussion shows that there cannot be any correct description of the magnetic field in spherical symmetry. Starting from two-dimensional numerical models, Dexheimer \textit{et al.}~\cite{dexheimer-17b,dexheimer-17} performed a fit to the shapes of the magnetic field profiles following the stellar polar direction as a function of the chemical potentials (as in \cite{dexheimer-12}) by quadratic polynomials instead of exponential ones as \begin{equation} B(\mu_B) = \frac{(a+b\mu_B + c\mu_B^2)}{B_c^2} \mu ~, \end{equation} where $a,b,c$ are coefficients determined from the numerical fit. Unfortunately, no check of the validity of this fit has been shown in these works for other directions. In Ref.~\cite{mallick}, a density dependent profile is applied within a perturbative axisymmetric approach à la Hartle and Thorne~\cite{hartle-68}, but without solving Maxwell's equations. It remains, however, that the star's deformation due to the magnetic field implies that such a density (or equivalent) dependent profile depends on the direction, thus will be different looking \textit{e.g.} in the polar or the equatorial direction. In view of all these intrinsic difficulties, we will not propose here a simple scheme for solving structure equations of magnetized stars -- to that end we refer to the publicly available numerical codes assuming {\em axial\/} symmetry~\cite{chatterjee-15,xns}. Instead, since in many cases it might be sufficient to have an idea of the order of the value of the magnetic field strength to test its potential effect on matter properties, our aim is to provide a ``universal'' magnetic field strength profile from the surface to the interior obtained from the field distribution in a fully self-consistent numerical calculation from one of these codes. Further, we probe the applicability of this profile for determining the structure of magnetized neutron stars in an approximate way in spherical symmetry compared with full numerical structure calculations. As we will show, qualitatively the correct tendency can be reproduced for some NS properties, but to reproduce quantitatively correct results, the full solution has to be applied. The paper is organized as follows. Sec.~\ref{s:formalism} describes our physical models, including the EoSs we use in this manuscript, together with the numerical techniques applied to solve the models. Sec.~\ref{s:results} provides the magnetic field profiles derived numerically by varying certain physical parameters, to achieve a generic profile for the monopolar part of the norm of the magnetic field. This profile is then applied in Sec.~\ref{s:TOV} to a modified TOV system, to see its effect on NS masses and radii. Finally, Sec.~\ref{s:conc} gives a summary of our work, together with some concluding remarks. | \label{s:conc} Many attempts can be found in the literature trying to study strongly magnetized neutron stars and to include magnetic field effects on the matter properties. As mentioned in the introduction, most of these investigations suffer from different assumptions and approximations motivated by the complexity of the full system of equations. First, in order to avoid solving Maxwell's equations in addition to equilibrium and Einstein equations, often an \textit{ad hoc} profile for the magnetic field is assumed, which has no physical motivation. Second, spherical symmetry is assumed for modelling the star. In this work, we tackle the first point: we proposed a ``universal'' parameterization of the magnetic field profile (Eq.~\ref{eq:bprofile}) as a function of dimensionless stellar radius, obtained from a full numerical calculation of the magnetic field distribution. We tested this profile against several realistic hadronic EoSs, based on completely different approaches, and with different magnetic field strengths in order to confirm its universality. For the case of quark matter EoSs, preliminary investigations showed that although MIT bag models conform to the universality, other quark matter EoSs may not necessarily do so. The profile is intended to serve as a tool for nuclear physicists for practical purposes, namely to obtain an estimate of the maximum field strength as a function of radial depth, within the error bars observed in our study, \textit{e.g.} in Fig.~(\ref{f:uprof}), in order to deduce the composition and related properties. We applied the proposed magnetic field profile in a modified TOV-like system of equations, that include the contribution of magnetic field to the energy density and pressure, and account for the anisotropy by introducing a Lorentz force term. Compared with full numerical structure calculations, we find that qualitatively the correct tendency is reproduced and quantitatively the agreement is acceptable for large masses and small magnetic fields ($b_c \lesssim 10^{17}$~G). However, we find that the standard TOV system with no magnetic field reproduces much better mass-radius relations, even for strong magnetic fields, than any modified TOV system, with poorly defined magnetic corrections. This is mostly due to the fact that the mean radius is only marginally changed by the magnetic field. We thus think that future studies should employ the profile proposed here to conclude about the importance of magnetic field effects on matter properties, and use TOV system at $B=0$ for calculating mass-radius diagrams. For any other property of magnetized stars, we can only recommend the use of a full axisymmetric numerical solution for modelling magnetized neutron stars. | 18 | 8 | 1808.01778 |
1808 | 1808.06472_arXiv.txt | \noindent Traditional computations of the dark matter (DM) relic abundance, for models where attractive self-interactions are mediated by light force-carriers and bound states exist, rely on the solution of a coupled system of classical on-shell Boltzmann equations. This idealized description misses important thermal effects caused by the tight coupling among force-carriers and other charged relativistic species potentially present during the chemical decoupling process. We develop for the first time a comprehensive ab-initio derivation for the description of DM long-range interactions in the presence of a hot and dense plasma background directly from non-equilibrium quantum field theory. Our results clarify a few conceptional aspects of the derivation and show that under certain conditions the finite temperature effects can lead to sizable modifications of DM Sommerfeld-enhanced annihilation and bound-state decay rates. In particular, the scattering and bound states get strongly mixed in the thermal plasma environment, representing a characteristic difference from a pure vacuum theory computation. The main result of this work is a novel differential equation for the DM number density, written down in a form which is manifestly independent under the choice of what one would interpret as a bound or a scattering state at finite temperature. The collision term, unifying the description of annihilation and bound-state decay, turns out to have in general a non-quadratic dependence on the DM number density. This generalizes the form of the conventional Lee-Weinberg equation which is typically adopted to describe the freeze-out process. We prove that our % number density equation is consistent with previous literature results under certain limits. In the limit of vanishing finite temperature corrections our central equation is fully compatible with the classical on-shell Boltzmann equation treatment. So far, finite temperature corrected annihilation rates for long-range force systems have been estimated from a method relying on linear response theory. We prove consistency between the latter and our method in the linear regime close to chemical equilibrium. | \label{sec:intro} The cosmological standard model successfully describes the evolution of the large-scale structure of our Universe. It requires the existence of a cold and collisionless matter component, called dark matter (DM), which dominates over the baryon content in the matter dominated era of our Universe. The Planck satellite measurements of the Cosmic Microwave Background (CMB) temperature anisotropies have nowadays determined the amount of dark matter to an unprecedented precision, reaching the level of sub-percentage accuracy in the observational determination of the abundance when combining CMB and external data \cite{Ade:2015xua, Aghanim:2018eyx}, e.g.\ measurements of the baryon acoustic oscillation. Interestingly, astrophysical observation and structure formation on sub-galactic scales might point towards the nature of dark matter as velocity-dependent self-interacting elementary particles. On the one hand, observations of galaxy cluster systems, where typical rotational velocities are of the order $v_0 \sim 1000 \; \text{km}/\text{s} $, set the most stringent bounds on the self-scattering cross section to be less than $\sigma/m_{\text{DM}} \lesssim 0.7 \;(0.1) \;\text{cm}^2/\text{g}$ in the bullet cluster \cite{Randall:2007ph} (in order to guarantee the production of elliptical halos \cite{MiraldaEscude:2000qt, Peter:2012jh}). On the other hand, a DM self-scattering cross section of the order $\sigma/m_{\text{DM}} \sim 1 \;\text{cm}^2/\text{g}$ on dwarf-galactic scales, where velocities are of the order $v_0 \sim 30-100 \; \text{km}/\text{s} $, would lead to a compelling solution of the cusp-core and diversity problem without strongly relying on uncertain assumptions of modelling the barionic feedbacks in simulations. This velocity-dependence of the self-scattering cross section can naturally be realized in models where a light mediator acts as a long-range force between the dark matter particles. For a recent review on self-interacting DM, see \cite{Tulin:2017ara}. Generically, long-range forces can lead to sizable modifications of the DM tree-level annihilation cross section in the regime where the annihilating particles are slow. For the most appealing DM candidates, known as WIMP Dark Matter~\cite{Lee:1977ua, Ellis:1983ew, Arcadi:2017kky}, such that the relic abundance in the Early Universe is set by the thermal freeze-out mechanism when the DM is non-relativistic, these effects can be sizable already at the time of chemical decoupling. Then the inclusion of the long-range force modification in the computation of the relic abundance is necessary to reach the required level of the accuracy set by the Planck precision measurement \cite{Ade:2015xua, Aghanim:2018eyx}. If the light mediators induce an attractive force between the annihilating DM particles, the total cross section is typically enhanced~\cite{Hisano:2003ec, Hisano:2006nn} which is often referred as the \emph{Sommerfeld enhancement} \cite{doi:10.1002/andp.19314030302} or \emph{Sakharov enhancement} \cite{Sakharov:1948yq}. Additionally, such attractive forces can lead to the existence of DM \emph{bound-state} solutions~\cite{Pospelov:2008jd,MarchRussell:2008tu,Shepherd:2009sa}. This opens the possibility for conversion processes between scattering and bound states via radiative processes, influencing the evolution of the abundance of the stable scattering states during the DM thermal history. DM scenarios with Sommerfeld enhancement or with bound states have been widely studied in the literature~\cite{Belotsky:2004st, ArkaniHamed:2008qn, Slatyer:2009vg, Feng:2010zp, vonHarling:2014kha, Petraki:2015hla, An:2016gad,Asadi:2016ybp,Johnson:2016sjs, Hryczuk:2010zi, Beneke:2016ync, Freitas:2007sa, Hryczuk:2011tq, Harigaya:2014dwa, Harz:2014gaa, Beneke:2014gja, Ellis:2015vna, Kim:2016kxt, ElHedri:2016onc, Liew:2016hqo, Mitridate:2017izz, Harz:2018csl, Petraki:2016cnz, Harz:2017dlj, Cirelli:2007xd, MarchRussell:2008yu, Hisano:2004ds, Cirelli:2008id,Cirelli:2016rnw, Fan:2013faa, Bhattacherjee:2014dya, Ibe:2015tma, Beneke:2016jpw, Berger:2008ti, Blum:2016nrz, Biondini:2017ufr, Biondini:2018pwp, Biondini:2018xor} and it has been shown that the main effect of such corrections is to shift in the parameter space the upper bounds on the DM mass, otherwise the theoretically predicted DM density would be too large (overclosure bound). Classic WIMP candidates with large corrections via Sommerfeld enhancement or bound states are particles charged under the electroweak interactions, like the Wino neutralino in supersymmetric models~\cite{Jungman:1995df} or the first Kaluza-Klein excitation of the gauge boson in models with extra dimensions~\cite{Servant:2002aq}. For the supersymmetric case it was realized very early on by \cite{Hisano:2003ec, Hisano:2006nn} that the Sommerfeld effect reduces the Wino density up to 30~\% and pushes the mass of Wino Dark Matter candidate to few TeVs in order to obtain the correct relic density. These studies have later been extended to the case of general components of neutralino~\cite{Hryczuk:2010zi, Beneke:2016ync}. Similar and even stronger effects from the Sommerfeld enhancement and bound states were found in the case of coannihilation of the WIMP particle with charged or colored states \cite{Freitas:2007sa, Hryczuk:2011tq, Harigaya:2014dwa, Harz:2014gaa, Beneke:2014gja, Ellis:2015vna, Kim:2016kxt, ElHedri:2016onc, Liew:2016hqo, Mitridate:2017izz, Harz:2018csl}. If the electroweakly charged Dark Matter is sufficiently heavy, the Sommerfeld enhancement or the presence of bound states due to the exchange of electroweak gauge or Higgs bosons, see e.g.~\cite{Petraki:2016cnz,Harz:2017dlj}, are very generic as it was shown for example in the minimal Dark Matter model \cite{Cirelli:2007xd,Mitridate:2017izz} and in Higgs portal models~\cite{MarchRussell:2008yu}. In these cases, long-range force effects play an important role also for the indirect detection limits~\cite{Hisano:2004ds, Cirelli:2008id, Pospelov:2008jd,MarchRussell:2008tu,Cirelli:2016rnw} and especially for the Wino the Sommerfeld enhancement has lead to the exclusion of most parameter space~\cite{Fan:2013faa, Bhattacherjee:2014dya, Ibe:2015tma, Beneke:2016jpw}. Note that this effect can be important also when the Dark Matter is not itself a WIMP, but it is produced by WIMP decay out-of-equilibrium, like in the SuperWIMP mechanism \cite{Covi:1999ty, Feng:2003xh}. Indeed in such scenario, the DM inherits part of the energy density of the mother particle and so any change in the latter freeze-out density is directly transferred to the superweakly interacting DM and can relax the BBN constraints on the mother particle~\cite{Berger:2008ti}. While a lot of effort has been made to compute quantitatively the effects of a long-range force on the DM relic density employing the classical Boltzmann equation method, it is still unclear if that is a sufficient description. Indeed, considering the presence of a thermal plasma on the long-range force leads on one side to a possible screening by the presence of a thermal mass, on the other to the issue if the coherence in the (in principle infinite) ladder diagram exchanges between the two slowly moving annihilating particles is guaranteed. Moreover, from a conceptional point of view, there is yet no consistent formulation in the existing literature of how to deal with long-range forces \emph{at finite temperature}, especially if the dark matter is, or, enters an out-of-equilibrium state (already the standard freeze-out scenario is a transition from chemical equilibrium to out-of-chemical-equilibrium). The main concern of our work will be to clarify conceptional aspects of the derivation and the solution of the number density equation for DM particles with attractive long-range force interactions in the presence of a hot and dense plasma background, starting from first principles. From the beginning, we work in the \emph{real-time formalism}, which has a smooth connection to generic out-of-equilibrium phenomena. The simplified DM system we would like to describe in the presence of a thermal environment is similar to heavy quarks in a hot quark gluon plasma. For this setup it has been shown that finite temperature effects can lead to a melting of the heavy-quark bound states which influences, e.g.\ the annihilation rate of the heavy quark pair into dilepton \cite{Burnier:2007qm}. For DM or heavy quark systems, the Sommerfeld enhancement at finite temperature has been discussed in the literature, where the chemical equilibration rate is {\it i)} estimated from \emph{linear response theory}~\cite{Bodeker:2012zm, Kim:2016zyy, Kim:2016kxt} and {\it ii)} based on \emph{classical} rate arguments \cite{Bodeker:2012gs}, is then inserted into the \emph{non-linear} Boltzmann equation for the DM number density 'by hand'. Relying on those estimates, it has been shown that the overclosure bound of the DM mass can be strongly affected by the melting of bound states in a plasma environment \cite{Biondini:2017ufr, Biondini:2018pwp, Biondini:2018xor}. However, strictly speaking, the linear response theory method is only applicable if the system is close to chemical equilibrium. Indeed the computation has been done in the \emph{imaginary-time formalism} so far, capturing the physics of thermal equilibrium. One of our goals is to obtain a more general result directly from the \emph{real-time} formalism, valid as well for systems way out of equilibrium. Most of the necessary basics of the real-time method we use are provided in Section \ref{sec:rtf} as a short review of out-of-equilibrium Quantum Field Theory. Within this mathematical framework, an exact expression for the DM number density equation of our system is derived in Section \ref{sec:eoms}, where the Sommerfeld-enhanced annihilation or decay rate at finite temperature can be computed from a certain component of a four-point correlation function. We derive the equation of motion for the four-point correlation function on the real-time contour in Section \ref{sec:closedequations} which becomes in its truncated form a Bethe-Salpeter type of equation. Since we close the correlation functions hierarchy by truncation, the system of coupled equations we have to solve contains only terms with DM two- and four-point functions. In Section \ref{sec:solutions}, we derive a simple semi-analytical solution of the four-point correlator under certain assumptions valid for WIMP-like freeze-outs. Our result does not rely on linear response theory and it is therefore quite general applying also in case of large deviations from chemical equilibrium. The limit of vanishing finite temperature corrections is taken in Section~\ref{sec:vacuum}, showing the consistency between our general results and the classical Boltzmann equation treatment. Here, we also compare to the linear response theory method and clarify the assumptions needed to reproduce those results. Our main numerical results for the finite temperature case are given in Section~\ref{sec:finitetemp}, both for a gauge theory and for a Yukawa potential, and discussed in detail in Section \ref{sec:discussion}. Finally, we conclude in Section \ref{sec:conclusion}. | \label{sec:conclusion} Traditional computations of DM Sommerfeld-enhanced annihilation and bound-state decay rates rely on the assumption that reactions of such processes are taking place under perfect vacuum conditions. In this work we developed a comprehensive derivation of a more general description, taking into account non-ideal contributions arising from simultaneous interactions with the hot and dense plasma environment in the early Universe. We have derived the evolution equation for the DM number density which is applicable to the case where scattering and bound states get strongly mixed due to the influence of the thermal plasma surrounding. Our master Eq.~(\ref{eq:numbergrandcanonicalgeneral}) for the total DM density simultaneously accounts for annihilation and bound-state decay and hence its collision term is in general not quadratic in the DM number density. We showed that finite temperature effects can lead to strong modifications of the shape of the two-particle spectrum, which in turn modifies the DM annihilation or decay rates. The Keldysh formalism we adopted throughout this work applies for the description of the dynamics of generic out-of-equilibrium states. Within this mathematical framework, we derived in the first part of this work directly from our nonrelativistic effective action the exact equation of motion of the DM two-point correlation functions. We extracted for the first time from those EoM the differential equation for the DM number density [see Eq.~(\ref{eq:numberp}) and (\ref{eq:numberantip})], which turns out to only depend on a special component of the DM four-point function on the Keldysh contour, namely $G^{++--}_{\eta \xi}$. Let us emphasize again that this equation for the number density is exact within our nonrelativistic effective action, however not closed since it depends on the solution of this four-point correlation function. The long-range force enhanced annihilations, the decay of bounded particles as well as the finite temperature corrections are all contained in the solution of this one single four-point correlator. In the second part of this work, we derived the EoM for the DM four-point function on the Keldysh contour. We developed the approximations needed in order to close the hierarchy of correlators but at the same time keep the resummation of Coulomb divergent ladder diagrams as well as the finite temperature corrections. Based on our approximation and resummation scheme, the final form of the equation for our target component $G^{++--}_{\eta \xi}$ is physically sound and maintains important relations like the KMS condition in equilibrium. The coupled system of equations is general enough to apply for the description of DM out-of-chemical equilibrium states. In the third part, we explored further approximations needed in order to obtain a simple solution to our target component and to reproduce from our general equations the results in the literature, based on different assumptions. So far existing literature has estimated transport coefficients from linear response theory and entered those into a non-linear Boltzmann equation by classical rate arguments \cite{Burnier:2007qm, Bodeker:2012gs,Biondini:2017ufr, Biondini:2018pwp, Biondini:2018xor, Bodeker:2012zm, Kim:2016zyy, Kim:2016kxt}. We have proven that our master Eq.~(\ref{eq:numbergrandcanonicalgeneral}) is equivalent to the method of linear response only in the linear regime close to chemical equilibrium. Finally, we must point out that the Lee-Weinberg equation, adopted in \cite{Kim:2016zyy, Kim:2016kxt, Biondini:2017ufr, Biondini:2018pwp, Biondini:2018xor} to re-derive the DM overclosure bound in the non-linear regime, is not the correct form of the number density equation to use if bound-state solutions exist in the spectrum. The ionisation fraction causes the difference as discussed in great detail in our work. When taking the vacuum limit, our master equation reduces correctly to the coupled system of classical Boltzmann equations for ideal number densities of bound and scattering states \emph{in the limit of ionization equilibrium}. In our method, it came out as a consequence of assuming the system is in a grand canonical state. Namely, we have proven that the assumption of a grand canonical state automatically implies the Saha ionization equilibrium if bound-state solution exist. One has to take the assumption of ionization equilibrium to be fulfilled for all times with a grain of salt for the following reason. From the vacuum treatment it is known that the duration of Saha ionization equilibrium is limited. Therefore, when using our Master equation one has to carefully check that this condition is satisfied for a sufficiently long period. And especially when the assumption of ionization equilibrium is not justified, one has to make sure that at least the abundance of the stable scattering states are not affected by out-of-ionization equilibrium effects which might be model dependent. The reason why in our Keldysh formalism we can not resolve this issue at the moment lies in one particular approximation, made from the beginning. Ultra-soft emissions and absorptions were dropped for simplicity. We leave the inclusion of those quantities for future work, but expect once they are included we can fully recover the general set of coupled classical Boltzmann equations in the vacuum limit of our (future) updated equations. Moreover, this would allow us to describe Sommerfeld-enhanced annihilation and bound-state decay at finite temperature for the first time beyond the ionization equilibrium. In the regime where ionization equilibrium is maintained, we have shown that finite temperature effects strongly mix bound and scattering states and the effects are all encoded in the solution of the two-particle spectral function. Let us remark that the numerical results for the spectral function obtained in Section \ref{sec:finitetemp} are compatible with the linear response theory approach \cite{Burnier:2007qm, Bodeker:2012gs,Biondini:2017ufr, Biondini:2018pwp, Biondini:2018xor, Bodeker:2012zm, Kim:2016zyy, Kim:2016kxt}, although we started from a completely different method. The component $G_{\eta \xi,s}^{++--}\big|_{\text{eq}}$ in our master Eq.~(\ref{eq:numbergrandcanonicalgeneral}) can be enhanced by much more than $10 \%$. In addition, our master equation is applicable to the non-linear regime beyond the limitation of linear response if, at least, the ionization equilibrium is maintained. These results make it definitely worthwhile to further generalize our Keldysh description in order to correctly describe the out-of-ionization equilibrium transition at late times by including contributions from the ultra-soft scale. | 18 | 8 | 1808.06472 |
1808 | 1808.09469_arXiv.txt | We present a detailed abundance analysis of the bright ($V =$~9.02), metal-poor ([Fe/H]~$= -$1.47~$\pm$~0.08) field red horizontal-branch star HD~222925, which was observed as part of an ongoing survey by the \textit{R}-Process Alliance. We calculate stellar parameters and derive abundances for 46~elements based on 901~lines examined in a high-resolution optical spectrum obtained using the Magellan Inamori Kyocera Echelle spectrograph. We detect 28 elements with 38~$\leq Z \leq$~90; their abundance pattern is a close match to the Solar \textit{r}-process component. The distinguishing characteristic of HD~222925 is an extreme enhancement of \textit{r}-process elements ([Eu/Fe]~$= +$1.33~$\pm$~0.08, [Ba/Eu]~$= -$0.78~$\pm$~0.10) in a moderately metal-poor star, so the abundance of \textit{r}-process elements is the highest ([Eu/H]~$= -$0.14~$\pm$~0.09) in any known \textit{r}-process-enhanced star. The abundance ratios among lighter ($Z \leq$~30) elements are typical for metal-poor stars, indicating that production of these elements was dominated by normal Type~II supernovae, with no discernible contributions from Type~Ia supernovae or asymptotic giant branch stars. The chemical and kinematic properties of HD~222925 suggest it formed in a low-mass dwarf galaxy, which was enriched by a high-yield \textit{r}-process event before being disrupted by interaction with the Milky Way. | 18 | 8 | 1808.09469 |
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1808 | 1808.00548_arXiv.txt | We study the observational signatures of two-form field in the inflationary cosmology. In our setup a two-form field is kinetically coupled to a spectator scalar field and generates sizable gravitational waves and smaller curvature perturbation. We find that the sourced gravitational waves have a distinct signature: they are always statistically anisotropic and their spherical moments are non-zero for hexadecapole and tetrahexacontapole, while the quadrupole moment vanishes. Since their amplitude can reach $\mathcal{O}(10^{-3})$ in the tensor-to-scalar ratio, we expect this novel prediction will be tested in the next generation of the CMB experiments. | The inflationary scenario elegantly explains the anisotropy of cosmic microwave background radiation (CMB) and the seed of the large scale structure in our universe. On top of them, it quantum-mechanically generates the fluctuations of spacetime, namely primordial gravitational waves, and imprints the B-mode polarization pattern in the CMB map. The detection of the primordial B-mode polarization originating from the inflationary universe is therefore one of the most important targets in cosmology. Its amplitude is parameterized by tensor-to-scalar ratio $r$ and recent joint collaboration of Planck and BICEP2/Keck array have constrained its amount as $r \lesssim 0.07$ \cite{Ade:2015lrj}. In the next decades, the sensitivity will increase up to $r \sim 10^{-3}$ by the appearance of LiteBIRD \cite{Matsumura:2013aja} and CMB-S4 \cite{Abazajian:2016yjj}. The energy scale probed by CMB observations is around the scale of grand unification theory $10^{16}\text{GeV}$, and thus we have a chance to obtain indispensable clues to develop the high energy physics such as GUT, supergravity or superstring through the detection of primordial gravitational waves. Conventionally primordial gravitational waves are considered to be provided by the vacuum fluctuation, whose power spectrum is almost scale invariant (slightly red-tilted) and statistically isotropic. However, these features are not necessarily true if the matter sector significantly contributes to the generation of gravitational waves in the early universe. In a reduced four-dimensional action of string theory, for instance, a dilatonic scalar sector is generically coupled to an one-form field (gauge field) or a two-form field through their kinetic functions. Once these couplings are introduced during inflation, the time variation of kinetic function can amplify the quanta of the form field on superhorizon scales. Among these couplings, the particle production of U(1) gauge field has been motivated to explain the presence of intergalactic magnetic field \cite{Ratra:1991bn,Martin:2007ue, Demozzi:2009fu, Kanno:2009ei,Durrer:2010mq, Fujita:2012rb, Fujita:2013pgp, Fujita:2014sna, Obata:2014qba, Fujita:2016qab,Caprini:2017vnn}. Furthermore, some models of inflation have been investigated in the framework of anisotropic inflation, where the inflaton is kinetically coupled to U(1) gauge field or two-form field~\cite{Watanabe:2009ct, Watanabe:2010fh, Kanno:2010nr, Watanabe:2010bu, Do:2011zza, Soda:2012zm, Bartolo:2012sd, Ohashi:2013qba, Ohashi:2013pca, Naruko:2014bxa, Abolhasani:2015cve, Ito:2016aai, Ito:2017bnn, Fujita:2017lfu, Ohashi:2013mka, Ito:2015sxj}. In these models the background form field naturally appears owing to the amplification on large scales and breaks the isotropy of universe. The broken rotational invariance caused by the presence of background form field allows the perturbation of form field to interact with other scalar or tensor perturbations at linear level. As a result, the power spectra of some observables can be statistically anisotropic due to the enhanced perturbation of the form fields. The generation of such statistical anisotropy was originally motivated to explain the quadrupole anisotropy of the temperature fluctuation in the WMAP data \cite{2010ApJ...722..452G}, while current Planck data has not observed this signal and implies that its amplitude should be small, if any~\cite{Kim:2013gka, Rubtsov:2014yua, Ade:2015lrj, Ramazanov:2016gjl}. It is interesting to note that a little attention was paid to the statistical anisotropy of the primordial gravitational waves so far, because its generation by the U(1) gauge field is slow-roll suppressed compared to that of the curvature perturbation in the original model \cite{Watanabe:2010fh} and it is not produced at all by the two form field~\cite{Ohashi:2013mka}. Recently, however, it has been found that sizable amount of statistically anisotropic gravitational waves can be provided in an extended model of anisotropic inflation \cite{Fujita:2018zbr}. In this scenario, a U(1) gauge field is coupled to a spectator scalar field which enables to avoid the overproduction of statistical anisotropy in the curvature perturbation. Furthermore, the mixing between the linear perturbations of the U(1) gauge field and the spectator field generates higher statistical anisotropies beyond quadrupole in the tensor power spectrum. This is a totally new prediction from the model of anisotropic inflation and incentivizes the observational search for the statistical anisotropy of the tensor perturbation. Hence, now it is time to revisit the case of two-form field and explore its new prediction in the extended scenario. In this work, we study a model of inflation where a two-form field kinetically coupled to a spectator scalar field. This situation allows the sizable mixing between the perturbations of the spectator scalar and the two-form field so that the amplified form field fluctuation sources that of the spectator field. Remarkably, we find that the sourced spectator field produces gravitational waves and finally generate statistically anisotropies in the tensor power spectrum. Intriguingly, the statistical anisotropies does not depend on the model parameters and higher harmonics beyond quadrupole moment are created. This paper is organized as follows. In section \ref{Model Action and Setup}, we explain our model and explore the time evolution of the background fields. In section \ref{Perturbation Dynamics}, we solve the linear perturbations of the two-form field and the spectator scalar field. The productions of the curvature perturbation and gravitational waves, in particular their statistical anisotropies, are studied in section \ref{Generation of Statistical Anisotropy}. The detectability of the prediction of our model is discussed in section \ref{Detectability}. Finally we present our conclusions in section \ref{Conclusion} with prospects for future work. | \label{Conclusion} In this study, we developed the phenomenology of anisotropic inflation with two-form field. More precisely, we studied the model of inflation where a two-form field is kinetically coupled to a spectator scalar field. As to the background dynamics of the spectator field, we considered the situation where it slowly rolls down at first and get stabilized at a certain time on its potential. Depending on the evolution of the form field, the background dynamics is separated into three phases: (i) growing phase, (ii) attractor phase and (iii) damping phase. During the growing phase, the energy density of background form field $\bar{\rho}_E$ is negligibly small but grows as $a^{2\Delta n}$ due to the time variation of kinetic function. Simultaneously, on superhorizon scales perturbation of form field $\bar{I}\delta B/a^2$ also amplifies as $a^{\Delta n}$ which sources that of spectator field $\delta\sigma$ growing up as $a^{2\Delta n}$. When the backreaction of $\bar{\rho}_E$ becomes significant, $\bar{\rho}_E$ get balanced to the kinetic energy of the spectator field and stays constant. At this attractor phase, $\bar{I}\delta B/a^2$ and $\delta\sigma$ also stop growing and get constant values whose ratio depends on the angle of wave number $\theta$. Finally, at the damping phase $\sigma$ starts to oscillate around the minimum of potential and $\bar{\rho}_E$ decays as $a^{-2}$. We solved above dynamics and derived the analytical expressions of background and perturbation both of which are confirmed through numerical calculations. The main prediction of this work is that the sourced $\delta\sigma$ generates the statistically anisotropic gravitational waves via the presence of the background form field. Interestingly, only one linear polarization mode couples to the scalar perturbation and the resultant power spectrum is linearly polarized. This feature is distinct from another inflationary models with gauge fields topologically coupled to scalar sectors \cite{Sorbo:2011rz, Cook:2011hg, Anber:2012du, Barnaby:2012xt, Dimastrogiovanni:2012ew, Adshead:2013qp, Mukohyama:2014gba, Obata:2014loa, Namba:2015gja, Obata:2016tmo, Domcke:2016bkh, Maleknejad:2016qjz, Guzzetti:2016mkm, Obata:2016xcr, Dimastrogiovanni:2016fuu, Adshead:2016omu, Garcia-Bellido:2016dkw, Obata:2016oym, Fujita:2017jwq, Thorne:2017jft, Ozsoy:2017blg, Agrawal:2018mrg}. Furthermore, we found that the resultant tensor power spectrum is written by the combination of angular functions $\cos^n\theta \ (n = 2, 4, 6)$ and the statistical anisotropy does not depend on any model parameters. Remarkably, the quadrupole moment vanishes at leading order and only higher harmonics appear. This result should be compared with the case of U(1) gauge field in our previous work \cite{Fujita:2018zbr} and can be an unique property from the phenomenology of inflation with two-form field. We estimated the detectability of the sourced gravitational waves. We derived several constraints on the parameters and show a viable example of parameter set where the amplitude of tensor power spectrum is detectable in near future. Since we have some concrete upcoming experiment such as LiteBIRD, it would be interesting to estimate the testable amplitude of the statistical anisotropy based on their realistic sensitivities~\cite{Hiramatsu:2018vfw}. We leave this issues for future work. | 18 | 8 | 1808.00548 |
1808 | 1808.10672_arXiv.txt | { Being observed only one billion years after the Big Bang, $z \sim 7$ quasars are a unique opportunity for exploring the early Universe. However, only two $z \sim 7$ quasars have been discovered in near-infrared surveys: the quasars ULAS J1120+0641 and ULAS J1342+0928 at $z = 7.09$ and $z = 7.54$, respectively. The rarity of these distant objects, combined with the difficulty of distinguishing them from the much more numerous population of Galactic low-mass stars, requires using efficient selection procedures. The Canada-France High-z Quasar Survey in the Near Infrared (CFHQSIR) has been carried out to search for $z \sim 7$ quasars using near-infrared and optical imaging from the Canada-France Hawaii Telescope (CFHT). Our data consist of $\rm{\sim 130\,deg^{2}}$ of Wide-field Infrared Camera (WIRCam) Y-band images up to a $5\,\sigma$ limit of $\rm{Y_{AB} \sim 22.4}$ distributed over the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) Wide fields. After follow-up observations in J band, a first photometric selection based on simple colour criteria led us to identify 36 sources with measured high-redshift quasar colours. However, we expect to detect only $\sim$ 2 quasars in the redshift range $6.8 < z < 7.5$ down to a rest-frame absolute magnitude of $\rm{M_{1450}} = -24.6$. With the motivation of ranking our high-redshift quasar candidates in the best possible way, we developed an advanced classification method based on Bayesian formalism in which we model the high-redshift quasars and low-mass star populations. The model includes the colour diversity of the two populations and the variation in space density of the low-mass stars with Galactic latitude, and it is combined with our observational data. For each candidate, we compute the probability of being a high-redshift quasar rather than a low-mass star. This results in a refined list of the most promising candidates. Our Bayesian selection procedure has proven to be a powerful technique for identifying the best candidates of any photometrically selected sample of objects, and it is easily extendable to other surveys.} | Quasars reside at the centres of active galactic nuclei (AGNs) and are believed to be powered by mass accretion onto a supermassive black hole (SMBH). Thanks to their strong intrinsic luminosity, quasars are bright enough \citep[$\rm{L\sim10^{14} L_{\odot}}$ for the most luminous quasar ever discovered at $z = 6.30$, ][]{Wu2015} to be detected at high redshifts, where they can be used to explore the early Universe. Along with other cosmological probes, high-redshift quasars (hereafter, "high-redshift" refers to redshifts $z \gtrsim 5.6$) have proved to be powerful tools for studying not only the epoch of cosmic reionisation \citep[e.g.][]{Fan2006, Jiang2008, Becker2015}, but also for investigating the formation and evolution of primordial SMBHs \citep[e.g.][]{Willott20102}. The relations between luminosity, black hole mass, and broad emission line velocity have been demonstrated at low redshifts by reverberation mapping studies \citep[e.g.][]{Kaspi2000, Vestergaard2002, Bentz2009}. Spectroscopy of high-redshift quasars (high-z quasars) can therefore be exploited in order to measure SMBHs masses, estimate their mass function, and place solid constraints on SMBH formation models, under the assumption that these local relations are still valid at high redshifts. Using this technique, it has been possible to confirm black holes with masses exceeding $\rm{M_{BH}} \gtrsim 10^{9} \rm{M_{\odot}}$ at redshifts $z \gtrsim 6$ \citep{Mortlock2011, Wu2015, Banados2018}. How such massive objects could have formed so quickly in less than 1 Gyr after the Big Bang is still a fundamental question arising from these discoveries \citep[see reviews by][]{Volonteri2010, Haiman2013, Smith2017}. Several scenarios for the formation of SMBHs seeds, including, for instance, remnants of Population III stars \citep[e.g.][]{Madau2001, Volonteri2003} or a direct collapse of gas in atomic cooling halos \citep[DCBH, e.g.][]{Visbal2014, Smidt2017} have been proposed, but they are widely debated, partly because known bright high-z quasars are likely to be the tip of an iceberg that is mainly composed of fainter quasars. The cosmic reionisation that ended the so-called dark ages during which the first sources of the Universe ionised the hydrogen in the intergalactic medium (IGM) is a major event in the Universe's history, and many questions related to the onset, duration, topology, and the sources responsible for this process remain unsolved. High-redshift quasars can be used as background sources whose UV radiation is absorbed at the resonant Lyman lines by intervening neutral hydrogen along the line of sight. Their spectra are therefore reliable tools for absorption studies since they show spectral signatures of the IGM state. The hydrogen neutral fraction $x_{HI}$ can indeed be determined by making a range of measurement on high-z quasar spectra, such as the Gunn-Peterson test \citep[e.g.][]{Gunn1965, Fan2006, Becker2015b}, near-zone measurement \citep[e.g.][]{Venemans2015, Mazzucchelli2017}, dark gaps and dark pixels statistics \citep[e.g.][]{McGreer2015}, and Lyman-$\alpha$ damping wing reconstruction \citep[e.g.][]{Greig2017}. Measurements of the quasar luminosity function (QLF) at $z\sim6$ have shown that the quasar ionising flux was not sufficient to keep the Universe ionised, with a photon rate density lower by between 20 and 100 times than required \citep{Willott2010}. Even though the faint end of the QLF remains poorly constrained, it is now generally agreed that AGNs do not contribute significantly to the required ionising photon budget at $z \sim 6$ \citep{Onoue2017}. \\ If there are compelling reasons to search for high-z quasars, the quest is no less challenging because of their rarity: \citet{Willott2010} predicted a number of quasars of the order of $\rm{\sim 0.1\,deg^{-2}}$ brighter than $\rm{H_{AB} \simeq 24}$ in the redshift range $6.5 < z < 7.5$. In the past few years, substantial progress has been made in this field, where more than 100 high-z quasars have been identified \citep{Banados2016}. Wide area surveys greatly contributed to this success, with surveys first carried out in optical bands, such as the Sloan Digital Sky Survey \citep[SDSS ]{York2000} and the Canada-France High-z Quasar Survey \citep[CFHQS;][]{Willott2005, Willott2007, Willott2009, Willott2010}, providing more than 50 quasars up to redshifts $z \simeq 6.4$. At higher redshifts, the Lyman-$\alpha$ emission line is shifted into the near-infrared (NIR) and becomes undetectable at observed wavelengths $\rm{\lambda_{obs}} \lesssim 0.9\,\rm{\mu} m$ because of IGM absorption; this makes the use of near-IR bands necessary. Ongoing near-IR surveys such as the United Kingdom Infrared Telescope (UKIRT) Infrared Deep Sky Survey \citep[UKIDSS; ][]{Lawrence2007}, the Visible and Infrared Survey Telescope for Astronomy (VISTA) Kilo-degree Infrared Galaxy\citep[VIKING; ][]{Emerson2004}, the Panoramic Survey Telescope \& Rapid Response System \citep[Pan-STARRS; ][]{Kaiser2010}, the Dark Energy Survey \citep[DES; ][]{DES2016}, the VISTA Hemisphere Survey \citep[VHS; ][]{McMahon2013}, and the Subaru HSC-SSP Survey with the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) project \citep{Miyazaki2012, Matsuoka2016} have started to increase the number of known $z \gtrsim 6.5$ quasars by employing filters centred on $\rm{1\,\mu m}$. The use of such data allowed \citet{Mortlock2011} to discover the previous redshift record holder, ULAS J1120+0641 at $z=7.09$, before it was superceded by ULAS J1342+0928 at $z=7.54,$ for which \citet{Banados2018} mined data from the UKIDSS Large Area Survey \citep{Lawrence2007}, the Wide-field Infrared Survey Explorer \citep[ALLWISE, ][]{Wright2010}, and the DECam Legacy Survey (DECaLS\footnote{\url{http://legacysurvey.org/decamls/}}). However, despite all these efforts, these two quasars are the only ones found at redshift $z > 7$ to date. The Canada-France High-z Quasar Survey in the Near Infrared (CFHQSIR) has been designed to find more $z \sim 7$ quasars that can be used to constrain the reionisation epoch as well as the initial growth of SMBHs. \\ The inevitable contamination of any photometric sample by Galactic low-mass stars (main-sequence stars and brown dwarfs) increases the difficulty of finding such rare objects. Colour-colour cuts are commonly used for high-z quasars searches to separate the two populations of sources \citep[e.g.][]{Willott2005, Venemans2013}. However, the photometric noise implies that the resulting candidate list is likely to be still dominated by low-mass stars, which are much more numerous than high-z quasars. Here we adopt a powerful classification technique that is based on Bayesian inference. It was first developed by \citet{Mortlock2012} but was also applied by \citet{Matsuoka2016}, who discovered 39 quasars in the redshift range $5.7 \leq z \leq 6.9$ \citep{Matsuoka2016, Matsuoka2018}. The technique allows assigning to each candidate a probability of being a high-z quasar rather than a low-mass star by combining all the information (observations and prior knowledge) available for each source in an optimal way. Although this approach has not been frequently used, it has proved to be a powerful method since \citet{Mortlock2011} successfully found the second most distant quasar at redshift $z = 7.09$. \\ This paper describes an improved method for searching for $z\sim 7$ quasars, and we report our initial results. In the next section we present the CFHQSIR data and our colour selection criteria. In Sect. \ref{sec3} we describe our photometric candidate selection and detail our Bayesian method of classifying candidates. Our spectroscopic observations and initial results are presented in Sect. \ref{secresults}. Section \ref{sec5} summarises these results and presents our conclusions. All magnitudes in the optical and near-IR bands in this paper are in the AB system. Cosmological parameters of $\rm{H_{0}} = 68$ \mbox{km s$^{-1}$ Mpc$^{-1}$}, $\rm{\Omega _{M} = 0.31}$ and $\rm{\Omega _{\Lambda} = 0.69}$ are assumed throughout \citep{Planck2016}. | \label{sec5} We have presented a complete method for selecting and classifying $z \sim 7$ quasar candidates using optical and NIR photometric data as part of the CFHQSIR survey. After visual inspection and removal of artefacts, we selected 228 candidates with red $\rm{z-Y}$ colours. The sample was eventually culled to 36 sources by considering candidates with $\rm{Y-J}$ colours consistent with being high-z quasars after NIR follow-up in J band. We extended and refined the Bayesian formalism developed by \citet{Mortlock2012} in order to improve our selection of high-z quasar candidates. This robust statistical approach allowed us to classify our candidates in the best possible way according to their probability of being a high-redshift quasar. Applying a Bayesian method is indeed very efficient to identify the most promising candidates in any photometrically selected sample since it allows combining the prior knowledge of the brown dwarf and quasar populations and the filter and noise properties of the observational data. Moreover, we demonstrated the importance of acquiring sufficiently precise photometric measurements to clearly determine the nature of the objects. \\ The application of the Bayesian formalism revealed a promising list of six candidates with a probability $\rm{P_{q}} > 0.1$. Only three of these have a chance higher than 60\% of being a high-z quasar. Even though one of them has been observed spectroscopically with the FORS2 instrument, we were unable to draw any conclusions about its nature because its spectral S/N is low. Our immediate goal is to complete the spectroscopic follow-up of our most promising candidates, according to their probability of being a high-z quasar. The full analysis of our search for $z \sim 7$ quasars will be reported in a future paper, including the analysis of our spectroscopic data. A non-detection indicates that the quasar density at $z \sim 7$ is at a 90\% and 75\% confidence level lower than the density inferred from the QLF of \citet{Willott2010} and \citet{Jiang2016}, respectively. Conversely, the discovery of one high-redshift quasar in CFHQSIR would be 23\% and 35\% consistent with the QLF of \citet{Willott2010} and \citet{Jiang2016}, respectively. \\ Our Bayesian method can be consolidated in several aspects, however. Early-type galaxies at $z \sim 2$ may appear compact at faint magnitudes and therefore represent a second source of contamination that would also need to be modelled precisely, in addition to the low-mass stars. \\ Furthermore, the brown dwarf population could be modelled more accurately by considering the stars from the Galactic thick disc and the halo, in addition to the thin disc. There is also further room for improvement concerning the local spatial density of brown dwarfs. Using observed spatial density measurements instead of model-predicted ones would be interesting \citep[see e.g.][]{Reyle2010, Kirkpatrick2011}. As the number of known ultracool dwarfs continues to rise, more precise estimates of their spatial densities will be essential ingredients of an improved Bayesian model. Our results may also be biased as they are based on a heterogeneous collection of L- and T-dwarf spectra coming from various surveys, provided by the SpeX Prism library. In particular, our fundamental assumption that the measured colours of these sources are representative of the colours of the L and T populations may no longer be valid when considering unresolved binaries and peculiar sources. The unusual colours of these rare sources, as well as the uncertainty in their spectral classification, can introduce an intrinsic scatter in the colours that is not taken into account in our model. Unresolved binaries can be an important source of uncertainty, as they could represent $\sim$ 40\% of the dwarf population \citep{Liu2006, Burgasser2007}. To finish, the newly discovered spectral type, the ultracool Y-dwarf class \citep[e.g. ][]{Cushing2011}, should also be included in our model, although these sources are likely to be too faint at our limiting magnitude to represent a real source of contamination.\\ Nevertheless, the Bayesian technique presented in this paper remains a powerful approach to efficiently prioritize high-z quasar candidates, and it is moreover easily adaptable to any other high-z object surveys, whether they are dedicated to the search for quasars or not (e.g. high-z galaxies in deep fields). This technique will be critical to the discovery of many more distant quasars by future NIR surveys such as the Euclid-wide imaging survey \citep{Laureijs2011} or the WFIRST High Latitude Survey \citep[HLS, ][]{Spergel2013}. Thanks to the high sensitivity of these upcoming surveys, high-z quasars will be identified in an unprecedented number. Scheduled to be launched in 2021 and in the mid-2020s, respectively the Euclid space mission is expected to discover $\sim$ 30 quasars at redshifts $z > 8.1$ with $J < 22.0$ over 18 000 $\rm{deg^{2}}$ , and WFIRST will find $\sim$ 500 $z \gtrsim 8$ quasars over 2\,000 $\rm{deg^{2}}$ above 10$\,\sigma$ \citep[mag $\approx$ 26 limit, ][]{Spergel2013}. \\ A great challenge for these high-depth surveys will be the increasing number of contamination sources. In addition to the L and T dwarfs, a significant number of Y dwarfs will be detected, and possibly free-floating planets as well \citep[see e.g.][for free-floating planets detected by microlensing]{Han2004}. The increased number of contamination populations will require careful modeling in Bayesian frameworks such as the one presented in this work. This will be an essential requirement for culling the number of high-z candidates from these surveys before spectroscopic observations with the Extremely Large Telescope (ELTs\footnote{\url{https://www.eso.org/sci/facilities/eelt/docs/E-ELTScienceCase_Lowres.pdf}}) or the James Webb Space Telescope \citep[JWST, ][]{Gardner2006} can be attempted. | 18 | 8 | 1808.10672 |
1808 | 1808.10028_arXiv.txt | Cosmic-ray electrons and positrons (CREs) at GeV-TeV energies are a unique probe of our local Galactic neighborhood. CREs lose energy rapidly via synchrotron radiation and inverse-Compton scattering processes while propagating within the Galaxy and these losses limit their propagation distance. For electrons with TeV energies, the limit is on the order of a kiloparsec. Within that distance there are only a few known astrophysical objects capable of accelerating electrons to such high energies. It is also possible that the CREs are the products of the annihilation or decay of heavy dark matter (DM) particles. VERITAS, an array of imaging air Cherenkov telescopes in southern Arizona, USA, is primarily utilized for gamma-ray astronomy, but also simultaneously collects CREs during all observations. We describe our methods of identifying CREs in VERITAS data and present an energy spectrum, extending from 300 GeV to 5 TeV, obtained from approximately 300 hours of observations. A single power-law fit is ruled out in VERITAS data. We find that the spectrum of CREs is consistent with a broken power law, with a break energy at 710 $\pm$ 40$_{stat}$ $\pm$ 140$_{syst}$ GeV. | } Despite constituting only a small fraction of the total cosmic-ray flux, cosmic-ray electrons and positrons (CREs) provide an important and unique probe of our local Galactic neighborhood. They rapidly lose energy while propagating in the Galaxy via synchrotron radiation and inverse-Compton scattering processes. This limits the propagation distance for TeV electrons to of order $\sim$1 kpc~\cite{COWSIK}~\cite{Grasso2009}~\cite{Pohl1998} and implies that CREs at TeV energies can provide constraints on local cosmic-ray accelerators and diffusion effects. The ${\it Fermi}$-LAT~\cite{LAT} collaboration and the AMS-02 collaboration~\cite{AMS}, have measured the CRE spectrum up to energies of $\sim$1 TeV. More recently, both the DAMPE~\cite{DAMPE} and CALET~\cite{CALET} collaborations have measured the CRE spectrum to a few TeV with excellent energy resolution. At higher energies these instruments run out of statistics due to the combination of the steep CRE spectrum and their relatively small acceptances. Ground-based imaging atmospheric Cherenkov telescopes (IACTs) can extend the CRE spectrum to higher energies due to their large collection areas ($\sim10^{5}$ m$^{2}$). H.E.S.S.~\cite{HESS1, HESS2} and MAGIC~\cite{MAGIC} have demonstrated this ability and have measured the CRE spectrum up to energies of several TeV. Their results agree with the space-based measurements, within systematic uncertainties, in the energy range where the sensitivities overlap. The combined picture that has emerged is one where the CRE spectrum can be described by a simple power law from $\sim$10 GeV up to just below $\sim$1 TeV. At higher energy H.E.S.S. sees a spectral steepening\footnotemark[1] while MAGIC data are consistent with a single power law up to $\sim$3 TeV, although with larger statistical uncertainties. The DAMPE and CALET data also see a break in the CRE spectrum at $\sim$1 TeV~\cite{CALET}~\cite{DAMPE}. \footnotetext[1]{The H.E.S.S. collaboration has recently reported preliminary results, obtained with higher statistics over an extended energy range, which support this trend.} The inclusive CRE spectrum is understood to have contributions from both electrons and positrons and some instruments are able to separate the two components. The energy dependence of the positron fraction, $e^+/(e^+ + e^-)$, has been measured for energies greater than 10 GeV by the HEAT~\cite{HEAT}, PAMELA~\cite{PAM}, {\it Fermi}-LAT~\cite{LATfrac}, and AMS-02~\cite{AMSfrac} collaborations. The fraction is found to rise with increasing energy up to $\sim$200 GeV, above which it appears to flatten out. Positrons are believed to be produced mainly in interactions between cosmic rays and interstellar gas and this results in a positron fraction that decreases with energy. The unexpected increase could imply the existence of additional local sources such as pulsars or supernovae remnants. A more exotic explanation for the excess would be the annihilation or decay of DM particles. More conventional methods such as an improved propagation model~\cite{prop} or a better accounting of secondary production might explain the results. A full understanding of this situation will require detailed input about both the positron fraction and the CRE spectrum. Given that the CRE spectrum, including its behavior at TeV energies, is such an integral component, it is important for all instruments capable of making such measurements to contribute. | } CRE results shown here are consistent with prior ground-based and space-borne measurements at similar energies. This result represents the second ground-based, high-statistics measurement of a break in the CRE spectrum around $\sim$1 TeV, seen by H.E.S.S., CALET and DAMPE, but not seen by MAGIC or {\it Fermi}- LAT. The precise value of this break energy is an important parameter in any successful model of our local CRE environment. Based on the fit of the CRE spectrum in the previous section, two power laws with a break between the indices best describes the data. However, a power law with an exponential cutoff is not completely ruled out. A single power law is ruled out by the VERITAS data. Several different sources in our local neighborhood have been speculated as the accelerators of electrons at TeV energies, including supernova remnants and pulsars. The decay or annihilation of WIMP DM has also been proposed as the dominant source of CREs and a reason for the positron fraction rising with energy, \cite{Bertone2005} but it is currently not possible to discriminate dark matter models from other sources with the available data \cite{Grasso2009}. Nearby pulsars with distances less than 1 kpc may also be sources of relativistic electrons and positrons \cite{COWSIK}\cite{Pohl1998}. Because of synchrotron and inverse-Compton energy losses, the age of TeV electrons is $\sim$10$^5$ years, and decreases with increasing energy. Very few of the know pulsars are capable of accelerating electrons to TeV-scale energies, namely Geminga, Monogem and a handful of others. Breaks in the spectrum at TeV energies are expected as the number of astrophysical sources capable of accelerating CREs to those energies decreases \cite{Grasso2009}. Refined measurements of CRE spectra from IACTs, including VERITAS and the upcoming CTA observatory \cite{CTA}, should help with understanding the number and distribution of sources capable of accelerating CREs to TeV-scale energies. | 18 | 8 | 1808.10028 |
1808 | 1808.00901_arXiv.txt | A measurement of the history of cosmic star formation is central to understand the origin and evolution of galaxies. The measurement is extremely challenging using electromagnetic radiation: significant modeling is required to convert luminosity to mass, and to properly account for dust attenuation, for example. Here we show how detections of gravitational waves from inspiraling binary black holes made by proposed third-generation detectors can be used to measure the star formation rate of massive stars with high precision up to redshifts of \si 10. Depending on the time-delay model, the predicted detection rates ranges from $\sim \NoneMonthSlow$ to $\sim \NoneMonthPrompt$ per month with the current measurement of local merger rate density. With three months of observations, parameters describing the volumetric star formation rate can be constrained at the few percent level, and the volumetric merger rate can be directly measured to 3\% at $z\sim 2$. Given a parameterized star formation rate, the characteristic delay time between binary formation and merger can be measured to $\sim 60\%$. | The binary black holes (BBHs) detected by the ground-based gravitational-wave (GW) detectors LIGO~\citep{Harry:2010zz} and Virgo~\citep{TheVirgo:2014hva} all merged in the local universe~\citep{2016PhRvL.116x1102A,GW151226-DETECTION,2016PhRvX...6d1015A,2017PhRvL.118v1101A,2017ApJ...851L..35A,2017PhRvL.119n1101A,2018arXiv180511579T}. These detections have allowed to measure the \emph{local} merger rate of BBHs at {$[24.4-111.7]$}~\rateunits (90\% credible interval~\citep{o2rates}). The current sensitivity of advanced detectors limits to {z\si0.3} the maximum redshift at which heavy BBH such as \TheEvent{} can be detected, while heavier objects could be observed farther away~\citep{2016PhRvL.116x1102A,GW151226-DETECTION,2016PhRvX...6d1015A,2017PhRvL.118v1101A,2017ApJ...851L..35A,2017PhRvL.119n1101A,2018arXiv180511579T,2017PhRvD..96b2001A,o2rates}. As the LIGO and Virgo instruments progress toward their design sensitivity~\citep{2016LRR....19....1A}, and the network of ground-based detectors grows, it will be possible to detect BBH at redshifts of \si1 (the exact value depending on the BBH mass). This can potentially allow to probe the merger rate of BBHs through a significant distance range, and check how it varies with redshift~\citep{2018arXiv180510270F}. While this might provide precious information on the evolution of the merger rate, it would be interesting to access sources at even higher redshifts. Since compact binaries are constituted of neutron stars and black holes, leftovers of main-sequence stars, a measurement of their abundance at different stages of cosmic history can potentially tell us something about the star formation rate (SFR). This latter is currently measured using various electromagnetic probes (see~\cite{2014ARA&A..52..415M} for a recent review). However, electromagnetic probes do not directly track the amount of matter being formed on a galaxy. Instead, they track the luminosity, which then is linked to the mass production through several steps of modeling (e.g. on the initial mass function). Furthermore, dust extinction can significantly reduce the bolometric luminosity of a galaxy, or alter the its spectral content, which is a key ingredient to infer the SFR from light. These limitations are particularly severe at redshifts above 3 where, additionally, fewer data points are available from electromagnetic observations. Gravitational-wave probes do not suffer from these issues: they cannot be altered by dust and they directly encode information about the mass of the source. Two proposals for third-generation (3G) ground-based detectors are currently being pursued, which would allow to detect BBHs at large redshifts: the Einstein Telescope~\citep{2010CQGra..27s4002P} (ET) and Cosmic Explorer (CE)~\citep{2017CQGra..34d4001A}. Using the local merger rate calculated by the LIGO and Virgo collaborations it has been estimated that $[1-40]\times10^4$ BBHs merge in the universe per year~\citep{2017PhRvL.118o1105R}. ~\cite{Vitale3G} has shown how BBH can be detected all the way to redshift of \si15 by networks of 3G detectors. Since that is a significant fraction of the volume of the universe, one would thus expect that a large fraction of merging BBH would be detectable. Indeed, \cite{2017PhRvL.118o1105R} estimates that 99.9\% of the BBH mergers will be detectable by 3G detectors~\footnote{In this Letter we solely focus on BBHs. Previous work exists for binary neutron stars~\citep{VanDenBroeck:2010vx,2019ApJ...878L..13S}.}. In this Letter we show how, under quite generic hypotheses, accessing BBHs with 3G gravitational-wave detectors, allows for a direct inference of the merger rate and the SFR all the way to redshifts of $\sim 10$. | \label{sec:discussion} In this Letter we have shown how next-generation ground-based detectors will enable using gravitational waves from binary black hole to infer their merger rate throughout cosmic history, even in absence any model for the star formation history. On the other hand, if a modeled template is available for the star formation rate and for the time-delay distribution between formation and merger, we have shown how their characteristic parameters can be measured with just three months of data. We have simulated four different ``Universes'', assuming the formation rate matches the Madau-Dickinson star formation rate, and four different prescriptions for the delay between formation and merger: flat in the logarithm of the time-delay, or exponential, with e-fold time of 0.1, 1 or 10~\gyr. The unmodeled approach yields a direct measurement of the volumetric merger rate $\vmr\equiv \ud N/\ud V_c\ud t_d$. Fig~\ref{Fig.MeasuredGP} shows the measurement obtained with three months of data. The four models are clearly distinguishable, and have uncertainties much smaller than their separation for redshifts below $\sim 4$. At larger redshifts, the uncertainties increase due to the smaller number of sources, and the larger uncertainty on their redshifts. Including a model for the star-formation history and the time-delay distribution dramatically increases the power of the method, and the expense of its generality. Using the Madau-Dickinson SFR, Eq.~\ref{Eq.MDSFR} and an exponential time-delay distribution with unknown e-fold time $\tau$ as templates, we have shown how all unknowns can be measured with good precision after three months of data. The measurement of the SFR parameters is not accurate for the universe with flat-in-log time delays, as one would have expected given the mismatch between the time-delay template and the actual time-delay distribution. This kind of issues can be mitigated using templates with more parameters. The number of parameters will increase the computational cost of the analysis, and the uncertainty in the measurement. However, the number of detectable BBH is in the hundreds of thousand per year, which will compensate for the extra complexity of the model. In this work we have made a few simplifying assumptions to keep the computational cost under control. {First, we have assumed that the time-delay distribution is the same for all sources at all redshifts, while in reality it will depend on the redshift of the source through the metallicity of the environment~\citep{2019MNRAS.482.5012C}. This limitation can be lifted, introducing a functional form that relates time delay to redshift and possible other parameters, that will eventually be marginalized over.} Relatedly, we have neglected the dependence of the SFR and time-delay distribution on the mass and spins of the sources. This is not an intrinsic limitation of the method, and can be easily folded in the analysis. As these extra parameters are accounted for, we would expect that more sources will be required to achieve the same precision. But, as mentioned above, in this work we have considered three months worth of data. Many more detections will be available for these tests, and hence compensate for the increased complexity of the model. Finally, while generating the simulated signals, we have assumed that all sources come from galactic fields. There is growing evidence that at least a fraction of BBH detected by LIGO and Virgo have been formed in globular clusters~\citep{2015PhRvL.115e1101R,2016PhRvD..93h4029R}. These sources would show a very different evolution with redshift, with a peak of the merger rate at higher redshift. If black holes from population III stars merge, they could also contribute to the total merger rate, probably with a peak above $z\sim 10$~\citep{Belczynski2016,2016MNRAS.456.1093K}. {Depending on the relative abundance of mergers in these channels, one could be able to calculate their branching ratios as a function of redshift. This would give information which is complementary to what can be obtained studying the mass, spin, and eccentricity distribution of gravitational-wave detections. The method we developed can be extended to account for multiple population, which we will explore in a future publication.} | 18 | 8 | 1808.00901 |
1808 | 1808.03075_arXiv.txt | Imaging Atmospheric Cherenkov Telescopes have revealed more than 100 TeV sources along the Galactic Plane, around 45\% of them remain unidentified. However, radio observations revealed that dense molecular clumps are associated with 67\% of 18 unidentified TeV sources. In this paper, we propose that an electron-positron magnetospheric accelerator emits detectable TeV gamma-rays when a rapidly rotating black hole enters a gaseous cloud. Since the general-relativistic effect plays an essential role in this magnetospheric lepton accelerator scenario, the emissions take place in the direct vicinity of the event horizon, resulting in a point-like gamma-ray image. We demonstrate that their gamma-ray spectra have two peaks around 0.1 GeV and 0.1 TeV and that the accelerators become most luminous when the mass accretion rate becomes about 0.01\% of the Eddington accretion rate. We compare the results with alternative scenarios such as the cosmic-ray hadron scenario, which predicts an extended morphology of the gamma-ray image with a single power-law photon spectrum from GeV to 100~TeV. | \label{intro} The Imaging Atmospheric Cherenkov Telescopes (IACTs) provides a wealth of new data on various energetic astrophysical objects, increasing the number of detected very-high-energy (VHE) gamma-ray sources, typically between 0.01 and 100 TeV, from 7 to more than 200 in this century \footnote{TeV Catalog (http:www.tevcat.uchicado.edu)}. Among the presently operating three IACTs, High Energy Stereoscopic System (HESS) \cite{wilhelmi09} has so far discovered 42 new VHE sources along the Galactic Plane, 22 of which are still unidentified. The nature of these unidentified VHE sources may be hadronic origin \cite{black73,issa81}, because protons can be efficiently accelerated into VHE in a supernova remnant to penetrate into adjacent dense molecular clouds, which leads to an extended gamma-ray image. By a systematic comparison between the published HESS data and the molecular radio line data, 38 sources are found to be associated with dense molecular clumps out of the 49 Galactic VHE sources covered by 12 mm observations \cite{dewilt17}. There is, however, an alternative scenario for the VHE emissions from gaseous clouds. In the Milky Way, molecular gas is mostly located in giant molecular clouds, in which massive stars are occasionally formed. If a massive star evolves into a black hole and encounters an adjacent molecular clouds, it accretes gases. It is, therefore, noteworthy that a rapidly rotating, stellar-mass black hole emits copious gamma-rays in 0.001-1 TeV \cite{hiro16a}, provided that its dimensionless accretion rate $\dot{m} \equiv \dot{M}/\dot{M}_{\rm Edd}$, satisfies $6 \times 10^{-5} < \dot{m} < 2 \times 10^{-4}$, where $\dot{M}$ designates the mass accretion rate, $\dot{M}_{\rm Edd} \equiv 1.39 \times 10^{19} M_1 \mbox{g s}^{-1}$ is the Eddington accretion rate, $M_1= M/(10 M_\odot)$ and $M_\odot$ denotes the solar mass. The electric currents flowing in such an accreting plasma create the magnetic field threading the event horizon. In this leptonic scenario, migratory electrons and positrons ($e^{\pm}$’s) are accelerated to TeV by a strong electric field exerted along these magnetic field lines, and cascade into many pairs as a result of the collisions between the VHE photons emitted by the gap-accelerated $e^\pm$'s and the IR photons emitted by the hot $e^-$'s in the equatorial accretion flow. The resulting gamma radiation takes place only near the black hole; thus, their VHE image should have a point-like morphology with a spectral turnover around TeV. | \label{sec:6} Let us compare the related gamma-ray emission scenarios. In the protostellar jet scenario \cite{bosch10}, electrons and protons are accelerated at the termination shocks when the jets from massive protostars interact with the surrounding dense molecular clouds. Thus, the size of the emission region becomes comparable to the jet transverse thickness at the shock. In the hadronic cosmic ray scenario \cite{ginz64,blandford87}, protons and helium nuclei are accelerated in the supernova shock fronts and propagate into dense molecular clouds, resulting in a single power-law photon spectrum in $0.001-100$~TeV through neutral pion decays. The size becomes comparable to the core of a dense molecular cloud. In the leptonic cosmic ray scenario \cite{aharon97,swaluw01,hillas98}, electrons are accelerated at pulsar wind nebulae or shell-type supernova remnants, and radiate gamma-rays via IC process and radio/X-rays via synchrotron process. Since the cosmic microwave background radiation provides the main soft photon field in the interstellar medium, the size may be comparable to the plerions, whose size increases with the pulsar age. In the black-hole lepton accelerator scenario \cite{bes92,hiro98,neronov07,levinson11,globus14,brod15,hiro17,levinson17}, emission size does not exceed $10 r_{\rm g}$. Noting that the angular resolution of the CTA is about five times better than the current IACTs, we propose to discriminate the present black-hole lepton accelerator scenario from other scenarios by comparing the gamma-ray image and spectral properties. Namely, if a VHE source has a point-like morphology like HESS J1800-2400C in a gaseous cloud (section S1), and has two spectral peaks in $0.01-3$~GeV and $0.01-1$~TeV, but shows (synchrotron) power-law component in neither radio nor X-ray wavelengths, we consider that the present scenario accounts for its emission mechanism. | 18 | 8 | 1808.03075 |
1808 | 1808.08960_arXiv.txt | We describe a new hybrid framework to model non-thermal spectral signatures from highly energetic particles embedded in a large-scale classical or relativistic MHD flow. Our method makes use of \textit{Lagrangian} particles moving through an Eulerian grid where the (relativistic) MHD equations are solved concurrently. Lagrangian particles follow fluid streamlines and represent ensembles of (real) relativistic particles with a finite energy distribution. The spectral distribution of each particle is updated in time by solving the relativistic cosmic ray transport equation based on local fluid conditions. This enables us to account for a number of physical processes, such as adiabatic expansion, synchrotron and inverse Compton emission. An accurate semi-analytically numerical scheme that combines the method of characteristics with a Lagrangian discretization in the energy coordinate is described. In presence of (relativistic) magnetized shocks, a novel approach to consistently model particle energization due to diffusive shock acceleration has been presented. Our approach relies on a refined shock-detection algorithm and updates the particle energy distribution based on the shock compression ratio, magnetic field orientation and amount of (parameterized) turbulence. The evolved distribution from each \textit{Lagrangian} particle is further used to produce observational signatures like emission maps and polarization signals accounting for proper relativistic corrections. We further demonstrate the validity of this hybrid framework using standard numerical benchmarks and evaluate the applicability of such a tool to study high energy emission from extra-galactic jets. | Magnetized and relativistic large scale flows in the form of jets are a common observational feature seen for example in active galactic nuclei (AGNs), Gamma-ray bursts and micro-quasars. The dominant emission is originated by non-thermal processes from high energy particles. Multi-wavelength observations covering a wide spectrum from Radio wavelengths to TeV Gamma ray emission provides valuable insights into the micro-physical processes that occur in jets and lead to the observed radiation. The length scales associated with these micro-physical processes are many orders of magnitude smaller than the physical jet scales that can range up to few tens of kilo-parsec. Connecting a bridge between these scales poses a serious challenge to theoretical modeling of the emission from AGN jets. In the present work, we aim to build a quantitative connection between such disjoint scales by developing a numerical tool that could simulate multi-dimensional flow pattern treating small-scale processes in a sub-grid manner. In this work, we describe such a tool that consistently accounts for most of the micro-physical processes. The general analytical picture of multi-wavelength radiation from beamed relativistic magnetized jet was proposed by works in the eighties \citep[e.g.][]{Blandford:1979, Marscher:1980, Konigl:1981}. Since then, synchrotron emission signatures from large scale jets are obtained from time-dependent simulations through post-processing. In the relativistic hydrodynamic context, transfer functions between thermal and non-thermal electrons in jet are used \citep{Gomez:1995, Gomez:1997, Aloy:2000} whereas in case of relativistic MHD calculations, the magnetic structure inside the jet is used to compute synchrotron emission maps \citep[e.g.][]{Porth:2011, Hardcastle:2014, English:2016}. {\blue Formalism to study the micro-physics of particle acceleration at shocks using hybrid implementations combining both particles and grid-based fluid descriptions have also been developed targeting different scales of interest. At the scales of electron's gyro radius, the most consistent approach is that of Particle in Cell (PIC). Several groups have applied this kinetic approach to understand shock acceleration at relativistic shocks \citep[e.g.,][and references therein]{Sironi:2015}. A hybrid MHD-PIC approach can be used to study the shock acceleration phenomenon on slightly large length scales typically of the order of few thousands of proton gyro-scales. Such an approach developed by \citep[e.g.,][]{Bai:2015, vanMarle:2017, Mignone:2018} describes the interaction between collisionless cosmic ray particles and a thermal plasma. Similarly, \cite{Daldorff:2014} proposed a hybrid approach for the BATS-R-US code that combines Hall-MHD and PIC methods in order to capture small-scale kinetic effects in magnetosphere simulations.} An alternative approach in numerical modeling of non-thermal emission from astrophysical jet treats the population of non-thermal electrons as separate particle entities suspended in fluid. Effects due to synchrotron aging in presence of shock acceleration under the test particle limit were studied for radio galaxies using multi-dimensional classical MHD simulations by \citep{Jones:1999, Tregillis:2001}. Acceleration of test particles and subsequent radiative losses in presence of shocks formed via hydro-dynamic Kelvin Helmholtz vortices were studied by \cite{Micono:1999}. Such an hybrid framework of combining test particles with classical fluid has also been used effectively to study cosmic-ray transport in cosmological context \citep{Miniati:2001}. For relativistic hydrodynamic flows, populations of non-thermal particles (NTPs) have been included to study non-thermal emission from internal shocks in Blazars \citep{Mimica:2009, Mimica:2012, Fromm:2016}. Recent relativistic hydro-dynamical simulations using NTPs have also been applied for a study of star-jet interactions in AGNs \citep{DeLaCita:2016}. There are two most critical limitations with above models using NTPs. Firstly as the fluid simulations are done with RHD, magnetic field strengths are assumed to be in equipartition with the internal energy density. This ad-hoc parameterized assumption of magnetic field strengths can affect the estimation of the spectral break in the particle distribution due to synchrotron processes. The second simplifying assumption in these models is the choice of a constant value for the power law index $\mathcal{N}(E) \propto E^{-m}$, ($m = 2.0$ \citep{DeLaCita:2016} and $m = 2.23$ \citep{Fromm:2016}) in the recipe of particle injection at shocks. In the present work, we describe methods used to overcome the above limitations with an aim to build a state-of-the-art hybrid framework of particle transport to model high energy non-thermal emission from large scale 3D RMHD simulations. Our sub-grid model for shock acceleration incorporates the dependence of the spectral index on the shock strength and magnetic field orientation. The magnetic fields obtained from our RMHD simulations are used to compute radiation losses due to synchrotron and Inverse Compton (IC) emission in a more accurate manner without any assumption on equipartition. Further, we also incorporate the effects of relativistic aberration in estimating of the polarized emission due to synchrotron processes. \blue Unlike the MHD-PIC approach \citep[e.g.][]{Bai:2015, vanMarle:2017, Mignone:2018}, we do not consider the feed-back of motion of particles on the fluid. This surely does not allow us to study the associated non-linear coupling effects. However, we can certainly extend the applicability of the presented hybrid framework, to observable scales, whereby micro-physical aspects of spectral evolution are treated using sub-grid physics based on local fluid conditions. Further, we have only considered the spectral evolution for electrons in presence of magnetic fields and shocks. Modifications in the mass and time scales would be required if the physics of acceleration of protons are to be incorporated. Also, the protons are expected to suffer from an negligible amount of synchrotron loss in comparison with electrons which would significantly reflect in the spectral behavior of high energy protons in comparison to electrons. Additionally, the post-shock spectral evolution is different for protons as demonstrated by PIC simulations for all kinds of shocks \cite[e.g.][]{Sironi:2013aa, Park:2015, Marcowidth:2016}. This sub-grid physics associated with acceleration and radiative loss of protons is not included in the present work. \black The paper is organized as follows - detailed theoretical description used for our hybrid particle \& fluid framework is described in Sec.~\ref{sec:numframe}. In particular, the transport equation for particle spectral evolution is given in Sec.~\ref{sec:cr_transeq}, details of numerical implementation are outlined in Sec.~\ref{sec:lp}, different micro-physical processes considered are elaborated in details in Sec.~\ref{ssec:radloss} and ~\ref{ssec:dsa}. The post-processing methods used to obtain emissivity and polarization signatures from particles are described in Sec~\ref{ssec:postproc}. In Sec.~\ref{sec:numtests}, we demonstrate the accuracy of the developed hybrid framework using standard tests and further go on to describe the astrophysical applications in Sec.~\ref{sec:application}. | \label{sec:summary} We have presented a state-of-the-art hybrid framework for the PLUTO code that describes the spectral evolution of highly energetic particles by means of (mesh-less) Lagrangian macro-particles embedded in a classical or relativistic MHD fluid. The main purpose of this work is that of including sub-grid micro-physical processes at macroscopic astrophysical scales where the fluid approximation is adequate. While the MHD equations are integrated by means of standard Godunov-type finite-volume schemes already available with the code, macro-particles obey the relativistic cosmic-ray transport equation in the diffusion approximation. Back reaction from particle to the fluid is not included and will be considered in forthcoming works. The main features that characterize our hybrid framework are summarized below. \begin{itemize} \item Lagrangian macro-particles follow fluid streamlines and embody a collection of actual physical particles (typically electrons) with a finite distribution in energy space. For each macro-particle we solve, away from shocks, the cosmic ray transport equation in momentum (or energy space) to model radiation losses due to synchrotron, adiabatic expansion and inverse Compton effects based on local fluid conditions. The transport equation is solved semi-analytically using the method of characteristics to update the energy coordinates in a Lagrangian discretization. \item In presence of magnetized shocks, we have described a novel technique to account for particle energization due to diffusive shock acceleration processes. This involves sampling the local fluid quantities (such as velocity, magnetic field and pressure) in the upstream and downstream states to estimate the shock velocity along with the shock normal. These quantities are critical to perform the transformation to the normal incidence frame where the compression ratio can then be calculated. We have verified the validity of our shock-detection scheme by comparing it against theoretical estimates from 2D planar shocks. The technique works also for curved as well as oblique shocks with very good accuracy. The knowledge of the shock normal and of the local magnetic field direction enables us to include obliquity dependence in the estimate of the post-shock power-law index of the particle energy distribution. In such a way our model is able to distinguish between quasi-parallel (more efficient) and quasi-perpendicular shocks (less efficient), the latter resulting in a steeper spectrum and depending on the amount of parameterized (unresolved) turbulence. In both cases, the high energy cut-off is estimated consistently from the acceleration time scale derived without assuming equipartition but, rather, by considering particle diffusion along and across the magnetic field lines. \item The spectral distribution from each macro-particle is then further employed to compute observable such as emissivity and the degree of polarization due to synchrotron processes. Numerical benchmarks involving a relativistically expanding shell have been used to demonstrate the accuracy of our implementation against theoretical expectation. We adopt appropriate relativistic kinematic effects to estimate the observed degree of polarization and study its dependence on the viewing angles, $\theta_{\rm obs}$. We observe that the value of polarization degree saturates for larger viewing angles. For $\gamma$-ray energies, we obtain $\Pi \approx 56\%$ for a power-law distribution with $m = 3$, smaller than the theoretical upper limit of 75\%. This effect of depolarisation is consistent with values estimated by \cite{Lyutikov:2003}. \end{itemize} We have further applied our new framework to problems of astrophysical relevance involving either classical MHD or relativistic magnetized shocks. Two examples have been proposed. \begin{itemize} \item \textbf{SN 1006}: In the first application, we have studied diffusive shock acceleration and non-thermal emission in the context of supernova remnants with particular attention to SN1006. Our study of particle acceleration at classical MHD shocks using axisymmetric SNR simulations has shown that the average spectral index for particles is around $m = 2.1$ consistent with values obtained for strong shocks. The maximum spectral energy of 20 TeV obtained for the magnetic field of $ \sim 8 \mu$\,G is about a factor two times less than the upper limits obtained from fitting of observed spectra from SN 1006. \item \textbf{Slab Jet}: In the second application, we have investigated particle acceleration at shocks in a two-dimensional relativistic slab jet. Unlike previous authors who employed a constant value for the spectral index of shocked particles, our method self-consistently determines the shock compression ratio and distinguishes between quasi parallel or quasi-perpendicular shocks. This has shown to produce a considerable spreading in the electron spectral index (see Fig.\ref{fig:slabjet_f1}). Also, we observe knotty emission features for X-ray energies and mis-aligned emissivity features indicating the effects of oblique shocks. The polarization degree is also found to be larger at the jet/ambient interface, in agreement with radio and optical polarisation signatures from 3C 264 \cite{Perlman:2010}. \end{itemize} {\blue Forthcoming extensions of this work will aim at relaxing some of the simplifying assumptions adopted here. In particular, efforts will be taken to: i) incorporate energy dependence in the free parameter $\eta$ for quasi-perpendicular relativistic shocks along with magnetic field amplification through feedback, ii) include macro-particle backreaction on the underlying fluid which can also account for modifications in the shock structure \citep{Blasi:2002}, iii) extend our framework to also include spectral evolution of protons with an aim to compare leptonic and hadronic emission from jets. The ultimate goal of this framework would be to model multi-wavelength emission from AGN jets by using three dimensional simulations.} | 18 | 8 | 1808.08960 |
1808 | 1808.03243_arXiv.txt | Using data from the MEarth-North and MEarth-South transit surveys, we present the detection of eclipses in four mid M-dwarf systems: LP~107-25, LP~261-75, LP~796-24, and LP~991-15. Combining the MEarth photometry with spectroscopic follow-up observations, we show that LP~107-25 and LP~796-24 are short-period (1.388 and 0.523 day, respectively) eclipsing binaries in triple-lined systems with substantial third light contamination from distant companions. LP~261-75 is a short-period (1.882 day) single-lined system consisting of a mid M-dwarf eclipsed by a probable brown dwarf secondary, with another distant visual brown dwarf companion. LP~991-15 is a long-period (29.3 day) double-lined eclipsing binary on an eccentric orbit with a geometry which produces only primary eclipses. A spectroscopic orbit is given for LP~991-15, and initial orbits for LP~107-25 and LP~261-75. | Eclipsing binaries are important astrophysical tools because they are able to provide largely model-independent, precise measurements of stellar masses and radii. Observations of the best-characterized examples reveal a systematic tendency of theoretical stellar evolution models to underpredict the radii of main sequence stars with convective outer envelopes (e.g., \citealt{1991A&ARv...3...91A,2010A&ARv..18...67T}). Due to the special geometric configuration required for a spectroscopic binary to eclipse, such systems are rare. Observations are particularly sparse for fully convective M-dwarfs (stars with masses below approximately $0.35\ \msol$; e.g., \citealt{1997A&A...327.1039C}), and while recent observational progress has begun to fill in the parameter space between $0.2\ \msol$ and $0.35\ \msol$, there are still very few systems containing components below $0.2\ \msol$ with precisely measured parameters (e.g., \citealt{2013MNRAS.431.3240N,2017ApJ...836..124D}). We operate the MEarth project, an all-sky survey using two robotic telescope arrays to search for transiting planets orbiting fully convective M-dwarfs within $33\ {\rm pc}$ by obtaining high-cadence time series differential photometry \citep{2008PASP..120..317N}. This survey is also highly sensitive to eclipsing binaries, which present much larger photometric signal sizes than transiting planets, and has been optimized for efficient recovery of objects with long orbital periods. In previous papers, we have presented three eclipsing stellar systems \citep{2009ApJ...701.1436I,2011ApJ...742..123I,2017ApJ...836..124D} and one brown dwarf system \citep{2010ApJ...718.1353I} detected with MEarth. This paper presents details of four additional eclipsing systems detected over the same time period. Three are stellar systems (LP~107-25, LP~796-24 and LP~991-15), for which we report initial observations and characterization, but several concerns must be addressed before masses and radii of the components can be determined at the level required to test stellar models. The fourth (LP~261-75) is a single-lined system with a probable brown dwarf companion. | \label{disc_sect} In this section, we first discuss a difficulty common to several of the objects, and then present solutions and discussion for each of the four objects individually. We give the jump parameters used in the Monte Carlo simulations and any derived parameters such as masses which are determined robustly. Derived parameters which are not well-determined are not presented, and while we have given sufficient information to calculate these we caution against doing so given their uncertainties. Consequently we also do not present comparisons to theoretical models, which would be premature given the preliminary nature of the solutions. \subsection{Spectroscopic vs photometric light ratios} \label{spec_vs_phot_sect} An important source of uncertainty, and potentially also systematic error, in the models of the multiple-lined systems presented here (LP~107-25 and LP~991-15) results from the need to compute light ratios appropriate for models of the MEarth photometry using quantities measured spectroscopically with the TODCOR or TRICOR $\alpha$ and $\beta$ parameters. These problems arise if the components of the multiple system are not spectroscopically identical. In such cases the $\alpha$ or $\beta$ parameters then depend not only on the appropriate light ratio, but also on the degree to which the depths of the absorption lines resemble the ones in the template (in this case, Barnard's Star). The addition of rotational broadening and the need to correct for differences between the spectroscopic and photometric bandpasses present further complications. We conducted simulations using PHOENIX model atmospheres from \citet{2013A&A...553A...6H} to estimate the appropriate transformation between the measured spectroscopic ratios and light ratios in the MEarth bandpass. We find that these appear to depend strongly on metallicity in addition to effective temperature (we speculate that this may be due to the use of molecular absorption features, predominantly due to TiO, when computing the spectroscopic ratios). Given that neither of these quantities are well determined for our targets, we have not attempted to apply any corrections for the present analysis. Instead, we simply use the spectroscopic values without correction and adopt an uncertainty of $\pm 0.05$, which we find to be a reasonable approximation to the error introduced by not applying the corrections over realistic ranges in effective temperature and metallicity. This strongly downweights the small value of $\alpha$ for LP~107-25, where we find the appropriate correction factor is ill-determined due to the large difference in stellar type between the primary and the secondary. In this system, the third light parameter appropriate for the light curve models is better determined by virtue of a smaller spectral mismatch between the tertiary and primary so is given more weight in the solution. The alternative assumption of a constant relative error in the light ratio would assign too much weight to ratios far from unity. We caution that this procedure is still somewhat arbitrary and has an impact on the resulting uncertainties in the physical parameters of interest, which is clearly undesirable. At present, it is difficult to make further progress using the same method until effective temperatures and metallicities can be constrained observationally for our targets, and even with this information the results would still depend on the model atmospheres. A possible solution to the latter problem would be to use multiple systems which are resolved both visually and spectroscopically to calibrate empirical relations between photometric and spectroscopic light ratios, but there are not currently enough examples of such objects known to attempt to derive these relations. A potentially superior approach for the two triple systems with distant tertiaries (LP~107-25 and LP~796-24) may be to attempt to resolve the tertiary from the inner binary using imaging observations in order to measure $L_3/(L_1+L_2)$ directly. Such observations are not currently available, and these systems are distant, resulting in small expected angular separations, but this may be a fruitful avenue for future work. Light curves obtained in the same bandpass as the imaging observations could then be analyzed by imposing the measured light ratios directly, without incurring transformation uncertainties. \subsection{LP~107-25} Figure \ref{lp107_25_modelfit} shows the light curve and radial velocities for this system, and Table \ref{lp107_25_params} gives our preliminary orbital solution. There is a small displacement in the secondary eclipse timing, where the eclipse appears approximately two minutes early compared to the prediction for a circular orbit. We have allowed non-zero eccentricity in the solution to account for this, which appears predominantly as a non-zero value of $e \cos \omega$. The value of $e \sin \omega$ is consistent with zero within reasonable uncertainties, especially when accounting for the tendency of solutions with limited numbers of radial velocities to overfit this quantity. Consequently the argument of periastron $\omega$ is ill-determined and we do not provide individual values for $e$ and $\omega$ in the table. \begin{figure*} \centering \includegraphics[angle=270,width=6in]{f2a.eps} \vspace{4ex} \includegraphics[angle=270,width=6in]{f2b.eps} \vspace{2ex} \caption{Top panels: phase-folded light curve for LP~107-25. Bottom panels: radial velocity curve. In each case there are two sub-panels, with the upper showing the data with the best fit overlaid, and the lower showing the residuals from the best fit. For the light curves, the magnitude zero point offsets and common mode have been removed to flatten the instrumental baseline, leaving only suspected astrophysical variations. Outliers rejected from the solution are shown in red. When plotting the residuals, the original data are shown in grey, and black points show the same data binned in phase into 100 equal size bins. For the radial velocities, square symbols show the velocities for the primary and filled circles for the secondary. The residuals for the two components are offset vertically for clarity.} \label{lp107_25_modelfit} \end{figure*} \begin{deluxetable}{lr} \tablecaption{\label{lp107_25_params} Parameters and uncertainties for LP~107-25.} \tablecolumns{2} \tablehead{ \colhead{Parameter} & \colhead{Value} } \startdata \hline \multicolumn{2}{l}{Jump parameters}\\ \hline $J$ & $0.5035 \pm 0.0029$ \\ $(R_1+R_2)/a$ & $0.13931 \pm 0.00077$ \\ $R_2/R_1$ & $0.431 \pm 0.012$ \\ $\cos i$ & $0.0202 \pm 0.0062$ \\ $e \cos \omega$ & $-0.001564 \pm 0.000081$ \\ $e \sin \omega$ & $0.0040 \pm 0.0021$ \\ $q$ & $0.3529 \pm 0.0075$ \\ $a_{11}$ & $-0.00111 \pm 0.00016$ \\ $b_{11}$ & $-0.00348 \pm 0.00023$ \\ $(K_1+K_2)$ (km/s) & $159.3 \pm 1.3$ \\ $\gamma$ (km/s) & $-5.29 \pm 0.54$ \\ $C$ & $0.557 \pm 0.021$ \\ $s_{1}$ (km/s) & $1.50 \pm 0.45$ \\ $s_{2}$ (km/s) & $2.26 \pm 0.66$ \\ \hline \multicolumn{2}{l}{Derived parameters}\\ \hline $i$ (deg) & $88.84 \pm 0.36$ \\ $M_1$ ($\msol$) & $0.430 \pm 0.010$ \\ $M_2$ ($\msol$) & $0.1518 \pm 0.0046$ \\ $(R_1+R_2)$ ($\rsol$) & $0.6092 \pm 0.0061$ \\ $R_1$ ($\rsol$) & $0.4256 \pm 0.0065$ \\ $R_2$ ($\rsol$) & $0.1836 \pm 0.0031$ \\ \enddata \end{deluxetable} A background star is seen overlapping the MEarth photometric aperture in Figure \ref{charts}. This is not the star responsible for the third light, and is not included in the TRES fiber, which has a smaller diameter than the MEarth photometric aperture. This contaminating star is $4.72$ magnitudes fainter than the target in the GAIA $G_{\rm RP}$ passband, and is bluer than the target in the $G_{\rm BP}-G_{\rm RP}$ color, so the contribution to the MEarth photometry should be negligible compared to the uncertainty inherited from the TRICOR-derived value of $\beta / (1 + \alpha + \beta)$ for the brighter star that is the source of the third light in the spectroscopy. We regard our solution as preliminary in both the masses, due to the limited number and quality of the radial velocities, and the possibility of a long-term trend due to the outer orbit; and in the radii due to the large amount of third light contamination. It is likely the uncertainties are underestimated as a result of these issues, and due to neglecting correlated noise in the analysis. Comparison of these quantities to the predictions of theoretical models would therefore be premature, and we have not undertaken such an analysis at present. \subsection{LP~261-75} \label{lp261_75_sect} Table \ref{lp261_75_params} gives our orbital solution for LP~261-75, and Figures \ref{lp261_75_lcfit} and \ref{lp261_75_vrad} show this model overplotted on the data used in the analysis. We also observed several secondary eclipse windows which were not included in the models, but are shown in Figure \ref{lp261_75_sec} to justify the choice of fixing $J = 0$ in the solution. \begin{deluxetable}{lr} \tablecaption{\label{lp261_75_params} Parameters and uncertainties for LP~261-75.} \tablecolumns{2} \tablehead{ \colhead{Parameter} & \colhead{Value} } \startdata \hline \multicolumn{2}{l}{Light curve jump parameters}\\ \hline $R_2/R_1$ & $0.29484 \pm 0.00034$ \\ $(R_1+R_2)/a$ & $0.08843 \pm 0.00035$ \\ $\cos i$ & $0.0152 \pm 0.0011$ \\ $F_1$ & $0.84704 \pm 0.00019$ \\ $a_{11}$ & $0.00299 \pm 0.00025$ \\ $b_{11}$ & $0.00866 \pm 0.00025$ \\ $a_{12}$ & $-0.00125 \pm 0.00019$ \\ $b_{12}$ & $0.00396 \pm 0.00021$ \\ $C$ & $0.787 \pm 0.069$ \\ \hline \multicolumn{2}{l}{Radial velocity jump parameters}\\ \hline $\gamma$ (km/s) & $-5.193 \pm 0.054$ \\ $K_{1}$ (km/s) & $21.942 \pm 0.081$ \\ $s_{1}$ (km/s) & $0.125 \pm 0.037$ \\ \hline \multicolumn{2}{l}{Derived parameters (MLR-independent)}\\ \hline $i$ (deg) & $89.131 \pm 0.065$ \\ $e$ (95\% credible) & $< 0.007$ \\ $f_1(M)$ (${\rm M}_\odot$) & $0.002060 \pm 0.000023$ \\ \hline \multicolumn{2}{l}{Derived parameters (MLR-dependent)}\\ \hline $q$ & $0.2166 \pm 0.0041$ \\ $M_1$ (${\rm M}_\odot$) & $0.300 \pm 0.015$ \\ $M_2$ (${\rm M}_\odot$) & $0.0650 \pm 0.0020$ \\ $R_1$ (${\rm R}_\odot$) & $0.3131 \pm 0.0049$ \\ $R_2$ (${\rm R}_\odot$) & $0.0923 \pm 0.0015$ \\ $v_{{\rm rot},1}$ (km/s) & $7.13 \pm 0.11$ \\ \enddata \end{deluxetable} \begin{figure*} \centering \includegraphics[width=3.5in]{f3a.eps} \includegraphics[width=3.5in]{f3b.eps} \caption{Light curves for LP~261-75 with the best fit overlaid. Left panels: primary eclipse windows with the out-of-eclipse modulation and magnitude zero point offsets removed to flatten the baseline. Different eclipses are offset vertically for clarity, and the cycle number (integer part of the normalized orbital phase) is given on the right. Right panels: out-of-eclipse modulation with the eclipse windows removed. Only the instrumental effects (magnitude zero point offsets and common mode) were corrected. The phases where eclipses were observed are indicated with arrows at the top of the diagram, giving the appropriate cycle numbers. When plotting the residuals, the original data are shown in grey, and black points show the same data binned in phase into 50 equal size bins.} \label{lp261_75_lcfit} \end{figure*} \begin{figure} \centering \includegraphics[width=3.5in]{f4.eps} \caption{Single-lined radial velocity orbit for LP~261-75 with the best fit overlaid (top) and residuals (bottom).} \label{lp261_75_vrad} \end{figure} \begin{figure} \centering \includegraphics[width=3.5in]{f5.eps} \caption{Secondary eclipse window for LP~261-75. Top panel: individual light curves with baseline flattened as Figure \ref{lp261_75_lcfit}, with the secondary eclipse duration indicated by vertical red lines. Bottom panel: combined, phase-folded light curve, with bins as described for Figure \ref{lp261_75_lcfit}. No secondary eclipse is detected.} \label{lp261_75_sec} \end{figure} We caution that the primary eclipse light curves show evidence of frequent spot crossings in the residuals, and the depths appear to be somewhat variable, meaning our nominal value for the radius ratio may exhibit systematic errors depending on the distribution of spots on the stellar photosphere. The stellar spin and orbital period are not synchronized, which provides some information on the influence of the asymmetric component of the spot distribution (e.g., as discussed in \citealt{2011ApJ...742..123I}) but the number of eclipses available at present is rather limited so we have not attempted such an analysis. Additional trial solutions were run allowing a different radius ratio for each of the $8$ primary eclipses to estimate the contribution of this source of error. The resulting unweighted mean of these radius ratios was found to be compatible with the joint solution given in Table \ref{lp261_75_params} but the empirical error in the mean was $0.0012$, or $0.00064$ rejecting one outlier (the eclipse numbered $7$ in Fig. \ref{lp261_75_lcfit}). We therefore suggest the uncertainty reported for this parameter in the table may need to be inflated to account for the effect of the spot crossings. We further note that the two velocities close to orbital phase $1.0$ shown at the right-hand side of Figure \ref{lp261_75_vrad} inadvertently overlapped the primary eclipse at the end of the exposures, so could be influenced by the Rossiter-McLaughlin effect. The resulting velocity anomaly would be approximately $+0.1\ \kms$ for these data points if the system is spin-orbit aligned. While they do show slightly elevated positive residuals compared to the model, we do not consider them to be significant at present. The Rossiter-McLaughlin effect has not been accounted for in modeling, and while the estimated observational uncertainties (via the $s_{1}$ parameter) are inflated by the presence of these residuals it is still possible some systematic errors exist in $\gamma$ and $K_{1}$ and any parameters derived therefrom. Since this is a single-lined spectroscopic binary, an estimate of the primary mass is needed to derive the properties of the secondary. LP~261-75 is a close kinematic match to the AB Dor moving group (e.g., \citealt{2015ApJS..219...33G}), so we must first assess the age of the system in order to determine which relations are appropriate for estimating the primary mass. Using our value for the $\gamma$ velocity and the astrometric parameters in Table \ref{photparams} we obtain $(U, V, W) = (-5.9 \pm 1.1, -28.7 \pm 1.3, -14.8 \pm 0.9)\ \kms$. We quantify the kinematic match to AB Dor using the BANYAN $\Sigma$ web tool \citep{2018ApJ...856...23G}, obtaining a membership probability of $99\%$. However, there must also be independent observational evidence of youth before an object can be considered a moving group member, which we now proceed to examine. This analysis is complicated by the structure of the AB Dor moving group. AB Dor ``stream'' stars do not appear to all have the same age and chemical composition, with the population likely consisting of a subsample of young stars which share a common origin with the main AB Dor ``nucleus'', whereas the rest probably do not (e.g., \citealt{2013ApJ...766....6B}). The age of the nucleus and young stream members of AB Dor is estimated to be 130--200 Myr in the recent work of \citet{2015MNRAS.454..593B}. Ages in this range have also been suggested to explain the observed properties of the M-dwarf primary in the present system, predominantly its high activity level (e.g., \citealt{2006PASP..118..671R,2009ApJ...699..649S}), but it is important to note that activity can be influenced by tides in close spectroscopic binaries, and we further find that strong H$\alpha$ activity and rotation periods of a few days may persist beyond $1$ Gyr in some mid-M systems (e.g., \citealt{2011ApJ...727...56I,2016ApJ...821...93N}). We do not find any clear observational evidence of youth in LP~261-75 at present. The position of the system on an $M_G$ vs $G_{\rm BP}-G_{\rm RP}$ color-magnitude diagram (Figure \ref{lp261_75_cmd}) falls at the red end of the main locus of MEarth targets, which could simply result from high metallicity (e.g., \citealt{2016ApJ...818..153D}). The density of the primary is constrained from the light curve analysis, but is not strongly discriminating once we account for the known tendency of stellar models to underpredict the radii of field stars. The properties of the secondary are more sensitive to age, with evolutionary models \citep{2000ApJ...542..464C,2003A&A...402..701B} predicting the secondary would be approximately $0.14-0.15\ \rsol$ and sufficiently luminous to produce a secondary eclipse of several percent in MEarth if it was in the $100-200$ Myr age range. The observed properties of the secondary and the lack of secondary eclipses are instead more consistent with the model predictions for Gyr ages. \begin{figure} \centering \includegraphics[width=3.5in]{f6.eps} \caption{$M_G$ versus $G_{\rm BP}-G_{\rm RP}$ color-magnitude diagram of the \citet{2008PASP..120..317N} parent sample for MEarth-North, using the 2MASS cross-match table provided in GAIA DR2 to retrieve the GAIA data, and excluding known unresolved multiples. The criteria given in \citet{2018arXiv180409378G} were used to filter potentially contaminated $G_{\rm BP}$ and $G_{\rm RP}$ measurements based on the excess factor. LP~261-75 is plotted in solid black, and the position is indicated by the dashed lines.} \label{lp261_75_cmd} \end{figure} Based on this argument, we conclude that the system is likely sufficiently old to apply relations for normal field stars to estimate the primary mass. We therefore use the K-band mass-luminosity relation (MLR) from \citet{2016AJ....152..141B} in conjunction with the 2MASS K-band magnitude and parallax from Table \ref{photparams}. We assume an uncertainty of $0.09$ mag in absolute magnitude on the MLR, as stated in Table 12 of \citet{2016AJ....152..141B}, and use the double-exponential form (absolute magnitude as a function of mass) which we find is better behaved at the extremes of the mass range than the polynomial relations. The parameters depending on the adopted MLR are indicated in Table \ref{lp261_75_params}. \subsection{LP~796-24} Figure \ref{lp796_24_lcfit} shows the light curve for this system. As discussed in \S \ref{vrad_sect}, the spectroscopic quantities are not reliably measured, so we have not attempted a full solution and provide only the orbital ephemeris determined from the MEarth light curves in Table \ref{ephparams}. Higher signal to noise ratio spectra, reliably detecting all three components, would be needed for a full analysis. \begin{figure*} \centering \includegraphics[angle=270,width=6.0in]{f7.eps} \vspace{2ex} \caption{Phase-folded light curve for LP~796-24 with best fit overlaid. Panels are the same as described for Figure \ref{lp107_25_modelfit}.} \label{lp796_24_lcfit} \end{figure*} \subsection{LP~991-15} \label{lp991_15_sect} Figure \ref{lp991_15_pri} shows the eclipse light curves for this system, and Figure \ref{lp991_15_ooe_vrad} shows the out-of-eclipse modulation and the radial velocities. The orbital solution is given in Table \ref{lp991_15_params}. \begin{figure} \centering \includegraphics[angle=270,width=3.3in]{f8.eps} \vspace{2ex} \caption{Primary eclipses for LP~991-15. Vertical offsets and light curve corrections are the same as described for Figure \ref{lp261_75_lcfit}.} \label{lp991_15_pri} \end{figure} \begin{figure*} \centering \includegraphics[angle=270,width=6in]{f9a.eps} \vspace{4ex} \includegraphics[angle=270,width=6in]{f9b.eps} \vspace{2ex} \caption{Top panels: out-of-eclipse light curve for LP~991-15, plotted as for Figure \ref{lp261_75_lcfit} with the observed primary eclipse epochs indicated by arrows. Bottom panels: radial velocity curve. Symbols and vertical offsets are the same as for Figure \ref{lp107_25_modelfit}.} \label{lp991_15_ooe_vrad} \end{figure*} \begin{deluxetable}{lr} \tablecaption{\label{lp991_15_params} Parameters and uncertainties for LP~991-15.} \tablecolumns{2} \tablehead{ \colhead{Parameter} & \colhead{Value} } \startdata \hline \multicolumn{2}{l}{Jump parameters}\\ \hline $J$ (see note) & $0.93 \pm 0.12$ \\ $(R_1+R_2)/a$ & $0.01455 \pm 0.00021$ \\ $\cos i$ & $0.01957 \pm 0.00071$ \\ $e \cos \omega$ & $0.0136 \pm 0.0011$ \\ $e \sin \omega$ & $0.51645 \pm 0.00095$ \\ $q$ & $0.8489 \pm 0.0024$ \\ $F_1$ & $0.86340 \pm 0.00056$ \\ $a_{11}$ & $0.00622 \pm 0.00031$ \\ $b_{11}$ & $0.00578 \pm 0.00031$ \\ $(K_1+K_2)$ (km/s) & $57.605 \pm 0.088$ \\ $\gamma$ (km/s) & $8.727 \pm 0.026$ \\ $C$ & $1.042 \pm 0.025$ \\ $s_{1}$ (km/s) & $0.143 \pm 0.020$ \\ $s_{2}$ (km/s) & $0.277 \pm 0.037$ \\ \hline \multicolumn{2}{l}{Derived parameters}\\ \hline $i$ (deg) & $88.878 \pm 0.041$ \\ $e$ & $0.51664 \pm 0.00096$ \\ $\omega$ (deg) & $88.49 \pm 0.13$ \\ $M_1$ ($\msol$) & $0.1969 \pm 0.0011$ \\ $M_2$ ($\msol$) & $0.16715 \pm 0.00072$ \\ \enddata \tablecomments{The value of $J$ is determined by the combination of the priors on $R_2/R_1$ and $L_2/L_1$ and is not constrained observationally. We state it only for completeness.} \end{deluxetable} Due to the lack of secondary eclipses, the light curve parameters in this system depend on the assumptions (in particular, the spectroscopic light ratio $\alpha$ and the adopted prior in the radius ratio) to a greater degree than is usual for double-lined eclipsing binaries with more normal configurations showing two eclipses. The surface brightness ratio parameter $J$, which is usually derived from the relative depths of the primary and secondary eclipses, is largely unconstrained by the data in this system, but it is still needed to interpret the observed primary eclipse depth to extract $\cos i$ and $(R_1+R_2)/a$. While the radius ratio is not determined, in theory the sum of the radii is still constrained by the observed eclipse duration. In practice, however, this inference also depends on other assumptions such as limb darkening parameters and third light to an extent which is not taken into account by the Monte Carlo procedure we have used to estimate uncertainties, and we do not attempt to provide or interpret this parameter given these difficulties. This system is therefore not currently useful to test the mass-radius relation. It is possible future highly precise light curves may be able to alleviate some of these degeneracies in models of the primary eclipse. The component masses are well-determined, and while they depend on $\cos i$ from the light curve solution, the mere existence of primary eclipses is largely sufficient to constrain $\sin i$ for this purpose given the long orbital period. We caution that it is likely the uncertainties in the masses stated in Table \ref{lp991_15_params} have been underestimated due to neglecting correlated noise in the radial velocity analysis, where the residuals in Figure \ref{lp991_15_ooe_vrad} do appear to be correlated at a level approximately equal to the uncertainties, but we suspect they are indeed determined to better than $2\%$. Combined with the astrometric parallax, this system could therefore potentially be used to calibrate the mass-luminosity or absolute magnitude relations. | 18 | 8 | 1808.03243 |
1808 | 1808.08017_arXiv.txt | The Earth's ionosphere refracts radio waves incident on an interferometer, resulting in shifts to the measured positions of radio sources. We present a method to smoothly remove these shifts and restore sources to their reference positions, in both the catalogue and image domains. The method is applicable to instruments and ionospheric weather such that all antennas see the same ionosphere. The method is generalisable to repairing any sparsely-sampled vector field distortion to some input data. The code is available under the Academic Free License\footnote{https://opensource.org/licenses/AFL-3.0} from \texttt{https://github.com/nhurleywalker/fits\_warp}. | \label{sec:intro} In recent years there has been a resurgence in low-frequency radio observing, in part due to endeavors to detect the Epoch of Reionisation via its redshifted 21-cm emission. Covering frequencies between 30 and 300\,MHz, low-frequency telescopes built in the last decade include the Long Wavelength Array (LWA; \citealt{Taylor}), the Low-Frequency Array (LOFAR; \citealt{vanHaarlem}) and the Murchison Widefield Array (MWA; \citealt{Tingay13, Lonsdale}). Construction of the low-frequency component of the Square Kilometer Array is imminent. These telescopes make use of an interferometric design, in which the signals from multiple antennas are correlated together to produce a set of ``visibilities'', which is a sampled Fourier Transform of the sky. \subsection{The problem of ionospheric distortion} When performing imaging operations with these telescopes, a common issue faced by observers is that of ionospheric distortions to the incident radio waves from celestial radio sources. The Earth's ionosphere consists of layers of partly-ionised plasma at altitudes from around 60 to 1,000\,km. Its electron density varies with altitude and time of day and ranges between $10^4$ and $10^6$\,cm$^{-3}$. As such it acts as a refractive medium for incident radio waves, with line-of-sight refractive shifts proportional to the square of the wavelength of the incident wave. The total electron column density (``total electron content'' (TEC)) adds an equal phase to all interferometric antennas. Interferometers measure angular positions using phase differences between antennas, and so are insensitive to this constant offset component. Instead, the transverse gradient $\nabla_{\perp}$ in the TEC toward the source introduces an angular shift $\Delta \theta$ in the position of a radio source, which is given by \cite{TMS}: \begin{equation} \Delta \theta = - \frac{1}{8\pi^2}\frac{e^2}{\eta_0 m_e } \frac{1}{\nu^2} \nabla_\perp \mathrm{TEC} \label{eq:d_theta} \end{equation} $e$ and $m_e$ are the electron charge and mass, $\eta_0$ is the vacuum permittivity, and $\nu$ is the radio observing frequency. The negative sign indicates that the direction of refraction is toward decreasing TEC. \citet{2005ASPC..345..399L} explore some of the considerations for designing low-frequency radio telescopes in this regime. \fig~1 of that paper shows a schematic overview of the different conditions that may be faced by these arrays: a telescope may have short baselines, in which case all antennas see the same $\nabla_\perp \mathrm{TEC}$ along a particular line-of-sight, or it may have long baselines, in which case antennas could see a different $\nabla_\perp \mathrm{TEC}$. A telescope with a narrow field-of-view will only see a single $\nabla_\perp \mathrm{TEC}$ and thus need a single phase correction over the field. Whereas, a telescope with a wide field-of-view can possibly see multiple different $\nabla_\perp \mathrm{TEC}$ and therefore need multiple phase corrections over the field. Since the field of view is set by the individual antennae and the baseline length is set by the telescope layout, telescopes can conceivably be built with any combination of baseline length and field-of-view. Interferometers with a wide field-of-view and short baselines require a direction dependent phase correction, but can use the same phase correction for all antennae. If such an instrument can be calibrated, the direction dependent phase corrections can be applied in the image domain by warping the resulting images, thus undoing the position shifts described by \eqn~\ref{eq:d_theta}. A critical quantity for the calibration of an interferometer is the diffractive scale size, $r_\mathrm{diff}$, which is the ionospheric patch size over which the phase difference due to changes in $\mathrm{TEC}$ is less than $\pi$\,rad, compared to the longest baseline of the telescope (\citet{2016RaSc...51..927M}). The variance in phase $\phi$, seen on a baseline of length $r$, in the presence of power-law ionospheric turbulence, is: \begin{equation} D(r) = \langle\left( \phi(r') - \phi(r'+r)\right)^2\rangle = \left(\frac{r}{r_\mathrm{diff}}\right)^\beta \label{eq:dr} \end{equation} When $r_\mathrm{diff}$ becomes small the phase variance on long baselines becomes large and it becomes necessary to derive baseline-dependent calibration solutions. A small $r_\mathrm{diff}$ also corresponds to a shorter timescale for the phase variance and thus the calibration solutions need to be derived at a higher cadence, quickly reducing the signal to noise (and availability) of suitable calibrator sources. When $r_\mathrm{diff}$ is large compared to the longest baseline, the phase variance between antennae becomes small as they effectively see the same ionosphere. In such cases a solely antenna-based gain calibration can be calculated and applied, often without the need for any time dependence. Interferometers with a wide ($\approx30^\circ$) field-of-view and relatively short baselines, such as the MWA, may sample the ionosphere every $\approx1$--$20$\,km, over projected areas of $\approx15$--$300$\,km, depending on altitude, allowing relatively easy calculation of the critical $r_\mathrm{diff}\sim 4$\,km. \citet{2017MNRAS.471.3974J} made extensive investigations into typical ionospheric behaviour above the MWA and estimated that $r_\mathrm{diff}$ varies from $\approx3$--8\,km above the MWA, compared to its original maximum baseline length of 2.5\,km. Over their 19~nights of observing, they found that $r_\mathrm{diff}<4$\,km occurs only $\approx10\%$ of the time. \citet{GLEAMEGC} found a similar result, observing 30 nights and only discarding two due to poor ionospheric conditions indicative of low $r_\mathrm{diff}$. In the Northern hemisphere, \citet{2016RaSc...51..927M} draw similar conclusions from LOFAR data: $r_\mathrm{diff}<5$\,km for about 10\% of their 29 nights of observing. For those observations with wide fields-of-view, and $r_\mathrm{diff}$ larger than the longest baseline of the interferometer, the resulting image of the sky still contains phase variations across the image, which can be seen via the $\Delta \theta$ of the individual radio sources. As \citet{2016RaSc...51..927M} points out, these large scale variations in $\nabla_\perp \mathrm{TEC}$ are not part of the power-law turbulence described by \eqn~\ref{eq:dr}, but are due to coherent structures in the ionosphere such as traveling ionospheric disturbances, or field aligned plasma tubes \citep{2015GeoRL..42.3707L}. The $\Delta \theta$ are essentially a foreground effect which for most astronomical purposes needs to be modeled and removed, for instance so that association with sources from other astronomical catalogues can be accurately performed, or to successfully combine multiple observations without blurring the resulting effective resolution element, or ``point spread function''. \subsection{Existing solutions} The optical and infrared astronomy community face similar challenges: the alignment of charge-coupled devices (CCDs) may not be precisely known, introducing an instrumental shift to the position of the detected sources, and for ground-based telescopes, the troposphere may refract and scintillate incident wavefronts. The timescales of the latter distortion are so short ($\approx$milliseconds) that the real-time hardware solution of adaptive optics must be used for optimum imaging fidelity (see \citet{2012ARA&A..50..305D} for a review). While the first problem bears some similarity to the ionospheric distortion of radio images, the instrumental shifts are usually fairly simple in form, e.g. a set of linear translations, scale changes, and rotations. Solutions such as the MoSaic data REDuction (\textsc{mscred}) tool in the Image Reduction and Analysis Facility \citep[\textsc{IRAF};][]{1986SPIE..627..733T,1993ASPC...52..173T}\footnote{http://iraf.noao.edu/} package, or Software for Calibrating AstroMetry and Photometry \citep[\textsc{SCAMP}; ][]{2006ASPC..351..112B} in the \textsc{Astromatic}\footnote{http://www.astromatic.net/} ecosystem allow the user to match detected source positions with objects with known high-precision positions, such as stars, and then calculate the resulting transforms that need to be applied, which are usually saved to the \textsc{FITS} header rather than applied to the image data itself. Unfortunately, no combination of these transforms is adequate to describe the complex ionospheric distortions, and there is the added complication that the image projections used by optical astronomers (such as Distorted Tangential; TPV) are not optimal for the extremely wide field-of-view of telescopes like the MWA, requiring reprojections that would distort the radio images and add complication to the calculation of the point spread function. Correcting radio astronomy data for ionospheric distortions is not a new problem, but the regime faced by the MWA is substantially different from previous experiments and requires a different approach. For example, \citet{2005ASPC..345..337C} use a field-based calibration technique to improve image fidelity of the Very Large Array in its long-baseline “A” (baseline lengths $\leq36.4$\,km) and “B” (baseline lengths $\leq11.1$\,km) configurations. This technique finds a phase correction for each antenna toward a bright source in the field-of-view, fits the ionospheric phase gradient over the telescope array, and then applies that model during the imaging process. This technique works for the VLA due to the very high sensitivity of each individual antenna, which allows the gain solutions to be calculated every thirty seconds for every antenna. The Source Peeling and Atmospheric Modeling \citep[SPAM; ][]{2009A&A...501.1185I} improves on this by using 10--20 sources in the field-of-view, and is typically used by the Giant Metrewave Radio Telescope \citep[GMRT; ][]{1991CuSc...60...95S} to form high-fidelity low-frequency images. In comparison to the VLA and the GMRT, the MWA has a field-of-view an order of magnitude larger, and a $\approx50\times$ lower antenna sensitivity. Solving for per-antenna phases toward all bright sources in the field-of-view over short temporal cadences to a sufficiently accurate level to model the ionosphere is challenging because of the comparably lower signal-to-noise on each source. \citep{2016MNRAS.458.1057O} use clusters of sources to build up signal-to-noise on each cluster, solving for the per-antenna gains and peeling the clusters of sources from the data. However, this technique currently only works at high elevations in the middle of the MWA band, where the telescope is most sensitive. These visibility-based techniques are not necessary for the ionospheric regime where all antennas of the array view the same ionosphere, i.e. the array is not defocussed. In this situation, we can attempt an image-based solution, which is the focus of this work. \subsection{This work} \citet{GLEAMEGC} briefly introduce a method to perform an image-based correction; this work provides a more extensive explanation of the technique (\sect~\ref{sec:method}) including details of the implementation, tests on the effectiveness and robustness of the method (\sect~\ref{sec:results}), and concludes with thoughts on future uses of this code (\sect~\ref{sec:conclusions}). | \label{sec:conclusions} We have demonstrated an algorithm which can de-distort the refractive effects of the ionosphere on astronomical FITS images, given a reliable input reference catalogue. It is useful in ionospheric regimes where the scale size of coherent ionospheric features is larger than that of the longest baseline of the telescope being used, i.e. $r_\mathrm{diff}>D$. We note that this algorithm is general-purpose to de-distort any image distorted by some vector field which is sampled by some sparse pierce-points. This may have applications outside the field of low-frequency radio astronomy. The authors welcome contact and discussions on making the code more general-purpose. \appendix \begin{table} \caption{MWA observations used in this work.} \label{tab:obsids} \centering \begin{tabular}{cccc} 1061673800 & 1062276944 & 1062880096 & 1063483240 \\ 1064689544 & 1067102136 & 1068480760 & 1068911584 \\ 1069514728 & 1070117880 & 1091400432 & 1092520568 \\ 1093037552 & 1094330008 & 1094760832 & 1095536312 \\ 1096139456 & 1097345752 & 1098207400 & 1099069040 \\ \end{tabular} \end{table} | 18 | 8 | 1808.08017 |
1808 | 1808.08826_arXiv.txt | {} {The aim of our study is to investigate the physical properties of the star-forming interstellar medium (ISM) in the Large Magellanic Cloud (LMC) by separating the origin of the emission lines spatially and spectrally. The LMC provides a unique local template to bridge studies in the Galaxy and high redshift galaxies because of its low metallicity and proximity, enabling us to study the detailed physics of the ISM in spatially resolved individual star-forming regions. Following Okada\ et~al. (2015, Paper I), we investigate different phases of the ISM traced by carbon-bearing species in four star-forming regions in the LMC, and model the physical properties using the KOSMA-$\tau$\ PDR model.} {We mapped 3--13 arcmin$^2$ areas in 30~Dor, N158, N160 and N159 along the molecular ridge of the LMC in \cii\ 158\um\ with GREAT on board SOFIA. We also observed the same area with CO(2-1) to (6-5), \thco(2-1) and (3-2), \ci\ \transl\ and \transu\ with APEX. For selected positions in N159 and 30~Dor, we observed \oi\ 145\um\ and \oi\ 63\um\ with upGREAT. All spectra are velocity resolved.} {In all four star-forming regions, the line profiles of CO, \thco, and \ci\ emission are similar, being reproduced by a combination of Gaussian profiles defined by CO(3-2), whereas \cii\ typically shows wider line profiles or an additional velocity component. At several positions in N159 and 30~Dor, we observed the velocity-resolved \oi\ 145\um\ and 63\um\ lines for the first time. At some positions, the \oi\ line profiles match those of CO, at other positions they are more similar to the \cii\ profiles. We interpret the different line profiles of CO, \cii\ and \oi\ as contributions from spatially separated clouds and/or clouds in different physical phases, which give different line ratios depending on their physical properties. We model the emission from the CO, \ci, \cii, and \oi\ lines and the far-infrared continuum emission using the latest KOSMA-$\tau$ PDR model, which treats the dust-related physics consistently and computes the dust continuum SED together with the line emission of the chemical species. We find that the line and continuum emissions are not well-reproduced by a single clump ensemble. Toward the CO peak at N159~W, we propose a scenario that the CO, \cii, and \oi\ 63\um\ emission are weaker than expected because of mutual shielding among clumps.} {} | \label{sec:intro} The life cycle of the interstellar medium (ISM) is a central part of understanding star formation and galaxy evolution. The ISM not only influences present and future star formation but it also interacts with recently formed stars and continues evolving. A photon-dominated region \citep[PDR,][]{TH85I,Sternberg1995} is one of the places with such interactions, where the ultra-violet (UV) radiation from stars dominates the physical and chemical conditions of the surrounding ISM. In the Galaxy, detailed analyses of PDRs that take account of the source geometry have been performed \citep[e.g.][]{Andree-Labsch2017}. On the other hand, some of the dominant emission lines such as \cii\ 158\um\ or \oi\ 63\um\ are often used to probe star formation in distant galaxies where individual star-forming regions are rarely resolved. In order to bridge our understanding in Galactic regions to high redshift work, studies in nearby galaxies with low (or different from solar) metallicity are necessary. The best local templates are the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) since they have significantly sub-solar metallicity ($0.5$\,$Z_\odot$ and $0.2$\,$Z_\odot$ for carbon \citep{Garnett1999}, where $Z_\odot$ is the solar abundance by \citet{Sofia2004}). They are also the nearest gas-rich systems (50~kpc and 63~kpc, respectively, where we quote the median distance from the NASA/IPAAC Extragalactic Database), enabling excellent spatial resolution compared to other extragalactic targets. \subsection{\cplus/\czero/CO in low metallicity} Carbon is the second most abundant metal in the ISM. Dominant carbon-bearing species in PDRs are \cplus, \czero, and CO. The \cii/CO ratio in environments with different metallicities has been studied observationally and theoretically \citep{Mochizuki1994,Poglitsch1995,Israel1996,Madden1997,Madden2011,Bolatto1999,Roellig2006}, with nearly all studies finding that ratio increases with decreasing metallicity. This can be understood as a thicker \cplus\ layer in regions where the UV radiation penetrates deeper due to lower dust extinction and, to a lesser extent, less self-shielding. By contrast, the transition H$^0$/\hh\ does not shift as much as that of \cplus/\czero\ or \cplus/CO at lower metallicity because \hh\ self-shielding is the dominant factor controlling the H$^0$/\hh\ transition and is metallicity independent. An ISM phase where hydrogen is in molecular form but CO is photo-dissociated is called the CO-dark molecular gas. Understanding the mass and spatial distribution of this phase is important for estimates of the total gas mass using CO emission \citep{Bolatto2013}. However, it is not clear whether a similar explanation applies to the \ci/CO ratio. \citet{Bolatto2000a} show that the gradient of \ci/CO against metallicity is slightly shallower than the case A model by \citet{Bolatto1999}, which assumes that the extent of the \czero\ layer in a clump scales linearly with the inverse of the metallicity (1/$Z$) and uses a mean column density of \cplus, \czero, and CO over a clump size distribution. The latest KOSMA-$\tau$ PDR model (see Sect. \ref{sec:PDRintro}) show different dependencies of \cplus/CO and \czero/CO on metallicity; the difference in \czero/CO between the Galactic model and LMC model is much smaller than for \cplus/CO, for reasons that are not yet well-understood. \subsection{Line profiles of CO, \ci, \cii, and \oi} The velocity profile of spectral line emission represents the turbulent motions of emitting material. In our observing beam, different phases of the ISM co-exist on spatial scales smaller than the beam and along the line-of-sight. When their motions are significantly different along the line-of-sight, we can distinguish them as separate velocity components in the line profile. This is especially useful for \cii\ emission, which can originate from ionized gas, atomic gas, and molecular gas phases \citep{Fahrion2017,Roellig2016,Carlhoff2013,PerezBeaupuits2012}. \citet[][hereafter Paper I]{Okada2015} show that the \cii\ emission line profile is substantially wider than that of CO and \ci\ in the N159 star-forming region in the LMC. The fraction of the \cii\ integrated intensity that cannot be fitted by the CO-defined line profile varies across the map from 20\% to 50\%. The significant difference in the velocity profile of the \cii\ emission observed in many sources is interpreted as an indication of a substantial fraction of the \cii\ emitting material being accelerated relative to the quiescent material, e.g. it undergoes ablation \citep{Dedes2010,Mookerjea2012,Okada2012,Schneider2012,Simon2012,Pilleri2012b}, or photoevaporated \citep{Sandell2015}. Although an order of a few \kms\ displacement is consistent with modeled photoevaporation in globules \citep{Lefloch1994}, only a few studies to compare the observed line profiles of different emission lines with simulation incorporating full PDR chemistry have been conducted \citep{Bisbas2018}. An interesting question is whether the velocity profile difference is observed only in \cii\ or also in \oi, because the \oi\ intensities constrain physical conditions of the ablated material. Since 2014 the German REceiver for Astronomy at Terahertz Frequencies (GREAT) on board the Stratospheric Observatory for Infrared Astronomy (SOFIA) enables observations of velocity-resolved \oi\ 63\um\ emission. These observations often show strong absorption features \citep{Ossenkopf2015,Leurini2015}. Since the \oi\ 145\um\ emission is typically optically thin, the velocity profile of this line gives unambiguous information about the gas dynamics with minimal opacity effects on the line profile. \subsection{Observed regions} \begin{figure*} \centering \includegraphics{plot_regions_CII_CO43_res16.eps} \caption{\emph{Center:} IRAC 8\um\ map with boxes showing the areas we observed. \emph{Four inset color maps with contours:} Integrated intensity map of \cii\ (color) overlaid with contours of CO(4-3) integrated intensity at 16\arcsec\ resolution. The red lines outline the area observed in \cii. Contour levels are at intervals of 5~K\,\kms\ for N158, 10~K\,\kms\ for N160, and 15~K\,\kms\ for N159 and 30~Dor. The unit of color bar is K\,\kms. In the maps of N159 and 30~Dor, the positions of the \oi\ observations are marked following the numbering in Table~\ref{table:oi_detected}. In 30~Dor, the position of R136 is shown as a red circle, and the two cuts to make position-velocity diagrams (Fig.~\ref{figure:pvdiagram_30Dor}) are shown as black lines. In N160, two \hii\ regions N160A1 and A2 \citep{MartinHernandez2005} are marked.} \label{figure:cii_co_integ} \end{figure*} As mentioned above, the LMC provides a good low metallicity template to bridge Galactic and high redshift observations, since it is close enough that star-forming regions are spatially well-resolved, and independent resolution elements do not show significant blending of different velocity components. In the LMC, 30~Doradus (30~Dor) and other high-mass star-forming regions in the molecular ridge south of 30~Dor (see Fig.~\ref{figure:cii_co_integ}), provide a good opportunity to study star formation and the ISM in a low metallicity environment. 30~Dor is a well-studied, prominent star-forming region excited by the super star cluster R136, where 117 massive stars provide a total ionizing flux of $4\times 10^{51}$ Ly\,photons\,s$^{-1}$ \citep{CrowtherDessart1998}. Many observations suggest that the ISM must be highly clumped; \citet{Poglitsch1995} show that the integrated intensity maps of the \cii\ and CO(1-0) emission are spatially strongly correlated, suggesting that the molecular and the photodissociated gas appear coextensive over $\sim 30$\,pc. \citet{Kawada2011} show that the \oiii\ emission is widely extended spanning more than 150~pc from R136. \citet{Indebetouw2013} resolved clumps with the Atacama Large millimeter/submillimeter Array (ALMA) and show that most of the flux in the CO map is contained within an area of 5\% to 10\%. They also show that relative velocities of individual clumps, typically with a line width of 2--3\,\kms, dominate the velocity structure, with an additional overall east-west gradient. \citet{Yeh2015} suggest that the H$_2$ rotational-vibrational transition in 30~Dor is due to fluorescence without evidence of shock excitation. \citet{Chevance2016} model FIR fine-structure lines and determine the three-dimensional structure of the gas by comparing the modeled UV radiation field strength with the emitted radiation by stars. N158 is located south of 30~Dor with an elongated \hii\ region \citep{Henize1956}. The southern part excited by the OB association L101 \citep{LuckeHodge1970} is identified as N158C or NGC2074. LH101 contains two populations of massive stars \citep[$\leq 2$~Myr and 3--6\,Myr;][]{TestorNiemela1998}, creating elongated \hii\ regions in a north-south direction with an extension to the west seen in H$\alpha$ and the optical \oiii\ emission \citep{Fleener2010,Galametz2013}. \citet{Fleener2010} found that the majority of the YSOs and central stars of ultracompact \hii\ regions in NGC2074 are not earlier than the late O-type, whereas there are several evolved early O-type stars, indicating that their formation may have started at a similar time, a few $10^5$ years ago. N160 is the hottest among the star-forming regions in the molecular ridge in terms of the dust temperature \citep{Galametz2013} and the CO excitation \citep{Bolatto2000b,Heikkila1999}. N160A is the brightest cloud in the radio continuum which has three compact \hii\ regions \citep{HeydariMalayeriTestor1986,Indebetouw2004}. In the southwest of N160A, there is another radio continuum source N160D, where the ionized gas has a shell-like structure with a WR star as well as several OB stars at the center \citep{HeydariMalayeriTestor1986,MartinHernandez2005,Farina2009}, and two compact \hii\ regions are located at the eastern edge of the shell. N159 is the most southern region among the four regions that we study here. Three CO cores are identified as N159~W, E, and S by \citet{Johansson1998}. Recent ALMA observations reveal detailed filamentary structures and converging flows at N159~W and E \citep{Fukui2015,Saigo2017}. \citet{Lee2016} report that the PDR properties that produce a good fit to the \oi, \cii\, and \ci\ emission predict too low CO intensities compared to the observations, suggesting that the CO emission may be excited by low-velocity C-type shocks. A global age gradient from 30~Dor southwards to N159 has been suggested by various studies. \citet{Nakajima2005} found an age gradient of the YSOs from N160 to N159 toward the tip of N159~S and suggest a propagation of triggered star formation from north to south along the molecular ridge. \citet{Israel1996} measure a lower CO luminosity compared to \cii\ and far-infrared (FIR) in 30~Dor compared to N159 and N160, presumably reflecting that 30~Dor is the most evolved region. On the other hand, since both N160 and N159 contain young objects as well as evolved objects, \citet{Farina2009} suggest a common time for the origin of recent star formation in the N159/N160 complex as a whole, while sequential star formation at different rates is probably present in several subregions. The analysis by \citet{Gordon2017} indicated that N159 is indeed younger than N160, but these authors did not conclude whether there is an overall north-south age gradient. \citet{deBoer1998} proposed a scenario in which star formation is triggered at the leading edge due to the bow-shock of the LMC with its motion through the halo of the Milky Way; in this scenario, an age gradient is expected because of the rotation of LMC. We performed velocity-resolved mapping observations of CO, \thco, \ci\ \transl\ and \transu, and \cii\ in N159, N160, N158, and 30Dor, and velocity-resolved pointed observations of \oi\ 145\um\ and 63\um\ at selected positions in N159 and 30~Dor. In Sect.~\ref{sec:obs} we present the data that we use in this study. A brief summary of the KOSMA-$\tau$ PDR model is given in Sect.~\ref{sec:PDRintro}. Sect.~\ref{sec:results} presents all the results and discussion. We start by presenting a line profile analysis of the \oi\ emission (Sect.~\ref{subsec:result_oi_profile}) and other emission lines (Sect.~\ref{subsec:result_lineprofile}). Next we estimate the contribution of the atomic gas (Sect.~\ref{subsec:hi_cii}) and ionized gas (Sect.~\ref{subsec:ionized_to_cii}) to the \cii\ emission. An overview of the line profile analysis is given in Sect.~\ref{subsec:discuss_lineprofile}. In Sect.~\ref{subsec:spatial_dist} we present details of the spatial distribution of detected emission lines in individual regions, and discuss the column density of CO, \czero, and \cplus\ in the low metallicity LMC environments in Sect.~\ref{subsec:columndensity}. The results of the PDR model fitting are given in Sect.~\ref{subsec:pdrmodeling}. Our main findings are summarized in Sect.~\ref{sec:summary}. | result_oi_profile}, the \oi\ emission has a profile between CO(4-3) and \cii. The Gaussian fit result confirms this conclusion: the fraction of the \oi\ emission that cannot be fit by the CO-defined Gaussians are clearly correlated to its fraction for the \cii\ emission, and somewhat smaller than the \cii\ emission. In N159, this fraction for the \oi\ 145\um\ is about 25\% at position 1 and 3, whereas the fraction for the \cii\ is 35-45\%. In 30Dor, the fraction for \oi\ 145\um\ is 0--20\%, \oi\ 63\um\ is 0--30\%, and \cii\ is 15--45\%. \subsection{Contribution of the atomic gas to the \cii\ emission}\label{subsec:hi_cii} \begin{figure} \centering \includegraphics[width=0.9\hsize]{plot_comp_paper.eps} \caption{\cii\ and \hi\ spectra at a \cii\ blob in N159 (05:39:45.9, -69:44:32.2, upper panel) and 30~Dor (05:38:31.6, -69:04:50.0, lower panel) at 1\arcmin\ spatial resolution.} \label{figure:cii_hi_spec} \end{figure} In order to estimate the contribution of the atomic gas to the \cii\ emission, we compared the \cii\ spectra with the \hi\ spectra at 1\arcmin\ resolution. In general, the \hi\ emission has much broader line profiles than those of \cii\ in N159, N160, N158, and regions not associated with CO peaks in 30~Dor. Towards CO peaks in 30~Dor, the \hi\ shows absorption features. Figure ~\ref{figure:cii_hi_spec} shows the \cii\ and \hi\ spectra at two positions in N159 and 30~Dor, where the \cii\ emission dominates over the CO and \ci\ emission. At the position in 30~Dor, the \cii\ velocity component at $\sim 255$~\kms\ has a counterpart in the CO emission, but the component at $\sim 265$~\kms\ is only seen in \cii\ and not in CO, and the \hi\ emission shows an absorption feature at this velocity. This is consistent with a picture of the \hi\ self-absorption by cold molecular clouds with a mixture of atomic hydrogen \citep{LiGoldsmith2003,Gibson2005,Kavars2005,Klaassen2005,Tang2016}, although we do not resolve individual clouds in the LMC and the absorption feature is not as narrow as specified in their studies. We estimate the \hi\ gas contribution to the \cii\ emission using the line profile. We scaled the \hi\ spectra to fit the wing of the \cii\ emission and attributed it as a contribution of the \hi\ gas to the \cii\ emission. In most regions in N158, N159 and N160, the estimated fraction of the \hi\ gas contribution to the \cii\ emission is 15\% or less, except for N159~E and the western edge of N160, where the fraction is higher. In 30~Dor, we could not fit the wing well because the velocity profile is more complex than in other regions. Since the \hi\ profile is much broader than the \cii\ line profile, subtracting this contribution does not make the \cii\ line profile significantly narrower, and it still cannot be explained by the CO-defined line profile. We then estimate the thermal pressure (or density) of the \hi\ gas that is required to emit the fitted wings of the \cii\ intensity assuming a temperature \citep{Pineda2017}. Using the equation of optically thin subthermal \cii\ emission from \citet{Goldsmith2012} and the gas temperature of 100~K, the derived thermal pressure is $4\times 10^3$--$10^5$~K\,cm$^{-3}$ in three regions except for 30~Dor. They are higher than the standard Galactic ISM \citep[e.g. the cold neutral medium with $T_k=100$~K and $n=30$~\cc;][]{Draine2011a}, and consistent with previous studies suggesting higher thermal pressure in the LMC \citep{Welty2016,Pineda2017}. Regions with higher pressure $\ge 3\times 10^4$~K\,cm$^{-3}$ occur around N159~E, the \cii\ peak in N159~W, the N160 peak and its southern and western part. This is consistent with \citet{Welty2016}, who find higher pressure toward complex regions including \hii\ regions, molecular clumps and supernova remnants, where the pressures may be enhanced by energetic activities. The derived pressure is not sensitive to the assumed temperature for $T>80$~K \citep{Pineda2017}. With the above method, we may underestimate the \cii\ integrated intensity that can be attributed to the atomic phase because we assume that the \hi\ line profile is optically thin. \citet{Braun2009} and \citet{Braun2012} show that flat-topped \hi\ emission profiles can be modeled by an opacity effect, and the opacity correction of the \hi\ column density can be an order of magnitude in our observed regions. In the above method, we do not use the \hi\ column density itself but use the \hi\ profile to fit the \cii\ emission. A flat-topped profile and steeper line wings of the \hi\ emission lead to an underestimate of the corresponding \cii\ emission, if the \cii\ emission is not as optically thick as the \hi\ emission. \subsection{Contribution of the ionized gas to the \cii\ emission}\label{subsec:ionized_to_cii} \begin{figure} \centering \includegraphics[bb=45 0 405 350,width=0.53\hsize,clip]{residual_red_CII_over_Halpha_paper.eps} \includegraphics[bb=100 0 405 350,width=0.45\hsize,clip]{residual_blue_CII_over_Halpha_paper.eps} \caption{The integrated intensity of the red-side (left) and blue-side (right) residual of the \cii\ emission after subtracting the CO-defined line profile (see text) in N159 (color, at 30\arcsec\ resolution) overlaid with contours of H$\alpha$\ \citep{Chen2010}.} \label{figure:CII_residual_N159} \end{figure} \begin{figure*} \centering \includegraphics[width=\hsize]{N160_channelmap_CII_w_CO43_onfile.eps} \caption{1\kms\ wide channel maps of the \cii\ emission (color) overlaid with contours of CO(4-3) emission in N160. The contours start at 1.5~K\,\kms\ with an interval 1.5~K\,\kms. The central velocity is written in each panel.} \label{figure:N160_channelmap} \end{figure*} As shown for the case of N159 in Paper I, the velocity-resolved \nii\ spectra are a useful tool to investigate the contribution of the ionized gas to the \cii\ emission. However, the \nii\ observations were made only in N159. Here we examine a possible ionized gas contribution through the spatial distribution of the residual of the \cii\ emission after subtracting the CO-defined profile. In contrast to Galactic-scale analysis \citep[e.g.][]{Pineda2014}, the contribution of the ionized gas is expected to vary locally in spatially resolved massive star-forming regions. As described in Sect.~\ref{subsec:result_lineprofile}, we fit the \cii\ spectra with Gaussians defined by the CO profile. We refer to the residual at greater velocities than the peak of the Gaussian (if more than one Gaussians are used in the fit, the peak with the largest velocity) as the red-side residual, and the residual at smaller velocities than the bluest Gaussian peak as the blue-side residual. The spatial distributions of the integrated intensity of the red-side residual and blue-side residual are clearly different in all regions. The left panel of Fig.~\ref{figure:CII_residual_N159} shows that the integrated intensity of the red-side residual in N159 correlates with the H$\alpha$\ emission, which confirms the result of Paper I, i.e. that the ionized gas makes some contribution to red wings of the \cii\ emission. On the other hand, the blue residual is strong in N159~E and the \cii\ blob (see Paper I). In N159~E, ALMA observations resolved a complex velocity structure consist of a few colliding filaments \citep{Saigo2017}. The \cii\ blue residual in this study may be a gas component at peculiar velocities in this kinematically complex region with physical conditions that emits dominantly in \cii, rather than CO. In N160, neither the red-side nor blue-side residual shows a correlation with the H$\alpha$ emission. The red-side residual is strong towards the extended \cii\ emission in the northwest (Fig.~\ref{figure:cii_co_integ}), which may be the ionized gas contribution because the radio continuum emission extends weakly there \citep{Mills1984,Israel1996}. In other regions, the spatial distribution of the red-side and blue-side residuals do not give a strong indication of an ionized gas contribution. In 30~Dor, the region $\sim 1$\arcmin\ northeast of the \cii\ peak at 30~Dor-10 shows a strong blue-side residual, which may be due to a gas stream (Sect.~\ref{subsec:spatial_dist}). \subsection{Discussion of the line profile shapes}\label{subsec:discuss_lineprofile} The pointed observations of \oi\ 145\um\ and 63\um\ at N159 and 30~Dor suggested that neither the CO nor the \cii\ line profiles simply represent the \oi\ profile. Since 16\arcsec\ corresponds to $\sim 4$~pc at the distance of LMC, the observed line profile must be a composite of different cloud components. This interpretation is consistent with the fact that the \oi\ 63\um\ profile varies among the 4 raster positions with a spacing of 4\arcsec\ (Fig.~\ref{figure:oi_raster_30Dor}), and that individual clumps detected by ALMA in 30~Dor typically have linewidths of 2--3\,\kms\ \citep{Indebetouw2013}, which is narrower than the results presented here within a 30\arcsec\ beam. We propose the following interpretation for the observed different line profiles among CO, \cii\ and \oi\ in the LMC. In addition to a possible ionized gas contribution to the \cii\ emission, we consider that our beam includes several PDR components that are spatially separated and/or are in different physical phases, and each component contributes to a certain velocity range in the observed line profiles depending on their dynamics. In this case, line ratios of individual velocity components can vary depending on the physical properties of the corresponding gas component. When a PDR component emits dominantly the \cii\ line and the intensity of the CO emission is below our detection limit (for example, a low density case), we detect it as a \cii\ component which cannot be reproduced by the CO-defined velocity profile. As far as the contribution of the \hi\ gas and ionized gas to the \cii\ emission is excluded, we could call it CO-dark molecular gas. We should, however, keep in mind that the derived fraction depends on the detection limit of the CO emission. \subsection{Spatial distributions in individual regions} \label{subsec:spatial_dist} \begin{figure*} \centering \includegraphics[width=\hsize]{NGC2074_channelmap_CII_w_CO43_onfile.eps} \caption{Same as Fig.~\ref{figure:N160_channelmap} but for N158.} \label{figure:NGC2074_channelmap} \end{figure*} \begin{figure*} \centering \includegraphics[width=\hsize]{30Dor_channelmap_CII_w_CO43_onfile.eps} \caption{Same as Fig.~\ref{figure:N160_channelmap} but for 30~Dor.} \label{figure:30Dor_channelmap} \end{figure*} Figure~\ref{figure:cii_co_integ} shows the integrated intensity map of CO(4-3) and \cii\ in the observed four regions, and Figures~\ref{figure:N160_channelmap}--\ref{figure:30Dor_channelmap} show the channel maps (N159 is not shown). As discussed in Paper I, the spatial distribution of the integrated intensity of \cii\ and CO(4-3) emission is not the same in N159. This is also the case for N158 to some degree, whereas in 30~Dor and N160, they are more similar. The integrated intensity maps of all detected emissions converted to 30\arcsec\ are shown in Appendix~\ref{app:map_and_spectra}. In the following, we describe the detailed morphology in each region except for N159, for which we refer the reader to Paper I. \subsubsection{N160} \begin{figure} \centering \includegraphics[width=\hsize]{N160_CII_stars.eps} \caption{The \cii\ integrated intensity map of N160 (color scale is the same in Fig.~\ref{figure:cii_co_integ}). Open blue squares show the position of stars with a spectral type of O7 or earlier, while red triangles indicate stars with spectral type O7 to B1 \citep{Farina2009}. The blue asterisks are compact \hii\ regions \citep{Indebetouw2004}, and the red diamond marks the position of an H$_2$O master \citep{Lazendic2002}.} \label{figure:N160_cii_stars} \end{figure} The peak of the \cii\ integrated emission is located at N160A, which is the brightest region in the radio continuum and H$\alpha$ emission \citep{HeydariMalayeriTestor1986,MartinHernandez2005}. N160A consist of subregions A1, A2, and another cluster in between \citep{HeydariMalayeri2002}. Both CO(4-3) and \cii\ emission show an elongated shape tracing those subregions (Fig.~\ref{figure:cii_co_integ}). In radio continuum emission, another \hii\ region is identified as N160D southwest of N160A, with the ionized gas having a shell-like structure with a WR star as well as several OB stars at the center \citep{HeydariMalayeriTestor1986,MartinHernandez2005,Farina2009}. Two compact \hii\ regions are located at the eastern edge of the shell, where our CO(4-3) has the strongest peak and the \cii\ has a peak as well. It corresponds to N160-4 in \citet{Johansson1998}. The shell structure can be traced in the \cii\ map in the bottom panels of Fig.~\ref{figure:N160_channelmap} and Fig.~\ref{figure:N160_cii_stars}, where positions of OB stars and compact \hii\ regions are marked. OB stars in \citet{Farina2009} are distributed not only in N160A and D, but continue towards the southeast of the observed region toward another radio continuum peak \citep{Mills1984}. The \cii\ emission extends northwards from N160A, which can be also seen in the \cii\ map by \citet{Israel1996}. There is one late O-star to the north of this extended distribution \citep{Farina2009}. To the east of N160A, we detected two clouds in CO(4-3), where the \cii\ emission is very weak \citep[N160-1 and N160-3 in][]{Johansson1998}. Fig.~\ref{figure:integmap_N160} shows that these clouds are bright in \ci\ \transl\ and low-J CO, while CO(6-5) is not detected, indicating a cold and quiescent environment. However they must have exciting UV sources because the \cii\ emission is weakly detected and the IRAC 8\um\ map shows diffuse structure as well as cores. The \cii\ and CO(4-3) channel maps (Fig.~\ref{figure:N160_channelmap}) show an overall good correlation, with a global velocity gradient from the northeast to the southwest. The shell structure in N160D also follows the gradient, but the \cii\ emission at the eastern edge of the shell extends in velocity up to 244\,\kms\ (it is also seen as a \cii\ wing in the spectrum of position 4 in Fig.~\ref{figure:integmap_N160}). The \cii\ emission to the north of N160A appears at a velocity of 235--236\,\kms, and it connects to clouds at N160A, while the CO(4-3) emission is detected at 233-235\,\kms\ and is somewhat isolated from N160A. \subsubsection{N158} The observed region is N158C. The southeast and the most northwestern CO peaks (Fig.~\ref{figure:cii_co_integ}) correspond to N158-2 and N158-1 respectively in \citet{Johansson1998}. The channel maps (Fig.~\ref{figure:NGC2074_channelmap}) indicate three different cloud components: north-south structures at right ascensions of 05:39:17 and 05:39:07, and an east-west structure with a declination of -69:30:00. The \hii\ region traced by H$\alpha$ is also elongated in the north-south direction \citep[slightly inclined from northeast to southwest;][]{Fleener2010}, and is located between the two north-south structures seen in \cii\ emission. The eastern CO(4-3) peak corresponds to the prominent dust lane in the H$\alpha$ image \citep{Fleener2010}. The strongest peak of the CO(4-3) and \cii\ towards the southeast is shifted, and two compact \hii\ regions identified by \citet{Indebetouw2004} are located between the CO(4-3) peak and the \cii\ peak. The ionized gas extends also in an east-west direction at the northern edge of our observed region. This clearly shows that the \cii\ emission is distributed dominantly outside the ionization front, together with the CO emission. On the other hand, the \cii\ distribution is more or less continuous spatially and spectrally, while the CO(4-3) emission shows more clearly separated clouds. \subsubsection{30~Dor} \begin{figure} \centering \includegraphics[width=0.95\hsize]{plot_pvdiagram_paper.eps} \caption{Position-velocity diagrams of \cii\ (color) and CO(4-3) (contour) emission along the cuts shown in Fig.~\ref{figure:cii_co_integ}. The contour spacing is 1~K.} \label{figure:pvdiagram_30Dor} \end{figure} There are two main clouds of CO and \cii\ emission in our observed regions (Fig.~\ref{figure:cii_co_integ}): northeast (30~Dor-10) and southwest of R136 \citep[30~Dor-12,][]{Johansson1998}. The brightest part of 30~Dor-10 is closer to R136 with a relatively sharp boundary on the side facing R136, while both CO(4-3) and \cii\ are extended towards the northeast. \citet{Indebetouw2013} identify about one hundred clumps with the ALMA observations at the central part of 30~Dor-10. Their clumps 52 and 72 are the main contributors to our brightest peak and the neighboring peak towards the east. In the channel maps, the peak velocities of 30~Dor-10 and 30~Dor-12 appear similar, while the emission at $>255$~\kms\ appears only in 30~Dor-10 (Fig.~\ref{figure:30Dor_channelmap}). In 30~Dor-10, we see four different velocity streams, connecting at the CO(4-3) and \cii\ emission peaks: northeast-southwest direction at $\sim 244$\,\kms, north-south direction at $\sim 247$\,\kms, east-west direction at $\sim 256$\,\kms, and south-north direction at $\sim 260$\,\kms. The CO(4-3) and \cii\ emission show basically similar structures, except for the following few differences. At $\sim 243$\,\kms, the \cii\ emission has an additional northwest-southeast stream, which is not seen in CO(4-3). The CO(4-3) has a peak northeast of the brightest peak (see the channel map at $\sim 251$\,\kms), which does not have a corresponding \cii\ peak; \cii\ instead shows a hole there (Fig.~\ref{figure:cii_co_integ}). At $\sim 260$\,\kms, the CO(4-3) shows a cloud south of 30~Dor-10, while the \cii\ emission extends continuously towards the south and it extends further in the velocity domain up to $\sim 266$\,\kms. Position-velocity diagrams along two cuts (Fig.~\ref{figure:cii_co_integ}) are shown in Fig.~\ref{figure:pvdiagram_30Dor}. Cut (a) goes through the so-called `stapler nebula', where \citet{Kalari2018} found three molecular clouds with CO(2-1). These authors suggested that we see the tails of pillar-like structures whose ionized heads are pointing toward R136, and that the large observed velocity dispersion can be explained by the velocity difference between the head and tail of a photoevaporating cloud. In our observations, the \cii\ velocity is shifted compared to the CO(4-3) velocity (Fig.~\ref{figure:pvdiagram_30Dor}a, see also position 10 and 11 in Fig.~\ref{figure:selected_spectra_30Dor}), which is consistent with their picture since the contribution from the head should be more dominant in \cii\ emission than the CO(4-3) emission. Cut (b) goes through two weak \cii\ blobs in the integrated intensity map, which appear as a velocity component at $\sim 265$\,\kms. Positions 10 and 11 in Fig.~\ref{figure:selected_spectra_30Dor} also show this velocity component at 30\arcsec\ resolution. The p-v diagrams show that there is no clear connection between different velocity components among these two cuts. As discussed in Sect.~\ref{subsec:hi_cii}, the \hi\ spectra show an absorption feature at $\sim 265$\,\kms. Unfortunately the spatial resolution of the \hi\ observations is insufficient to determine whether the absorption is spatially associated with the \cii\ blobs. \subsection{Column densities}\label{subsec:columndensity} \begin{figure} \centering \includegraphics[width=\hsize]{compare_CO_CI_CII_paper.eps} \caption{The column density $N$(C) (upper panels) or $N$(\cplus) (lower panels) against $N$(CO) for the beam filling factor of $0.1$ (left panels) and $0.5$ (right panels). The SMC data are taken from \citet{Requena-Torres2016}. The black line indicates that the two column densities are the same.} \label{figure:columndensity} \end{figure} We derive column densities of \cplus, C, and CO at each position in our four regions. The detailed derivation is presented in Paper I. Here we describe it briefly. We assume local thermodynamic equilibrium (LTE) for each species, and a uniform excitation temperature (\tex) for different velocity bins at each position. Assuming that CO and \thco\ have the same \tex, beam (area) filling factor ($\eta$), and an isotope ratio $^{12}$C/$^{13}$C of 49 \citep{Wang2009}, we derive the optical depth of \thco(3-2) ($\tau_{13}$) from the intensity ratio CO(3-2)/\thco(3-2). With the absolute intensity of \thco(3-2) and $\tau_{12}$ we can estimate \tex, and then the CO column density for a given beam filling factor ($\eta$). To estimate the \czero\ column density, we defined \tex\ of the \ci\ emission as follows. In N159 and 30~Dor, we derived \tex\ by the ratio of the two \ci\ intensities where both lines are detected and took its median. We used this median \tex\ as a constant \tex\ over the whole map in each region. For the other two regions, where we do not have the \ci\ \transu\ line, we use the \tex\ obtained in N159. To estimate the \cplus\ column density we have to assume \tex\ of \cii. Here we also used a constant \tex\ over the map in each region, which is determined so that it is above the \tex\ lower limit at any position of the map (i.e. for a $\tau\gg 1$ case). Figure~\ref{figure:columndensity} shows the relation between the column density $N$(CO), $N$(C), and $N$(\cplus) integrated over the whole velocity range. Here we present beam averaged column densities, i.e. the column densities presented in the Paper I multiplied by the beam filling factor. In most of the positions $N$(\cplus) is in the range of 1--10 times $N$(CO), and $N$(\czero) is $0.1$--1 times $N$(CO). There is some hint that N159 has a lower $N$(\cplus)/$N$(CO) ratio compared to other regions, but the trend is weak. N160 appears to have two different populations; for the two clouds in the northeast, where the \cii\ emission is very weak and the \ci\ emission is strong, there are several positions with lower $N$(\cplus) and higher $N$(C). This may be due to a lower radiation field in this region. Toward the main cloud of N160 and in N158, the $N$(C)/$N$(CO) ratio is smaller than in N159 and 30~Dor, while the $N$(\cplus)/$N$(CO) ratio is in a similar range as N159 and 30~Dor. This result is not very sensitive to a different \tex\ assumption for the \ci\ emission in N160 and in N158, for example using \tex\ of CO, since it is above the energy of the \ci\transl\ transition (24~K) at most positions. It is most likely not a radiation field effect since the representative radiation field strength is $\chi=60$--220 in N159 and N160 \citep{Israel1996,Pineda2008,Lee2016} and $10^3$--$10^4$ in 30~Dor \citep{Chevance2016,Pineda2012}. It is also inconsistent with a scenario that a more evolved region has less CO, since 30~Dor is the most evolved region and N159 is likely to be one of the youngest regions in our analysis. A comparison with the SMC data is also puzzling. In Fig.~\ref{figure:columndensity} the data of N66 (plume and ridge), N25, and N88 by \citet{Requena-Torres2016} are plotted. Their $N$(\cplus)/$N$(CO) ratio falls within the range of values obtained for LMC regions, while they find a larger $N$(C)/$N$(CO) ratio. As mentioned in Sect.~\ref{sec:intro}, $N$(\cplus)/$N$(CO) is expected to be large in a lower metallicity environment, while $N$(C)/$N$(CO) is expected to be less dependent on metallicity. We do not see this effect. For N25 and N88, where the radiation field is $\chi=20$--80 \citep{Israel2011}, the high $N$(C)/$N$(CO) may be due to the low radiation field. However the data point with the highest $N$(C)/$N$(CO) comes from N66, where the radiation field is estimated as 80--570 \citep{Israel2011}, which is not very different to the LMC regions. The result here indicates that $N$(\cplus)/$N$(CO) and $N$(C)/$N$(CO) in resolved regions are affected significantly by local conditions and are not a simple function of metallicity. \subsection{PDR modeling} \label{subsec:pdrmodeling} \subsubsection{Assumptions and fitting procedure} We fit the KOSMA-$\tau$ PDR model (Sect.~\ref{sec:PDRintro}) to the absolute intensities of the observed line emission and continuum SED at each position of the 30\arcsec\ resolution maps. We assume uncertainties of emission lines to be 10\% for the APEX and continuum observations \citep{Meixner2013} and 15\% for GREAT and PACS observations \citep[PACS Spectroscopy performance and calibration document, ][]{Cormier2015}. In case the baseline noise is bigger than these uncertainties, we take the baseline noise as an uncertainty. We use the clump ensemble model with a lower mass limit of $10^{-3}M_\sun$ and an upper mass limit of $10^3 M_\sun$. The upper mass limit is consistent with the ALMA result for the LMC \citep{Indebetouw2013}. For the dust model, \citet{WD2001} provide 6 different models for the LMC; two types of environment characterized by different extinction curves (LMC average and LMC 2) with 3 different abundances of very small grains each. LMC 2 is a supergiant shell southeast of 30~Dor that partially overlaps our observed regions \citep{Misselt1999}. We selected the LMC average environment with the abundance of very small grains of $10^5b_c=2.0$ (model 28; numbering by the rows of \citet{WD2001} Tables 1 and 3), which is consistent with the polycyclic aromatic hydrocarbon (PAH) abundance quoted by \citet{Galametz2013}. We used a sum of the Gaussians defined by the CO velocity profiles (Sect.~\ref{subsec:result_lineprofile}) as input intensities except for the \oi\ emission, where we use the integrated intensity from the velocity-unresolved PACS data. In this way, the derived physical properties are the average of different gas components that are detected in CO(3-2). The effects of different model assumptions and input intensities are discussed in Sect.~\ref{subsec:PDR_compare_assumptions}. We select the emission to be used in the model fit as follows. We consider two cases, where we fit only the line emission or both the line and continuum emission. We consider five continuum data (Sect.~\ref{subsec:obs_continuum}) as independent data points and treat them as if they were individual line data in the $\chi^2$ fit. For the selection of line emission to be included in the fit, we have four cases: using all lines, using all lines except for the \oi\ lines, using all lines except for the \ci\ lines, and using only optically thin lines (\thco, \ci, and \oi\ 145\um). For every selection, we consider the map positions where at least four lines are detected in order to derive three model parameters ($n$, $m$, and $\chi$, see Sect.~\ref{sec:PDRintro} for their definitions). The exception is the case for the optically thin case fitted together with the continuum. In this case, we accept positions with three lines since otherwise most of the map positions do not fulfill the criteria, and it gives still a reasonable fit because the number of the total data points is more than four together with the continuum. The original model grid covers $\log(n)=2$ to 7 in density, $\log(m)=-3$ to 3 in total mass, and $\log(\chi)=0$ to 6 in the UV field strength, all with a logarithmic step of 1. We first extend the mass grid to $\log(m)=6$. In a clumpy model, no extrapolation is needed to extend the mass range because it is just a scaling of the total intensity. We interpolate the model to a $0.1$ step in the logarithmic scale of $n$, $m$, and $\chi$. Then we calculate the reduced $\chi$-square ($\chi^2$) of all the grid points and take the grid point with the minimum $\chi^2$ as a solution. In this way, we can avoid to fall into a local minimum. \subsubsection{Result}\label{subsec:PDRfit_result} \begin{figure*} \centering \includegraphics[width=0.9\hsize]{result_SED_selected_paper.eps} \caption{Results of fitting the line and continuum emission at the CO peaks in N159~W (upper two panels), in N160A (middle panels), and in 30~Dor-10 (lower panels). Black points are the observed data and colored points represent the models. The left panels are the line SED of CO(2-1) to (6-5), \ci\transl, \ci\transu, \cii, \oi\ 63\um, and \oi\ 145\um. $^{12}$CO and \thco\ are plotted together. For N159, CO(2-1) and \thco(2-1) are not used in the fit because it is a pointed observation and the beam sizes are slightly different. The red model uses all line emissions but no continuum in the fit. The blue model excludes \oi\ from the fit but includes the continuum emission. The green model fits all the lines and the continuum emission. The purple model fits only optically thin lines and the continuum. Input line intensities are the sum of Gaussians except for the \oi\ lines, where the integrated intensities are used (see Table~\ref{table:PDR_input}).} \label{figure:PDRmodel_result_SED} \end{figure*} \begin{table*} \caption{Input intensities for the fit example in Fig.~\ref{figure:PDRmodel_result_SED}. They are the sum of Gaussians except for the \oi\ lines, where the integrated intensities are used.} \label{table:PDR_input} \centering \begin{tabular}{cccc} \hline\hline & N159~W CO peak$^{\textrm{a}}$ & N160~A CO peak$^{\textrm{b}}$ & 30~Dor-10 CO peak$^{\textrm{c}}$ \\ \hline Lines [W\,m$^{-2}$\,sr$^{-1}$] &&&\\ \hline CO(2-1) & $(1.4 \pm 0.1)\times 10^{-9}$ $^{\textrm{d}}$ & $(4.0 \pm 0.4)\times 10^{-10}$ & $(8.0 \pm 0.8)\times 10^{-10}$ \\ CO(3-2) & $(3.5 \pm 0.3)\times 10^{-9}$ & $(1.4 \pm 0.1)\times 10^{-9}$ & $(2.9 \pm 0.3)\times 10^{-9}$ \\ CO(4-3) & $(6.1 \pm 0.6)\times 10^{-9}$ & $(2.8 \pm 0.3)\times 10^{-9}$ & $(7.1 \pm 0.7)\times 10^{-9}$ \\ CO(6-5) & $(1.4 \pm 0.1)\times 10^{-8}$ & $(9.3 \pm 1.0)\times 10^{-9}$ & $(2.7 \pm 0.3)\times 10^{-8}$ \\ \thco(2-1) & $(2.9 \pm 0.3)\times 10^{-10}$ $^{\textrm{d}}$ & $(6.4 \pm 0.7)\times 10^{-11}$ & $-$ \\ \thco(3-2) & $(6.5 \pm 0.7)\times 10^{-10}$ & $(2.3 \pm 0.2)\times 10^{-10}$ & $(4.4 \pm 0.4)\times 10^{-10}$\\ \ci\ \transl & $(2.1 \pm 0.2)\times 10^{-9}$ & $(5.3 \pm 1.3)\times 10^{-10}$ & $(1.5 \pm 0.2)\times 10^{-9}$ \\ \ci\ \transu & $(8.9 \pm 0.9)\times 10^{-9}$ & $ <8.0\times 10^{-9}$ & $(7.6 \pm 2.8)\times 10^{-9}$ \\ \cii & $(4.6 \pm 0.9)\times 10^{-7}$ & $(8.6 \pm 1.6)\times 10^{-7}$ & $(1.7 \pm 0.3)\times 10^{-6}$ \\ \oi\ 63\um & $(4.8 \pm 0.7)\times 10^{-7}$ & $(2.8 \pm 0.4)\times 10^{-6}$ & $(3.3 \pm 0.5)\times 10^{-6}$ \\ \oi \ 145\um & $(1.1 \pm 0.2)\times 10^{-7}$ & $(1.9 \pm 0.3)\times 10^{-7}$ & $(2.6 \pm 0.4)\times 10^{-7}$ \\ \hline Continuum [Jy\,sr$^{-1}$]&&&\\ \hline 70\um & $(3.6 \pm 0.4)\times 10^{9}$ & $(8.6 \pm 0.9)\times 10^{9}$ & $(1.2 \pm 0.1)\times 10^{10}$\\ 100\um & $(8.3 \pm 0.8)\times 10^{9}$ & $(1.2 \pm 0.1)\times 10^{10}$ & $(2.0 \pm 0.2)\times 10^{10}$\\ 160\um & $(5.4 \pm 0.5)\times 10^{9}$ & $(6.0 \pm 0.6)\times 10^{9}$ & $(9.6 \pm 1.0)\times 10^{9}$ \\ 250\um & $(2.0 \pm 0.2)\times 10^{9}$ & $(1.7 \pm 0.2)\times 10^{9}$ & $(3.0 \pm 0.3)\times 10^{9}$ \\ 350\um & $(6.9 \pm 0.7)\times 10^{8}$ & $(6.1 \pm 0.6)\times 10^{8}$ & $(1.1 \pm 0.1)\times 10^{9}$ \\ \hline\hline \end{tabular} \begin{list}{}{\setlength{\itemsep}{0ex}} \item[$^\textrm{a}$] 05:39:36.8, -69:45:28.9 \qquad $^\textrm{b}$ 05:39:45.9, -69:38:34.6 \qquad $^\textrm{c}$ 05:38:48.8, -69:04:42.1 (J2000) \item[$^\textrm{d}$] Not used in the fit because of a slightly different beam size. \end{list} \end{table*} \begin{table*} \caption{Derived physical properties in the fit in Fig.~\ref{figure:PDRmodel_result_SED}. The derived physical properties of all positions for the green model are shown in Figs.~\ref{figure:nmuv_N159}--\ref{figure:nmuv_30Dor}.} \label{table:PDRproperties} \centering \begin{tabular}{lllllr} \hline\hline Position & model in Fig.~\ref{figure:PDRmodel_result_SED} & $\log(n)$ & $\log(m)$ & $\log(UV)$ & Area filling factor \\ \hline N159~W & red (w/o cont.) & $ 3.5 $ & $ 4.9 $ & $ 1.3$ & $ 42.5$ \\ & blue (w/o \oi) & $ 3.7 $ & $ 4.9 $ & $ 1.8$ & $ 31.3$\\ & purple (thin) & $ 3.6 $ & $ 5.1 $ & $ 1.5$ & $ 57.8$\\ & green (all) & $ 3.5 $ & $ 5.0 $ & $ 1.4$ & $ 53.6$\\ \hline N160~A & red (w/o cont.) & $ 3.9 $ & $ 4.3 $ & $ 2.2$ & $ 5.8$\\ & blue (w/o \oi) & $ 4.7 $ & $ 4.2 $ & $ 3.7$ & $ 1.3$\\ & purple (thin) & $ 6.2 $ & $ 4.1 $ & $ 4.8$ & $ 0.1$\\ & green (all) & $ 5.9 $ & $ 4.2 $ & $ 4.4$ & $ 0.2$\\ \hline 30~Dor-10 & red (w/o cont.) & $ 3.8 $ & $ 4.7 $ & $ 1.9$ & $ 16.9$\\ & blue (w/o \oi) & $ 4.9 $ & $ 4.5 $ & $ 3.8$ & $ 2.0$\\ & purple (thin) & $ 3.5 $ & $ 5.1 $ & $ 1.8$ & $ 67.4$\\ & green (all) & $ 3.8 $ & $ 4.9 $ & $ 2.2$ & $ 26.8$\\ \hline\hline \end{tabular} \end{table*} \begin{figure} \centering \includegraphics[width=0.9\hsize]{plot_chi2contour.eps} \caption{The contours of $\chi^2$ at the 30~Dor-10 CO peak position for (a) the green model (fit all line and continuum emission) and (b) the blue model (excluding \oi) in the lower panel of Fig.~\ref{figure:PDRmodel_result_SED}.} \label{figure:chi2contour} \end{figure} We calculate the best-fitting model at each position of the 30\arcsec\ resolution maps of the four star-forming regions. Figure~\ref{figure:PDRmodel_result_SED} and Table~\ref{table:PDRproperties} show an example fit (the coordinates and input intensities are listed in Table~\ref{table:PDR_input}). In most of the observed positions within the four star-forming regions (except for the CO peak at N159~W), we find the following overall trend. When fitting with only the line emission (red lines in Fig.~\ref{figure:PDRmodel_result_SED}), the lines are relatively well fit, with some cases the model underestimating the \ci\ emission. However the continuum emission is clearly underestimated especially at shorter wavelengths, indicating that the dust temperature in the best-fitting model is too low. It is consistent with the fact that the CO-ladder starts to be flat already around $J=5$ or 6, resulting in an underestimate of CO(6-5). When we exclude the \oi\ lines and include the continuum in the fit (blue lines), the estimated UV field is much stronger. The continuum SED as well as the rising trend from CO(4-3) to CO(6-5) are relatively well reproduced, but the \oi\ lines are heavily overestimated and the \ci\ emission is even more severely underestimated than in the first model. When we fit everything (green lines), the fit of \oi\ improves with compromising other parts. In most cases, fitting only optically thin lines (purple lines) or fitting without \ci\ lines (not shown) does not change the result much, or makes the fit worse. The fundamental problem for fitting the line emission is that the CO and \ci\ have two solutions at low $n$ -- low $\chi$ and at high $n$ -- high $\chi$ range for their given intensities (Fig.~\ref{figure:chi2contour}). The \cii\ intensity contours are also aligned from low $n$ -- low $\chi$ to high $n$ -- high $\chi$. In principle the \oi\ emission lines have a different dependency on $n$ and $\chi$, and hence including the \oi\ emission in the fit should provide a good constraint. However, for most positions that we study here, the solutions of $n$ and $\chi$ indicated by the \oi\ emission do not overlap with those that other emissions suggest (Fig.~\ref{figure:chi2contour}a). This is why it looks like that the fit excluding \oi\ (blue lines in Fig.~\ref{figure:PDRmodel_result_SED}) look the most reasonable for lines other than the \oi. However, in this case the low $n$ -- low $\chi$ solution and high $n$ -- high $\chi$ solution are degenerate (Fig.~\ref{figure:chi2contour}b), and very different physical conditions are obtained for spatially adjacent pixels. It is also not justified to simply ignore the \oi\ emission, because it is difficult to explain the overestimate of both \oi\ lines. For these reasons, we consider that fitting with all the lines and the continuum (green model) gives the most stable solution for representative physical properties in the sense that it excludes physical properties that would yield completely different line or continuum intensities compared to what is observed. Since we fit the absolute intensities, the model results include the area filling factor as well (Table~\ref{table:PDRproperties}). However it is sensitive to the derived density and it ranges from the order of 0.01 to 100 in four regions even with the same model assumption, which is again an effect of the degeneracy of the low $n$ -- low $\chi$ solution and high $n$ -- high $\chi$ solution. The CO peak of N159~W shows a different result (Fig.~\ref{figure:PDRmodel_result_SED} top panel). There all models fail to reproduce the \cii\ emission and the \oi\ 63\um\ to 145\um\ ratio \citep{Lee2016}. When we fit only the optically thin lines, the model overestimates all the CO, \cii, and \oi\ 63\um\ line intensities, which is qualitatively consistent with an argument that it is an optical depth effect among clumps. Quantitatively, we assume that the $N_\textrm{cloud}$ clouds are aligned along the line of sight, with each having a line intensity of $I_\textrm{line}$ and the optical depth of $\tau_\textrm{line}$. The model predicts the line intensity of $I_\textrm{line}\times N_\textrm{cloud}$, while the observed line intensity is $I_\textrm{line}\times \sum_{i=0}^{N_\textrm{cloud}-1} e^{-i\tau_\textrm{line}}$ \citep{Okada2003}. To obtain one order of magnitude difference between the model and observations as seen in Fig.~\ref{figure:PDRmodel_result_SED}, we need $N_\textrm{cloud}=10$ for a $\tau_\textrm{line}=\infty$ case and $N_\textrm{cloud}=15$ for a $\tau_\textrm{line}=1$ case. The fitted clump ensemble model when using only optically thin lines gives an area filling factor of $>20$ for any combination of model assumptions, which supports the idea of heavily overlapping clumps, although the filling factor is sensitive to the derived density as mentioned above. \begin{figure} \centering \includegraphics[width=0.9\hsize]{result_SED_selected_paper_w_highjco_N159.eps} \caption{The CO ladder including the high-J CO data by \citet{Lee2016} at the CO peak in N159~W. Black data points and the model lines are the same as in the upper panel of Fig.~\ref{figure:PDRmodel_result_SED}. Blue data points are Herschel/SPIRE observations at 42\arcsec\ resolution \citep{Lee2016}.} \label{figure:PDRmodel_result_SED_N159_CO} \end{figure} \citet{Lee2016} modeled \oi\ 145\um, \ci\transu, \cii\ and FIR with the Meudon PDR code and derived P/k=$10^6$ K\cc\ and $G_0=100$. Their model underestimates the CO emission, especially high-J CO, and they concluded that CO is heated by low-velocity shocks. When we use a non-clumpy model of the KOSMA-$\tau$ model and exclude the CO emissions from the fit, we reproduced qualitatively their results. In Fig.~\ref{figure:PDRmodel_result_SED_N159_CO}, we compare our clumpy PDR model with the high-J CO intensities observed with the Spectral and Photometric Imaging REceiver (SPIRE) on Herschel provided by \citet{Lee2016}. The gap between CO(6-5) and CO(7-6) is partially because the SPIRE data is convolved to the 42\arcsec\ beam size. The original beam size of CO(7-6) is 33\arcsec\ \citep{Lee2016}, close to our 30\arcsec, and its value is 15\% higher. The figure shows that the clumpy model provides a reasonable fit to the CO up to around $J=10$. The very shallow slope of the higher-J CO-ladder is consistent with the shock contribution, while low- and mid-J CO can be also explained by a PDR model when we introduce clumpiness. In fact the very similar line profiles of the CO and \ci\ is consistent with the picture that they are both emitted by a PDR gas, although the proposed shock in \citet{Lee2016} has a velocity of only $\sim 10$\,\kms, which may be hard to see in an emission line with a width of $\sim 8$\,\kms\ (Paper I). For the continuum SED, the model prediction of the SED is typically broader than the observed SED, independent of which model we adopt. It is typically characterized by a strong drop of 70\um\ continuum (e.g. N159 in Fig.~\ref{figure:PDRmodel_result_SED}). When we choose a dust model with fewer small grains (see Sect.~\ref{subsec:PDR_compare_assumptions}), the model SED is slightly narrower because of weaker 70\um\ emission, but the fit to the observed SED is not significantly better. This is consistent with the model SED by \citet{Bron2014} where the contribution of PAHs to the 70\um\ emission is a few percent for $\chi=1$--$1000$. At the column density peak, it is possible that the optically thin assumption for the 70\um\ continuum emission does not fully hold; we estimated the total hydrogen column density from $N$(CO), $N$(\czero), and $N$(\cplus) in Sect.~\ref{subsec:columndensity} with the carbon abundance of $7.9\times 10^{-5}$ \citep{Garnett1999} and converted it to a dust opacity using the extinction cross section \citep{WD2001}, which is at maximum 0.15 at the peak of 30~Dor-10 in case of $\eta=0.1$. This adds $\sim10$\% uncertainty to a few positions around the CO peak, but does not have a significant impact on the continuum fit, although it is not excluded that the beam filling factor is less than 0.1 and the 70\um\ continuum is marginally optically thick. \citet{Chevance2016} suggest that the FIR continuum has a significant contribution from the ionized gas outside of the molecular clouds in 30~Dor by analyzing its correlation with PAH and \oiii\ emission. This may cause an overestimate of the UV field in the fit with the continuum SED, but it does not explain the observed narrow peak in the continuum SED and its contribution should be higher outside of molecular clouds. \begin{figure*} \centering \includegraphics[bb=40 0 404 355,width=0.26\hsize,clip]{density_N159_onemodel.eps} \includegraphics[bb=80 0 404 355,width=0.23\hsize,clip]{mass_N159_onemodel.eps} \includegraphics[bb=80 0 404 355,width=0.23\hsize,clip]{uv_N159_onemodel.eps} \includegraphics[bb=80 0 404 355,width=0.23\hsize,clip]{chi2_N159_onemodel.eps} \caption{Derived density, mass, UV field, and the $\chi^2$ of the fit (from left to right) for the N159 region. The results are obtained using a fit to all emission lines and the continuum (green lines in Fig.~\ref{figure:PDRmodel_result_SED}). Areas surrounded by black lines are where at least one of the \oi\ lines is detected.} \label{figure:nmuv_N159} \end{figure*} \begin{figure*} \centering \includegraphics[bb=0 0 424 355,width=0.26\hsize,clip]{density_N160_onemodel.eps} \includegraphics[bb=40 0 414 355,width=0.23\hsize,clip]{mass_N160_onemodel.eps} \includegraphics[bb=40 0 414 355,width=0.23\hsize,clip]{uv_N160_onemodel.eps} \includegraphics[bb=40 0 414 355,width=0.23\hsize,clip]{chi2_N160_onemodel.eps} \caption{Same as Fig.~\ref{figure:nmuv_N159} but for N160.} \label{figure:nmuv_N160} \end{figure*} \begin{figure*} \centering \includegraphics[bb=20 0 394 355,width=0.265\hsize,clip]{density_NGC2074_onemodel.eps} \includegraphics[bb=80 0 394 355,width=0.22\hsize,clip]{mass_NGC2074_onemodel.eps} \includegraphics[bb=80 0 394 355,width=0.22\hsize,clip]{uv_NGC2074_onemodel.eps} \includegraphics[bb=80 0 394 355,width=0.22\hsize,clip]{chi2_NGC2074_onemodel.eps} \caption{Same as Fig.~\ref{figure:nmuv_N159} but for N158.} \label{figure:nmuv_N158} \end{figure*} \begin{figure*} \centering \includegraphics[bb=40 0 394 355,width=0.28\hsize,clip]{density_30Dor_onemodel.eps} \includegraphics[bb=100 0 384 355,width=0.22\hsize,clip]{mass_30Dor_onemodel.eps} \includegraphics[bb=100 0 384 355,width=0.22\hsize,clip]{uv_30Dor_onemodel.eps} \includegraphics[bb=100 0 384 355,width=0.22\hsize,clip]{chi2_30Dor_onemodel.eps} \caption{Same as Fig.~\ref{figure:nmuv_N159} but for 30~Dor.} \label{figure:nmuv_30Dor} \end{figure*} \subsubsection{Comparison of different inputs and model assumptions}\label{subsec:PDR_compare_assumptions} Here we discuss the effect of different model assumptions and inputs on the obtained physical properties. First, we compare the results between the model with an upper mass limit of $10^3$ and $10^1 M_\odot$. In the model, a smaller clump has a higher mean density (see the mass-size relation in Sect.~\ref{sec:PDRintro}), and removing clumps with the mass range of $10^1$--$10^3$ increases the mean ensemble density by a factor 3.7. The derived densities using an upper mass limit of $10^1$ in the fit are typically higher than the results with an upper mass limit of $10^3$ by a factor of 1--4. On the other hand, the choice of the lower mass limit between $10^{-3}$ and $10^{-2}$ does not make a significant difference. This is because clumps with a mass of $10^{-3}$ are dominated by \cplus\ and do not contribute much to the CO and \ci\ emissions in most of our density and UV field strength parameter space; for example with $n=10^4$ and $\chi=10^2$, a clump with $m=10^{-3}$ gives line ratios of \cii/CO(3-2)$\sim 5\times 10^5$ and \cii/\ci\transl$\sim 7\times 10^4$. We also ran the KOSMA-$\tau$ model with the smallest number of very small grains with the extinction curve of LMC average (model 26) and LMC 2 (model 29) in \citet{WD2001}. The extinction curve in the LMC 2 shows a weaker 2175\AA\ bump than that of the LMC average. Thus the model 29 has a size distribution with the fewest small grains in \citet{WD2001}. The smaller amount of small grains results in a lower heating efficiency, and consequently a lower temperature, which changes the continuum SED shape. The most affected emission line is \oi\ because the \oi\ lines have the highest level energies. When we compare the fitting result of model 26 and model 28 (same extinction curve, but a different amount of very small grains), the derived density and UV field of model 26 are higher than those of model 28, because it has a lower heating efficiency and requires a larger density and/or stronger UV field to produce the same amount of the line emission. The derived mass is not significantly different, because the mass is well constrained by the continuum emission, which does not depend significantly on small grains. The density and UV field derived with the model 29 is even slightly higher, but the difference between model 26 and model 29 (different extinction curve) is not as significant as the difference between model 28 and 26. As input intensities, we examine the following cases; (1) integrated intensities over the whole velocity range, (2) a sum of the Gaussians defined by the CO velocity profiles together with the integrated intensity of \oi\ emissions, (3) same as (2) but scale the PACS \oi\ intensities using the fraction of the sum of Gaussians to the integrated intensity for the \cii. The default input used above is case (2). Case (2) corresponds to the assumption that the \oi\ emission has the same line profile as CO lines, and case (3) corresponds to the assumption that the \oi\ emission has the same line profile as \cii. The pointed observations at a few positions in N159 and 30Dor (Sect.~\ref{subsec:result_oi_profile}) show that the real case is somewhere between those two assumptions. The obtained mass is stable against the choice of the input intensities. The obtained density and mass shows a significant scatter ($\leq 1$ dex) but no systematic trend. \subsubsection{Spatial distribution of density, mass, and UV field} Figures~\ref{figure:nmuv_N159}--\ref{figure:nmuv_30Dor} shows the spatial distribution of density, mass, and UV field in our four regions obtained by the model fit using all line and continuum emissions. Areas where at least one of the \oi\ lines is detected are indicated in the figures, since the fitting with and without \oi\ emission makes a difference to the obtained range of density and the UV field strength (see Sect.~\ref{subsec:PDRfit_result}). On the other hand, the derived mass distribution is stable against different fitting and model assumptions, tracing the CO clouds. When we only look at areas where \oi\ emission detected, the UV field and mass distribution appear anti-correlated, indicating that the areas outside of giant molecular clouds are more excited by OB stars that are not embedded by molecular clouds. Surprisingly, the distribution of the density is quite similar to that of the UV field. This may mean that only dense clumps survive in higher UV field regions. However it contradicts the interferometry observations, where high density tracers (HCO$^+$ and HCN) are detected toward the center of molecular clouds in N159 \citep{Seale2012} and the detection of NH$_3$ toward N159~W \citep{OttJ2010}. In N160, there are patches with almost 2 orders of magnitude stronger UV field than surrounding pixels, which are not fully consistent with the positions of early type stars (Fig.~\ref{figure:N160_cii_stars}). Also, the derived density at these positions are $10^6$--$10^7$~\cc, which suggests a very high pressure. It is unlikely that this jump in the UV field is real. Instead we think that it is due to the degeneracy problem between a high $n$ -- high $\chi$ solution and a low $n$ -- low $\chi$ solution (see Sect.~\ref{subsec:PDRfit_result}). In 30~Dor, the derived UV field strength close to R136 is somewhat too high because it is slightly higher than the radiation field derived by the star radiation in the plane of R136 \citep{Chevance2016}. \subsubsection{Discussion} Overall, the results of the PDR model fit suggest that a model with one clump ensemble component cannot reproduce all of the line and continuum emissions consistently at most of the observed positions. A natural next step would be to consider two clump ensembles with different physical properties. With the velocity-resolved spectra, it is well justified; instead of using the sum of Gaussians that conform to the CO line profiles, we would assign each velocity component to a separate clump ensemble. They should be fitted simultaneously, with free parameters to distribute the continuum emission to each component. We did not pursue this strategy in this paper since we do not have enough data points to fit additional free parameters. A very useful future addition to the present data would be velocity-resolved high-$J$ CO spectra and mid- (to high-$J$) \thco\ spectra, to better constrain the density and UV field, and investigate the origin of low-$J$ and high-$J$ CO emissions. The results of the PDR model fit using different tracers provide a warning in interpreting the ``best'' fit of the model. When excluding one line or continuum emission from the fit, the physical properties of the best fit model vary significantly, and can jump by a few orders of magnitude in some cases. This clearly indicates that we should use as many tracers as possible to obtain a consistent picture. We mapped 3--13 arcmin$^2$ areas in 30~Dor, N158, N160, and N159 in \cii\ 158\um\ with GREAT on board SOFIA, as well as CO(2-1) to (6-5), \thco(2-1) and (3-2), \ci\ \transl\ and \ci\ \transu\ with APEX. We also observed the velocity-resolved \oi\ 145\um\ and 63\um\ at selected positions in N159 and 30~Dor for the first time. The results are as follows. \begin{itemize} \item In all four star-forming regions, the line profiles of the CO, \thco, and \ci\ emission are similar while \cii\ typically has a wider line profile or an additional velocity component. On average, 30\% of the emission in \cii\ cannot be reproduced by the CO-defined line profile. This fraction is lower toward molecular clouds. \item The \oi\ line profiles match those of CO at some positions, but are more similar to the \cii\ profiles at other positions. This indicates that we cannot simply assume that the velocity components of the \oi\ emission are the same as either CO or \cii. \item Using the \hi\ and \cii\ line profiles, we estimated that contribution of atomic gas to the \cii\ emission is 15\% or less. The thermal pressure that is required to emit the \cii\ associated with the atomic gas is $4\times 10^3$--$10^5$~K\,\cc, which is higher than the standard Galactic ISM value and consistent with previous studies. For some positions in 30~Dor, the \hi\ absorption coincides with a velocity component in \cii, which may be because of a cold molecular cloud with a mixture of atomic hydrogen. \item We interpret the different line profiles among CO, \cii, and \oi\ in the LMC as contributions from spatially separated clouds and/or clouds in different phases, which give different line ratios depending on their physical properties. \item We investigate channel maps in individual regions and distinguish clouds. \item We derived the column density of CO, \czero, and \cplus\ and compared them to those of SMC regions measured by \citet{Requena-Torres2016}. We do not see a clear correlation between $N$(\cplus)/$N$(CO) and metallicity. The trend cannot be fully explained by a different UV field strength and metallicity. \item We modeled the line and continuum emission using the latest KOSMA-$\tau$ PDR model, which treats the dust-related physics consistently and computes the dust continuum SED as well as the line emission. At most positions, a single clump ensemble does not satisfactorily reproduce all the observed emission lines and continuum. Toward the CO peak at N159~W, we propose a scenario in which the CO, \cii\ and \oi\ 63\um\ emission are affected by mutual shielding between clumps. \item We show that the best fit model results depend sensitively on which combination of continuum and emission lines are used in the fit. \end{itemize} | 18 | 8 | 1808.08826 |
1808 | 1808.00183_arXiv.txt | We present the absolute properties of the double-lined eclipsing binary KIC 6206751 exhibiting multiperiodic pulsations. The ${\it Kepler}$ light curve of this system was simultaneously solved with the radial-velocity data given by Matson et al. (2017). The results indicate that the binary star is a short-period semi-detached system with fundamental parameters of $M_1$ = 1.66$\pm$0.04 M$_\odot$, $M_2$ = 0.215$\pm$0.006 M$_\odot$, $R_1$ = 1.53$\pm$0.02 R$_\odot$, $R_2$ = 1.33$\pm$0.02 R$_\odot$, $L_1$ = 5.0$\pm$0.6 L$_\odot$, and $L_2$ = 0.96$\pm$ 0.09 L$_\odot$. We applied multiple frequency analyses to the eclipse-subtracted light residuals and detected the 42 frequencies below 2.5 d$^{-1}$. Among these, three independent frequencies of $f_2$, $f_3$, and $f_4$ can be identified as high-order (38 $\le n \le$ 40) low-degree ($\ell$ = 2) gravity-mode oscillations, whereas the other frequencies may be orbital harmonics and combination terms. The ratios between the orbital frequency and the pulsation frequencies are $f_{\rm orb}$:$f_{\rm 2-4}$ $\simeq$ 2:3, which implies that the $\gamma$ Dor pulsations of the detached primary star may be excited by the tidal interaction of the secondary companion. The short orbital period, and the low mass ratio and $M_2$ demonstrate that KIC 6206751 is an R CMa-type star, which is most likely evolving into an EL CVn star. Of seven well-studied R CMa-type stars, our program target is the only eclipsing binary with a $\gamma$ Dor pulsating component. | R CMa-type stars are eclipse binaries (EBs) with characteristics of both a short orbital period and a low mass ratio among Algol systems (Varricatt \& Ashok 1999; Budding \& Butland 2011; Lehmann et al. 2013; Lee et al. 2016b). The initially more massive star becomes the present oversized secondary with a mass less than $\sim$0.3 M$_\odot$ through mass loss caused by stellar wind and mass transfer, and the gainer becomes the present early-type main-sequence primary as the result of mass accretion (Lee et al. 2018). The R CMa-type EBs are thought to have formed by non-conservative binary evolution and ultimately evolve into EL CVn stars, which are composed of a massive A(F)-type main-sequence star and a hotter helium white dwarf precursor with a mass of $\sim$0.2 M$_\odot$ in almost constant luminosity phase (Maxted et al. 2014; Chen et al. 2017). At present, there have only been six R CMa-type binaries with reliable physical parameters: R CMa (Budding \& Butland 2011; Lehmann et al. 2018), AS Eri (van Hamme \& Wilson 1984; Ibano\v{g}lu et al. 2006), OGLEGC 228 (Kaluzny et al. 2007), KIC 10661783 (Southworth et al. 2011; Lehmann et al. 2013), KIC 8262223 (Guo et al. 2017), and OO Dra (Zhang et al. 2014; Lee et al. 2018). Five stars except for OGLEGC 228 are EBs with a pulsating component, and they all exhibit $\delta$ Sct-type pulsations. Pulsating EBs that show both eclipses and pulsations serve as a Rosetta Stone for the study of stellar structure and evolution through asteroseismology and binary properties. About 22 of them have been known to contain $\gamma$ Dor-type pulsating components (Ibanoglu, \c Cakirli \& Sipahi 2018). $\gamma$ Dor pulsators are A$-$F stars of luminosity class IV$-$V pulsating in high-order gravity ($g$) modes with periods of 0.4$-$3 d and pulsation constants of $Q >$ 0.23 d (Kaye et al. 1999; Henry, Fekel \& Henry 2005). The pulsations are driven by a mechanism known as convective blocking (Guzik et al. 2000). Generally, the $\gamma$ Dor stars are cooler than $\delta$ Sct pulsators, which pulsate in low-order pressure ($p$) modes driven by the $\kappa$ mechanism with relatively short periods of 0.02$-$0.2 d and small pulsation constants of $Q <$ 0.04 d (Breger 2000). Nonetheless, the overlap in their instability regions indicates the possible existence of hybrid pulsators exhibiting two types of pulsations. Recently, the $\gamma$ Dor$-\delta$ Sct hybrids in several EBs have been detected from space missions such as {\it Kepler} and {\it CoRot} (see Samadi Ghadim, Lampens \& Jassur 2018). Such hybrid stars provide significant information about the structure from core to surface layers because the $g$ modes help to probe the deep interior near core region of a pulsator and the $p$ modes to probe its envelope (Kurtz et al. 2015). In order to advance this subject, we have been looking for pulsating components in EBs using the highly precise {\it Kepler} data (Lee et al. 2014, 2016a,b, 2017; Lee 2016) and then performing high-resolution time-series spectroscopic observations (Hong et al. 2015, 2017; Koo et al. 2016; Lee et al. 2018). This paper presents a continuation of detailed studies of pulsating EBs. KIC 6206751 (ASAS J192938+4130.8, TYC 3142-1295-1; $K_{\rm p}$ = $+$12.142, $V\rm_T$ = $+$12.527, $(B-V)\rm_T$ = $+$0.142) was announced as a short-period Algol with a binary period of about 1.2453 d (Hartman et al. 2004; Pigulski et al. 2009). Using the eclipse times from the {\it Kepler} photometry, Gies et al. (2012, 2015) reported that the orbital period of the system is decreasing. The authors assumed that the timing variation could be caused by the light-travel-time effect due to the possible presence of a circumbinary object. Gies et al. (2012) also noticed both pulsation and starspot activity in the light curve. On the other hand, double-lined radial-velocity (RV) curves of our program target were presented by Matson et al. (2017, hereafter MGGW). They derived the velocity semi-amplitudes of the primary and secondary components to be $K_1$ = 26.8$\pm$0.5 km s$^{-1}$ and $K_2$ = 203$\pm$3 km s$^{-1}$, respectively; hence, a mass ratio of $q$ = 0.132$\pm$0.003 was determined. With these values and the inclination angle taken from Slawson et al. (2011), they obtained a semimajor axis of $a$ = 5.81$\pm$0.08 R$_\odot$ and masses of $M_1$ = 1.50$\pm$0.05 M$_\odot$ and $M_2$ = 0.198$\pm$0.007 M$_\odot$. In this article, we analyse in detail the {\it Kepler} photometric data of KIC 6206751 together with MGGW's RVs. From this analysis, we derive the unique physical properties of the binary system, and show that it is an R CMa-type EB with a $\gamma$ Dor-type pulsating component. In Section 2, the observations are discussed, including basic data reduction. In section 3, we present the binary modeling and absolute dimension. Section 4 describes the multiple frequency analyses for the residual light curve after removal of the binarity effects. We summarize and discuss our conclusions in section 5. | In this paper, we presented and analysed the {\it Kepler} light curve of KIC 6206751 obtained during a four year period, together with the RV curves of MGGW. The binary modeling shows that the EB system is a semi-detached Algol with parameters of $q$ = 0.129, $i$ = 75$^\circ$.22, $T_1$ = 6965 K, $T_2$ = 4959 K, and $l_{3}$ = 5.81 \%, in which the detached primary fills about 50 \% of its inner Roche lobe. Because the contamination level of the {\it Kepler} observations by nearby stars is estimated to be 0.009, the third light source could be a circumbinary object gravitationally bound to the eclipsing pair, as suggested by the timing analysis (Gies et al. 2012, 2015). From the combined light and RV solution, the absolute dimensions for both components were determined to be $M_1$ = 1.66 M$_\odot$, $M_2$ = 0.215 M$_\odot$, $R_1$ = 1.53 R$_\odot$, $R_2$ = 1.33 R$_\odot$, $L_1$ = 5.0 L$_\odot$, and $L_2$ = 0.96 L$_\odot$. The short $P$, and low $q$ and $M_2$ of KIC 6206751 imply that it is an R CMa-type EB (Budding \& Butland 2011; Lehmann et al. 2013; Lee et al. 2016b). The program target may have formed via non-conservative binary evolution and most likely evolve into an EL CVn star (Chen et al. 2017; Lee et al. 2018). The position of the components of KIC 6206751 in the HR diagram are displayed in Figure 6, together with those of the components of six well-studied R CMa-type stars and three EL CVn stars (cf. Lee et al. 2018). Here, the up- and down-pointing triangles denote detached and semi-detached configurations, respectively. The dashed and dash-dotted lines represent the theoretical blue and red edges of $\gamma$ Dor and $\delta$ Sct instability strips, respectively, and the cross symbols are $\gamma$ Dor pulsators in EBs with known parameters (Ibanoglu, \c Cakirli \& Sipahi 2018). The same figure displays three evolutionary models of low-mass white dwarfs with helium cores in the mass range of 0.179 M$_\odot$ to 0.234 M$_\odot$ calculated by Driebe et al. (1998). As shown in the figure, the primary component of KIC 6206751 lies in the $\gamma$ Dor region on the zero-age main sequence (ZAMS), and the low-mass secondary is noticeably evolved. As the result of non-conservative mass transfer (Chen et al. 2017), the original more massive star of KIC 6206751 became the present low-mass and oversized secondary component, and the gainer became the pulsating primary located in the $\gamma$ Dor region due to mass accretion. Later on, our program target will become a detached R CMa-type star similar to KIC 8262223 (Guo et al. 2017) and OO Dra (Lee et al. 2018) after stopping its mass transfer. Then, KIC 6206751 will evolve into an EL CVn-like star, following the evolutionary tracks presented in Figure 6. To find the pulsation frequencies of KIC 6206751, we removed the binarity effects from the observed {\it Kepler} SC data and performed a multiple frequency analysis in the whole outside-eclipse light residuals. As a consequence, we detected 42 frequencies with S/N values larger than the empirical threshold of 4.0. Three ($f_2$, $f_3$, and $f_4$) of these may be pulsation frequencies originating from the primary component, while the other frequencies may be orbital harmonics and combination terms. Applying the absolute parameters in the pulsation-subtracted SC data of Table 1 to the equation of $\log Q_i = -\log f_i + 0.5 \log g + 0.1M_{\rm bol} + \log T_{\rm eff} - 6.456$ (Petersen \& J\o rgensen 1972), we obtained the pulsation constants $Q$ as listed in Table 3. The pulsation periods ($P_{\rm pul}$) of 0.812$-$0.859 d and the $Q$ values of 0.550$-$0.582 d correspond to the $g$ modes of typical $\gamma$ Dor pulsators (Kaye et al. 1999; Henry, Fekel \& Henry 2005). The ratios of the orbital frequency to the three pulsation frequencies are $f_{\rm orb}$:$f_{\rm 2-4}$ $\simeq$ 2:3. The results indicate that the $\gamma$ Dor pulsations of KIC 6206751 may be excited by the tidal interaction of the secondary companion onto the pulsating primary. If a $\gamma$ Dor star has a rotational velocity of $v \sin i \la$ 70 km s$^{-1}$ and at least three $g$-mode frequencies, it is possible to identify the radial order ($n$) and spherical degree ($\ell$) for the pulsation frequencies with the Frequency Ratio Method (Moya et al. 2005; Su\'arez et al. 2005). The rotational velocity of KIC 6206751 is not known, but it is a short-period semi-detached EB; hence, it is expected to be in a synchronised rotation. Then, the pulsating primary may have a synchronous rotation of $v_{\rm sync}$ $\simeq$ 62 km s$^{-1}$. The pulsation modes listed in Table 3 for the three independent frequencies were identified following the procedure used by Lee et al. (2014). We found the model frequency ratios ($f_i$/$f_2$)$_{\rm model}$ best-fitting to the observed ratios ($f_i$/$f_2$)$_{\rm obs}$. The $f_2$, $f_3$, and $f_4$ frequencies were identified as degree $\ell$ = 2 for three consecutive radial orders of $n$ = 38, 39, and 40, respectively. The observed Brunt-V\"ais\"al\"a frequency integral of $\cal J_{\rm obs}$ = 700.1$\pm$3.5 is a good match to the theoretical value of $\cal J_{\rm theo}$ $\approx$ 700 $\mu$Hz for a model of $\log$ $T_{\rm eff}$ = 3.843, 1.6 M$_\odot$, and [Fe/H] = 0.0 in the $\cal J -$ $\log$ $T_{\rm eff}$ diagram described in Figure 5 of Moya et al. (2005). Including our program target, seven EBs with reliable physical properties are known to be R CMa-like stars, of which KIC 6206751 is the first binary system displaying $\gamma$ Dor pulsations. The results presented in this paper make KIC 6206751 an ideal target for asteroseismology and the study of EL CVn stars. | 18 | 8 | 1808.00183 |
1808 | 1808.03149_arXiv.txt | Using the gravitational microlensing event OGLE-2014-BLG-1186 as an instructive example, we present a systematic methodology for identifying the nature of localised deviations from single-lens point-source light curves, which ensures that 1) the claimed signal is substantially above the noise floor, 2) the inferred properties are robustly determined and their estimation not subject to confusion with systematic noise in the photometry, 3) there are no alternative viable solutions within the model framework that might have been missed. Assessing the photometric noise by means of an effective model significantly increases the sensitivity arising from an analysis of the total microlensing data set to more subtle perturbations, and thereby in particular to low-mass planets. With a time-scale $t_\mathrm{E} \sim 300~\mbox{d}$ and the brightness being significantly above baseline for four years, OGLE-2014-BLG-1186 is particularly long. Consequently, annual parallax and binarity could be separated and robustly measured from the wing and the peak data, respectively. While we were able to establish the presence of binarity, we find model light curves matching the features indicated by the acquired data (within the estimated noise) that involve either a binary lens or a binary source. Our binary-lens models indicate a planet of mass $M_2 = (45 \pm 9)~M_\oplus$, orbiting a star of mass $M_1 = (0.35 \pm 0.06)~M_{\odot}$, located at a distance $D_\mathrm{L} = (1.7 \pm 0.3)~\mbox{kpc}$ from Earth, whereas our binary-source models suggest a brown-dwarf lens of $M = (0.046 \pm 0.007)~M_{\odot}$, located at a distance $D_\mathrm{L} = (5.7 \pm 0.9)~\mbox{kpc}$, with the source potentially being a (partially) eclipsing binary involving stars predicted to be of similar colour given the ratios between the luminosities and radii. The ambiguity in the interpretation would be resolved in favour of a lens binary by observing the luminous lens star separating from the source at the predicted proper motion of $\mu = (1.6 \pm 0.3)~\mbox{mas}\;\mbox{yr}^{-1}$, whereas it would be resolved in favour of a source binary if the source could be shown to be a (partially) eclipsing binary matching the obtained model parameters. We experienced that close binary source stars pose a challenge for claiming the detection of planets by microlensing in events where the source trajectory passes close to the central caustic near the lens star hosting the planet. | The vast majority of claimed microlensing planet detections are based on a pretty obvious signal in the acquired photometric data \citep[e.g.][]{OB03235,OB05071,OB05390,OB07368,Gaudi:doubleplanet,KB09266}. This makes one wonder why detections from less obvious signals \citep[e.g.][]{KB07400,KB08310} are scarce, given that more subtle features should be quite common. Clearly, if more subtle features are discarded altogether, we lose out on the significance of the planet population statistics arising from the acquired data, and we lose sensitivity particularly to low-mass companions. Moreover, sampling events more densely than necessary can be quite a waste of telescope resources, and strongly diminish the overall detection efficiency of follow-up campaigns \citep[e.g.][]{Horne:metric, Dominik:PLANET, SIGNALMEN, MiNDSTEp,RoboNet-II}. The detection efficiency \citep[e.g\ ][]{GS:deteff,BenRhie:deteff} is a crucial characteristic, with planets probabilistically escaping their detection through microlensing even with perfectly sampled and precise photometric light curves \citep{MP91}, depending on where they happen to be located along their orbit during the course of a microlensing event. If we assume a photometric time series composed of $N$ data points $(t_i, F_i, \sigma_i)$ with measured fluxes $F_i$ and estimated uncertainties $\sigma_i$, as well as a theoretical light curve $F(t_i)$, one finds the sum of the squared standardised residuals as \begin{equation} \chi^2 \equiv \sum_{i = 1}^{N} \left(\frac{F_i-F(t_i)}{\sigma_i}\right)^2\,. \end{equation} As compared to gravitational microlensing by a single isolated lens star \citep{Ein36,Pac1}, a quasi-static binary lens system (e.g. a star with a single planet) is characterised by an additional three parameters \citep{MP91}. Moreover, a planetary signature also usually reveals the angular size of the source star, described by a further parameter. For such a signature, one therefore finds only a small probability ${\cal P}_4(\Delta \chi^2 \geq 20) = 4\times 10^{-4}$ for a difference in $\chi^2$ in excess of 20 for 4 additional degrees of freedom. This means that a likelihood ratio test suggests a clear signal for e.g. as few as 5 data points at the 2-$\sigma$ level, under the provision that the measurement uncertainties are accurately estimated, uncorrelated, and follow a Gaussian profile. However, in reality it cannot be tacitly assumed that these conditions hold, and we rather need to be careful about false positives lurking in the actual noise of the photometric measurements. Even a high detection threshold does not provide an insurance policy on this because correlated noise (or ``red noise'') can lead to ``pseudo-detections'' at arbitrarily large $\Delta \chi^2$ if just the cadence of the photometric time series is high enough. In fact, in at least one case, the careful analysis of an observed gravitational microlensing event arrived at the conclusion that a putative planetary signal is likely due to red noise \citep{Bachelet:noise}. A consistent interpretation of data requires to demonstrate that putative signals are not likely to arise from noise, and adequate criteria are required to distinguish signals from the noise floor. It would be obviously inconsistent to claim a detection of a signal from data that show deviations that are similar to what is being considered ``noise'' for other data. It is therefore indicated to establish a suitable ``noise'' model and estimate some ``noise'' statistics. Blind searches in high-dimensional non-linear parameter spaces bear a substantial risk of confusing true signals in the data with noise. It is rather straightforward to find a good match between noise patterns and models describing small localised deviations, as previous analyses of microlensing events explicitly demonstrated \citep[e.g.][]{OB08510}. Signals of low-mass planets and satellites may be subtle, but fortunately these are well localised. In other words, the vast majority of photometric data provide no relevant constraint to the model parameters that describe the anomaly. Moreover, all the other parameters can usually be well determined from the data not containing the anomaly. This permits splitting up parameter space into two subspaces with disjoint associated data sets. Looking at the effect of the anomaly region on the anomaly-independent parameters provides a valuable consistency check, while the data not covering the putative anomaly can be used to infer parameters describing noise statistics that do not depend on any assumptions about the anomaly. It should however be noted that while such an approach works well for weak anomaly features, strong features (e.g.\ due to caustic passages) can be highly sensitive to the track of the source relative to the lens system, thereby substantially affecting a large number of model parameters. In this article, we discuss the microlensing event OGLE-2014-BLG-1186, which not only is of exceptionally long duration, but also shows a putative anomaly in the form of a close double peak. We explicitly demonstrate how this anomaly can be systematically and robustly identified and present viable interpretations of its physical nature. Gravitational microlensing events that show a photometric light curve involving two peaks can result from either (or both) a lens binary \citep{MP91,GL92,GS98} or a source binary \citep{GriHu92}. \citet{Gaudi:source} discussed an ambiguity between planetary binary-lens and binary-source models for putative planetary signatures that arise from the source passing close to one of the `planetary caustics' (see Sect.~\ref{sec:BLspace}), so that the light ray passes close to the planet \citep{Erdl}. In the case of OGLE-2014-BLG-1186, we are however facing a different situation, where the source passes close to the central caustic of the putative binary-lens system, located near the position of the planet's host star. In Sect.~\ref{sec:data}, we describe our data acquisition and original identification of a putative anomaly over the peak of the light curve, while Sect.~\ref{sec:model} is devoted to a detailed account of our modelling efforts. We discuss the physical nature of the lens and source objects and the wider significance of our findings in Sect.~\ref{sec:interpretation}. We draw final conclusions in Sect.~\ref{sec:conclusions}. | \label{sec:conclusions} The power of inferred planet population statistics from gravitational microlensing campaigns greatly increases with the ability to distinguish low-amplitude signals from the noise floor of photometric data. Separating model parameters and subsets of data has been demonstrated to be a generic and powerful approach for characterising localised effects in photometric light curves. In particular, this allows us to build effective models of the photometric noise on data that do not contain the putative signal under investigation, and thereby enables a meaningful probabilistic assessment of the significance of such a signal under the assumption that the data for epochs not covering the signal are reasonably well understood. Hence, signals of planets that are otherwise missed become detectable. While we laid the groundwork for a detailed assessment of the feasibility of potential alternative model interpretations of the observed data, it turned out that for the concrete case of the microlensing event OGLE-2014-BLG-1186, we can straightforwardly rule out any binary-lens alternatives to the four configurations presented. Rather than claiming that our models are the right ones because no viable alternatives have been found, an analysis of the underlying mathematical properties of potential solutions that can provide matching morphologies enabled us to restrict all viable alternatives within the adopted model framework to a small finite number of prototypes, similar to what was suggested by \citet{Liebig}, which then either turned out to lead to a match to the data that cannot be improved, or an obvious mismatch. However, we can only check the adopted model framework for plausibility and consistency, whereas it is fundamentally impossible to rule out the existence of further plausible interpretations beyond the adopted model framework, given that our knowledge will always remain limited and incomplete. In fact, we experienced that close binary source stars pose a challenge for claiming the detection of planets by microlensing in events where the source trajectory passes close to the central caustic near the lens star hosting the planet \citep{GS98}. This is different from the ambiguity between binary-lens and binary-source interpretations discussed by \citet{Gaudi:source}, which relates to planetary signatures arising from approaching planetary caustics. We note that while in this case a small luminosity offset ratio $\omega \la 10^{-2}$ is required, such a restriction does not hold for the type of ambiguity that we encountered. Close binary-source models come with a large number of degrees of freedom, involving two source size parameters as well as parameters that describe the orbital motion, which is likely to significantly affect the light curve over the peak due to orbital periods of the order of days. Binary-source interpretations must not be discarded prematurely on the basis of comparing binary-lens models with static binary-point-source models. In order to resolve such ambiguities, uninterrupted high-cadence multi-band photometric observations over the peak would be useful. Simultaneous or quasi-simultaneous observations with different bandpass filters can not only measure chromaticity, but moreover increase the statistical significance of signals due to correlations \citep{DoHi,Street:Luhman}. Source binarity could also be indicated by means of spectra taken at either peak. Moreover, the astrometric signature of binary-lens and binary-source events with similar photometric signature is substantially different \citep{Han:astrometry1,Han:astrometry2,Han:astrometry3}. \citet{Calchi:resolve} also recently discussed a case of binary-lens vs binary-source ambiguity for an event that shows an anomaly signature both from ground- and space-based photometric observations, providing complementary information due to the different lines of sight. We finally note that gravitational microlensing events such as OGLE-2014-BLG-1186 for which both the source size parameter $\rho_\star$ and the parallax parameter $\pi_\mathrm{E}$ can be reliably measured provide a valuable sample for testing models that describe the mass distribution and kinematics of the Milky Way, given that with an estimate of the angular size $\theta_\star$ of the source star from a colour-magnitude diagram, one directly obtains the mass $M$ of the lens system (as well as the individual masses of its constituents), its distance $D_\mathrm{L}$ from the observer, as well as the effective proper motion $\mu$. | 18 | 8 | 1808.03149 |
1808 | 1808.04133_arXiv.txt | We present the study of the dynamical status of the galaxy cluster CL1821+643, a rare and intriguing cool-core cluster hosting a giant radio halo. We base our analysis on new spectroscopic data for 129 galaxies acquired at the Italian Telescopio Nazionale {\it Galileo}. We also use spectroscopic data available from the literature and photometric data from the Sloan Digital Sky Survey. We select 120 cluster member galaxies and compute the cluster redshift $\left<z\right>\sim 0.296$ and the global line-of-sight velocity dispersion $\sigma_{\rm V}\sim 1100$ \kss. The results of our analysis are consistent with CL1821+643 being a massive ($M>10^{15}$\m) dynamically relaxed cluster dominated by a big and luminous elliptical at the centre of the cluster potential well. None of the tests employed to study the cluster galaxies kinematics in the 1D (velocity information), 2D (spatial information), and 3D (combined velocity and spatial information) domains is able to detect significant substructures. While this picture is in agreement with previous results based on X-ray data and on the existence of the central cool core, we do not find any evidence of a merging process responsible for the radio halo discovered in this cluster. Thus, this radio halo remains an open problem that raises doubts about our understanding of diffuse radio sources in clusters. | \label{intro} A fraction of the most massive galaxy clusters exhibits in their inner regions diffuse radio sources named {\it radio haloes} (also {\it giant radio haloes}, or GRHs). They are extended (on $~$1 Mpc scales) unpolarized synchrotron sources produced by relativistic electrons and large-scale magnetic fields spread out the intracluster medium (ICM), not associated with compact radio sources like radio galaxies (see e.g., Feretti et al. \citeyear{fer12} for a review). The existence of GRHs indicates the presence in the ICM of particle acceleration mechanisms. In particular, GRHs are probably related to turbulence induced in the ICM by recent mergers (e.g. Brunetti \& Jones \citeyear{bru15}). In fact, for several decades after their discovery, these sources have always been found in dynamically disturbed systems, i.e. massive merging clusters characterized by the absence of a cool core (Feretti et al. \citeyear{fer12} and references therein). This picture has dramatically changed in 2014, when Bonafede et al. (\citeyear{bon14}, hereafter B14) published the discovery of a GRH in the cool-core cluster CL1821+643. More recently, Sommer et al. (\citeyear{som17}) found diffuse radio emission at Mpc scale on two $z\sim 0.22$ relaxed clusters, Abell 2390 and Abell 2261. Another case is Abell 2142 ($z\sim 0.09$), where Venturi et al. (\citeyear{ven17}) surprisingly found a GRH despite the fact that its optical and X-ray properties do not reveal a major merger. Finally, Savini et al. (\citeyear{sav18}) reported the detection of diffuse radio emission on scales larger than the core in the cool-core cluster PSZ1G139.61+24 ($z\sim 0.27$). In summary, these recent findings suggest the possible existence of a new class of dynamically relaxed clusters with GRHs. In the framework of turbulent models this is surprising and challenges the idea that major mergers, necessary to power GRHs, always disrupt the cool core. In this paper, we focus on one of the puzzling clusters cited above: CL1821+643 (hereafter CL1821). CL1821 hosts an extended central diffuse emission with linear size $\sim 1.1\hhh$ and an extrapolated radio power $P_{\rm 1.4\ GHz} \sim (3.6-3.8)\ 10^{24}$ W Hz$^{-1}$ elongated along the SE--NW direction (see B14). Because of its location and size, B14 classified this source as a GRH. From the optical point of view, CL1821 (at $z\sim$ 0.299, Schneider et al. \citeyear{sch92}) is dominated by the central quasar H1821+643 (e.g. Hutchings \& Neff \citeyear{hut91}; Aravena et al. \citeyear{ara11}; Reynolds et al. \citeyear{rey14}; Walker et al. \citeyear{wal14}), an uncommon example of an optically very luminous quasar hosted by the central dominant elliptical galaxy of a massive cluster (see Fig.~\ref{figimage}). Moreover, CL1821 appears slightly elongated in the SE--NW direction, as inferred from its weak lensing properties (Wold et al. \citeyear{wol02}). However, our present knowledge on this cluster is mainly based on X-ray data. Russell et al. (\citeyear{rus10}) analysed {\it Chandra} data taken with the ACIS-S instrument to study the ICM properties. In particular, they found that the ICM temperature drops from $\sim$9 to $\sim$1 keV, with a short central cooling time of $\sim$ 1 Gyr typical of a relaxed strong cool-core cluster. They also concluded that the quasar did not have a strong impact on the large-scale ICM properties. The ACIS-S images suggest a projected morphology elongated on the SE--NW direction (a feature revealed also by radio and weak lensing data, see above and Fig.~\ref{figimage}) but do not show any evidence of a major merger in this cluster similar to those detected in other clusters with GRHs. Moreover, an analysis of CL1821 based on classical X-ray morphological estimators (concentration parameter $c$ and power ratio $P_3/P_0$; see B14 and references therein) also supports the hypothesis that it is a relaxed galaxy system. Only the estimator $w$ (centroid shift parameter), could suggest the existence of an undergoing minor or off-axis merger (see B14). A more recent work by Kale and Parekh (\citeyear{kal16}) partially disagrees with the findings of B14, claiming that a morphological analysis of the same {\it Chandra} data (based on the parameters Gini, $M_{20}$, and $c$; see Parekh et al. \citeyear{par15}) puts CL1821 in the category of relaxed/non-relaxed clusters when H1821+643 is included/excluded in/from the analysis. Nevertheless, the X-ray morphological indicators cited above are not sensitive to eventual mergers along the line of sight (LOS). The only way to explore this possibility and to finally assess the dynamical status of this intriguing cluster is to perform spectroscopic observations of the cluster member galaxies. In fact, the spatial and kinematical analysis of member galaxies constitute an effective tool to detect substructures in clusters and highlight eventual pre-merging subgroups or merger remnants (e.g. Boschin et al. \citeyear{bos04}; Boschin et al. \citeyear{bos13}). The optical information complements the results of X-ray studies, also considering that the collisional and non-collisional components of clusters (ICM and galaxies, respectively) exhibit different behaviours during mergers (see e.g. simulations by Roettiger et al. \citeyear{roe97}). \begin{figure*} \centering \includegraphics[width=18cm]{figmultia8.ps} \caption{The cluster CL1821 in the optical, X-ray and radio bands. The TNG grey--scale image (FOV $\sim$8 arcmin $\times$ 8 arcmin) in the background corresponds to the optical $r'$-band. Red thin contours show the cluster X-ray emission in the 0.5--7 keV band (from \textit{Chandra} archival image ID~9398; Texp: 34 ks). Thick green contours are the contour levels of a GMRT 323 MHz low-resolution image and show the radio halo (from B14). Top left hand inset is the TNG wavelength-calibrated spectrum of the central quasar H1821+643 (ID~94; see Table~\ref{catalogCL1821}). Other labels indicate galaxies mentioned in the text. The diffuse emission visible in the optical image NW of the galaxy ID~85 is the planetary nebula PN G094.0+27.4.} \label{figimage} \end{figure*} At the moment only a few dozen of galaxies have known redshifts in an area 30 arcmin wide around H1821+643. Therefore, we decided to perform a spectroscopic survey of CL1821, mainly sampling the central $\sim$1 Mpc size region of the cluster characterized by the diffuse X-ray and radio emissions. In particular, we obtained new spectroscopic data at the Italian Telescopio Nazionale {\em Galileo} (TNG), whose facilities are well suited for the study of a galaxy cluster at $z\sim 0.3$ like CL1821 (see e.g. the DARC project, Girardi et al. \citeyear{gir11} and references therein \footnote{see also http://wwwuser.oats.inaf.it/girardi/darc, the web site of the DARC project.}). This paper is organized as follows. We describe the optical observations and present our spectroscopic data catalogue in Sect.~\ref{data}. In Sect.~\ref{optanalysis} we explain the results of our analysis of the cluster structure. We discuss our results and present the conclusions in Sect.~\ref{disc}. Throughout this paper, we use $H_0=70$ km s$^{-1}$ Mpc$^{-1}$ and $h_{70}=H_0/(70$ km s$^{-1}$ Mpc$^{-1}$) in a flat cosmology with $\Omega_0=0.3$ and $\Omega_{\Lambda}=0.7$. In the adopted cosmology, 1 arcmin corresponds to $\sim 265$ \kpc at the cluster redshift. Unless otherwise stated, we indicate errors at the 68\% confidence level (hereafter c.l.). | 18 | 8 | 1808.04133 |
|
1808 | 1808.02322_arXiv.txt | {Recent observations of unexpected structures in the Galactic Cosmic Ray (GCR) spectrum and composition, as well as growing evidence for episodes of intense dynamical activity in the inner regions of the Galaxy, call for an evaluation of the high-energy particle acceleration associated with such activity and its potential impact on the global GCR phenomenology.} {We investigate whether particles accelerated during high-power episodes around the Galactic center can account for a significant fraction of the observed GCRs, or, conversely, what constraints can be derived regarding their Galactic transport if their contributions are negligible.} {% Particle transport in the Galaxy is described with a two-zone analytical model. We solve for the contribution of a Galactic Center Cosmic-Ray (GCCR) source using Green functions and Bessel expansion, and discuss the required injection power for these GCCRs to influence the global GCR phenomenology at Earth.} {We find that, with standard parameters for particle propagation in the galactic disk and halo, the GCCRs can make a significant or even dominant contribution to the total CR flux observed at Earth. Depending on the parameters, such a source can account for both the observed proton flux and boron-to-carbon ratio (in the case of a Kraichnan-like scaling of the diffusion coefficient), or potentially produce spectral and composition features.} {Our results show that the contribution of GCCRs cannot be neglected \emph{a priori}, and that they can influence the global GCR phenomenology significantly, thereby calling for a reassessement of the standard inferences from a scenario where GCRs are entirely dominated by a single type of sources distributed throughout the Galactic disk.} | The sources of Galactic cosmic rays (GCRs) remain elusive in spite of decades of intense observational and theoretical efforts. Supernova remnants (\cite{blandford1978particle}, \cite{krymsky1979formation}, \cite{meyer1997galactic}) and superbubbles (\cite{higdon1998cosmic}, \cite{Binns2005}, \cite{bykov1992non}, \cite{parizot2004superbubbles}) have long been acknowledged as promising candidates, based on energy considerations, isotopic composition arguments and a detailed understanding of the characteristics of particle acceleration. Several issues remain outstanding, however, including the $^{22}$Ne signature of GCRs and the maximum energy levels that can be accounted for \citep{lagage1983maximum}. Furthermore, while there is no doubt that these astrophysical environments do accelerate particles, as shown by the high-energy radiation that they generate (\cite{koyama1995evidence}), many questions remain about the magnitude of their actual contribution to the locally observed GCRs. In addition, new observations of unexpected structures in the low-energy GCR spectrum and composition (\cite{pamela2011}, \cite{AMS2015}) raise questions about the respective contributions of different sources in different energy ranges. In this context, growing evidence for episodes of intense dynamical activity in the inner regions of the Galaxy (\cite{acero2016development}, \cite{abramowski2016acceleration}) justifies an evaluation of their potential contributions to GCRs and implications for the characteristics of high-energy particle acceleration (\cite{Cheng2012}, \cite{Tibolla2018}). Indeed, a total energy release of up to $10^{57}$~ergs has been proposed (\cite{guo2012fermi}), which is enough to compete with the average SNR power in the entire Galaxy if the repetition time is of the order of $10^{7}$~years. From a study of how so-called \emph{Fermi bubbles} interact with the Milky Way hot gas halo, \cite{miller2016interaction} have estimated that the average energy injection rate is in a 1--7$\,10^{42}$~erg s$^{-1}$ range, which exceeds the kinetic power due to SN explosions in the interstellar medium. These results have motivated us to investigate whether the particles accelerated during these episodes may account for a significant fraction of the GCRs, at Earth and/or elsewhere in the Galaxy, or, conversely, what constraints can be derived about Galactic transport of these particles if their contribution is negligible. In the following, we will refer to these particles as Galactic Center Cosmic Rays (GCCRs). In this paper, we make a first attempt to address these important questions by studying the contribution of a continuous source of energetic particles at the center of the Galaxy to the local GCRs. Our calculations rely on a simplified propagation model similar to that which is used in generic studies of GCR phenomenology (\cite{ginzburg2013origin}, \cite{Strong1998}, \cite{taillet2003spatial}, \cite{Bringman2007}, \cite{boudaud2015fussy}, \cite{Giesen2015}, \cite{genolini2015}). This model includes energy-dependent diffusion and advection in a Galactic wind, energy losses and particle re-acceleration, and is described in Sect.~\ref{sec:model}. The formalism and resolution scheme are presented in Sect.~\ref{sec:ResolutionScheme} and results are shown in Sect.~\ref{sec:Results}. A summary and discussion of the results are proposed in Sect.~\ref{sec:discussion}. | \label{sec:discussion} In the absence of a definite model that would be supported by clear evidence, it appears important to revisit in a broader perspective what is often considered common knowledge regarding cosmic ray origin and propagation in the Galaxy. Most of the GCR phenomenological studies assume that cosmic ray sources are distributed throughout the Galatic disk, with a space and time granularity that can be neglected, at first order, with respect to the typical source seperation distances and repetition times. While this is a reasonable assumption, especially since such distributed sources are indeed known (notably SNRs and superbublles), it does not exclude that other types of sources may also contribute to the GCRs. In the framework of GCR studies assuming distributed sources, reasonable estimates of the GCR diffusion coefficient and confinement time could be obtained, which in turn provided an estimate of the required GCR source power, comparable to a fair fraction of the total power released by SN explosions in the Galaxy. It turns out, however, that similar or even possibly larger average power is now known to be released around the Galactic center through episodic events, and that these events lead to astrophysical conditions that appear to be potentially propitious for particle acceleration. According to \cite{guo2012fermi} and \cite{miller2016interaction}, the event that led to the so-called \textit{Fermi bubbles} released a total energy of $10^{57}$~ergs, for an average injection rate of 1--7 $10^{42}$ erg/s, which exceeds the total kinetic power of SN explosions in the interstellar medium by large amounts. It is thus natural to investigate whether such events could play a role in the global GCR phenomenon, and if so how the phenomenology would be affected. The main result of this paper is the confirmation that, with the same type of parameters as those derived from distributed-sources GCR studies, the contribution of the GCCRs cannot be a priori neglected. We found, indeed, that save for models with very thin halos (e.g. MIN), the required injection power to match the observed GCR fluxes ($\mathcal{P}_\mathrm{inj} \lesssim 10^{41}$ erg/s) is only a fraction of the inferred available power. For some transport parameters, the GCCRs could even dominate the GCR flux over a large range of energies. If this is the case, then they will have to satisfy the observational constraints directly. To see if this could be possible, we investigated the caracteristics of the GCCRs as if they were alone in the Galaxy, and found that, even with simple generic assumptions and first order modelling (see Sect.~\ref{sec:model}), it is indeed possible to reproduce the locally observed primary CR spectra as well as secondary-to-primary ratios (B/C) and secondary radioactive-to-stable ratio ($^{10}$Be/$^9$Be), although the latter is only true for a Kraichnan-like energy dependence of the diffusion coefficient. However, even a subdominant (but non negligible) contribution of the GCCRs may have important consequences on the general CR phenomenology. In particular, the source composition and source spectrum of the GCCRs may be expected to be somewhat different from those of the other sources. In regions of the spectrum where both contributions are roughly similar in magnitude, this may lead to gradual changes in the composition (hence different spectra for different nuclei), or to specific features in the elemental spectra. Such effects will be studied in a forthcoming paper. If the GCCRs are able to contribute at a non negligible level, some of the conclusions of the standard approach regarding the transport parameters of the energetic particles in the Galaxy may also have to be revised, which can result in the relaxation of some of the usual constraints. In particular, the modelling of the multi-wavelength emission of SNRs may not have to be done with the requirement that the associated energetic particles be also compliant with the entire GCR phenomenology, including the maximum energy problem or the elemental and isotopic ratios. Likewise, it may be possible to relax the constraints associated with the study of the so-called cosmic-ray clocks (radioactive secondary nuclei), if two main components with different timescales are mixed together among the GCRs. The fact that GCCR typically need more time to reach the Solar System than the average cosmic ray from more evenly distributed sources has also some consequences on the link between CR nuclei and leptons. Since electrons and positrons rapidly lose energy as they propagate in the Galactic magnetic field, those observed at Earth must have been generated relatively nearby. GCCRs can only contribute secondary $e^{\pm}$, e.g. produced by collisions of high energy protons and helium nuclei on the atoms of the ISM (see e.g. \cite{delahaye2009galactic}), while the bulk of the energetic leptons should still be due to local Galactic sources. Of course, such a ``decoupling" between nuclei and lepton sources is not specific to our approach, and is also suggested for instance in the context of the observed positron anomaly (\cite{adriani2009anomalous}) where nearby pulsar sources can be invoked (\cite{hooper2009pulsars}, \cite{profumo2012dissecting}, \cite{linden2013probing}). Note that this decoupling may also alleviate some of the problems that arise when trying to reconcile observations with models of dark matter (\cite{boudaud2015new}, \cite{cirelli2009model}). In this paper, we have estimated the average contribution of the GCCRs in the vicinity of the solar system, assuming steady state. Because of the very nature of the potential GCCR sources, the assumption of a constant particle injection is clearly wrong. However, for not too high energies, i.e. as long as the ``confinement time" of the particles is much larger than the repetition time between acceleration events, the steady state solution provides an acceptable approximation. To estimate the energy range where the steady state assumption can be expected to be valid, we can compare the relevant timescales. The most recent major event in the Galatic center is suggested to have occurred $\sim 3$ Myr ago (\cite{miller2016interaction}) and to have lasted for $\sim 0.1 - 0.5$ Myr (\cite{guo2012fermi}), leading to the so-called Fermi Bubbles (\cite{acero2016development}). We may thus assume a repetition time of the order of a few Myr. For each event, GCCR injection occurs on a much shorter timescale and can be approximated here as being instantaneous. This gives rise to a diffusion front propagating outwards from the Galactic center. If diffusion were isotropic in a homogeneous medium with diffusion coefficient $D$, the density of particles at distance $r$ from the source, at a time $t$ after injection, would be simply given by the Green function: \begin{equation} \Psi_G(\vec{r},t>0) = \frac{N_0}{(4\pi D t)^{3/2}} \exp\left\lbrace-\frac{\vec{r}\,^2}{4Dt}\right\rbrace, \label{eq:PsiGreenInf} \end{equation} where $N_0$ is the number of particles injected at $\vec{r} = 0$ at $t=0$. At any given position $r$, this density rapidly increases to a maximum and decreases more slowly as the diffusion sphere expands. The typical duration of the event, as seen at radius $r$, can be estimated as the time during which the particle density is larger than half of its maximum value: $\Delta t_{1/2} \simeq 0.45 r^2/D$. Thus, at radius $r$, the steady-state solution provide a good approximation of the actual GCCR flux at any given time up to an energy $K$ such that $D(K) < 0.45 r^2/\Delta t_\mathrm{s}$, where $\Delta t_\mathrm{s}$ is the typical time interval between two source episodes. Numerically, at the solar radius, this gives: \begin{equation} D(K) \la (12 \,\mathrm{kpc}^2/\mathrm{Myr}) \times \left(\frac{\Delta t_\mathrm{s}}{3\,\mathrm{Myr}}\right)^{-1} \times \left(\frac{r}{r_\odot}\right)^2. \label{eq:Dmax_steady} \end{equation} With the parameterization of the diffusion coefficient adopted above, $D = D_{0} \, \beta \, R_{\mathrm{GV}}^{\delta}$, with $D_0 \sim 0.07$--0.1~kpc$^2$/Myr, this corresponds to rigidities \begin{equation} R \la (200^{1/\delta} GV) \times \left(\frac{\Delta t_\mathrm{s}}{3\,\mathrm{Myr}}\right)^{-1/\delta} \times \left(\frac{r}{r_\odot}\right)^{2/\delta}. \label{eq:Rmax_steady} \end{equation} In particular, for the Kr2.4 model, the above solution is roughly valid up to $\sim 40$~TeV, and for the Kol2.55 model, up to 8~PeV. At higher energy, however, the intermittent nature of the central source will affect the main characteristics of the GCCR. Qualitatively, one should expect a reduction of the high energy particles at any time when the diffusion front from the last event at these energies has already passed the solar radius, producing a knee-like feature. Ankle-like features can also be obtained at energies where the diffusion front from the last event is arriving at the solar radius at the time of observation, while the previous one has already left. These effects will be studied in more detail together with associated composition features in a forthcoming paper \citep{JaupartTransient}. The previous considerations can be extended to any position inside the Galactic disk. For any galactocentric radius $r<20$ kpc, there is a critical rigidity $R_\mathrm{crit}$ (given by Eq. \ref{eq:Rmax_steady}) above which the steady state approximation is no longer valid. More specifically, in the inner region of the Galaxy, at $r \simeq 1$ kpc for example, this yields $R_\mathrm{crit} \sim 2.8^{1/\delta} $ GV, corresponding to a few GeV of kinetic energy in the Kr2.4 and Kol2.55 models. The diffusive front from the last event has thus gone through the inner regions of the Galaxy ($r \lesssim 1$~kpc) for GCCRs with a kinetic energy above the GeV level. Thus, these regions are depleted in these GCCRs, which acts to flatten the distribution given by Fig. \ref{fig:halo}. This is also the energy range which dominates the production of gamma-rays from $\pi^0$ decay. Therefore, in order to compute the gamma-ray background associated with the GCCRs and compare it to the observation, a more detailed, time-dependent treatment is needed. This will be addressed in a separate paper. | 18 | 8 | 1808.02322 |
1808 | 1808.01784_arXiv.txt | The cosmic distance duality relation (DDR), which connects the angular diameter distance and luminosity distance through a simple formula $D_A(z)(1+z)^2/D_L(z)\equiv1$, is an important relation in cosmology. Therefore, testing the validity of DDR is of great importance. In this paper, we test the possible violation of DDR using the available local data including type Ia supernovae (SNe Ia), galaxy clusters and baryon acoustic oscillations (BAO). We write the modified DDR as $D_A(z)(1+z)^2/D_L(z)=\eta(z)$, and consider two different parameterizations of $\eta(z)$, namely $\eta_1(z)=1+\eta_0 z$ and $\eta_2(z)=1+\eta_0 z/(1+z)$. The luminosity distance from SNe Ia are compared with the angular diameter distance from galaxy clusters and BAO at the same redshift. Two different cluster data are used here, i.e. elliptical clusters and spherical clusters. The parameter $\eta_0$ is obtained using the Markov chain Monte Carlo methods. It is found that $\eta_0$ can be strictly constrained by the elliptical clusters + BAO data, with the best-fitting values $\eta_0=-0.04\pm 0.12$ and $\eta_0=-0.05\pm 0.22$ for the first and second parametrizations, respectively. However, the spherical clusters + BAO data couldn't strictly constrain $\eta_0$ due to the large intrinsic scatter. In any case studied here, no evidence for the violation of DDR is found. | The cosmic distance duality relation (DDR) plays an important role in cosmology and astronomy. According to this relation, the luminosity distance $D_L(z)$ is strictly correlated to the angular diameter distance by a simple formula, i.e. $D_A(z)(1+z)^2/D_L(z)=1$ \citep{Etherington:1933,Etherington:2007}. The DDR holds in any metric theory of gravity such as the general relativity, as long as the photons travel along null geodesics and the photon number is conserved during the propagation \citep{Ellis:1971,Ellis:2007}. The violation of DDR may be caused by e.g. the coupling of photon with unknown particles \citep{Bassett:2003vu}, the extinction of photon by intergalactic dust \citep{Corasaniti:2016}, the variation of fundamental constants \citep{Ellis:2013}, and so on. The modern cosmology is strongly dependent on the validity of DDR. Any violation of DDR would imply that there are new physics beyond the standard cosmological model. Therefore, testing the validity of DDR is of very importance and has aroused great interests in recent years. A straightforward way to test the DDR is to measure the luminosity distance $D_L(z)$ and angular diameter distance $D_A(z)$ at the same redshift. A lot of works have already been done along this line \citep{Bernardis:2006,Holanda:2010vb,Piorkowska:2011nhd,Yang:2013coa,Costa:2015lja,Holanda:2016msr,Ma:2016bjt,Holanda:2016zpz,Li:2018,Hu:2018yah}. The luminosity distance is usually measured from type-Ia supernovae (SNe Ia), which are perfect standard candles and are widely used to measure the cosmological distance \citep{Perlmutter:1998np,Riess:1998mnb}. However, there is no optimal way to measure the angular diameter distance. The possible methods to determine $D_A$ include (1) by using the combined data of the $X$-ray and Sunyaev--Zeldovich (SZ) effect of galaxy clusters \citep{Filippis:2005,Bonamente:2006ct}, (2) by measuring the baryon acoustic oscillations (BAO) signal in the galaxy power spectrum \citep{Beutler:2011hx,Anderson:2013zyy,Kazin:2014qga,Delubac:2015aqe}, (3) by measuring the angular size of ultra-compact radio sources based on the approximately consistent linear size \citep{Kellermann:1993mki,Gurvits:1994fgs,Gurvits:1999hs,Jackson:2004jw}, (4) by measuring the images of quasars that are strongly gravitational lensed by foreground galaxies \citep{Cao:2015,Liao:2016uzb}, etc. All of these methods to measure the angular diameter distance have their own advantage and shortcoming. The distance of cluster obtained using SZ effect is available in the full redshift range $z<1$, but it strongly depends on the mass profile of cluster hence induces large uncertainty. The BAO method has a high accuracy, but the number of available data points is very limited. The radio source sample is large and spans a wide redshift range, but the low redshift sources confront serious evolution effect thus are not suitable to be used as standard rulers. The strong gravitational lensing can reach to a relatively high redshift, but can only give the ratio of lens-source distance to source-observer distance, and thus signals of DDR violation, if really exists, may be partially canceled out. Until now, no evidence for the violation of DDR is found by any of these method. For example, using two different galaxy cluster data, \citet{Yang:2013coa} found that the DD relation is well compatible with observations. \citet{Ma:2016bjt} used the BAO data and found 5\% constraints in favor of DDR validity. With the ultra-compact radio source data, \citet{Li:2018} also found null result of DDR violation. \citet{Liao:2016uzb} combined the strong gravitational lensing data with cluster data and still found no evidence for the violation of DDR. One problem of testing DDR is that the $D_L$ data and $D_A$ data are usually not measured at the same redshift. To solving this problems, several methods have been proposed, such as the nearest neighborhood method \citep{Holanda:2010vb,Liao:2016uzb}, the interpolation method \citep{Liang:2013mnf}, and the Gaussian processes \citep{Rana:2017sfr,Li:2018}. Only the data in the overlapping redshift range are available to test DDR. The furthest SNe Ia in previous datasets such as Union2.1 \citep{Suzuki:2012dhd} and JLA \citep{Betoule:2014frx} are usually bellow redshift $1.4$. Recently, a new SNe Ia sample called Pantheon is released \citep{Scolnic:2017caz}. This is the most up-to-date and largest SNe Ia sample at present. This sample consists of 1048 SNe Ia and the systematic uncertainty is reduced compared the previous compilations. Moreover, the furthest SNe reaches to redshift $z_{\rm max}\sim 2.3$ (for comparison, $z_{\rm max}\sim 1.4$ in Union2.1 and $z_{\rm max}\sim 1.3$ in JLA), which is close to the redshift of the furthest available BAO data point. So it is interesting to test DDR with the Pantheon dataset. In this paper, we use the Pantheon compilation of SNe Ia, combined with the galaxy clusters and BAO data to test the possible violation of DDR in a model independent way. The luminosity distance of SNe Ia is first reconstructed using the Gaussian processes, then it is fitted to the combined data of clusters and BAO. The rest of the paper is organized as follows: The data samples and methodology to test DDR is illustrated in section \ref{sec:method}. The constraining results are presented in section \ref{sec:results}. Finally, discussions and conclusions are given in section \ref{sec:conclusions}. | \label{sec:conclusions} In this paper, we used the SNe Ia, combined with the galaxy clusters and BAO data to constrain the possible violation of DDR. We first reconstructed the $\mu-z$ relation from the most up-to-date Pantheon compilation of SNe Ia, and then used the reconstructed $\mu-z$ relation to fit to the $D_A$ data obtained from clusters and BAO. Since the angular diameter distance measured from clusters depends on the mass profile of cluster, two different mass profiles have been used, i.e. the elliptical cluster and spherical cluster. The former contains 25 data points and the latter contains 38 data points. It was showed that the cluster(E)+BAO data have a negligible intrinsic scatter and the DDR violation can been tightly constrained in both parametrizations, i.e. $\eta_0=-0.04\pm 0.12$ and $-0.05\pm 0.22$ in the first and second parametrizations, respectively. In both parametrizations, no signal of the DDR violation was found. On the other hand, although the cluster(S)+BAO dataset is also consistent with the DDR, the intrinsic scatter of this dataset is large. This may imply that the spherical profile is not a good approximation to model the mass distribution of galaxy clusters. We note that there is only one BAO data point at redshift $z=2.34$, while the other BAO and cluster data points all locate at redshift $z<1.0$. There is a wide redshift range between $1.0<z<2.3$ lacking of data. Therefore, it is interesting to test if the $z=2.34$ BAO data point has some influence on the results. We redo the previous calculations but omitted the $z=2.34$ BAO data point. We find that the results are almost unaffected. This is not surprising, because the reconstructed $\mu-z$ function has large uncertainty at $z=2.34$, therefore the $z=2.34$ data point has small weight in the fitting. We have also tried to fill the redshift gap between $1.0<z<2.3$ with the binned ultra-compact radio source data from \citet{Li:2018}. However, adding the radio source introduces an additional parameter (the linear size of the radio source) so couldn't help to improve the constraints. | 18 | 8 | 1808.01784 |
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