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1609 | 1609.06883_arXiv.txt | {}{We aim to study the standing fundamental kink mode of coronal loops in the nonlinear regime, investigating the changes in energy evolution in the cross-section and oscillation amplitude of the loop which are related to nonlinear effects, in particular to the development of the Kelvin-Helmholtz instability (KHI). } {We run ideal, high-resolution three-dimensional (3D) magnetohdydrodynamics (MHD) simulations, studying the influence of the initial velocity amplitude and the inhomogeneous layer thickness. We model the coronal loop as a straight, homogeneous magnetic flux tube with an outer inhomogeneous layer, embedded in a straight, homogeneous magnetic field. } {We find that, for low amplitudes which do not allow for the KHI to develop during the simulated time, the damping time agrees with the theory of resonant absorption. However, for higher amplitudes, the presence of KHI around the oscillating loop can alter the loop's evolution, resulting in a significantly faster damping than predicted by the linear theory in some cases. This questions the accuracy of seismological methods applied to observed damping profiles, based on linear theory.} {} | With the first observations of transverse oscillations in coronal loops by TRACE \citep{1999ApJ...520..880A,1999Sci...285..862N} a new era has begun in the exploration and understanding of the solar corona. These observations of waves allow the inference of different physical parameters which were previously largely unknown, a method called coronal seismology. It was quickly noted that the observed coronal loop oscillations were strongly damped, and if such a high dissipation was due to viscous or resistive damping, then the associated transport coefficients must be orders of magnitude higher than predicted by the classical theory. Nearly all of the observed, high-amplitude, lower coronal eruption-related coronal loop oscillations \citep{2015A&A...577A...4Z} are strongly damped, with rare but nevertheless very intriguing exceptions (see, e.g. \citet{2002SoPh..206...99A, 2011ApJ...736..102A,2012ApJ...751L..27W}). Recently, small amplitude decayless kink oscillations were observed in coronal loops \citep{2013A&A...552A..57N,2013A&A...560A.107A}, and are thought to be ubiquitous in active regions \citep{2015A&A...583A.136A}. These oscillations appear to be constantly driven, and do not originate from an impulsive or eruptive event like the high amplitude oscillations. It is generally accepted that the mechanism responsible for the fast damping of transverse oscillations is the extensively studied resonant absorption or mode coupling \citep[e.g.][]{1978ApJ...226..650I,1984ApJ...277..392H,2002ApJ...577..475R,2002A&A...394L..39G}. For resonant absorption to damp the oscillations, the existence of a surface within the limits of the loop, with Alfvén speed matching the global kink phase speed, is required. This is usually portrayed as a smooth layer around a homogeneous flux tube, but resonance has been proven to exist regardless of the geometrical shape of such a layer \citep{2008ApJ...679.1611T,2011ApJ...731...73P}. The linear theory of kink oscillations is well studied \citep[for a review, see][]{2009SSRv..149..199R}. The damping profile of oscillations, in the presence of a driver (or initial perturbation in the case of standing modes) has been shown to deviate from a purely exponential decay, being described rather by an initially Gaussian damping profile followed by an exponential damping profile \citep{2012A&A...539A..37P,2013A&A...551A..39H,2013A&A...551A..40P,2016A&A...585L...6P,2016A&A...589A.136P}. Observed average periods, amplitudes and exponential damping times of kink oscillations in coronal loops were reported by, \citet{2002SoPh..206...99A}, for example. In their analysis of 26 loop oscillation events, they find average oscillation periods of $321 \pm 140\ \mathrm{s}$, oscillation amplitudes of $2200 \pm 2800\ \mathrm{km}$ and damping times of $580 \pm 385\ \mathrm{s}$. The measured amplitudes correspond to relative amplitudes (to the loop length $L$) of approximately 1-5\%. \citet{2007A&A...463..333A} and \citet{2008A&A...484..851G} used the analytical formula for the damping time \citep{2002ApJ...577..475R} to construct a seismological method for inferring the loop parameters from the observed damping time and period. \\Waves in the solar atmosphere often have high enough amplitudes to be considered nonlinear. The study of nonlinear waves in the solar atmosphere has been carried out especially in the context of chromospheric and coronal heating. For a review of earlier theoretical work on the subject, see \citet{2006RSPTA.364..485R}. In particular, the analytical theory of nonlinear kink oscillations has been studied, both for propagating \citep{2010PhPl...17h2108R}, and standing waves \citep{2014SoPh..289.1999R}. In these studies it was shown that damping of propagating kink waves can be enhanced by the nonlinearity of an $m$-mode resonance, where energy from the $m=1$ kink mode is transferred to $m \geq 2$ fluting modes, which, by resonant absorption, can damp faster due to shorter wavelengths. It was noted that the $m$-mode resonance can damp the kink wave even in the absence of a resonant layer. However, in an axially inhomogeneous flux tube, due to density stratification, for example, the $m$-modes no longer have the same phase speed, thus the $m$-mode resonance and enhanced damping disappears. These calculations were valid for weakly nonlinear oscillations, and the authors anticipated that the amplitude would be affected in the fully nonlinear case. In general, the study of fully nonlinear problems is only possible numerically. Numerical studies of nonlinear kink oscillations of coronal loops have been carried out by, \citet{2004ApJ...610..523T,2005SSRv..120...67O,2008ApJ...687L.115T,2009ApJ...694..502O, 2014ApJ...787L..22A,2015ApJ...809...72A,2015A&A...582A.117M,2016arXiv160404078M}, for example.\ See also \citet{2009SSRv..149..153O} for a review. Of particular and renewed interest in nonlinear evolution of transverse waves, even for low amplitudes, is the susceptibility of the resonant layer, due to its high velocity shear, to the Kelvin-Helmoltz instability (KHI) \citep{1983A&A...117..220H,1984A&A...131..283B,1994ApJ...421..372K,1994GeoRL..21.2259O,1997SoPh..172...45P}. This can enhance the wave energy dissipation via local turbulence, and thus is also relevant in the coronal heating problem. Direct observational evidence is lacking of the KHI in coronal loops. However, it has been observed in coronal mass ejections and quiescent prominences \citep{2010ApJ...716.1288B,2010SoPh..267...75R,2011ApJ...729L...8F,2011ApJ...734L..11O}, and it was suggested that, in fact, the KHI may appear as strands of coronal loops as seen in EUV \citep{2014ApJ...787L..22A}. The previous statement is strengthened by the first observational evidence of resonant absorption in prominences \citep{2015ApJ...809...71O,2015ApJ...809...72A}. Recently, the idea of observing the damping profile of kink oscillations of coronal loops in order to infer various local parameters such as density ratios and inhomogeneous layer widths in the context of coronal seismology was put forward. \citep{2016A&A...589A.136P}. Therefore, it is essential to know the effects that nonlinearity might have on damping profiles. New observational evidence suggests that the damping of the transverse oscillations of coronal loops is dependent on the amplitude \citep{2016A&A...590L...5G}. \\ In this paper we investigate the nonlinear standing kink oscillation of coronal loops, for which the main effect of nonlinearity is the development of the KHI at the loop edges, altering the energy distribution in the loop cross section and ultimately leading to a change in the damping profile of the loop displacement. | In this study, we investigated the standing kink oscillations of a straight flux tube, aiming to model transverse oscillations of coronal loops. We ran 3D ideal MHD simulations, exploring the parameter space of initial amplitudes and inhomogeneous layer thicknesses. The chosen amplitudes cover the weakly linear and fully nonlinear regimes. The resulting oscillation periods are well described by the linear theory. Furthermore, for low amplitudes, we find that the resulting damping of the oscillation is close to the damping times computed by linear theory. However, for higher amplitudes, nonlinear effects have a definitive impact on the resulting oscillation characteristics, especially the development of the KHI around the loop edges where the velocity shear is highest, coinciding with the layer where resonant absorption is taking place. The development of KHI (and ultimately the threshold amplitude at which its effects become important) is dictated by its growth rate, which in turn depends on the ratio of loop radius to length, oscillation amplitude, Alfvén speeds, inhomogeneous layer thickness and numerical dissipation. We show that even for initially thin inhomogeneous layers, the oscillations undergo rapid damping due to the presence of KHI. For high amplitudes (with KHI developing in under one oscillation period), the damping time is almost independent of the initial thickness of the inhomogeneous layer. On the other hand, for thick inhomogeneous layers, the damping time does not seem to depend on the initial amplitude of the perturbation. To put things in perspective, the highest amplitude perturbation used in our simulations initially displaces the loop by less than its radius, and is thus at the lower boundary of observed flare-related coronal loop oscillation displacements \citep{2002SoPh..206...99A}. Studying the energy distribution in the anti-node cross-section of the loop, we arrive at the conclusion that the kinetic energy in the inhomogeneous layer is converted to plasma internal energy more quickly in the presence of KHI. The increase in average internal energy is less than one percent, thus the energy budget of the wave is not enough to cause any significant temperature change in the 0.9 MK plasma. However, this heating might be significant for prominences \citep{2015ApJ...809...72A}. Even if the dissipated wave energy is not enough to cause significant heating, we show that if the loop is surrounded by hotter plasma, mixing induced by the KHI can increase the average temperature of the loop. In the presence of KHI, the peak value of average kinetic energy deposited in the inhomogeneous layer is lower than in simulations without KHI. This is a consequence of the accelerated conversion of kinetic to internal energy in the presence of KHI, which cascades energy to smaller scales where it can be dissipated (by numerical dissipation) more efficiently. The disruption of the resonant layer may also contribute to the reduction in the peak value of average kinetic energy, though it is unclear how effective the resulting `patchy' resonant absorption is. \\ According to the present study, it becomes uncertain whether seismology schemes based on the linear theory for the damping rates of coronal loops are valid for high-amplitude, non-linear transverse oscillations. Using the observed switch between Gaussian and exponential damping profiles of transverse coronal loop oscillations for coronal seismology has recently been suggested. However, because of the nature of nonlinear kink oscillations it is questionable how accurately one can infer parameters such as inhomogeneous layer thickness and density ratio from the observed damping profiles, given that the non-linear damping times are nearly insensitive to them. {However, it is important that future studies also include Gaussian damping profiles in their analyses, as this profile seems to better describe the damping of nonlinear transverse oscillations of coronal loops.} The new observations of amplitude-dependent damping times qualitatively support our conclusions. | 16 | 9 | 1609.06883 |
1609 | 1609.03973_arXiv.txt | We have investigated a recently proposed halo-based model, \textsc{Camelus}, for predicting weak-lensing peak counts, and compared its results over a collection of 162 cosmologies with those from N-body simulations. While counts from both models agree for peaks with $\mathcal{S/N}>1$ (where $\mathcal{S/N}$ is the ratio of the peak height to the r.m.s. shape noise), we find $\approx 50\%$ fewer counts for peaks near $\mathcal{S/N}=0$ and significantly higher counts in the negative $\mathcal{S/N}$ tail. Adding shape noise reduces the differences to within $20\%$ for all cosmologies. We also found larger covariances that are more sensitive to cosmological parameters. As a result, credibility regions in the $\{\Omega_m, \sigma_8\}$ are $\approx 30\%$ larger. Even though the credible contours are commensurate, each model draws its predictive power from different types of peaks. Low peaks, especially those with $2<\mathcal{S/N}<3$, convey important cosmological information in N-body data, as shown in \cite{DietrichHartlap, Kratochvil2010}, but \textsc{Camelus} constrains cosmology almost exclusively from high significance peaks $(\mathcal{S/N}>3)$. Our results confirm the importance of using a cosmology-dependent covariance with at least a 14\% improvement in parameter constraints. We identified the covariance estimation as the main driver behind differences in inference, and suggest possible ways to make \textsc{Camelus} even more useful as a highly accurate peak count emulator. | Weak gravitational lensing (WL) of background sources by large-scale structure (LSS) is a promising technique to study dark matter (DM) and dark energy (DE) \cite{DETF} as a consequence of its sensitivity to both structure growth and the expansion history of the universe. Ongoing and future surveys such as the Dark Energy Survey (DES\footnote{\url{http://www.darkenergysurvey.org}}), the Euclid Mission\footnote{\url{http://sci.esa.int/euclid/}}, the Wide Field Infrared Survey Telescope (WFIRST\footnote{\url{http://wfirst.gsfc.nasa.gov}}) and the Large Synoptic Survey Telescope (LSST\footnote{\url{http://www.lsst.org}}) will deliver WL datasets with unprecedented precision, sky coverage and depth. For a comprehensive treatment of weak lensing in a cosmological context, we refer the reader to the following reviews \cite{BartelmannSchneider, Refregier03, Kilbinger15}. On small scales, WL probes the matter density field in the non-linear regime, independent of the matter's nature or dynamic state. Thus, in order to optimally extract cosmological information from the upcoming WL surveys, we need observables that go beyond quadratic statistics such as the two-point correlation function or its Fourier transform, the power spectrum. Various strategies have been proposed to capture non-Gaussian information, from the use of higher-order moments and correlation functions such as the bispectrum (\cite{Bernardeau1997, Hui99, TakadaJain2003, Schneider2005}), to the adoption of topological features from WL maps such as Minkowski functionals \cite{Kratochvil2012, Petri2015} or peak counts \cite{Jain2000}. Lensing peaks, defined as local maxima of the convergence or shear field, are particularly simple to extract from mass-aperture maps, and have been shown to constrain cosmology both theoretically \cite{DietrichHartlap, Kratochvil2010, Marian2012} and, recently, observationally \cite{Liu2015, LiuPan2015, DES2016}. Peaks are usually classified based on their absolute height or significance level, defined as their signal-to-noise ratio $(\mathcal{S/N})$, the noise being caused by our imperfect knowledge of the intrinsic shapes of the background galaxies. Peak counts are also special because their physical origin and sensitivity to cosmology can, in principle, be understood and related to specific structures of the cosmic web. While our understanding is not yet complete, it is clear that halos are important contributors to peak counts. Shear peaks were initially considered for cluster selection, and the connection of high--significance peaks $(\mathcal{S/N}>4-5)$ to single massive halos has been established in the literature \cite{White2002, Hamana2004, Hennawi2005}. Lower--significance peaks are typically associated with constellations of lower-mass halos \cite{Yang2011,Liu2016} and contribute significantly to the cosmological information in convergence maps \cite{Kratochvil2010,Yang2011}. Predicting analytically the abundance of peaks is difficult, as it depends on projections of non-linear structures. N-body simulations can predict peak counts at a high computational cost that will only increase with the high volumes required by upcoming WL surveys. The need to predict not only the peak number density but also its covariance would further raise the total cost. The halo-peak connection has inspired some models that would circumvent the need for full N-body simulations by using either analytical models based on Gaussian random fields \cite{Fan2010,Maturi2010,Reischke2016} or stochastic fast simulations based on the halo model \cite{Kainulainen2009, LKI}. This could prove extremely useful by reducing the computational requirements for N-body simulations by 2-3 orders of magnitude. The main goal of this work is to assess the validity of halo-based models for cosmological parameter inference. In particular, we compare results from full N-body simulations with those of a recent publicly available algorithm, \textsc{Camelus} \cite{LKI}. In previous work \cite{LKI}, this model was found to predict accurately peak counts from N-body simulations for a specific cosmology. Here, we expand the comparison of peak counts to a wide range of different cosmologies, and also examine their predicted covariance matrices, showing how differences affect the resulting parameter credibility regions. We also review the importance of the cosmology-dependence of the covariance matrix in the context of precision parameter inference \cite{LKII}. The rest of the paper is organized as follows. In Sec.~\ref{methods} we describe the methods used to predict peak counts using N-body simulations and \textsc{Camelus}, and infer constraints for cosmological parameters. In Sec.~\ref{results} we show how both models compare in terms of peak counts, covariance matrices, and credible contours. We then discuss our main findings (Sec.~\ref{discussion}), identifying potential origins for the differences between the two models and how \textsc{Camelus} could be modified to match N-body predictions more accurately. Our main conclusions are summarized in Sec.~\ref{conclusions}. | In this work we compared the outcomes from the fast halo-based algorithm \textsc{Camelus} with those of N-body simulations for a suite of cosmologies spanning a wide range of values in the $\{\Omega_m, \sigma_8\}$ plane. We found larger (by $\approx30\%$ in area), more significantly tilted (by $\approx 13\%$ in angle) credible contours from N-body data. Importantly, the two models draw their predictive power from a different types of peaks. While \textsc{Camelus} constrains cosmology through high--$\mathcal{S/N}$ peaks associated with massive halos, the N-body data are highly sensitive to lower-$\mathcal{S/N}$ peaks. The larger thickness and overall area of the N-body credible contours are mostly driven by the covariances, with peak counts showing a higher variance than expected from pure shot noise. This suggest that modifying the placement of halos in \textsc{Camelus} to account for the correlations in their locations is a promising way to improve its covariance estimation and accuracy as a WL peak count emulator. Using a cosmology-dependent covariance matrix for likelihood estimation improves constraints by $14-20\%$, and thus will be needed in order to achieve high-precision parameter estimations. Finally, we have found that optimal sampling of a high-dimensional parameter space with expensive N-body simulations to define credibility regions with high precision is a topic that requires further investigation, and a fast simulator like \textsc{Camelus} could prove itself particularly valuable by providing a first estimation of the likelihood. | 16 | 9 | 1609.03973 |
1609 | 1609.03697_arXiv.txt | We present a measurement of two-dimensional (2D) redshift-space power spectrum for the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11 CMASS galaxies in the North Galactic Cap (NGC) based on the method developed by \cite{2001MNRAS.325.1389J}. In this method, we first measure the 2D redshift-space correlation function for the CMASS galaxies, and obtain the 2D power spectrum based on Fourier Transform of the correlation function. The method is tested with an N-body mock galaxy catalog, which demonstrates that the method can yield an accurate and unbiased measurement of the redshift-space power spectrum given the input 2D correlation function is correct. Compared with previous measurements in literature that are usually based on direct Fourier Transform in redshift space, our method has the advantages that the window function and shot-noise are fully corrected, while those measured in previous studies for the CMASS galaxies are usually the one convolved with the window function. In fact, our 2D power spectrum, by its construction, can accurately reproduce the 2D correlation function, and in the meanwhile can reproduce, for example, the 2D power spectrum of \cite{2014MNRAS.443.1065B} accurately if ours is convolved with the window function they provided. Thus, our measurement can facilitate a direct comparison with the theoretical predictions. With this accurate measurement of the 2D power spectrum, we then develop a method to measure the structure growth rate, by separating the anisotropic redshift-space power spectrum from the isotropic real-space power spectrum. We have also carefully corrected for the nonlinearities in the mapping from real space to redshift space, according to the theoretical model of \cite{2013PhRvD..87f3526Z}. Finally, we obtain $f(\zeff)\sigma_8(\zeff)=0.438\pm0.037$ at the effective redshift $\zeff=0.57$, where $f(\zeff)$ is the linear growth rate and $\sigma_8(\zeff)$ is the rms density fluctuation in the sphere of comoving radius $8 \mpch$ at $\zeff$. The result is useful for constraining cosmological parameters. The measurements of 2D power spectrum will be released soon. | \label{intro} Redshift space distortion (RSD) is emerging as a major probe of cosmology, and is playing an important role in ongoing and upcoming dark energy surveys (e.g. \citet{Snowmasschapter4,stage5}). Peculiar velocities of galaxies distort their distribution in redshift space through the Doppler effect. They render the otherwise statistically isotropic distribution of galaxies in real space into a statistically anisotropic distribution in redshift space with a unique pattern. Through such unique anisotropic pattern, in principle one is able to infer statistical properties of peculiar velocities {\it at cosmological distances}. These statistics depend on both the law of gravity, and the nature of gravitational sources (dark matter, dark energy, etc.). It then provides us a precious tool to measure the structure growth of the universe and to probe properties of dark energy and gravity (e.g. \citet{Amendola05,Yamamoto05,Jain08,Linder08,Wang08,Percival09, White09,Song09,Jennings11,Cai12}). Furthermore, the combination of weak lensing and RSD allows for a test of General Relativity (GR), insensitive to unknown galaxy bias and cosmic variances, through the $E_G$ method \citep{2007PhRvL..99n1302Z,2010Natur.464..256R,2015JCAP...12..051L, 2015MNRAS.449.4326P,2015arXiv151104457P,2016MNRAS.456.2806B}. A major challenge of RSD studies in the era of precision cosmology lies in its theoretical modelling, due to several nonlinear processes entangled in the redshift-space clustering of galaxies. However, precision measurement of RSD also faces unresolved problems. RSD has been measured extensively using correlation function \citep{1993ApJ...417...19H,1994MNRAS.267..927F, 1996ApJ...468....1L,1998MNRAS.296..191R,2001Natur.410..169P, 2008Natur.451..541G,2008ApJ...676..889O,2009MNRAS.393.1183C, 2009MNRAS.396.1119C,2012MNRAS.423.3430B,2012MNRAS.426.2719R, 2013arXiv1312.4889C,2014MNRAS.444..476R,2014MNRAS.437.1109R, 2014MNRAS.439.3504S,2014MNRAS.440.2692S,2015MNRAS.449..848H, 2015MNRAS.453.1754A,2016PASJ...68...38O}. It has also been measured through the redshift-space power spectrum \citep{1994ApJ...431..569P,1995MNRAS.275..515C,1996ApJ...456L...1L, 2001MNRAS.325.1389J,2004ApJ...617..782J,2006PASJ...58...93Y, 2008PThPh.120..609Y,2010PhRvD..81j3517Y,2011MNRAS.415.2876B, 2013JCAP...08..019H,2014MNRAS.439.2515O,2014MNRAS.443.1065B, 2015PhRvD..92b3523K,2016MNRAS.tmp..927G,2016arXiv160600439G, 2016MNRAS.458.2725J} and bispectrum \citep{2015MNRAS.451..539G,2015MNRAS.452.1914G, 2016arXiv160600439G}. The redshift-space power spectrum is more directly connected to the theory of large scale structure (LSS). However, its precision measurement faces two difficulties. One problem is that RSD effect is along different line-of-sights (LOS) for different galaxies, while Fourier transform tends to mix different LOSs. In early works, the power spectrum analysis was usually based on the parallel-plane approximation, that is, all galaxies in the survey share one unique LOS direction. Then one can rely on the Fast Fourier Transform (FFT) technique to accelerate the power spectrum calculation. However, the sky area covered by galaxy surveys becomes larger and larger. The parallel-plane approximation becomes less and less accurate and systematics introduced by the variation of LOSs in the survey becomes non-negligible. One solution beyond the parallel-plane approximation was proposed by \cite{2006PASJ...58...93Y} (Y06 hereafter). It has been implemented in various recent galaxy surveys \citep{2006PASJ...58...93Y, 2008PThPh.120..609Y, 2010PhRvD..81j3517Y, 2013JCAP...08..019H, 2014MNRAS.439.2515O, 2014MNRAS.443.1065B, 2015PhRvD..92b3523K, 2016MNRAS.tmp..927G, 2016arXiv160600439G, 2016MNRAS.458.2725J}. In the Y06 method, each galaxy pair shares a common LOS, which is further approximated as that of one galaxy in the pair. With this `moving-LOS approximation', the pair summation can be implemented by two Fourier transforms and then can be accelerated by FFT. Nevertheless, this may introduce notable systematics on the hexadecapole power spectrum for wide galaxy surveys \citep{2012MNRAS.420.2102S,2015MNRAS.447.1789Y}. Another proposed solution is to decompose the 3D density field with the spherical harmonics and spherical Bessel functions, and is referred as SFB\footnote{In some literatures, it is called the spherical Fourier-Bessel expansion (SFB for short).} hereafter \citep{1995MNRAS.275..483H,1995MNRAS.272..885F,1999MNRAS.305..527T, 2000MNRAS.317L..23H,2001MNRAS.327..689T,2002MNRAS.335..887T, 2004ApJ...606..702T,2004MNRAS.353.1201P,2006MNRAS.373...45E, 2012A&A...540A..92L,2012A&A...540A..60L,2012A&A...540A.115R, 2015A&A...578A..10L}. This decomposition keeps the LOS information (and therefore RSD information) exactly. However, the measured SFB power spectrum differs from the redshift-space power spectrum predicted by most commonly used RSD models. Furthermore, it mixes clustering at different redshifts. Both bring inconveniences when one compares the data with models. Another important issue in the power spectrum measurements is the deconvolution of window function. Unlike that in the correlation function, it is nontrivial to correct the window function in Fourier space. On one hand, the window function couples different Fourier modes. On the other hand, the window function introduces non-uniform distribution of $\mu=\hat{k}\cdot\hat{n}_\mathrm{LOS}$. Here, $\hat{k}$ is the unit wavenumber vector and $\hat{n}_\mathrm{LOS}$ is the unit LOS vector. Such non-uniform $\mu$ distribution may bias the measurement of power spectrum multipoles \citep{2012MNRAS.420.2102S,2015MNRAS.447.1789Y}. In this paper, we propose to use the two-dimensional (2D) galaxy power spectrum in redshift space to measure the RSD effect, instead of using the multipole power spectrum or SFB coefficients. We revisit the method of measuring the 2D galaxy power spectrum through Fourier transform of the 2D galaxy correlation function in redshift space developed by \cite{2001MNRAS.325.1389J}. This method improves the parallel-pane approximation and the `moving-LOS' approximation. In measurement of 2D correlation function, LOS is defined on each galaxy pair, usually to be the position vector of pair center with respect to the observer. The LOS defined in this way captures all information of RSD under the assumption of distant observer and neglecting wide-angle effect. Furthermore, the window function can be corrected in configuration space robustly and efficiently since the deconvolution in Fourier space becomes division in configuration space. The non-uniform $\mu$-distribution can also be solved by uniformly weighting the correlation function in $(s,\mu)$ space. Next, we propose a method to measure the structure growth rate through the 2D power spectrum measurement. We separate the anisotropies on the galaxy power spectrum in redshift space from the isotropic galaxy power spectrum in real space by introducing a new statistics - anisotropic measure. When modeling the anisotropic measure, we have corrected for the nonlinearities with the theoretical model of Zhang et al (2013). In this way, the RSD parameter and galaxy bias can be measured independently. We apply the method to the BOSS-DR11 CMASS galaxy sample and obtain a robust measurement of the structure growth rate. The paper is organized as follows. In \S 2, we introduce the method of measuring the 2D power spectrum in redshift space for a large galaxy survey and test it with a mock galaxy catalog based on an $N$-body simulation. In \S 3, we introduce the data set used in this paper: BOSS-DR11 CMASS galaxy sample and the MD-Patchy mock galaxy catalogs. In \S 4, we show the measured 2D power spectrum of BOSS-DR11 CMASS galaxies. We measure the structure growth rate from the measured 2D power spectrum and compare it with previous studies in \S 5. We end the paper with a brief summary in \S 6. | \label{Sec:Conclusion} In this paper, we use the two-dimensional power spectrum in redshift space to measure the RSD effect. We revisit the method of measuring the galaxy 2D power spectrum by measuring and Fourier transforming the 2D correlation function. The 2D power spectrum measured in this way has several advantages: \begin{inparaenum}[(A)] \item they can improve the parallel-plane approximation and `moving-LOS' approximation and capture all RSD information under the assumption of distant observer and neglecting wide-angle effect; \item they are unbiased and free of normalization and shot-noise subtraction; \item the survey window function can be dealt with in configuration space; \item the nonuniform distribution of cosine angle $\mu$ can be solved. \end{inparaenum} Most importantly, working on 2D power spectrum opens the opportunity to separate the nonlinearities in the real-to-redshift space mapping at data level. We have tested the 2D power spectrum measurements using mock galaxies constructed from high resolution CosmicGrowth $N$-body simulation and concluded that our method can give unbiased measurement of 2D power spectrum for large galaxy surveys. After applying the method on the BOSS-DR11 CMASS galaxy sample, we report for the first time the measurement of 2D power spectrum for this sample. We have introduced a new statistics, anisotropic measure, to extract the structure growth rate from the 2D power spectrum measurements. In this paper we used a simple model with two parameters $\beta$ and $\tilde{\sigma}_v$ to interpret this new measurement. We obtained $\beta=0.3403\pm0.0285$ and $\tilde{\sigma}_v=2.40\pm0.44\,h^{-1}\mpc$ for BOSS-DR11 CMASS galaxies. We further measured the galaxy bias factor from the real-space power spectrum, which is $b_g\sigma_8(\zeff)=1.274\pm0.007$. Combining the measurement of $\beta$ and $b_g\sigma_8(\zeff)$, we got the following measurement of the structure growth rate, $f(\zeff=0.57)\sigma_8(\zeff=0.57)=0.438\pm0.037$. This measurement together with the 2D power spectrum can be used to put interesting constraints on cosmological models. For this reason, we will release our results of 2D power spectrum soon. | 16 | 9 | 1609.03697 |
1609 | 1609.01692_arXiv.txt | The binary millisecond radio pulsar PSR J1023+0038 exhibits many characteristics similar to the gamma-ray binary system PSR B1259--63/LS 2883, making it an ideal candidate for the study of high-energy non-thermal emission. It has been the subject of multi-wavelength campaigns following the disappearance of the pulsed radio emission in 2013 June, which revealed the appearance of an accretion disk around the neutron star. We present the results of very high-energy gamma-ray observations carried out by VERITAS before and after this change of state. Searches for steady and pulsed emission of both data sets yield no significant gamma-ray signal above 100\,GeV, and upper limits are given for both a steady and pulsed gamma-ray flux. These upper limits are used to constrain the magnetic field strength in the shock region of the PSR J1023+0038 system. Assuming that very high-energy gamma rays are produced via an inverse-Compton mechanism in the shock region, we constrain the shock magnetic field to be greater than $\sim$2\,G before the disappearance of the radio pulsar and greater than $\sim$10\,G afterwards. | Radio millisecond pulsars (MSPs) are old neutron stars that have been spun up to millisecond periods via accretion of material from a companion star in a low-mass X-ray binary~\citep[LMXB;][]{alpar1982}. In the past few years, new MSP discoveries have taken place at a greatly elevated rate due to searches for radio pulsars in unassociated {\it Fermi}-LAT-detected gamma-ray sources~\citep{paulray2012}. This new population of MSPs has enriched the known diversity of binary MSP companions. This is especially true for eclipsing systems, which were rarely seen outside of globular clusters: the ``black widows'' with very low-mass (M $\ll$ 0.1M{$_{\odot}$) companions and ``redback'' systems with more massive (M$_c \gtrsim$ 0.1M{$_{\odot}$), non-degenerate companions~\citep{roberts2011}. Some of these redbacks have been observed to transition between LMXB and MSP states, providing the first direct observational evidence to support the theory of the MSP formation mechanism. There are now three systems where transitions have been observed: PSR J1023+0038~\citep{archibald2009} and XSS 12270--4859~\citep{bassa2014,roy2015} in the Galactic plane, and PSR J1824--2452I~\citep{papitto2013}, located in the globular cluster M28. Additionally, it has recently been suggested that the galactic binary 1RXS J154439.4--112820 may also be a transitional system~\citep{2015arXiv150805844B}. Very high-energy (VHE) gamma-ray emission ($E > 100$\,GeV) from binaries containing MSPs has been predicted to occur through diverse mechanisms. \cite{harding05} propose that leptons accelerated above the polar cap can produce inverse-Compton or curvature radiation emission that could potentially be identified as gamma-ray pulsations at energies up to and above 100\,GeV, similar to what has been observed from the young Crab pulsar~\citep{aliu2008,aliu2011}. Additionally, leptons could be accelerated at the shock that appears as a result of the interaction between the pulsar wind and material ablated off of the companion. These leptons could then radiate VHE gamma rays via inverse-Compton scattering, which could be modulated with the binary orbital period. This emission scenario is thought to occur in the VHE-detected binary system PSR B1259--63/LS 2883, a radio pulsar in a $\sim$3.4\,yr orbit around a massive, luminous Be star~\citep{aharonian2005}. \begin{table*} \centering \begin{tabular}{c c c c c c c c} \hline Binary State & On & Off & $\alpha$ & Excess & LiMa & 95\% CL flux UL & 95\% CL flux UL (flux units) \\ & Events & Events & & Events & Significance & (cm$^{-2}$s$^{-1}$) & (erg cm$^{-2}$s$^{-1}$) \\ \hline Radio MSP & 287 & 1815 & 0.17 & -15.5 & -0.8 & 8.1 $\times 10^{-13}$ & $5.8 \times 10^{-13}$ \\ Accretion/LMXB & 72 & 422 & 0.17 & 1.7 & 0.2 & 9.6 $\times 10^{-13}$ & $6.9 \times 10^{-13}$ \\ \hline \end{tabular} \caption{\normalfont{VERITAS analysis results for the location of PSR J1023+0038 for each of the two different binary states. The parameter $\alpha$ indicates the ratio of the on- to off-source region exposure, and the LiMa significance is calculated using equation 17 in~\cite{lima1983}.}} \label{tab:steadyfluxtable} \end{table*} The theory of VHE gamma-ray emission from PSR B1259--63~\citep{tavani1994} was first explored in the context of the original Black Widow Pulsar system~\citep{arons1993}, which is a binary comprising the 1.6\,ms pulsar PSR B1957+20 in a 9.2\,hr orbit around a $\sim$0.02 $M_{\odot}$ companion. However, no VHE emission has been detected from the Black Widow~\citep{otte2007}. Searches for VHE emission from several globular clusters have been undertaken, since they are known to contain many of these eclipsing binary systems. Recently, H.E.S.S. has detected VHE emission from the direction of the cluster Terzan 5~\citep{abramowski2011}, which is especially rich in eclipsing binary systems among globular clusters~\citep{2008IAUS..246..291R}. This emission is thought to originate in a bow shock region where interaction between leptons from MSP winds and the galactic medium occur~\citep{2014MNRAS.445.2842B}. However, searches for VHE emission from the globular clusters 47 Tuc~\citep{aharonian2009}, M5, M15 (McCutcheon et al. 2009), and M13~\citep{anderhub2009, 2012PhDT.......343M} have revealed no such emission. The aforementioned eclipsing binary systems in globular clusters can be seen as smaller-scale versions of PSR B1259--63, because their more massive, nearly Roche-lobe-filling companions provide much larger targets and more copious seed photons for inverse-Compton scattering than companions of black widows. With the discovery of nearby redbacks in the Galactic field, it is thought that a single, energetic Galactic-field redback could be brighter at VHE energies than the combined emission from many eclipsing systems in a distant cluster~\citep{roberts2011}. PSR J1023+0038 is a redback system containing a 1.69\,ms MSP in a 4.8\,hr orbit around a G star with a mass of $\sim$0.2M$_{\odot}$~\citep{archibald2009}. PSR J1023+0038 was selected as a promising candidate for VHE observations with VERITAS based on three parameters thought to be responsible for the VHE emission from PSR B1259--63: the high spin-down luminosity of the pulsar, the presence of an intense target photon field for inverse-Compton scattering provided by the companion, and the relatively small distance from Earth. Although the optical luminosity of the companion in PSR J1023+0038 is a factor of $\sim$10$^{4}$ less than that for the companion of PSR B1259--63, this discrepancy is possibly compensated by the much smaller distance separating the pulsar and its companion in PSR J1023+0038, potentially making the energy density of seed photons at the shock comparable for the two systems. However, the PSR B1259--63 system has a circumstellar disk that the pulsar passes through at periastron~\citep{1998MNRAS.298..997W}, though PSR J1023+0038 shows no evidence of such a disk. While the actual VHE emission will depend on the details of the flow and the magnetic field at the shock, the inverse-Compton emission should roughly scale as $F_{{\rm IC}} \propto f (\dot E/d^2)u_{{\rm ph}}$ where $d$ is the distance to the binary, $u_{{\rm ph}} \sim (R_c/R_s)^2 \sigma T_c^4/c$ is the photon energy density at the shock, $R_c$ is the radius of the companion, $R_s$ is the radius of the shock measured from the companion, and $f$ is a geometrical factor representing the fraction of the pulsar wind involved in the shock. If the shock region of PSR J1023+0038 (and by extension other redbacks and black widows) is very near the surface of the companion, as proposed by~\cite{bogdanov2011}, then $R_c/R_s \sim 1$, and $f$ is related to the angle subtended by the companion in the pulsar sky. In the extreme case of a shock only near the surface of the companion, $f$ is approximately $0.01$ % if the pulsar wind is isotropic, and $f$ is approximately $0.07$ if the wind is confined to the equatorial plane. Based on this simple estimation, the expected TeV flux from PSR J1023+0038 would be on the order of $\sim$\,0.1$f$ that of PSR B1259--63 near periastron, where it has an observed flux $F(E>1{\rm TeV})\sim 10^{-11}{\rm cm}^{-2}\,{\rm s}^{-1}$~\citep{2013A&A...551A..94H}. We note that PSR J1023+0038 was selected for observations before the publication of the revised estimates for the distance and spin-down power % given in~\cite{deller2015}, in which case the estimated TeV flux would have been closer to $1f$ that of PSR B1259--63. Orbitally modulated X-ray emission has been observed from PSR J1023+0038, suggesting that the system contains shocked material~\citep{archibald2010}, and the observed radio eclipses suggest that the shock region may be quite large.~\cite{tam10} found strong evidence of gamma-ray emission from the direction of PSR J1023+0038 in the high-energy (HE; $100$\,MeV $\lesssim$ $E \leq 100$\,GeV) gamma-ray band using {\it Fermi}-LAT data. Given the observed steep spectrum of this emission ($\Gamma\sim3$), the authors suggest that the gamma rays likely originate from the pulsar magnetosphere rather than the intrabinary shock. Indeed,~\cite{archibald2013} have reported a hint of pulsed HE gamma-ray emission from the pulsar magnetosphere with a statistical significance of $3.7\sigma$. A sudden change of state in PSR J1023+0038 was reported to have occurred in 2013 June after the pulsed radio emission from the MSP was no longer detected~\citep{stappers2013}, and optical evidence for an accretion disk in the system was found for the first time since 2001 December~\citep{halpern2013, 2003AJ....126.1499S}. The X-ray emission increased only moderately~\citep{kong2013, patruno2013}, implying that accretion may still be inhibited due to the influence of the pulsar magnetosphere, although low-level X-ray pulsations, thought to be powered by accretion, have been detected~\citep{archibald2014}. All of this new behavior coincided with a five-fold increase in the HE gamma-ray flux from PSR J1023+0038~\citep{2014ApJ...790...39S}. The similarities between PSR J1023+0038 and PSR B1259--63/LS 2883 motivated the first VERITAS observations of the PSR J1023+0038 in 2010. Follow-up observations took place after the system was reported to have transitioned to an accretion/LMXB state in 2013, prompted by the substantial increase in flux in the HE gamma-ray band observed with the {\it Fermi}-LAT. Here we report the results of these observations of PSR J1023+0038, the first ever made in the VHE band, covering the two different states of this exceptional transitional object. After describing the observations (\S~2), the analysis and results are presented (\S~3), including searches for steady emission from the binary and pulsed emission from the pulsar magnetosphere. In the final section we provide a simple spectral model to interpret and discuss the results (\S~4). | During the last decade, PSR J1023+0038 has been intensively investigated in different energy bands. In this paper we have reported two sets of VERITAS observations, taken during the radio MSP state and the accretion/LMXB state, that have both yielded upper limits on a VHE gamma-ray flux. While the beginning of the accretion phase was marked by a sharp rise of the luminosity both in X-rays and HE gamma rays as observed by {\it Swift} and the {\it Fermi}-LAT~\citep{stappers2013, takata2014}, the source was not detected by VERITAS. In the following, we discuss the constraints that can be placed on the physical properties of PSR J1023+0038 with the VERITAS upper limits. First we will discuss the system when PSR J1023+0038 exhibited detectable radio pulses, and then will investigate what changed after the reappearence of the accretion disk. \subsection{Millisecond pulsar phase} During the millisecond pulsar phase, radio emission from PSR J1023+0038 was characterized by highly frequency-dependent eclipses at superior conjunction accompanied by short, irregular eclipses at all orbital phases~\citep{archibald2009}. Assuming a pulsar mass $M=1.4M_\odot$ and an orbital inclination $i\sim 46^\circ$, it has been shown that the line of sight between the pulsar and the Earth does not intersect the Roche lobe of the companion at any point of the orbit~\citep{archibald2009}. Therefore, the eclipses must be caused by material driven off the surface of the companion by the impinging pulsar wind. The V magnitude of the system is orbitally modulated, reaching a minimum during the inferior conjunction of the companion star~\citep{thorstensen2005}. Such behavior is consistent with a Roche-lobe-filling companion near $T_{\rm eff} = 5650$\,K being illuminated by a pulsar with an isotropic luminosity of $\sim$2$L_\odot$. \begin{figure}[h!] \includegraphics[width=3.30in]{first_mw_2mod_rev01.pdf} \caption{Broadband spectrum of PSR J1023+0038 during the millisecond pulsar phase. Thick blue bars show the detection of the X-ray emission by {\it XMM}-Newton in 2008~\citep{archibald2010} and the {\it Fermi}-LAT GeV detection~\citep{tam10}. The black solid line represents synchrotron emission in a 40\,G magnetic field, and the black dashed line represents the component due to inverse-Compton scattering of optical photons. The solid and dashed green lines represent those same components in the case of a 2\,G magnetic field. The red dashed line represents a typical power-law model with an exponential cut-off spectrum of a GeV millisecond pulsar. The arrow represents the VERITAS flux upper limit reported in this work.} \label{bbsp} \end{figure} Orbitally modulated X-ray emission from PSR J1023+0038 was observed by the {\it XMM}-Newton and {\it Chandra} X-ray observatories in 2004, 2008, and 2010~\citep{homer2006, archibald2010, bogdanov2011}. In \cite{archibald2010}, it is shown that in the energy range 0.25 -- 2.5 keV, the X-ray emission is also modulated at the 1.6\,ms rotational period of the MSP with a mean-squared pulsed fraction of 0.11(2). X-ray emission observed with the {\it Swift}-XRT in the 0.3 -- 8 keV energy range suggests a dominant non-thermal synchrotron component originating at the intrabinary shock. In the case of a magnetically dominated wind (with a ratio of magnetic energy to kinetic energy $\sigma \gg 1$), the shock should occur in a relatively strong magnetic field ($B\sim 40$\,G) due to the small separation between the pulsar and the companion~\citep{bogdanov2011}. In \cite{bogdanov2011} it is shown that the depth and duration of the X-ray eclipses imply that the intrabinary shock is localized close to the L1 Lagrangian point and has a size of about $R\sim5\times10^{10}$\,cm. {\it NuSTAR} has detected a power-law throughout the 3 -- 79\,keV band with an estimated luminosity of $7.4\times 10^{32}\,\textrm{erg}\,\textrm{s}^{-1}$ \citep{2014ApJ...791...77T}. If the estimate of the shock size by~\cite{bogdanov2011} is correct, then a very large fraction of the energy in the shocked portion of the wind must be converted to X-ray emission, which supports the high $\sigma$ scenario. In~\cite{archibald2010} it is also noted that emission from the pulsar magnetosphere can contribute to the non-thermal X-ray emission, but the orbital modulation indicates that this component is not dominant. In addition to the aforementioned non-thermal emission, there also is a faint thermal component possibly originating from the hot polar caps of the pulsar and optically thin thermal plasma responsible for the radio eclipses. There is no evidence in X-ray data for a wind nebula associated with the pulsar. The observed X-ray luminosity in the 0.5 -- 10 keV energy range of $L_{\rm X} \sim 10^{32}$\,erg\,s$^{-1}$~\citep[assuming a distance of 1.4\,kpc;][]{2012ApJ...756L..25D} is much less than the spin-down luminosity: $L_{{\rm sd}}\simeq3.2 \times 10^{34}$\,erg\,s$^{-1}$~\citep{archibald2013}. % The broadband spectrum of PSR J1023+0038 from X-rays to VHE gamma rays is shown in Figure~\ref{bbsp}. While the X-ray data can be described by synchrotron emission from relativistic electrons exhibiting a power law with an exponential cut-off spectral shape, $dN/dE \propto E^{-2.52}\textrm{exp}(-E/E_{\textrm{cut}})$, the GeV data are not readily fitted with the same component. However, since the X-ray and GeV gamma-ray data are not strictly contemporaneous, spectral variability cannot be ruled out. The situation is similar if the observed GeV emission is produced in the pulsar magnetosphere. The typical spectral shape of the GeV millisecond pulsars is a power law with an exponential cut-off, e.g.~\cite{espinoza2013}; see the red dashed line in Figure~\ref{bbsp} for a best fit to the {\it Fermi}-LAT data~\citep{tam10}. This spectral shape is thought to be a result of curvature acceleration in a gap region in the magnetosphere~\citep{harding05}. More data are needed to distinguish between a synchrotron or curvature radiation origin of the GeV emission, although neither predicts emission above 10 GeV. Synchrotron photons can inverse-Compton scatter on relativistic electrons and become VHE photons. The ratio of the total power radiated by the synchrotron radiation and by inverse-Compton scattering by the same distribution of electrons is equal to $\eta=\frac{(dE/dt)_{\textrm{sync.}}}{(dE_e/dt)_{\textrm{IC}}}$. The value for $\eta$ reaches a maximum in the Thomson limit in which $\eta_{\textrm{T}}=\frac{B^2/8\pi}{U_{\textrm{rad}}}$, where $U_{\textrm{rad}}$ is the energy density of the synchrotron photons. It turns out that for PSR J1023+0038, the total energy of scattered photons is much smaller than the total energy of the synchrotron photons even in the Thomson limit where \begin{equation} \eta_\textrm{T} \sim 600 \frac{(B/40{\rm G})^2(R/5\times 10^{10} {\rm cm})^2 }{L/10^{32}{\rm erg/s}}. \label{etaT} \end{equation} An additional potential source of VHE emission is external inverse-Compton scattering of soft photons from the optically bright companion with an effective temperature of $T=5650\,K$~\citep{thorstensen2005}. This inverse-Compton component is shown in Figure~\ref{bbsp} as a black dashed line. Given the assumed value of the magnetic field, $B=40\,{\rm G}$, the component lies well below the VHE flux upper limit. However, for a lower magnetic field strength, the difference between the peak flux values of the synchrotron and inverse-Compton components will become smaller, allowing VERITAS observations to set a lower limit on the magnetic field strength. As shown by the green lines in Figure~\ref{bbsp}, the case of a 2\,G magnetic field gives close to the peak inverse-Compton flux allowed by the upper limit derived from the VERITAS data. Note that for a 2\,G magnetic field, $\eta_\textrm{T}$ defined by Equation~\ref{etaT} is close to unity. However, X-ray photons will be up-scattered in the Klein-Nishina regime, and in this case the total energy of scattered photons is much smaller than in the Thomson regime: \begin{equation} \eta_{\textrm{KN}}=\frac{B^2/8\pi}{\frac{9}{32}U_{\textrm{rad}}}\frac{\textrm{ln} (\frac {\hbar \omega_0 \gamma}{m_ec^2}) }{\gamma^2 \hbar^2 \omega_0^2 / (m_ec^2)^2}\sim \eta_\textrm{T}/2000 \end{equation} for 1 keV photons scattered into the VHE band by electrons with $\gamma=10^4$~\citep{2011hea..book.....L}. Although lower-energy photons are scattered in the transition regime between the Thomson and Klein-Nishina regimes, their energy density is much lower than that of the X-ray photons, and so the self-scattering process is not important in this case either. \begin{figure}[h] \includegraphics[width=3.30in]{first_accr_rev01.pdf} \caption{Broadband spectrum of PSR J1023+0038 after the reappearance of the accretion disk. The thick blue bar shows the X-ray emission detected by {\it Swift} in 2013 November \citep{takata2014}. Black triangles represent the {\it Fermi}-LAT HE gamma-ray detection in 2013~\citep{takata2014}. The arrow shows the VERITAS upper limit for the accretion/LMXB state, as reported in this work. Solid and dashed lines correspond to the synchrotron and inverse-Compton emission coming from the shock for the case of a 10\,G (green lines) and 80\,G (black lines) magnetic field. The spectral signature of inverse-Compton scattering of photons emitted by the accretion disk on the unshocked electrons is shown with a red dash-dotted line.} \label{acr} \end{figure} \subsection{Accretion phase} The reappearance of the accretion disk in 2013 June was accompanied by the disappearance of radio pulsations and an increase of the X-ray and HE gamma-ray luminosities. Accreting binary systems are not typically bright in the GeV domain. The only two binaries detected by the {\it Fermi}-LAT in which the presence of an accretion disk is certain are Cyg X-3 and Cyg X-1~\citep{corbel2012,malyshev2013}, and in both cases the HE emission is not believed to come from the disk, but rather to be generated in the relativistic jet. The formation of a jet in PSR J1023+0038 has not been observed in VLBI imaging, although variable point-source emission has been seen~\citep{deller2015}. Further, it appears that the X-ray pulsations, indicating accretion onto the neutron star surface, are intermittent~\citep{archibald2014}. Therefore it could be the case that, as discussed by~\cite{takata2014,coti2014,li2014,papitto2015}, the rotation-powered MSP is still at least partially active in PSR J1023+0038, and the complete disappearance of the pulsations is due to absorption by matter evaporating from the accretion disk. In this case, the principal differences from the radio MSP state discussed in the previous section would be a) the presence of additional soft photons emitted by the accretion disk and b) the shift of the shock closer to the pulsar due to the inward pressure of the disk. The presence of additional photons from the accretion disk leads to an increase of the HE luminosity as a result of scattering of those photons on the unshocked electrons of the pulsar wind~\citep{takata2014}. The result of the scattering of the UV photons with temperature $T=10$\,eV on the cold relativistic electrons with Lorentz factor $\gamma=10^4$ is shown in Figure~\ref{acr} with a red dash-dotted line. The shift of the shock closer to the pulsar up to a distance $r=5 \times 10^{10}$\,cm~\citep{takata2014} will lead to the increase of the magnetic field by a factor of two in comparison to the field strength discussed in the previous section if the magnetic field is dominated by that in the pulsar wind. The resulting synchrotron and inverse-Compton emission from the shocked electrons generated in the region with $B=80$\,G is shown in Figure~\ref{acr} with black solid and dashed lines, respectively. The VERITAS upper limit clearly shows that the field in the region cannot be much smaller than 10\,G (green lines in Figure~\ref{acr}). Thus the VERITAS observations before and after the source state change put limits on the minimum value of the magnetic field in a compact, synchrotron-emitting region, regardless of the precise mechanism of the charge acceleration or the source of the magnetic field. We note that~\cite{papitto2015} have proposed pulsar magnetic field threading of the accretion disk down to the corotation radius of PSR J1023+0038 ($\sim$\,24\,km) as a field source for the synchrotron emission. Were this the case, the strength of the magnetic field could be much larger. The VERITAS limits support the conclusion of the magnetically-dominated pulsar wind discussed in~\cite{bogdanov2011}. However, in both the MSP and accretion/LMXB states, there are alternative sources of magnetic fields that should be considered, namely that of the companion in both cases and that of the accretion disk itself in the second case. Assuming that the companion is tidally locked, observations of rapidly-rotating, low-mass stars suggest a surface magnetic field strength on the order of 1\,kG~\citep{morin2012}. The observed orbital variations may also indicate a strong, subsurface magnetic field in the companion~\citep{archibald2013}. | 16 | 9 | 1609.01692 |
1609 | 1609.02372_arXiv.txt | Rayleigh-B\'enard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use three-dimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning $3\times 10^{-7} \leq E \leq 10^{-1}$, Rayleigh numbers within the range $10^3 < Ra < 2\times 10^{10}$ and a Prandtl number unity. \modif{The radius ratio $r_i/r_o$ is 0.6 in all cases and the gravity is assumed to be proportional to $1/r^2$.} We investigate the scaling behaviours of both local (length scales, boundary layers) and global (Nusselt and Reynolds numbers) properties across various physical regimes from onset of rotating convection to weakly-rotating convection. Close to critical, the convective flow is dominated by a triple force balance between viscosity, Coriolis force and buoyancy. For larger supercriticalities, a small subset of our numerical data approaches the asymptotic diffusivity-free scaling of \modif{rotating convection $Nu\sim Ra^{3/2}E^{2}$} in a narrow fraction of the parameter space delimited by $6\,Ra_c \leq Ra \leq 0.4\,E^{-8/5}$. Using a decomposition of the viscous dissipation rate into bulk and boundary layer contributions, we establish a theoretical scaling of the flow velocity that accurately describes the numerical data. In rapidly-rotating turbulent convection, the fluid bulk is controlled by a triple force balance between Coriolis, inertia and buoyancy, while the remaining fraction of the dissipation can be attributed to the viscous friction in the Ekman layers. Beyond $Ra \simeq E^{-8/5}$, the rotational constraint on the convective flow is gradually lost and the flow properties continuously vary to match the regime changes between rotation-dominated and non-rotating convection. We show that the quantity $Ra E^{12/7}$ provides an accurate transition parameter to separate rotating and non-rotating convection. | Convection-driven flows under the influence of rotation are an ubiquitous physical phenomenon in the fluid interiors of natural objects. The liquid iron core of terrestrial planets, the envelopes of gas giants, or the convective regions of rapidly-rotating cool stars harbour highly turbulent convective flows strongly constrained by the dominant role of the Coriolis force. Rayleigh-B\'enard convection (hereafter RBC) is a classical framework to examine the influence of rotation on turbulent convection. In its canonical form, rotating RBC consists of a planar fluid layer confined between two horizontal rigid plates separated from a distance $L$, rotating about the vertical axis with a constant rotation rate $\Omega$. In this setup configuration, convective motions are driven by a fixed imposed temperature contrast $\Delta T$ between the two plates. The dynamics is then controlled by three dimensionless numbers, namely the Rayleigh number $Ra = \alpha_T g L^3 \Delta T / \nu\kappa$, the Ekman number $E=\nu/\Omega L^2$, and the Prandtl number $Pr=\nu/\kappa$, where $\nu$ and $\kappa$ are the viscous and thermal diffusivities, $\alpha_T$ is the thermal expansivity and $g$ is the gravity. A combination of these parameters, named the convective Rossby number $Ro_c = Ra^{1/2}E/Pr^{1/2}$, is frequently employed as a reasonable proxy of the ratio between the global-scale buoyancy and Coriolis forces \citep{Gilman77}. The key issue in RBC is to explore the efficiency of the heat and momentum transports across the layer. Important quantities in this regard are the Reynolds number $Re$ and the dimensionless heat transport, defined by the Nusselt number $Nu = \mathcal{Q} L /\rho c_p \kappa \Delta T$, where $\mathcal{Q}$ is the total heat flux, $\rho$ is the density and $c_p$ the heat capacity. The Nusselt number is the most widely studied diagnostic since it can be easily measured experimentally and numerically and then compared to numerical and theoretical predictions. The understanding of the scaling dependence of $Nu$ upon the control parameters $Ra$, $E$ and $Pr$ is of paramount importance to identify the different regimes and to possibly extrapolate the scaling behaviours to natural objects. Rotational constraints delay the onset of convection and the critical Rayleigh number increases with increasing rotation rates as $Ra_c\sim E^{-4/3}$ when $E\rightarrow 0$ \citep{Chandra61}. The convective pattern takes the form of elongated Taylor columns which have a typical horizontal size $\ell\sim E^{1/3}L$ and are aligned with the rotation axis. Beyond $Ra_c$, the heat transport rises much more rapidly than for non-rotating convection \citep[e.g.][]{Rossby69,Boubnov90}. Hence, if the Rayleigh number is continuously increased far beyond $Ra_c$ at a given Ekman number, the heat transfer properties will eventually transition to a state where rotational effects become secondary. In this weakly-rotating regime with $Ro_c \gg 1$, the scaling properties become essentially reminiscent to non-rotating RBC \citep[e.g.][]{Liu97,Zhong09}. The heat transport scaling is then expected to become independent of the Ekman number and to approach the scalings obtained in classical RBC, i.e. $Nu\sim Ra^{\nu_{\text{eff}}}$, with $0.27 \leq \nu_{\text{eff}} \leq 1/3$ for $10^5 \leq Ra \leq 10^{12}$ \citep[e.g.][]{Grossmann00, Funfschilling05, Ahlers09, Chilla12}. A turbulent regime of rotating convection is expected when both $Ro_c \ll 1$ and $Re \gg 1$. This implies large supercriticalities in combination with low Ekman numbers to ensure that the rotational constraints are not lost. This parameter range is therefore particularly difficult to explore with current-day laboratory experiments and numerical simulations \citep[see][]{Aurnou15}. In the following, we make the assumption that the heat transport scaling can be written as \[ Nu \sim Ra^{\alpha}E^{\beta}Pr^{\gamma}\, \] in this regime. In general though, the values of the exponents $\alpha$, $\beta$ and $\gamma$ might well continuously vary with $Ra$ similarly to classical RBC \citep{Grossmann00}. In contrast to non-rotating convection where the heat transport is controlled by diffusive processes in the thermal boundary layers, a dominant fraction of the temperature difference is accommodated in the fluid bulk when $Ro_c \ll 1$ \citep[e.g.][]{Boubnov90,Schmitz09,Kunnen10,Julien12,King13}. We can therefore hypothesise that the heat transport is controlled by the fluid bulk rather than by the thermal boundary layers that play an important role in the weakly-rotating limit. Because the viscous dissipation is rather weak in the fluid interior, \modif{we make the assumption that $Nu$ will thus become} independent of the diffusivities $\nu$ and $\kappa$ \modif{in the asymptotic limit of rapidly-rotating convection} \citep{Gillet06,Jones15}. From the definition of $Ra$, $E$, $Pr$ and $Nu$, this requirement yields the following combination of the scaling exponents \[ -\alpha+\beta+\gamma=0, \quad \alpha+\gamma=1\,. \label{eq:scalingExpos} \] \modif{In the limit of non-rotating convection, the dependence on $E$ vanishes (i.e. $\beta=0$) and the previous relationship between the scaling exponents relating $\alpha$ and $\gamma$ yields the so-called \emph{ultimate regime} of classical RBC $Nu\sim Ra^{1/2}Pr^{1/2}$ \citep{Kraichnan62}.} Numerical models of rotating convection by \cite{King12} further indicate that the heat flux might only depend on the supercriticality $Ra/Ra_c$ when $Ro_c \ll 1$ \citep[see also][]{Julien12a,Stellmach14}. This second hypothesis yields $\beta = 4\alpha/3$ when $E \rightarrow 0$ and allows us to derive the following diffusivity-free scaling for rotating convection \begin{equation} Nu \sim Ra^{3/2}E^2Pr^{-1/2}\,. \label{eq:asymptotic} \end{equation} \cite{Gillet06} derive the same equation under the hypothesis that a triple force balance between Coriolis force, inertia and buoyancy controls the asymptotic regime of rapidly-rotating turbulent convection \citep[see also][]{Stevenson79,Barker14}. The analysis carried out by \cite{Julien12a} leads to the same inviscid scaling in the framework of asymptotically-reduced equations expected to hold when $E \rightarrow 0$. The evidence for such a low-$Ro_c$ scaling law is however strongly debated. Specifically, \cite{King12} suggest a much steeper heat transport scaling $Nu \sim Ra^3E^4$ for $E=\mathcal{O}(10^{-5})$ and $Ro_c=\mathcal{O}(0.1)$, based on laboratory experiments \modif{in water} complemented by numerical simulations of rotating convection with rigid mechanical boundaries in cartesian coordinates \citep[see also][]{King13}. Similar numerical models by \cite{Schmitz09} that instead employ stress-free boundaries rather found $Nu \sim (Ra\,E^{4/3})^{1.22}$ for a comparable parameter range. This discrepancy implies that the viscous boundary layers might still have a direct influence on the heat transport even at low $E$. The recent comparative study by \cite{Stellmach14} for rigid and stress-free numerical models at lower Ekman numbers $E=\mathcal{O}(10^{-7})$ indeed reveals an active role of the Ekman boundary layers \citep[see also][]{Kunnen16,Plumley16}. While the stress-free models gradually approach the diffusivity-free scaling (\ref{eq:asymptotic}) \citep[see also][]{Barker14}, the Ekman pumping in the cases with rigid boundaries leads to increasing scaling exponents when $E$ is decreased towards geophysical values \citep{Cheng15,Julien16}. This prominent role of the boundary layers therefore questions the relevance of the inviscid scaling (\ref{eq:asymptotic}) for rigid boundaries. Although the spherical geometry is more natural for studying rotating convection in astrophysical and geophysical objects, the majority of the rotating RBC laboratory experiments developed over the past three decades have been carried out in planar and cylindrical cells, in which the rotation axis and the gravity are aligned. The cartesian geometry also allows the computation of efficient local direct numerical simulations that operate at low Ekman numbers \citep[e.g.][]{Kunnen10,Ecke14,Horn15}. Hence, the fruitful interplay between numerical and laboratory experiments in planar or cylindrical geometry enabled a complementary coverage of the parameter space in the low-$Ro_c$ regime \citep[e.g.][]{Aurnou07,Stellmach14,Cheng15,Aurnou15}. However, it remains unclear whether the planar RBC results can be directly applied to rotating convection in spherical geometry. Two specific features of thermal convection in rotating spherical shells are indeed expected to yield significant dynamical differences with the planar or cylindrical RBC setups: (\textit{i}) in most of the fluid volume of spherical shells, gravity is inclined with respect to the rotation axis; (\textit{ii}) due to both curvature and radial variations of the gravitational acceleration, spherical RBC features a significant asymmetry between the hot and the cold bounding surfaces \citep[e.g.][]{Bercovici89,Jarvis93,Gastine15}. Besides the micro-gravity experiments that operate at relatively large Ekman numbers due to their moderate sizes \citep[$E =\mathcal{O}(10^{-3})$, see][]{Hart86,Egbers03}, most of the laboratory investigations of spherical rotating RBC make use of the centrifugal force as a surrogate for the radial gravitational acceleration \citep{Busse74,Cardin94,SumitaOlson03,Shew05}. The combined influence of the laboratory gravity and the centrifugal acceleration of the rotating vessel indeed allows to generate surfaces of gravity potential close to the spherical surfaces in the lower hemisphere of the spherical shell \citep[see for a review][]{Cardin15}. This technique was first employed to explore the onset of convection in rotating spherical RBC \citep{Cordero92}. \cite{SumitaOlson03} studied the scaling behaviours of the heat transport for a relatively low Ekman number ($E\simeq 5\times 10^{-6}$) but with a strong convective forcing ($Ra\geq 200\,Ra_c$). In this parameter range, they obtained $Nu \sim Ra^{0.41}$, a scaling exponent that is hardly steeper than non-rotating RBC and therefore suggests that Coriolis force only plays a minor role on the heat transfer. Numerical simulations of three-dimensional convection in spherical shells have been developed since the late 1970s as a complementary approach to the laboratory experiments \citep[e.g.][]{Gilman77,Tilgner97,Christensen02}. \cite{Christensen06}, later complemented by \cite{King10}, conducted a systematic parameter study of the scaling properties of convective dynamo models with rigid boundaries and reported the scaling $Nu \sim Ra^{6/5}E^{8/5}$ for $E=\mathcal{O}(10^{-5})$. These studies were however carried out in the presence of a self-sustained magnetic field that can possibly impinge on the heat transport. More recently, \cite{Yadav16} studied the influence of both the presence of a magnetic field and the nature of the mechanical boundary condition on the heat transfer in spherical RBC. Magnetic and non-magnetic models were found to exhibit similar heat transfer scaling behaviours possibly because of the parameter space limitation to $E = \mathcal{O}(10^{-5})$ \citep[see also][]{Soderlund12,Garcia14}. Furthermore, these authors did not observe the steep increase of the $Ra$-scaling exponent beyond $3/2$ reported in the cartesian calculations \citep[e.g.][]{King12} when rigid boundaries were employed. Since the heat transport in spherical shells is dominated by the equatorial regions where the gravity is nearly perpendicular to the rotation axis \citep{Tilgner97,Yadav16}, it is not entirely surprising that the scaling properties differ from the cartesian models that would best represent the high-latitude dynamics of a spherical shell. While $Nu$ is an ubiquitous diagnostic quantity studied in both laboratory experiments and numerical models; numerical calculations also enable the computation of additional diagnostics that can provide direct insights on the dynamical regimes. In that regard, the scaling analysis of the convective flow speed $Re$ and the typical length scale $\ell$ can be used to disentangle the underlying force balance in rotating RBC \citep{Aubert01,KingBuffett13}. Two theoretical scalings for $Re$ and $\ell$ have been put forward. The first one, frequently called the inertial scaling of rotating convection, hypothesises a triple force balance between Coriolis, inertia and Archimedean forces \citep[CIA scaling, see][]{Stevenson79,Cardin94,Aubert01,Barker14}, while the second rather relies on a triple balance between viscosity, Archimedean and Coriolis forces \citep[VAC scaling, see][]{King13}. These two concurrent theories however lead to scaling exponents for $Re(Ra,E,Pr)$ close to each other. Using the numerical dataset by \cite{Christensen06}, \cite{KingBuffett13} even demonstrated that the limited data can support both $Re$-scalings at the same statistical confidence level. This study indicates a sizeable role played by viscosity in rotating RBC models with $E \geq 10^{-5}$. To decrease the numerical cost of direct three-dimensional calculations, the quasi-geostrophic approximation of spherical convection \citep[hereafter QG, see][]{Busse86,Cardin94} has been developed. In the limit of $E\rightarrow 0$ and $Ro_c \ll 1$, convection is strongly constrained by rotation and can be approximated by a quasi two-dimensional flow, which allows to decrease the Ekman number to $E=\mathcal{O}(10^{-7})$ \citep{Aubert03,Gillet06,Guervilly10}. However, the scaling analyses carried out by \cite{Gillet06} and \cite{Guervilly10} did not show any clear evidence of convergence towards the diffusivity-free scalings for both $Nu$ and $Re$, even when $E \lesssim 10^{-6}$. Furthermore, the lack of a direct one-to-one comparison between the QG results and the fully three-dimensional computations makes the interpretation of these results difficult. Hence, the determination of an accurate scaling law for both $Re$ and $\ell$ in rapidly-rotating spherical RBC forms one of the main goals of this work. The aims of this study are twofold: (\textit{i}) determine the boundaries of the different physical regimes of rapidly-rotating convection in spherical shells by means of three-dimensional numerical simulations; (\textit{ii}) establish the scaling behaviours of both the local (length scale, boundary layers) and the global ($Nu$ and $Re$) properties that hold within each of these different regimes. We conduct a systematic parameter study varying the Ekman number within the range $3\times 10^{-7} \leq E \leq 10^{-1}$ and the Rayleigh number within the range $10^3 \lesssim Ra \lesssim 2\times 10^{10}$ for a unity Prandtl number spherical shell of radius ratio $r_i/r_o=0.6$. To do so, we construct a dataset of 227 rotating simulations that complements our previous non-rotating calculations \citep{Gastine15}. Recent improvements of pseudo-spectral numerical codes \citep{Schaeffer13} enabled us to decrease the Ekman number to values comparable to these used in present-day local cartesian calculations. Our dataset allows us to determine the regime boundaries for rotating convection and to check the validity of the diffusivity-free scaling (\ref{eq:asymptotic}) in the low-$E$ regime. We examine the scaling behaviours of seven different diagnostics: $Nu$ and $Re$, the viscous dissipation rate, the typical flow length scale, the interior temperature gradient and the viscous and the thermal boundary layer thicknesses. In \S~\ref{sec:model}, we introduce the hydrodynamical model and the various diagnostic quantities of interest. The numerical results are presented in \S~\ref{sec:results}. We conclude with a summary of our findings in \S~\ref{sec:conclu}. | \label{sec:conclu} \begin{figure} \centering \includegraphics[width=8.5cm]{regime} \caption{Regime diagram that summarises the regime transitions. The black circles correspond to the numerical simulations carried out in this study, while the red crosses mark the critical Rayleigh numbers $Ra_c$ given in table~\ref{tab:rac}.} \label{fig:regime} \end{figure} We have studied rotating convection in spherical shells by means of three-dimensional direct numerical simulations. We have constructed a dataset of more than 200 models that cover a broad parameter range with Ekman numbers spanning $3\times 10^{-7} \leq E \leq 10^{-1}$, Rayleigh numbers within the range $10^3 < Ra < 2\times 10^{10}$. The Prandtl number $Pr$ is one and the radius ratio $r_i/r_o$ is 0.6 in all cases. Figure~\ref{fig:regime} shows the parameter space covered by our numerical dataset as well as the regime boundaries of rotating convection derived in this work. We have studied seven different diagnostic quantities and investigated their scaling properties across the regime changes from onset of rotating convection to weakly-rotating convection. These quantities encompass the Nusselt number $Nu$, the Reynolds number $Re_c$, the dimensionless viscous dissipation rate $\tilde{\epsilon}_U$, the interior temperature gradient $\tempgrad$, the average flow length scale $\ell$ and the thermal and viscous boundary layer thicknesses $\lambda_T$ and $\lambda_U$. The scaling behaviours of these seven quantities of interest are summarised in table~\ref{tab:results}. \begin{sidewaystable} \centering \vspace{14cm} \begin{tabular}{ccccccc} \hline \\ \multirow{3}{*}{Regime} & \multicolumn{2}{c}{Weakly non-linear} & \multicolumn{2}{c}{Rapidly-rotating} & \multicolumn{2}{c}{Non-rotating} \\ & \multicolumn{2}{c}{$ Ra_c <Ra < 6\,Ra_c$} & \multicolumn{2}{c}{$6\,Ra_c <Ra < 0.4\,E^{-8/5}$} & \multicolumn{2}{c}{$Ra>100\,E^{-12/7}$} \\ & \multicolumn{2}{c}{VAC} &\multicolumn{2}{c}{bulk CIA+Ekman friction} & \multicolumn{2}{c}{IA} \\ \hline \\ & \multirow{2}{*}{Scaling} & \multirow{2}{*}{Reference} & \multirow{2}{*}{Scaling} & \multirow{2}{*}{Reference} & \multirow{2}{*}{Scaling} & Reference\\ & & & & & & \citep{Gastine15} \\ \\ \multirow{2}{*}{ $Nu$ } & \multirow{2}{*}{$a\lp\dfrac{Ra}{Ra_c}-1\rp+1$ } & Equation~(\ref{eq:NuWnl}) & \multirow{2}{*}{$\dfrac{Ra^{3/2}E^2}{Pr^{1/2}}$} & Equation~(\ref{eq:asymptotic}) & \multirow{2}{*}{$Ra^{0.27}$ to $Ra^{1/3}$} & \multirow{2}{*}{Figures~\ref{fig:nura} and \ref{fig:nutransition}} \\ & & Figure~\ref{fig:wNL}(\textit{a}) & & Figures~\ref{fig:nuraek}-\ref{fig:NuExpLoc} & & \\ \\ \multirow{2}{*}{$\tilde{\epsilon}_U$} & \multirow{2}{*}{$\dfrac{Re_c^2}{E^{2/3}}$} & \multirow{2}{*}{Equation~(\ref{eq:epsvac})} & \multirow{2}{*}{$a\dfrac{Re_c^{2}}{E^{1/2}}+b\dfrac{Re_c^{5/2}}{E^ {1/2}}$} & Equation~(\ref{eq:dissip_theory}) & \multirow{2}{*}{$a\,Re_c^{5/2}+b\,Re_c^3$} & \multirow{2}{*}{Figure~\ref{fig:reytransition}(\textit{a})} \\ & & & & Figure~\ref{fig:dissip} & & \\ \\ \multirow{2}{*}{$Re_c$} & \multirow{2}{*}{$\lp\dfrac{Ra_{\mathcal{Q}}E^{2/3}}{Pr^2}\rp^{1/2}$} & Equation~(\ref{eq:revac}) & \multirow{2}{*}{$\lp\dfrac{Ra_{\mathcal{Q}}E^{1/2}}{Pr^2}\rp^{1/2}$ to $\lp\dfrac{Ra_{\mathcal{Q}}E^{1/2}}{Pr^2}\rp^{2/5}$} & Equation~(\ref{eq:reybounds}) & \multirow{2}{*}{$Ra^{0.46}$ to $Ra^{1/2}$} & \multirow{2}{*}{Figure~\ref{fig:reytransition}(\textit{b})} \\ & & Figure~\ref{fig:wNL}(\textit{b}) & & Figure~\ref{fig:rey_scaling} && \\ \\ \multirow{2}{*}{$-\tempgrad$} & \multirow{2}{*}{$\dfrac{4\eta}{(1+\eta)^2}$} & \multirow{2}{*}{Equation~(\ref{eq:dtcdr})} & \multirow{2}{*}{$\dfrac{Nu}{Re_c^{3/2}E^{1/2}}$?} & Equation~(\ref{eq:betacia}) & \multirow{2}{*}{0} & \multirow{2}{*}{Figures~\ref{fig:beta} and \ref{fig:lbetatransition}(\textit{a})} \\ & & & & Figure~\ref{fig:beta} & & \\ \\ \multirow{2}{*}{$\ell/L$} & \multirow{2}{*}{$E^{1/3}$} & Equation~(\ref{eq:lperpvac}) & \multirow{2}{*}{$Re_c^{1/2}\,E^{1/2}$} & Equation~(\ref{eq:lperpcia}) & \multirow{2}{*}{$\dfrac{Ra^{1/2}}{Nu^{5/2}}$} & Equation~(\ref{eq:lengthscalesRBC}) \\ & & Figure~\ref{fig:lengthscalesOnset} & & Figure~\ref{fig:lengthscalesNL} & & Figure~\ref{fig:lbetatransition}(\textit{b}) \\ \\ \multirow{2}{*}{$\lambda_T/L$} & \multirow{2}{*}{Undefined} & \multirow{2}{*}{} & \multirow{2}{*}{$0.2\,Nu^{-1+o(E)}$?} & Equation~(\ref{eq:tblrot})& \multirow{2}{*}{$0.5\,Nu^{-1}$} & Equation~(\ref{eq:tblrot}) \\ & & & & Figure~\ref{fig:tempLayers} & & Figures~\ref{fig:tempLayers} and \ref{fig:bLayersTransition}(\textit{a})\\ \\ \multirow{2}{*}{$\lambda_U/L$} & \multirow{2}{*}{$ E^{1/2}$} & Equation~(\ref{eq:ekmanLayers}) & \multirow{2}{*}{$E^{1/2}$} & Equation~(\ref{eq:ekmanLayers}) & \multirow{2}{*}{$Re^{-1/2}$} & Equation~(\ref{eq:RBCbl})\\ && Figure~\ref{fig:ekLayers} && Figure~\ref{fig:ekLayers} & & Figures~\ref{fig:ekLayers} and \ref{fig:bLayersTransition}(\textit{b}) \\ \hline \\ \end{tabular} \caption{Summary table of the scaling properties of the quantities of interest in the different regimes of rotating convection derived in this work. The acronyms employed on the third line stand for the leading-order force balance: \emph{Visco-Archimedean-Coriolis} (VAC), \emph{Coriolis-Inertia-Archimedean} (CIA) and \emph{Inertia-Archimedean} (IA). The notation $o(E)$ designates a weak-dependence on the Ekman number, while the question marks highlight possible uncertainties on the scaling laws. See text for the successive derivation of scalings.} \label{tab:results} \end{sidewaystable} For $Ra$ just above critical (i.e. $Ra \gtrsim Ra_c$), our numerical simulations have confirmed the scaling relation of the form $Nu-1\sim Ra/Ra_c -1$, predicted by the perturbation analysis by \cite{Busse86} and \cite{Gillet06}. In this weakly non-linear regime of rotating convection, the convective flow is laminar and takes the form of a drifting thermal Rossby wave with a typical size of $\ell /L \sim E^{1/3}$. The triple force balance between viscosity, Coriolis force and buoyancy (the so-called VAC balance), suggests the scaling for \modif{the flow velocity $Re_c \sim Ra_{\mathcal{Q}}^{1/2}E^{1/3}$}, which is in good agreement with the numerical data. In the limit of small Ekman numbers, an increase of the supercriticality is accompanied by a gradual transition to a turbulent quasi-geostrophic regime (when $Ra \geq 6\,Ra_c$ and $Nu >2$). The heat transport scaling is then expected to become independent of the thermal and viscous diffusivities and to depend only on the supercriticality $Ra/Ra_c$, \modif{yielding $Nu \sim Ra^{3/2}E^2$} \citep[see][]{Gillet06,Julien12,Stellmach14}. A small subset of our numerical data has been found to approach this asymptotic scaling in a narrow fraction of the parameter space delimited by $6\,Ra_c \leq Ra \leq 0.4\,E^{-8/5}$. In good agreement with the theory by \cite{Julien12}, we have observed a breakdown of the $Ra^{3/2}$ scaling law when the thermal boundary layer is not dominated by rotational effects any longer, i.e. when $RaE^{8/5}=\mathcal{O}(1)$. Thanks to a decomposition of the dimensionless viscous dissipation rate $\tilde{\epsilon}_U$ into bulk and boundary layer contributions, we derived a theoretical scaling of the form $\tilde{\epsilon}_U\,E^{1/2} \sim (a\,Re^{5/2}+b\,Re^2)$, which accurately describes the numerical data when adjusting the two fit parameters $a$ and $b$. A sizeable fraction of the dissipation occurs in the fluid bulk, which is dominated by a triple force balance between Coriolis, Inertia and buoyancy \citep[the so-called inertial theory of rotating convection or CIA balance, e.g.][]{Aubert01}. The remaining fraction of the dissipation can be attributed to the viscous friction in the Ekman boundary layers. In contrast to the existing scalings that neglect the boundary layer dissipation \citep[][]{Aubert01,Gillet06,KingBuffett13,Barker14}, this scaling law accurately captures the scaling behaviour of the Reynolds number. Our scaling further predicts that the bulk dissipation will dominate when $Re_c > 5000$. Beyond this value, the inertial scaling for rotating convection $Re_c\sim Ra_{\mathcal{Q}}^{2/5}E^{1/5}$ and $\ell\sim \sqrt{Re_c E}\,L$ (Rhines scaling) should be gradually approached. Beyond $Ra = 0.4\,E^{-8/5}$, the rotational constraint on the convective flow gradually decreases until the dynamics resembles non-rotating convection. Within this parameter range, that we designate as the \emph{transitional regime}, we have observed continuous changes of the flow properties. The heat transfer scaling exponents show continuous variations that depend on $Ra$ and $E$ rather than simple polynomial laws. This makes the derivation of asymptotic scalings inherent to this physical regime extremely difficult. From the intersection between the steep $Nu\sim Ra^{3/2}E^{2}$ scaling for rapidly-rotating convection and the shallow exponent for non-rotating convection $Nu\sim Ra^{1/3}$, we have defined a transition Rayleigh number $Ra_T\sim E^{-12/7}$, which indeed allows to separate the rotation-influenced solutions from those resembling non-rotating convection. Beyond $RaE^{12/7} \sim \mathcal{O}(10^2)$, all the diagnostic quantities studied here follow the scalings for non-rotating convection \citep{Gastine15}. This defines the upper bound of the transitional regime displayed in the regime diagram (figure~\ref{fig:regime}). Our systematic study of rotating convection in spherical shells revealed interesting differences to the local simulations carried out in cartesian coordinates \citep{King12,Stellmach14,Cheng15}. In the limit of small Ekman numbers ($E=\mathcal{O}(10^{-7}$), these studies have obtained much steeper heat transfer scaling laws (from $Nu \sim Ra^3E^4$ to $Nu \sim Ra^{3.6}E^{4.8}$) than our findings. This has been attributed to an active role of the Ekman boundary layers, which supposedly promotes very efficient heat transfer, much steeper than the diffusivity-free asymptotic scaling \citep{Julien16}. In spherical geometry, the Ekman pumping might play a significant role and may indeed affect the heat transport in the polar regions where gravity is aligned with the rotation axis. As shown by \cite{Yadav16}, the heat transport in spherical shells with rigid mechanical boundaries is however dominated by the equatorial regions, where the influence of Ekman pumping on the heat transfer might be negligible. A regional analysis of the heat transport in spherical shell models as well as the computation of new cartesian models in which gravity is orthogonal to the rotation axis could possibly help to ascertain this scenario. Dynamo processes and convection in planetary and stellar interiors frequently operate at Prandtl numbers much smaller than unity. The parameter study presented here has been focused on the peculiar case of $Pr=1$. It would be interesting to complement our study with simulations with $Pr = \mathcal{O}(10^{-2}-10^{-1})$ to verify the theoretical $Pr$-scalings derived here (see table~\ref{tab:results}). Recent studies by \cite{King13PNAS} and \cite{Guervilly16} indeed reveal interesting new physical phenomena inherent to small Prandtl number fluids that could possibly impact the scaling properties. | 16 | 9 | 1609.02372 |
1609 | 1609.05764_arXiv.txt | Some discrepancies have been reported between observed and simulated muon content of extensive air showers: the number of observed muons exceeded the expectations in HiRes-MIA, Yakutsk and Pierre Auger Observatory data. Here, we analyze the data of the Moscow State University Extensive Air Shower (EAS--MSU) array on $E_{\mu} \gtrsim 10$~GeV muons in showers caused by $\sim (10^{17}-10^{18})$~eV primary particles and demonstrate that they agree with simulations (QGSJET-II-04 hadronic interaction model) once the primary composition inferred from the surface-detector data is assumed. | \label{sec:intro} Ultra-high-energy cosmic rays provide % a unique laboratory to study hadronic interactions at the center-of-mass energies and in kinematical regimes not accessible at colliders. Modelling of the development of an extensive air shower (EAS), a cascade process in the terrestrial atmosphere initiated by an energetic cosmic particle, requires an extrapolation of verified interaction models. Not surprisingly, this often results in discrepancies between measured and simulated EAS properties, or between physical properties of the primary particle reconstructed by different methods. A well-known result, \red possibly related to the lack of understanding of the EAS development \cite{New-PAO}, \black is the systematic difference between the primary energies $E$ reconstructed by the fluorescen\red{}ce\black \ detectors and by surface arrays for very same events, as seen by the Pierre Auger Observatory (PAO) \cite{Engel} and the Telescope Array (TA) experiment \cite{TA-E}. It may or may not be related to the apparent excess of muons ($E_{\mu } \gtrsim$GeV\red)\black \ in EAS reported at $E \gtrsim 10^{19}$~eV by the PAO \green \cite{New-PAO, Engel, PAOmu2} \black and Yakutsk \cite{Yak-mu} experiments. A similar excess had been observed earlier by the HiRes/MIA experiment at $E \gtrsim 10^{17}$~eV~\cite{HiRes-MIA}. The purpose of the present study is to compare observed and simulated densities of $E_{\mu }>10$~GeV muons in air showers induced by $E\sim 10^{17}$~eV primaries, based on the EAS-MSU data. A subtle point of all comparisons of this kind is that the muon content of a EAS depends strongly on the type of a primary particle. As a result, the average muon content in the MC set depends not only on the hadronic interaction model used, but also on the primary composition assumed at the simulation. Therefore, for a meaningful comparison, one needs an independent estimator of the primary composition in the very same data set for which the muon data are ana\green{l}\black{}ysed. An estimator of this kind is often missing. In this work, we take advantage of the knowledge of the primary composition obtained from the surface-detector data only, as discussed below. The rest of the paper is organized as follows. In Sec.~\ref{sec:data}, a brief description of the installation and of the data set is given, together with references to previous more detailed publications \red about the EAS-MSU array\black. In Sec.~\ref{sec:anal}, we discuss the analysis performed in this work. Section~\ref{sec:results} presents our results, while Sec.~\ref{sec:concl} summarizes our conclusions. | \label{sec:concl} We have analyzed the \red densities \black of muons ($E_{\mu }>10$~GeV) registered by underground detectors of the EAS-MSU experiment. Starting from the Monte-Carlo simulation based on the primary composition inferred from the surface-detector data alone and on the QGSJET-II-04 hadronic interaction model, we obtain a good agreement between the simulations and the data. Assuming that the number of muons in air showers scales with a coefficient $k$ with respect to the simulation, we constrain \red $k=0.92 \pm 0.0\green 6\black$\black, so that no muon excess ($k>1$) is observed and $k=1$ agrees with the data at the $90\%$ confidence level. Similar conclusions are obtained for primary composition assumptions favoured by the results of other experiments. We note that the nice agreement between predicted and observed muon \red densities \black reported here does not necessarily mean that QGSJET-II-04 gives a correct description of the muon production in any case. The agreement observed here relates to $E \sim (10^{17}-10^{18})$~eV, $E_{\mu} \gtrsim 10$~GeV and inner parts of the shower, $r \lesssim (2-3)R_{0}$. Previous results, collected in Table~\ref{tab:exps}, \begin{table} \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline Experiment & \red altitude,&\red $X$, \black& $E$, eV & $E_{\mu}$, & $r/R_{0}$ &\green$\theta$\black & muon excess\\ & \red m a.s.l. &\red g/cm$^{2}$ \black& & GeV && & \red(data over MC)\black \\ \hline HiRes-MIA~\cite{HiRes-MIA} &\red 1500&\red 860 \black& $10^{17}-10^{18}$ & $\gtrsim 0.85$ & $\gtrsim 10$& N/A & \red yes\\ PAO~\cite{Engel, PAOmu2} &\red 1450&\red 880\black& $\gtrsim 10^{19}$ & $\gtrsim 1$ & $\gtrsim 10$&\green 70$^{\circ}$ & \red yes\\ Yakutsk~\cite{Yak-mu} &\red 100&\red 1020\black& $\gtrsim 10^{19}$ & $\gtrsim 1$ & $\gtrsim 10$ &\green 45$^{\circ}$ & \red yes\\ IceTop~\cite{IceTop} &\red 2835&\red 680\black& $10^{15}-10^{17}$ & $\gtrsim {\green 0.2}$ & $\gtrsim 3$&\green 13$^{\circ}$ {\small mean} & \red no\\[3pt] \hline \begin{minipage}[c]{2cm} EAS-MSU\\ (this work) \end{minipage} &\red 190&\red 990\black& $10^{17}-10^{18}$ & $\gtrsim 10$ & $\lesssim 3$ &\green 30$^{\circ}$ & \red no\\ \hline \end{tabular} \end{center} \caption{\label{tab:exps} Comparison with previous studies of the muon excess (see the text for notations and discussions). } \end{table} have been obtained in various different regimes\red, and some at different altitudes\black. The muon excess reported \red by PAO \black \green Refs.~\cite{Engel, PAOmu2} \black \red and Yakutsk \black \cite{Yak-mu} was observed at primary energies $E \gtrsim 10^{19}$~eV and muon energies $E_{\mu} \gtrsim 1$~GeV. HiRes-MIA~\cite{HiRes-MIA} observed the excess for $E_{\mu } \gtrsim 0.85$~GeV at $10^{17}$~eV$\lesssim E \lesssim 10^{18}$~eV. \red Contrary\black, recent preliminary IceTop results~\cite{IceTop} for GeV muons and $10^{15}$~eV$\lesssim E \lesssim 10^{17}$~eV suggest that no excess is seen. One should not forget also the important difference between our work and all these studies: here we investigate the inner parts of EAS, $\red r\black \lesssim (2-3)\, R_{0}$, while the results of other experiments refer to the outer parts, $\red r \black \sim 10 \,R_{0}$. Note that at even lower $E$ and higher $E_{\mu} \gtrsim 1$~TeV, the muon excess may be probed with the help of atmospheric muons \cite{DedJETPL}, and it has been reported \red in \black \cite{1504.05853} that QGSJET-II-04 \red seems to \black \emph{overestimate} the number of muons in this regime. Preliminary results of the KASCADE-Grande experiment \red (110~m a.s.l., 1022 g/cm$^{2}$) \black at $E\sim 10^{17}$~eV suggest \cite{KASCADE-muon-att} that the atmospheric attenuation of the muon number \green ($E_{\mu} \gtrsim 0.23$~GeV, $r/R_{0} \gtrsim 3$) \black is underestimated by all \red high-energy \black hadronic \red interaction \black models studied there, including QGSJET-II-04. Clearly, further experimental and theoretical studies are required to understand the origin of the reported discrepancies and to arrive at a succesful model of the air-shower development. \appendix | 16 | 9 | 1609.05764 |
1609 | 1609.05287_arXiv.txt | We investigate the recent star formation history (SFH) in the inner region of 57 nearly face-on spiral galaxies selected from the Calar Alto Legacy Integral Field Area (CALIFA) survey. For each galaxy we use the integral field spectroscopy from CALIFA to obtain two-dimensional maps and radial profiles of three parameters that are sensitive indicators of the recent SFH: the 4000\AA\ break (\dindex), and the equivalent width of \hd\ absorption (\ewhda) and \ha\ emission (\ewha). We have also performed photometric decomposition of bulge/bar/disk components based on SDSS optical image. We identify a class of 17 ``turnover'' galaxies whose central region present significant drop in \dindex, and most of them correspondingly show a central upturn in \ewhda\ and \ewha. This indicates that the central region of the turnover galaxies has experienced star formation in the past 1-2 Gyr, which makes the bulge younger and more star-forming than surrounding regions. We find almost all (15/17) the turnover galaxies are barred, while only half of the barred galaxies in our sample (15/32) are classified as a turnover galaxy. This finding provides strong evidence in support of the theoretical expectation that the bar may drive gas from the disc inward to trigger star formation in galaxy center, an important channel for the growth/rejuvenation of pseudobulges in disc galaxies. | \label{sec:introduction} Bars are commonly found in spiral galaxies. In the local universe, about 30\% disc galaxies are barred, and the fraction increases to 50-70\% if weak bars are included or if NIR images are used for bar identification \citep[e.g.][]{deVaucouleurs63, knapen00, marinova-jogee07, eskridge00, masters11, lee-park12}. The bar fraction decreases with increasing redshift, dropping to about 20\% for all bars and below 10\% for strong bars at $z\sim0.8$ \citep{sheth08}. In theory and $N$-body simulations bars play crucial roles in driving the secular evolution of disc galaxies. Bars grow through transfering angular momentum to the outer disk, or even to the speriod/halo \citep{athanassoula03}. This process drives the gas in the disc either outward to form ring-like structure in the outskirt, or inward to trigger star formation in the central region \citep[e.g.][]{athanassoula92, sellwood93, piner95, knapen00, sheth02, regan-teuben04, zurita-perez08}. The gas inflow to the center is believed to make pseudobulges \citep[][and reference therein]{kormendy04}. Bar-induced gas inflow and the related central star formation have been reported in many observational studies. Compared with unbarred galaxies, barred galaxies are found to have higher gas concentrations \citep{sakamoto99, jogee05, sheth05, regan06}, higher central star formation rates (SFRs) \citep{dejong84, hawarden86, devereux87, puxley88, ho97}. Flatter chemical abundance gradients were found in barred galaxies from previous studies \citep{zaritsky94, martin94}, while recent results shown no difference in gas-phase \citep{sanchez14,sanchez-menguiano16} or stellar \citep{cacho14,sanchez-blazquez14} metallicity gradients between galaxies with or without bar. A recent study by \citet{wang12} based on a volume-limited sample of galaxies in the Sloan Digital Sky Survey \citep[SDSS;][]{york00} found strong correlation between the central-to-global SFR and the presence of a bar in face-on spiral galaxies: more than half of the galaxies with highly concentrated SFR are barred. The authors suggested that the central star formation of the other half galaxies which are unbarred may be triggered by tidal interactions with companion galaxies, an idea which is supported by the following two observational facts. On one hand, galaxy-galaxy interactions are known to be able to trigger strong star formation in galaxy centers \citep[e.g.][]{li08}. On the other hand, the presence of a bar in galaxies is found to have weak/no correlation with galaxy-galaxy interactions \citep{li09, lin14}. These two findings combine to suggest that, the central star formation as triggered by interactions and the central star formation induced by bar-driven gas inflow are distinct events, and both are expected to contribute to bulge growth. Some studies suggested that bulges may be rejuvenated systems \citep{thomas06, carollo07, obreja13, erwin15}. Old and young stellar populations coexist in one bulge and these two populations are kinematically distinguishable, with the old population having spheroid kinematics and the secondary population being rotationally supported \citep{emsellem01, perez09}. High frequency of young stellar populations in bulges have been found in both barred galaxies \citep{coelho11, mendez-abreu14} and close pairs \citep{kannappan04}, supporting both bars and interactions to be responsible for the rejuvenation of the central bulge. Our understanding of the stellar populations and star formation history of different structural components in galaxies has improved rapidly in recent years, thanks to the many integral field spectroscopy (IFS) surveys. These surveys have obtained spatially resolved spectroscopy for samples of galaxies in the local Universe, providing both two-dimensional maps and radial profiles of the stellar population properties and kinematics across each galaxy. For instance, using data from the Calar Alto Legacy Integral Field Area (CALIFA) survey \citep{sanchez12,sanchez16}, \citet{holmes15} detected non-circular flows in 12 gas rich disc galaxies with intermediate inclinations, and found 11 of them have a bar, providing strong evidence in support of bars as the driver of gas flow and thus secular galaxy evolution. Another nice example of IFS observations of barred galaxies is presented in \citet{gadotti15} which studied kinematics and stellar population content of NGC 4371, a massive barred galaxy in the core of the Virgo Cluster, using data from the Multi-Unit Spectroscopic Explorer (MUSE), an IFS instrument recently commissioned at the VLT. The MUSE data revealed an inner disc and a nuclear ring, which are rotationally supported and dominated by stars older than 10 Gyr. This suggested the bar in the galaxy formed at $z\sim1.8$, and thus may have an extended impact on the galaxy evolution over a long time. In this work we make use of data from the second data release of the CALIFA survey \citep{garciabenito15} and study the recent star formation history of the inner region for 57 nearly face-on spiral galaxies. In particular, we aim to improve our understanding of the physical link between the central star formation history and the presence of the bar structure. For this purpose we measure three spectral indices: \dindex\ (the break at around 4000\AA\ in optical spectra of galaxies), \ewhda\ (equivalent width of the \hd\ absorption line) and \ewha\ (equivalent width of the \ha\ emission line), which are known to be sensitive indicators of stellar populations formed at different times in the past 1-2 Gyr. Therefore one may have an indication of the recent star formation history by combining the three parameters \citep[e.g.][]{bruzual03, kauffmann03, li15}. As we will show, quite a large fraction of our galaxies show clear signature of recent/ongoing star formation in the central region and almost all these galaxies are barred. On the other hand, interestingly, the bar structure is presented in only half of the galaxies that show the central star formation. We will first describe the CALIFA sample and our methodology of measuring the SFH diagnostic parameters (\S\ref{sec:data}), and then present our results in \S\ref{sec:results}. We discuss the implications of our results on bar-driven gas inflow and bulge growth/rejuvenation in \S\ref{sec:discussion}, and summarize our conclusions in \S\ref{sec:conclusions}. | \label{sec:conclusions} For a sample of 57 nearly face-on spiral galaxies selected from the CALIFA/DR2 sample, we have performed photometric decomposition of their bulge/bar/disk components using optical image from SDSS, and obtained two-dimensional maps and radial profiles of \dindex, \ewhda\ and \ewha\ using the integral field spectroscopy from CALIFA. We identify a class of ``turnover'' galaxies whose inner-most region shows significant drop in \dindex, and/or corresponding upturn in \ewhda\ and \ewha. We investigate the recent star formation history, as indicated by the three diagnostic parameters, for the central region of the both turnover and non-turnover galaxies, and we compare the results for barred and unbarred populations, as well as for galaxies with different global properties. Our conclusions can be summarized as follows. \begin{enumerate} \item We find strong link between the central turnover feature with the bar structure in galaxies. Out of the 57 galaxies in our sample, 17 are identified as a turnover galaxy, of which 15 are barred. On the other hand, however, only half of the barred galaxies present the central turnover, indicating that the presence of a bar is a necessary, but not sufficient condition for the turnover feature to occur, at least for the sample being studied. \item The majority of the turnover galaxies identified by the central turnover in \dindex\ also present corresponding turnover feature in the profiles of \ewha\ and \ewhda. Both the observed values of these diagnostic parameters and the values from inward extrapolation of the linear fits to the profiles at larger radii are consistent with models in which star formation declines continuously, suggesting that the central region of these galaxies have been forming stars continuously in the past 1-2 Gyr. \item The turnover galaxies are found to have intermediate \nuvr\ colors ($3<$\nuvr$<5$), while their centers are mostly classified as star-forming regions according to both the central \dindex\ and the BPT diagram. When using the measurements from inward extrapolation of radial profiles at larger radii, these galaxies move largely towards the quiescent sequence with \dindex$>1.6$ and the AGN or AGN/SF composite regions. \item In addition to the presence of the bar structure, the size of the bar (normalized by the disk radius) is the only galaxy property that is found to correlate with the turnover feature: the longer the bar, the larger the turnover region. There is no correlation of turnover size with galaxy stellar mass, \nuvr\ color, or the axial ratio of the bar. \item Our results provide strong support to the expectations that bar-driven gas inflow triggers star formation in galaxy centers, which makes/grows/rejuvenates pseudobulges. \end{enumerate} Our work demonstrates the power of integral field spectroscopy for studying the resolved star formation history of galaxies. The complementary photometric decomposition is also helpful and even necessary in this work. A lesson we have learned is that, one may easily mis-identify the turnover feature due to incorrect radial range adopted for the linear fitting. The bulge/bar radii obtained from the photometric decomposition have allowed us to take data well within the inner region, avoiding contamination from the spiral disk. We would like to point out that, however, the current work is limited by the small sample size of the CALIFA survey. The exclusion of merging systems from our sample is another thing one should keep in mind. A more complete sample covering wide ranges of galaxy mass, morphology and environment is needed in order for a full understanding of the central turnover. Such data is becoming available thanks to the SDSS-IV/MaNGA survey \citep{bundy15}. We plan to extend our analysis to a much larger sample based on the MaNGA data, including galaxies with masses down to $10^{9}$M$_\odot$ and those in merging/interacting systems, and examining the connections with both the internal structural properties such as the bar and external environment. | 16 | 9 | 1609.05287 |
1609 | 1609.00970_arXiv.txt | Supersymmetric extensions of the standard model predict the existence of non-topological solitons, $Q$-balls. Assuming the standard cosmological history preceded by inflation, $Q$-balls can form in the early universe and can make up the dark matter. The relatively large masses of such dark-matter particles imply a low number density, making direct detection very challenging. The strongest limits come from the existence of neutron stars because, if a baryonic $Q$-ball is captured by a neutron star, the $Q$-ball can absorb the baryon number releasing energy and eventually destroying a neutron star. However, in the presence of baryon number violating higher-dimension operators, the growth of a $Q$-ball inside a neutron star is hampered once the $Q$-ball reaches a certain size. We re-examine the limits and identify some classes of higher-dimensional operators for which supersymmetric $Q$-balls can account for dark matter. The present limits leave a wide range of parameters available for dark matter in the form of supersymmetric $Q$-balls. | Supersymmetric (SUSY) extensions of the standard model predict a scalar potential with a large number of flat directions \cite{ghergetta96}. Such potentials admit stable configurations, SUSY $Q$-balls \cite{kusenko97.1,kusenko97.2,dvali99}. Even if the scale of supersymmetry breaking is well above the reach of the present collider experiments, the flat directions can exist at a high scale and can play an important role in cosmology. If inflation took place in the early universe, a scalar condensate can form along the flat directions, leading to matter--antimatter asymmetry\cite{affleck85,dine95,Dine:2003ax}. In general, this scalar condensate is unstable with respect to fragmentation into $Q$-balls \cite{kusenko97.2,Kusenko:1997vp,Enqvist:1997si,Kasuya:1999wu}, which can be entirely stable and can play the role of dark matter \cite{kusenko97.2,Dine:2003ax,Enqvist:2003gh,Hong:2016ict}. This scenario offers a common origin to ordinary matter and dark matter. Dark-matter $Q$-balls have relatively large masses, and, therefore, very small number densities. A direct detection of such dark matter is extremely challenging \cite{Kusenko:1997vp,Kasuya:2015uka}. These flat directions are only flat at tree level, and in general they are lifted by non-renormalizable terms in the potential coming from loop corrections and GUT or Planck-scale physics, taking the form of polynomials in the squark fields and their conjugates \begin{gather} V_\text{lifting} = \frac{g}{\Lambda^{n+m-4}} \phi^n (\phi^*)^m + \text{c.c.} \label{eq:LiftingPotential} \end{gather} suppressed by some energy scale $\Lambda \sim 10^{16} \text{ GeV}$. If $n \not= m$, then baryon number is no longer conserved, fulfilling one of the Sakharov conditions for baryogenesis \cite{sakharov67}. The same operators will destabilize the $Q$-ball \cite{Kawasaki:2005xc} and allow it to decay via processes that do not conserve the baryon number. If supersymmetric $Q$-balls make up the main component of dark matter, limits on their lifetimes (namely $\tau \gtrsim H^{-1}$) restrict the set of operators in the lifting potential in order to prevent their decay on too short of a timescale. \newparagraph However, one can set additional constraints on the types of operators in the lifting potential by examining the effects of a star infected with a $Q$-ball. A $Q$-ball composed of squarks in the presence of baryonic matter absorbs the net baryon number and radiates pions on its surface \cite{kusenko04}. For a main sequence star, a $Q$-ball should pass through with a negligible change in velocity, due to the relatively low density of the star, and high inertia of the $Q$-ball. A neutron star, however, has a high enough density of baryons that a collision with a $Q$-ball should slow it to a crawl, at which point it would sink to the center of the star and begin to consume it from the inside out \cite{kusenko98,kusenko05}. If the $Q$-ball is absolutely stable, it grows without bound as it absorbs more neutrons until either the neutron star is completely consumed, or the $Q$-ball collapses into a black hole, causing the neutron star to collapse. Either way, we find the star dies relatively quickly on cosmological timescales, on the order of $10^8$ years.\newparagraph However, the baryon number violation at a high scale is both plausible and necessary for the Affleck-Dine baryogenesis to work. In the presence of baryon-number violating operators, the growth of a $Q$-ball inside a neutron star may be stymied by the baryon number destruction in the $Q$-ball interior, which becomes important once the $Q$-ball VEV reaches a certain magnitude \cite{kusenko05,Kasuya:2014ofa}. In this paper, we will re-examine the astrophysical bounds taking into account the baryon number violating operators. The paper is organized as follows: section \ref{sec:QballStates} provides a brief review of allowed $Q$-ball states, section \ref{sec:DecayRates} explains the machinery of calculating the decay rate of the $Q$-ball, section \ref{sec:Qball+NS} details the interaction of the $Q$-ball with a neutron star, and section \ref{sec:BaryonEvolution} explains the evolution of the baryon number within the $Q$-ball and star. Section \ref{sec:Limits} takes this analysis and applies limits to the class of baryon-violating operators. | \label{sec:Conclusion} We have shown here that $Q$-balls can make up dark matter if baryon-violating terms of dimension $n+m > 5$ are present in the scalar potential. Cases in which there is no baryon violation ($n=m$) are ruled out as well due to unrestricted $Q$-ball growth. The baryon number violation is also necessary for the Affleck-Dine mechanism to work. This eliminates the neutron star bounds. Beyond this, there appears to be no restriction on these operators, even at very high dimension. The low level of baryon number violation does not affect the experimental limits based on IceCube \cite{Kasuya:2015uka}, Super-Kamiokande \cite{Arafune:2000yv} and other direct detection experiments. However, one should keep in mind that $Q$-balls may carry some electric charge \cite{Kusenko:1997vp,Arafune:2000yv,Shoemaker:2008gs}, making them almost invisible to most direct-detection searches. (A positively charged $Q$-ball cannot destabilize nuclei because the Coulomb repulsion prevents any strong interactions between non-relativistic $Q$-balls and matter nuclei.) This leaves a wide range of parameters available for dark matter in the form of supersymmetric $Q$-balls. \newparagraph | 16 | 9 | 1609.00970 |
1609 | 1609.02144_arXiv.txt | Pulsar-timing datasets have been analyzed with great success using probabilistic treatments based on Gaussian distributions, with applications ranging from studies of neutron-star structure to tests of general relativity and searches for nanosecond gravitational waves. As for other applications of Gaussian distributions, \emph{outliers} in timing measurements pose a significant challenge to statistical inference, since they can bias the estimation of timing and noise parameters, and affect reported parameter uncertainties. We describe and demonstrate a practical end-to-end approach to perform Bayesian inference of timing and noise parameters \emph{robustly} in the presence of outliers, and to identify these probabilistically. The method is fully consistent (i.e., outlier-ness probabilities vary in tune with the posterior distributions of the timing and noise parameters), and it relies on the efficient sampling of the hierarchical form of the pulsar-timing likelihood. Such sampling has recently become possible with a ``no-U-turn'' Hamiltonian sampler coupled to a highly customized reparametrization of the likelihood; this code is described elsewhere, but it is already available online. We recommend our method as a standard step in the preparation of pulsar-timing-array datasets: even if statistical inference is not affected, follow-up studies of outlier candidates can reveal unseen problems in radio observations and timing measurements; furthermore, confidence in the results of gravitational-wave searches will only benefit from stringent statistical evidence that datasets are clean and outlier-free. | 16 | 9 | 1609.02144 |
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1609 | 1609.00188_arXiv.txt | Single pulses preserve information about the pulsar radio emission and propagation in the pulsar magnetosphere, and understanding the behaviour of their variability is essential for estimating the fundamental limit on the achievable pulsar timing precision. Here we report the findings of our analysis of single pulses from PSR~J1713+0747 with data collected by the Large European Array for Pulsars (LEAP). We present statistical studies of the pulse properties that include distributions of their energy, phase and width. Two modes of systematic sub-pulse drifting have been detected, with a periodicity of 7 and 3 pulse periods. The two modes appear at different ranges of pulse longitude but overlap under the main peak of the integrated profile. No evidence for pulse micro-structure is seen with a time resolution down to 140\,ns. In addition, we show that the fractional polarisation of single pulses increases with their pulse peak flux density. By mapping the probability density of linear polarisation position angle with pulse longitude, we reveal the existence of two orthogonal polarisation modes. Finally, we find that the resulting phase jitter of integrated profiles caused by single pulse variability can be described by a Gaussian probability distribution only when at least 100 pulses are used for integration. Pulses of different flux densities and widths contribute approximately equally to the phase jitter, and no improvement on timing precision is achieved by using a sub-set of pulses with a specific range of flux density or width. | \label{sec:intro} Millisecond pulsars (MSPs) that were spun up in accreting binary systems to reach rotational periods $\lesssim30$\,ms \citep{acrs82}, are noted for their highly precise timing behaviour \citep[e.g.][]{abb+15,dcl+16,rhc+16}. Their short and stable rotational period make them excellent tools for probing tiny spacetime perturbations and performing gravity experiments, including tests of General Relativity with great precision \citep[e.g.][]{ksm+06,wnt10}, stringent constraints on alternative theories of gravity \citep[e.g.][]{fwe+12,afw+13}, probes of neutron star equations-of-state \citep[e.g.][]{dpr+10,opr+10}, and the ongoing search for gravitational waves in the nanohertz regime \citep[e.g.][]{ltm+15,srl+15,abb+16}. The success of the aforementioned timing experiments is attributed to both the regular rotation of the pulsars, and their stable integrated pulse profiles formed by averaging over tens of thousands of periods. Nevertheless, it has been known since the discovery of pulsars that the pulsed emission from every single rotation (thus single pulses) of a pulsar is highly variable. This was first noticed in canonical pulsars and more recently in MSPs \citep[e.g.][]{jak+98,sc12,lkl+15}. A consequence of such variability is the so-called pulse phase jitter phenomenon in integrated profiles, which for a given integration time places a fundamental limit on the achievable timing precision on short timescales. Timing precision has already reached the jitter-limited regime for a few MSPs \citep{lkl+11,sc12}, and this limit is expected to be reached for many more when the next generation of radio telescopes (e.g., the Square Kilometre Array) comes online \citep{lvk+11,jhm+15}. Most recent timing analysis has started to take into account the effect of phase jitter when modelling the noise in the timing data \citep[e.g.][]{ls15,zsd+15,cll+16}. Detailed studies of single pulse variability in MSPs are crucial for building a comprehensive understanding of this phenomenon, if we are to push beyond this limitation. Such investigations will also provide input for the efforts to either model or mitigate jitter noise in timing data \citep{ovh+11,ick+15}. The origin of pulsar radio emission is associated with plasma processes in the highly-magnetised pulsar magnetosphere \citep[e.g.][]{cr77,cor79,cjd04}, the understanding of which has still been elusive. Single pulse data preserve information of the intensity, polarisation, and even waveform (if dual-polarization Nyquist sampled time series are recorded) of the emission from every single rotation. Studying single pulses can shed light on the nature of the pulsar emission mechanism, by, e.g., revealing the fundamental units of coherent radiation \citep{cor76a,gil85,jap01}, distinguishing different modes of polarised emission \citep{gl95,es04}, characterising the temporal variability in pulse intensity \citep{rs75,gmg03,wes06}, and so forth. Studying pulsars that display the drifting sub-pulse phenomenon can also assist in determining the viewing geometry and provide insight into the structure of the emission region \citep{dc68,rs75,ran86,qlz+04}. The vast majority of single pulse emission studies has been mostly of canonical (normal, non-recycled) pulsars \citep[see][for an overview]{lg06}. Extending this work to include MSPs will establish a bridge between the understanding of emission physics in canonical pulsars and that in MSPs, so as to see if a common theory or model of pulsar radio emission can be applied. A small fraction of MSPs emit occasional giant radio pulses, which have been studied in detail \citep{cstt96,kbm+06b,kni07,zps+13,bpd+15}. However, investigations into ordinary single pulses of MSPs have been carried out only for a limited number of bright sources \citep{jak+98,es03a,sc12,bil12,ovb+14,sod+14,lkl+15}, one of which is PSR~J1713+0747. This pulsar is one of the most precisely timed pulsars and has been included in current pulsar timing array campaigns to detect gravitational waves in the nanohertz frequency range \citep{vlh+16}. The binary system it inhabits is also an ideal test laboratory for alternative theories of gravity \citep{zsd+15}. \cite{es03a} showed that there is clear modulation in the pulses from PSR~J1713+0747 and that it varies across the pulse profile and as a function of observing frequency. In the fluctuation spectra, they showed that the pulsar exhibited two broad maxima corresponding to fluctuations at 0.17 and 0.35\,cycles-per-period (cpp). However, the longitude dependence and a correlation with drifting sub-pulses could not be established due to the lack of sensitivity. \cite{sc12} have shown that single pulses from PSR~J1713+0747 are highly variable in phase, which already limits its timing precision with the current observing sensitivity. Thus, understanding single pulse variability of this pulsar in order to potentially mitigate its contribution to the timing noise is clearly necessary and will be the focus of this work. The rest of this paper is structured as follows. In Section~\ref{sec:obs}, we provide the details of the observation and preprocessing of the data. Section~\ref{sec:res} presents the results from our data analysis on single pulse variability, polarisation and timing properties. We conclude in Section~\ref{sec:conclu} with a brief discussion and prospects for future work. | \label{sec:conclu} We have studied the properties of single pulses from PSR~J1713+0747 using 15 minutes of data (corresponding to $\sim197,000$ pulses) collected by LEAP when the pulsar was extremely bright. The pulse energy distribution is shown to be consistent with a log-normal distribution. The pulse widths are typically around 0.04\,ms for the bright pulses. In addition, we have confirmed the detection of periodic intensity modulation by \cite{es03a}, and in addition revealed its association with systematic drifting sub-pulses. From the 2DFS, $P_2$ and $P_3$ of the two modes were measured to be ($15^{+2}_{-6}$\,deg, $6.9\pm0.1$\,$P$) and ($23^{+2}_{-14}$\,deg, $2.9\pm0.1$\,$P$), respectively. The occurrence of the two modes is found to overlap at the phase of the main peak in the integrated profile, providing the first evidence for superposed modes of drifting sub-pulse in MSPs. The mode at 0.14\,cpp was also apparent at the trailing edge of the integrated profile, where the other was not detected. We did not find any evidence of periodic pulse micro-structure with a time resolution of up to 140\,ns. With full polarisation data, we have shown that the bright pulses are significantly linearly polarised. On average, the fractional polarisation of the pulses increases with increasing pulse peak flux density. Using single pulse polarisation, we have presented a longitude-resolved probability density map of P.A., and shown the existence of two orthogonal modes of polarisation that are clearly distinct in pulse phase. Finally, we found that jitter noise induced by pulse variability can be described as Gaussian only when at least 100 pulses have been integrated. Statistically, pulses of different properties contribute equally to the resulting jitter noise, though pulses with high peak flux density have slightly less effect. By timing sub-sets of pulses with respect to their relative peak flux density, relative total flux density and pulse width, we did not find any significant improvement on the overall timing precision. Changing the time resolution used on 1-s integrations from 8.9\,$\mu$s to 140\,ns does not result in significant difference in their TOA uncertainties, meaning that most features on those integrated profiles are resolved with time resolution beyond 10\,$\mu$s. Micro-structure in pulsed radio emission has mostly been searched for in canonical pulsars, and most of the searches that have sufficient time resolution and sensitivity have achieved successful detection \citep[e.g.][]{lkwj98,mar15}. On the other hand, besides PSR~J1713+0747, micro-structure has also been searched for in another two MSPs, PSR~J0437$-$4715 and PSR~B1937+21, with no detection \citep{jak+98,jap01}. Using observations of canonical pulsars, \cite{kjv02} established a relation between micro-structure width and pulsar rotational period. A simple extrapolation from that relation leads to a micro-structure width of $0.5-10$\,$\mu$s for MSPs, well above the time resolutions of the data used for the searches in MSPs. Thus, the non-detections may imply that either micro-structure is less common in MSPs compared with the situation in canonical pulsars, or the relation between micro-structure width and rotational period is different in MSPs. Nevertheless, this needs to be further verified by more sample studies. The discovery of drifting sub-pulses in PSR~J1713+0747 increases the number of MSP ``drifters'' to three, together with PSR~J1012+5307 and J1518+4904 \citep{es03a}. As high-sensitivity searches for drifting sub-pulses have been performed in no more than ten MSPs, drifting sub-pulses do not seem to be an unusual phenomenon among this part of the pulsar population. It is interesting to note that all three exhibit a quasi-periodic drifting fashion, and are classified as ``diffuse'' drifter by the definition in \cite{wes06}. Given that nearly half of the drifters in canonical pulsars show a precise drifting period (referred to as ``coherent'' drifters), quasi-periodic drifting may be comparatively more common in MSPs. Again, robust statistics of the ratio requires future work including an expanded number of samples. Searching for drifting sub-pulses in more MSPs will also show if the phenomenon is correlated with any pulsar properties, such as the characteristic age which has been discovered among the population of non-recycled pulsars \citep{wes06,wse07}. Despite the vast increase in sensitivity delivered by LEAP, a thorough understanding of single pulse properties, in particular those from the lower end of the energy distribution, is still limited by S/N. The situation is likely to be significantly improved when coherent addition of the pulse signal is achieved with more telescopes, as also suggested in \cite{dlc+14}. Eventually, the next generation of radio telescopes, e.g., the Square Kilometre Array and the Five hundred meter Aperture Spherical Telescope, will provide the best opportunity ever to study single pulse emission from MSPs. The behaviour of pulse variability is seen to be a source-dependent phenomenon among pulsars including MSPs. Despite the lack of improvement in the timing precision of PSR~J1713+0747, single pulse data could still be used to mitigate jitter noise in some other pulsars, especially when pulses with different properties exhibit different distributions in phase. In this case, a weighting scheme concerning their contribution to jitter noise may be introduced when integrating the pulses, so as to optimally use the signal of the pulses which show less variability in phase. An approach in a similar framework has already been discussed in \cite{ick+15}. Nevertheless, implementation of such methods is yet to be thoroughly investigated. | 16 | 9 | 1609.00188 |
1609 | 1609.05849_arXiv.txt | Recent measurements of the cosmic microwave background (CMB) \cite{planck15,planckbicep} provide important constraints on the scalar tilt $n_s$ and tensor-to-scalar ratio $r$ in the perturbation spectrum, which in turn provide important restrictions on possible models of cosmological inflation \cite{reviews}. Among the models that fit the data very well is the Starobinsky model \cite{Staro,MC,Staro2} that is based on an $R + R^2$ modification of minimal Einstein gravity. Another model that is consistent with the CMB data is Higgs inflation \cite{Higgsinf}, which assumes a non-minimal coupling of the Standard Model Higgs field to gravity\footnote{This model is disfavoured by current measurements of the top and Higgs masses, which indicate that the effective Higgs potential becomes negative at large field values~\cite{Buttazzo}, unless the Standard Model is supplemented by new physics.}. A central challenge in inflationary model-building is therefore the construction of a model that incorporates not only the Standard Model but also plausible candidates for new physics beyond, such as neutrino masses and oscillations, dark matter, and the baryon asymmetry of the Universe. Among the leading frameworks for physics beyond the Standard Model at the TeV scale and above is supersymmetry. It has many advantages for particle physics, could provide the astrophysical dark matter, offers new mechanisms for generating the baryon asymmetry, and could also stabilize the small potential parameters required in generic models of inflation \cite{ENOT}. In cosmological applications, it is essential to combine supersymmetry with gravity in the supergravity framework~\cite{nost,hrr,gl1}. However, generic supergravity models are not suitable for cosmology, since their effective potentials contain `holes' of depth ${\cal O}(1)$ in natural units \cite{eta}, an obstacle known as the $\eta$ problem. One exception to this `holy' rule is provided by no-scale supergravity \cite{no-scale,LN}, which offers an effective potential that is positive semi-definite at the tree level, and has the added motivation that it appears in compactifications of string theory \cite{Witten1985}. In this case, the $\eta$ problem can be avoided \cite{GMO} and it is natural, therefore, to consider inflationary models in this context \cite{gl2,KQ,EENOS,otherns}. Consequently \cite{ENO6}, there has been continuing interest in constructing no-scale supergravity models of inflation \cite{ENO7,ENO8,KL,others,EGNO4,EGNO5,EGNO6,GM}, which lead naturally to predictions for the CMB variables $(n_s, r)$ that are similar to those of the Starobinsky model~\cite{ENO6}. In particular, no-scale models have been constructed in which the inflaton could be identified with a singlet (right-handed) sneutrino \cite{ENO8,EGNO4,EGNO5}, and also no-scale GUT models have been constructed in which the inflaton is identified with a supersymmetric Higgs boson, avoiding the problems of conventional Higgs inflation \cite{sHiggs}. In this paper we take an alternative approach to the construction of a no-scale GUT model of inflation, namely we consider a supersymmetric SO(10) GUT in which the sneutrino is embedded in a $\mathbf{16}$ of the gauge group and the inflaton is identified with a singlet of SO(10). We show that this model also makes Starobinsky-like predictions for the CMB variables $(n_s, r)$. However, achieving this result makes non-trivial demands on the structure of the SO(10) model, which we study in this paper. One issue is the behaviour of the GUT non-singlet scalar fields during inflation, which we require to be such that the model predictions are Starobinsky-like. Another issue is the form of the neutrino mass matrix. In our model, the superpartner of the inflaton field mixes with the doublet (left-handed) and singlet (right-handed) neutrino fields, leading to a double-seesaw structure, which must satisfy certain conditions if it is to give masses for the light (mainly left-handed) neutrinos that are compatible with oscillation experiments and late-time cosmology. Finally, we also consider the issue of reheating and the generation of the baryon asymmetry following inflation, which, in addition to being compatible with the Planck constraints on $n_s$, should not lead to overproduction of gravitinos. We find parameters for the no-scale SO(10) GUT model that are compatible with all these cosmological and neutrino constraints, providing an existence proof for a more complete model of particle physics and cosmology than has been provided in previous Starobinsky-like no-scale supergravity models of inflation. The structure of this paper is as follows. In Section~\ref{sec:setup} we set up our inflationary model, including the no-scale and SO(10) aspects of its framework. The realization of inflation in this model is described in Section~\ref{inflation}, paying particular attention to the requirements that its predictions resemble those of the Starobinsky model. Section~\ref{sec:neutrinomass} explores the generation of neutrino masses in this model, as they are generated via a double-seesaw mechanism. Reheating and leptogenesis after inflation is discussed in Section~\ref{sec:reheating}, with particular attention paid to the gravitino abundance. Finally, our conclusions are summarized in Section~\ref{sec:summary}. | \label{sec:summary} It has been shown previously that no-scale supergravity with bilinear and trilinear self-couplings of a singlet inflaton field provides an economical way to realize a model of inflation whose predictions for the inflationary observables $(n_s, r)$ are similar to those of the Starobinsky model. In this paper we have studied how this scenario may be embedded in a supersymmetric GUT that is able to address other interesting phenomenological issues such as fermion (particularly neutrino) masses, proton decay, leptogenesis, gravitino production and the nature of dark matter. In this paper we have addressed these issues in a supersymmetric SO(10) GUT model. In general, sneutrino inflation is an attractive scenario, but this cannot be realized in an SO(10) GUT, because sneutrinos are embedded in matter $\mathbf{16}$ representations of SO(10), but there are no $\mathbf{16}^2$ or $\mathbf{16}^3$ couplings in SO(10). We therefore consider an SO(10) GUT model with a singlet inflaton field, in which there is an intermediate stage of symmetry breaking provided by a Higgs $\mathbf{16}$ multiplet. This model has the K\"ahler potential shown in (\ref{Kgen}) and the superpotential shown in (\ref{Wgen}). As discussed in Section~\ref{sec:setup}, we consider various possible patterns of symmetry breaking, paying careful attention to the vacuum conditions in each case. We have shown that inflation can be realized in such a framework, studying numerically the behaviours of the scalar fields during the inflationary epoch. In particular, we tracked the evolution of the the three Standard Model singlets in the {\bf 210} responsible for breaking SO(10), the single in the Higgs {\bf 16} simultaneously with the inflaton. One of the important phenomenological issues in constructing such a GUT model is doublet-triplet mass splitting. As we have discussed, the proton stability constraint requires either a very high supersymmetry-braking scale and/or some additional mechanism to suppress the color-triplet Higgs exchange contribution. These issues may be more easily resolved in a flipped ${\rm SU}(5)\otimes {\rm U}(1)$ model \cite{flipped2} where the Higgs structure is greatly simplified (only a {\bf 10}, {$\mathbf{\overline{10}}$}, {\bf 5}, {$\mathbf{\bar{5}}$} of Higgses are needed instead of the {\bf 210}, {\bf 16}, and {$\mathbf{\overline{16}}$} considered here). We have discussed the fermion masses in this model, point out that it predicts the (phenomenologically successful) unification of the $b$ and $\tau$ Yukawa couplings, and similar unification between the Yukawa couplings in the up-type quark and neutrino sectors. The neutrino masses have a double-seesaw structure involving the left- and right-handed neutrinos and the singlino partner of the inflaton field. We have explored the constraints that neutrino masses impose on this structure, and shown that it can lead to successful leptogenesis. Two specifically supersymmetric issues are gravitino production during reheating at the end of inflation and the nature of dark matter. Avoiding the overproduction of gravitinos imposes a reasonable constraint on the inflaton Yukawa coupling, which should be at most comparable to that of the electron. In this model $R$ parity is not conserved, so one might fear for the stability of supersymmetric dark matter. However, the lifetime of the lightest supersymmetric particle is typically much longer than the age of the Universe, so this is still a plausible candidate for dark matter. The no-scale SO(10) GUT scenario for inflation described here has many attractive features, since it combines Starobinsky-like predictions for the inflationary perturbations with many phenomenological desiderata. We therefore consider it a significant step forward in inflationary model-building, while admitting that it has some issues, notably proton stability. Thus there is still significant scope for further improvement. | 16 | 9 | 1609.05849 |
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1609 | 1609.05308_arXiv.txt | Cold Fronts and shocks are hallmarks of the complex intra-cluster medium (ICM) in galaxy clusters. They are thought to occur due to gas motions within the ICM and are often attributed to galaxy mergers within the cluster. Using hydro-cosmological simulations of clusters of galaxies, we show that collisions of inflowing gas streams, seen to penetrate to the very centre of about half the clusters, offer an additional mechanism for the formation of shocks and cold fronts in cluster cores. Unlike episodic merger events, a gas stream inflow persists over a period of several $\unitstx{Gyrs}$ and it could generate a particular pattern of multiple cold fronts and shocks. | \label{sec:intro} X-ray observations of the gaseous Intra-Cluster Medium (ICM) reveal it is rife with features including merging substructures, cavities, shock waves and Cold Fronts (CF) \citep{Markevitch2007}. The Cold Fronts are contact discontinuities of constant or smoothly changing pressure and velocity over a sharp interface between two regions in which one is denser and cooler than its neighbor. A discontinuous drop in temperature across the interface is paired with a jump in density. If no significant non-thermal pressure components are present, the temperature and density contrasts across the interface will be inversely equal. Shocks on the other hand are characterized by discontinuous jumps in the pressure, density and temperature, all of which increase in value across the shock front. The two phenomena are connected since many processes by which a shock is formed also entail the formation of a contact discontinuity behind it. CFs are very common in clusters (see \citealt{Markevitch2007} for a comprehensive review) and have been found in a variety of sizes and shapes (e.g.\@ concentric arcs, filaments, radial or spiral) both in observations \citep{Ghizzardi2010} and simulations \citep{Bialek2002,Nagai2003,Poole2006,Hallman2010}, and are found in all environments (e.g.\@ disturbed versus quiescent). The accepted measure of a CF strength is the density or temperature contrast which is commonly observed to be scattered about a value of $\simeq 2$ \citep{Owers2009}. In many cases a jump in gas metallicity is also observed, possibly suggesting that enriched low entropy gas stripped from satellite galaxies in the cluster is at play \citep{Markevitch2000}. Signatures of substantial shear flows in CF were detected in relaxed cores \citep{Keshet2010b}. \citet{Reiss2014} found evidence for strong magnetic fields parallel to the CF, which may contribute to their stability. Several different mechanisms have been put forward to explain the origin of CFs. They may form as the interface between the low entropy gas left over from merging satellites and the hot diffuse ICM \citep{Markevitch2000}. Other mechanisms invoke shocks, since contact discontinuities are often found behind shocks. Many processes which can induce shocks in the ICM will lead to the formation of CFs: merging substructure \citep{Nagai2003,Owers2011}, `gas sloshing' about the centre of the potential well of the cluster due to mergers \citep{Churazov2003,Ascasibar2006,ZuHone2010,ZuHone2013} or oscillations of the dark Matter distribution \citep{Tittley2005}. Processes which produce local instabilities can also lead to the formation of CF in the ICM. Local thermal instabilities can lead to the condensations of cold gas, even when the ICM is globally stable \citep{Sharma2012,Gaspari2012,Li2015,Prasad2015}. \citet{Balbus2010} speculate that the non-linear evolution of over-stable states which occur when radiative and thermal processes act to stabilize the heat-flux-driven buoyancy instability \citep[HBI,][]{Parrish2008a} and the magneto-thermal instability \citep[MTI,][]{Parrish2008} can in turn lead to the formation of CF. The mechanisms cited above are noteworthy in that they offer an explanation for the existence of CFs in relaxed clusters which are thought to be devoid of dynamically violent processes. A merger of two cluster sized systems can generate myriad structures and features in the ICM of the merger remnant. In \citet{Poole2006}, a survey of simulated merger events is carried out and shows that CFs of different forms, as well as other transient morphological features (`bridges', `bubbles', `edges', etc.\@) can be generated in these cataclysmic events. \citet{Birnboim2010} showed that when trailing shocks merge a CF is formed and thus co-centric CFs in the ICM can be the result of shocks which originated at the centre and merged with the virial accretion shock in the past. In this paper we suggest yet another mechanism for generating shocks and CFs in the ICM, related to the smooth accretion of mass along filaments into the cluster. In the past decade, the issue of gas accretion on to galaxies and clusters has been overhauled, with the idealized spherical infall scenario \citep{White1978} being replaced by accretion that occurs predominately along filamentary streams which flow along the large-scale dark matter cosmic web \citep{Birnboim2003,Keres2005,Dekel2006,Dekel2009,Keres2009}. Two modes of gas accretion are identified in cosmological simulations in galactic haloes at high redshift: hot gas which has been shock-heated by the virial shock and accretes spherically via cooling to the centre and cold gas which accretes through dense filaments originating in the cosmic web which, due to their higher density and shorter cooling times, are impervious to the formation of a shock \citep{Birnboim2003}. The cold mode accretion is dominant for low-mass haloes while the hot mode accretion becomes more important for high-mass haloes \citep{Dekel2006}. The new understanding that gas streams are an important feature in the formation of galaxies and clusters, especially in terms of mass accretion into the system, may have far reaching implications on the way cluster-sized systems are formed and maintained. \citet{Dekel2006} and \citet{Dekel2009} show that the coexistence of the hot and cold modes of accretion reflects the interplay between the shock-heating scale and the dark matter non-linear clustering scale (the Press-Schechter mass), \mstar. In standard cosmologies, the large-scale structure of the dark matter is roughly self-similar. Haloes of mass \mbox{$\sim M_{\ast}$} are embedded within the filaments and as a result, mass infall will be scattered over a wide solid angle. In the much rarer haloes of \mbox{$M\gg M_{\ast}$}, and galaxy clusters fall firmly into this category, the accretion will be predominately along filaments which are thin in comparison to the halo size, and significantly denser than their host haloes. For massive filaments, more massive than $10^{12}\msun/\units{Mpc}$, a shock is expected to form at the edges of filaments which feed low-redshift clusters with $M_{halo}\gtrsim 10^{15}\msun$ \citep{Birnboim2016}. Thus, gas which is accreted along filaments on to clusters is pre-heated to $\gtrsim 10^6\units{K}$ prior to its entry to the cluster virial radius. In \citet{Zinger2016}, a study of a suite of simulated clusters demonstrated that the filamentary streams which flow from the cosmic web into the cluster, are still found in clusters at \zeq{0} and are still the channel in which most of the mass accretion into the cluster takes places. In about half of these clusters, the streams were found to penetrate into the inner regions of the cluster to within 25 per cent of the cluster virial radius, and often even within $0.1\Rv$. The gas in these streams, already at $\gtrsim 10^6\units{K}$, is further heated as it flows towards the centre. By the time it reaches the inner regions of the cluster, the gas stream is at the virial temperature and no longer cooler than the ambient gas. Of the clusters examined by \citet{Zinger2016}, in which the streams penetrate into the very centre of the cluster, all were independently classified as dynamically `unrelaxed'. Conversely, in the `relaxed' clusters examined, the streams did not penetrate deeper than $\gtrsim 0.35 \Rv$. Thus the dynamical state of the cluster was shown to be linked with the presence or absence of deeply penetrating streams in the central regions, such that a deeply penetrating stream can lead to an unrelaxed cluster. In addition, it was found that the degree of penetration of the streams in a given cluster can change over the evolution of the cluster over typical timescales of $\sim\unitstx{Gyr}$, with the dynamical state changing accordingly. The purpose of this paper is to demonstrate that the inflowing gas streams in clusters can generate shocks and CFs in the ICM, and to this end we have chosen to focus with some detail on three cluster outputs, where this phenomenon is convincingly exhibited. The paper is organized as follows. In \rfsec{coldFronts}, we treat the case of gas stream collision and CF formation via a simple analytic model. In \rfsec{sims}, we describe the simulations used for the analysis and in \rfsec{results} we present three representative examples of gas streams colliding in simulated clusters and forming shocks and CFs. In \rfsec{detect} we examine the potential for observationally detecting the CFs and shocks in our examples and in \rfsec{discuss} we summarize and discuss our findings. \begin{figure} \centering \subfloat[Instance of collision]{\label{fig:collision_initial} \includegraphics[width=8cm,keepaspectratio,bb=0 0 9in 5.01in]{fig1a}}\\ \subfloat[Pressure at a later stage]{\label{fig:collisionPressure_later} \includegraphics[width=8cm,keepaspectratio,bb=0 0 10in 7.5in,trim=0.4in 1.30in 0.85in 1.20in, clip]{fig1b}}\\ \subfloat[Density at a later stage]{\label{fig:collisionDensity_later} \includegraphics[width=8cm,keepaspectratio,bb=0 0 10in 7.5in,trim=0.4in 1.30in 0.85in 1.20in, clip]{fig1c}} \caption{ Schematic representation of the collision between two homogeneous media. In the instance of collision \subrf{fig:collision_initial}, two media of constant pressure and density are colliding. At a later time, two shocks have formed and are propagating in opposite directions. Between the two shocks a third post-shock state of constant pressure and velocity has formed \subrf{fig:collisionPressure_later}. The density in the post shock \subrf{fig:collisionDensity_later} region has one of two values (set by the jump conditions for each shock wave) bridged by a contact discontinuity which forms at the Lagrangian location of the initial collision site and moves at the post-shock velocity.} \label{fig:collision} \end{figure} \begin{figure} \centering \includegraphics[width=8.5cm,keepaspectratio,bb=0 0 5.4in 4.32in]{fig2} \caption{The value of the ratio of the post-shock density contrast to the initial density contrast $\alpha=q/q_0$ in an idealized stream collision scenario for a range of Mach numbers for the two shocks, for an ideal mono-atomic gas with $\gamma=5/3$. Contours mark significant values of $\alpha$. We find that $\alpha\approx 1$ (white regions) for a large range of values, especially in the strong shock regime.} \label{fig:qFactor} \end{figure} | \label{sec:discuss} In this paper we report a robust mechanism for generating shocks and CFs in the central regions of clusters via the inflowing gas streams, which are seen in simulations to be prevalent in many clusters. This mechanism should be particularly relevant in unrelaxed clusters (see e.g. \citealt{Hallman2010}) in which gas streams are seen to penetrate into the core \citep{Zinger2016}. Inflowing gas streams, originating in the large scale filaments of the cosmic web, account for most of the mass accretion into the systems and can travel at high velocities with $\gtrsim 1000 \units{km\,s^{-1}}$, carrying with them a significant amount of energy. In clusters, they are heated to the virial temperature as they penetrate through the halo. In some cases, streams are seen to penetrate into the central regions of the cluster whereas in others, the stream stop or dissipate before reaching the centers. The dynamical state of the clusters was found to be linked to the degree of penetration \citep{Zinger2016}. These penetrating streams often collide either with other streams or with the existing ICM, and thus can lead to the formation of shocks and CFs. We examined an idealized 1D scenario for a collision between two streams (or a single stream and the relaxed ambient gas) of constant density and pressure and found that as a result of the collision, two shocks are formed, propagating in opposite directions. Between the two shocks a contact discontinuity in density invariably forms, which travels at the velocity of the post-shock gas. The contact discontinuity is in pressure equilibrium, thus a jump in temperature is expected to be compensated by a drop in gas density, except in the exceptional case of completely identical streams in both density and pressure. This simple, idealized picture is a far cry from the complex 3D structures and processes found in the ICM in observations and in simulations such as the ones analysed here. However, detailed examination of stream collisions in simulated clusters revealed configurations which resemble the idealized test-problem. In the cluster CL6, at the site of the stream collision, two shocks moving in opposite directions were identified with a distinct CF found between them, whose density and temperature contrasts are (inversely) equal to within $\lesssim 5$ per cent. The absence of any form of substructure and the dearth of metals in the gas at the CF location enables us to rule out satellites as a source of the CF. An additional shock, likely formed earlier, was found beyond the leading shock and analysis of the shock properties suggests that the shocks will merge and lead to the formation of another CF \citep{Birnboim2010}. We investigated the CF formation in a fashion similar to observations, namely analysing a single snapshot to determine the link between the CFs and the streams that generated them. A future study, utilizing simulations with improved temporal resolution is planned in order to study the formation and evolution of CFs formed by stream collision over time. The primary objective of this paper is to provide a proof of concept for the formation of shocks and CFs by the collisions of inflowing gas streams from the cosmic web. The particular clusters presented here were chosen since it demonstrated a clear and compelling example for the mechanism. The stream collision site was fortuitously situated in such a way as to allow easy visualization of the CF along the Cartesian projections of the simulation. Examining the potential to detect such CFs in observations, we found that for prominent cases, such as the CF found in CL6, observational detection is definitely within the current capabilities of deep {\em Chandra} observations, although identifying the full configuration of two oppositely oriented shocks with a CF in between may prove challenging. In addition, one must bear in mind that while stream collisions and subsequent formation of CFs can occur anywhere in the cluster, the potential to detect them is highest in the central regions where the X-ray emmission is strongest. The cases examined in this paper are by no means the only instances of CFs which are associated with stream collisions in the simulation suite we have examined. A visual survey of the entire simulation suite at \zeq{0} yielded multiple CFs in all the simulated clusters with roughly half of all CFs showing a possible connection to the inflowing streams. In our rough estimation, \mbox{$\sim 15$} per cent of all CFs are potentially detectable with current instruments. Linking CFs to streams unequivocally is only possible with an in-depth analysis as presented in the paper, but we found CFs that resulted from the collision of inflowing streams in nearly all clusters we examined. One such example is presented in \rfsec{cl107}, where we examine an additional cluster (CL107) in which colliding gas streams generate shocks and CFs. In this cluster, the shock front at the collision site is comprised of two distinct shocks, one originating from the stream collision and the other from the motion of a large satellite travelling with the stream. In the latter, the resulting CF contains a metallicity gradient across the CF, indicating that gas stripped from the satellite is partially responsible for the CF. The examples brought forth in this paper highlight the challenge of disentangling the contribution of the gas flowing along the stream and contribution of the merging sub-structure to the formation of the shocks and CFs. Since the gas streams mark the preferred direction of accretion into the cluster, merging satellites are often found travelling along the inflowing streams. In addition, it has been shown that the gas stripped in major mergers in the cluster can stream towards the centre in high-velocity flows which resemble the large scale gas streams we describe here \citep{Poole2006}. In many of the other examples of CFs found at stream collision sites in our simulation suite we found additional features, such as satellites, which made it difficult to link the CF to the stream unequivocally. To complement the findings in this paper, a study of the prevalence of CFs at stream collision sites and their properties is in order. In particular, it is important to ascertain how common this mechanism is compared to other processes which form CFs. It may be argued that since both mergers and streams are aspects of the mass accretion, there is no point in differentiating between them as mechanisms of CF formation. Indeed, as shown in \rfsec{coldFronts}, high-velocity streams, regardless of their origin, will lead to the formation of shocks and CFs in the ICM. However, merger events in the core are episodic by nature and their effect on the ICM only lasts for $\sim 0.1\textrm{--}1 \units{Gyr}$ \citep{Churazov2003,Tittley2005,Ascasibar2006,Poole2006} whereas the accretion through streams can be continuous for longer periods of time. Beyond the simple considerations of detectability, the ability to observe CFs is dependent on their stability to various physical processes which can destroy them. Thermal conduction and particle diffusion, for example, can smear out the features of CFs on time-scales of $\sim 10\units{Myr}$ \citep{Markevitch2007}, which implies that in order for CFs to be observed as much as they are, they must either be formed frequently, or that other factors, such as magnetic fields \citep{Carilli2002}, are suppressing the thermal conduction. Magnetic fields can also suppress Kelvin-Helmholtz instabilities from breaking up CFs \citep{Keshet2010b,Roediger2013,ZuHone2011,ZuHone2015}. Shocks crossing the CF can also disrupt it via the Richtmeyer-Meshkov instability \citep{Brouillette2002}. An important aspect of generating CF by stream collisions is that while individual CF may disappear, new ones will constantly form on time-scales of several $\unitstx{Gyr}$ as long as the streams persist. When comparing the cluster CL6 at two different epochs we found that the inflowing gas streams persisted over several $\unitstx{Gyrs}$, but that the penetration depths and thus the shocks and CFs generated changed over time. As a case in point, at the stream collision site at \zeq{0} we found two shocks propagating upwards (red and green arrows in \cref{fig:cl6Maps}) which are expected to merge in \mbox{$\sim 350\units{Myr}$}. At the location where the shocks merge, a new CF will be formed \citep{Birnboim2010}. Another point to consider is that formation of CFs via stream collisions is a natural explanation for CFs found in clusters in which there is no evidence of merger events. In absence of instruments that can directly observe the gas streams in clusters, identifying the shocks and CF formed at the collision site may afford an indirect way to identify the streams. Observation of a double shock configuration with a CF found in between, as presented above, would constitute a strong piece of evidence for the existence of gas streams in clusters, beyond the realm of cosmological simulations. | 16 | 9 | 1609.05308 |
1609 | 1609.09126_arXiv.txt | We calculate the evolution of gas giant planets during the runaway gas accretion phase of formation, to understand how the luminosity of young giant planets depends on the accretion conditions. We construct steady-state envelope models, and run time-dependent simulations of accreting planets with the Modules for Experiments in Stellar Astrophysics (MESA) code. We show that the evolution of the internal entropy depends on the contrast between the internal adiabat and the entropy of the accreted material, parametrized by the shock temperature $T_0$ and pressure $P_0$. At low temperatures ($T_0\lesssim 300$--$1000\ {\rm K}$, depending on model parameters), the accreted material has a lower entropy than the interior. The convection zone extends to the surface and can drive a large luminosity, leading to rapid cooling and cold starts. For higher temperatures, the accreted material has a larger entropy than the interior, giving a radiative zone that stalls cooling. For $T_0\gtrsim 2000\ {\rm K}$, the surface--interior entropy contrast cannot be accommodated by the radiative envelope, and the accreted matter accumulates with high entropy, forming a hot start. The final state of the planet depends on the shock temperature, accretion rate, and starting entropy at the onset of runaway accretion. Cold starts with $L\lesssim 5\times 10^{-6}\ L_\odot$ require low accretion rates and starting entropy, and that the temperature of the accreting material is maintained close to the nebula temperature. If instead the temperature is near the value required to radiate the accretion luminosity, $4\pi R^2\sigma T_0^4\sim (GM\dot M/R)$, as suggested by previous work on radiative shocks in the context of star formation, gas giant planets form in a hot start with $L\sim 10^{-4}\ L_\odot$. | \label{sec: Intro} The direct detection of young gas giant planets is an important test of planet formation mechanisms, because at young ages the planet has had less time to thermally relax and so its thermal state depends on how it formed \citep{Stevenson1982,Fortney2005,Marley2007,Fortney2008}. Traditional cooling models for brown dwarfs and giant planets were based on hot initial (post-formation) conditions, in which case the thermal time is short and the planet quickly forgets the initial conditions and evolves onto a cooling track that depends only on the mass (e.g.~\citealt{Burrows1997,Baraffe2003}). \cite{Fortney2005} and \cite{Marley2007} pointed out that gas giants formed by core accretion might be much colder than these earlier ``hot start'' models. They showed that the core accretion model described in the series of papers \cite{Pollack1996}, \cite{Bodenheimer2000}, and \cite{Hubickyj2005} produced planets that were significantly less luminous, implying that giant planets instead have a ``cold start''. Given uncertainties in planet formation models and the potential large range in luminosity of newly formed gas giant planets, \cite{Spiegel2012} took the approach of treating the internal entropy of the gas giant after formation as a free parameter, producing a range of ``warm starts''. The predicted cooling tracks then depend on the planet mass and initial entropy. \cite{Bonnefoy2013} and \cite{Marleau2014} explored the joint constraint on these two parameters that can be inferred from a directly imaged planet with a known luminosity and age. For hot initial conditions, the cooling tracks depend only on the mass; cold initial conditions require a more massive planet to match the observed luminosity. Fitting hot start cooling curves therefore gives a lower limit on the planet mass. Matching the observed luminosity gives a lower limit on the initial entropy, because of the sensitive dependence of luminosity on the internal entropy (e.g.~fig.~2 of \citealt{Marleau2014}). Additional information about the planet mass, such as an upper limit from dynamics, can break the degeneracy and reduce the allowed range of initial entropy. The population of directly-imaged planets shows a wide range of luminosity (e.g.~\citealt{Neuhauser2012,Bowler2016}), with most being too luminous to be cold starts. Examples are $\beta$ Pic b with $L\approx 2\times 10^{-4}\ L_\odot$ \citep{Lagrange2009,Lagrange2010,Bonnefoy2013}, or the HR8799 planets with $L\approx 2\times 10^{-5}\ L_\odot$ for HR8799c, d, and e, and $8\times 10^{-6}\ L_\odot$ for HR8799b \citep{Marois2008,Marois2010}. The inferred initial entropies in these cases are significantly larger than in \cite{Marley2007} (\citealt{Bonnefoy2013,Bowler2013,Currie2013,Marleau2014}). The best case for a cold start is the young giant planet 51 Eri b, which has a projected separation of 13~au from its star and $L\approx 1.4$--$4\times 10^{-6}\ L_\odot$ \citep{Macintosh2015}. This luminosity is consistent with the value $\approx 2\times 10^{-6}\ L_\odot$ predicted by \citep{Marley2007}, but it also matches a hot start for a planet mass $2$--$3\ M_J$ at the stellar age $\approx 20\ {\rm Myr}$. Similarly, the low effective temperature of $850\ {\rm K}$ for HD 131399Ab corresponds to a hot start mass of $4\ M_J$ at $16\ {\rm Myr}$ \citep{Wagner2016}. Another cold object is GJ~504b, which has an effective temperature of only $510\ {\rm K}$ \citep{Kuzuhara2013}, but indications that the star is Gyrs old imply that it may be a low-mass brown dwarf rather than a planet \citep{Fuhrmann2015,DOrazi2016}. Interesting from the point of view of testing formation models has been the discovery of protoplanets still embedded in a protoplanetary disk. For example, HD~100546 b is a directly-imaged object 50~au from its Herbig Ae/Be host with a luminosity $\sim 10^{-4}\ L_\odot$ \citep{Quanz2013,Currie2014a,Quanz2015}, and the star may host a second planet closer in \citep{Currie2015,Garufi2016}. \cite{Sallum2015} identified two and perhaps three accreting protoplanets in the LkCa~15 transition disk. The infrared and H\,$\alpha$ luminosities were consistent with expected accretion rates: \citet{Sallum2015} report $M\dot M\sim 10^{-5}\ M_J^2\ {\rm yr}^{-1}$, where $M$ and $\dot M$ are respectively the planetary mass and accretion rate, which agrees with typical accretion rates of $\sim 10^{-3}$--$10^{-2}\ M_\oplus\ {\rm yr^{-1}}$ in models (e.g.~\citealt{Lissauer2009}) for $M\sim M_J$. The young ages of these stars $\lesssim 10\ {\rm Myr}$ correspond to early times when there is greater potential for distinguishing formation models (e.g.~fig.~4 of \citealt{Marley2007}), \update{especially since the planets could be substantially younger than the star \citep{Fortney2005}.} The interpretation of the observations is complicated, however. Contributions from the environment around the protoplanet, which is likely still accreting, need to be considered, and if accretion is ongoing the accretion luminosity $L_{\rm accr}\approx GM\dot M/R$, where $R$ is the planetary radius, may dominate the internal luminosity. \update{Nevertheless, these effects can potentially be distinguished by studying the spectral energy distribution or spatially resolving the emission. For example, observations of HD~100546 b are able to make out a point-source component (surrounded by spatially-resolved emission) with blackbody radius and luminosity consistent with those of a young gas giant \citep{Currie2014b,Quanz2015}.} Interpreting the current and upcoming observations of young gas giants requires understanding more fully the physics that sets the thermal state of the planet during and immediately after formation. \cite{Marley2007} emphasized that because most of the mass of the gas giant is delivered through an accretion shock, the efficiency with which the shock radiates away the gravitational energy of the accreted matter is a key uncertainty, determining the temperature of the material added to the planet by accretion. The need to accurately treat the radiative cooling at the shock (in particular whether the shock is supercritical, e.g.~see \citealt{Commercon2011}) has been discussed in \textsection~8.1 of \citet{Mordasini2012} and in reviews such as \cite{Chabrier2014}. \cite{Mordasini2013} also identified the planetesimal surface density in the disk as a key ingredient since it sets the core mass. He simulated the growth of planets under cold- and hot-start conditions by changing the outer boundary condition for the planet during the accretion phase. In the cold case, the final entropy of the planet was found to depend sensitively on the resulting core mass through the feedback action of the accretion shock. Most recently, \cite{Owen2016} pointed out the potential importance of non-spherical accretion and studied the role of an accretion boundary layer in setting the thermal state of the accreted matter. In this paper, we focus on the phase of the core accretion scenario in which the accreting matter forms a shock at the surface of the planet. This runaway accretion phase occurs once the contraction rate of the gas envelope surrounding a newly formed core of $\sim 10\ M_\oplus$ becomes larger than the rate at which the disk can supply mass to the envelope (e.g.~\citealt{Helled2014,Mordasini2015}). The planet then shrinks within its Hill sphere and mass flows hydrodynamically onto the planet. Given the uncertainty in the temperature of the post-shock material, we treat the entropy at the surface of the planet as a free parameter. The aim is to better understand how the matter deposited by the accretion shock becomes part of the planet and therefore sets the internal entropy. This approach is similar to previous work on accreting protostars in which the efficiency of the accretion shock is treated as a free parameter (e.g.~\citealt{Prialnik1985,Siess1997,Baraffe2009}; see discussion in \S~\ref{sec:previoushotcold}). We improve on the previous calculations of core accretion with hot outer boundaries by \cite{Mordasini2012} and \cite{Mordasini2013}, which assumed constant luminosity inside the planet and only global energy conservation, by following the full internal energy profile during accretion. \begin{figure} \epsscale{1.2} \plotone{f1.pdf} \caption{Diagram of a spherically-symmetrically accreting gas giant. Shown are the last parts of the accretion flow (\textit{top}), the radiative envelope (\textit{middle}), and the convective interior (\textit{bottom}). Matter accretes onto the envelope with a rate $\dot{M}$, where it shocks and releases energy as an accretion luminosity $L_\mathrm{accr}$. Immediately after the shock, the matter has temperature $T_0$, pressure $P_0$ equal to the ram pressure (eq.~[\ref{eq:Paccr}]), and thus entropy $S_0$. As the material settles down through the envelope to the convective core with a velocity $v=\dot M/4\pi r^2\rho$, it releases an additional luminosity $L_\mathrm{comp}$ from compressional heating and finally reaches the radiative-convective boundary (RCB). The convective core has entropy $S_c$ and supplies a luminosity $L_\mathrm{RCB}$ to the base of the envelope.} \label{fig:schematic} \end{figure} A schematic diagram of the different regions we consider in this paper is shown in Figure \ref{fig:schematic}. We start in \S~\ref{sec:entropy} by discussing the expected values of entropy of the accreted material deposited by the accretion shock at the surface of the planet. In \S~\ref{sec:theorymodels} we compute thermal steady state models of the accreting envelope to understand how freshly accreted material becomes part of the planet, following \cite{Stahler1988} who studied the envelopes of accreting low-mass protostars. We show that there are three regimes of accretion depending on how the entropy of the newly accreted material compares to the internal adiabat. In \S~\ref{sec:mesamodels}, we numerically calculate the evolution of gas giants accreting matter with a range of entropy, using the Modules for Experiments in Stellar Astrophysics (MESA) code \citep{Paxton2011,Paxton2013,Paxton2015}, and investigate the sensitivity of the final thermal state of the planet to the shock conditions and starting entropy at the onset of accretion. We summarize, compare our results to observed systems, and discuss the implications in \S~\ref{sec:summdisc}. Finally, analytical formul\ae\ for the entropy of an ideal gas as well as analytic solutions of envelope structures of accreting atmospheres are presented in Appendices~\ref{append A} and~\ref{append B} respectively. | \label{sec:summdisc} In this paper, we investigated the fate of newly accreted matter during the runaway accretion phase of gas giant formation. Since most of the mass of the planet is added during this phase, it is crucial for determining the luminosity of the planet once it reaches its final mass. \subsection{The Accretion Process} We showed that solutions for the envelope of an accreting planet take three different forms (\S~\ref{sec:envelope models} and \S~\ref{sec:hot boundary model}) which leads to three different accretion regimes (\S~\ref{sec:acc regimes} and Fig.~\ref{fig:entropy_profiles}). Figure \ref{fig:TP grid scan} shows the final outcome of accretion: the internal entropy of the planet resulting from accretion with different choices of outer boundary temperature and pressure $T_0$ and $P_0$. The accretion regime depends on the difference between the entropy of the material deposited by the accretion shock $S_0(T_0,P_0)$ and the initial internal entropy $S_i$: \begin{itemize} \item The {\em cooling regime}. For $S_0\lesssim S_i$, the planet becomes fully convective, and the superadiabatic gradient drives a large luminosity that leads to rapid cooling. The cooling luminosity is sensitive to the boundary pressure $P_0$, with larger $P_0$ leading to faster cooling. If the cooling is rapid enough compared to the accretion timescale, the end state of this regime is that the internal entropy becomes equal to the surface entropy $S_f\approx S_0$. This regime occurs for low boundary temperatures $T_0\lesssim 500$--$1000\ {\rm K}$. \item The {\em stalling regime}. For $S_0\gtrsim S_i$, the entropy decreases inwards in a radiative envelope. Provided the entropy contrast is not too great, the envelope joins smoothly onto the interior convection zone. The hot envelope causes the radiative-convective boundary (RCB) to lie at higher pressure than in an isolated cooling planet with the same internal entropy, lowering the luminosity at the RCB and slowing the cooling. In this regime, the final entropy lies close to the initial value of entropy at the onset of accretion $S_f\lesssim S_i$, depending on how much the cooling is slowed. This regime occurs at intermediate temperatures $T_0\approx 1000$--$2000\ {\rm K}$. \item The {\em heating regime}. For boundary temperatures $T_0\gtrsim 2000\ {\rm K}$, the entropy difference $\Delta S=S_0-S_i$ cannot be accommodated by the radiative envelope. Instead, the entropy decreases inwards through the envelope to a value $S_{\rm min}>S_i$ (\S~\ref{sec:hot boundary model}, Appendix~\ref{append B}, Fig.~\ref{fig:Smin}) and a second convection zone with entropy $S_{\rm min}$ accumulates on top of the original convective core. Because the minimal entropy $S_{\rm min}$ decreases with increasing planet mass, the envelope quickly moves into the stalling regime as the planet mass increases, and the planet accumulates most of its mass with entropy close to the original $S_{\rm min}$. \end{itemize} Our results show that the luminosity of a young gas giant formed by core accretion depends not only on the outer boundary conditions (e.g.~the shock temperature $T_0$) and accretion rate, but also the initial entropy $S_i$ when runaway accretion begins, since it determines whether accretion occurs in the cooling, stalling, or heating regimes. Therefore the thermal state of the young planet in principle provides a link to the structure of the accreting core soon after the crossover mass is reached. This point was also made by \cite{Mordasini2013}, who found that the final entropy depended sensitively on the core mass because it sets the entropy of the envelope at detachment. We see here that for a wide range of intermediate temperatures for which accretion is in the stalling regime ($T_0\approx 1000$--$2000\ {\rm K}$, see Fig.~\ref{fig: ram entropy results}), the final entropy is close to the entropy at the start of runaway accretion. \begin{figure*} \epsscale{1.1} \plotone{f11.pdf} \caption{Luminosity at the onset of post-accretion cooling as a function of surface temperature during accretion for $\dot M=10^{-2}\ M_\oplus\ {\rm yr^{-1}}$ (\textit{left panel}) or $\dot M=10^{-3}\ M_\oplus\ {\rm yr^{-1}}$ (\textit{right panel}). The colors indicate the final planet mass, while the different symbols indicate the initial entropy of the object at the beginning of accretion (\textit{see legend}). For visual clarity, the markers are given a temperature offset of $-25$, 0, and $+25$~K for a respective final mass of 2, 5, and $10\ M_J$.} \label{fig: ram pressure cooling curves} \end{figure*} \begin{figure*} \epsscale{1.05} \plotone{f12.pdf} \caption{Post-accretion cooling compared with directly-imaged exoplanets. The curves show the evolution of the luminosity after accretion ends for final masses $M_f=2$, $5$, and $10\ M_J$ in MESA (\textit{line style}) and surface temperature during accretion $T_0=100$--2500~K (\textit{line color}). \update{The entropy at the beginning of accretion (the accretion rate) is constant along columns (rows); see top (right) titles.} Because these are post-accretion luminosities, the curves begin at different ages based on the total accretion time, which depends on $\dot M$ and the final mass. The data points are for objects with hot-start mass $\lesssim 10\ M_J$ from the compilation of \cite{Bowler2016} as well as the protoplanet HD 100546 b, and use the age \textit{of the host star}: \textbf{1}:~ROXs 42B b \citep{Currie2014a}, \textbf{2}:~2M0441+2301B b \citep{Todorov2010}, \textbf{3}:~HD 106906 b \citep{Bailey2014}, \textbf{4}:~2M1207 3932 b \citep{Chauvin2004}, \textbf{5}:~HD 95086 b \citep{Rameau2013}, \textbf{6}:~HR 8799 d \citep{Marois2008}, \textbf{7}:~HR 8799 b \citep{Marois2008}, \textbf{8}:~51 Eri b \citep{Macintosh2015}, \textbf{A}:~HD100546 b \citep{Quanz2015}. \update{The symbol type indicates objects around brown dwarfs (\textit{open squares}), objects at $>100\ \rm{au}$ (\textit{open triangles}), planets at $<100\ \rm{au}$ orbiting stars (\textit{closed circles}), and protoplanets (\textit{open circle}).} % } \label{fig: cooling curves with data} \end{figure*} \subsection{Cold or Hot Starts?} The luminosity of the planet after formation $L_p$ is shown in Figure \ref{fig: ram pressure cooling curves}. We calculate this luminosity by taking the internal entropy at the end of accretion (for the hot cases, this is the entropy in the hotter, outer convection zone) and constructing a new planet with the same mass and internal entropy in MESA. This avoids convergence issues that arise when changing from accreting to cooling surface boundary conditions at the end of accretion. Figure \ref{fig: ram pressure cooling curves} shows that cold starts require that we choose the lowest values of boundary temperature $T_0<300\ {\rm K}$ (comparable to typical nebula temperatures $T_{\rm neb}$), accretion rate $\dot M=10^{-3}\ M_\oplus\ {\rm yr^{-1}}$, and initial entropy $S_i=9.5\ k_{\rm B}/m_p$. In these cases we find luminosities that are comparable to and even lower than the cold-start luminosities of \cite{Marley2007}, who found $2$--$3\times 10^{-6}\ L_\odot$ for $M=4$--$10\ M_J$ and $\approx 6\times 10^{-6}\ L_\odot$ for $M=2\ M_J$. However, increasing any of these parameters beyond these lowest values gives luminosities larger than \cite{Marley2007}. For example, $\dot M=10^{-2}\ M_\oplus\ {\rm yr^{-1}}$ (the limiting accretion rate assumed by \citealt{Marley2007}) gives $L_p\gtrsim 5\times 10^{-6}\ L_\odot$, even for $T_0=100\ {\rm K}$. Increasing $T_0$ beyond $300\ {\rm K}$ gives $L_p\gtrsim 5\times 10^{-6}\ L_\odot$ even for $\dot M=10^{-3}\ M_\oplus\ {\rm yr^{-1}}$. \update{Temperatures as low as $T_0\sim T_{\rm neb}$ are possible within the boundary prescription of \cite{Bodenheimer2000}, in the case where the flow remains optically thin throughout the growth of the planet. However, the situation in the literature regarding the outer boundary conditions for cold accretion is somewhat confused. The boundary conditions often used in energy approaches to cold accretion, namely that $L\approx 4\pi R^2 \sigma T_{\rm eff}^4$ and $P_0=(2/3)(g/\kappa)$ (e.g.~\citealt{Hartmann1997,Mordasini2013}, see \S~\ref{sec:previoushotcold}), where $T_{\rm eff}$ is the effective temperature, i.e. the usual boundary conditions for a cooling planet, give temperatures significantly larger than $T_{\rm neb}$. In our models these conditions do not lead to cold starts. The cooling time of the planet is generally longer than the accretion timescale (lower panel of Fig.~\ref{fig:LS}), so that this cooling boundary condition leads to only a small change in entropy during accretion (see the difference between the horizontal solid and dashed lines in Fig.~\ref{fig:center_v_surf}). Only by holding the boundary temperature to a low value are we able to drive a large enough luminosity to accelerate the cooling and reduce the internal entropy significantly on the accretion timescale.} \update{However, as discussed in \S \ref{sec:previoushotcold}, shock models developed in the context of star formation \citep{Stahler1980,Commercon2011} and planet accretion \citep{Marleau2016} suggest that the surface temperature is likely to be significantly larger than either of these prescriptions for cold starts. In these models, the gas at the surface of the planet is heated by some fraction of the accretion luminosity generated at the shock to a temperature $T_{\rm{hot}}$ given by $4\pi R^2\sigma T_{\rm{hot}}^4\sim L_{\rm accr} \approx GM\dot{M}/R$. In that case our results suggest that core accretion will result in hot starts, with high entropy $S_c\sim 12\ k_{\rm B}/m_p$ set by $S_{\rm{min}}$ (\S~ \ref{sec:hot boundary model}) and luminosity $L_p \gtrsim 10^{-4}\ L_\odot$. The planet grows by accumulating hot material on the outside of the original convective core. The entropy $S_{\rm min}$ depends on the accretion rate, but will be difficult to constrain from observed luminosities given the initial rapid cooling for hot starts.} \subsection{Comparison to Data} \update{The subsequent cooling of the planets is shown in Figure \ref{fig: cooling curves with data} and compared to measured luminosities of directly-imaged planets. We include those planetary-mass companions listed in Table~1 of \cite{Bowler2016} that are consistent with a hot-start mass $\lesssim 10\ M_J$ (the maximum mass in our models) with ages $\lesssim 10^8\ \rm{yr}$, as well as the protoplanet HD 100546 b which has a bolometric luminosity given by \cite{Quanz2015}. The four points numbered 5--8 refer to planetary companions orbiting at $< 100\ \rm{au}$, and so are perhaps most likely to have formed by core accretion. The cooling curves depend on both $S_i$ and $T_0$ (which set the post-formation entropy), and the planet mass, so that determining the formation conditions is difficult without an independent measurement of the planet mass (e.g.~\citealt{Marleau2014}). Even then, Figure \ref{fig: cooling curves with data} shows that, at the age of these planets ($\approx 20$--40~Myr), the variation in luminosity with shock temperature $T_0$ is less than a factor of a few and can be much smaller for low planet masses and hotter initial conditions. Younger planets (with ages $\sim 10^6$--$10^7\ \rm{yr}$) have a better memory of their post-formation state. However, of the other low-mass objects shown, 2M~0441~b and 2M~1207~b orbit brown dwarfs, and ROXs~42Bb and HD~106906 are both seen at wide separations (140 and 650~au respectively), so it is not clear whether they formed by core accretion.} \update{The remaining data point is HD 100546 b, which is thought to be a protoplanet that is currently undergoing accretion from the circumstellar disk. The evidence for core accretion, along with its younger age of $\sim 5 \times 10^6\ \rm{yr}$, puts it in the range of planets that will be the most useful in understanding the properties of planets produced by core accretion. Additionally, as previously mentioned in \S \ref{sec: Intro}, it appears that the intrinsic luminosity of the planet can be distinguished from the accretion luminosity, which is an important point to consider when discussing accreting objects. Figures \ref{fig: ram pressure cooling curves} and \ref{fig: cooling curves with data} show that a luminosity of $>10^{-4}\ L_\odot$ is obtained in our models only for hot outer boundaries $T_0\gtrsim 2000\ {\rm K}$ or higher entropies at the onset of runaway accretion $S_i\gtrsim 10\ k_B/m_p$.} \update{Of all the objects mentioned above,} the need to tune parameters to small values to achieve a cold start has the greatest implications for 51 Eri b, which, with a bolometric luminosity of $1.6$--$4\times 10^{-6}\ L_\odot$ \citep{Macintosh2015}, is perhaps the most likely observed candidate for a cold start. Figure \ref{fig: cooling curves with data} shows that the mass of 51 Eri b could be $10\ M_J$ if $T_0=100\ {\rm K}$, but even a small increase to $T_0=300\ {\rm K}$ requires a lower mass $M\lesssim 3\ M_J$. Therefore it seems likely that the mass of 51 Eri b is close to the hot-start mass, unless the shock temperature can be maintained close to $T_{\rm neb}$ throughout accretion. \subsection{Future Work} Our results were obtained holding $T_0$ and $\dot M$ constant during accretion, as the focus of this work was a parameter space study of the effect of particular boundary conditions on the formation of the planet. However, considering a more complex (and realistic) accretion history with time-dependent boundary conditions could result in a different dependence on final mass. For example, the hot-start models produced in our hot accretion regime have a final internal entropy that is relatively independent of planet mass. This differs from the hot-accretion models of \cite{Mordasini2013}, that show increasing entropy as the planet grows in mass, as in the standard hot-start branch of the tuning-fork diagram (e.g.~compare fig.~2 of \citealt{Mordasini2013} with fig.~2 of \citealt{Marley2007}). \update{Indeed, preliminary work in which we use a surface temperature that depends on the accretion luminosity (as in \citealt{Stahler1980}) shows agreement with traditional tuning fork diagrams for hot starts, i.e.\ an increasing entropy with final mass.} An additional point related to the consequences of a non-constant surface temperature concerns \S~\ref{sec:acc regimes}, where it was seen that for heating models an outer convective zone made up of the hotter accreted material forms above the initial, lower-entropy core. In the case of constant $T_0$, the planet immediately enters the heating regime, so that at the end of accretion the higher-entropy zone constitutes a large fraction of the mass (95\% in our 10-$M_J$ models). \update{ However, when $T_0$ is set to the time-dependent $T_{\rm hot}$, it increases with time, and with it the entropy of the accreted material. Therefore, the final internal structure of the planet is different from what is currently seen. This has bearings on the cooling of the object if, for example, an inner radiative region forms \citep{Leconte2012}, but the extent of this effect is presently unclear. A possibility is that thermally irregular internal structures lead to differences even between hot-start cooling curves, implying further uncertainties when estimating the masses of such planets.} One of the other goals of this work has been to develop MESA as a tool to study planet formation; we make our \texttt{inlist} and \texttt{run\_star\_extras} files available at \url{http://mesastar.org}. It would be interesting to explore further modelling of gas giant formation in MESA, and overcome some of the limitations of our models. This will require taking into account energy deposition by planetesimals (see review in \S~5.7 of \citealp{Mordasini2015}), modeling the contribution of dust grains to the envelope opacity (e.g.~\citealt{Ormel2014,Mordasini2014b}), including possible composition effects on convection (e.g.~\citealt{Nettelmann2015}), and extending to lower masses than considered here (see \citealt{Chen2016}). \subsection{Concluding remarks} We have focused on the runaway accretion phase of gas giant formation and its role in determining the luminosity of young gas giant planets. The results highlight the importance of understanding the physical factors that set the entropy of the planetary embryo while it is still attached to the nebula, and the temperature of the post-shock gas during runaway accretion. \update{This in particular calls for further investigation of the physics occurring directly at the accretion shock, as in \citet{Marleau2016}.} Depending on the shock temperature, the post-formation luminosity spans the full range from cold start to hot start models. This further emphasizes the point made by \cite{Mordasini2013} that large luminosities need not be associated exclusively with formation by gravitational collapse. Beyond the standard core-accretion models, accretion is possibly not spherically symmetric \citep{Lovelace2011,Szulagyi2016,Owen2016}, which also needs to be taken into account. \update{ We conclude with a few comments pertaining to observations. Obtaining spectroscopy of young forming objects could significantly help separate the contribution of the shock (also as traced by H\,$\alpha$ as for the LkCa~15 system; \citealp{Sallum2015}) from that of the photosphere. The latter is likely akin to a \mbox{(very-)}low-gravity L/M brown dwarf due to the protoplanet's large radius and surface temperature (see eq.~[\ref{eq:hotT}]). Also, determining the mass by radial velocity or astrometry, or deriving constraints on it from the morphology of the disk \citep{Bowler2016} would make it possible to break the degeneracy between hot and cold starts \citep{Marleau2014}. Finally, once mass information is available for a sufficient number of directly-imaged planets, it might be feasible to constrain statistically parameters such as the entropy at the beginning of accretion, for instance in the framework of population synthesis \citep{Mordasini2012}. Thus, exploiting direct-imaging observations by combining them to studies of all factors setting the post-formation thermal state will help constrain the formation mechanism of gas giants. } | 16 | 9 | 1609.09126 |
1609 | 1609.02923_arXiv.txt | \noindent In Paper I of this series, we showed that the ratio between stripped-envelope (SE) supernova (SN) and Type II SN rates reveals a significant SE SN deficiency in galaxies with stellar masses $\lesssim 10^{10}~{\rm M}_\sun$. Here, we test this result by splitting the volume-limited subsample of the Lick Observatory Supernova Search (LOSS) SN sample into low- and high-mass galaxies and comparing the relative rates of various SN types found in them. The LOSS volume-limited sample contains 180 SNe and SN impostors and is complete for SNe Ia out to 80 Mpc and core-collapse SNe out to 60 Mpc. All of these transients were recently reclassified by us in \citet{2016arXiv160902922S}. We find that the relative rates of some types of SNe differ between low- and high-mass galaxies: SNe Ib and Ic are underrepresented by a factor of $\sim3$ in low-mass galaxies. These galaxies also contain the only examples of SN 1987A-like SNe in the sample and host about $9$ times as many SN impostors. Normal SNe Ia seem to be $\sim 30$\% more common in low-mass galaxies, making these galaxies better sources for homogeneous SN Ia cosmology samples. The relative rates of SNe IIb are consistent in both low- and high-mass galaxies. The same is true for broad-line SNe~Ic, although our sample includes only two such objects. The results presented here are in tension with a similar analysis from the Palomar Transient Factory, especially as regards SNe IIb. | \label{sec:intro} This is the second paper in a series that reanalyzes the supernova (SN) sample assembled by the Lick Observatory Supernova Search (LOSS; \citealt{2000AIPC..522..103L,2001ASPC..246..121F,2003fthp.conf..171F,2005ASPC..332...33F}) in order to constrain SN progenitor models. In Paper I \citep{2016arXiv160902921G}, we remeasured the LOSS SN rates (first measured by \citealt{li2011rates}) and found that the ratio between the rates of stripped-envelope supernovae (SE~SNe; i.e., SNe~IIb, Ib, Ic, broad-lined Ic or Ic-BL, and peculiar examples of these subtypes; see \citealt{1997ARA&A..35..309F} for a review) and SNe II (i.e., SNe IIP, IIL, IIn, and peculiar examples of these subtypes) was smaller, by a factor of $\sim 3$, in galaxies with stellar masses $\lesssim 10^{10}~{\rm M}_\sun$ than in more massive galaxies. The SN rates in Paper I can be regarded as ``absolute'' rates---they measured how many SNe, of a given type, explode per unit time per unit mass. We measured these rates for three broad SN categories: SNe~Ia, SNe~II, and SE~SNe. In this paper, we use a subsample of the LOSS SN sample to measure the fractions of different SN subtypes within this sample. These fractions can be thought of as ``relative'' rates---they measure which fraction of all SNe that explode in nature are of a given subtype. If relative rates are measured from a SN sample that is complete within a given volume (i.e., ``volume-limited''), and the host galaxies of these SNe are representative of the galaxy luminosity function within that volume, the relative SN rates should correlate with the relative rates of their respective progenitor stars. Throughout this work, we use the terms ``relative rates'' and fractions interchangeably. Owing to the careful way in which the LOSS volume-limited subsample was constructed (see below), the relative rates we measure from it allow us to go a step further than in Paper I and study different subtypes of SNe (e.g., SNe~IIb, Ib, and Ic) in detail. The subsample of the full LOSS SN sample we used here was constructed by \citet[hereafter L11]{li2011LF} to measure SN luminosity functions and relative rates. This sample is complete to all core-collapse (CC) SNe out to 60 Mpc and SNe Ia out to 80 Mpc (and hence it is volume limited). We describe this sample in detail in Section~\ref{sec:galaxies}. Recently, \citet{2016arXiv160902922S} reclassified the SNe in this sample and found that SNe Ib, which L11 initially suggested were roughly half as common as SNe Ic, are actually $1.7 \pm 0.9$ times as common. \citet{2011MNRAS.412.1522S} used the L11 sample to argue that for a standard initial mass function (IMF), Wolf--Rayet stars could account for only half of the observed fractions of SE SNe. However, in that work, the authors took a conservative tack and treated the LOSS SN relative rates as monolithic, in the sense that the same rates applied to all types of galaxies. In Paper I we showed that galaxies with stellar masses lower than $\sim10^{10}~{\rm M}_\sun$ were less efficient at producing SE SNe than more massive galaxies. In Section~\ref{sec:vol_lim}, we split the LOSS volume-limited sample according to this mass criterion to test whether the same trend is evident in the relative SN rates. If so, we expect to see a lower fraction of SE SNe in galaxies with $M_\star \lesssim 10^{10}~{\rm M}_\sun$. In Paper I we calculated the rates of SNe Ia, SE SNe, and SNe II. Here, we further subdivide these SN types into various subtypes (e.g., SE SNe into SNe Ib, Ic, Ic-BL, IIb, etc.) and measure the relative rates of each subtype. We further compare the relative rates of each subtype in low- and high-mass galaxies, using different mass cuts. We find that SNe Ib and Ic are underrepresented in low-mass galaxies by a factor of $\sim 3$. On the other hand, the relative rates of SNe IIb are consistent between low-mass and high-mass galaxies. There are about $9$ times more SN impostors in low-mass galaxies than in high-mass galaxies (but this might be due to a selection effect). The low-mass galaxies also host the only SN 1987A-like SNe in the LOSS volume-limited sample. Importantly for cosmology, normal SNe Ia are more common in low-mass galaxies. These results are in tension with those of the Palomar Transient Factory (PTF; \citealt{2009PASP..121.1334R}), as presented by \citet{2010ApJ...721..777A} and \citet{2012IAUS..279...34A}. We discuss the differences between the LOSS and PTF results---and their SN and galaxy samples---in Section~\ref{subsec:vol_PTF}. Although \citet{smartt2009mnras} also measured SN relative rates, we do not compare the results shown here to theirs. First, their sample consisted of all SNe whose discovery was made public, through International Astronomical Union Circulars, between 1998 January 1 and 2008 June 30 out to 28 Mpc. As these SNe were discovered by different surveys, the completeness of this sample is unknown. Second, \citet{smartt2009mnras} did not split their sample according to either the mass (as done here) or the luminosity (as in \citealt{2010ApJ...721..777A}) of their SN host galaxies. For a discussion of the differences between the overall LOSS relative rates from L11 and the rates reported by \citet{smartt2009mnras}, see \citet{2011MNRAS.412.1522S}. Relative SN rates measured from a complete sample can also be compared to absolute SN rates from volumetric surveys of the local Universe (e.g., \citealt{li2011rates} and our Paper I). \citet{1997A&A...322..431C} combined SN samples from five different surveys and measured SN Ia, SE SN, and SN~II rates in galaxies of different morphological types. However, owing to the small number of SE SNe in their sample, it is hard to draw any conclusions regarding this family of SNe, and we do not compare our results to theirs. We summarize our results in Section~\ref{sec:discuss}. | \label{sec:discuss} This is the second of a series of papers that further explore the implications of the LOSS SN rates. Here, we examined the relative rates of different SN subtypes in the volume-limited LOSS sample. This sample, which contains 180 SNe and SN impostors, is complete for SNe Ia out to 80 Mpc and CC SNe out to 60 Mpc. Our analysis was based on a reclassification of the SNe in this sample \citep{2016arXiv160902922S}. Where L11 originally did not distinguish between galaxy types, we split the LOSS volume-limited sample into two galaxy samples, using different mass cuts, and compared the relative rates of different SN subtypes in low- and high-mass galaxies. This split was motivated by our finding in Paper I that the absolute rates of SE SNe, relative to SNe II, are lower in low-mass galaxies by a factor of $\sim3$. We have found the following trends (Figure~\ref{fig:pie}). \begin{enumerate} \item SNe Ib are underrepresented in low-mass galaxies by a factor of 3--6. Taken together, SNe Ib and Ic are underrepresented in low-mass galaxies by a factor of $\sim 3$. Both results are statistically significant, given our significance threshold of 5\%. \item On the other hand, the relative rates of SNe IIb are consistent with each other in both low- and high-mass galaxies. \item SN 1987A-like SNe prefer low-mass galaxies. \item SN impostors, many of which could signify the death throes of CC SN progenitors, are overrepresented in low-mass galaxies by a factor of $\sim 9$. This could be due to selection effects, however, as the SN impostors in the LOSS volume-limited sample have not been corrected for completeness, and these objects tend to have lower peak luminosities than SNe. \item Normal SNe Ia are overrepresented in low-mass galaxies by a factor of $\sim 1.3$. \item As expected, subluminous SN 1991bg-like SNe~Ia are only found in high-mass galaxies, but intriguingly, they cut into the share of the normal SNe Ia. \end{enumerate} We find that the first trend is the most robust to the choice of mass cut, followed by trends 3, 5, and 6. Although not formally statistically significant, trend 2 is qualitatively present regardless of which mass cut is used. The underrepresentation of SNe Ib and Ic in low-mass galaxies strengthens our finding in Paper I that the SE SN rates, relative to the SN II rates, are lower in low-mass galaxies than in high-mass galaxies. In the latter type of galaxy, we find the same fraction of SNe Ib and Ic, combined, as \citet{2011MNRAS.412.1522S} did. This strengthens their point that single stars, on their own, cannot account for the observed fractions of SE SNe, at least in high-mass galaxies. This is true if one were to assume that all galaxies have the same IMF. Recent studies, however, have reported that galaxies with higher star-formation rates show more top-heavy IMFs (e.g., \citealt{2011MNRAS.415.1647G,2013ApJ...771...29G,2013MNRAS.436.3309W,2014MNRAS.442.1003P}). We leave it to a future paper to explore whether the larger fraction of massive stars produced by such IMFs could account for the higher fraction of SNe Ib and Ic we observe in high-mass (and hence highly star-forming) galaxies. It is interesting that the relative rates of SNe IIb are consistent between low- and high-mass galaxies. This adds another reason why the exclusion of this type of SN from the SE SN rates in Paper I should not bias our findings in that paper. It also raises the question whether SNe IIb come from different progenitors than other SE SNe. If, instead, SNe IIb, Ib, and Ic all come from the same type of progenitor stellar system, it remains to be seen what property (or combination of properties, such as metallicity, IMF, or binarity fraction) of galaxies at $M_\star \lesssim 10^{10}~{\rm M}_\sun$ could hinder the production of SNe Ib and Ic, but not of SNe IIb. Our result is in tension with binary evolution models, which predict that the SN~IIb rate should indeed be higher in low-mass low-metallicity galaxies---as claimed by the PTF---since line-driven winds should be less efficient at removing the residual H envelope of the low-metallicity SN~IIb progenitor \citep{2011A&A...528A.131C,2014ARA&A..52..487S}. A larger sample of SE~SNe in low-mass galaxies is required to test whether at a lower mass cut the fractions of SNe~IIb will remain the same, will begin to exhibit the type of deficiency we have shown here for SNe~Ib and Ic, or become overabundant, as claimed by the PTF. The overrepresentation of normal SNe~Ia in low-mass galaxies strengthens the conclusion of \citet{2015MNRAS.450..905G} that in order to construct homogeneous SN Ia samples for cosmology, it would be best to select them from low-mass (or low-luminosity) galaxies, and not just from star-forming galaxies, as suggested by \citet{2014MNRAS.445.1898C}. The results of this work differ from those of \citet{2010ApJ...721..777A} and \citet{2012IAUS..279...34A}, especially in regard to SNe~IIb. Our samples differ as well, as LOSS is a targeted survey, while PTF is untargeted. We argue here that the LOSS volume-limited sample, with its known sensitivity and completion caveats, is better suited for studying relative rates than the preliminary PTF sample used by \citet{2010ApJ...721..777A}. Still, as the samples from both studies suffer from small-number statistics, we look forward to our results being tested by ongoing and future untargeted surveys. | 16 | 9 | 1609.02923 |
1609 | 1609.05674_arXiv.txt | {15 years of \xmm\ observations have established that ultra-fast, highly ionized winds (UFOs) are common in radio-quiet AGN. A simple theory of Eddington-limited accretion correctly predicts the typical velocity ($\sim$0.1$c$) and high ionization of such winds, with observed flow energy capable of ejecting star-forming gas. An extended \xmm\ observation of the archetypal UFO, \pg\, recently found a more complex flow pattern, suggesting that intensive \xmm\ observations offer exciting potential for probing the inner accretion disc structure and SMBH growth.} | X-ray spectra from an \xmm\ observation of the luminous Seyfert galaxy \pg\ in 2001 provided the first detection of strongly blue-shifted absorption lines of highly ionized gas in a non-BAL Active Galactic Nucleus (AGN), corresponding to a sub-relativistic outflow velocity of $\sim$0.1$c$ (Pounds \et\ 2003), later adjusted to 0.15$\pm$0.01$c$ with the identification of additional absorption lines and broad-band spectral modelling (Pounds \& Page 2006). Further observations of \pg\ over several years with \xmm, \chandra\ and \suzaku\ found the high velocity outflow to be persistent but of variable strength (Reeves \et\ 2008). Evidence that the outflow in \pg\ was both massive and energetic - with potential importance for galaxy feedback (King 2003, 2005) - came from the detection of a P-Cygni line profile and other broad emission features by combining the 2001, 2004 and 2007 \xmm\ EPIC spectra (Pounds \& Reeves 2009). Examination of archival data from \xmm\ and \suzaku\ has since shown ultra-fast, highly-ionized outflows (UFOs) to be common in nearby, luminous AGN (Tombesi \et\ 2010, 2011; Gofford \et\ 2013). The frequency of these detections suggest a wide angle outflow, with mass rate and kinetic energy in a persistent wind capable of curtailing star formation and black hole growth (Pounds 2014), and providing the link between black hole and stellar bulge masses implied by the observed $M-\sigma$ relationship (Gebhardt \et\ 2000; Ferrarese \& Merritt 2000). An extended \xmm\ observation of \pg\ in 2014 has now provided uniquely high quality X-ray spectra of \pg, revealing previously unseen velocity structure in the $\sim$6--10\,keV energy band. Spectral modelling of data from the high-energy pn camera (Strueder \et 2001) identified the observed absorption lines with resonance and higher order transitions of highly-ionized Fe, consistent with two distinct outflow velocities $v \sim 0.066c$ and $v \sim 0.13c$ (Pounds \et\ 2016a: hereafter P16). In that first report of a dual velocity, primary (high column) wind it was suggested that the simultaneous observation of two `Eddington Winds' (King \& Pounds 2015) might be evidence of `chaotic accretion', where a clump of matter approaching the black hole divides to form prograde and retrograde accreting flows, with a corresponding difference in accretion efficiency and potential wind velocity. Marginal evidence in P16 for a third velocity component component ($v \sim 0.19c$) has since been supported in an analysis of the higher resolution soft X-ray spectra from the Reflection Grating Spectrometer (RGS; den Herder \et\ 2001) during the same 2014 \xmm\ observation (Pounds \et\ 2016b). Here we discuss that further challenge to the simple Eddington Wind model and suggest that future well-sampled observations of a powerful UFO, as observed in \pg, have exciting potential to study the accretion physics determining how the super-massive black hole (SMBH) continues to grow in the interval between mergers. | The extended \xmm\ observation of \pg\ in 2014 provided uniquely high quality hard X-ray spectra of this archetypal UFO, revealing previously unseen structure in the $\sim$6--10\,keV energy band. Spectral modelling has identified the observed absorption structure with line series of H- and He-like Fe, consistent with three distinct outflow velocities. The analysis is a strong demonstration of the power of modelling UFOs with grids of pre-computed absorption spectra, which take proper account of all absorption line and continua effects. Given the success of the Black Hole Winds model (King \& Pounds 2003) in predicting the group properties of UFOs, we consider the more complex velocity structure in the same context. The properties of such `Eddington winds' are described in greater detail in King \& Pounds (2015), which includes a discussion on the observability of UFOs as they evolve from being optically thick at launch to transparency after radial expansion. For winds launched in the inner accretion disc the visibility timescale for high velocity winds can be on order months or less. That view is supported by a review of the recent archival searches (Tombesi \et\ 2011; Gofford \et\ 2013), leading King \& Pounds (2015) to suggest that currently observed AGN winds are more likely to be composed of sporadic, quasi-spherical shells, than a continuous outflow, with only the most recently launched shells remaining visible. Considering the new 2014 observation of \pg\ in that context, in P16 we suggested the $v \sim$0.066$c$ and $v \sim$0.13$c$ outflows represent recently launched shells, corresponding to local super-Eddington episodes from prograde and retrograde accretion, with the higher efficiency of the former (due to the inflow remaining stable to a smaller radius) yielding the higher wind velocity (ref. equation 3). The simultaneous detection of 3 primary wind velocities now suggests a still more complex picture, and in Section 4 we note that multiple `accretion dumps' at different regions in the inner disc, leading to corresponding wind launches, might arise from disc warping (and breaking) due to the Lense-Thirring effect (Nixon \et\ 2012). Monitoring the resulting pattern of disc winds over the next decade of \xmm\ observations offers the exciting prospect of constraining detailed models of accretion and black hole growth. While the robustness of the dual velocity absorption model described in P16, implying line resolution comparable with the intrinsic energy resolution of the pn camera, was an indication of what can be achieved with data of high statistical quality and from a well calibrated and stable detector, higher resolution data remain vital for observation and interpretation of more complex outflows. Combination of the EPIC and RGS instruments will remain important in \xmm\ observations of AGN outflows in the years ahead. With the unfortunate loss of the \hitomi\ spacecraft, that approach is likely to remain the best opportunity to explore accretion physics and black hole growth by intensive mapping of powerful AGN available prior to the launch of \athena. | 16 | 9 | 1609.05674 |
1609 | 1609.00098_arXiv.txt | We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers. The robustness of the discontinuous Galerkin method allows for the use of high-resolution shock capturing methods in regions where (relativistic) shocks are found, while exploiting high-order accuracy in smooth regions. A task-based parallelism model allows efficient use of the largest supercomputers for problems with a heterogeneous workload over disparate spatial and temporal scales. We argue that the locality and algorithmic structure of discontinuous Galerkin methods will exhibit good scalability within a task-based parallelism framework. We demonstrate the code on a wide variety of challenging benchmark problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the code's scalability including its strong scaling on the NCSA Blue Waters supercomputer up to the machine's full capacity of $22,380$ nodes using $671,400$ threads. | Numerical simulation of astrophysical phenomena is a computationally challenging task. The relevant equations are often coupled nonlinear partial differential equations (PDEs) with complicated microphysics. High fidelity simulations necessarily require extremely large computational grids in all three spatial dimensions on which non-uniform workloads must be efficiently parallelized. A simulation may involve large spatial and temporal dynamic ranges, and develop (magneto-)hydrodynamic shocks and turbulent flows. Accurate numerical simulations of astrophysical systems such as neutron star mergers~\cite{eichler:89,1992ApJ...395L..83N,moch:93} and core-collapse supernovae~\cite{janka:12review,burrows:13a,ott:16} are crucial for achieving the full scientific potential of current and future experiments such as the Fermi Gamma-Ray Space Telescope~\cite{fermiweb} and the Laser Interferometer Gravitational-Wave Observatory~\cite{ligo}. Yet for many of these systems the computational errors are often too large (or not even quantifiable) with current algorithmic and hardware limitations. The simulations also take too long, several weeks to many months of wall time on present supercomputers, precluding explorations of the theoretical parameter space. Within the astrophysics communities employing grid-based methods, the industry standard has been finite-volume or finite-difference methods parallelized by distributing cells across processors and communicating data with message passing interface (MPI). The evolution is synchronized according to a global simulation time. A variety of astrophysics codes (e.g., Refs.~\cite{Fryxell:2000zz,bryan2014enzo,ott:16,mignone2011pluto,almgren2010castro,Loffler:2011ay,SpECwebsite}) have been designed based on these fundamental building blocks. These strategies work well when the computations are reasonably homogeneous or when one seeks good parallelization to only a few thousand cores. As the number of MPI processes increases, so does the cost of communication which, together with non-uniform workload typical of astrophysics problems, limits the maximum number of useful cores that codes can run on. Efficient core utilization becomes non-trivial, often requiring careful optimization by hand to achieve good scalability~\cite{woodward2013scaling}. Standard finite-volume and finite-difference methods achieve higher order accuracy with increasingly large (overlapping) stencil sizes, and may require additional effort to achieve scalability on massively parallel machines. As one looks ahead to the arrival of exascale computing, it will become increasingly important to focus on developing algorithms that can take full advantage of these very large machines. Discontinuous Galerkin (DG) methods~\cite{Reed.W;Hill.T1973,Hesthaven2008,Cock01,cockburn1998runge,Cockburn.B1998,Cockburn.B;Karniadakis.G;Shu.C2000}, together with a task-based parallelization strategy, have the potential to tackle many of these problems. DG methods offer high-order accuracy in smooth regions (although, for stability, increasing the scheme's order requires decreasing the timestep, which restricts the largest usable order in practice), robustness for shocks and other discontinuities, and grid flexibility including a formulation that allows for comparatively straightforward $hp$-adaptivity and local timestepping. DG methods can be combined with positivity preserving strategies~\cite{zhang2010positivity,balsara2016subluminal,balsara2012self} or ``atmosphere treatments"~\cite{Muhlberger2014} which seek to maintain non-negative values of the pressure and density in challenging regions such as those containing high-speed astrophysical flow. DG methods are also well suited for parallelization: Their formulation in terms of local, non-overlapping elements requires only nearest-neighbor communication regardless of the scheme's order of convergence. Despite extensive success in engineering and applied mathematics communities over the past two decades, applications in relativity~\cite{Field:2010mn,brown2012numerical,field2009discontinuous,zumbusch2009} and astrophysics~\cite{Radice:2011qr,mocz:14,zanotti:14,endeve:15} have typically been exploratory or confined to simple problems. Within the past year, however, there have been significant advances toward production codes for non-relativistic~\cite{schaal2015astrophysical} and relativistic~\cite{teukolsky2015,Bugner:2015gqa} hydrodynamics, special relativistic magnetohydrodynamics~\cite{zanotti2015}, and the Einstein equations~\cite{Miller:2016vik}. These codes use MPI to implement a data parallelism strategy. In this paper, we describe SpECTRE, a general purpose discontinuous Galerkin solver for relativistic astrophysics. A distinguishing feature of SpECTRE is its task-based parallelism model. Instead of dividing work between parallel processes based on cell ownership, the algorithm is decomposed into a list of tasks and their inter-dependencies. Examples of tasks include, for example, computing a derivative in an element, computing a numerical flux on a boundary or taking a time step. Tasks are assigned to processes/threads dynamically during the computation, in such a way as to satisfy dependencies and to minimize the number of idle cores. When a core becomes idle, it is given another task to complete. This framework is very different from the more traditional synchronous, data parallelism model used in other grid-based astrophysics codes. The algorithm's scalability is achieved through (i) separation of the tasks of communication and computation, so that they can be overlapped, (ii) asynchronous, non-blocking communication so that cores are not idle, and (iii) a runtime system to manage task queues, distribute tasks to cores, and gather timing statistics to inform load-balancing decisions. The power of task-based parallelism has already shown impressive performance in other application domains, for example Refs.~\cite{2016arXiv160602738S,phillips2005scalable,OpenAtomWebsite,jetley2008massively,uintah,berzins2010uintah,martyna2012openatom}. SpECTRE uses the Charm++ library~\cite{CharmWebsite,kale1993charm++,shu1991chare,kale2016parallel} to implement this parallelism model. This paper is organized as follows. The hydrodynamic systems currently solved by SpECTRE are summarized in \S\ref{sec:laws}, and include the non-relativistic Euler equation and the relativistic (magneto-)hydrodynamics systems in arbitrary gravitational fields. Next, in \S\ref{sec:galerkin} we describe a nodal DG scheme and those approximate Riemann solvers and high-resolution shock capturing limiters that we implement within SpECTRE. DG schemes naturally map into a task-based parallelism framework, and in \S\ref{sec:tasks} we describe how the algorithm can be broken down into tasks and subsequently parallelized using Charm++. Next, we present a sampling of results for standard performance (see \S\ref{sec:performance}) and benchmark (see \S\ref{sec:tests}) tests. Our scalability experiments demonstrate the power of a task-based approach. A key result is Fig.~\ref{fig:StrongScaling-BWs}, which shows excellent strong scalability on the Blue Waters machine up to its full capacity of $22,380$ nodes using $671,400$ threads. | We have described a new relativistic astrophysics code SpECTRE. The code differs from other codes in many important respects. In particular, we use a discontinuous Galerkin numerical solver and a task-based parallelism model. To the best of our knowledge, this is the first DG solver parallelized using a task-based model and the first DG treatment of the general relativistic MHD system. As DG methods are comparatively new to astrophysics (see Refs.~\cite{zanotti2015,Bugner:2015gqa,schaal2015astrophysical} for recent work), we have provided a detailed description of our numerical scheme including those approximate Riemann solvers and high-resolution shock capturing limiters we have implemented. Our main results are the performance and benchmark tests given in \S\ref{sec:performance} and \S\ref{sec:tests}. In particular, we have shown that the code can solve a wide variety of challenging astrophysics benchmark tests, including highly-relativistic shocks with blast waves (see \S\ref{sec:RP_RE1d}), shock-shock interactions (see \S\ref{sec:OTVortex}), and the steady-state GRMHD solution of Michel (see \S\ref{sec:Bondi}). For smooth solutions, we have shown the expected exponential convergence with increasing grid resolution, for example in the case of smooth relativistic flow, \S\ref{sec:RESmooth}. In \S\ref{sec:TimeProfile} we demonstrate how asynchronous, non-blocking communication promotes efficient resource usage by reducing the amount of idle core time. The scalability experiments of \S\ref{sec:strongscaling} demonstrate the code's performance on large machines. We observe excellent strong scaling on Blue Waters up to the machine's full capacity of $22,380$ nodes using $671,400$ worker cores/threads. Because of the generality and robustness of the DG method, it can serve as the core kernel for the solution of multi-physics problems that require an ensemble of interacting physical descriptions. Work toward this is underway. To evolve dynamical spacetimes we are implementing the Einstein equations using a generalized harmonic formulation~\cite{Pretorius2005c,Gundlach2005} written with first-order time and first-order space derivatives~\cite{Lindblom:2007}. We consider the fully first-order generalized harmonic system because it has been successfully evolved with pseudospectral methods for a variety of astrophysical configurations~\cite{Haas:2016,SpECwebsite}. To tackle challenging multi-scale problems, we are adding local time stepping techniques and mesh refinement strategies to either split the elements into smaller elements ($h$-adaptivity) or increase the number of basis functions in an element ($p$-adaptivity). The locality of the DG scheme facilitates adaptive resolution refinement and local timestepping, and good results have been shown in other contexts. And while current large codes often struggle to achieve good performance with local time-stepping~\cite{dubey14}, task-based parallelism and asynchronous communication are promising tools to overcome this problem. Looking forward, we believe that the benefits of task-based parallelism will become increasingly important in these more complicated contexts. More generally, accurate numerical methods and efficient usage of massively parallel supercomputers will be essential for the high-fidelity simulations needed to realize the promise of current and future experiments. | 16 | 9 | 1609.00098 |
1609 | 1609.06488_arXiv.txt | We present the results of a cluster search in the \emph{Fermi}-LAT Pass 8 $\gamma$-ray sky by means of the Minimum Spanning Tree algorithm, at energies higher than 10 GeV and at Galactic latitudes higher than 25\degr. The selected clusters have a minimum number of photons higher than or equal to 5, a high degree of concentration, and are without a clear corresponding counterpart in blazar catalogues. A sample of 30 possible $\gamma$-ray sources was obtained. These objects were verified by applying the standard Maximum Likelihood analysis on the \emph{Fermi}-LAT data. A search for possible radio counterparts in a circle having a radius of 6\arcmin\ was performed, finding several interesting objects, the majority of them without optical spectroscopical data. These can be considered as new blazar candidates. Some of them were already noticed as possible blazars or Active Galactic Nuclei in previous surveys, but never associated with high energy emission. These possible counterparts are reported and their properties are discussed. | \label{s:introduction} The \emph{Fermi}-Large Area Telescope (LAT) sky survey at $\gamma$-ray energies has shown that blazars constitute the largest class of extragalactic high energy sources \citep[see, e.g., the review paper by][]{massaro16}. For this reason, since a few years the searches for new blazars based on multifrequency approaches have been very successful, providing new samples of blazars and candidates as, for example, WIBRaLS \citep{dabrusco14} and 1WHSP \citep{arsioli15}. \citet[Paper I]{paperI} applied successfully the Minimum Spanning Tree (hereafter MST) algorithm for searching new spatial clusters of $\gamma$ rays which could be an indication for localized faint high energy sources. In particular, it was illustrated how MST is useful for finding clusters having a small number of photons, but likely related to pointlike sources. In two other previous papers \citep[][hereafter Paper II and III]{paperII,paperIII} we reported samples of blazars and blazar candidates associated with photon clusters found by means of the MST algorithm. These sources were included in the 5th Edition of the Roma-BZCAT \citep{massaro14} and in the 1WHSP sample. In this paper we extend our MST analysis of the \emph{Fermi}-LAT $\gamma$-ray sky at energies higher than 10 GeV, reporting the discovery of 30 new photon clusters not associated with known blazars but having interesting radio counterparts with blazar-like characteristics at angular distances lower than a few arcminutes. Some of them where already reported in recent samples of quasar candidates. Optical spectra are available from the Sloan Digital Sky Survey \citep[SDSS,][]{alam15} for four objects and only one from the 6dF survey \citep{jones04,jones09}, therefore for a better classification we considered the mid-infrared photometric colours from the WISE \citep[Wide-field Infrared Survey Explorer,][]{wright10} database according the criteria introduced by \cite{massaro11} and for the WIBRaLS sample \cite{dabrusco12}. As in the previous papers, in this search we considered the Fermi-LAT Pass 8 sky for Galactic latitudes higher than $|25\degr|$. | We analysed the first 7 years of \emph{Fermi}-LAT sky at energies higher than 10 GeV by means of the MST algorithm, allowing a robust detection of photon clusters having typical sizes comparable with the instrumental point spread function. In the selection procedure we adopted rather severe threshold values to reduce the possibility of spurious detections due to local background fluctuations. In the present paper we report 30 new clusters, 26 of them were fully confirmed by the ML analysis that gave $\sqrt{TS}$ higher than 5; for two clusters we obtained values higher than 4.5, while the remaining two have too low $TS$ to be considered as confirmed. These clusters were also associated with blazar candidates selected on the basis of radio and optical detections. For few of them 6dF and SDSS spectra are available, while some sources appear to be low redshift radio galaxies. The nature of the other sources must be confirmed by new spectroscopic observations. The blazar nature of our candidates is also supported by their WISE two-colour plot, in which all selected sources are in the blazar region, with a clear dominance for that of BL Lacs. It appears quite unlikely that radio sources, with likely counterparts in the high energy $\gamma$-rays, exhibit mid-IR colours typical of BL Lacs and do not belong to this class of AGNs. These researches extend the knowledge on the BL Lac population in two directions: one is towards low brightness sources and the other is concerning the existence of a subclass of BL Lacs too faint in radio band to be detected in the available surveys. We think that a systematic search for some possible counterparts of $\gamma$-ray clusters with $M$ values lower than the threshold considered here and based on a multifrequency approach, particularly in the mid IR band, could be useful to enrich these studies with new observational results. Considering the results of Papers I, II, and III, together with those of the present work, to now we have found evidence for 90 blazar or candidate selected for their emission above 10 GeV detected by means of MST cluster search. We remark, however, that these discoveries are due not only to our clustering method but mainly to the improvement of instrumental response functions used for producing the Pass 8 sky and to about double exposure duration with respect to that considered at the epoch of 3FGL catalogue. | 16 | 9 | 1609.06488 |
1609 | 1609.04444_arXiv.txt | SPIRITS---SPitzer InfraRed Intensive Transients Survey---is an ongoing survey of nearby galaxies searching for infrared (IR) transients with \textit{Spitzer}/IRAC. We present the discovery and follow-up observations of one of our most luminous ($M_{[4.5]} = -17.1\pm0.4$~mag, Vega) and red ($[3.6] - [4.5] = 3.0 \pm 0.2$~mag) transients, SPIRITS\,15c. The transient was detected in a dusty spiral arm of IC~2163 ($D\approx35.5$~Mpc). Pre-discovery ground-based imaging revealed an associated, shorter-duration transient in the optical and near-IR (NIR). NIR spectroscopy showed a broad ($\approx 8400$~km~s$^{-1}$), double-peaked emission line of He~\textsc{i} at $1.083~\mu$m, indicating an explosive origin. The NIR spectrum of SPIRITS\,15c is similar to that of the Type IIb SN~2011dh at a phase of $\approx 200$~days. Assuming $A_V = 2.2$~mag of extinction in SPIRITS\,15c provides a good match between their optical light curves. The IR light curves and the extreme $[3.6]-[4.5]$ color cannot be explained using only a standard extinction law. Another luminous ($M_{4.5} = -16.1\pm0.4$~mag) event, SPIRITS\,14buu, was serendipitously discovered in the same galaxy. The source displays an optical plateau lasting $\gtrsim 80$~days, and we suggest a scenario similar to the low-luminosity Type~IIP SN~2005cs obscured by $A_V \approx 1.5$~mag. Other classes of IR-luminous transients can likely be ruled out in both cases. If both events are indeed SNe, this may suggest $\gtrsim 18\%$ of nearby core-collapse SNe are missed by currently operating optical surveys. | \label{sec:intro} In the last few decades, the study of astrophysical transients has been revolutionized by the introduction of all-sky, high cadence surveys dedicated to their discovery. The largest advances have been made in the optical where the majority of time-domain surveys operate, but the dynamic infrared (IR) sky is only now beginning to be explored. IR follow-up of optically discovered transients has revealed new classes of events that can be dominated by IR emission, especially at late times. At least two known classes of transients with peak luminosities between those typical of novae and SNe can develop IR-dominated spectral energy distributions (SEDs) as they evolve: \begin{inparaenum}[1)] \item stellar mergers, or luminous red novae, e.g., V1309 Sco \citep{tylenda11}, V838 Mon \citep{bond03, sparks08}, the 2011 transient in NGC~4490 (hereafter NGC~4490-OT, \citealp{smith16}), and M101~OT2015-1 (M101-OT, \citealp{blagorodnova16}), \item SN~2008S-like events, or intermediate luminosity red transients \citep{prieto08, thompson09, kochanek11}, also including NGC~300~OT2008-1 (hereafter NGC~300-OT, \citealp{bond09, humphreys11}), and PTF\,10fqs \citep{kasliwal11}. \end{inparaenum} Furthermore, otherwise luminous optical sources such as SNe may suffer extinction from obscuring dust, lending themselves to discovery and follow-up at IR wavebands where the effect of dust extinction is significantly reduced. Previous searches for obscured SNe have thus been motivated by the notion that if a significant fraction of SNe are heavily obscured, measurements of the SN rate from optical searches will only be lower limits \citep[e.g.][]{grossan99, maiolino02, cresci07}. Searches at near-IR (NIR) wavelengths have focussed on the dense, highly star-forming, nuclear regions of luminous infrared galaxies (LIRGS) and ultra-luminous infrared galaxies (ULIRGs) \citep[e.g.][]{vanburen94,grossan99,maiolino02,mannucci03,mattila05a,mattila05b,fox15}. These searches have had variable success, largely limited by insufficient angular resolution to probe the densest regions of starburst galaxies. High angular resolution studies using space-based telescopes or adaptive optics have found several candidates and 4 confirmed obscured SNe \citep{cresci07,mattila07,kankare08,kankare12}. Radio observations have also allowed the discovery of a few obscured SNe (SNe~II) in dense star-forming regions, e.g., an SN in the starburst galaxy Mrk~297 \citep{yin91}, and SN~2008iz in M82 ($A_V > 10$~mag; \citealp{brunthaler09, brunthaler10, mattila13}). The SN rate estimates from such searches are still a factor of 3--10 lower than is expected from the high star formation rates inferred from the far-IR luminosities of the surveyed galaxies \citep[e.g.][]{cresci07}. It has also been suggested that even in ``normal'' star-forming galaxies in the nearby universe, where extinction is much less extreme, the measured rates of core-collapse SNe (CCSNe) are still low compared to those expected from star formation rates \citep{horiuchi11}. This indicates that optical surveys may be missing populations of nearby SNe that are either intrinsically faint or hidden by dust. Moderate levels of visual extinction ($A_V \sim \mathrm{few}$~mag) in the less extreme star-forming environments of such galaxies are sufficient to dim some SNe beyond the detection limits of current optical surveys, further motivating IR transient searches of such hosts. Since December 2013, we have been conducting a systematic search for transients in the infrared (IR) with the SPitzer InfraRed Intensive Transients Survey (SPIRITS; PID11063; PI M. Kasliwal). This is an ongoing, 3-year targeted survey of 194 galaxies within 20~Mpc using the InfraRed Array Camera (IRAC; \citealp{fazio04}) aboard the \textit{Spitzer Space Telescope} (\textit{Spitzer}; \citealp{werner04,gehrz07}) at $3.6$ and $4.5~\mu$m ([3.6] and [4.5], respectively). Every galaxy in our sample has archival \textit{Spitzer}/IRAC imaging, such that our observing cadence covers time baselines from one week to several years. In our first year, SPIRITS discovered over 1958 infrared variable stars, and 43 transients. Four of these transients were in the luminosity range consistant with classical novae, and 21 were known SNe (for details see \citealp{johansson14}, \citealp{fox16}, and \citealp{tinyanont16}). 14 were in the IR luminosity gap between novae and supernovae and had no optical counterparts, possibly constituting a newly discovered class of IR-dominated transients (Kasliwal et al. 2016, submitted to ApJ). Here we report the discovery of two transients discovered in dusty spiral arms of the galaxy IC~2163, SPIRITS\,15c and SPIRITS\,14buu. The IR luminosity of SPIRITS\,15c was brighter than $-17$~mag, one of the most luminous transients discovered by SPIRITS to date and more luminous than the new classes of IR-dominated transients discussed above. Additionally, the spectrum of SPIRITS\,15c is dominated by a broad emission line of He~\textsc{i}, suggesting this is an explosive event such as an SN, but with significant dust extinction that obscured the transient in the optical. In \S~\ref{sec:discovery}, we describe the discovery and optical/IR follow up observations of SPIRITS\,15c, and the subsequent post-outburst, serendipitous discovery of SPIRITS\,14buu. In \S~\ref{sec:analysis}, we describe the analysis of our photometric and spectroscopic data. In \S~\ref{sec:discussion}, we explore the possibility that SPIRITS\,15c is an obscured SN based on the similarity of its NIR spectrum to that of the well studied Type IIb SN~2011dh. Using a similar analysis we consider that SPIRITS\,14buu is yet another obscured SN, likely of Type IIP. We also consider non-supernova IR transient scenarios in \S~\ref{sec:non-SN}, including stellar mergers, SN~2008S-like events, and the proposed helium nova V445 Pup. Finally, in \S~\ref{sec:conclusions}, we summarize the observational characteristics of SPIRITS\,15c and SPIRITS\,14buu and present our conclusions. | \label{sec:conclusions} SPIRITS\,15c is a luminous ($M_{[4.5]} = -17.1 \pm 0.4$), red ($[3.6] - [4.5] = 3.0 \pm 0.2$~mag), IR-dominated transient discovered by the SPIRITS team. The transient was accompanied by an optical precursor outburst with $M_i = -15.1 \pm 0.4$~mag that was quickly overtaken by IR emission within $\approx 100$~days. The most prominent feature of the NIR spectrum is a broad ($\approx 8000$~km~s$^{-1}$), double-peaked emission line at $1.083~\mu$m, likely due to He~\textsc{i}, and possibly indicating a He-rich, bi-polar or toroidal outflow associated with the transient. We explored several possible scenarios to explain the unusual observed properties of SPIRITS\,15c. Both the stellar merger and SN~2008S-like scenarios can likely be ruled out by the high luminosity of SPIRITS\,15c and the explosive velocities and lack of hydrogen in its spectrum. In the case of a helium nova, the strong He~\textsc{i} emission and high-velocity, bipolar outflow of SPIRITS\,15c is similar to that observed in the candidate prototype helium nova V445 Pup, but again, the optical luminosity of SPIRITS\,15c is too extreme. We conclude that SPIRITS\,15c is a stripped envelope, CCSN explosion similar to the well studied Type~IIb SN~2011dh, but extinguished by dust in the optical and NIR at a level of $A_V \approx 2.2$~mag. The spectrum of SPIRITS\,15c is very similar to that of SN~2011dh at a phase of $\approx 200$~days, but SPIRITS\,15c shows a distinct double-peaked profile in the broad, strong He~\textsc{i} emission line that is not observed in SN~2011dh. The assumption of $A_V = 2.2$~mag with a standard $R_V = 3.1$ extinction law in SPIRITS\,15c provides a good match between the optical light curves and observed colors of SPIRITS\,15c and those of SN~2011dh. In the IR, however, SPIRITS\,15c is more luminous than SN~2011dh, except at [3.6] where it is significantly under-luminous, illustrated by its extreme $[3.6]-[4.5]$ color. Thus, we find that a shift in phase or simply a steeper extinction law cannot explain the observed differences between SPIRITS\,15c and SN~2011dh. SPIRITS\,14buu, an earlier transient in IC\,2163, was serendipitously discovered in the SPIRITS data during the analysis of SPIRITS\,15c. The source was also luminous in the IR at $M_{[4.5]} = -16.1 \pm 0.4$~mag, and developed a fairly red $[3.6] - [4.5]$ color of $1.2 \pm 0.2$~mag by 166~days after its first detection. The optical and NIR light curves showed plateau lasting at least 80 days, similar to that observed in SNe~IIP. Scenarios involving a stellar merger or SN~2008S-like transient can again likely be ruled out. A comparison to the low-luminosity Type IIP SN~2005cs assuming $\approx 1.5$~magnitudes of visual extinction produced a reasonable match to the properties of SPIRITS\,14buu, and we find an obscured SN~IIP to be the most likely interpretation for SPIRITS\,14buu considered here. The key to fully understanding the nature of these events is MIR spectroscopy, the likes of which will become available with the launch of the James Webb Space Telescope (JWST). A MIR spectrum would, for example, enable us to elucidate the origin of the extreme $[3.6]-[4.5]$ color observed in SPIRITS\,15c, and identify spectral features contributing to the flux at these wavelengths, e.g., the fundamental vibrational overtones of CO that may contribute to the high luminosity at [4.5]. Moreover, photometric coverage further into the MIR with JWST would allow us to detect the presence of a cooler dust component than is accessible with the warm \textit{Spitzer}/IRAC bands. The census of SNe in nearby galaxies from optical searches, even at only 35~Mpc, is incomplete. In less than 3 years of monitoring nearby galaxies at IR wavebands, SPIRITS has discovered at least one, and possibly two, moderately extinguished SNe that went unnoticed by optical surveys, SPIRITS\,15c and SPIRITS\,14buu. Since the start of the SPIRITS program, our galaxy sample has hosted 9 optically discovered CCSNe. This may suggest a rate of CCSNe in nearby galaxies missed by current optical surveys of at least $10\%$. If SPIRITS\,14buu is also indeed an SN, this estimate increases to 18\%. In a future publication, we will present an analysis of the full SPIRITS sample of SN candidates to provide a more robust estimate of the fraction of SNe being missed by optical surveys. If this fraction is high, this could have significant implications for our understanding of the CCSN rate and its connection to star formation rates. Additionally, the discovery of IR transients such as SPIRITS\,15c and SPIRITS\,14buu in a galaxy-targeted survey indicates that the night sky is ripe for exploration by dedicated wide-field, synoptic surveys in the IR. | 16 | 9 | 1609.04444 |
1609 | 1609.06993_arXiv.txt | \subsection{Introduction} Current cosmological observations are well-described by the $\Lambda$CDM model. This model assumes an almost scale-invariant initial power spectrum of fluctuations in a specific scalar mode, known as the adiabatic mode. These initial conditions are elegantly derived from inflation, where the (approximate) scale invariance follows from one of the isometries of (quasi) de Sitter spacetime. One of the simplest realizations of this scenario is a single scalar field that slowly rolls towards the bottom of a potential, thus providing a physical clock for the the inflationary period. This particular model of slow-roll inflation has indeed received a great deal of attention. An exciting signature of inflation are primordial tensor modes. However, despite much observational effort, a detection of primordial tensor perturbations has so far proven elusive, and current bounds for the tensor-to-scalar ratio $r$ give $ r<0.07 $ ($ 95\% $ CL) \cite{Array:2015xqh}. It is important to ask what we learn from this bound and from the many future improvements thereof. Naively, besides the exclusion of a handful of models, the \textit{absence} of a detection of $ r $ gives us little new information about the early universe. In this paper, we point out that, within single-field, slow-roll, canonical models, the non-detection of $ r $ actually teaches us a great deal. The experimental detection of a deviation from the Harrison-Zeldovich spectrum, together with the current lower bound for the amplitude of tensor modes, implies a hierarchy between the slow-roll parameters that characterize the time dependence of the Hubble parameter during inflation. A consequence of this hierarchy is that all primordial correlators are constrained by conformal symmetry. Using this hierarchy, which we dub the {\it conformal limit of inflation}, we can determine completely the shape of the power spectrum and bispectrum of scalar fluctuations. Our method combines conformal symmetry and a consistency condition for the squeezed limit of the bispectrum. The bispectrum contains a local shape and a ``conformal" shape that has been studied in a different context in the literature~\cite{Zaldarriaga:2003my,Seery:2008qj,Creminelli:2011mw,Kundu:2014gxa}. The amplitude of this bispectrum is small, as the local shape is parametrically of the size of the scalar tilt, while the conformal shape is of the size of the running of the tilt. One nice implication of this result is that the overall size of the bispectrum is tied to observables in the scalar power spectrum, namely the tilt and its running. Hence, a new single-field consistency condition emerges in the scalar sector, which is in principle testable even for negligible tensor modes. If future experiments keep pushing the upper bounds on $r$ and $f_{\rm NL}$, this consistency condition may turn out to be the ultimate test of the simplest single-field inflationary models. Below we summarize our main results more quantitatively, while outlining the various sections of the paper. \subsection{Summary of Results} The simplest model of inflation consists of a single, canonical, minimally coupled scalar field. Assuming that gravity is described by General Relativity (GR), one is lead to consider the action \bea\label{equ:infac} S=\int \dd^4x\sqrt{-g} \left[ \frac{\Mpl^2}{2} R-\frac{(\nabla\phi)^2}{2}-V(\phi)\right]\,. \eea We will focus exclusively on this action and postpone further comments on more general single-clock models to the discussion, in \refsec{disc}. The background solution of \eqref{equ:infac} is a FLRW spacetime with Hubble parameter $H(t)$ which is approximately constant in the slow-roll regime. Small time dependence is parametrized by the two slow-roll parameters $\varepsilon\equiv -\dot H/H^2$ and $\eta\equiv \dot\varepsilon/(\varepsilon H)$. Within the model \refeq{equ:infac}, in the first order slow-roll approximation, one finds the well-known expressions \be\label{srns} 1-n_{s}=2\e+\eta\,,\quad r=16\e\,, \ee where $ n_{s} $ is the scalar spectral tilt and $ r $ is the tensor-to-scalar ratio. Since observations tell us that \cite{Ade:2015lrj,Array:2015xqh} \be\label{data} 1-n_{s}=0.0355 \pm0.005 \, \text{(68\% CL)}\quad \text{and}\quad r<0.07 \, \text{(95\% CL)}\,, \ee we conclude that \be\label{hiercl} \boxed{\e<0.0044< \frac{\eta}{6}\ll \eta\,.} \ee In words, \textit{since we have observed a non-vanishing scalar spectral index but no primordial tensor modes, we have discovered a new hierarchy of the slow-roll parameters, namely $ \e\ll \eta $}.\footnote{The generalization to $ c_{s}\neq1 $ is discussed in \refsec{disc}.} As CMB polarization experiments forge ahead in their quest for primordial tensor modes, in the event of no detection, the upper bound on $ r $ gets stronger and this hierarchy becomes more and more pronounced. Since $ \e $ and $ \eta $ have traditionally been treated on the same footing, some of the discussion of slow-roll inflation might need to be updated in light of this new hierarchy. We call the model in \refeq{equ:infac} in the regime $ \e\ll\eta $ the \textit{conformal limit of inflation}. This limit is spelled out in detail in \refss{ss:conflim}. The conformal limit describes all viable, single-field, slow-roll canonical models. For example, small-field models with a subPlanckian inflaton displacement, $ \Delta\phi\ll \Mpl $ are a specific case of \refeq{hiercl}. In fact, the Lyth bound \cite{Lyth:1996im} implies \be\label{smallfield} \e\lesssim \left( \frac{\Delta \phi}{\Mpl} \right)^{2}\frac{1}{N^{2}}\ll \frac{1}{N^{2}}\lesssim \eta^{2}\,, \ee where $ N\sim 60 $ is the duration of the observable part of inflation, $ \e $ and $ \eta $ are evaluated at CMB scales and the last inequality follows from $ \eta\simeq 1-n_{s}\simeq 0.035 > 1/60 $. Certain models with Planckian field excursion, such as Starobinsky-like inflation, are also particular cases of the conformal limit (see \refsec{ssec:staro}). One remarkable fact about the conformal limit, which according to \refeq{hiercl} might well describe our universe, is that \textit{all primordial correlators are constrained by conformal symmetry}, up to small, slow-roll suppressed corrections.\footnote{A large body of work has been devoted to the study of conformal symmetry and inflation, see \cite{Creminelli:2011mw,Antoniadis:2011ib,Bzowski:2011ab,Maldacena:2011nz,Mata:2012bx,Arkani-Hamed:2015bza,Baumann:2015xxa} for a partial list. When appropriate, we will give the specific references in the body of the paper.} This is because, in this regime, the theory of inflaton fluctuations is approximately invariant under de Sitter isometries, which at late times, on superHubble scales, are isomorphic to the 3-dimensional Euclidean conformal group. In \refsec{s:softth}, we use these symmetries to fully fix the shape and the amplitude of the spectrum and bispectrum in the conformal limit. For instance, consider the equal-time power spectrum of inflaton perturbations $ \varphi\equiv \phi-\bar\phi $ around a background $ \bar\phi $. On superHubble scales, the time dependence of $\varphi$ is the same as that of the background. Dilation symmetry fixes the $ k $-dependence in terms of the time dependence, yielding \be \ex{\varphi_\k(\tau)\varphi_{-\k}(\tau)}'=C\frac{(k\tau)^{-\eta}}{k^{3}}\,, \ee where $ C $ is a constant and a prime indicates that we dropped $ \left( 2\pi \right)^{3} $ and a Dirac delta function (we present our conventions below). Notice that, for $ \eta \neq 0 $, $ \varphi $ evolves on superHubble scales, as expected. Using $ \varphi=-\zeta \sqrt{2\e} \Mpl$, we can convert to the curvature perturbations $ \zeta $, which are conserved on superHubble scales. We choose to convert to $ \zeta $ at some late conformal time $ \tau=\tau_{\ast} $, the \textit{same} for every wavenumber $ k $. We find \bea \ex{\zeta_{\k}\zeta_{-\k}}'=\frac{\tilde C \tau_{\ast}^{-\eta }} {k^{3+\eta} }\,, \eea where we have absorbed the $ k $-independent factor $ \e(\tau_{\ast}) $ into the constant $ \tilde C $. The spectral tilt is then easily seen to be $ \eta $, in agreement with \refeq{srns} for $ \e\ll\eta $. Notice that we did not have to solve the constraint equations of GR. Also, the $ \eta $ contribution to the observed spectral tilt $ n_{s} $, which is the largest one since $ \e\ll \eta $, does \textit{not} signal a breaking of dilation invariance during inflation. Rather, it is a precise consequence of the invariance of $ \varphi $ correlators under dilations (but not of $ \zeta $ correlators). The bispectrum of $\varphi$ is also constrained by de Sitter isometries; it is the sum of two different shapes with arbitrary coefficients. To fix them we calculate the squeezed limit and impose that it matches the squeezed limit of the $ \varphi $ bispectrum derived using a background-wave argument. This is analogous to Maldacena's consistency condition in comoving gauge \cite{Maldacena:2002vr}.\footnote{One crucial difference is that our derivation is valid only in perturbation theory for the short modes, which is sufficient for our purposes. This is a weaker result than the standard $ \zeta $ soft theorem.} This uniquely fixes the three-point function of $\varphi$ (see \refeq{B32sym}). Performing the second order gauge transformation from $\varphi$ to curvature perturbations $\zeta$ gives \be\label{bisp2} \langle \zeta_{\k_{1}} \zeta_{\k_{2}} \zeta_{\k_{3}}\rangle &=& \left( \frac{H^2}{4 \e\Mpl^2} \right)^{2}_{\ast} \Bigg\{\frac{\eta_{\ast}}{2} \frac{k_1^3 + k_2^3+k_3^3}{k_1^3 k_2^3k_3^3}+ \frac{\dot{\eta}_*}{2H_*}\frac{1}{k_1^3k_2^3k_3^3}\times \\ && \Big[(-1+\gamma_E+ \log{(-K \tau_*)})\sum_{i=1}^3 k_i^3-\sum_{i\neq j}k_i^2 k_j + k_1 k_2 k_3\Big]\Bigg\}\,, \nonumber \ee where all time-dependent factors are evaluated at $\tau_*$ independently of $ k $. In \refsec{s:bisp}, we show that \refeq{bisp2} agrees with the direct calculation using the in-in formalism \cite{Burrage:2011hd}, and satisfies the squeezed limit consistency relation of Maldacena to next-to-leading order. An alternative derivation of the bispectrum using the wave functional formalism is presented in \refsec{sec:MMM}. The non-Gaussian shape appearing in the second line of \refeq{bisp2} has been previously derived for spectator fields in de Sitter in \cite{Zaldarriaga:2003my,Seery:2008qj,Creminelli:2011mw,Kundu:2014gxa}. Our new result is to point out that these shapes with specific relative coefficients follow from symmetry arguments, and describe non-Gaussian features of primordial fluctuations in single-field inflation in the conformal limit. We recognize the first term in \refeq{bisp2} as the usual local shape with coefficient $ (n_{s}-1)/2\sim \eta/2 $, which is not locally observable to leading order in derivatives \cite{Pajer:2013ana}. The second term, proportional to $ \dot\eta $, is the next-to-leading order result, first derived in \cite{Burrage:2011hd}. We dub its $ k $-dependence the \textit{conformal shape}, since it is invariant under special conformal transformations (see \refsec{s:confinv}) and we show it in \reffig{shapes}. In the conformal limit of inflation, the following simple relation arises between the amplitude of the conformal shape and the running of the power spectrum ($\alpha_s = d n_s/d\log k$): \beq\label{equ:ncc} \boxed{f^{\rm{conf.}}_{NL} =-\frac{25}{36} \alpha_{s}}\,. \eeq This is a new single-field consistency relation, which can in principle be tested within the scalar sector alone. Given the small expected size of the running, this relation will not be tested in the near future. Nevertheless, it is worth keeping in mind that the most natural, non-informative prior on $ r $ is a log-flat prior extending all the way to $ 10^{-55} $ or less. With this prior, the tensor consistency condition $r=-8n_t$ might well be even harder to test than this new, scalar one given by \refeq{equ:ncc}.\\ Finally, a few additional new results are scattered around the paper. For the convenience of the reader, we provide here an executive summary: \begin{itemize} \item We show in \refsec{s:bisp} how to derive the bispectrum in comoving gauge, without any field redefinition. This clarifies when and why the \textit{boundary terms} in the $ \zeta $ action are important. In particular, they need to be included to obtain constant correlators of $ \zeta $ on superHubble scales (see also \cite{Burrage:2011hd}). \item In \refapp{a:A}, we note that the GR constraint equations are easier to solve in flat gauge. Since the conformal limit implies the decoupling limit (see \refeq{declimit}), we can use the hierarchy between the scalar and gravitational perturbations to solve the constraints in an $\Mpl\rightarrow \infty$ expansion, but \textit{to all orders in the field fluctuations}. The structure of the solutions to the constraint equations in comoving gauge is then a simple consequence of the change of coordinates from flat to comoving gauge. \item It is well-known that the constraint equations can be solved to first order in perturbations if one is interested in the cubic action \cite{Maldacena:2002vr}. We prove in \refapp{constrtoorder} that the constraint solution to order $ n $ is sufficient to derive the action to order $ (2n+1) $, failing for the first time only at order $ (2n+2) $. This is a stronger result than the one proven in \cite{Chen:2006nt}, where the $ n $-th order constraint solution was proved to be sufficient for the action only up to order $ n+2 $. In particular, the known solution of the constraint equations to order 2 (see e.g. \cite{Arroja:2008ga}) can already be used to derive the action to 5th order. \end{itemize} {\bf Notation and conventions} We use natural units, $c=\hbar=1$, with reduced Planck mass $\Mpl^2\equiv1/8\pi G$. Our metric signature is $(-+++)$. Overdots and primes will denote derivatives with respect to physical time $t$ and conformal time $\tau$, respectively. The conformal time $\tau$ is defined by $dt \equiv a(\tau)d\tau$. We use the Hubble slow-roll parameters defined by \be\label{defSR} \e\equiv - \frac{\dot H}{H^2}\,,\quad \eta\equiv \frac{\dot\e}{H\e}\,,\quad \xi_{n\geq3}\equiv \frac{\partial \ln\xi_{n-1}}{\partial N}\,, \ee where $ \xi_{2}\equiv \eta $ and $ dN=Hdt $ is the number of e-foldings. We denote by the same symbol $N$ the lapse function in ADM decomposition, however the distinction between the two is always clear from the context. We use the label $ _{V} $ to indicate the potential slow-roll parameters, defined by \be \e_{V}\equiv \frac{\Mpl^{2}}{2}\left( \frac{V'}{V} \right)^{2}\,,\quad \eta_{V}\equiv\Mpl^{2}\frac{V''}{V}\,. \ee We indicate by $k$ the magnitude of the comoving wavenumber $\textbf{k}$. Our Fourier conventions are \begin{equation} F(\v{x})=\intk \tilde{F}(\v{k})e^{i\v{k}\cdot \v{x}}, \quad \text{where we use the shorthand} \quad \intk\equiv \int \frac{d^3\v{k}}{(2\pi)^3}. \end{equation} A prime on a correlator indicates that we dropped the Dirac delta function and a factor of $(2\pi)^3$, \be \ex{\varphi(\k_{1})\dots\varphi(\k_{n})}\equiv\left( 2\pi\right)^{3}\delta^{3}\left( \sum \k_{i}\right)\,\ex{\varphi(\k_{1})\dots\varphi(\k_{n})}'\,. \ee | \label{disc} \begin{figure} \centering \includegraphics[width=.5\textwidth]{./figures/r_cs_plot} \caption{Schematic plot of the current experimental constraints on the tensor to scalar ratio $r$ and the scalar speed of sound $c_s$. As the bound on $ r $ and $ c_{s} $ (from $ f_{NL}^{\rm eq.} $) improves, we will exclude the region where $ \varepsilon>\eta $.}\label{figrcs} \end{figure} In this paper, we pointed out that, within single-field slow-roll inflation, the non-detection of tensor modes implies $\varepsilon\ll\eta$. We elucidate the consequences of this new hierarchy, which we dub the {\it conformal limit} of inflation: all primordial correlators are constrained by conformal symmetry (a.k.a. de Sitter isometries). Because of the emergent conformal symmetry and with the aid of a new consistency relation, we were able to fully determine the shape and amplitude of the bispectrum as well as the tilt of the power spectrum. Within single-field slow-roll inflation, the predicted size of non-Gaussianity is very small. Our approach relies on the power of symmetries to constrain primordial correlators. The conformal limit is based on the observation that, given the current CMB bounds, the level of tensor fluctuations is small, and might well turn out to be beyond the reach of any human detection apparatus. In this case, the single-field consistency relation, $r=-8n_t$, might be impossible to test. Nonetheless, another single-field consistency relation arises in the scalar sector as well \cite{Maldacena:2002vr}. Here we have shown that, beyond the well-known local non-Gaussian shape with coefficient $ (n_{s}-1) $, there is a subleading conformal shape, whose amplitude is fixed as well, this time in terms of the running $\alpha_s$. While both these signals are challengingly small, they might well be enormously larger than any tensor observables, for which our theoretical prior extends down to $ r\sim 10^{-55} $. The slow-roll parameter $\varepsilon$ is fixed by the tensor-to-scalar ratio $r$ only in slow-roll single-field inflation with a canonical kinetic term. In almost any deviation from this minimal model (such as multifield inflation or $P(X)$ theories) it is possible to produce unobservable tensor modes while keeping $\varepsilon \sim \eta$. However, at the same time, this leads to observable non-Gaussianity. Therefore, by producing stronger bounds on $f_{\rm NL}$ and $r$, future experiments will be able to unequivocally establish that the hierarchy $\varepsilon\ll\eta$ is realized in our universe. As an example, let us consider inflationary models with small speed of sound $c_s$. In the plot of \reffig{figrcs}, we show the current bounds on $r$ (from searches for B-mode polarization in the CMB) and $c_s$ (from constraints in non-Gaussianity) in the shaded regions, and divide between the $\varepsilon >\eta$ and $\varepsilon<\eta$ scenarios. To draw \reffig{figrcs}, we use the current measurement of $n_s-1$ as a constraint on $2\varepsilon+\eta$. Future experiments, such as COrE \cite{Bouchet:2011ck}, will be able to rule out entirely the $\varepsilon>\eta$ region, by decreasing the upper bound on $r$. As the experimental bounds become more stringent, the current hierarchy $\varepsilon<\eta/6$ for $c_s=1$ can increase more than ten-fold, confirming our working assumption that $\varepsilon<\eta^2$, such that the bispectrum that we calculate in this paper is the dominant one. One might be worried that the amplitude of the bispectrum of order $\mathcal O(\eta^2)$ is so small that any correction to the minimal inflationary scenario (such as derivative interactions or heavy fields) would spoil the predictions. While this might be the case in some scenarios, there are natural models in which the bispectrum we calculate in this paper is parametrically larger than all other contributions. As a concrete example, let us consider a Starobinsky-like inflation with the potential \refeq{staro}. Without fine-tuning, derivative operators such as $(\partial \phi)^4/M^4$ must be present and, if $M$ is small, they lead to enhanced equilateral non-Gaussianity. We can estimate this as \cite{Cheung:2007st} \be \left. f_{\rm NL}^{\rm eq.} \zeta \sim \frac{\mathcal{L}_3}{\mathcal{L}_2}\right|_{k/a \sim H}. \ee Using $\mathcal{L}_3 \sim \frac{\dot{\bar\phi}}{M^4} \dot\varphi^3$, $\zeta \sim H^2/{\dot{\bar\phi}}$ and $\dot{\bar\phi}^2 = 2\e \Mpl^2 H^2$, we get \be f_{\rm NL}^{\rm eq.} \sim \frac{\dot{\bar \phi}^2}{M^4} \sim \frac{1}{N^2} \left( \frac H M \right)^2 \sim \eta^2 \left( \frac H M \right)^2 \;, \ee where we used \be\label{epeta} \varepsilon \simeq \left( \frac M{M_{\rm Pl}} \right)^2 \frac{2}{N^2} \simeq \left( \frac M{M_{\rm Pl}} \right)^2 \frac{\eta^{2}}{2} \;. \ee Therefore, as long as $H\ll M \ll M_{\rm Pl}$, the bispectrum up to next-to-leading order is the one calculated in this paper. The same argument is expected to apply to all models with small field range $M$, as long as the scale suppressing derivative interactions is of order of or larger than $M$. In this case the first estimate in \eqref{epeta} is a consequence of the Lyth bound \cite{Lyth:1996im}, and $1/N<\eta $ is an empirical constraint. \\ \\ \noindent{\bf Acknowledgments} We are grateful to Mehrdad Mirbabayi and Marko Simonovi\'{c} for collaboration during various stages of this project. We also thank Daniel Baumann, Giovanni Cabass, Garrett Goon, Hayden Lee and Yvette Welling for discussions and comments on a draft of this paper. A special thanks to Hayden Lee for help with producing the plots in \reffig{shapeplot} and \reffig{figrcs}. E.P. is supported by the Delta-ITP consortium, a program of the Netherlands organization for scientific research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW). G.P. acknowledges support from a Starting Grant of the European Research Council (ERC STG Grant 279617). \appendix | 16 | 9 | 1609.06993 |
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1609 | 1609.03264_arXiv.txt | \label{sec:intro} Supernova remnants (SNRs) are believed to be the major sources of Galactic cosmic rays (CRs), although their efficiency in accelerating protons -- that make most of the CRs, but are difficult to detect -- is not firmly established. Understanding the origin of Galactic CRs requires a joint modeling of the remnant evolution and of particle acceleration by shock waves. We have developed a framework for simulating this in a 3-dimensional and time-dependent manner, which allows us to produce realistic synthetic maps of the broadband emission from the SNR including the effect of efficient particle acceleration at the blast wave \citep{Ferrand2010a, Ferrand2012g, Ferrand2014b}. We applied our simulations previously to the case of the remnant from a typical thermo-nuclear (TN) supernova (Type Ia), evolving in a uniform medium. We showed how energetic protons affect the emission from the remnant: they impact the dynamics of the shock wave, and therefore the thermal emission from the shell (in optical and X-rays), and they impact the evolution of the magnetic field, and therefore the non-thermal emission from the electrons (in radio to X-rays and $\gamma$-rays). Here we present our first results for the case of the remnant of a core-collapse (CC) supernova (type II or Ib/c), that is still evolving inside the wind of its progenitor. While our previous results were most relevant to an object like Tycho's SNR (G120.1+1.4), our new simulations are more appropriate for an object like Cas~A SNR (G111.7-02.1). | \label{sec:conc} As in our previous simulations, the impact of particle acceleration is dependent on the photon energy observed as well as on the magnetic field evolution assumed. In our current model for a CC SNR it appears to be similar for the particles' emission and less visible for the plasma emission. Note that we have not considered here acceleration at the reverse shock. We emphasize that the broad-band emission from a SNR is the result of an integration over space and time of the history of the shock strength, particle acceleration, and magnetic field amplification, which makes it difficult to match observations with a one-zone model. \small % | 16 | 9 | 1609.03264 |
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1609 | 1609.04819_arXiv.txt | \label{sec:abstract} We investigate the integrated far-ultraviolet (FUV) emission from globular clusters. We present new FUV photometry of M~87's clusters based on archival \hst WFPC2 F170W observations. We use these data to test the reliability of published photometry based on \hst STIS FUV-MAMA observations, which are now known to suffer from significant red-leak. We generally confirm these previous FUV detections, but suggest they may be somewhat fainter. We compare the FUV emission from bright ($M_{V} < -9.0$) clusters in the Milky Way, M~31, M~81 and M~87 to each other and to the predictions from stellar populations models. Metal-rich globular clusters show a large spread in $FUV-V$, with some clusters in M~31, M~81 and M~87 being much bluer than standard predictions. This requires that some metal-rich clusters host a significant population of blue/extreme horizontal branch (HB) stars. These hot HB stars are not traditionally expected in metal-rich environments, but are a natural consequence of multiple populations in clusters -- since the enriched population is observed to be He-enhanced and will therefore produce bluer HB stars, even at high metallicity. We conclude that the observed FUV emission from metal-rich clusters in M~31, M~81 and M~87 provides evidence that He-enhanced second populations, similar to those observed directly in the Milky Way, may be a ubiquitous feature of globular clusters in the local universe. Future \hst FUV photometry is required to both confirm our interpretation of these archival data and provide constraints on He-enriched second populations of stars in extra-galactic globular clusters. | \label{sec:intro} Far ultraviolet (FUV) observations of early-type galaxies and globular clusters offer a unique probe into their stellar populations. Main sequence and red giant branch stars in these old stellar populations are too faint at these wavelengths to contribute significantly. Instead, the integrated FUV emission is likely dominated by the He-core burning horizontal branch (HB) stars, as observed in the Galactic globular clusters \citep{Catelan09, Dalessandro12}. Indeed, these stars are leading contenders in explaining the `UV-upturn' observed in early-type galaxies \citep[e.g.][]{OConnell99, Brown00}. Observations of the Galactic globular clusters have shown complex HB star morphologies. The long proposed `first parameter' that is known to influence HB star morphology is metallicity, with metal-rich globular clusters having redder HB stars \citep{Sandage60}. However, there is significant scatter around this correlation, with similar metallicity clusters having different HB morphologies \citep[e.g. NGC~288 and NGC~362][]{Bellazzini01} and some clusters showing significant tails of hotter `extreme'-HB stars \citep[which may not follow the same metallicity correlation;][]{OConnell99}. This has lead to a variety of proposed `second parameters', many of which may influence the HB stars. These include: age; He-abundance; stellar core rotation; and globular cluster core density \citep[see e.g.][]{Fusi_Pecci97, Catelan09}. He-enhanced stars may be expected in globular clusters. Observations have demonstrated the ubiquity of multiple stellar populations in the Galactic globular clusters \citep[see e.g.][for a review]{Gratton12}. To explain the observed abundances of light elements, current theories of the formation of second population stars invoke H-burning at high temperatures \citep[e.g.][]{DAntona07, Bragaglia10}. Therefore, a natural prediction of these theories is that the second population stars should be significantly enriched in Helium. Observations of the Galactic globular clusters appear to confirm this (see Section \ref{sec:He-enhanced}, and the references therein). These studies have demonstrated that the combination of first population stars and He-enhanced second populations can help to explain the complex HB star morphologies observed. In this paper, we consider the integrated FUV properties of globular clusters. Such data only exists for the globular cluster systems of the Milky Way \citep{Dalessandro12}, M~31 \citep{Rey07}, Cen~A \citep{Rey09} and M~87 \citep{Sohn06}. We review these data in Section \ref{sec:fuv_data}. Interestingly, \citet{Sohn06} observed potential ``excess'' FUV emission from M~87's clusters. However, their STIS MAMA observations have subsequently been found to suffer from significantly more red-leak than previously thought \citep{Boffi08, Biretta16}. Therefore, in Section \ref{sec:m87}, we use WFPC2 F170W observations to confirm this previous FUV photometry. In Section \ref{sec:fsps}, we consider the influence of different hot populations on the FUV emission from clusters and (in Section \ref{sec:gc_fuv}) compare these models to the observed FUV emission from clusters in the Milky Way, M~31, M~81 and M~87. We conclude in Sections \ref{sec:He-enhanced} and \ref{sec:conclusions}, where we discuss the results in the context of He-enhanced second population stars in these globular clusters. | \label{sec:conclusions} \begin{itemize}[leftmargin=1pc, labelsep=*, itemsep=.5em] \item We analyse archival WFPC2 F170W far-ultraviolet (FUV) observations of M87's globular clusters. These data confirm the general FUV detection of M87's clusters from earlier work with the STIS FUV-MAMA detector and F25SRF2 filter. \item Our analysis of these F170W data suggests that the STIS FUV magnitudes may be $\sim 0.5$ mag too bright. This might be due to calibration uncertainties, such as a red-leak in the STIS observations, which was discovered only after publication of the initial STIS results. This shift produces $FUV-V$ colours of metal-poor clusters that are similar to those of the Milky Way, M~31 and models. However, we caution on the accuracy of this correction based on these marginal WFPC2 detections and propose that future \hst observations using a dual FUV filter approach can more accurately measure the FUV magnitudes of these and other extra-galactic globular clusters. \item Metal-rich globular clusters show a broad spread in $FUV - V$. This includes clusters whose $FUV - V$ colours are much bluer (by $2-4$ mags) than the predictions from standard models. We note that metal-rich clusters with blue $FUV-V$ colours are found in all galaxies we consider (M~87, M~31, and M~81) and based on data from different telescopes and instruments ({\it GALEX} and \hst). \item The blue $FUV-V$ colours of some metal-rich globular clusters require that they host blue/extreme-HB stars, unlike the classical expectation for a simple stellar population, where metal-rich globular clusters are expected to have a red-HB star morphology. \item We propose that He-enhanced second population stars are the natural source for these hot HB stars in metal-rich globular clusters -- since He-enhanced populations produce bluer HB stars, even at high metallicity. \item FUV observations of metal-rich clusters therefore have the power not only to test for second populations using the integrated light from globular clusters, but also to constrain He-enhancement and factors that drive its variation. \end{itemize} | 16 | 9 | 1609.04819 |
1609 | 1609.00501_arXiv.txt | In laboratory experiments, we studied collisions of ensembles of compact (filling factor 0.33) millimeter dust aggregates composed of micrometer quartz grains. We used cylindrical aggregates, triangular aggregates, square aggregates, and rectangular aggregates. Ensembles of equal size aggregates as well as ensembles with embedded larger aggregates were studied. The typical collision velocities are 10--20~mm~s$^{-1}$. High spatial and temporal resolution imaging unambiguously shows that individual collisions lead to sticking with a high probability of 20\%. This leads to connected clusters of aggregates. The contact areas between two aggregates increase with collision velocity. However, this cluster growth is only temporary, as subsequent collisions of aggregates and clusters eventually lead to the detachment of all aggregates from a cluster. The contacts are very fragile as aggregates cannot be compressed further or fragment under our experimental conditions to enhance the contact stability. Therefore, the evolution of the ensemble always leads back to a distribution of individual aggregates of initial size. This supports and extends earlier experiments showing that a bouncing barrier in planetesimal formation would be robust against shape and size variations. | \label{sec:intro} This work is focused on a process, discussed in the context of the early phases of planetesimal formation, known as the bouncing barrier \citep{Zsom2010}. Initially, dust grains in protoplanetary disks collide, stick together and grow \citep{Dominik1997, Wurm1998, Blum2008, Wada2009}. The aggregates are initially fractal or very porous and if they consist of sub-micron icy grains they might grow large in the above fashion \citep{Okuzumi2012, Kataoka2013}. However, if they consist of micrometer sized silicates they are supposed to become compact at millimeter to centimeter sizes. \citet{Weidling2009} showed that an initially highly porous aggregate with a volume filling factor of 0.15 has a volume filling factor of 0.36 after many collisions with a wall at velocities up to 0.35~m~s$^{-1}$. Experiments by \citet{Teiser2011} and \citet{Meisner2012} showed that a filling factor of 0.3--0.4 seems to be a common value in collisional evolution up to high speeds of several tens of meters per second for (sub-) millimeter aggregates. In any case, aggregates are eventually compacted to such a level that further collisions no longer include large dissipations of energy through restructuring the whole aggregate. The aggregates then tend to bounce off each other in mutual collisions, as observed in many individual experiments. This has also triggered theoretical work on understanding bouncing \citep{Wada2011, Seizinger2013}, which supports that growth no longer proceeds under the premise of continuous bouncing. This barrier was introduced by \citet{Zsom2010} as the bouncing barrier. The existence of a bouncing barrier has severe consequences for planetesimal formation. If the aggregate size where bouncing dominates and growth becomes stalled is too small, pure growth of planetesimals cannot proceed. If larger seeds are provided by some mechanism, the growth of larger bodies is possible by mass transfer \citep{Teiser2009, Windmark2012a, Deckers2014}. In that case the bouncing barrier is required to keep high the number of small aggregates on which the larger seeds can feed. Alternatively, large objects can form by gravitational collapse of clumps of particles concentrated previously e.g. in zonal flows or by streaming instabilities \citep{Dittrich2013, Johansen2014}. Early work mostly considered particles to be concentrated by streaming instability if their Stokes numbers (the ratio between gas--grain coupling time and orbital period) are on the order of 1. However, recent work showed that much lower Stokes numbers might suffice. \citet{Bai2010} find the onset of a streaming instability for Stokes numbers larger than $10^{-2}$. This is consistent with work by \citet{Carrera2015} who find the onset of streaming instability at Stokes numbers between $10^{-3}$ and $10^{-2}$. In this work this is equivalent to millimeter-sized particles and we also consider the possibility that collisions of millimeter-sized particles (chondrules or chondrule aggregates) at low speeds might lead to further growth, enhancing the effect of the streaming instability. \citet{Drazkowska2014} combine a model for streaming instability and particle coagulation, and show that the bouncing barrier for silicate dust might be below the limit required for streaming to set in (Stokes number $10^{-2}$). In general, a particle reservoir at the bouncing barrier (often referred to as pebbles) might benefit accretion by larger bodies \citep{Johansen2015}. Due to the importance of the bouncing barrier, we extend earlier laboratory experiments on this topic. \citet{Kelling2014} supported the existence of a bouncing barrier. They studied ensembles of compact aggregates interacting with each other in thousands of collisions per aggregate. They found no long-term growth of a larger cluster of aggregates. In those earlier experiments the sticking probability in individual collisions could not be determined unambiguously as the spatial and time resolutions were not sufficient. Also, only one size and shape of initial aggregates was used. To elaborate more on the robustness of the bouncing barrier we improve the set-up and extend the parameter set studied. A high resolution camera system was installed to allow the study of individual collisions. We now can clearly classify individual collisions in terms of bouncing or sticking and quantify contact areas. Also, various aggregate shapes were studied. The reason behind the choice of triangular- and square-shaped aggregates is that sticking at long sides might form stronger bonds. This might enhance the stability of clusters in comparison to cylindrical aggregate clusters where curvature would, e.g., prevent sticking at several distinct sides of two aggregates. We do not expect aggregates in protoplanetary disks to be such shapes. In fact, if aggregates grow and are compacted by colliding with other grains from all sides they will tend to be roundish. However, this depends on the overall distribution of solids within the disk, e.g., a fraction of large bodies might exist at the same time (as needed in pebble accretion scenarios, \citet{Johansen2015}). Fragments of their collisions might join the sub-bouncing barrier particle fraction. Then aggregates might not be spherical but have angular shapes. So our choice is meant to evaluate the possible extremes that might break the bouncing barrier. In addition, the ensemble evolution was studied with individual larger aggregates embedded. The idea here is that larger aggregates might act as seeds for more stable clusters. In summary, we consider the influence of (1) aggregate shape and (2) aggregate size differences, and (3) quantify the underlying fraction of individual sticking collisions as necessary for growth.\\ | \label{sec:conlusions} Whatever the shape of compact dust aggregates in the studied range of sizes and collision velocities, the result is always the same. Although individual collisions, studied in detail for cylindrical aggregates, lead to sticking between two aggregates with a high probability, this has no effect on the long-term evolution of an aggregate ensemble. The aggregate contacts within a cluster are so weak that clusters are never stable in the given data sets (low collision velocities). In the long-term clusters are always destroyed again. This also holds for the ensembles of different shapes and sizes, although we did not quantify these in high resolution imaging. Following \citet{Windmark2012b}, one might estimate that the probability, $p$, to obtain a large cluster consisting of $n$ aggregates would be ${p=x^n}$, where $x$ is the sticking probability. This might eventually lead to a large cluster or a lucky winner. However, this cannot be applied at the bouncing barrier as, in addition to sticking and bouncing, there is also detachment, which is a fragmentation but only undoing a previous collision. With 20\% sticking all aggregates should form dimer clusters after five collisions on average, and so on. However, even after more than 1000 collisions for each aggregate there is no stable growth. The probabilities of growing a large cluster are obviously suppressed. Currently, we cannot quantify the detachment probability from observations directly, but it prohibits the formation of larger clusters in our experiments. So at the bouncing barrier -- at least in the cases studied -- the detachment probability has to be on the same order as the sticking probability or larger. This behavior does not rule out further growth but this requires, e.g., a seed large enough that collision velocities go beyond meters per second where fragmentation becomes important. Still, a bouncing barrier in such scenarios among the smaller aggregates would be important or beneficial \citep{Teiser2009, Windmark2012a}. The velocities considered for collisions by \citet{Carrera2015} for growth are in the sub-millimeter per second range. These are included in our collisions but we cannot say what the lowest limit of detaching collisions is. So we cannot rule out that growth can proceed at significantly lower velocity ranges. The aggregates used in this study are composed of silicate grains that are micrometer sized. It is well known that the grain size as well as material have major effects on sticking \citep{Okuzumi2012, Wada2013, Gundlach2015, Musiolik2016}. How variations of size and material would change the outcome of collisions is a subject for future studies. We also did not study how aggregation would approach the bouncing barrier and what the final size of aggregates would be, but concentrated on a saturated case of compact aggregates. A more self-consistent growth starting from smaller and more porous aggregates is also planned for the future. In any case, without loss of generality, our experiments show that the bouncing barrier among small compact aggregates is very robust. | 16 | 9 | 1609.00501 |
1609 | 1609.05923_arXiv.txt | {} {For the first time the astrometric capabilities of the Multi-Conjugate Adaptive Optics (MCAO) facility GeMS with the GSAOI camera on Gemini-South are tested to quantify the accuracy in determining stellar proper motions in the Galactic globular cluster NGC~6681. } {Proper motions from HST/ACS for a sample of its stars are already available, and this allows us to construct a distortion-free reference at the epoch of GeMS observations that is used to measure and correct the temporally changing distortions for each GeMS exposure. In this way, we are able to compare the corrected GeMS images with a first-epoch of HST/ACS images to recover the relative proper motion of the Sagittarius dwarf spheroidal galaxy with respect to NGC~6681.} { We find this to be $(\mu_{\alpha}\cos\delta, \mu_{\delta}) = (4.09,-3.41)$ \masyr, which matches previous HST/ACS measurements with a very good accuracy of 0.03 \masyr and with a comparable precision (r.m.s of 0.43 \masyr).} {This study successfully demonstrates that high-quality proper motions can be measured for quite large fields of view ($85$\arcsec$\times85$\arcsec) with MCAO-assisted, ground-based cameras and provides a first, successful test of the performances of GeMS on multi-epoch data. } | Proper motions (PMs) are an extremely powerful tool to investigate the kinematics and dynamics of stellar systems. However, since their size depends on the distance of the objects under study and on the temporal baseline between the observations, PMs can be very small and difficult to measure. For example an object moving at 100 km/s at a distance of 100 kpc, has a PM of only $\sim0.2$ \masyr. This is why the internal kinematics of stellar systems have only been studied for the closest of them, i.e. Galactic Globular Clusters (GCs). The most reliable examples available in literature (see e.g. \citealt{mcl06, avdm10, mcnamara12, bellini14, watkins15}) exploit the exceptional astrometric performance of the {\it Hubble Space Telescope} (HST), whose diffraction-limited PSF and geometric distortions proved to be well determined and extremely stable over more than 20 years of operations (e.g. \citealt{anderson07, bellini11}). Recently, diffraction limited observations have also been possible for ground-based telescopes and over quite large fields of view (FoV), thanks to the Multi-Conjugate Adaptive Optics (MCAO) technique (\citealt{ragazzoni00}). This was first successfully tested on sky with the Multi-conjugate Adaptive optics Demonstrator (MAD, \citealt{marchetti08}) at the Very Large Telescope. Because of the size of the telescope, ground-based diffraction-limited observations provide higher spatial resolution than those coming from HST and the related astrometric measurements are thus potentially more precise. This will be especially true in the future, with the advent of Extremely Large Telescopes (ELTs), which will be larger by more than a factor of five than any future space telescope. In preparation for this future leap in telescope size available to ground-based astrometry, it is important to explore the technical requirements that will lead to the full exploitation of MCAO for PM measurements on an ELT. Currently, the only operational MCAO facility is the Gemini Multi-Conjugate Adaptive Optics System (GeMS, \citealt{rigaut14, neichel14a}) mounted at the Gemini-South telescope. GeMS has been shown to be able to reach a good astrometric precision of $\sim0.2$ mas for bright stars and exposure times exceeding one minute on single-epoch observations (\citealt{neichel14b}). However, GeMS performance on multi-epoch data, even if separated by only few hours, has turned out to be a more complicated matter. In general, several distortion effects contribute to move a star around on the detector of a MCAO-assisted camera (e.g. \citealt{trippe10}). One of the biggest problems is the time variablity of the distortions which make it complex to calibrate or model them. This explains why only one previous PM study of a GC exists using MCAO data (\citealt{ortolani11}, using MAD observations of the cluster HP1). Moreover, in the particular case of GeMS, the distortions also have an extra component that varies quickly, possibly due to gravity flexure or to the movement of the AO-bench (\citealt{neichel14b, lu14, ammons14}). This component makes PMs with GeMS even more complex to measure. Here, we present the first multi-epoch astrometric study from our Gemini/GSAOI campaign targeting Galactic GCs using GeMS (\citealt{turri14, turri15, massari16}). In this work, we present a method that is able to correct MCAO distortions by exploiting previously measured distortion-free stellar positions and PMs. This allows us to test the GeMS astrometric performance for the first time on PM measurements obtained from multi-epoch data separated by few years. The initial test case that we present in this Letter is the GC NGC~6681, whose stars PMs have already been measured with HST by \cite{massari13} (hereafter Ma13). The Letter is structured as follows. In Section \ref{method} we describe in detail the data analysis and the method we used to model GeMS distortions. In Section \ref{pm} we check our PMs for systematic errors and compare them to the previous HST measurements. Finally, we summarise our conclusions in Section \ref{concl}. | In this work we present the first PM measurements obtained exploiting the potential of the MCAO GeMS/GSAOI camera. We used the a-priori knowledge of independently measured PMs for stars in the FoV of interest to model the distortions affecting the camera, finding a different distortion solution for each of the GeMS exposures. After combining the corrected GeMS images with observations coming from HST, providing a temporal baseline of $\Delta t=6.914$ yr, we were able to determine the relative PM between the globular cluster NGC~6681 and the Sgr dSph galaxy. The value we found of $(\mu_{\alpha}\cos\delta, \mu_{\delta}) = (4.09,-3.41)$ \masyr matches the previous HST measurement with an accuracy of $0.03$ \masyr. Also the achieved precision turns out to be comparable to that of HST, and become worse by a factor of two at the faint magnitudes of Sgr dSph stars. Our findings demonstrate that GeMS is potentially useful to obtain high-quality PMs from the ground, when combined with space-based observations. We are waiting for two GeMS epochs sufficiently distant in time to test the astrometric performances achievable using only MCAO datasets. This work sets the stage for future PM measurements with this complex AO instrumentation, providing strong support for the need of a careful treatment of time-varying distortions. Following the effective investigation discussed in this Letter, our group is now testing a new observational strategy to use GeMS for PM measurements without the support of previous HST data. This involves the combined use of the FLAMINGOS-2 (\citealt{eiken04}) and GeMS/GSAOI images. According to our strategy, distortion-corrected FLAMINGOS-2 seeing-limited observations will precede any GeMS dataset to provide an independent reference frame to be used as a corrector for the distortions of each GeMS exposure. In order to make the above procedure possible, we have obtained dedicated time to model the FLAMINGOS-2 camera distortions (PI A. McConnachie). The proposed strategy will pave the road for future astrometric MCAO observations, including those with ELTs. | 16 | 9 | 1609.05923 |
1609 | 1609.05748_arXiv.txt | Wide-field ($\gtrsim$ 100 deg\sS{2}) hard X-ray coded-aperture telescopes with high angular resolution ($\lesssim$ 2$'$) will enable a wide range of time domain astrophysics. For instance, transient sources such as gamma-ray bursts can be precisely localized without assistance of secondary focusing X-ray telescopes to enable rapid followup studies. On the other hand, high angular resolution in coded-aperture imaging introduces a new challenge in handling the systematic uncertainty: average photon count per pixel is often too small to establish a proper background pattern or model the systematic uncertainty in a time scale where the model remains invariant. We introduce two new techniques to improve detection sensitivity, which are designed for, but not limited to high resolution coded-aperture system: a self-background modeling scheme which utilizes continuous scan or dithering operations, and a Poisson-statistics based probabilistic approach to evaluate the significance of source detection without subtraction in handling the background. We illustrate these new imaging analysis techniques in high resolution coded-aperture telescope using the data acquired by the wide-field hard X-ray telescope \pe2 during the high-altitude balloon flight in Fall, 2012. We review the imaging sensitivity of \pe2 during the flight, and demonstrate the performance of the new techniques using our balloon flight data in comparison with simulated ideal Poisson background. | Near-arcmin angular resolution for wide-field\footnote{Here we loosely define wide field as a solid angle $\gtrsim$ 100 deg\sS{2}, which enables all sky survey in a reasonable time scale and depth. For instance, a telescope with a 100 deg\sS{2} field of view can scan the entire sky in roughly 2 yr with an average exposure of 100 ks.} hard X-ray coded-aperture telescopes is within reach in near future. The Burst Alert Telescope (BAT) on \swift, which have been operating successfully for more than a decade, covers a 1.4 sr field (50\% coding\footnote{Field of views of coded-aperture systems quoted in this paper refer to 50\% coding unless otherwise noted.}) with the 22\arcmin\ angular resolution in the 15--150 keV band \citep{Gehrels04}. The Imager on Board the {\it INTEGRAL} Satellite (IBIS) and the Joint European X-ray Monitor (JEM-X) can observe a $\sim$ 19 \x19 deg\sS{2} field with the 12\arcmin\ resolution in the 15 keV -- 10 MeV band and a 7.5\Deg diameter field with the 3\arcmin\ resolution in the 3--35 keV band, respectively \citep{Winkler03}. Recently we have achieved the 5\arcmin\ angular resolution over a 20 \x 20 deg\sS{2} field in the 5 -- 200 keV band with a balloon-borne hard X-ray coded-aperture telescope \pe2 \citep{Hong13} by employing an array of CdZnTe detectors with the Application Specific Integrated Circuits (ASICs) of a high pixel density used in Nuclear Spectroscopic Telescope Array (\nustar) \citep{Harrison13}. Next generation ASICs with a higher pixel density will soon enable $\lesssim$ 2\arcmin\ resolution, which will allow source localization within 20\arcsec. High precision source localization from a wide-field hard X-ray telescope can initiate rapid follow-up studies of transient sources with many telescopes around the world without assistance of secondary focusing X-ray telescopes, and thus open a wide range of discovery space in the time domain astrophysics. High resolution in coded-aperture telescopes introduces a new challenge in handling the systematics such as non-uniform detector background. Even with a decent exposure, observed photon counts per pixel often remain too low to establish the precise pattern of non-uniformity in the detector plane, which can limit the detection and localization sensitivity. Novel observing schemes such as continuous scan or dithering can reduce the unknown systematic errors \citep{Grindlay04}, but as the pixel density increases, additional care in the analysis is required to ensure the high sensitivity. Here we introduce two new techniques to alleviate the effects of systematics and improve detection sensitivity even under low count statistics of high resolution coded-aperture telescopes. We illustrate these new imaging analysis techniques using the data acquired by the wide-field high resolution hard X-ray telescope \pe2 during the high-altitude balloon flight in Fall, 2012. In Section \ref{s:instr}, we review the basic parameters of the \pe2 telescope. In Section \ref{s:aspect}, we describe the boresight calibration and the performance of our pointing and aspect system during the high altitude balloon flight in Fall, 2012. In Section \ref{s:sens}, we estimate the sensitivity limit of the \pe2 telescope and illustrate the challenge of high resolution coded-aperture telescopes using the \pe2 observations during the flight. In Section \ref{s:sbc}, we introduce a self-correcting background modeling scheme, which utilizes continuous scan or dithering operations. In Section \ref{s:tm}, we introduce a Poisson statistics based detection significance map called `trial map' \citep{Hong16} to coded-aperture imaging, which can handle the background without subtraction. \begin{table} \small \caption{Telescope Parameters of \pe2} \label{t:telpar} \begin{tabular*}{0.470\textwidth}{r@{\extracolsep{\fill}}l} \hline\hline Parameters & Values \\ \hline Sensitivity & $\sim$ 140 mCrab/hr\sS{a} \\ Energy Range & 5 -- 200 keV \\ Energy Resolution & 2 -- 3 keV \\ Field of View & 20\Deg \x 20\Deg (50\% Coding) \\ Angular Resolution & 4.8$'$ \\ \hline CZT Detector & 56 crystals \x (1.98 \x 1.98 cm\sS{2}) \\ Active Area & 220 cm\sS{2} \\ Pixel, Thickness & 0.6 mm, 5 mm \\ \hline Tungsten Mask & 4 layers \x 0.1 mm thick \\ Coding Area & 33.3 \x 33.3 cm\sS{2} \\ Pixel, Grid, Thickness & 1.1 mm, 0.1 mm, 0.4 mm \\ Pattern & Random \\ \hline Mask-Det. Separation & 90 cm \\ Rear and Side Shields & {Graded Pb/Sn/Cu} \\ \sS{241}Am Cal. Source & {220 nCi each, $\sim$ 36 cm above det} \\ \hline \end{tabular*}\\ (a) Without atmospheric absorption. The atmospheric absorption at altitude of 40 km can reduce the signal by a factor of $\sim$ 3 in the 30--100 keV band, which depends on the source spectrum and the pointing elevation. \end{table} | \label{s:conclusion} In future, direct localization of transient sources like gamma-ray bursts without assistance of secondary instruments will enable a wide range of the time domain astrophysics. To achieve this, next generation wide-field hard X-ray telescopes should be capable of sub 2\arcmin\ angular resolution. In high resolution coded-aperture telescopes, new challenges arise in handling non-uniformity in the detector system due to low count statistics per pixel. During a high altitude balloon flight in 2012, the \pe2 telescope of 4.8\arcmin\ resolution collected about 3 counts per hr in each detector pixel on average, which illustrates this new challenge. Dithering or continuous scan as shown in BATSS alleviates the effects of the systematics by automatically averaging out the non-uniformity even without special treatment but large scale variations still remain in their sky images, which can limit the detection and localization sensitivity. We presented a method to improve the sensitivity of high resolution coded-aperture systems by self-correcting the non-uniform background of low statistics efficiently. Combining simulated sources with the real balloon flight data of the \pe2 telescope, which exhibits pixel-dependent background variations, we demonstrated that the proposed techniques can reduce the large scale variation dramatically and improve the SNR by a few to 10\% depending on the input SNR. We also proposed a new method to estimate detection significance using a Poisson statistics based probabilistic approach without relying on subtraction in background handling. We plan to apply these techniques to the \swift/BAT data to evaluate the improvements in a wide range of operating environments for further optimization. | 16 | 9 | 1609.05748 |
1609 | 1609.00392_arXiv.txt | The low mass X-ray binary Aquila X-1 is one of the most active neutron star X-ray transients. Despite its relatively bright quiescent optical counterpart, the detection of its companion has been hampered by the presence of a nearby interloper star. Using the infrared integral field spectrograph SINFONI on the VLT-8.2m telescope, we unambiguously single out Aquila X-1 from the interloper. Phase-resolved near infrared spectroscopy reveals absorption features from a $\rm{K}4\pm 2$ companion star moving at a projected velocity of $K_2= 136\pm 4 \, \rm{km \, s^{-1}}$. We here present the first dynamical solution and associated fundamental parameters of Aquila X-1, imposing new constraints on the orbital inclination ($36 \, ^{\circ} < i < 47 \, ^{\circ}$) and the distance ($d = 6\pm 2\, \rm{kpc}$) to this prototypical neutron star transient. | \label{intro} Neutron star X-ray transients (NSXRTs) are a sub-type of low mass X-ray binaries harbouring a low mass star ($\lesssim 1 \,M_\odot$) and a neutron star (NS). They spend most of their lives in a faint, quiescent state, but show occasional outbursts where their X-ray luminosity increases above $\sim 10$ per cent of the Eddington luminosity. Observing NSXRTs in outburst, while convenient for accretion studies (e.g. \citealt{Munoz-Darias2014}), implies that most of the system luminosity arises from non-stellar components, completely veiling the companion star spectral features and preventing a dynamical solution even in the infrared (e.g. \citealt{MataSanchez2015}). On the other hand, the study of NSXRTs in their fainter, quiescent state -- where the relative contribution of the companion star to the total flux is larger -- depends greatly on the distance to the source and the Galactic extinction. Aquila X-1 (hereafter Aql X-1, discovered by \citealt{Kunte1973}) is a recurrent NSXRT which has exhibited both coherent millisecond X-ray pulsations at $\sim 1.8\, \rm{ms}$ \citep{Casella2008} and thermonuclear bursts (e.g. \citealt{Galloway2008}). Despite showing recurrent outbursts and having a relatively accessible quiescent optical magnitude (V=21.6, \citealt{Chevalier1999}), a radial velocity study of the donor star is still missing. This has been prevented by the presence of an interloper star placed less than 0.5 arcsec apart from Aql X-1 \citep{Chevalier1999}. The interloper is $\sim 2$ mag brighter than Aql X-1 in the V-band but of comparable brightness at NIR wavelengths. In this work, we exploit the better spatial resolution inherent to the near-infrared (nIR) observations as well as adaptive optics techniques to obtain phase resolved, Integral Field Spectroscopy (IFS), which allow us to clearly resolve Aql X-1 from the interloper star. | \label{conclusion} We used near infrared integral field spectroscopy to single out Aquila X-1 from a nearby interloper star. The spectra reveal, for the first time, absorption features corresponding to a $\rm{K}4\pm2$ donor, veiled by $\sim 36\%$ in the K-band, and moving at a projected orbital velocity of $K_2=136\pm 4\, \rm{km\, s^{-1}}$. We further refine the ephemerides of the system to $T_0=2455810.387\pm 0.005 \rm{d}$ and $P_{\rm{orb}}= 0.7895126\pm 0.0000010 \, \rm{d^{-1}}$, and constrain the orbital inclination to $36 \, ^{\circ} < i < 47 \, ^{\circ}$. Using the de-reddened K-band magnitude and the constraints on the spectral type we infer a distance to the source of $d = 6\pm 2\, \rm{kpc}$. | 16 | 9 | 1609.00392 |
1609 | 1609.00995_arXiv.txt | We describe the preliminary design of a magnetograph and visible-light imager instrument to study the solar dynamo processes through observations of the solar surface magnetic field distribution. The instrument will provide measurements of the vector magnetic field and of the line-of-sight velocity in the solar photosphere. As the magnetic field anchored at the solar surface produces most of the structures and energetic events in the upper solar atmosphere and significantly influences the heliosphere, the development of this instrument plays an important role in reaching the scientific goals of The Atmospheric and Space Science Coordination (CEA) at the Brazilian National Institute for Space Research (INPE). In particular, the CEA's space weather program will benefit most from the development of this technology. We expect that this project will be the starting point to establish a strong research program on Solar Physics in Brazil. Our main aim is acquiring progressively the know-how to build state-of-art solar vector magnetograph and visible-light imagers for space-based platforms to contribute to the efforts of the solar-terrestrial physics community to address the main unanswered questions on how our nearby Star works. | \label{intro} Living in the surroundings of the atmosphere of a highly variable star allows us to observe in high spatial and temporal resolution the universal processes that occur in its outer layers. This is our main motivation to propose the development of instruments and models to study the evolution of the magnetic structure of the Sun on timescales that range from seconds to millenia. The solar electromagnetic and corpuscular emissions are strongly modulated by the evolution of the solar magnetic field. Systematic observations of sunspots, since the invention of the telescope, are the main indicator that the solar activity changes on timescales from days to millennia. These changes drive long-term evolution of the heliosphere (space climate) as well as violent events (space weather). In particular, the near-Earth region is strongly affected by the evolution of the solar magnetic structure. Early observations of the sunspots clearly indicated that their presence on the solar surface varies cyclically with a period of approximately 11 years, the so-called solar activity cycle. Subsequently, it was observed that the latitudinal distribution of sunspots varies throughout the cycle and follows a pattern that begins at middle latitudes ($\pm 35^\circ$), reaches a maximum, and decays near the equator ($\pm 5^\circ$). Following a minimum of activity, the pattern repeats itself. Magnetic field is found at different spatial scales all over the solar surface. Most part of the magnetic flux is filamented into a range of flux tubes with field strength of 100\,mT while the largest photospheric magnetic flux tubes are sunspots with diameters between a few Mm and 50\,Mm, which represent the biggest accumulations of magnetic flux in the photosphere. Additionally, observations indicate that sunspots in the same hemisphere but belonging to distinct cycles have opposite polarities. Consequently, the predominant magnetic field signal in each hemisphere varies with a period of approximately 22 years. Dark features appearing on the solar surface (i.e. sunspots and pores) cause a detectable depletion in the flux density. This depletion occurs because intense magnetic fields within sunspots block the convection and decreases the transport of thermal energy from the base of the convection zone to the photosphere. The reduction of the temperature within the sunspots causes a reduction of the surface opacity. Note that the depletion depends on the relative position of the sunspot on the solar surface and the observer. The maximum depletion occurs when the sunspots are near the disk center and can be as large as $\sim$ 0.3\%. On the other hand, small flux tubes (e.g., faculae) appear brighter than the surrounding average solar surface because their partially evacuated interior is efficiently heated by radiation from their surroundings in the deeper layers and, presumably, also by dissipation of mechanical energy in their higher atmospheric layers. Averaged over the whole Sun, the enhanced brightness of the magnetic elements dominates over the reduced energy flux in the sunspots, so that the total radiation output increases with growing magnetic flux in the photosphere. As a consequence, the brightness of the Sun increases by about 0.1\% from minimum to maximum during the solar activity cycle (see e.g. \cite[Domingo et al. 2009]{Domingo2009-vie}, \cite[{Fr{\"o}hlich} 2013]{froehlich2013-vie}). Long-term changes of the solar activity are observed directly from, among other indices, the sunspot records and indirectly in natural archives such as cosmogenic isotopes. These proxies indicate periods of high (grand maxima) and low (grand minima) solar activity. These changes in the solar energy output clearly impact the Earth's climate, although the relative role of the several drivers (solar, volcanic, anthropogenic, etc) are still under debate. We emphasize that these long-term changes impact not just the troposphere-land-ocean system, but also the neutral and ionized components of the middle and upper atmosphere (\cite[Solanki et al. 2013]{solanki2013-vie}). In spite of the increasing interest of the solar physics community to unveil the mechanisms responsible for such variations, still there is no complete physical explanation for the origin of the observed solar activity. So far the preferred paradigm used to explain the production and periodic occurrence of sunspots is the action of the magnetohydrodynamic dynamo driven by the differential rotation of the star and the convection of the magnetic field to the surface. At the moment, dynamo models can reproduce cyclic modulation of the Sun's activity, and even some features of the 11-year sunspot cycle, but cannot explain the varying amplitudes of the maxima or long-term changes in the Sun's magnetic activity. The magnetic field has also an important role as the driver and energy source for highly dynamical and energetic events such as flares and coronal mass ejections that take place in the outer layers of the solar atmosphere. Measurements of the full vector magnetic field result indispensable in order to answer the main open questions on the origin and evolution of such phenomena. In this context, we have proposed to develop a magnetograph and visible-light imager instrument in order to study the solar dynamo processes that give rise to the rich variety of phenomena observed at different layers of the solar atmosphere through observations of the surface magnetic field distribution. | 16 | 9 | 1609.00995 |
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1609 | 1609.09085_arXiv.txt | We present \textsc{The-wiZZ}, an open source and user-friendly software for estimating the redshift distributions of photometric galaxies with unknown redshifts by spatially cross-correlating them against a reference sample with known redshifts. The main benefit of \textsc{The-wiZZ} is in separating the angular pair finding and correlation estimation from the computation of the output clustering redshifts allowing anyone to create a clustering redshift for their sample without the intervention of an ``expert''. It allows the end user of a given survey to select any sub-sample of photometric galaxies with unknown redshifts, match this sample's catalog indices into a value-added data file, and produce a clustering redshift estimation for this sample in a fraction of the time it would take to run all the angular correlations needed to produce a clustering redshift. We show results with this software using photometric data from the Kilo-Degree Survey (KiDS) and spectroscopic redshifts from the Galaxy and Mass Assembly (GAMA) survey and the Sloan Digital Sky Survey (SDSS). The results we present for KiDS are consistent with the redshift distributions used in a recent cosmic shear analysis from the survey. We also present results using a hybrid machine learning-clustering redshift analysis that enables the estimation of clustering redshifts for individual galaxies. \textsc{The-wiZZ} can be downloaded at \url{http:// github.com/morriscb/The-wiZZ/}. | Current and future photometric galaxy surveys are designed to measure the properties and evolution of galaxies as well as constrain cosmological parameters and the properties of the Universe. In order to enable this, accurate and unbiased estimates of galaxy redshifts are required to extract the maximum amount of information. Until recently, redshift information in photometric surveys was only gained through spectroscopic followup or photometric redshifts (photo-$z$s) from multi-band photometry. Many techniques exist for deriving photo-$z$s \citep[see][for a partial review]{hildebrandt10}, however all these techniques rely on a calibration set of spectroscopic redshifts that is representative of the survey galaxy population. Such a sample of spectra is only possible for the shallowest surveys and still requires a significant amount of telescope time. For future deep, large-area surveys such as The Large Synoptic Survey Telescope\footnote{\url{http://www.lsst.org/}} (LSST), a sample of representative spectra will be even more difficult. Such challenges are presented in \citet{newman15}. An alternative and complementary method to photo-$z$s is that of clustering redshift estimation (clustering-$z$s). Clustering redshifts make use of the fact that galaxies with unknown redshifts reside in the same structures as galaxies that have known redshifts. Thus, spatial cross-correlations can be used to estimate the redshift distribution of the sample with unknown redshifts. The basic method bins the sample with known redshifts in $z$ and then spatially cross-correlates each of these bins against the unknown sample. The amplitude of the resultant correlation can then be used to estimate the amount of redshift overlap and thus the redshift distribution of the sample with unknown redshifts. One of the first suggestions of such a method can be seen in \citet{schneider06} with the formalism for this method written out in \citet{newman08} and later generalized in \citet{schmidt13} and \citet{menard13} with quadratic estimators laid out in \citet{mcquinn13} and \citet{johnson16}. The method has some drawbacks from sensitivity to galaxy bias both from the reference sample with known redshifts and the sample with unknown redshifts which can affect clustering-$z$s. However, suggestions to mitigate this bias exist in the literature \citep{newman08, menard13, schmidt13}. Cross-correlation techniques are beginning to be applied to real data \citep{rahman15, choi15, rahman16a, rahman16b, scottez16, hildebrandt16, johnson16} with an eye towards future surveys. A failing of this method, however, is that the current implementations of clustering redshifts are not as easy to use as their photo-$z$ counterparts and nominally require spatial correlations to be run and re-run for each galaxy sub-sample of interest. This is a time-consuming process and could limit clustering redshift's adoption by the larger community. Suggestions exist such as producing clustering-$z$s in color-color space cells \citep{rahman16a, scottez16} but this will have limitations for some samples and precludes the ability to weight galaxies in the clustering redshift estimation in the same way as in a given analysis or utilize additional information after the correlations are run for each cell. A more flexible method that separates the spatial correlation computation from the act of creating clustering redshifts would be ideal. In this article we present \textsc{The-wiZZ}\footnote{Available at: \url{http://github.com/morriscb/The-wiZZ/}}, a method for estimating redshift distributions from clustering designed for ease of use by survey end users. \textsc{The-wiZZ} separates the difficult step of finding close angular pairs from the act of creating a clustering redshift estimate. In this way the correlations between close pairs can be run once by the survey data pipeline and then an end user can create a clustering redshift estimate for their unique sub-sample of galaxies in a matter of, in some cases, seconds. \textsc{The-wiZZ} can add to the legacy of galaxy surveys by producing a stable data product that can continue to be used by the astronomy community without a large amount of specialized software, much like how photo-$z$s are used today. \textsc{The-wiZZ} can of course also be used by individuals with any data overlapping a spectroscopic sample allowing them to produce clustering-$z$s quickly and easily. This document is laid out as follows. In Section \ref{sec:method} we give an overview of the method and software including showing how it can be used in the context of a galaxy survey. Section \ref{sec:data} explains the data products we use to test \textsc{The-wiZZ}. In Section \ref{sec:recoveries} we show the resultant clustering redshift estimates and present a novel method of color-redshift mapping made possible by the speed of \textsc{The-wiZZ}. Section \ref{sec:discussion} discusses these redshift estimates and \textsc{The-wiZZ} in the context of current surveys. Finally in Section \ref{sec:conclusions} we present our conclusions with an eye toward future surveys such as LSST, Euclid\footnote{\url{http://sci.esa.int/euclid/}}, and The Wide Field Infrared Survey Telescope\footnote{\url{http://wfirst.gsfc.nasa.gov/}} (WFIRST). Throughout this analysis we use the WMAP5 \citep{komatsu09} cosmology for consistency between the code we use for spatial pair finding, \textsc{STOMP}\footnote{Available at: \url{http://github.com/ryanscranton/astro-stomp/}}, and \textsc{The-wiZZ}. The choice of cosmology will, however, have little effect on the resultant clustering-$z$s \citep{newman08, matthews10}. | \label{sec:conclusions} In this work we have presented \textsc{The-wiZZ} an open source clustering redshift estimation code designed to add legacy value to current and future photometric and spectroscopic surveys. The software attempts to make using clustering redshifts as easy as photometric redshifts are by separating out the step of computing the 2-point, cross-correlation statistics required for computing a clustering redshift for a given sample from creating a final clustering-$z$. \textsc{The-wiZZ} is designed for ease of use by end users of current and future surveys and produces clustering redshifts for any subsample of objects without the intervention of a clustering redshift ``expert''. We have shown robust results from both preselecting objects from a catalog (in this case photo-$z$) as well as from a hybrid machine learning-clustering redshift method using \textsc{kdTree}s in color-magnitude space. The results from the photo-$z$ selection reinforce other work that showed how preselecting objects in narrow redshift regions helps mitigate the effect of galaxy bias in clustering redshifts \citep{menard13, schmidt13, rahman16b, scottez16}. The \textsc{kdTree} clustering redshift method also shows robust results for estimating the redshift of individual galaxies. Such clustering redshifts are very interesting for survey users studying individual or small samples of objects and could possibly be used as priors for future photometric redshift codes. Assuming that one can measure narrow-peaked redshift distributions for a sample of individual objects one could use this sample as a training set for photo-$z$s. This will be especially useful for high redshift, faint objects that will likely not have an observable spectra even on future 30-meter class telescopes. \textsc{The-wiZZ} will be an extremely useful clustering redshift code for future photometric surveys such as LSST, Euclid, and WFIRST given its speed and flexibility. These surveys are planning to rely at least in part on clustering redshifts to reach the precision required of their redshift distributions \citep{newman15} and a public code such as \textsc{The-wiZZ} can fit perfectly into these surveys collaborative software development environments. Future spectroscopic efforts such as the Dark Energy Spectroscopic Instrument \footnote{\url{http://desi.lbl.gov/}} (DESI), Prime Focus Spectrograph\footnote{\url{http://sumire.ipmujp/en/}} (PFS), and the 4-metre Multi-Object Spectroscopic Telescope\footnote{\url{http://www.4most.eu/}} (4MOST) will soon provide the reference catalogs needed for this goal. The code will likely require an amount of optimization in both the \textsc{pair\_maker} and \textsc{pdf\_maker} modules to minimize the size of the data file and reduce the run time per-core further. However given the relatively simple nature of the algorithm we have no doubt such optimizations will be found. We will continue to develop \textsc{The-wiZZ} over the years before these surveys begin taking data to maximize its impact. Future development may also include a web based tool to allow users to request the distributions for a given sample or incorporating \textsc{The-wiZZ} into \textsc{SQL} catalog requests. These tools will be extremely useful and will speed up the adoption of clustering redshifts within the community. \textsc{The-wiZZ} will continue to be developed on \textsc{GitHub}\footnote{\url{http://github.com/morriscb/The-wiZZ/}}. If for some reason \textsc{GitHub} closes or \textsc{The-wiZZ} is moved to a new repository contact the authors\footnote{E-mail: [email protected]} for the location of the current repository. | 16 | 9 | 1609.09085 |
1609 | 1609.04863_arXiv.txt | { The core region of a neutron star may feature quark matter in the color-flavor-locked (CFL) phase. The CFL condensate breaks the baryon number symmetry, such that the phenomenon of superfluidity arises. If the core of the star is rotating, vortices will form in the superfluid, carrying the quanta of angular momentum. In a previous study we have solved the question of stability of these vortices, where we found numerical proof of a conjectured instability, according to which superfluid vortices will decay into an arrangement of so-called semi-superfluid fluxtubes. Here we report first results of an extension of our framework that allows us to study multi-vortex dynamics. This will in turn enable us to investigate the structure of semi-superfluid string lattices, which could be relevant to study pinning phenomena at the boundary of the core. } | \label{intro} In its densest form, matter appears in the color-flavor locked (CFL) phase \cite{Alford:1997zt}. The CFL condensate breaks the baryon number symmetry, which renders this phase a superfluid. If this form of matter is present in the core region of a rotating neutron star, vortices will carry the angular momentum of the spinning core. In a recent study \cite{Alford:2016dco}, we addressed the question of stability of these superfluid vortices, using a Ginzburg-Landau effective theory. There, from a topological point of view, stable vortex solutions are expected, since the first homotopy group of the vacuum manifold is non-trivial \cite{Balachandran:2005ev}. However, the global vortex solution does \textit{not} possess the lowest energy, and it has been conjectured that the vortex undergoes a decay into a configuration of a triplet of well-separated semi-superfluid strings \cite{Nakano:2007dq}. In our study \cite{Alford:2016dco}, we not only observed and numerically confirmed this decay, but we also mapped out the stability-/metastability boundary in the parameter space of the couplings. We furthermore identified an analytically constructed mode that proved to be sufficient to trigger the decay of a global vortex. Let us briefly review our findings here. Assuming $m_u=m_d=m_s=0$, the Ginzburg-Landau Lagrangian of the effective theory reads \beq \label{Lagrangian} \Lagr = \Tr \left[-\frac{1}{4} F_{ij} F^{ij} + D_{i} \Phi ^{\dagger} D^{i} \Phi + m^2 \Phi ^{\dagger} \Phi - \lambda_{2} (\Phi ^{\dagger} \Phi)^2 \right] - \lambda_{1}(\Tr[\Phi^{\dagger} \Phi])^2 + \dfrac{3m^{4}}{4\lambda}\ , \eeq where $D_{i} = \partial_{i} - i g A_{i}$ is the covariant derivative, $F_{ij} = \partial_{i} A_{j} - \partial_{j} A_{i} - ig \left[ A_{i},A_{j} \right] $ is the gauge field-strength tensor, and the $A_{i}$ represent the gauge fields (gluons). The coupling $\lambda$ is a linear combination of the original self-couplings of the condensate, \beq \label{eq:lambda_def} \lambda \equiv 3 \lambda_{1} + \lambda_{2}. \eeq The matter field $\Phi$ represents the CFL condensate, and has a $3_c\times3_f$ complex matrix structure. A general entry of the $\Phi$ matrix is thus characterized by a color index $\alpha$ and a flavor index $a$, $\phi_{\alpha a}$. In the broken phase, the vacuum expectation value (vev) is given by \beq \label{eq:vev} A_i = 0 \ , \quad \Phi = \bar \phi \textbf{1}_{3 \times 3} \ , \quad \bar\phi = \sqrt{\frac{m^2}{2 \lambda}} \ . \eeq A (global) \textit{superfluid vortex} can then be written as \beq \label{eq:superfluid_solution} A_i = 0 \ ,\quad \Phi_{\mathrm{sf}} = \bar\phi\, \beta(r) e^{i \theta} \,\textbf{1}_{3 \times 3} \ , \eeq where $\beta(r)$ is the radial profile obtained from solving \beq \label{eq:radial_profile} \beta^{''} + \frac{\beta^{'}}{r} - \frac{\beta}{r^{2}} - m^{2} \beta (\beta^{2} - 1) = 0 \ , \eeq with the boundary conditions $\beta \rightarrow 0 \ \mathrm{as} \ r \rightarrow 0 \ $, and $\beta \rightarrow 1 \ \mathrm{as} \ r \rightarrow \infty \ $. A (red) \textit{semi-superfluid flux tube}, on the other hand, can be written as \beq \label{SemisuperfluidSoln} \Phi_{\rm ssft}(r, \theta) = \bar\phi\, \left(\ba{ccc}f(r){\rm e}^{i \theta} & 0 & 0 \\ 0 & g(r) & 0 \\ 0 & 0 & g(r) \ea \right), \eeq \beq A^{\rm ssft}_{\theta}(r) = - \dfrac{1}{gr} ( 1-h(r)) \left(\ba{ccc}-\frac{2}{3} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & \frac{1}{3} \ea \right), \eeq \beq A^{\rm ssft}_{r} = 0 \ . \eeq and the solutions for the green and blue flux tubes follow from swapping the diagonal elements of the matrix. The profile functions $f(r)$, $g(r)$ and $h(r)$ obey a set of coupled differential equations, see equations (10)-(14) in \cite{Alford:2016dco}. As discussed in our paper, far from the core of the vortex, the energy density of one semi-superfluid flux tube is one ninth of the energy density of a global vortex, \beq \ba{rcl} \eps_{\rm sf} &=& 3 \bar\phi^2/r^2, \\[1ex] \eps_{\rm ssft} &=& \third \bar\phi^2/r^2, \ea \label{eq:edens} \eeq which is the cause of the instability. In the case of vanishing gauge coupling, we identified an unstable mode analytically, \beq \ba{rcl} \delta \Phi^{(8)} &=& \eps\, \hat n\!\cdot\!\nabla \psi(r,\th)\, T_8 \ . \\[1ex] \ea \label{eq:unstable-mode} \eeq This mode establishes a distortion of the red and green components of the vortex by a small amount $\eps$ in direction of the unit vector $\hat n$, while shifting the blue component by an amount of $2\eps$ in the opposite direction. This perturbation of the global vortex can be plugged into the Hamiltonian density, and the change in energy density evaluates to \beq\label{eq:prediction} \delta E_{8} = \epsilon^{2} (\lambda_{2} -\lambda) \dfrac{\pi m^4 }{\lambda^{2}} \int_{0}^{\infty} \! r \mathrm{d}r \beta^{'2} \beta^{2} \ . \eeq For $\lambda_2>\lambda$, this clearly lowers the energy and is thus an unstable direction. Depending on the gauge coupling $g$ and the condensate self-couplings $\lambda_1$ and $\lambda_2$, there are regions in parameter space where the global vortex solution is unstable and decays immediately, but we could also identify regions of meta-stability, see Figures \ref{fig:parameter_space_scan_plot} and \ref{fig:parameter_space_contour_plot}. In Figure \ref{fig:parameter_space_contour_plot}, the solid line corresponds to the instability boundary in parameter space as derived from the perturbation (\ref{eq:unstable-mode}), which seems to hold approximately for small gauge couplings. \begin{figure} \bc \includegraphics[width=0.5\hsize]{parameter_space_scan_plot.pdf} \caption{The parameter space of the couplings $g$, $\lambda$ and $\lambda_2$. Points behind the surface form the region of meta-stability, all other points constitute the region of instability.} \label{fig:parameter_space_scan_plot} \ec \end{figure} \subfiglabelskip=0pt \begin{figure*} \centering \subfigure[][]{ \label{fig:parameter_space_contour_plot_a} \includegraphics[width=0.40\hsize]{g_slice_plot_a.pdf} }\hspace{8pt} \subfigure[][]{ \label{fig:parameter_space_contour_plot_b} \includegraphics[width=0.40\hsize]{g_slice_plot_b.pdf} }\\ \subfigure[][]{ \label{fig:parameter_space_contour_plot_c} \includegraphics[width=0.40\hsize]{g_slice_plot_c.pdf} } \hspace{8pt} \subfigure[][]{ \label{fig:parameter_space_contour_plot_d} \includegraphics[width=0.40\hsize]{g_slice_plot_d.pdf} } \caption[]{Slices through the parameter space of the couplings for different values of $g$. The shaded area is the region of meta-stability, its complement constitutes regions of instability. The dashed line is the projection of the plane of weak-coupling results, see text. The solid line represents $\lambda=\lambda_2$, which, in the case of vanishing gauge coupling, should yield the boundary of stability/meta-stability. Note that the metastability region can be characterized by $\lambda_1\lsim -0.16g$. For fixed values of $g$ and $\lambda_1$, a change in $\lambda_2$ has almost no effect on the stability boundary.} \label{fig:parameter_space_contour_plot} \end{figure*} The dashed line in Figure \ref{fig:parameter_space_contour_plot} corresponds to the region in parameter space where $\lambda_1=\lambda_2$. This has been identified as the physically relevant regime at ultra-high density, where the coupling is sufficiently small to allow for mean-field calculations, \cite{Iida:2000ha,Giannakis:2001wz}, \beq \label{LambdaExpressions} \lambda_{1} = \lambda_{2} = \dfrac{\lambda}{4} = \dfrac{36}{7} \dfrac{\pi^4}{\zeta(3)} \left(\dfrac{T_{c}}{\mu} \right) ^{2}.\eeq If this result can be extrapolated to densities where the system is strongly coupled, our study indicates that there are no regions of metastability for the physically relevant case. This is supported by the fact that the region of metastability dies away quickly with increasing coupling $g$. | \label{sec-3} In this progress report we have reviewed our findings from our previous study \cite{Alford:1997zt}, where we have found numerical proof of the instability of superfluid vortices in CFL quark matter. We identified regions of stability and metastability in the parameter space of the couplings, and connected our result to the physically relevant regime by extrapolating weak coupling results. This indicates that superfluid vortices are unstable in CFL quark matter. An analysis of the coupling dependence of the stability/metastability boundary revealed that it seems to be independent of the coupling $\lambda_2$, which raises the question of the role of the condensate self-couplings in the decay process. We also constructed a mode that is sufficient to trigger the decay of a superfluid vortex into the triplet of semi-superfluid fluxtubes. The phenomenological consequences of the instability, for example on neutron star glitches, remain elusive for now, since that requires a thorough understanding of a pinning mechanism. As a first step towards a better understanding of the dynamics of a system with high vorticity we extended our framework and presented first results for the time evolution of a multi-superfluid-vortex system. We modified the boundary conditions slightly, which allows for a better initial setting of a multi-vortex state, and simulated a system of 90 superfluid vortices in a controlled and stable way. Because it is numerically less expensive, we started with the zero-gauge coupling case, and focused on the stable regime of condensate self-couplings. As a next step, we intend to study the non-zero gauge coupling case. This is numerically more expensive, since, on the lattice, gauge fields are represented as link variables corresponding to group elements, and their time evolution involves a matrix exponential. In order to speed up the code, we thus plan to use Graphics Processing Units (GPUs), which allows for much faster evolution on larger lattices. | 16 | 9 | 1609.04863 |
1609 | 1609.04264_arXiv.txt | We have investigated the photo-stability of pristine and super-hydrogenated pyrene cations (C$_{16}$H$_{10+m}^+, m = 0,6, \mathrm{\ or\ }16$) by means of gas-phase action spectroscopy. Optical absorption spectra and photo-induced dissociation mass spectra are presented. By measuring the yield of mass-selected photo-fragment ions as a function of laser pulse intensity, the number of photons (and hence the energy) needed for fragmentation of the carbon backbone was determined. Backbone fragmentation of pristine pyrene ions (C$_{16}$H$_{10}^+$) requires absorption of three photons of energy just below 3 eV, whereas super-hydrogenated hexahydropyrene (C$_{16}$H$_{16}^+$) must absorb two such photons and fully hydrogenated hexadecahydropyrene (C$_{16}$H$_{26}^+$) only a single photon. These results are consistent with previously reported dissociation energies for these ions. Our experiments clearly demonstrate that the increased heat capacity from the additional hydrogen atoms does not compensate for the weakening of the carbon backbone when pyrene is hydrogenated. In photodissociation regions, super-hydrogenated Polycyclic Aromatic Hydrocarbons (PAHs) have been proposed to serve as catalysts for H$_2$-formation. Our results indicate that carbon backbone fragmentation may be a serious competitor to H$_2$-formation at least for small hydrogenated PAHs like pyrene. | Molecular hydrogen (H$_2$) is the smallest and most abundant molecule in the universe. Further, H$_2$ is the key to star formation and the starting point for the gas-phase chemistry of the interstellar medium (ISM) \citep{Tielens2005}. Polycyclic Aromatic Hydrocarbons (PAHs), along with fullerenes like C$_{60}$ \citep{Cami2010,Campbell2015}, may be among the largest molecules in the ISM. As a class, PAHs are widely believed to be responsible for the ubiquitous infrared emission bands observed throughout the ISM \citep{Tielens2008}. Despite their difference in size and complexity, the origin and fate of H$_2$ and PAHs may be closely intertwined in certain regions. Elevated H$_2$ formation rates have been observed in photodissociation regions (PDRs) with high PAH abundances \citep{Habart2003,Habart2004}. This has led to the suggestion \citep{BauschlicherJr1998,Hirama2004} that PAHs may play a role as catalysts for H$_2$ formation in PDRs. It is, however, hard to understand how PAHs could survive in such harsh environments with strong UV-radiation. As a solution to this problem, \citet{Reitsma2014} recently suggested that PAH carbon backbones could be protected by the addition of hydrogen atoms and thus be able to catalyze H$_2$ formation in PDRs. Super-hydrogenated PAHs (HPAHs), which contain additional H atoms beyond the native hydrogen already present in pristine PAHs, may, as indicated above, play an important role in molecular hydrogen formation \citep{Menella2012}. Formation of HPAHs should be efficient as the energy barriers for binding additional H atoms to PAHs are in most cases very low or even non-existent \citep{Rauls2008,Cazaux2016}. Highly hydrogenated species (up to and including fully saturated HPAHs) have indeed been produced in different laboratory experiments in which PAHs are bombarded with low-energy hydrogen or deuterium atoms \citep{Thrower2012,Boschman2012,Klaerke2013,Cazaux2016}, or through interaction with hydrogenated carbon surfaces \citep{Thrower2014}. Highly efficient H$_2$ emission from HPAHs has also been reported in infrared multi-photon dissociation \citep{Vala2009,Szczepanski2010} and UV matrix isolation spectroscopy experiments \citep{Fu2012}. This is in contrast to pristine PAHs, where single H-loss (although it is energetically disfavored \citep{Paris2014}) is much more common than H$_2$-loss at the excitation energies that are relevant in PDRs \citep{West2014,Chen2015} While serving as nurseries for H$_2$ formation, HPAHs may also be protected by the additional H atoms. When excited by photo-absorption or through a collisions with energetic particles, HPAHs may relax by boiling off the weakly-bound excess H atoms, perhaps in the form of H$_2$. The existence of such a protective effect was inferred from the pioneering experiments by \citet{Reitsma2014}, where super-hydrogenated coronene cations (C$_{24}$H$_{12+m}^+; m=$ 0–-7) were found to lose fewer of their native H atoms than pristine coronene following core-electron excitation by soft x-rays. However, collision induced dissociation (CID) experiments by \citet{Gatchell2015} showed that super-hydrogenation of a smaller PAH, pyrene (C$_{16}$H$_{10+m}^+, m=0, 6, 16$), leads to a strong increase in the cross section for carbon backbone fragmentation. An earlier study of the photo-stability of small PAHs found that super-hydrogenation was associated with a greatly reduced barrier to single H-loss \citep{Jochims1999}. Although this work did not investigate H$_2$-formation or backbone fragmentation, it clearly indicated that single-H loss is an even stronger competitive channel for super-hydrogenated than for pristine PAHs. At a first glance this appear to speak in favor of the suggestion by \citet{Reitsma2014} as HPAH molecules would cool very efficiently by emission of the additional H-atoms. Competition between hydrogen emission and backbone fragmentation may, however, depend on additional factors such as the size of the underlying PAH, the site(s) of hydrogenation, or the details of the excitation mechanisms. Is there, for example, a difference in the fragmentation of HPAHs excited with photons or in collisions with ions or atoms? In the case of x-ray excitation, highly electronically excited HPAH dications are formed as intermediaries and one may ask how the amount of internal excitation energy influences the fragmentation. Indeed it has been shown that the branching between H-loss and backbone fragmentation is highly sensitive to the internal excitation energy in other experiments on PAH dications \citep{Martin2012,Bredy2015}. In the CID experiments by \citet{Gatchell2015} and \citet{Wolf2016}, hydrogenated or pristine pyrene cations collided with He atoms at center-of-mass energies of 30--200~eV, simulating PAH-processing by supernova shocks \citep{Micelotta2010}. Collisions in this energy range activate nuclear motion directly in Rutherford-like scattering on the individual atoms in the molecule while they do not lead to significant electronic excitation or ionization. In this article, we present action spectroscopy measurements in which gas-phase pristine or hydrogenated pyrene cations (see Figure~\ref{fig: ELISA}) undergo fragmentation following the absorption of one or more optical photons with energies slightly below 3~eV. This mimics the conditions in the PDRs. We find that hydrogenation leads to larger, not smaller, rates of PAH carbon backbone fragmentation. This is clearly demonstrated by measurements of the backbone fragmentation yields as functions of laser power, from which we find the average number of absorbed photons needed to induce fragmentation. Pristine pyrene cations (C$_{16}$H$_{10}^+$) must absorb three photons for carbon backbone fragmentation, super-hydrogenated hexahydropyrene (C$_{16}$H$_{16}^+$) must absorb two, while the fully hydrogenated hexadecahydropyrene (C$_{16}$H$_{26}^+$) fragments after absorbing a single photon. Taken together with earlier collision experiments \citep{Gatchell2015,Wolf2016} and quantum chemical calculations \citep{Gatchell2015}, these results lead to clear conclusions. Regardless of the excitation mechanism, weakening of the carbon skeleton of small PAHs (by converting aromatic bonds to aliphatic ones) is more important than the cooling due to evaporation of additional H atoms in HPAHs. | \subsection{Action Spectra} \begin{figure}[ht!] \epsscale{1.2} \plotone{f2} \caption{Measured prompt (filled symbols) and delayed (open symbols) action spectra of C$_{16}$H$_{10+m}^+, m = 0,6, \mathrm{\ and\ }16$. The neutral fragment yield includes carbon backbone fragmentation as well as pure hydrogen losses. \label{fig: wavelengths}} \end{figure} In Figure~\ref{fig: wavelengths} we show the prompt and delayed action spectra of C$_{16}$H$_{10+m}^+ (m = 0,6, \mathrm{\ and\ }16$) measured at ELISA. The spectra have been corrected for the variation in the laser power across the spectral range and for the photon number dependence. This is achieved by dividing the background-corrected action signal at each wavelength by the number of photons per laser shot (the laser pulse energy divided by the photon energy) raised to the power of $n$, the number of photons absorbed in the dissociation process (determined in Section \ref{sec_powdep}, indicated in the Figure). It is non-trivial to extract the intrinsic absorption cross section from such a multi-photon dissociation action spectrum \citep{Wellman2015}, and clear interpretations of detailed band shapes are difficult. The prompt action spectrum of pristine pyrene (C$_{16}$H$_{10}^+$, top panel) has a maximum at 450~nm. Delayed action with a dissociation lifetime of about 100~$\mu$s was observed, but the signal was quite weak. Previous gas-phase measurements of \textit{cold} pyrene cations in a supersonic expansion by \citet{Biennier2004} found an absorption band maximum at 436~nm. In a cold Ne matrix, this band is somewhat shifted to 440~nm \citep{Salama1993}. Multi-photon dissociation experiments performed by \citet{Useli-Bacchitta2010} using an ion trap observed the 436~nm band as well as a feature at 450~nm which was interpreted as a hot band. This is presumably the feature we observe in the present spectrum of room-temperature pyrene cations. For C$_{16}$H$_{16}^+$ (middle panel), dissociation occurs with a lifetime of hundreds of $\mu$s. In the delayed action spectrum, a broad band with a maximum near 570~nm is observed. This band is also seen in the prompt action spectrum, where the dissociation yield is biased towards blue wavelengths. The absorption spectrum of C$_{16}$H$_{16}^+$ has not been reported previously, though it may be expected to resemble that of the naphthalene cation (C$_{10}$H$_8^+$) due to its similar $\pi$-orbital structure \citep{Halasinski2005}. Naphthalene has electronic transitions with origins near 670 and 455~nm \citep{Romanini1999, Pino1999}. Differences between prompt and delayed action spectra, whereby fragmentation induced by low-energy photons is observed on longer timescales than that induced by higher energy photons, are not uncommon in action spectroscopy experiments \citep{Lifshitz2002} and show the value of using an ion storage ring like ELISA to observe delayed fragmentation. The band maximum of fully hydrogenated C$_{16}$H$_{26}^+$ (bottom panel in Figure~\ref{fig: wavelengths}) appears to be below the lower limit of our laser's tuning range, but it is clear that the absorption is blue-shifted relative to that of pristine pyrene. In this case the prompt and delayed action (lifetime $\sim 50\ \mu$s) spectra are nearly identical. \subsection{Daughter Ion Mass Spectrometry} \begin{figure}[ht!] \epsscale{1.2} \plotone{f3} \caption{Daughter ion mass spectra (full lines) of C$_{16}$H$_{10+m} (m = 0,6, \mathrm{\ and\ }16)$ when irradiated at the indicated wavelengths with full laser power. Dashed lines are CID mass spectra resulting from collisions with He at 110~eV center-of-mass energy, $E_\text{CM}$ \citep{Gatchell2015}.\label{fig: mass spec}} \end{figure} Fragmentation mass spectra, shown in Figure~\ref{fig: mass spec} (full lines), were recorded using excitation wavelengths near the absorption maxima in Figure~\ref{fig: wavelengths}. For C$_{16}$H$_{16}^+$, experiments were performed with both 420 and 570~nm excitation; the resulting mass spectra were found to be very similar. Carbon backbone fragmentation is clearly visible in all cases. Each peak in the mass spectrum corresponds to daughter ions with different numbers of carbon atoms; it is not possible to resolve individual hydrogenation states. Also shown (dashed gray lines) are mass spectra for these same ions following collisions with He atoms at a center-of-mass energy $E_\text{CM} = 110$~eV previously measured at the DESIREE facility at Stockholm University \citep{Gatchell2015}. This is representative of the processing of PAHs by supernova shocks \citep{Micelotta2010}. Through nuclear stopping processes, such collisions deposit higher excitation energies (up to 40 eV \citep{Stockett2014b,Chen2014}) than the photon energies used at ELISA (below 3~eV), leading to more extensive fragmentation as can be seen in Figure~\ref{fig: mass spec}. For pristine pyrene (C$_{16}$H$_{10}^+$, top panel of Figure~\ref{fig: mass spec}), peaks at masses corresponding to the loss of two and four carbon atoms are observed in the photo-induced dissociation (PID) mass spectrum at 176 and 160~amu. This is in agreement with the well-known tendency of small PAHs to decay via C$_2$H$_2$-emission \citep{Wacks1964,Ekern1998,Holm2010,Lawicki2011}. Notably absent in the PID spectrum for C$_{16}$H$_{10}^+$ are fragments which have lost a single C atom (\textit{i.e.} CH$_x$-loss). In CID such losses are due to non-statistical single carbon knockout \citep{Stockett2014,Stockett2015,Gatchell2014b} and clearly seen in the collision experiments. The mass spectra of C$_{16}$H$_{16}^+$ (middle panel of Figure~\ref{fig: mass spec}) are rather similar for the two experiments, although no fragments having lost four or more C atoms are seen in the PID data, presumably due to the lower excitation energy compared to CID. The presence of a CH$_x$-loss peak in the PID spectrum (around 192~amu) confirms earlier CID results which have shown statistical single carbon loss from HPAHs at collision energies below the knockout threshold \citep{Wolf2016}. For C$_{16}$H$_{26}^+$, the peak near 172~amu corresponding to the loss of three C atoms is much more prominent in the PID case than in the collision experiments, where all the fragment peaks are of similar intensity. \subsection{Laser Pulse Energy Dependence} \label{sec_powdep} \begin{figure}[ht!] \epsscale{1.1} \plotone{f4} \caption{Above: Laser pulse energy dependence of prompt action yields. The exponents found from power-law fits to the data give the average number of photons absorbed in the process. \\ Below: Laser pulse energy dependence of mass-selected daughter ion yields for the most abundant fragments (see Figure~\ref{fig: mass spec})}. \label{fig: power dep} \end{figure} The upper panel of Figure~\ref{fig: power dep} shows the total prompt neutral fragment yield as a function of the laser pulse energy. The excitation wavelengths are very similar and are chosen to be near the prompt action maxima (Figure~\ref{fig: wavelengths}). The yields follow power laws, where the exponents give the average number of photons absorbed \citep{Andersen2004}. For C$_{16}$H$_{16}^+$, we have performed such measurements both at 430~nm and at 570~nm, the maximum of the \textit{delayed} action spectrum. The photon number dependencies for 570~nm (open squares in Figure~\ref{fig: power dep}) were found to be nearly identical to those for 430~nm (closed squares). Fits to the data give photon number dependencies of $2.85\pm0.10$ for C$_{16}$H$_{10}^+$, $1.79\pm0.11$ at 430~nm and $2.09\pm0.12$ at 570~nm for C$_{16}$H$_{16}^+$, and $1.02\pm0.03$ for C$_{16}$H$_{26}^+$. This is consistent with dissociation resulting mainly from three-, two-, and one-photon absorption events, respectively. The yield of the most abundant daughter ion for each molecule (see Figure~\ref{fig: mass spec}) as a function of laser pulse energy is shown in the lower panel of Figure~\ref{fig: power dep}. In each case, the power-law fit to the mass-selected daughter ion yield agrees with the corresponding total prompt action yield. Our experimental results are consistent with density functional theory calculations of the dissociation energies of these ions which have been reported by \citet{Gatchell2015}. Based on the laser pulse energy dependence, the total energy deposited in photo-absorption events leading to backbone fragmentation of C$_{16}$H$_{10+m}^+$ is 8.17~eV ($3\times 2.73$~eV), 5.77~eV ($2\times 2.88$~eV), and 2.95~eV for $m = 0,6, \mathrm{\ and\ } 16$, respectively. The calculated dissociation energies for the most abundant carbon-loss daughter ions are C$_2$H$_2$-loss with 6.30~eV, C$_2$H$_4$-loss with 3.88~eV, and C$_3$H$_6$-loss with 2.19~eV for $m = 0,6, \mathrm{\ and\ } 16$, respectively \citep{Gatchell2015}. While C$_2$H$_2$-loss is the backbone fragmentation channel with the lowest dissociation energy for pristine pyrene, C$_{16}$H$_{16}^+$ and C$_{16}$H$_{26}^+$ have CH$_3$-loss as their lowest dissociation-energy channels at 2.26 and 1.60~eV, respectively \citep{Gatchell2015}. Measurements of the CH$_x$-loss yields give photon number dependencies of $1.69\pm0.12$ and $0.95\pm0.15$ for C$_{16}$H$_{16}^+$ and C$_{16}$H$_{26}^+$, respectively, which are consistent with both the total prompt action and the other, more abundant, daughter ion channels measured for these two molecules. We note that, unlike the more abundant fragmentation channels, CH$_3$-loss requires an H-migration and may thus be slowed down by energy barriers. In the upper panel of Figure~\ref{fig: power dep}, a deviation from power-law behavior is seen for the total fragmentation yield of C$_{16}$H$_{10}^+$ at the lower laser pulse energies. This could be due to a fragmentation channel with a lower activation energy (and hence power dependence), such as H-loss, which has a dissociation energy of 5.16~eV \citep{Gatchell2015}. This is below the excitation energy obtained by absorption of two photons ($2 \times 2.73=5.46$~eV) and together with the initial internal excitation energy of around 1~eV (room temperature value -- see the experimental section) this could give sufficient energy for H-loss on the microsecond timescale. Interestingly this kind of deviation is not seen in the measurement of the yield for the dominant fragmentation channel (C$_2$H$_2$-loss -- see the lower panel of Figure~\ref{fig: power dep}) as a function of laser pulse energy. The reason is, most likely, that the corresponding dissociation energy (6.3~eV) is too high to allow C$_2$H$_2$-loss on sufficiently short time scales. | 16 | 9 | 1609.04264 |
1609 | 1609.01507_arXiv.txt | We report lessons learned during the friendly user block operation period of the new system at the Leibniz Supercomputing Centre (SuperMUC Phase 2). | The new PetaScale System SuperMUC Phase2 consists of 6 Islands of Lenovo’s NeXtScale nx360M5 WCT system each with 512 nodes. Each node contains 2 Intel Haswell Xeon E5-2697v3 processors with 28 cores and 64 GB RAM . The compute nodes are connected via an Infiniband FDR14 network with a non-blocking intra-island and a pruned 4:1 inter-island tree topology. The complete system contains 86,016 cores and 194 TB RAM. The double precision LINPACK Performance was measured as 2.81 PetaFlop/s. Attached to the compute nodes is a parallel filesystem based on IBM’s GPFS with 15 PetaBytes. The system runs Novell’s SUSE Linux Enterprise Edition 11, IBM’s LoadLeveler is used as batch system, Intel's C and Fortran compiler, Intel and IBM MPI and is in operation for selected users since May 12th 2015. For an extensive system description, please see www.lrz.de/services/compute/supermuc/system\_description. | The workshop at LRZ showed that preparation of a simulation campaign is crucial for the success of the project. All aspects like scaling tests, choice of OpenMP/MPI balance, interval for checkpoint and restart files, good preparation of input files, I/O strategy, and risk management have to be addressed. Under these conditions it was possible to use a brand new system like SuperMUC Phase 2 directly after installation and obtain scientific results right from the start. One big advantage of the extreme scale-out workshop was that only one code was running at a time and this code was filling up the whole system. Thus, hardware bugs were much easier to detect and resolve. One especially hard to find bug was a combination of two timeouts and a hardware problem. During normal user operation this error would have been close to impossible to detect because of the low probability of three errors occurring simultaneously for smaller jobs. It also became obvious that MPI is at its limits. The size of the MPI stack is growing on each node and for a system of almost 100,000 cores it occupies a significant amount of memory. The startup time can exceed the range of minutes and become a significant part of the overall run time. One way to overcome this bottleneck is the use of hybrid OpenMP/MPI programming models. However, this implies very deep system knowledge on the user side, since process pinning and the choice of the OpenMP/MPI balance has to be evaluated and decided by the user. Furthermore, I/O strategies have to be developed and tested before the complete system can be used. In the future, I/O libraries which can mediate this task become more and more important. Even for hybrid openMP/MPI set-ups with a single MPI-task per node, problems arise due to internal limit of the MPI send/receive buffer. This limit is caused by the Integer*4 Byte implementation of the MPI index values. Such problems can be overcome by using application internal buffering. | 16 | 9 | 1609.01507 |
1609 | 1609.06920_arXiv.txt | We study cosmological field configurations (solutions) in a model in which the pseudo-scalar phase of a complex field couples to the Pontryagin density of a massive non-abelian gauge field, in analogy to how the Peccei-Quinn axion field couples to the $SU(3)$-color gauge field of QCD. Assuming that the self-interaction potential of the complex scalar field has the typical {\it Mexican hat} form, we find that the radial fluctuations of this field can act as {\it Dark Matter}, while its phase may give rise to tracking {\it Dark Energy}. In our model, Dark-Energy domination will, however, not continue for ever. A new component of dark matter, namely the one originating from the gauge field, will dominate in the future. | Current observations \cite{Planck2015} show that about $95 \%$ of the energy in the universe does not come from visible matter observed in ordinary laboratory experiments, but from a new kind of matter in the form of {\it Dark Energy} and {\it Dark Matter}. Evidence for Dark Matter and Dark Energy comes exclusively from gravitational effects: {\it Dark Matter} was first introduced to account for the missing mass in galaxies \cite{Zwicky, Rubin} and galaxy clusters. Dark Matter has the same gravitational interactions and produces the same gravitational effects as regular matter in the form of a pressure-less gas, but it interacts only very weakly with visible matter and photons. The presence of Dark Matter is required in order to obtain the observed agreement between the angular power spectrum of cosmic microwave background (CMB) fluctuations and the power spectrum of density fluctuations; (see, e.g., \cite{RHBrev} for a discussion of this point). As compared to Dark Matter, far less is known about {\it Dark Energy}. Its presence in the cosmos is required to explain the apparent accelerated expansion of the Universe, as inferred from Supernova observations \cite{Perlmutter, Riess}, and to reconcile the spatial flatness of the Universe, as derived from CMB anisotropy measurements \cite{Planck2015}, with the total energy density due to matter, including Dark Matter, inferred from the observed dynamics of galaxies and galaxy clusters. In order to explain the data provided by these observations, the equation-of-state parameter $w$ of Dark Energy (namely the ratio of pressure to energy density) is now known to be close to $w = -1$. Dark Energy could be due to a \textit{cosmological constant} in Einstein's field equation of the general theory of relativity. It could also be a manifestation of \textit{modified laws of gravity}, which become manifest only on cosmological scales. Or Dark Energy could be caused by a \textit{new matter field} (``quintessence field'') with an unusual equation of state, $w \simeq -1$; (see, e.g., \cite{DEreviews} for recent reviews on the Dark Energy puzzle). In this paper we focus our attention on the third scenario, which we call the {\it quintessence} approach; (see \cite{quintessence} for some original references). A fairly popular candidate \cite{axionDM} for Dark Matter is the {\it invisible axion} \cite{axion, invisible}, a very light pseudo-scalar field originally introduced to solve the {\it strong CP problem} of quantum chromodynamics (QCD) \cite{PQ}. This axion field couples linearly to the instanton (Pontryagin) density of the $SU(3)$-color gauge field of QCD; (it plays the role of a dynamical vacuum angle). If the VEV of the axion field can be shown to vanish the strong CP problem of QCD is solved. It has been postulated recently \cite{us} that {\it Dark Energy} could arise from another pseudo-scalar field, a new axion, that couples linearly to the Pontryagin density of a heavy non-abelian gauge field operating at a high energy scale. The new axion could be conjugate to an anomalous current, $j^{\mu}_{\ell}$, that couples to the gauge field; see, e.g., \cite{Weinberg}. The chiral anomaly would then explain why the axion couples to the Pontryagin density of the gauge field. (One might speculate that the anomalous current is leptonic and the gauge field is the weak $SU(2)$-gauge field.) One of the challenges in the {\it quintessence} approach is to explain why Dark Energy is becoming dynamically important around the present time, and not already in the very early universe, or in the remote future. If a cosmological constant were to be the source of Dark Energy we would be faced with the problem of explaining the precise, \textit{very small} value that the cosmological constant would have to be given in order to explain the observational data. In our {\it quintessence} approach to Dark Energy we want to avoid to be forced to introduce a comparably tiny number by hand. {\it Tracking Quintessence} \cite{tracking} is a way to cope with this problem. In models of tracking quintessence, the energy density of the field responsible for Dark Energy follows the energy density of the dominant matter field until times when a dynamical crossover prevents further decline of its energy density, and Dark Energy becomes the dominant form of energy in the Universe. In \cite{us} we have observed that the coupling of an axion to the Pontryagin density of a massive non-Abelian gauge field can cause slow rolling of the axion field, so that, as a consequence, the equation of state of the axion field is the one required of Dark Energy, and this has yielded an interesting scenario of tracking quintessence. In this paper, we introduce a toy model of a complex field whose phase (angular component) plays the role of a pseudo-scalar axion that is linearly coupled to the instanton density of a massive non-abelian gauge field. This gauge field is invisible below rather high energy scales. Our model appears to describe, at once, Dark Matter and Dark Energy. Both the radial and the angular components of the complex scalar field describe dynamical degrees of freedom. While the radial component leads to Dark Matter, its phase is a source of Dark Energy; (tracking quintessence). If the coupling of the axion to the instanton density of the gauge field were neglected our model would yield a renomalizable quantum field theory, in contrast to the model studied in \cite{us}. The organization of this paper is as follows: In the next section we introduce our model and derive its field equations (of motion). In Section 3 we discuss cosmological solutions of the classical field equations, assuming that the fields only depend on cosmological time. We show how the radial component of the scalar field can play the role of Dark Matter, whereas its phase is a candidate for Dark Energy, for reasons similar to those advanced in \cite{us}. A discussion section concludes our paper. The following notations and units will be used throughout: the cosmological scale factor is denoted by $a(t)$, $z(t)$ is the associated cosmological redshift, and the Hubble expansion rate by $H(t)$; space-time indices are denoted by Greek letters, group indices by latin letters; and we use natural units in which the speed of light, $c$, and Planck's constant, $\hbar$, are set to $1$. | We have proposed a model involving a complex scalar field $\varphi$ that can give rise to both {\it Dark Matter} and {\it Dark Energy}. {\it Dark Matter} is provided by the radial oscillations of the field $\varphi$ about its symmetry breaking minimum, {\it Dark Energy} by the angular variable, which is a new axion. A key feature of our model is a coupling of the axion to the Pontryagin density of a non-abelian gauge field. The field $\varphi$ is introduced in analogy to the Peccei-Quinn scalar of QCD. The phase of $\varphi$ couples to the Pontryagin density of the gauge field. This provides a mechanism for very slow rolling of the angular variable $\theta$, so that $\theta$ can yield {\it Dark Energy}. In turn, the dynamics of $\theta$, assisted by an additional axial chemical potential, induces secular growth of the electric component, $E$, of the gauge field. Once the secular growth term in $E$ starts to dominate over the usual term, the contribution of $\theta$ to the total energy density starts to grow. Thus, $\theta$ is a candidate for {\it tracking quintessence}. In our model, the energy density, $\rho_A$, of the gauge field represents an extra contribution to Dark Matter. For sufficiently large values of the coefficient $\alpha$ one can ensure that $\rho_A$ is negligible at the present time. However, eventually $\rho_A$ will grow faster than the density of Dark Energy. Thus, our model predicts that the period of Dark Energy domination does not continue arbitrarily far into the future. In our setup, the approximate equality of the energy densities in {\it Dark Matter} and {\it Dark Energy} has a natural explanation since the energy densities of the two components are proportional during most of the evolution of the universe (from $t_m$ until $t_{eq}$). For $t_i < t_m$ and for $t_{eq} < t_{sec}$ the contribution of $\theta$ decays relative to that of {\it Dark Matter}, whereas it increases after $t_{sec}$.We need $t_{sec}$ to lie in the interval $[t_{eq}, t_0]$. If $\theta$ is to be a viable candidate for {\it Dark Energy}, it has to be very weakly coupled to electromagnetism \cite{Carroll}. This is why we need to introduce a new gauge field which $\varphi$ couples to. Since, in our setup, {\it Dark Matter} and {\it Dark Energy} belong to the same sector, our model predicts that {\it Dark Matter} has negligible interactions with regular matter. Direct detection of {\it Dark Matter} in accelerator experiments or in underground laboratories would rule out our scenario. In our model, {\it Dark Matter} is coupled to {\it Dark Energy}. This coupling gives rise to interesting predictions on observations, as was studied in toy models of the two dark sectors in \cite{Abdalla} and references therein. Work on this topic is in progress. As for the QCD axion, we have to cope with a potential domain wall problem \cite{DW}. If the values of the potential at field values $\theta = 0$ and $\theta = \pi$ are exactly the same, then if the $\varphi$ field begins in thermal equilibrium and undergoes a symmetry breaking phase transition a network of domain walls will inevitably form by causality \cite{Kibble}. This network would acquire a ``scaling solution'' (the network looks the same at all times when lengths are scaled to the Hubble radius $t$) and would persist to the present time. A single domain wall in our Hubble radius would overclose the universe if the symmetry breaking scale is above roughly $1 {\rm TeV}$; (see e.g. \cite{CSrevs} for reviews of the cosmology of topological defects). We can avoid this domain wall problem in the same way it is avoided for QCD axions. For example, we could slightly lift the potential to make $\theta = 0$ the unique vacuum state. We could also assume that an early period of cosmological inflation provides the causal connections on super-Hubble scales which leads $\varphi$ to fall into the same vacuum state everywhere in the observable part of the Universe. There has been other recent work connecting the two dark sectors in the context of QCD-like theories; see, e.g., \cite{Stephon1} (which is based on \cite{Stephon2}). | 16 | 9 | 1609.06920 |
1609 | 1609.01731_arXiv.txt | In a seminal 1960 Nature article~\citep{bondi1960}, Hermann Bondi presented a new approach to the study gravitational waves in Einstein's theory of general relativity. It was based upon the outgoing null rays along which the waves traveled. It was followed up in 1962 by a paper by Bondi, Metzner and van der Burg~\citep{bondi1962}, in which the details were given for axisymmetric spacetimes. In his autobiography~\cite[page 79]{Bondi1990}, Bondi remarked about this work: ``The 1962 paper I regard as the best scientific work I have ever done, which is later in life than mathematicians supposedly peak''. Soon after, Rainer Sachs~\citep{sachs1962} generalized this formalism to non-axisymmetric spacetimes and sorted out the asymptotic symmetries in the approach to infinity along the outgoing null hypersurfaces. The beautiful simplicity of the Bondi-Sachs formalism was that it only involved 6 metric quantities to describe a general spacetime. At this time, an independent attack on Einstein's equations based upon null hypersurfaces was underway by Ted Newman and Roger Penrose~\citep{np1962,npScolar2009}. Whereas the fundamental quantity in the Bondi--Sachs formalism was the metric, the Newman-Penrose approach was based upon a null tetrad and its curvature components. Although the Newman-Penrose formalism involved many more variables it led to a more geometric treatment of gravitational radiation, which culminated in Penrose's~\citep{penrose1963} description in terms of the conformal compactification of future null infinity, denoted by ${\mathcal I}^+$ (pronounced ``scri plus'' for script I plus). It was clear that there were parallel results emerging from these two approaches but the two formalisms and notations were completely foreign. At meetings, Bondi would inquire of colleagues, including one of us (JW), ``Are you you a qualified translator?''. This article describes the Bondi-Sachs formalism and how it has evolved into a useful and important approach to the current understanding of gravitational waves. Before 1960, it was known that linear perturbations $h_{ab}$ of the Minkowski metric $\eta_{ab} = \mathrm{diag}(-1,1,1,1)$ obeyed the wave equation (in geometric units with $c=1$) \begin{equation} \label{pert_wave} \Big(-\df{^2}{t^2} +\delta^{ij}\df{^2}{y^i\partial y^j}\Big)h_{ab} = 0 \, , \end{equation} where the standard Cartesian coordinates $y^i =(y^1,y^2,y^3)$ satisfy the harmonic coordinate condition to linear order. It was also known that these linear perturbations had coordinate (gauge) freedom which raised serious doubts about the physical properties of gravitational waves. The retarded time $u$ and advanced time $v$, \begin{equation} u = t-r\;\;,\;\; v = t+r\;\;,\;\; r^2 = \delta_{ij} y^i y^j \; , \end{equation} characteristic hypersurfaces of the hyperbolic equations \eqref{pert_wave}, i.e. hypersurfaces along which wavefronts can travel. These characteristic hypersurfaces are also null hypersurfaces, i.e. their normals, $k_a = -\nabla_a u$ and $n_a = -\nabla_a v$ are null, $\eta^{ab} k_a k_b = \eta^{ab} n_a n_b = 0$. Note that it is a peculiar property of null hypersurfaces that their normal direction is also tangent to the hypersurface, i.e. $k^a=\eta^{ab} k_b$ is tangent to the $u=const$ hypersurfaces. The curves tangent to $k^a$ are null geodesics, called null rays, and generate the $u=const$ outgoing null hypersurfaces. Bondi's ingenuity was to use such a family of outgoing null rays forming these null hypersurfaces to build spacetime coordinates for describing outgoing gravitational waves. An analogous formalism based upon ingoing null hypersurfaces is also possible and finds applications in cosmology \citep{Ellisetal.(1985)} but is of less physical importance in the study of outgoing gravitational waves. The new characteristic approach to gravitational phenomenon complemented the contemporary 3+1 treatment being developed by \citet{ADM1961}. | 16 | 9 | 1609.01731 |
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1609 | 1609.01513_arXiv.txt | { The Auger Engineering Radio Array (AERA) is an extension of the Pierre Auger Cosmic-Ray Observatory. It is used to detect radio emission from extensive air showers with energies beyond \SI{E17}{eV} in the \unit[30 - 80]{MHz} frequency band. After three phases of deployment, AERA now consists of more than 150 autonomous radio stations with different spacings, covering an area of about \unit[17]{km$^2$}. It is located at the same site as other Auger low-energy detector extensions enabling combinations with various other measurement techniques. The radio array allows different technical schemes to be explored as well as cross-calibration of our measurements with the established baseline detectors of the Auger Observatory. We report on the most recent technological developments and give an overview of the experimental results obtained with AERA. In particular, we will present the measurement of the radiation energy, i.e., the amount of energy that is emitted by the air shower in the form of radio emission, and its dependence on the cosmic-ray energy by comparing with the measurement of the the well-calibrated Auger surface detector. Furthermore, we outline the relevance of this result for the absolute calibration of the energy scale of cosmic-ray observatories. } | The Auger Engineering Radio Array is the world's largest radio detector for high-energy cosmic rays consisting of 153 autonomously-operating radio stations covering an area of \SI{17}{km^2}. Its location within the Pierre Auger Observatory creates a large scientific potential as air showers are measured with four independent detection techniques simultaneously. The radiation energy of air showers was measured and compared with the accurate cosmic-ray energy information of the Auger surface detector. Furthermore, the radiation energy can be calculated from first principles for an independent determination of the cosmic-ray energy scale. | 16 | 9 | 1609.01513 |
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1609 | 1609.03982_arXiv.txt | Momentum-space curvature, which is expected in some approaches to the quantum-gravity problem, can produce dual redshift, a feature which introduces energy dependence of the travel times of ultrarelativistic particles, and dual lensing, a feature which mainly affects the direction of observation of particles. In our recent arXiv:1605.00496 we explored the possibility that dual redshift might be relevant in the analysis of IceCube neutrinos, obtaining results which are preliminarily encouraging. Here we explore the possibility that also dual lensing might play a role in the analysis of IceCube neutrinos. In doing so we also investigate issues which are of broader interest, such as the possibility of estimating the contribution by background neutrinos and some noteworthy differences between candidate ``early neutrinos" and candidate ``late neutrinos". | The possibility of an energy dependence of the travel times from a given source to a given detector of ultrarelativistic particles (particles whose mass is zero or is anyway negligible) has been motivated in several quantum-gravity-inspired models (see {\it e.g.} Refs.\cite{gacLRR,jacobpiran,gacsmolin,grbgac,gampul,urrutia,gacmaj,myePRL,gacGuettaPiran,steckerliberati} and references therein). It is emerging that the most powerful perspective on this feature is that the relevant models have their momentum space curved (see {\it e.g.} Refs.\cite{bob,principle,kbob,Lateshift,tetradi,SpecRelLoc} and references therein), and an effect dual to redshift produces the energy dependence of travel times. Famously ordinary redshift due to spacetime curvature is such that particles emitted at different times with the same energy by the same source reach the detector with different energy, and with dual redshift the curvature of momentum space induces the feature that ultrarelativistic particles emitted at the same time with different energy by the same source reach the detector at different times. It was recently realized \cite{freidelsmolin,ourlensing,transverseproceedings,stefanobiancolensing} that typically curvature of momentum space also produces, in addition to dual redshift, the effect of ``dual lensing", which affects the direction of detection: just like ordinary spacetime-curvature lensing, with dual lensing the direction by which a particle is detected might not point to where actually the source is located. While dual redshift has been much studied and is at this point rather well understood, for dual lensing there have been so far only a few exploratory studies and several grey areas remain for its understanding. Correspondingly there is nothing much on model building for dual lensing in phenomenology. Aware of these challenges we nonetheless here explore the possibility that dual lensing might play a role in observations by the IceCube neutrino telescope. The prediction of a neutrino emission associated with gamma ray bursts (GRBs) is generic within the most widely accepted astrophysical models~\cite{fireball}. After a few years of operation IceCube still reports \cite{icecubeUPDATEgrbnu} no conclusive detection of GRB neutrinos, contradicting some influential predictions \cite{waxbig,meszabig,dafnebig,otherbig} of the GRB-neutrino observation rate by IceCube. Of course, it may well be the case that the efficiency of neutrino production at GRBs is much lower than had been previously estimated~\cite{small1,small2,small3}. However, from the viewpoint of quantum-gravity/quantum-spacetime research it is interesting to speculate that the IceCube results for GRB neutrinos might be misleading because of the assumption that GRB neutrinos should be detected in very close temporal coincidence with the associated $\gamma$-rays and from a direction which agrees (within errors) with the direction by which the $\gamma$-rays are observed: a sizeable mismatch between GRB-neutrino detection time and trigger time for the GRB could be caused by dual redshift (see Refs.\cite{gacLRR,jacobpiran,gacsmolin,grbgac,gampul,urrutia,gacmaj,myePRL,gacGuettaPiran,steckerliberati} and references therein) and in presence of dual lensing there might also be a directional mismatch. In Ref.\cite{Ryan} we observed that allowing for dual redshift one gets a rather plausible picture in which some of the neutrinos observed by IceCube actually are GRB neutrinos. We here explore the possibility that also dual lensing might play a role in the analysis of IceCube neutrinos. In doing so we investigate issues which are also relevant for more refined analyses of dual redshift, such as the possibility of estimating the contribution by background neutrinos and some noteworthy differences between candidate ``early neutrinos" and candidate ``late neutrinos". | We set the stage for our investigations of dual lensing by revisiting the most significant points of the analysis we recently reported in Ref.\cite{Ryan}, tentatively assuming pure dual redshift. It is convenient to introduce a ``distance-rescaled time delay" $\Delta t^*$ defined as \begin{equation} \Delta t^* \equiv \Delta t \frac{D(1)}{D(z)} \label{tstar} \end{equation} so that (\ref{main}) can be rewritten as \begin{equation} \Delta t^* = \eta \frac{E}{M_{P}} D(1) \pm \delta \frac{E}{M_{P}} D(1) \, . \label{maintwo} \end{equation} This reformulation of (\ref{main}) allows to describe the relevant quantum-spacetime effects, which in general depend both on redshift and energy, as effects that depend exclusively on energy, through the simple expedient of focusing on the relationship between $\Delta t$ and energy when the redshift has a certain chosen value, which in particular we chose to be $z=1$. If one measures a certain $\Delta t$ for a candidate GRB neutrino and the redshift $z$ of the relevant GRB is well known, then one gets a firm determination of $\Delta t^*$ by simply rescaling the measured $\Delta t$ by the factor $D(1)/D(z)$. And even when the redshift of the relevant GRB is not known accurately one will be able to convert a measured $\Delta t$ into a determined $\Delta t^*$ with accuracy governed by how much one is able to still assume about the redshift of the relevant GRB. In particular, even just the information on whether a GRB is long or short can be converted into at least a very rough estimate of redshift. In order to select some GRB-neutrino candidates we need a temporal window (how large can the $\Delta t$ be in order for us to consider a IceCube event as a potential GRB-neutrino candidate) and we need criteria of directional selection (how well the directions estimated for the IceCube event and for the GRB should agree in order for us to consider that IceCube event as a potential GRB-neutrino candidate). We focus \cite{Ryan} on neutrinos with energies between 60 TeV and 500 TeV, allowing for a temporal window of 3 days. We based \cite{Ryan} our directional criteria for the selection of GRB-neutrino candidates on the signal direction PDF depending on the space angle difference between GRB and neutrino: $P(\nu,GRB)=(2\pi\sigma^2)^{-1}\exp(-\frac{|\vec{x}_{\nu}-\vec{x}_{GRB}|^2}{2\sigma^2})$, a two dimensional circular Gaussian whose standard deviation is \begin{equation}\label{sigmas} \sigma=\sqrt{\sigma_{GRB}^2+\sigma_{\nu}^2} \, , \end{equation} where of course $\sigma_{GRB}$ and $\sigma_{\nu}$ denote respectively the uncertainties in the direction of observation of the GRB and of the neutrino. We then request that a GRB-neutrino candidate should be such that the pair composed by the neutrino and the GRB is at angular distance compatible within a 2$\sigma$ region. A key observation of our Ref.\cite{Ryan} is that whenever $\eta$ and/or $\delta$ do not vanish one should expect on the basis of (\ref{maintwo}) a correlation between the $|\Delta t^*|$ and the energy of the candidate GRB neutrinos. Our data set is for four years of operation of IceCube \cite{IceCube}, from June 2010 to May 2014. Since the determination of the energy of the neutrino plays such a crucial role in our analysis we include only IceCube ``shower events" (for ``track events" the reconstruction of the neutrino energy is far more problematic and less reliable \cite{IceCubeBackground,TRACKnogood1}). We have 21 such events within our 60-500 TeV energy window, and we find that 9 of them fit our requirements for candidate GRB neutrinos. The properties of these 9 candidates that are most relevant for our analysis are summarized in Table 1 and Figure 1. \begin{table}[htbp] \centering {\def\arraystretch{0.5}\tabcolsep=3pt \begin{tabular}{c|c|c|l|r|c|c} \hline $\,$ & \!\!\! E \!\!\!\! [TeV] \!\!\! & GRB & z & $\Delta t^*$ [s] & $\,$ & $\,$ \\\hline \hline IC9 & 63.2 & 110503A & 1.613 & 50227 & $\diamond$ & * \\\hline IC19 & 71.5 & 111229A & 1.3805 & 53512 & $\,$ & * \\\hline \multirow{3}{*}{IC42} & \multirow{3}{*}{76.3} & 131117A & 4.042 & 5620 & & $\,$ \\ & & 131118A & 1.497 * & -98694 & $\,$ & * \\ & & 131119A & \,\,\,\,\, ? & -146475 & $\diamond$ & $\,$ \\ \hline IC11 & 88.4 & 110531A & 1.497 * & 124338 & $\,$ & * \\\hline IC12 & 104.1 & 110625B & 1.497 * & 108061 & $\,$ & * \\\hline \multirow{3}{*}{IC2} & \multirow{3}{*}{117.0} & 100604A & \,\,\,\,\, ? & 10372 & & $\,$ \\ & & 100605A & 1.497 * & -75921 & $\,$ & * \\ & & 100606A & \,\,\,\,\, ? & -135456 & & $\,$ \\\hline IC40 & 157.3 & 130730A & 1.497 * & -120641 & $\diamond$ & * \\\hline \multirow{2}{*}{IC26} & \multirow{2}{*}{210.0} & 120219A & 1.497 * & 153815 & $\,$ & * \\ & & 120224B & \,\,\,\,\, ? & -117619 & & $\,$ \\ \hline IC33 & 384.7 & 121023A & \,\, 0.6 * & -289371 & $\,$ & * \\\hline \end{tabular} } \caption{Among the 21 ``shower neutrinos" with energy between 60 and 500 TeV observed by IceCube between June 2010 and May 2014 only 9 fit our directional and temporal criteria for GRB-neutrino candidates, and yet for 3 of them there is more than one GRB to be considered when pairing up neutrinos and GRBs. The last column highlights with an asterisk the 9 GRB-neutrino candidates ultimately selected in our Ref.\cite{Ryan} by our additional criterion of maximal correlation. Additionally here we highlight with a $\diamond$ the 3 cases such that the pair composed by the neutrino and the GRB is at angular distance compatible within a $\sigma$ region (all other candidates are compatible within a 2$\sigma$ region). Also shown in table are the values of redshift attributed to the relevant GRBs: the redshift is known only for GRB110503A, GRB111229A and GRB131117A. GRB111229A and GRB110503A are long GRBs and we assume that the average of their redshifts (1.497) could be a reasonably good estimate of the redshifts of the other long GRBs relevant for our 9 GRB-neutrino candidates. These are the 6 estimated values of redshift $z=1.497^*$, the asterisk reminding that it is a ``best guess" value. For analogous reasons we place an asterisk close to the value of 0.6 which is our best guess for the redshift of the only short GRB in our sample. The first column lists the ``names" given by IceCube to the neutrinos that end up being relevant for our analysis.} \label{table1} \end{table} \begin{figure}[h!] \includegraphics[scale=0.3]{Figura2.pdf} \caption{Points here in figure correspond to the 9 GRB-neutrino candidates highlighted with an asterisk in the last column of Table 1. Blue points correspond to ``late neutrinos" ($\Delta t^*>0$), while black points correspond to ``early neutrinos" ($\Delta t^*<0$).} \end{figure} As visible in Table 1, for some IceCube events our selection criteria produce multiple GRB-neutrino candidates. In Ref.\cite{Ryan} we handled this issue of multiple candidates by focusing on the case that provides the highest correlation. Another issue reflected by Table 1 comes from the fact that for only 3 of the GRBs involved in this analysis the redshift is known. We must handle only one short GRB of unknown redshift, and we assume for it a redshift of 0.6, which is a rather reasonable rough estimate for a short GRB. For some of our long GRBs we do have a redshift determination and we argued in Ref.\cite{Ryan} that consistently with the hypothesis here being tested one should use those known values of redshift for obtaining at least a rough estimate of the redshift of long GRBs for which the redshift is unknown. This is illustrated by the 9 GRB-neutrino candidates marked by an asterisk in table 1: those 9 candidates include 8 long GRBs, 2 of which have known redshift, and we assign to the other 6 long GRBs the average ${\bar{z}}$ of those two values of redshift (${\bar{z}}=1.497$). The correlation between $|\Delta t^*|$ and energy for the 9 GRB-neutrino candidates highlighted in Fig.1 is of 0.951. This is a strikingly high value of correlation but in itself does not provide what is evidently the most interesting quantity here of interest, which must be some sort of ``false alarm probability": how likely it would be to have accidentally data with such good agreement with the expectations of the quantum-spacetime models here contemplated? We proposed in Ref.\cite{Ryan} that one needs to estimate how often a sample composed exclusively of background neutrinos\footnote{Consistently with the objectives of our analysis we consider as ``background neutrinos" all neutrinos that are unrelated to a GRB, neutrinos of atmospheric or other astrophysical origin which end up being selected as GRB-neutrino candidates just because accidentally their time of detection and angular direction happen to fit our selection criteria.} would produce accidentally 9 or more GRB-neutrino candidates with correlation comparable to (or greater than) those we found in data. We did this by performing $10^5$ randomizations of the times of detection of the 21 IceCube neutrinos relevant for our analysis, keeping their energies and directions fixed, and for each of these time randomizations we redo the analysis\footnote{In particular for any given realization of the fictitious GRB-neutrino candidates we identify those of known redshift and use them to estimate the ``typical fictitious GRB-neutrino redshift", then attributed to those candidates of unknown redshift (procedure done separately for long and for short GRBs). When in the given realization of the fictitious GRB-neutrino candidates there is no long (short) GRB of known redshift we attribute to all of them a redshift of 1.497 (0.6).} just as if they were real data. Our observable is a time-energy correlation and by randomizing the times we get a robust estimate of how easy (or how hard) it is for a sample composed exclusively of background neutrinos to produce accidentally a certain correlation result. In the analysis of these fictitious data obtained by randomizing the detection times of the neutrinos we handle cases with neutrinos for which there is more than one possible GRB partner by maximizing the correlation, in the sense already discussed above for the true data. We ask how often this time-randomization procedure produces 9 or more GRB-neutrino candidates with correlation $\geq 0.951$, and remarkably we found that this happens only in 0.03$\%$ of cases. | 16 | 9 | 1609.03982 |
1609 | 1609.09091_arXiv.txt | The time lag between optical and near-infrared continuum emission in active galactic nuclei (AGN) shows a tight correlation with luminosity and has been proposed as a standardisable candle for cosmology. In this paper, we explore the use of these AGN hot-dust time lags for cosmological model fitting under the constraints of the new VISTA Extragalactic Infrared Legacy Survey \veils. This new survey will target a 9 deg$^2$ field observed in $J$- and $Ks$-band with a 14-day cadence and will run for three years. The same area will be covered simultaneously in the optical $griz$ bands by the Dark Energy Survey, providing complementary time-domain optical data. We perform realistic simulations of the survey setup, showing that we expect to recover dust time lags for about 450 objects out of a total of 1350 optical type 1 AGN, spanning a redshift range of $0.1 < z < 1.2$. We use the lags recovered from our simulations to calculate precise distance moduli, establish a Hubble diagram, and fit cosmological models. Assuming realistic scatter in the distribution of the dust around the AGN as well as in the normalisation of the lag-luminosity relation, we are able to constrain $\Omega_\Lambda$ in $\Lambda$CDM with similar accuracy as current supernova samples. We discuss the benefits of combining AGN and supernovae for cosmology and connect the present work to future attempts to reach out to redshifts of $z>4$. | Arguably 10 per cent of all large galaxies host an active galactic nucleus (AGN) in their centre. Given their high luminosities, AGN can be detected from low-redshift out to the early universe at $z>7$. Moreover, on human time scales, AGN are rather predictable with only a few sources turning on or off completely \citep[e.g.][]{Kee12a,Kee12b}. These traits would make them desirable tools for cosmology if their emission were standardisable. Several routes are currently being pursued to establish AGN as standard candles. \citet{Wat11} showed that the known relation between the size of the broad emission line region and AGN luminosity can be used to constrain cosmological parameters \citep[see also][]{Haa11,Cze13,Kin14}. The sizes of these structures are determined using the time lags between the incident radiation and the reaction in the reprocessed emission from the observed region. Alternatively to emission lines, the lag between the optical continuum and the dust continuum correlates with luminosity and can also serve as a standard candle \citep[e.g.][]{Okn99,Okn01,Hon14a,Yos14}. Beyond this, it was proposed to use either the emission line time lags \citep[in combination with interferometry;][]{Elv02}, lag profiles \citep[based on photoionisation modelling;][]{Hor03} or the dust lags \citep[with infrared interferometry;][demonstrated for NGC 4151]{Hon14b} as standard rulers, which set an absolute distance scale to AGN and directly measure the Hubble constant $H_0$. The major advantages of dust time lags as compared to emission line lags are (1) their tighter relation between lag and luminosity, when considering the same set of objects \citep[e.g.][]{Kos14}, and (2) the use of photometry instead of spectroscopy. On the other hand, broad emission line lags can be measured out to redshift 4 or even beyond \citep[e.g.][]{Wat11,Cze13,Kin14,Kin15}. When combined, both AGN standardised candles will explore a large region in redshift space. In this paper, we provide the scientific motivation, foundation, and simulations for using AGN hot-dust time lags as a standard candle in the redshift range $0.1 < z < 1.2$. This range is motivated by the fact that ground-based facilities with $\sim2\micron$ imaging capability can be used for a systematic survey. We focus on the design of the VISTA Extragalactic Infrared Legacy Survey \veils, a new ESO public survey scheduled to run on the 4m VISTA telescope for 3 years starting 2017. In the next section, we will briefly review the physical background of the size-luminosity relation in the near-infrared (IR) and discuss some characteristics as constrained by observations. In Sect.~\ref{sec:distmod}, we will derive the equations to turn lags into distance moduli, which are required to establish a Hubble diagram and fit cosmological models. In Sect.~\ref{sec:sim} we present our simulations of \veils\ AGN light curves and discuss the methods employed to recover time lags. In Sect.~\ref{sec:res} we show the results of our simulations and quantify the constraints on cosmological parameters we can expect from the survey, together with a comparison to type Ia supernovae. Practical challenges and strategies are outlined in Sect.~\ref{sec:chal}. Finally, we summarise our findings and present the broader context and legacy of the \veils\ AGN variability survey in Sect.~\ref{sec:sum}. | \label{sec:sum} In this paper, we introduce a new survey that will observationally establish AGN dust time lags as cosmological standardisable candles. We will utilise time-sampled near-IR $J$- and $Ks$-band data of well-studied extragalactic survey fields and combine them with simultaneous multi-band optical data to determine dust time lags of several hundred unobscured AGN. Here, we simulate the survey and evaluate its power in constraining cosmological parameters. We conclude: \begin{itemize} \item The new \veils \ public survey with VISTA VIRCAM has the capability to fully establish AGN dust time lags as a new standard candle for cosmology. It is complementary to type Ia supernovae and can assess hidden systematics in the same redshift range targeted by current SNe surveys (e.g. DES). \item We showed that the constraints on $\Omega_\Lambda$ obtained from the AGN dust lags will be competitive with type Ia supernovae while improvements in $w$ constraints will require a joint AGN+SNe analysis. Indeed, by combining both standard candles, we will be able to improve current $\Omega_\Lambda$ constraints by $\sim$20\% and by $\sim$10\% for $w$. This opens prospects to further narrow down any potential differences between low-redshift and higher redshift cosmological probes (e.g. BAO, CMB). \item Future efforts in cosmology will focus on higher redshift probes to constrain $w_a$ and $w_0$. The time lag between optical continuum emission in AGN and their broad emission lines will be a key standard candle to reach higher redshifts of $z\sim4$ \citep[e.g.][]{Wat11,Cze13,Kin14}. Since the AGN dust time lags probe exactly the same object class (=unobscured AGN), the dust time lags can provide the low-redshift normalisation for the high-redshift studies. Many of the \veils\ AGN will be monitored with OzDES spectroscopically, which allows for cross-calibration between dust lags and BLR lags and provide the springboard to high redshifts. \end{itemize} One of the most substantial advancements will be an immediate growth in the number of low-redshift standard candles when combining SNe with AGN. For that we will need a cross-calibration reference. \citet{Li11} find a SN Ia rate of $0.54\pm0.12$ per century for a Milky Way-type galaxy at $z=0$. Assuming that the Milky Way mass, luminosity, and Hubble type is typical of a Seyfert AGN-hosting galaxy, and considering an increase of the SNe Ia rate by at least a factor of 3 to redshift 0.5 \citep[see also][]{Li11}, we expect that about $5-15$ of the AGN hosts with an established dust lag in \veils\ will display a SN Ia during the life time of the survey. These galaxies will serve as the basis to merge the low-redshift standard candles. | 16 | 9 | 1609.09091 |
1609 | 1609.05089_arXiv.txt | The exoplanet revolution is well underway. The last decade has seen order-of-magnitude increases in the number of known planets beyond the Solar system. Detailed characterization of exoplanetary atmospheres provide the best means for distinguishing the makeup of their outer layers, and the only hope for understanding the interplay between initial composition chemistry, temperature-pressure atmospheric profiles, dynamics and circulation. % While pioneering work on the observational side has produced the first important detections of atmospheric molecules for the class of transiting exoplanets, important limitations are still present due to the lack of systematic, repeated measurements with optimized instrumentation at both visible (VIS) and near-infrared (NIR) wavelengths. It is thus of fundamental importance to explore quantitatively possible avenues for improvements. In this paper we report initial results of a feasibility study for the prototype of a versatile multi-band imaging system for very high-precision differential photometry that exploits the choice of specifically selected narrow-band filters and novel ideas for the execution of simultaneous VIS and NIR measurements. Starting from the fundamental system requirements driven by the science case at hand, we describe a set of three opto-mechanical solutions for the instrument prototype: 1) a radial distribution of the optical flux using dichroic filters for the wavelength separation and narrow-band filters or liquid crystal filters for the observations; 2) a tree distribution of the optical flux (implying 2 separate foci), with the same technique used for the beam separation and filtering; 3) an 'exotic' solution consisting of the study of a complete optical system (i.e. a brand new telescope) that exploits the chromatic errors of a reflecting surface for directing the different wavelengths at different foci. In this paper we present the first results of the study phase for the three solutions, as well as the results of two laboratory prototypes (related to the first two options), that simulate the most critical aspects of the future instrument. | The exoplanet revolution is well underway. More than 3\,000 extrasolar planets are known today and those which have been well characterised show an astonishing diversity concerning their orbital (period, semi-major axis, eccentricity) and physical (radius, mass, density) parameters; this diversity is related to different formation and evolution histories. The majority of the discovered exoplanets are small-size and low-mass planets. Indeed, planet occurrence rates derived from both radial velocity surveys and the \emph{Kepler} space telescope indicate that small and low-mass planets, i.e. mini-Neptunes, super-Earths and Earth-sized planets, occur far more frequently than giant planets (e.g., Howard et al. 2010\cite{2010Sci...330..653H}~; Fressin et al. 2013\cite{2013ApJ...766...81F}), and they are two-three times more common around M dwarfs than FGK main-sequence stars (Mulders et al. 2015\cite{2015ApJ...814..130M}). In particular, more than 50\% of M dwarfs have at least one planet with $1 \le R_{\rm p} \le 2~\rm R_{\oplus}$ and orbital period $P < 50$~d according to Dressing \& Charbonneau (2015)\cite{2015ApJ...807...45D}~. The frequency of giant planets orbiting solar-like stars is $\sim 5\%$ for $P < 400$~d and decreases to $\sim 1\%$ for $P < 10$~d (e.g., Santerne et al. 2016\cite{2016A&A...587A..64S}), that is for the so-called hot Jupiters (with high equilibrium temperatures, $T_{\rm eq} \gtrsim 1000$~K, given their proximity to the host star). The atmospheres of giant planets can be investigated with different techniques such as i) spectrophotometry and low-dispersion spectroscopy of transits and secondary eclipses from UV to mid-IR, ii) NIR and mid-IR phase curves, iii) high-dispersion spectroscopy, and iv) direct imaging (see, e.g., the reviews by Seager \& Deming 2010\cite{2010ARA&A..48..631S}~, Burrows 2014\cite{2014Natur.513..345B} and Crossfield 2015\cite{2015PASP..127..941C}~, and references therein). In particular, transit spectrophotometry consists in measuring the transit depth (hence the planetary radius) at multiple wavelengths ($\lambda$) to find out at which wavelengths the transit is deeper ($R_{\rm p}$ is larger) and thus the atmosphere is more opaque because of atomic and/or molecular transitions. In such a way, it is possible to obtain the planet's ``transmission spectrum". A theoretical transmission spectrum computed by Fortney et al. (2010)\cite{2010ApJ...709.1396F} is shown in Fig.~\ref{fig:transitfit} (dotted line) for a hot Jupiter with $R_{\rm p}=1.3~R_{\rm Jup}$, $T_{\rm eq} = 2000$~K, and surface gravity $g=25~\rm m~ s^{-2}$; the planetary radius is larger at the wavelength of the sodium and potassium doublets because of absorption of stellar light by these alkali species in the upper planetary atmosphere. Transmission spectra have been obtained with spectrophotometry for more than twenty hot Jupiters orbiting relatively bright host stars ($V < 12.5$) with both space-born facilities mainly onboard the Hubble Space Telescope (HST) and ground-based instrumentation at telescopes with apertures generally larger than 3.5~m (WHT, VLT, GTC, Gemini-South, etc.). Planets with ``inflated" radii (e.g., Baraffe et al. 2014\cite{2014prpl.conf..763B}~) and high temperatures are the most promising targets for atmospheric characterization thanks to their relatively large atmospheric scale heights (defined by $H = kT /\mu_m g$, where $k$ is Boltzmann's constant, $T$ is temperature, $\mu_m$ is mean molecular weight, and $g$ is surface gravity). The results obtained up to now show a surprising diversity of the atmospheres of hot Jupiters. Both Na and K have been detected for several of them but in some cases only one of the two species (Na or K) has been found. Some transmission spectra are ``clear" with possibly distinct pressure-broadened wings of Na and K features (Fischer et al. 2016\cite{2016arXiv160104761F}~); other spectra are dominated by hazes, i.e. clouds composed by small-size particles ($< 0.1~\rm \mu m$) that attenuate the Na and K absorption features and give rise to stronger Rayleigh scattering than clear spectra (e.g., Pont et al. 2013\cite{2013MNRAS.432.2917P}~, Nikolov et al. 2015\cite{2015MNRAS.447..463N}~); clouds with larger particles may flatten to a greater extent the planetary spectra especially in the NIR (Sing et al. 2015\cite{2015MNRAS.446.2428S}~). Moreover, recent observations with the WFC3 on board the HST led to the detection of H$_2$O in the atmosphere of some hot Jupiters but with a variety of absorption amplitudes (e.g., Kreidberg et al. 2014a\cite{2014ApJ...793L..27K}~, Madhusudhan et al. 2014\cite{2014ApJ...791L...9M}~). These H$_2$O varying amplitudes seem to be caused by different levels of obscuration by hazes/clouds rather than primordial water depletion during planet formation (Sing et al. 2016\cite{2016Natur.529...59S}~). However, the composition of these hazes/clouds and the reason why they are present at high altitudes in some exoplanetary atmospheres but not in others are completely unknown. Detections of Na and H$_2$O have been used to determine vertical temperature-pressure profiles (e.g., Sing et al. 2008\cite{2008ApJ...686..667S}~, Stevenson et al. 2014\cite{2014Sci...346..838S}~). In addition to Na, K, and H$_2$O, also TiO and VO are expected to be found in the atmospheres of the hottest giant planets (Fortney et al. 2008\cite{2008ApJ...678.1419F}~) and their presence would leave clear imprints in the transmission optical spectrum but no firm detection has been reported up to now. These species are thought to produce atmospheric temperature inversions according to theoretical models (even though several other compounds have also been suggested), and this prediction might be tested with emission spectroscopy in the near- and mid-IR, in case of TiO/VO detection. Transmission spectra of a few smaller planets, such as Neptune-size planets or mini-Neptunes, have been obtained with spectrophotometry and turned out to be flat, i.e. they do not show any molecular features. For the time being, it is not clear whether such flat spectra are due to high mean molecular weights (H-poor atmospheres) or the presence of hazes/clouds (e.g., Kreidberg et al. 2014b\cite{2014Natur.505...69K}~, Knutson et al. 2014\cite{2014Natur.505...66K}~). Here we report initial results of a feasibility study for the prototype of a versatile multi-band imaging system that exploits the choice of specifically selected narrow-band filters and novel ideas for the execution of simultaneous measurements at VIS \& NIR\footnote{according to the specifications for the NIR observations, sites like Paranal and Dome C (Antarctica) have atmospheric conditions transparent enough at the considered NIR bands (Sect.~\ref{subsec:OptoMechanicalSolutions}).} wavelengths. This instrument will allow us to obtain planetary transmission spectra from $0.35$ to $1.7~\rm \mu m$ and thus search at the same time for Na, K, TiO/VO, and H$_2$O % as well as the presence of hazes and/or clouds, even in a single observing night in some cases\footnote{depending also on the aperture of the telescope on which it will be possibly mounted.}. Therefore it would represent a step forwards with respect to current instrumentation given that multiple observations, sometimes separated by years, with multiple instruments are nowadays required to obtain a transmission spectrum in the same wavelength range. Moreover, simultaneous observations with our prototype will allow us to better correct for nightly (atmospheric and instrumental) variations and for long-term stellar behaviour due to changing starspot coverages, which may affect the derived planetary radius (e.g., Ballerini et al. 2012\cite{2012A&A...539A.140B}~). Only the GROND instrument mounted on the 2.2~m MPI/ESO telescope is capable to-date to undertake truly simultaneous observations at both optical and NIR wavelengths (Greiner et al. 2008\cite{2008PASP..120..405G}). However, the use of standard broad-band filters hampers the interpretation of any radius variation with wavelength (see, e.g, Mancini et al. 2013\cite{2013MNRAS.430.2932M}~, 2014\cite{2014MNRAS.443.2391M}), as most of the effects related to the presence of specific atmospheric compounds are materialized in terms of sharp spikes in $R_{\rm p}(\lambda)$ with widths of 10 nm, or less. Our prototype will be able to carry out simultaneous photometric measurements with ``higher resolution", realized in this case through the adoption of a significant number of {\it ad-hoc} narrow-band filters. | \label{sec:summary} The development of instrumentation specifically designed for the purpose of exoplanets' atmospheres characterization will allow in the future to move from the realm of exploratory work to that of systematic studies enabling the {\it repeatability} of the measurements. Similarly to the case of planet detection in the first place, the best results will be obtained by the implementation of a multi-technique approach, exploiting the potential of low- to high-resolution spectroscopy and very high-precision photometry, both from the ground and in space, and over a broad range of wavelength. We have presented here initial results of an ongoing feasibility study for the prototype of a versatile multi-band imaging system that exploits the choice of $a)$ specifically selected narrow-band filters and b) new ideas for the execution of high-precision simultaneous measurements at VIS $\&$ NIR wavelengths for the systematic characterization of extrasolar planets' atmospheres. The study has been setup with a two-tiered approach focused on $1)$ the development of a scientific simulator aimed at quantifying the performance in the retrieval of the fundamental physical quantity ($R_p$ vs. $\lambda$ ) as a function of instrument parameters, choices for the narrow-band filters, and details of proxies for observing campaigns. The simulator has allowed us to establish the fundamental system requirements driving $2)$ the investigation of a number of opto-mechanical solutions for the prototype. To understand the diversity of the atmospheres of hot Jupiters, that is how their compositions and circulations are related to planet formation, migration, and interactions with the host stars, we need an ever growing number of well-characterised planetary atmospheres. Our prototype may increase to a greater extent the number of well-studied atmospheres of giant planets around solar-like stars and of some Neptunes orbiting late K and M dwarfs. Only this way we will be able to search for correlations of the properties of exoplanetary atmospheres with both stellar and planetary parameters and evolution histories, in order to build a theoretical framework that may be able to explain their diversity. Upon identification of the final instrument design, such an imaging system will become a very important addition to the lot of existing and planned instruments devoted to exoplanets' atmospheric studies, particularly when seen as fundamental complement to lower-resolution spectroscopic measurements from space at IR wavelengths (with e.g. JSWT, ESA's M4 proposed mission ARIEL), as well as higher-resolution ground-based spectroscopy at VIS and NIR wavelengths carried out with e.g., HARPS and its NIR extension NIRPS, the GIARPS (GIANO+HARPS-N) facility, ESPRESSO@VLT, and HIRES@E-ELT. | 16 | 9 | 1609.05089 |
1609 | 1609.03336_arXiv.txt | { With the newest version of our Monte Carlo code for ultra-high-energy cosmic ray (UHECR) propagation, CRPropa 3, the flux of neutrinos and photons due to interactions of UHECRs with extragalactic background light can be predicted. Together with the recently updated data for the isotropic diffuse gamma-ray background (IGRB) by Fermi LAT, it is now possible to severely constrain UHECR source models. The evolution of the UHECR sources especially plays an important role in the determination of the expected secondary photon spectrum. Pure proton UHECR models are already strongly constrained, primarily by the highest energy bins of Fermi LAT's IGRB, as long as their number density is not strongly peaked at recent times. } | \label{intro} Recently the Fermi-LAT collaboration updated their measurements on the isotropic diffuse gamma-ray background (IGRB) and extended it up to 820 GeV~\cite{Ackermann:2014usa}. A possible source for part of the IGRB is secondary electromagnetic cascades initiated by interactions of ultra-high-energy cosmic rays (UHECRs) with the cosmic microwave background (CMB) or the extragalactic background light (EBL). In these same interactions secondary neutrinos can be produced. These neutrinos could possibly contribute to the astrophysical neutrino flux as measured by IceCube~\cite{Aartsen:2015zva}. The UHECR energy spectrum has been measured with unprecedented statistics by the Pierre Auger~\cite{Aab:2015bza,ThePierreAuger:2015rha} (Auger) and Telescope Array~\cite{Jui:2015tac} (TA) collaborations. The UHECR mass measured by these two collaborations can, however, still be interpreted in different ways. While the measurements of Auger show a depth of the shower maximum, $X_{\mathrm{max}}$, indicating an increasingly heavier mass composition for $E \gtrsim10^{18.3}$~eV~\cite{Porcelli:2015pac}, TA results in the same energy range are consistent with a pure proton composition~\cite{Fujii:2015tac}. Despite these differences the $X_{\mathrm{max}}$ measurements are in good agreement with each other~\cite{Unger:2015ptc}. The predictions of different air shower simulation models, however, leave room for varying interpretations of the data. Therefore many UHECR composition models are still viable. However, as shown e.g. in Refs.~\cite{Gavish:2016tfl,Berezinsky:2016jys,Supanitsky:2016gke}, the parameter range of possible pure proton models can be constrained when taking into account the secondary gamma-ray and neutrino production during the propagation of UHECRs from their sources to Earth. Ref.~\cite{Heinze:2015hhp} even claims that the proton dip model is challenged at more than $95\%$ C.L. by the cosmogenic neutrino flux alone. To obtain the predicted cosmogenic gamma-ray and neutrino flux for a certain UHECR model the propagation of UHECRs through the universe, including all relevant interactions with the CMB and EBL, has to be simulated. Here the newest version of our UHECR propagation code, CRPropa version 3~\cite{Batista:2016yrx}, is used to simulate the cosmic ray, electromagnetic cascade and neutrino propagation and obtain predictions for the cosmogenic gamma-ray and neutrino fluxes. CRPropa is a full simulation framework for Monte Carlo UHECR propagation including all relevant interactions for protons as well as for heavier nuclei (photo-meson production, pair production, photodisintegration, nuclear decay and energy reduction due to the adiabatic expansion of the universe). For the electromagnetic cascade propagation the specialized code DINT~\cite{Lee:1996fp}, interfaced and shipped with CRPropa 3, is used. DINT solves the one-dimensional transport equations for electromagnetic cascades initiated by electrons, positrons or photons and includes single, double and triplet pair production, inverse-Compton scattering and synchrotron radiation. | \seclab{Conclusions} Figs.~\ref{fig:Ev} and~\ref{fig:EvSpec} show that the IGRB measured by Fermi LAT is more constraining for UHECR models than the IceCube neutrino measurements. The bin with the highest energy (580-820 GeV) of the IGRB especially provides a strong constraint for pure proton UHECR models. For the scenarios investigated here, only in the case of source densities that are strongly decreasing with redshift (for instance in the case of HSP BL Lacs) is it possible to get a gamma-ray spectrum in agreement with that highest energy bin. With a few more years of data and, perhaps, an extension to even higher energies, Fermi LAT might be able to rule out all realistic UHECR pure proton models. \begin{acknowledgement} I want to thank Rafael Alves Batista and J\"org H\"orandel for helpful discussions and the Auger PC for their suggested corrections. I acknowledge financial support from the NWO Astroparticle Physics grant WARP. \end{acknowledgement} | 16 | 9 | 1609.03336 |
1609 | 1609.08024_arXiv.txt | PSR\,J1723$-$2837 is a ``redback'' millisecond pulsar (MSP) with a low-mass companion in a 14.8\,h orbit. The system's properties closely resemble those of ``transitional'' MSPs that alternate between spin-down and accretion-powered states. In this paper we report on long-term photometry of the 15.5\,mag companion to the pulsar. We use our data to illustrate that the star experiences sporadic activity, which we attribute to starspots. We also find that the companion is not tidally locked and infer $P_{\rm s}/P_{\rm b}= 0.9974(7)$ for the ratio between the rotational and orbital periods. Finally, we place constraints on various parameters, including the irradiation efficiency and pulsar mass. We discuss similarities with other redback MSPs and conclude that starspots may provide the most likely explanation for the often seen irregular and asymmetric optical lightcurves. | \label{sec:intro} Targeted radio searches towards Fermi-LAT unclassified point sources have unravelled numerous millisecond pulsars (MSPs) with non-degenerate companions \citep[][]{rob13}. Their defining properties include radio eclipses around superior conjunction (i.e. when the pulsar is behind the companion), $\gamma-$ and X$-$ray emission, rapid orbital-period modulations \citep{akh+13}, and strong optical variability. This rich phenomenology suggests that the pulsar companions are losing mass, thereby providing a unique opportunity to probe accretion physics and stellar evolution in the presence of a strong external heating source. Eclipsing MSPs are commonly classified as either ``black widows'' or ``redbacks'', depending on the mass of the companion ($m_{\rm c}$ of up to few $10^{-2}$\,M$_{\odot}$, and $m_{\rm c}\simeq 0.2-0.7$\,M$_{\odot}$ respectively). Even though the origin and evolution of these systems remain ambiguous \citep{cct+13,bdh+14}, the relative population sizes suggest that the two subclasses are not directly linked, but rather represent stable endpoints of distinct evolutionary paths \citep{cct+13}. This argument is somewhat challenged by recent observations illustrating that redback MSPs can transition between a spin-down radio MSP state and a low-mass X$-$ray binary (LMXB) state \citep{asr+09}. State changes have now been observed in three binaries, with recurrence time-scales of order few years \citep{asr+09,pfb+13, sah+14,pah+14,bph+14,bpa+14, tya+14,rrb+15}. According to the prevailing theory, transitions are likely driven by irradiation feedback on the companion, which alters its size and mass-loss rate, triggering propeller-type instabilities on an accretion disk \citep[see discussion in][]{pah+14}. Indeed, for most known redback MSPs the companion luminosity modulates strongly with the orbital period, presumably due to the varying view of a heated area on the stellar surface \citep[e.g.][]{bvr+13,dcm+14,bkb+16,rmg+15,drc+16}. Thus far however, interpretation of redback lightcurves has been proven challenging. For instance, models in which the companion's side facing the pulsar is directly heated by the pulsar wind do not adequately describe the asymmetries and phase-dependence of the observed ``day/night'' variations \citep[e.g.][]{rmg+15,drc+16}. Among alternatives, the most viable option appears to be a modified geometry in which the pulsar wind is reprocessed by intra-binary shocks, the presence of which is suggested by phase-resolved {X}-ray observations. \cite{rs16} recently demonstrated that one can introduce an arbitrary degree of asymmetries in the lightcurve, if the reflected radiation is modelled self-consistently. Their model seems to improve model fits substantially, at least in the case of PSR\,J2215+5135, a redback MSP with a lightcurve well-sampled in binary phase. Still, numerous questions remain. For instance, the intra-binary shock model does not provide a explanation for the often seen secular changes in average flux. Also, its long-term self-consistency remains to be tested as, thus far, most redback lightcurves have been sampled over a limited number of orbital cycles. Herein we present long-term optical photometry of PSR\,J1723$-$2837, a 1.86\,ms redback MSP in a 14.8\,h orbit around a main-sequence-like companion. PSR\,J1723$-$2837 was discovered in the Parkes Multibeam survey in 2004 \citep{fsk+04}. In a long-term radio-timing study, \cite{cls+13} find that the system shares common properties with transitional MSPs, including irregular radio eclipses around superior conjunction and timing noise suggestive of tidal interactions between the pulsar and its Roche-lobe filling companion. The system has a bright ($V_{\rm mean}\simeq15.5$\,mag) optical counterpart, making it an ideal case-study for redback MSPs. We use our data to illustrate that the companion star experiences periods of increased surface activity, leading to variability modulated at the rotational period, which is not synchronized with the orbital period. This behaviour can fully account for the (transient) asymmetries seen over individual orbital cycles. | 16 | 9 | 1609.08024 |
|
1609 | 1609.03100_arXiv.txt | Pickup ions are created when interstellar neutral atoms resonantly exchange charge with the solar wind (SW) ions, especially in the supersonic part of the wind, where they carry most of the plasma pressure. Here we present numerical simulation results of the 3D heliospheric interface treating pickup ions as a separate proton fluid. To satisfy the fundamental conservation laws, we solve the system of equations describing the flow of the mixture of electrons, thermal protons, and pickup ions. To find the density and pressure of pickup ions behind the termination shock, we employ simple boundary conditions that take into account the \emph{Voyager} observations that showed that the decrease in the kinetic energy of the mixture at the termination shock predominantly contributed to the increase in the pressure of pickup ions. We show that this model adequately describes the flow of the plasma mixture and results in a noticeable decrease in the heliosheath width. | The solar wind (SW) interaction with the local interstellar medium (LISM) is strongly affected by charge exchange between ions, predominantly protons, and neutral atoms, predominantly neutral hydrogen (H). The importance of charge exchange had been acknowledged before the first quantitative model of the SW--LISM interaction was put forward \cite{1969Natur.223..936B,1971NPhS..233...23W,1975Natur.254..202W,1977Holzer}. The reason for this is based on the partial ionization of the LISM. In particular, the neutral H density in the LISM is about three times greater than the proton density. In principle, there is no direct measurement of latter density because the plasma instrument onboard \emph{Voyager} 1 (\emph{V}1), which is believed to have been traversing the LISM since July 2012 \cite{Stone-etal-2013,Burlaga147,Krimigis-etal-2013,Webber-McDonald-2013,Burlaga-Ness-2014}. The electron density has been inferred to be about 0.08 cm$^{-3}$ from the plasma wave instrument observations \cite{Gurnett-etal-2013}. The neutral H density in the unperturbed LISM is usually derived from numerical simulations, in particular, to satisfy the condition that the H density be 0.08--0.09 cm$^{-3}$ in the inner heliosphere. These values are related to pickup ion (PUI) measurements by \textit{Ulysses} \cite{2009SSRv..143..163G,2009SSRv..143..177B} and SW ion deceleration at \emph{Voyager} 2 (\emph{V}2) due to charge exchange \cite{2008A&A...491....1R}. PUIs are secondary ions that are born when primary ions experience charge exchange with neutral atoms. As PUIs born from different H atoms in different regions of the SW--LISM interaction have substantially different properties, they should ideally be modeled as multiple populations, e.g., as in \cite{Malama}, and kinetically. The SW--LISM interface is usually, for convenience of interpretation, subdivided into 4 regions: (1) region~0 is in the LISM unperturbed by the presence of the heliosphere; (2) region~1 is the LISM plasma region modified due to the flow deceleration at the heliopause (HP) -- a tangential discontinuity which separates the SW from the LISM, if ideal MHD terminology is used; (3) region~2 is between the HP and the heliospheric termination shock (TS); and (4) region~3 is the supersonic SW. A PUI created in any of these regions experiences the action of an electric field that acts on it in the plasma frame until the PUI bulk velocity becomes equal to the plasma bulk velocity \cite{Parker-1965}. The newly created PUIs form essentially a ring-beam distribution with the speed ranging between 0 and 2$V_\mathrm{SW}$ in the Sun's inertial frame \cite{1976Vsyliunas}. Such distribution function is unstable to a number of instabilities (see \cite{1976Vsyliunas} and references therein), which results in a spherical shell distribution that becomes filled as the SW propagates outwards \cite{Isenberg87,1994JGR....9919229W}. The heliosphere beyond the ionization cavity is dominated thermally by PUIs \cite{Burlaga_etal_1994,Richardson_etal_1995a,Zank-1999,2014ApJ...797...87Z,Zank-2015}. According to~\cite{Decker_etal_2008,Decker_etal_2015}, the inner heliosheath (IHS) pressure contributed by energetic PUIs and anomalous cosmic rays far exceeds that of the thermal background plasma and magnetic field. The IHS here coincides with region~2 introduced above. A number of one-plasma-fluid models \cite{1993JGR....9815157B,Pauls95,2006ApJ...644.1299P,Jacob06,Jacob07,2005A&A...437L..35I,2009SSRv..146..329I,Opher-etal-2006} take into account the effect PUIs by assuming that they are in thermal equilibrium with the background plasma. Although this is not true, the conservation laws of mass, momentum, and energy for the mixture of electrons, ions, and PUIs are still satisfied approximately. According to \cite{2014ApJ...797...87Z,Zank-2015}, such approaches may be correct only if the heat conduction tensor and the dissipation coefficient due to ion-PUI interaction are both zero. This happens when PUIs are completely coupled with the thermal ions and the scattering time is infinitely small. It was shown in~\cite{Isenberg_1986} that the effect of PUIs can be quantified if they are treated as a separate fluid. In \cite{2006JGRA..111.7101U,2012ApJ...754...40U,2012AIPC.1436...48K,2011JGRA..116.3105D}, time-dependent simulations of the supersonic SW are presented with PUIs treated as a separate fluid and turbulence effects taken into account. These models still make the approximation of instantaneous isotropization, i.e., that the PUI description can be described as a filled shell, thus neglecting the nearly-isotropic character of the PUI distribution function when a finite scattering time is included \cite{2014ApJ...797...87Z}. In principle, any PUI fluid model is an approximation of their kinetic behavior. Such a model was developed by \cite{Malama} on the assumptions that PUIs are isotropic away from discontinuities and the TS is a perpendicular shock. However, proper boundary conditions are necessary to describe the PUI crossing the TS. Paper~\cite{Gamayunov} investigates the evolution of the PUI distribution function (in a pitch-angle-averaged approximation) together with the PUI-generated waves PUIs that heat the thermal SW ions. The extension of a 2-fluid SW model developed for the supersonic flows is not straightforward. This is because the pressure equation for PUIs used in such models is not valid across the TS. Instead, some boundary conditions should be developed for the PUI density and pressure, $\rho_\mathrm{PUI}$ and $p_\mathrm{PUI}$. Such boundary conditions are discussed in \cite{1996SoPh..168..389C,1996JGR...101..457Z,2008A&A...490L..35F,2010ApJ...708.1092Z,2012Ap&SS.341..265F,2013A&A...558A..41F}. It is known, e.g., the most of the SW kinetic energy was absorbed by PUI when the TS was crossed by \textit{V}1 \cite{Richardson_etal_2008Nature} (see also predictions in \cite{1996JGR...101..457Z}). One would not expect a simple finite approximation of $p_\mathrm{PUI}$ across the TS to satisfy such boundary conditions. In principle, as explained, e.g., in \cite{Kulik1}, one should either write out and solve a system of conservation laws across of a discontinuity or specify the boundary conditions at it. These approaches are equivalent, because the number of possible conservation laws is infinite, which results in an infinite number of shock boundary conditions. It is understood that only the fundamental physical conservation laws are appropriate for the description of magnetized fluid flows. In contrast, \cite{Usmanov16} solve non-conservative pressure equations everywhere in the SW--LISM interaction region, which violates the basic principles required to solve systems of hyperbolic equations. Moreover, the turbulence model of \cite{Breech_2008} used in \cite{Usmanov16} is based on an Alfv\'en-mode approximation and is invalid in the IHS. Moreover, the source terms used in \cite{Usmanov16} are valid only for ``cold'' plasma and are not applicable to the hot IHS plasma. In this paper, we use simple boundary conditions at the TS which allows us to demonstrate that the IHS width decreases when the PUI fluid is treated separately. | We have performed a SW--LISM simulations based on treating of PUIs as an individual plasma component and compared our results with our ``standard'' model where PUIs are immediately assimilated with background thermal protons. The neutral H flow was modeled using a multi-fluid approach. To make our simulations consistent with \emph{V}2 observations at the TS, we employed simple boundary conditions for the PUI pressure and density that ensured the preferential heating of PUIs across the TS. Our results show that treating PUIs as a separate plasma component indeed makes the inner heliosheath about 10~AU thinner that in a single-ion-fluid model. It should be understood, however, that while the HP was at 120~AU when V1 crossed it in August 2012, we have no information about the TS location at the same time. It is therefore possible that the heliosheath width is not equal to 28~AU, which one would predict on assuming that neither the HP nor the TS changed their position between 2004, when V1 crossed the TS, and 2012, when it left the heliosphere and entered the LISM. Most time-dependent SW--LISM models predict substantial variations in the TS heliocentric distance as a function of time \cite{2000Ap&SS.274..115P,2003JGRA..108.1240Z,2005A&A...429.1069I,Pogo09,2011MNRAS.416.1475W,Pogorelov-etal-2013}. Future work will focus on using better boundary conditions for PUIs at the TS, the implementation of a model with a kinetic treatment of H atoms, and including an extended treatment of the PUIs that goes beyond the assumption of complete isotropization. | 16 | 9 | 1609.03100 |
1609 | 1609.05456_arXiv.txt | {% The Auger Engineering Radio Array (AERA), at the Pierre Auger Observatory in Argentina, measures the radio emission of extensive air showers in the 30-80~MHz frequency range. AERA consists of more than 150 antenna stations distributed over 17 km$^2$. Together with the Auger surface detector, the fluorescence detector and the under-ground muon detector (AMIGA), AERA is able to measure cosmic rays with energies above 10$^{17}$~eV in a hybrid detection mode. AERA is optimized for the detection of air showers up to 60$^{\circ}$ zenith angle, however, using the reconstruction of horizontal air showers with the Auger surface array, very inclined showers can also be measured. In this contribution an analysis of the AERA data in the zenith angle range from 62$^{\circ}$ to 80$^{\circ}$ will be presented. CoREAS simulations predict radio emission footprints of several km$^2$ for horizontal air showers, which are now confirmed by AERA measurements. This can lead to radio-based composition measurements and energy determination of horizontal showers in the future and the radio detection of neutrino induced showers is possible. } | The radio detection of horizontal air showers reveals great potential to be a comprehensive detection method to access the electromagnetic component of the extensive air shower and for horizontal air showers this is only possible with radio detection. The analysis of the AERA data sample results in 427 high quality events in the zenith angle range from 62$^{\circ}$ to 80$^{\circ}$. The large radio footprint covering several km$^2$ could be detected for the first time with the large-scale radio detector AERA. The radio signal of horizontal air showers is understood within the uncertainties. Sparse antenna arrays are well-suited for horizontal air shower measurements. Now the physics of the radio detection of horizontal air showers for composition measurements and energy determination is in reach and the detection of neutrino induced air showers possible, but more studies are needed in sensitivity and systematics. | 16 | 9 | 1609.05456 |
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1609 | 1609.00273_arXiv.txt | Over the past decade, high-resolution optical spectropolarimeters have greatly enhanced our ability to study stellar magnetism across the Hertzsprung-Russell diagram. Low-mass, accreting, pre-main-sequence (PMS) stars are of particular interest, as they reveal the history of the Sun at a time when the planets of the Solar System were forming. The first magnetic maps of an accreting PMS star, V2129~Oph, were published by \citet{don07}. Constructed using the Zeeman-Doppler imaging technique, they revealed the long-suspected multipolar nature of PMS magnetism. The maps are constructed from a time series of circularly polarised spectra, and for accreting stars, by simultaneously considering the polarisation information contained in photospheric absorption lines and in accretion-related emission lines. Magnetic maps have now been published for the following accreting PMS stars, most at more than one epoch: V2129~Oph, BP~Tau, V2247~Oph, AA~Tau, TW~Hya, V4046~Sgr AB, GQ~Lup, DN~Tau, CV~Cha, and CR~Cha \citep{don07,don08,don10b,don10a,don11a,don11b,don11c,don12,don13,hus09}. All of them have multipolar magnetic fields. The majority of the magnetic maps were obtained as part of the multi-year Magnetic Protostars \& Planets (MaPP) large-observing program with the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii telescope, and its twin instrument NARVAL at T{\'e}lescope Bernard Lyot. The MaPP program spawned several additional, multi-wavelength, ground and space-based observations (e.g. \citealt{arg11,arg12,kas11,ale12}), as well as multiple theoretical / modelling papers (e.g. \citealt{gre08,gre10,gre11,jar08,lon11,rom11,joh14}). As more magnetic topology information becomes available for accreting PMS stars it is becoming clearer that the internal structure of the star plays an important role in controlling the external, large-scale, magnetic field topology \citep{gre12,gre14}. Accreting PMS stars, at least those more massive than $\sim$0.5$\,{\rm M}_\odot$, host strong axisymmetric large-scale magnetic fields while fully convective with the relative strength of the octupole to the dipole component increasing with age, see Figure \ref{BoctBdip}. The large-scale magnetic field then becomes more complex and non-axisymmetric once the stellar interior becomes mostly radiative. This stellar structure transition, and associated increase in magnetic field complexity, also has a signature in X-rays. The coronal X-ray emission decays once PMS stars have evolved onto Henyey tracks \citep{gre16}. \begin{figure} \centering \includegraphics[width=0.88\linewidth]{BoctBdip.pdf} \caption{The magnitude of the ratio of the polar strength of the octupole to the dipole component, $|B_{\rm oct}/B_{\rm dip}|$, versus age for accreting PMS stars. All stars shown are fully convective or have just developed radiative cores, based on their position in the Hertzsprung-Russell diagram. The vertical bars connect stars observed at two epochs. Accreting PMS stars with published magnetic maps and more complex magnetic fields (5 stars), that are not well represented by a dipole-plus-octupole component, are not shown. Figure from \citet{gre14}.} \label{BoctBdip} \end{figure} Little is known about the magnetic topology of accreting PMS stars of mass $\lesssim$0.5$\,{\rm M}_\odot$. However, based on the similarities between the magnetic topologies of main sequence M-dwarfs and of accreting PMS stars, see \citet{gre12}, it is expected that low-mass accreting PMS stars will show a variety of large-scale magnetic geometries, from simple and axisymmetric, to complex and non-axisymmetric. Our goal in this conference proceedings is to highlight some of the ways in which multipolar magnetic fields influence magnetospheric accretion / the star-disk interaction and (hopefully) to clear up some lingering misconceptions that persist in the literature. We do this using several straightforward, semi-analytic, back-of-the-envelope style calculations. In \S\ref{fields} we describe the field components for a stellar magnetic field consisting of a dipole plus an octupole component, an adequate first order approximation for the magnetosphere of many (but not all) accreting PMS stars (see \citealt{gre11} for extensive discussion). In \S\ref{disk} we demonstrate that, in most cases, the dipole component alone can be used to estimate the disk truncation radius, although little else in the star-disk system. In \S\ref{column} we illustrate the strong departure of $B$ along the accretion column from that of a pure dipole. In \S\ref{shock} we show that $B$ in the accretion shock can be multiple kilo-Gauss, even for accreting PMS stars with sub-kilo-Gauss dipole components, and that the disk truncation radius can be overestimated if $B$ at the accretion shock is (erroneously) assumed to be representative of a dipole large-scale magnetic field. We conclude in \S\ref{conclusions}. | Models of accretion flow, of the star-disk interaction, and of accretion shocks should incorporate multipolar magnetic fields. Dipole magnetic fields provide a poor representation of the true magnetic complexity of PMS stars. Even AA Tau, whose magnetic field is closest to a dipole \citep{don10b}, has a non-negligible $\sim$0.5$\,{\rm kG}$ octupole component. However, the large-scale magnetic fields of many accreting PMS stars are still somewhat simple, being dominantly axisymmetric and well-described by a (tilted) dipole component plus a (tilted) octupole component \citep{gre11}. Some of the best studied PMS stars have such magnetic field topologies, including AA~Tau, BP~Tau, V2129~Oph, TW~Hya, and others, although other higher order magnetic modes, and non-axisymmetric components are present too. Other stars, typically those that have developed large radiative cores, host more complex, multipolar, and non-axisymmetric large-scale magnetic fields \citep{hus09,gre12,gre14}. In this conference proceedings we used a simple model of a star with a dipole plus an octupole component. In order to make progress analytically, we assumed that both magnetic moments were aligned with the stellar rotation axis, and were parallel (the main positive pole of the octupole coincident with the main positive pole of the dipole).\footnote{Some stars, such as AA~Tau and TW~Hya, have field configurations that are closer to an anti-parallel dipole-plus-octupole, where the main positive pole of the octupole is close to coincident with the main negative pole of the dipole. For brevity we have not considered such magnetic fields in this work. Details can be found in \citet{gre11} and Gregory {\it et al.}, in prep.} Although these models are still simplified, they provide a far more realistic approximation to the true complexity of the magnetic fields of many accreting PMS stars than what can be achieved with a dipole. We have shown that: \begin{itemize} \item In most cases, as the higher order magnetic components decay faster with distance from the stellar surface, the disk truncation radius can be well approximated by using the polar strength of the dipole component alone. However, there are exceptions, including: i) when the mass accretion rate is large; ii) when the dipole component is weak; iii) when the higher order magnetic field components are very strong; iv) when the large-scale magnetosphere of the star is highly multipolar or tilted; and v) some combination of all of these which will result in a smaller disk truncation radius, where the impact of higher order magnetic components is larger. \item For the parallel dipole-plus-octupole magnetic fields, when the disk is truncated close to the magnetic null point, small changes in the mass accretion rate or the strengths of the magnetic field components can result in all of, or a portion of, the accretion flow impacting the star in low latitudes hot spots. This diversion of material from high to low latitude hot spots will alter the stellar variability. \item Although $B_{\rm dip}$ can often be used to calculate $R_t$, $B$ along the magnetic loops departs strongly from that of dipole magnetic field lines, as does the shape of the magnetic loops. \item $B$ in the accretion shock can reach multiple kilo-Gauss, even for stars with dipole components of only a few hundred Gauss. \item If the high field strengths measured in accretion hot spots are erroneously taken to be representative of the strength of the dipole component, and a dipole magnetic field is assumed, then the disk truncation radius will be overestimated. Likewise, use of the dipole component alone will often result in a significant underestimation of $B$ at the accretion shock. \end{itemize} In this work we have considered the impact of magnetic fields consisting of a dipole plus an octupole component on the disk truncation radius, $B$ along the accretion flow, and $B$ at the accretion shock. Dropping the observationally unrealistic assumption that accreting PMS stars have dipole magnetic fields has several additional effects on magnetospheric accretion, the star-disk system, and the stellar rotational evolution, which we have not discussed here. For example, the specific angular momentum transferred to the star through the star-disk interaction is an order of magnitude less for stars with octupole dominated fields compared to those with dominantly dipolar magnetic fields \citep{bat13}. For multipolar magnetic fields, and including the dipole-plus-octupole magnetic fields considered here, material accretes into smaller hot spots, with a (usually) smaller accretion filling factor (e.g. \citealt{ada12}). The accretion flow being funnelled into smaller spots increases the pre-shock density of the hot spots \citep{gre07,gre08,ada12} and increases their temperature \citep{ada12}. Although we can use $B_{\rm dip}$ to calculate $R_t$ in most cases, the dipole component alone provides a poor representation of the structure of accretion flow, of $B$ along accretion columns, and of $B$ where material impacts the star. Models of magnetospheric accretion, of accretion flow, and of accretion shocks, must incorporate multipolar magnetic fields. | 16 | 9 | 1609.00273 |
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1609 | 1609.02937_arXiv.txt | { We use cosmological hydrodynamical simulations to study the effect of screened modified gravity models on the mass estimates of galaxy clusters. In particular, we focus on two novel aspects: \textit{(i)} we study modified gravity models in which baryons and dark matter are coupled with different strengths to the scalar field, and, \textit{(ii)} we put the simulation results into the greater context of a general screened-modified gravity parametrization. We have compared the mass of clusters inferred via lensing versus the mass inferred via kinematical measurements as a probe of violations of the equivalence principle at Mpc scales. We find that estimates of cluster masses via X-ray observations is mainly sensitive to the coupling between the scalar degree of freedom and baryons -- while the kinematical mass is mainly sensitive to the coupling to dark matter. Therefore, the relation between the two mass estimates is a probe of a possible non-universal coupling between the scalar field, the standard model fields, and dark matter. Finally, we used observational data of kinetic, thermal and lensing masses to place constraints on deviations from general relativity on cluster scales for a general parametrization of screened modified gravity theories which contains $f(R)$ and Symmetron models. We find that while the kinematic mass can be used to place competitive constraints, using thermal measurements is challenging as a potential non-thermal contribution is degenerate with the imprint of modified gravity. } | Over a decade has passed since the indisputable discovery of the accelerated expansion of the Universe \citep{Riess1998AJ....116.1009R,Perlmutter1999ApJ...517..565P} but its physical origin is still unknown. A possible -- and rather popular -- solution is to modify the theory of general relativity (GR). This has been done for a number of years and lead to numerous theories of modified gravity \citep[for reviews, see, e.g.,][]{Amendola2010deto.book.....A,Clifton2012}. The main challenge for many modified gravity theories are measurements of the gravitational strength on Earth and in the solar system \citep[e.g.,][]{Berotti2003Natur.425..374B, Will2006LRR.....9....3W, Williams2004PhRvL..93z1101W}, which confirm the predictions of GR with great precision. One viable solution to this is to employ a so-called screening mechanism which restores GR in the solar system. Screening mechanisms are usually triggered by large local matter density or space-time curvature and lead to a convergence of the gravitational strength to its value predicted by GR. For the sub-category of the extension of GR in the scalar sector\footnote{Also, other extensions of GR, for example, in the vectorial sector are possible. However, apart from managing theoretical difficulties they are also obliged not to violate the local constraints mentioned, and, thus might also employ a screening mechanism.}, that is, by adding a coupled scalar field to the Einstein-Hilbert action, several possible screening mechanisms are on the market \citep[see, e.g.,][]{Khoury2010,Joyce2014}. They can be categorized as follows: \begin{itemize} \item \textit{Screening because of the scalar field value} -- also often denoted as Chameleon screening. This group can be further divided into screening mechanisms that affect directly the coupling strength -- such as the Dilaton \citep{Damour1994NuPhB.423..532D} and the Symmetron \citep{Hinterbichler,Hinterbichlera} screening -- as well as mechanisms that alter the range of the additional force. The latter screening is often dubbed Chameleon screening \citep{Khourya,2004PhRvD..69d4026K,gan,2007PhRvD..75f3501M}. \item \textit{Screening due to derivatives of the field value} -- also called Vainshtein-like screening. Here, one can differentiate between screening due to the first or the second derivative of the scalar field. Screening mechanisms belonging to the former group are the k-Mouflage \citep{2009IJMPD..18.2147B,mota3,2014PhRvD..90b3507B} and D-Bionic screening \citep{BurragePhysRevD.90.024001} whereas the latter group consists of the eponymous Vainshtein screening \citep{1972PhLB...39..393V}. \end{itemize} It is important to differentiate between the screening mechanism and the particular theory of gravity employing this mechanism. For instance, particular theories employing the Vainshtein screening are the DGP model \citep{2000PhLB..485..208D}, Galileons \citep{2009PhRvD..79f4036N}, and, massive gravity \citep{2014LRR....17....7D}. This wealth of theoretical alternatives to GR stands in stark contrast to the observational findings which, so far, confirm GR on a variety of environments \& scales \citep[for observational reviews see, e.g.,][]{2015arXiv150404623K,Baker2015ApJ...802...63B,2015arXiv151205356B} although deviations in many observables are predicted. Apart from the background cosmology \citep[e.g.,][for the Vainshtein, Chameleon and Symmetron, respectively]{2014PhRvD..90l4014K,2004PhRvD..70l3518B,Hinterbichlera} usually $N$-body codes are used to study screened modified gravity models \citep[for a review of the numerical techniques, see][]{Winther2015arXiv150606384W}. The most common approach is to start a $\Lambda$CDM and a modified gravity simulation using the same initial conditions and then analyze the deviations between the simulation outputs at later times. In this way, deviations in the matter power spectrum \citep{2008PhRvD..78l3524O,mota4,Li2012JCAP...01..051L,bour,2013JCAP...05..023L,2013PhRvL.110p1101L,Puchwein2013MNRAS.436..348P}, the halo mass function \citep{2010PhRvD..81j3002S,2013JCAP...10..027B,mota2,Davis2012ApJ...748...61D,2015arXiv151101494A}, the velocity field \citep{2014arXiv1408.2856C,2014PhRvL.112v1102H,Gronke2014b_dl,2016arXiv160303072F}, gravitational lensing \citep{2015MNRAS.454.4085B,2015JCAP...10..036T,2016arXiv160301325H} and many other quantities have been found. These predictions give valuable insights into the way in which mechanisms act on the environment. However, exactly how transferable to observations they are, is questionable due to the neglecting of baryonic effects which are somewhat degenerate with the enhancement of gravity \citep{Puchwein2013MNRAS.436..348P,2014MNRAS.440..833A,Hammami2015a}, and, more importantly the direct comparison with another, alternative `Universe' -- a technique which is certainly not possible with real data. Another problem associated with the confrontation of the numerical predictions with real data is the richness of the modified gravity landscape. Not only is the above mentioned number of models incomplete (and steadily increasing) but each model has its own (often multi-dimensional) parameter space. This makes the classical approach, by which we mean, using a suite of $N$-body simulations to constrain the model parameter spaces one-by-one, unfeasible. One alternative is to speed up the numerical simulations tremendously as done by \citet{Mead2014}, \citet{2015JCAP...12..059B} and \citet{2014arXiv1403.6492W}. Alternatively, one can try to unify the predictions of several modified gravity models potentially allowing to rule out (parts of parameter spaces) of several models at once. This path was taken theoretically by \citet{2012PhLB..715...38B,2012PhRvD..86d4015B} who developed a framework in which it is possible to describe the Chameleon-like screening mechanisms with two free functions. \citet{2015arXiv150507129G} present a fully empirical parametrization of screened modified gravity models using three parameters which captures a number of models \& model parameters. In this paper, we want to revisit some classical quantities associated with screened modified gravity models, namely the dynamical, lensing and thermal mass estimates of clusters of galaxies in the light of \textit{(i)} the \citet{2015arXiv150507129G} parameterisation, and, \textit{(ii)} the possibility of unequal coupling; that the enhancement of gravity is not the same for baryons and dark matter. In this work, we use $M_{\rm Pl}^{-2} \equiv 8 \pi G$, $\rho_c = 3 H^2 M_{\rm Pl}^2$, and, denote values today with a subscript zero. | Using a hydrodynamic $N$-body code, we studied the effect of screened modified gravity models on the mass estimates of galaxy clusters. In particular, we focused on two novel aspects: \textit{(i)} we studied modified gravity models in which baryons and dark matter are coupled with different strengths to the scalar field, and, \textit{(ii)} we put the simulation results into the greater context of a general screened-modified gravity parametrization. Our findings in these matters can be summarized as follows: \begin{itemize} \item The lensing mass of a cluster can differ tremendously from its kinematic or thermal mass in modified gravity theories. In screened modified gravity theories the magnitude of variation varies from a maximum to zero from the unscreened mass range to the screened one, respectively. This makes the mass measurements of clusters a powerful probe of gravity in different length scales and environments. \item Differently coupled dark matter and baryons are hard to detect observationally as degeneracies exist. However, as the thermal mass is stronger affected by the baryonic coupling than the kinetic mass, possessing information about the three discussed mass estimates can break this degeneracy. \item We placed the specific Symmetron and $f(R)$ models studied on a common parameter space which we also constrained using kinematic, lensing, and, thermal mass observations. \item The ratio of the kinetic and lensing mass yields competitive constraints on the modification of gravity. Using thermal measurements, on the other hand, is currently unfeasible since the effect of non-thermal contributions is degenerate with a potential signal of modified gravity. This well be alleviated when these contributions are quantified in a model-independent way. \end{itemize} In conclusion, using various observational mass estimates for cluster of galaxies are a powerful tool in order to constrain modified gravity theories which possess a screening mechanism -- especially as future surveys increase the number of observed galaxies. | 16 | 9 | 1609.02937 |
1609 | 1609.02106_arXiv.txt | The recent star formation history (SFH) in the outer disk of NGC~300 is presented through the analysis of color magnitude diagrams (CMDs). We analyze resolved stellar photometry by creating CMDs from four \textit{Hubble Space Telescope} fields containing a combination of images from the \textit{Advanced Camera for Surveys} and the \textit{UVIS} imager aboard the \textit{Wide Field Camera 3}. From the best models of these CMDs, we derive the SFH in order to extract the young stellar component for the past 200 Myrs. We find that the young stellar disk of NGC~300 is unbroken out to at least $\sim$8 scale lengths (including an upper limit out to $\sim$10 scale lengths) with $r_s=1.4\pm0.1$ kpc, which is similar to the total stellar surface brightness profile. This unbroken profile suggests that NGC~300 is undisturbed, similar to the isolated disk galaxy NGC~2403. We compare the environments of NGC~300, NGC~2403, and M33 along with the properties of the gas and stellar disks. We find that the disturbed HI outer disk morphology is not accompanied by a break in the young stellar disk. This may indicate that processes which affect the outer HI morphology may not leave an imprint on the young stellar disk. | A fundamental question in galaxy evolution is how the environment transforms disk galaxies. External processes can have a great effect on galaxies; in galaxy clusters there is a lower number of spiral types compared to field galaxies \citep{1980ApJ...236..351D}, and spirals that are clustered are observed to be redder than their non-clustered counterparts \citep{1983AJ.....88..483K, 1994A&A...289..715D}. In simulations, spiral galaxies interacting, either through mergers or close orbits, can become elliptical or S0 galaxies \citep{1985A&A...144..115I,1998ApJ...502L.133B}. Such gravitational interactions all impact the evolution of spiral galaxies.\\ \indent In particular, the outer disks of spirals give us a fossilized window into their evolution. Truncations in the exponential profile of spirals, known as disk breaks, may then provide clues about the effects of interactions on these outer disks. Present studies on disk breaks have built upon the work of \citet{1970ApJ...160..811F}, who began to classify spiral disks into different types, outlined nicely by \citet{2008AJ....135...20E}. \citet{2008AJ....135...20E} performed an extensive statistical study on spiral galaxies \citep[see also][]{2006A&A...454..759P,2011AJ....142..145G} finding that the majority of late-type spirals have truncations in their exponential disk. Furthermore, \citet{2012ApJ...744L..11E} and \citet{2012MNRAS.419..669M} find there is no difference between the disk-profiles of cluster galaxies and field galaxies, suggesting global galaxy environment does not play a significant role in the origin of breaks. Other local effects could then be the main driving force for outer disk evolution, but it is still a mystery why breaks would be independent of global environment.\\ \indent Individualized observations of the outer regions of local disks may help constrain current understanding of environmental effects in their evolution. Fortunately, there are three, representative, nearby disk galaxies in differing environments: M33, NGC~2403, and NGC~300. These are the closest pure disk galaxies for comparing the effects of different environments on disk evolution \citep[see Figure 1 and Table 1][hereafter W13]{2013ApJ...765..120W}. M33 is the least isolated, containing a warped HI disk likely due to a weak interaction with M31. NGC~2403 is the most isolated with no large nearby companion and an undisturbed HI field \citetext{\citetalias{2013ApJ...765..120W}; and references therein}. NGC~300, the focus of this study and of SA(s)d type \citep{1991rc3..book.....D}, is relatively isolated in that it has no massive companion. However, it does have a nearby low mass companion, NGC~55, and presents a severe HI warp in its outer parts which may be due to the closeness of this companion \citep{1990AJ....100.1468P}.\\ \indent The properties of the outskirts of these galaxies are probes of how the structure of outer disks may be related to their environment. Current observations of NGC~2403 show it to have no break \citepalias{2013ApJ...765..120W} in the young stellar component, while M33 does have a break possibly created from nearby M31 \citep{2007iuse.book..239F}. NGC~300 has no break in its overall surface brightness profile \citep{2005ApJ...629..239B}, suggesting little environmental influence. Based on M33 and NGC~2403, we might expect that environment affects outer disk structure. If so, NGC~300 probes an intermediate density environment, where we can obtain detailed information about outer disk structure. If the young component shows no evidence of a break, then the warp in the gas disk is likely due to environmental effects, as in M33; however, if the young component mimics that of NGC~2403, then environment is less likely to have influenced the structure of the outer disk of NCG~300. \\ \indent We extend the study of \citetalias{2013ApJ...765..120W} to examine the structure of the young outer disk of NGC~300 following a similar methodology, in this paper, to measure the recent star formation history (SFH) of the resolved stellar populations out to a galactocentric radius of $\sim$14 kpc in order to isolate the star-forming disk from the total stellar profile. In Section \hyperref[sec:dataAnalysis]{2} we present the data along with the reduction and analysis techniques applied. Section \hyperref[sec:results]{3} discusses our findings of NGC~300 including a comparison with NGC~2403 and M33, and we finish with a summary in Section \hyperref[sec:conclusion]{4}.\\ \indent We assume an inclination of $i=42.3^{\circ}$ \citep{1983A&A...118....4B} and a distance modulus of 26.5 from tip of the red giant branch measurements with similar Hubble Space Telescope (HST) fields (2.0 Mpc, \citealt{2009ApJS..183...67D}).\\ | \label{sec:conclusion} We measured resolved stellar photometry on four HST fields in the outer disk of NGC~300. We determined the recent stellar mass surface density from CMD fitting (using the package {MATCH}) out to $\sim$8 scale lengths with an upper limit out to $\sim$10 scale lengths. We find that the young population in NGC~300 is not centrally concentrated in the disk nor is there a break in the young stellar mass surface density, indicating NGC~300 has an undisturbed star forming outer disk. This young stellar mass surface profile is consistent with the unbroken total surface brightness profile.\\ \indent With this new knowledge of the young outer disk component of NGC~300, we revisited comparisons of the properties of the NGC~300 disk with those of 2 similar disk galaxies NGC~2403 and M33. While M33 appears consistent with having undergone gravitational interactions, NGC~2403 and NGC~300 do not. In this regard, the HI warp in NGC~300 is inconsistent with a gravitational interaction scenario and instead more likely attributed to infalling gas. Furthermore, the similarity of the young disk and total stellar profiles in NGC~300 suggest there is no significant halo component. We conclude that NGC~300 and NGC~2403 have then seen no significant interactions in the past compared to the apparent evolution of M33. \\ \indent Support for this work was provided by NASA through the grant GO-13461 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. We acknowledge the anonymous referee’s attention to the details of our writing style and presentation.\\ | 16 | 9 | 1609.02106 |
1609 | 1609.01532_arXiv.txt | Classical Supergiant X-ray Binaries host a neutron star orbiting a supergiant OB star and display persistent X-ray luminosities of $10^{35}$ to $10^{37}$\,erg$\cdot$\,s$^{-1}$. The stellar wind from the massive companion is believed to be the main source of matter accreted by the compact object. With this first paper, we introduce a ballistic model to characterize the structure of the wind at the orbital scale as it accelerates, from the stellar surface to the vicinity of the accretor. Thanks to the parametrization we retained and the numerical pipeline we designed, we can investigate the supersonic flow and the subsequent observables as a function of a reduced set of characteristic numbers and scales. We show that the shape of the permanent flow is entirely determined by the mass ratio, the filling factor, the Eddington factor and the $\alpha$-force multiplier which drives the stellar wind acceleration. Provided scales such as the orbital period are known, we can trace back the observables to evaluate the mass accretion rates, the accretion mechanism, the shearing of the inflow and the stellar parameters. We confront our model to three persistent Supergiant X-ray Binaries (Vela X-1, IGR J18027-2016, XTE J1855-026) and discuss the likelihood of wind-formed accretion discs around the accretors in each case, further investigated in a following paper. | For the last fifty years, X-ray observations have revealed a plethora of binary systems hosting a compact object accreting the gas from its stellar companion. While accretion proceeds mostly by overflow of the stellar Roche lobe (the Roche Lobe OverFlow - \textsc{rlof}) in systems where the mass of the star is low (Low Mass X-ray Binaries, {\sc lmxb}), we expect the dense and fast winds of massive stars to be the main responsible for mass transfer in High Mass X-ray Binaries ({\sc hmxb}). The structure of the wind in {\sc hmxb} has been found to be of two kinds \citep{Chaty2011a} : either it forms a circumstellar decretion disc around fast rotators Be stars (Be{\sc xb}) or it obeys the more isotropic sketch of the radiatively-driven wind for early-type supergiant stars \citep{Shakura:2014wk}. The latter sources of matter are believed to be associated to the class of the persistent classical Supergiant X-ray binaries (henceforth \sgx) when surrounded by a neutron star on a low eccentricity orbit thus making the compact object permanently embedded in the wind. The number of confirmed \sgx has doubled within the last ten years \citep{Walter15}. The theory of radiatively-driven winds (or \textsc{cak} winds) for isolated massive stars has been widely developed, refined and confronted to observations since the seminal papers of the 70's \citep{Lucy1970,Castor1975}. It describes how the resonant absorption of the high energy photons of hot stars by non fully ionized metals supplies the outer layers with net linear momentum. As they accelerate, they keep absorbing Doppler shifted photons previously untouched. In its most elementary form, steady-state solutions can be derived from 3 parameters, the force multipliers, which set the mass loss rate for a given mass and luminosity of the star. Radial velocity profiles have also been determined and have turned out to be well fitted by the so called $\beta$-laws. The terminal speeds involved are typically of the order of several escape velocities, which match the observationally derived values using a wide spectrum of methods summarized in the very comprehensive reviews of \cite{Kudritzki2000} and \cite{Puls2008}. This model has reached levels of reliability high enough, in particular in the case of supergiant stars \citep{Crowther2006}, so as to be confidently applied to the case of \sgx. In this paper, we focus on the self-consistency of the stellar, orbital, wind and accretion parameters in \sgx hosting a confirmed neutron star. Due to the high mass ratio in theses systems, we do not expect the star to fill its Roche lobe nor the launching of the wind to be altered by the presence of the neutron star ; yet, the non inertial forces at stake in those relatively short periods systems ($<20$ days) will modify the structure of the departed though still accelerating flow as it approaches the compact object, where the gravitational field of the latter will take over. Hence, an observable such as the spectral type of the supergiant plays a role in the determination of the force multipliers which determine the wind properties (\eg the mass loss rate), but also in shaping the Roche potential in which the modified velocity profile unfolds. In \sgx where the stellar companion has been identified, we usually rely on the spectral type to determine the stellar parameters, putting aside the specificities inherent to the binary secular evolution \citep{VandenHeuvel2009}. Still today, mass discrepancies subsist between the spectroscopic and evolutionary masses \citep{Searle2008,Puls2008a}. To those approaches we want to add measures derived from their consequences over the whole mass transfer phenomenon and considered in relation with each other through the launching mechanism, the orbital dynamics, the stellar model and the accretion process. Since \sgx are highly obscured systems \citep{Coleiro2013}, thorough observations of the star are challenging and sometimes impossible. Using accretion onto the compact companion could be used as a proxy to trace back information concerning the whole system, including the donor. Radiatively-driven winds are notoriously unstable to small-scale radial perturbations \citep{MacGregor1979, Owocki1984, Owocki1985} and tend to form clumps of overdense matter. Their accretion has been suggested as a possible source of X-ray variability \citep{Ducci2009} but other phenomena are expected to play a role \citep{Illarionov1975,Foulkes2006,Shakura2013a}, in particular in recently discovered Super Fast X-ray Transients \citep[\textsc{sfxt,}][]{Negueruela2006} where the X-ray dynamic range spans up to 5 orders of magnitude. Apart from the off-states, the X-ray emission is more persistent in classical \sgx with averaged X-ray luminosities of the order of $10^{35}$ to a few $10^{36}$\,erg\,s$^{-1}$. In this first paper, we try to represent the averaged behaviour with a steady-state framework and do not consider the possible switches which could occur due to the inhibition of the wind acceleration once the X-ray emission from the gas being accreted is large enough to fully ionize the wind \citep{Ho1987,Blondin1990}. We assume that permanent regime streamlines of the supersonic flow can tell us something about the properties of the system, regardless of ionizing effects or shocks at the orbital scale. This steady-state assumption serves another purpose in the attempt to understand variability in \sgx (\eg the off-states) and possibly in \textsc{sfxt}. The more regular and somewhat smoother accretion process at stake in \textsc{lmxb}, \textsc{rlof}, does not prevent those systems from undergoing important luminosity variations \citep[see \eg the Q-shaped diagram represented in Figure 2 of ][]{Belloni2005}, It turns out that phenomena occurring within the accretion disc itself could account for them. In the case of \sgx, highly obscured systems, we have few if not no proof of the existence of a disc-like structure around the accretor, except for a few ones which harbor fastly rotating pulsars such as Cen X-3 and are believed to undergo \rlof, in spite of the supergiant nature of the donor star. Some systems present observational signatures associated with direct impact at the poles where the matter could have been led by its interaction with the magnetosphere \citep{Davidson1973}. However, whether the gas is taped directly in a shocked wind or in a wind-formed disc, possibly transient, remains unknown. Thus, neglecting time-variability at the orbital scale is a way to decouple it from its small scale counterpart, in the vicinity of the neutron star where most of the X-ray emission comes from. Local triggers of instabilities in the shocked wind around the accretor do not necessarily require large scale excitation - whose damping or amplification remains largely unknown. \cite{Manousakis2015c} showed for instance that continuous homogeneous winds could lead to unstable front shocks due to X-ray ionizing feedback on the flow. The very stability of essentially planar supersonic accretion flows has been a long-lasting question \citep{Blondin2009,Blondin:2012vf} we want to address in the context of \sgx, in a similar way it has been addressed in the case of symbiotic binaries \citep{Theuns1993,Theuns1996,Jahanara2005,Mohamed2007,deValBorro:2009gk,HuarteEspinosa:2012wq}. We set the modelling stage of our toy-model in section \ref{sec:first_sec} and highlight its fundamental parameters. After a description of our numerical pipeline in section \ref{sec:second_sec}, we discuss the structure of the flow at the orbital scale and its properties (mass accretion rate onto the compact object and shearing of the flow) in section \ref{sec:structure_wind}. Eventually, in section \ref{sec:dim_res}, we evaluate the self-consistency of our cross-model by confronting the parameters we derive to three extensively studied \sgx : Vela X-1, XTE J1855-026 and IGR J18027-2016 (\aka SAX 1802.7-2017). Finally, we summarize our results and discuss their main implications in section \ref{sec:conclu}. | 16 | 9 | 1609.01532 |
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1609 | 1609.04121_arXiv.txt | We present the ``Galaxy Cluster Merger Catalog.'' This catalog provides an extensive suite of mock observations and related data for N-body and hydrodynamical simulations of galaxy cluster mergers and clusters from cosmological simulations. These mock observations consist of projections of a number of important observable quantities in several different wavebands as well as along different lines of sight through each simulation domain. The web interface to the catalog consists of easily browseable images over epoch and projection direction, as well as download links for the raw data and a JS9 interface for interactive data exploration. The data is presented within a consistent format so that comparison between simulations is straightforward. All of the data products are provided in the standard FITS file format. Data is being stored on the yt Hub~(\url{http://hub.yt}), which allows for remote access and analysis using a Jupyter notebook server. Future versions of the catalog will include simulations from a number of research groups and a variety of research topics related to the study of interactions of galaxy clusters with each other and with their member galaxies. The catalog is located at \url{http://gcmc.hub.yt}. | \label{sec:intro} Galaxy clusters are the largest gravitationally bound structures in the current universe. Originally identified as concentrations of galaxies in the optical, observations in the X-ray and millimeter wavelengths have revealed the bulk of baryonic material of clusters is comprised of a hot, magnetized plasma known as the intracluster medium \citep[ICM,][]{for72,sun72}. The kinetic energy of the galaxies and the temperature of the hot gas indicate that in order for the cluster to be gravitationally bound the majority of the mass must be in the form of cold dark matter \citep[CDM, first noted by][]{zwi37}. Mergers between galaxy clusters represent the latest stage of cosmological structure formation. The most energetic events in the universe, mergers drive shocks and turbulence into the ICM, heating and stirring the cluster gas. These mergers also accelerate relativistic particles, which then produce radio relics and halos \citep{fer05,bru07,vwe10,bru12}. Cluster mergers have also revealed the different dynamical properties of the CDM, galaxies, and ICM, seen most vividly in the case of the Bullet Cluster \citep[][]{clo04,mar04}. Understanding cluster mergers is therefore vital to answering questions about the detailed physics of galaxy clusters as well as providing insights into the formation of cosmic structure. The astrophysical literature is replete with simulations of galaxy cluster mergers, from binary merger simulations \citep[e.g.][]{ric01,poo06,zuh11a,don13} to studies of mergers in cosmological simulations \citep[e.g.][]{vaz09,ski13,yu15}. These simulations have often attempted to make predictions for what may be observed in a number of wavebands and made direct comparisons to observed merging systems. However, comparing the results of simulations of cluster mergers to these systems is often not straighforward; at what stage are we viewing the merger, and along what line of sight? To make matters more complicated, different combinations of merger epoch and line of sight can produce qualitatively similar projections of cluster emission, making it more difficult to use observations to determine these parameters and distinguish between different theoretical models. We seek to address these issues by releasing the ``Galaxy Cluster Merger Catalog,'' an extensive suite of mock observations and related data for simulations of galaxy cluster mergers. We have produced 2D projections and slices of a number of different quantities relevant to observations of galaxy clusters from simulations of binary cluster mergers and cosmological simulations. These data products include clusters in various stages of merging and interaction with other systems viewed along a number of relevant projection axes. The data from the various simulations are presented within a consistent format so that comparison between simulations with different physics or different initial conditions is straightforward. The inclusion of data from both simulation types emphasizes the strengths of each: idealized merger simulations, due to their typically higher resolution and controlled set up, can provide insights into what kind of physics and merger configurations lead to certain observable features in cluster mergers. On the other hand, cosmological simulations capture more realistic mergers between clusters with substructure as well as cosmological accretion, providing a more direct comparison with observations. The goal of this catalog is to provide a way to connect a variety of simulations of galaxy cluster mergers within a common interface with multiwavelength observations of real merging clusters, providing an opportunity for observers to compare clusters in their observations with a particular merging scenario. For example, the catalog may be used to interpret existing observations across multiple wavebands such as the Planck-Chandra Cluster Sample\footnote{\url{https://hea-www.harvard.edu/CHANDRA_PLANCK_CLUSTERS/}} \citep{and17}, or be analyzed to make predictions for what various investigations of real clusters may reveal for future observations and missions, such as {\it Athena}\footnote{\url{http://www.the-athena-x-ray-observatory.eu/}} and {\it Lynx}\footnote{\url{https://wwwastro.msfc.nasa.gov/lynx/}}. | 16 | 9 | 1609.04121 |
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1609 | 1609.00375.txt | We present a quantitative study of the X-ray morphology of galaxy clusters, as a function of their detection method and redshift. We analyze two separate samples of galaxy clusters: a sample of 36 clusters at $0.35 < z < 0.9$ selected in the X-ray with the \emph{ROSAT} PSPC 400 deg$^2$ survey, and a sample of 90 clusters at $0.25 < z < 1.2$ selected via the Sunyaev-Zel'dovich (SZ) effect with the South Pole Telescope. Clusters from both samples have similar-quality \emph{Chandra} observations, which allow us to quantify their X-ray morphologies via two distinct methods: centroid shifts ($w$) and photon asymmetry (\Aphot). The latter technique provides nearly unbiased morphology estimates for clusters spanning a broad range of redshift and data quality. We further compare the X-ray morphologies of X-ray- and SZ-selected clusters with those of simulated clusters. We do not find a statistically significant difference in the measured X-ray morphology of X-ray and SZ-selected clusters over the redshift range probed by these samples, suggesting that the two are probing similar populations of clusters. We find that the X-ray morphologies of simulated clusters are statistically indistinguishable from those of X-ray- or SZ-selected clusters, implying that the most important physics for dictating the large-scale gas morphology (outside of the core) is well-approximated in these simulations. Finally, we find no statistically significant redshift evolution in the X-ray morphology (both for observed and simulated clusters), over the range $z \sim 0.3$ to $z \sim 1$, seemingly in contradiction with the redshift-dependent halo merger rate predicted by simulations. | \label{sec:cmpcat_intro} % After Andersson2011 Large scale galaxy cluster surveys can make an important contribution to understanding the growth of structure in the Universe, delivering precise constraints on the nature of dark matter and dark energy, and providing insights into astrophysical processes in clusters. The primary interest in studying galaxy clusters from the cosmological point of view is in measuring their abundance as a function of mass and redshift, although alternative approaches to cluster-based cosmology that do not rely on precise masses have recently been proposed \citep{caldwell16,ntampaka16,pierre16}. The abundance of galaxy clusters as a function of mass and redshift currently provides constraints on cosmological models and parameters, most importantly matter density $\Omega_{\rm M}$ and the normalization of the matter power spectrum $\sigma_8$ \citep[see review by][]{allen11}. There are many subtleties, however, in interpreting abundance information from cluster surveys. First, since measuring the total mass is observationally expensive and highly uncertain (i.e., via weak lensing), most studies use scaling relations to link a low-scatter mass proxy (such as X-ray spectroscopic temperature or integrated SZ signal) to its mass. Both scatter and potential biases in the given scaling relation have an effect on constraints when fitting cosmological models. Second, one needs to understand the survey's completeness and purity. Finally, more subtle selection effects such as increased sensitivity to a particular sub-class of clusters may play a role. An example of such a bias would be an increased sensitivity of X-ray flux-limited samples to cool core clusters: as cool core systems have higher X-ray luminosity than non-cool core systems of the same mass, a flux-limited sample can potentially be biased towards cool core clusters \citep{hudson10, mittal11, eckert11}. The ratio of cool core to non-cool core systems at different redshifts is currently a subject of active research \citep{vikhlinin06b, santos10, samuele11, mcdonald11c, semler12, mcdonald13b}, so this bias effectively limits our understanding of completeness in the X-ray flux-limited samples. Many of the biases implicit in the selection of various galaxy cluster samples are well understood. X-ray luminosity is proportional to gas density squared, so X-ray detection is biased towards cool core systems that have high central densities. In contrast, the majority of the SZ signal originates from outside of the core. Consequently, SZ detection is biased towards the large-scale gas properties in the cluster. Because both X-ray and SZ detection methods are based on the physical properties of the ICM, they may have some common biases \citep{Maughan12,Angulo12,Lin15} that are completely different from the optical detection methods which are sensitive to a different component of galaxy clusters (i.e., the galaxies). The finer details of each detection method's sensitivity to specific cluster morphology or dynamical state are not well understood. It has been suggested that SZ-selected clusters are more often ``morphologically disturbed'' (i.e., ongoing mergers) than their X-ray-selected counterparts. This line of reasoning stems from 1) the presence of spectacular mergers among the first discovered by the SZ effect, such as El Gordo \citep{menanteau11} and PLCKG214.6+37.0 \citep{planck13c}; and 2) an extensive discussion of newly discovered mergers in the papers which originated from the \emph{Planck} \emph{XMM-Newton} follow-up program \citep{planckxmm11,planckxmm12,planckxmm13}. The latter program targeted 51 cluster candidates and led to the confirmation of 43 candidates, 2 of them being triple systems, and 4 double systems. The 37 remaining objects had 1) lower X-ray luminosity than expected from scaling relations and 2) shallower density profiles than the mean density profiles of X-ray detected clusters. These two observations served as the main arguments for \emph{Planck's} increased sensitivity to mergers. Indeed, recent studies have shown that \emph{Planck} clusters are, on average, more morphologically disturbed \citep{rossetti16} and have a lower occurrence rate of cool cores \citep{jones15} when compared to X-ray-selected clusters. While systems discovered by \emph{Planck} do have interesting morphological properties, the aforementioned findings do not necessarily indicate an inherent sensitivity of the SZ effect to merging clusters. The lower central density and luminosity of clusters may be related to greater than previously thought intrinsic scatter in these parameters, or factors other than merging processes. Several of the double and triple systems discovered by \emph{Planck} are clusters overlapping in projection, rather than interacting systems (although they still belong to the same supercluster structure). The increased sensitivity of \emph{Planck} to such multiple systems is unsurprising due to its large beam size and consequent inability to resolve multiple systems. %Finally, finding 37 previously undetected single systems that appear to have higher substructure rates may be not so surprising given that the full \emph{Planck} sample contains 861 confirmed entries \citep{planckszcat}. Another question that has been extensively discussed in the literature is whether cluster morphology depends on redshift. The motivation for these studies is the connection of merger rate (and consequently morphology) to the mean matter density $\Omega_{\rm M}$. The morphology-cosmology connection that was analytically developed by \citet{richstone92} and then confirmed in simulations by \cite{evrard93} and \cite{jing95} predicted that clusters in low $\Omega_{\rm M}$ models are much more regular and spherically symmetric than those in $\Omega_{\rm M}=1$ models. Consequently, there were efforts to constrain $\Omega_{\rm M}$ by finding the fraction of clusters with significant level of substructure as defined by various substructure statistics: \citet{mohr95} used centroid shifts, \citet{buote95} used power ratios, and \citet{schuecker01} used a trio of tests which quantify mirror symmetry, azimuthal symmetry, and radial elongation. % This approach to constraining cosmological parameters through substructure rates has not been as successful as other cluster-based cosmology tests owing to difficulties in robustly defining ``significant levels of substructure'', connecting observable substructure measures to theoretical merger definitions \citep{buote95}, and insufficiently low numbers of observed and simulated clusters for these tests. % %This approach to constraining cosmological parameters through substructure rates has not been as successful as other cluster-based cosmology tests due to the difficulties of defining the ``significant level of substructure'', insufficient number statistics of both observed and simulated clusters and possibly the discrepancy between the theoretical definition of a merger and what is measured by a substructure statistic \citep{buote95}. Modern halo abundance measurements provide much more precise constraints on $\Omega_{\rm M}$ than those obtained by merger fraction studies. Nevertheless, the question of substructure evolution in galaxy clusters is still relevant. The majority of studies have reported statistically significant evolution in cluster morphology \citep{jeltema05,andersson09,mann12}; while a smaller number \citep[e.g.][]{weissmann13b,mantz15} arrived at the conclusion that clusters at low- and high-$z$ are consistent with no morphological evolution. \citet{weissmann13b} performed a study of substructure evolution similar to ours, which is described later, using a slightly different cluster sample and substructure statistics, but arriving at similar results (See Sec.~\ref{sec:discussion} for more details). Our objectives in this paper are to test for any evidence of a difference in dynamical state between X-ray and SZ-selected clusters, low-z and high-z clusters, and observed and simulated clusters. The difference between X-ray and SZ-selected samples is of particular interest if we wish to combine the X-ray and SZ samples in order to obtain better statistics for various studies of cluster properties. In \S2, we describe the three cluster samples used in this paper, from the South Pole Telescope, ROSAT PSPC 400 deg$^2$ survey, and from numerical simulations. In \S3 we describe our methodology for quantifying X-ray morphology and the various tests that we will perform. In \S4 we will discuss results of these tests, focusing on the key questions of whether or not X-ray- and SZ-selected clusters are statistically different in terms of their X-ray morphology, whether simulated and real clusters have statistically different morphology, and whether there is any measurable redshift evolution in X-ray morphology. In \S5 we will discuss these results, placing them in context of previous work and considering their implications. We will conclude in \S6 with a brief summary and look forward to future studies. Throughout this work, we assume a flat $\Lambda$CDM cosmology with H$_0$=70 km s$^{-1}$ Mpc$^{-1}$ and $\Omega_{\rm M}$ = 0.27. | \label{sec:conclusions} Using samples of 36 X-ray selected clusters from the 400 deg$^2$ ROSAT survey, 91 SZ-selected clusters from the South Pole Telescope 2500 deg$^2$ survey, and 85 simulated clusters from the \emph{Omega}500 simulations, all observed (or mock observed) to roughly equal depth with the \emph{Chandra X-ray Observatory}, we investigated whether these samples have any bias towards cluster morphological type, and whether high-redshift clusters are more disturbed than their low-redshift counterparts. We considered two well-defined substructure statistics and tested for statistically significant differences in their distributions between different subsamples. In the mass and redshift range studied, we find no evidence for a statistically significant difference in the X-ray morphologies of clusters selected via X-ray or SZ, or at low or high redshift. Further, we found that simulated clusters had quantitatively similar morphology to X-ray- and SZ-selected systems, considering only the asymmetry of the hot gas (i.e., ignoring central cusps). Our results demonstrate that there is no significant bias for or against preferentially selecting mergers in high resolution ($\sim$1$^{\prime}$) SZ surveys. For SZ surveys with larger beam size (e.g., \emph{Planck}), morphological biases may exist due to the fact that multiple clusters or extended structures can contribute to the integrated signal. | 16 | 9 | 1609.00375 |
1609 | 1609.08625_arXiv.txt | We investigate the observed relationship between black hole mass ($M_{\rm BH}$), bolometric luminosity ($L_{\rm bol}$), and Eddington ratio (\Edd) with optical emission line ratios (\NIIHa, \SIIHa, \OIHa, \OIIIHb, \NeIIIHb, and \HeIIHb) of hard X-ray-selected AGN from the BAT AGN Spectroscopic Survey (BASS). We show that the \NIIHa\ ratio exhibits a significant correlation with \Edd\ ($R_{\rm Pear}=-0.44$, $p$-value=$3\times10^{-13}$, $\sigma=0.28$ dex), and the correlation is not solely driven by $M_{\rm BH}$ or $L_{\rm bol}$. The observed correlation between \NIIHa\ ratio and $M_{\rm BH}$ is stronger than the correlation with $L_{\rm bol}$, but both are weaker than the $\lambda_{\rm Edd}$ correlation. This implies that the large-scale narrow lines of AGN host galaxies carry information about the accretion state of the AGN central engine. We propose that the \NIIHa\ is a useful indicator of Eddington ratio with 0.6 dex of rms scatter, and that it can be used to measure $\lambda_{\rm Edd}$ and thus $M_{\rm BH}$ from the measured $L_{\rm bol}$, even for high redshift obscured AGN. We briefly discuss possible physical mechanisms behind this correlation, such as the mass-metallicity relation, X-ray heating, and radiatively driven outflows. | Nebular emission lines are a powerful tool for diagnosing the physical state of ionized gas and studying central nuclear activity. Optical emission line ratios can be used to discriminate between emission from the star formation in galaxies and harder radiation such as from the central nuclear activity around a supermassive black holes \citep[e.g.,][]{Baldwin81,Veilleux87,Kewley01, Kauffmann03}. Compared to star forming galaxies, active galactic nuclei (AGN) produce greater numbers of higher energy photons (e.g., UV and X-rays) and, therefore drive higher ratios of the collisionally excited forbidden lines compared to the photoionization-induced Balmer emission lines. Although such line ratios provide useful AGN diagnostics, even for obscured AGN \citep{Reyes08, Yuan16}, they may not be effective in selecting all heavily obscured AGN and/or AGN that lack significant amounts of low density gas \citep{Elvis81, Iwasawa93, Griffiths95, Barger01, Comastri02, Rigby06, Caccianiga07}. \begin{figure*} \includegraphics[width=\linewidth]{BPT_Edd_ratio_v7.ps} % \caption[Caption for LOF]{Emission line diagnostic diagrams for the BASS sources with signal-to-noise (S/N) ratio $>3$. Left: The \NIIHa\ versus \OIIIHb\ diagnostic diagram. Colour filled circles and triangles indicate type 1 AGNs (including type 1.9) and type 2 AGNs, respectively. The empirical star-formation curve obtained from \citet{Kauffmann03} (dashed curve) and the theoretical maximum starburst model of \citet{Kewley01} (solid curve) are used. The solid-straight line is the empirical demarcation of \citet{Schawinski07} distinguishing the Seyfert AGN from the LINERs. The Eddington ratio of BASS sources is shown with color-filled dots. Middle: The \SIIHa\ versus \OIIIHb\ diagnostic diagram. Right: The \OIHa\ versus \OIIIHb\ diagnostic diagram. Demarcation lines from \citet{Kewley01, Kewley06} are used. In all panels we also show more than 180,000 SDSS emission-line galaxies with filled contours chosen from the OSSY catalog ($z<0.2$) with S/N $>3$ for \NII, \Ha, \OIII, \Hb, \SIIa, \SIIb, and \OI. } \label{fig:bpt_Edd} \end{figure*} With the recent advent of hard X-ray ($>10$\,keV) facilities, such as \textit{INTEGRAL} \citep{Winkler03}, \textit{Swift} \citep{Gehrels04} and \textit{NuSTAR} \citep{Harrison13}, it is now possible to study samples of AGN that are less biased to obscuration and include even Compton thick sources ($N_{\rm H}>10^{24} {\rm cm}^{-2}$, \citealt{Ricci15, Koss16}). In particular, the Burst Alert Telescope (BAT, \citealt{Barthelmy05}) on board the \textit{Swift} satellite has been observing the sky in the 14-195 keV energy band since 2005, reaching sensitivities of $1.3\times10^{-11}\ergcms$ over 90\% of the sky. The 70 month \textit{Swift}-BAT all-sky hard X-ray survey\footnote{http://heasarc.gsfc.nasa.gov/docs/swift/results/bs70mon/} detected 1210 objects, of which 836 are AGN \citep{Baumgartner13}. While the BAT detection is relatively unabsorbed up to Compton thick levels (e.g., $N_{\rm H}<10^{24} {\rm cm}^{-2}$, \citealt{Koss16}) heavily Compton thick AGN ($N_{\rm H}>10^{25} {\rm cm}^{-2}$) are missed by X-ray surveys but may sometimes be detected using optical emission line diagnostics and strong \OIII\ emission lines (e.g., \citealt{Maiolino98}). \begin{figure*} \includegraphics[width=\linewidth]{Edd_ratio_6panels_v7_intr.ps} \caption{Optical emission line ratio versus Eddington ratio diagram. Black open circles and triangles indicate type 1 AGN (including type 1.9) and type 2 AGN, respectively. Median at each bin is shown with colour-filled symbols. Bin size is determined to have at least 10 sources. Black solid lines indicate the Eddington ratio - optical emission line ratio relations (equation~\ref{eq:regression}). The grey shaded regions account for the errors in the slope and intercept of the relation. The rms deviation is shown with dotted lines. An error bar in the bottom-left corner at each panel indicates typical uncertainties in Eddington ratio and optical emission line ratio. The ionization potential for each emission line is shown in the legends. Also, Pearson correlation coefficients and $p$-values are shown in the bottom-right corner of each panel. An emission line detection at S/N$<3$ (upper- or lower-limit) is shown with grey symbols. } \label{fig:ratio_Edd} \end{figure*} The relationship between Eddington ratio ($\lambda_{\rm Edd}\equiv L/L_{\rm Edd}$, where $L_{\rm Edd}\equiv 1.3 \times 10^{38} M_{\rm BH}/M_{\odot}$) and the position of AGN in emission-line diagrams is an important topic of study because of the difficulty in measuring black hole mass ($M_{\rm BH}$) from velocity dispersion in high redshift AGN. \citet{Kewley06} investigated host properties of nearby emission-line galaxies ($0.04<z<0.1$) from the SDSS. They found that the $\lambda_{\rm Edd}$ (inferred from $L_{\rm [OIII]}/{\sigma_{\star}}^{4}$, where $\sigma_{\star}$ is a stellar velocity dispersion) shows an increase with $\phi$, a measure of distance from the LINER regime in the \OIIIHb\ vs. \OIHa\ diagram. Similarly, an SDSS study of unobscured AGN by \citet{Stern13} found a dependence of emission-line diagnostics on the $\lambda_{\rm Edd}$. However, the estimation of $\lambda_{\rm Edd}$ and the introduced relationship between the angle $\phi$ and $L_{\rm [OIII]}/{\sigma_{\star}}^{4}$ were both dependent on the strength of \OIII. Also, the previous studies did not take into account X-ray selection focusing on the large sample of optically selected AGN. Both highly ionized optical emission lines and X-rays are thought to be a measure of the AGN bolometric luminosity. However, hard X-rays are less biased against dust obscuration and the contribution from star-forming activity than optical emission lines. The BAT AGN Spectroscopic Survey (BASS) Data Release 1 (Koss et al., in submitted) compiled 642 optical spectra of nearby AGN ($\langle z \rangle \sim 0.05$) from public surveys (SDSS, 6dF; \citealt{Abazajian09, Jones09, Alam15}) and dedicated follow-up observations (e.g., from telescopes at the Kitt Peak, Gemini, Palomar, and SAAO observatories). The data release provided emission line measurements as well as $M_{\rm BH}$ and $\lambda_{\rm Edd}$ estimates for the majority of obscured and un-obscured AGN (\Nmbhper, \Nmbh/\Ntot), including 340 AGN with $M_{\rm BH}$ measurements reported for the first time. In this paper, we use the BASS measurements to investigate the observed relationship between black hole mass ($M_{\rm BH}$), bolometric luminosity ($L_{\rm bol}$), and Eddington ratio (\Edd) with optical emission line ratios (\NIIHa, \SIIHa, \OIHa, \OIIIHb, \NeIIIHb, and \HeIIHb) for both obscured and unobscured AGN. We assume a cosmology with $h=0.70$, $\Omega_{\rm M}=0.30$, and $\Omega_{\Lambda}=0.70$ throughout this work. \begin{table*} \centering \begin{minipage}{160mm} \caption{Bayesian linear regression fit.} \label{tab:regression} \begin{tabular}{llcccccc} \hline line ratio & N & $\alpha$ & $\beta$ & RMSD & $R_{\rm Pear}$(\textit{p}-value) & $R_{\rm Pear, unobs}$(\textit{p}-value) & $R_{\rm Pear, obs}$(\textit{p}-value) \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) \\ \hline \NIIHa & 297 & $-0.42\pm0.04$ & $-0.19\pm0.02$ & 0.28 & -0.44 ($3 \times10^{-13}$) & -0.34 ($0.00002$) & -0.28 ($0.00128$) \\ \SIIHa & 288 & $-0.48\pm0.03$ & $-0.11\pm0.02$ & 0.25 & -0.29 ($9 \times 10^{-7}$) & -0.26 ($0.00080$) & 0.11 ($0.56180$) \\ \OIHa & 205 & $\cdot \cdot \cdot$ & $\cdot \cdot \cdot$ & $\cdot \cdot \cdot$ & (0.03314) & (0.02777) & (0.36499) \\ \OIIIHb & 286 & $\cdot \cdot \cdot$ & $\cdot \cdot \cdot$ & $\cdot \cdot \cdot$ & (0.32877) & (0.38456) & (0.34875) \\ \NeIIIHb & 125 & $\cdot \cdot \cdot$ & $\cdot \cdot \cdot$ & $\cdot \cdot \cdot$ & (0.87141) & (0.38163) & (0.78629) \\ \HeIIHb & 107 & $\cdot \cdot \cdot$ & $\cdot \cdot \cdot$ & $\cdot \cdot \cdot$ & (0.87516) & (0.56490) & (0.08583) \\ \hline \end{tabular} \medskip \\Note. (1) optical emission line ratio; (2) size of sample; (3) intercept; (4) slope; (5) rms deviation; (6) Pearson $R$ coefficient and \textit{p}-value; (7) Pearson $R$ coefficient and \textit{p}-value for unobscured AGN; (8) Pearson $R$ coefficient and \textit{p}-value for obscured AGN. \end{minipage} \end{table*} \begin{figure*} \includegraphics[width=1.0\textwidth]{BPT_Edd_ratio_distance_v7_intr.ps} \caption{${d}_{\rm LINER}$ and ${d}_{\rm SF}$ as a function of Eddington ratio. Left panel illustrates distances of two examples (star symbols) with corresponding color-coded Eddington ratio as in Fig.~\ref{fig:bpt_Edd}. Middle and right panels show the ${d}_{\rm LINER}$ and ${d}_{\rm SF}$ distributions, respectively. Bayesian linear regression fit, errors in the slope, intercept of the fit, and the rms deviation are shown with black straight lines, grey shaded regions and dotted lines, as in Fig.~\ref{fig:ratio_Edd}. } \label{fig:distance} \end{figure*} | We have presented the observed relationship between the $\lambda_{\rm Edd}$ and optical emission line ratios (\NIIHa, \SIIHa, \OIHa, \OIIIHb, \NeIIIHb, and \HeIIHb) using local obscured and unobscured AGN ($ \langle z \rangle = 0.05$, $z < 0.40$) from the 70-month \textit{Swift}-BAT all-sky hard X-ray survey with follow-up optical spectroscopy. We show that there is a significant anti-correlation between \NIIHa\ emission line ratio and $\lambda_{\rm Edd}$, and this correlation is stronger than trends with $M_{\rm BH}$ or $L_{\rm bol}$ or with other line ratios. The observed trend suggests that optical emission line ratios, which are widely used to classify sources as AGN, can also be an indicator of $\lambda_{\rm Edd}$. The use of \NII\ and \Ha\ emission lines as a $\lambda_{\rm Edd}$ indicator has potential implications for high redshift obscured AGN whose $M_{\rm BH}$ and $\lambda_{\rm Edd}$ are difficult to estimate. This would require to additionally assume that any relevant physical relations that might affect our $\lambda_{\rm Edd}$ - \NIIHa\ relation (e.g., the stellar mass-metallicity, AGN outflows), do not evolve significantly with redshift. The relationship shown in this work may serve as a basis for future studies toward measuring $M_{\rm BH}$ and $\lambda_{\rm Edd}$ of individual AGN. A number of complications arise when measuring $L_{\rm bol}$ and $M_{\rm BH}$ from a large ($N>100$) sample of galaxies. The majority of the total luminosity is emitted from the accretion disk in the extreme ultraviolet and ultraviolet energy bands \citep{Shields78, Malkan82, Mathews87}. While we used a fixed bolometric correction from the X-ray, this correction has been observed to vary depending on $\lambda_{\rm Edd}$ \citep{Vasudevan09} and $L_{\rm bol}$ (e.g., \citealt{Just07, Green09}). This issue deserves further study, though we would expect any biases to affect all line ratios whereas we find a much stronger correlation with \NIIHa. Another complication is the use of separate methods of BH mass estimates. We note, however, that these two methods are tied to reproduce similar masses for systems where both are applicable \citep{Graham11, Woo13}, and that we find significant correlations for both type 1 and type 2 AGN, separately (Table~\ref{tab:regression}). We will explore $M_{\rm BH}$ measurements for both types of AGN via different methods in a future study. There are several possible physical mechanisms that might lead to the trends found between $\lambda_{\rm Edd}$ and emission line ratios such as \NIIHa. \citet{Groves06} and \citet{Stern13} found a dependence of emission-line diagnostics, particularly of the \NIIHa, with host galaxy stellar mass. They postulated that this was a result of the mass metallicity relationship with more massive galaxies having more metals \citep{Lequeux79, Tremonti04, Erb06, Lee06, Ellison08, Maiolino08, Mannucci10, Laralopez10}. As more massive galaxies have more massive black holes, this follows the correlation found here with \NIIHa\ being positively correlated with $M_{\rm BH}$ and negatively correlated with $L_{\rm bol}$. \citet{Stern13} showed that \OIIIHb\ mildly decreases with stellar mass since reduced \OIII\ emission is expected from higher metallicity and massive systems as \OIII\ is a main coolant and the temperature will be lower in massive systems. The less significant correlation between \OIIIHb\ and $M_{\rm BH}$ shown in Fig.~\ref{fig:ratio_Mbh} as compared to the \NIIHa\ which scales strongly with metallicity can be explained in this context. Another interesting possibility affecting this correlation could be from higher $\lambda_{\rm Edd}$ AGN have relatively weaker \OIII\ lines, as found by the ``Eigenvector 1" relationships (e.g., \citealt{Boroson92}). A further possibility is that X-ray heating is inducing some of the negative correlation found between $L_{\rm bol}$ and the \NIIHa\ ratio. Ionizing ultraviolet photons produce a highly ionized zone on the illuminated face of the gas cloud while deeper in the cloud penetrating X-rays heat the gas and maintain an extended partially ionized region. Higher energy photons such as Ly$\alpha$ are destroyed by multiple scatterings ending in collisional excitation which enhances the Balmer lines \citep{Weisheit81, Krolik83, Maloney96}. Strong X-rays (i.e., harder SEDs) that heat up hot electrons in partially ionized region also enhance collisional excitation of ${\rm O}^{0}$, ${\rm N}^{+}$, and ${\rm S}^{+}$. As a result, it is expected to see high \NIIHa, \SIIHa, and \OIHa. Alternatively, the observed anti-correlation between emission line ratios (\NIIHa\ and \SIIHa) and $\lambda_{\rm Edd}$ may be due to radiatively driven outflows in high $\lambda_{\rm Edd}$ systems. Radiatively accelerated wind is predicted to be proportional to $\lambda_{\rm Edd}$ \citep{Shlosman85, Arav94, Murray95, Hamann98, Proga00, Chelouche01}. This is consistent with the observed blueshift of broad as well as narrow absorption lines \citep{Misawa07} often seen in quasars. In the context of a prevalent outflow in high $\lambda_{\rm Edd}$ AGN, the optical-UV SED of the accretion disk is expected to be softer when $\lambda_{\rm Edd}$ is $\gtrsim 0.3$ \citep{King03, Pounds03, Reeves03, Tombesi10, Tombesi11, Slone12, Veilleux16, Woo16}. As hot accreting gas is removed by ejecting outflows, the formation of collisionally excited emission lines is expected to be suppressed. It is important to note, however, that the anti-correlation between optical emission line ratio and $\lambda_{\rm Edd}$ is only appeared in \NIIHa\ and \SIIHa\ but not in other line ratios. | 16 | 9 | 1609.08625 |
1609 | 1609.07252_arXiv.txt | Infrared observations of the coma of 67P/Churyumov-Gerasimenko were carried out from July to September 2015, i.e., around perihelion (13 August 2015), with the high-resolution channel of the VIRTIS instrument onboard Rosetta. We present the analysis of fluorescence emission lines of H$_2$O, CO$_2$, $^{13}$CO$_2$, OCS, and CH$_4$ detected in limb sounding with the field of view at 2.7--5 km from the comet centre. Measurements are sampling outgassing from the illuminated southern hemisphere, as revealed by H$_2$O and CO$_2$ raster maps, which show anisotropic distributions, aligned along the projected rotation axis. An abrupt increase of water production is observed six days after perihelion. In the mean time, CO$_2$, CH$_4$, and OCS abundances relative to water increased by a factor of 2 to reach mean values of 32 \%, 0.47 \%, and 0.18\%, respectively, averaging post-perihelion data. We interpret these changes as resulting from the erosion of volatile-poor surface layers. Sustained dust ablation due to the sublimation of water ice maintained volatile-rich layers near the surface until at least the end of the considered period, as expected for low thermal inertia surface layers. The large abundance measured for CO$_2$ should be representative of the 67P nucleus original composition, and indicates that 67P is a CO$_2$-rich comet. Comparison with abundance ratios measured in the northern hemisphere shows that seasons play an important role in comet outgassing. The low CO$_2$/H$_2$O values measured above the illuminated northern hemisphere are not original, but the result of the devolatilization of the uppermost layers. | Comets are among the most pristine objects of the Solar System. The chemical composition of nucleus ices should provide insights for the conditions of formation and evolution of the early Solar System. A large numbers of molecules have now been identified in cometary atmospheres, both from ground-based observations and space, including in situ investigations of cometary atmospheres \citep{dbm2004,Cochran2015,Leroy2015,Biver2015a,Biver2016}. Molecular abundances relative to water present strong variations from comet to comet, and also vary along comet orbit \citep[e.g., ][]{Biver2016,Ootsubo2012,McKay2015,McKay2016}. This chemical diversity is often interpreted as reflecting different formation conditions in the primitive solar nebula \citep[e.g., ][]{Ahearn2012}. However, questions arise concerning the extent to which abundances measured in cometary atmospheres are representative of the pristine composition of nucleus ices. Models investigating the thermal evolution and outgassing of cometary nuclei show that the outgassing profiles of cometary molecules depend on numerous factors such as molecule volatility, thermal inertia of the nucleus material, nature of water ice structure, and dust mantling \citep{deSanctis2005,deSanctis2010a,deSanctis2010b,Marboeuf2014}. The study of the development of cometary activity, with the goal to relate coma and nucleus chemical properties, is one of the main objectives of the Rosetta mission of the European Space Agency \citep{Schulz2012}. Rosetta reached comet 67P/Churyumov-Gerasimenko (hereafter referred to as 67P) in August 2014 at $r_h$ = 3.5 AU from the Sun, and accompanied it in its journey towards perihelion (13 August 2015, $r_h$ = 1.24 AU), with the end of the mission in September 2016. The scientific instruments on the orbiter and Philae lander provided complementary information on the physical and chemical properties of the nucleus surface and subsurface, and of the inner coma. They revealed a dark, organic-rich and low-density bi-lobed nucleus with a morphologically complex surface showing different geological terrains, some of them with smooth dust-covered areas \citep{Sierks2015,Capaccioni2015,Patzold2016}. Dust jets originating from active cliffs, fractures and pits were observed \citep{Vincent2016}. Water vapour was first detected in June 2014, at 3.93 AU from the Sun \citep{Gulkis2014,Gulkis2015}. In data obtained pre-equinox (May 2015), the water outgassing was found to correlate well with solar illumination, though with a large excess from the brighter and bluer Hapi region situated in the northern hemisphere \citep{Biver2015b,dbm2015,Feldman2015,Migliorini2016,Fink2016,Fougere2016a}. In the Hapi active region, VIRTIS has observed that surficial water ice has diurnal variability showing sublimation and condensation cycle occurring with the change of illumination conditions \citep{deSanctis2015}. In contrast, CO$_2$ originated mainly from the poorly illuminated southern hemisphere \citep{Haessig2015,Migliorini2016,Fink2016,Fougere2016a}, where VIRTIS identified a CO$_2$ ice-rich area \citep[specifically in the Anhur region][]{Filacchione2016a}. The large obliquity (52$^{\circ}$) of the 67P rotation axis \citep{Sierks2015} leads to strong seasonal effects on its nucleus, with the northern regions experiencing a long summer at large distances from the Sun whereas the southern polar regions are subject to a short-lived, but extremely intense summer season around perihelion. In this paper, we present observations of H$_2$O, CO$_2$, $^{13}$CO$_2$, OCS, and CH$_4$ in the vapour phase undertaken with the high spectral resolution channel of the Visible InfraRed Thermal Imaging Spectrometer (VIRTIS) \citep{Coradini2007} near perihelion (early July to end of September 2015). The paper is organized as follow: Section~\ref{sec:obs} presents the VIRTIS-H instrument, the data set and raster maps of H$_2$O and CO$_2$ which provide the context for the off-limb observations studied in the paper; in Sect.~\ref{sec:model}, we present the detected molecular emission lines and the fluorescence models used for their analysis; section~\ref{sec:results} presents the data analysis and the column densities measured for H$_2$O, CO$_2$, CH$_4$, and OCS, and their relative abundances; an interpretation of the results and a discussion follows in Sect.~\ref{sec:discussion}. | This paper focussed on the perihelion period during which the southern regions of comet 67P were heavily illuminated. The measured abundance ratios of CO$_2$, CH$_4$ and OCS, and reported trends show that seasons play an important role in comet outgassing. The high CO$_2$/H$_2$O ratio measured in the coma is plausibly reflecting the pristine ratio of 67P nucleus, indicating a CO$_2$ rich comet. On the other hand, the low CO$_2$/H$_2$O values measured above the illuminated northern hemisphere are most likely not original, but the result of the devolatilization of the uppermost surface layers. The VIRTIS-H instrument acquired infrared spectra of H$_2$O and CO$_2$ during the whole Rosetta mission. Analysis of the whole data set will certainly provide further information on outgassing processes taking place on 67P's nucleus. \begin{table} \caption{Seasonal variations of abundance ratios (in \%) measured in 67P.} \centering \label{tab:abun-seasons} \begin{tabular}{lcccc} \hline Ratio & North & \multicolumn{2}{c}{South} & Other comets$^d$\\ (\%) & summer$^a$ & winter$^b$ & summer$^c$ & \\ \hline CO$_2$/H$_2$O & 1--3 & 80 &14--32 & 2.5--30 \\ CH$_4$/H$_2$O & 0.13 & 0.56 & 0.23-0.47 & 0.12--1.5 \\ OCS/H$_2$O & 0.017 & 0.098 & 0.12-0.18 & 0.03--0.4\\ \hline CH$_4$/CO$_2$ & 5 & 0.7 & 1.5--1.6 \\ OCS/CO$_2$ & 0.7 & 0.1 & 0.6--0.9 \\ \hline \end{tabular} {\raggedright $^a$ Values at $r_h$ = 3 AU from \citet{Leroy2015}, except for CO$_2$ measured at 1.8--2.9 AU \citep{dbm2015,Migliorini2016}. $^b$ Values at $r_h$ = 3 AU from \citet{Leroy2015}. $^c$ Values from this work at $r_h$ = 1.25--1.36 AU. $^d$ \citet{Biver2016}, \citet{Ootsubo2012}, \citet{McKay2016}, \citet{Mumma2011}. } \end{table} | 16 | 9 | 1609.07252 |
1609 | 1609.02477_arXiv.txt | {Exoplanet science has made staggering progress in the last two decades, due to the relentless exploration of new detection methods and refinement of existing ones. Yet astrometry offers a unique and untapped potential of discovery of habitable-zone low-mass planets around all the solar-like stars of the solar neighborhood. To fulfill this goal, astrometry must be paired with high precision calibration of the detector.} {We present a way to calibrate a detector for high accuracy astrometry. An experimental testbed combining an astrometric simulator and an interferometric calibration system is used to validate both the hardware needed for the calibration and the signal processing methods. The objective is an accuracy of $5\e{-6}$ pixel on the location of a Nyquist sampled polychromatic point spread function.} {The interferometric calibration system produced modulated Young fringes on the detector. The Young fringes were parametrized as products of time and space dependent functions, based on various pixel parameters. The minimization of function parameters was done iteratively, until convergence was obtained, revealing the pixel information needed for the calibration of astrometric measurements.} { The calibration system yielded the pixel positions to an accuracy estimated at $4\e{-4}$ pixel. After including the pixel position information, an astrometric accuracy of $6\e{-5}$ pixel was obtained, for a PSF motion over more than five pixels. In the static mode (small jitter motion of less than $1\e{-3}$ pixel), a photon noise limited precision of $3\e{-5}$ pixel was reached. } {} | \label{sec:Introduction} The year 2014 was marked by a symbolic yet significant milestone, the number of confirmed exoplanets exceeded 1000. The pace of discoveries is accelerating: at the time of writing, the exoplanet.eu database shows more than 3400 confirmed planets \citep{2011AA...532A..79S}, the last recent increase being mostly due to the success of the Kepler mission \citep{2014ApJ...784...45R}. Another interesting trend has been the discovery of increasingly smaller planets, down to the terrestrial ones. In some specific cases, we can detect these terrestrial planets in the habitable-zones of their stars, for example with transits \citep{2015arXiv150101101T} or for M stars \citep[][hereafter B13]{2013AA...549A.109B}. However, in the present state of exoplanet detection techniques, most likely none of the rocky planets of the Solar System would be discovered, even around a star as close as $\alpha$ Centauri, our closest Sun-like neighbor, located at the distance of 1.34 pc \citep{exoplanetDetMethods}. Rocky planets would only be found if the observer (located in a random direction near the Solar System) was lucky enough to observe their transits. Yet the rocky planets are a very strong constraint on the scenarios of formation of planetary systems \citep{2012AREPS..40..251M}. While for the question of planet formation, it is possible to rely on the power of statistics and the increasing number of detections, the question of life remains unanswered. Finding potentially habitable Earths twins in the Solar neighborhood would be a major step forward for exoplanet detection and these planets would be prime targets for attempting to find life outside of the Solar System \citep{2014SPIE.9148E..20M}. The next step is to search for bio-markers in their atmospheres by spectroscopy \citep{2010ARAA..48..631S}. Astrometry, by measuring the gravitational perturbation of planets on their central host stars, can determine the mass of planets and their orbits. From space, differential astrometry at a sub micro arcsecond ($\mu$as) accuracy around nearby solar-type stars can detect exoplanets down to one Earth mass in habitable-zone \cite[][hereafter M14]{2014SPIE.9143E..2LM}. The angular amplitude of the gravitational perturbation (the astrometric signal) is given by: \begin{equation}\label{eq:astrometric_signal} A = 3\,\mu \ml{as} \times \frac{M_{\ml{Planet}}}{\me} \times \left(\frac{M_{\ml{Star}}}{\ms}\right)^{-1} \times \frac{a}{1\ml{AU}} \times \left(\frac{D}{1\ml{pc}}\right)^{-1}. \end{equation} Where $D$ is the distance between the Sun and the observed star, $M_{\ml{Planet}}$ is the exoplanet mass, $a$ is the exoplanet semi major axis and $M_{\ml{Star}}$ is the mass of the observed host star. The constant $3$~$\mu$as corresponds to the signal of an exo-Earth observed from a distance of one parsec. In order to look for exo-Earths around Sun-like stars up to 10 pc (about one hundred targets), the signal to be detected is 0.3 $\mu$as. A crucial advantage expected for this method is that the astrometric jitter from stellar activity is small. Solar observations coupled with numerical models showed that the jitter should be smaller than the signal of an exo-Earth except for very active stars \citep{Makarov2010}, at least five times more active than the Sun \citep{Lagrange2011}. Given the current biases and limitations of the two major exoplanet detection techniques in use today (radial velocities and transits), current knowledge of exoplanets around nearby stars is still incomplete. % Out of the 455 main sequence stars of the Hipparcos catalog located at a distance of less than 20 pc from the Sun, only 43 (9.5\%) have known exoplanets. This statistic was obtained from a crossmatch between Hipparcos and the exoplanet.eu database, updated on 09 Mar 2016 \citep{2015PhDT.........7C}. The true occurrence rate of planets is significantly higher than 9.5\% \citep{Wolfgang2011,2013ApJ...764..105S}, therefore many more planets remain to be discovered. Past surveys only probed a small part of the orbital parameter space and we suspect that most of those stars have planets. \begin{figure*}[t] \sidecaption \includegraphics[width = 12cm]{neat_concept_diagram_v3.pdf} \caption{Schematic of the NEAT formation flying spacecraft. NEAT is composed of a mirror spacecraft and a detector spacecraft. The optical configuration is an off-axis parabola so there is no vignetting of the FoV. Sun shades prevent direct or reflected Sun light from reaching the CCD. A metrology system with laser beams launched from fibers located on the mirror projects dynamic Young fringes on the detector. The fringes allow a very precise calibration of the CCD. All three aspects (metrology, no vignetting, and Sun shades) are critical to reach micro arcsecond accuracy.} \label{neat_concept_diagram_v3} \end{figure*} This paper is about DICE, an interferometric calibration experiment of a (visible light) detector, which primary goal is to demonstrate the feasibility of sub-$\mu$as astrometry. The experiment is carried with a testbed that was assembled and operated at IPAG and funded by CNES in the context of the NEAT mission proposal to ESA in 2010 \citep{2012ExA....34..385M,2015PhDT.........7C}. The experiment only tackles the detector calibration issue (not the optical aspect). We have already presented the progress of the experiment \citep{crouzier12,crouzier13,crouzier14}. Here we present the scientific context (Sect. \ref{sec:Scientific context}), the experiment goal and principle (Sect. \ref{sec:Calibration experiment}), the data processing methods and their validation using numerical simulations (respectively Sect. \ref{sec:Data processing} and \ref{sec:Numerical simulations for DICE}) and the latest results obtained with testbed data (Sect. \ref{sec:Analysis of experimental data}). | The calibration system yielded the pixel positions to an accuracy estimated at $4\e{-4}$ pixel. After including the pixel position information, an astrometric accuracy of $6\e{-5}$ pixel was obtained, for a PSF motion over more than 5 pixels. Without the (flat and metrology) calibrations the astrometric accuracy is $1.4\e{-4}$ pixel (all other things equal). With the \textit{single-position} mode (small jitter motion of less than $1\e{-3}$ pixel), a photon noise limited precision of $3\e{-5}$ pixel was reached. The \textit{single-position} result shows that the detector and electronics dark and readout noises are well behaved and do not prevent reaching higher accuracies. The number that is relevant for an astrometric mission is the \textit{multi-position} analysis result: $6\e{-5}$ pixel. It characterizes the residual noise from pixelation errors after calibrations. As this accuracy was obtained for a motion over 5.4 pixels, a distance larger than the PSF diameter, it can be extrapolated to the whole CCD, considering only pixelation noise and assuming no spatial correlation of pixels properties. In the DICE experiment the translation stage tip tilt is responsible for the larger errors associated with wider motions. The \textit{single-position} results confirm that turbulence (in the closed vacuum chamber) is not an issue. A photon noise of $3\e{-5}$ pixel was reached for individual data cubes (results in Sect. \ref{sec:xp data pseudo stars}), which correspond to the expected photon noise. This first test on the main dataset presented here validates the absence of a lot systematics that could have been an issue, before even considering the \textit{multi-position} analysis, but still has a photon limit higher than the final requirement. Other tests on special datasets, also in air, and with much longer acquisition time showed that this \textit{single-position} precision can be improved further, at least to $10^{-5}$ pixel, while remaining at the photon limit. Some of the earlier datasets were taken in air and in vacuum, all other conditions unchanged, but no gain on the final astrometric accuracy was measured when going from air to vacuum. One of the main sources of noise for the metrology seems to be stray light, even after numerous baffle upgrades attempted to solve the issue. More work is needed to identify other possible sources of systematics and to understand what are the best ways to mitigate stray light. The limited effectiveness of the metrology calibration on astrometric accuracy ($\sim$2 fold improvement) could be caused by a spectral dependency of the PRFs. To first quantitatively assess and then mitigate the issue the same interferometric calibration should be performed at several wavelengths distributed across the visible spectrum. The final objective was set at $5\e{-6}$ pixel. In reality, the exact requirement depends on the spacecraft parameters and scientific objectives. For the new mission concept Theia, it is lightly easier: $10^{-5}$ pixel \citep{2015pathwaysMalbet,Malbet2016}. Theia can still detect nearby habitable Earths, even if it is restricted to slightly fewer and closer stars. Further progress is needed to reach the required Theia accuracy, but several leads have been identified to improve the metrology calibration. Additionally, as the experimental data showed, it could be possible to significantly enhance the final accuracy by averaging the relative star coordinates over several detector positions (previously refereed to as spatial averaging). In a real mission, one can reasonably conceive that up to 100 different positions (per epoch) could be used, resulting in the best case into a relaxing of the specification up to a factor 10 (the maximum gain is given by the square root of the number of positions). However spatial averaging is not desirable as a first approach to increase accuracy as it could impose significant additional constraints on the instrument capabilities, such as fast re-pointing, higher bandwidth or on-board processing (e.g. to "shift and add" images) and could decrease the overall instrument efficiency, by impacting the number of observable targets, or percentage of time spent collecting photons versus doing maneuvers). The experiment was put into storage in October 2015, but it is still functional and can be restarted if interest arises, for example in the context of a mission phase A study. | 16 | 9 | 1609.02477 |
1609 | 1609.05850_arXiv.txt | Because WISE J085510.83$-$071442.5 (hereafter \wise) is the coldest known brown dwarf ($\sim250$~K) and one of the Sun's closest neighbors (2.2~pc), it offers a unique opportunity for studying a planet-like atmosphere in an unexplored regime of temperature. To detect and characterize inhomogeneities in its atmosphere (e.g., patchy clouds, hot spots), we have performed time-series photometric monitoring of \wise\ at 3.6 and 4.5~\micron\ with the {\it Spitzer Space Telescope} during two 23~hr periods that were separated by several months. For both bands, we have detected variability with peak-to-peak amplitudes of 4--5\% and 3--4\% in the first and second epochs, respectively. The light curves are semi-periodic in the first epoch for both bands, but are more irregular in the second epoch. Models of patchy clouds have predicted a large increase in mid-IR variability amplitudes (for a given cloud covering fraction) with the appearance of water ice clouds at $T_{\rm eff}<$375~K, so if such clouds are responsible for the variability of \wise, then its small amplitudes of variability indicate a very small deviation in cloud coverage between hemispheres. Alternatively, the similarity in mid-IR variability amplitudes between \wise\ and somewhat warmer T and Y dwarfs may suggest that they share a common origin for their variability (i.e., not water clouds). In addition to our variability data, we have examined other constraints on the presence of water ice clouds in the atmosphere of \wise, including the recent mid-IR spectrum from \citet{ske16}. We find that robust evidence of such clouds is not yet available. | In multiple temperature regimes for brown dwarfs, condensates are predicted to form clouds, which can significantly influence the emergent spectra and colors \citep{ack01}. The spectra of L dwarfs \citep[1300--2200~K;][]{ste09} are best fit by models that include a thick cloud layer of iron, silicates, and corundum \citep{sau08}. Those clouds break up non-uniformly and disappear as brown dwarfs grow cooler and enter the T dwarf sequence \citep[500--1300~K;][]{ste09}, as indicated by the near-infrared (IR) colors \citep{bur02}, photometric and spectral variability \citep{bue14,bur14,rad14,radetal14,wil14,yan16}, and surface maps \citep{cro14,kar16} of objects near the L/T transition. Clouds may appear again below 900 K based on the colors of late T dwarfs, this time in the form of sulfides \citep{mor12}. Photometric variability at near-IR wavelengths has been reported in this temperature regime, which has been attributed to clouds \citep{yan16}. Among the Y dwarfs \citep[$<$500~K;][]{dup13}, additional clouds of water and ammonia are predicted to form at $<$350~K and $<$200~K, respectively \citep{burr03,mor14a}. When water clouds are present, they are expected to be patchy \citep{mor14a}, and hence amenable to detection through variability. The only Y dwarfs with published time-series photometry, WISE J140518.39+553421.3 (hereafter \wist) and WISEP J173835.52+273258.9, do exhibit variability but they are likely too warm to have water ice clouds \citep[$\sim$400~K;][]{cus16,leg16}. The most promising brown dwarf for the detection of water clouds is WISE J085510.83--071442.5 (hereafter \wise). It is the coldest known brown dwarf \citep[$\sim$250~K;][]{luh14}, making it the most likely one to harbor water clouds. In addition, it is the fourth closest system to the Sun \citep[2.23$\pm$0.04~pc;][]{luh14,luhes16}, so it is relatively bright for its low luminosity. As with other Y dwarfs\footnote{\wise\ has not been spectroscopically classified, but it is very likely to be a Y dwarf based on its luminosity.}, \wise\ is much too faint at near-IR wavelengths for accurate photometric monitoring \citep{bea14,fah14,kop14,luh14,wri14,luhes16,sch16}. Currently, such measurements are only feasible in mid-IR bands with the Infrared Array Camera \citep[IRAC;][]{faz04} on the {\it Spitzer Space Telescope} \citep{wer04}. In this paper, we present time-series IRAC photometry of \wise\ during two 23 hour periods. We begin by describing the observations and data reduction (Section~\ref{sec:obs}). We use these data to characterize the variability of \wise, which is then compared to the predictions of models that produce variability through either patchy clouds or hot spots (Section~\ref{sec:analysis}). We conclude by assessing the evidence of water ice clouds in the atmosphere of \wise\ from our variability measurements and previous observations (Section \ref{sec:disc}). | \label{sec:disc} Previous studies have attempted to constrain the presence of water ice clouds in the atmosphere of \wise\ using photometry and spectroscopy. \citet{fah14} reported a possible 2.6~$\sigma$ detection of \wise\ in a medium-band filter within the $J$ band. Those data were used to place the object in a diagram of $M_{W2}$ versus $J-W2$, where $W2$ is a band from the {\it Wide-field Infrared Survey Explorer} \citep{wri10} that is similar to [4.5] from {\it Spitzer}. The position of \wise\ in that diagram was better reproduced by cloudy models than cloudless models \citep{mor12,mor14a,sau12}, which was interpreted as evidence of water ice clouds. However, \citet{luhes14} demonstrated that \wise\ was roughly midway between those cloudless and cloudy models in a similar diagram of $M_{4.5}$ versus $J-[4.5]$, and that its position was best matched by cloudless models that employed non-equilibrium chemistry \citep{sau08,sau12}. After measuring photometry for \wise\ in several additional near-IR bands, \cite{sch16} and \cite{luhes16} found that no single suite of models provided a clearly superior match to the observed spectral energy distribution (SED), and that all of the models differed significantly from the data. Thus, the photometry and models that are currently available do not provide any indication of whether water ice clouds are present in \wise. A spectroscopic investigation of water ice clouds in \wise\ has been recently performed by \citet{ske16}. They obtained the only spectrum to date of the brown dwarf, which spans from 4.5--5.1~\micron. Although its resolution and S/N were low, the spectrum exhibited absorption features that appeared to be statistically significant, many of which coincided with features in model spectra computed by \citet{ske16}. The spectra predicted by cloudless and partly cloudy models were indistinguishable for the wavelength range and resolution of the data. The atmospheric temperature structure for a brown dwarf near the temperature of \wise\ does not converge with full coverage of water clouds \citep{mor14a}, so \citet{ske16} developed a simplified model for that scenario, which used a gray, fully absorbing cloud with no specified composition. The cloud-top pressure in that model was varied to optimize the match to the observed spectrum. The resulting best-fit spectrum agreed somewhat better with the data than the spectra from the cloudless and partly cloudy models, which was cited as a detection of clouds. Given the temperature of \wise, it is expected that such clouds would be composed of water \citep{burr03,mor14a}. It is unclear whether the spectrum from \citet{ske16} actually contains evidence of water clouds. The fully cloudy model from that study considered gray absorbers, whereas water ice is non-gray across the wavelength range of the spectrum of \wise\ \citep{mor14a}, and it assumed that the cloud coverage is uniform, which is not expected for water clouds \citep{mor14a}. In addition, models with patchy clouds have self-consistent temperature structures, which has not been possible for the fully cloudy models \citep{mor14a}. Given the variety of uncertainties in models of the coldest brown dwarfs \citep{mor14a} and the large differences between the observed and predicted SEDs for \wise\ \citep{sch16,luhes16}, the current models may not be sufficiently accurate for subtle differences in predicted spectra to provide meaningful insight into the physical properties of \wise. Our variability measurements can provide additional constraints on the existence of water ice clouds in the atmosphere of \wise. According to the partly cloudy models of \citet{mor14b}, cloud-induced variability at mid-IR wavelengths should become much larger (for a given cloud covering fraction) at temperatures below $\sim375$~K with the onset of water clouds. The amplitudes that we have measured for \wise\ ($\sim250$~K) are only a few percent, which would require very small deviations in cloud coverage between hemispheres ($\Delta h\sim0.01$) if water clouds are responsible for the variability. Meanwhile, the mid-IR amplitudes for \wise\ are similar to those observed for early Y dwarfs \citep[$\sim400$~K,][]{cus16,leg16} and late T dwarfs \citep[800--1000~K,][]{met15,yan16}, which should be too warm to harbor water clouds. If water clouds are producing the variability of \wise, then it must coincidentally have a value of $\Delta h$ that produces roughly the same amplitudes as the different variability mechanism that operates in those objects. Alternatively, the similarity in the amplitudes of \wise\ and somewhat warmer brown dwarfs may indicate that they share a common origin for their variability (i.e., not water clouds). Based on these results and the previous work that we have discussed, we conclude that robust evidence of water clouds in the atmosphere of \wise\ is not yet available. | 16 | 9 | 1609.05850 |
1609 | 1609.05899_arXiv.txt | Coevolution between supermassive black holes (BH) and their host galaxies is universally adopted in models for galaxy formation. In the absence of feedback from active galactic nuclei, simulated massive galaxies keep forming stars in the local Universe. From an observational point of view, however, such coevolution remains unclear. We present a stellar population analysis of galaxies with direct BH mass measurements and the BH mass--$\sigma$ relation as a working framework. We find that over-massive BH galaxies, i.e., galaxies lying above the best-fitting BH mass--$\sigma$ line, tend to be older and more $\alpha$-element enhanced than under-massive BH galaxies. The scatter in the BH mass--$\sigma$--[$\alpha/$Fe] plane is significantly lower than in the standard BH mass--$\sigma$ relation. We interpret this trend as an imprint of active galactic nucleus feedback on the star formation histories of massive galaxies. | The suppression of star formation via active galactic nucleus (AGN) feedback plays a crucial role in state-of-the-art numerical simulations \citep{Vogelsberger,Schaye}, but its observational effects are difficult to establish. The distribution of AGNs in the color--magnitude plane \citep{Martin07,Schawinski07} has been traditionally used as an indirect method to empirically constrain any AGN effect in nearby galaxies. With a detailed chemical evolution treatment in the most recent cosmological simulations \citep[e.g.][]{Crain15}, a new window of opportunity opens for understanding the effect of AGN on nearby objects. Based on the Evolution and Assembly of GaLaxies and their Environments (EAGLE) cosmological simulations, \citet{Segers} have recently linked AGN feedback to the over-abundance of $\alpha$-elements in massive galaxies -- a well-known property of nearby early-type galaxies \citep{Thomas,dlr11,Conroy14}. The existence of an [$\alpha$/Fe]--galaxy mass relation suggests a link between the star formation time-scale of a galaxy and its mass. Whereas $\alpha$-elements are produced in core collapse supernovae (SNe) with very short life-times, the onset of Type Ia SNe occurs later ($\sim 1$~Gyr), releasing mainly iron to the interstellar medium. Therefore the relative abundance of $\alpha$-elements to iron reflects how long SNe Ia have been able to pollute the medium: the less $\alpha$-enhanced a stellar population is, the more extended has been its star formation. In the scenario proposed by \citet{Segers}, more massive galaxies host and fuel more massive black holes (BHs) in their centers, leading to a stronger AGN effect which ultimately quenches the star formation more rapidly. The [$\alpha$/Fe]--galaxy mass relation would appear therefore as a natural consequence of the coevolution between BHs and galaxies. However, the (level of) coevolution is still under debate. The BH masses do correlate with the host galaxies properties \citep[see][for a review]{kh13}. The tightest correlation is the so-called M--$\sigma$ relation which links the BH mass and stellar velocity dispersion ($\sigma$) of the host galaxy \citep{Beifiori,vdB}. Whether this BH mass--$\sigma$ relation results from a causal connection \citep[e.g.][]{Silk98,Fabian,King} or not \citep{Peng07,Jahnke11} remains an open question. The effect of the AGN feedback depends strongly on the BH accretion rate. Close to the Eddington limit, the amount of energy radiated around the BH is expected to be large enough to effectively quench the ongoing star formation \citep{Fabian12}. This so-called quasar mode would take place at high redshifts ($z \sim 2-3$), and precedes the less energetic maintenance mode, which happens at lower BH accretion rates. The maintenance mode is thought to be responsible for continuously heating the gaseous halos around nearby massive galaxies. The properties of present-day massive galaxies would then be a combination of the early quenching associated with the quasar mode, and the more extended maintenance mode which inhibits further star formation \citep{Voit,Choi}. However, observational evidence of AGN feedback is inconclusive. On the one hand, strong nuclear outflows have been reported in a wide variety of environments, from luminous quasars \citep{Greene11} to nearby quiescent galaxies \citep{Cheung}. Moreover, \citet{Beifiori} have tentatively explored the connection between nuclear activity and the M--$\sigma$ relation. On the other hand, and contrary to what would be expected from negative AGN feedback, the most (X-ray) luminous AGNs are found in strongly star forming galaxies \citep{Rovilos}. In this Letter we report our attempts to quantify the effect of the central BH on the evolution of the host galaxy. We conduct a stellar population analysis of galaxies with known BH masses, finding significant differences in the stellar population properties depending on the location of the galaxy in the BH mass--$\sigma$ plane. This suggests a strong degree of coevolution between galaxies and their central BHs. | Understanding the mechanism responsible for quenching the star formation within massive galaxies is a difficult task. In the local Universe, a detailed analysis of their stellar populations is possible, but quenching is no longer taking place. At higher redshifts ($z\gtrsim2-3$), when massive galaxies ceased forming new generations of stars, obtaining sufficiently good spectra is out of reach for the current generation of telescopes. In this Letter we made use of two observables left behind in the natural evolution of galaxies: the BH as power source of the AGN activity, and the abundance pattern of stars as a proxy for the formation time-scale of the stellar populations. Our findings, summarized in Figs.~\ref{pop} and \ref{scatter}, indicate a strong connection between the stellar population properties of a galaxy and the mass of its central BH. In particular, stars within over-massive BH galaxies tend to be older and more $\alpha$-enhanced, suggesting a more rapid quenching process than in under-massive BH galaxies. It could be argued that our findings result from spurious correlations with unrecognized parameters. However, \citet{Beifiori} and \citet{vdB} have shown that the residuals of the BH mass--$\sigma$ relation do not correlate with structural parameters of galaxies. An alternative scenario could involve a sample biased towards later-type galaxies below the BH mass--$\sigma$ relation \citep{Kormendy}. Nevertheless, we rule out this possibility, first of all, because the observed trend also extends to the most massive galaxies in our sample, where only early-type galaxies are found. In addition, after removing the pseudo-bulges from the analysis, the same trends with BH mass are recovered. \citet{Greene} recently claimed that megamaser disk galaxies are slightly off-set from the main BH mass--$\sigma$ relation. Most of these objects were removed because their spectra displayed strong nebular emission within the H$_\beta$ line, and only one megamaser (NGC~2960) is present in the final sample. As expected from our findings, and given its relatively low BH mass, NGC~2960 shows almost no $\alpha$-enhancement ([Mg/Fe] = 0.003) Notice that, although not ideal, our approach for correcting the stellar continuum does not introduce any bias to our stellar population analysis, since it is completely independent of the mass of the BH. In principle, the mass of the BH in $\alpha$-enhanced galaxies could be over-estimated if a solar-scaled ([Mg/Fe] = 0) mass-to-light ratio (M/L) is assumed. However, the effect of the abundance pattern on the M/L is very mild, and only significant for filters bluer than $\lambda_\mathrm{eff}\sim4000$ \AA \ \citep{alpha}. Moreover, since dynamical models commonly assume a radially constant M/L, a pronounced gradient may also affect the BH measurement. In this regard, \citet{Pat} have shown that more massive and $\alpha$-enhanced ETGs galaxies have flatter gradients in their stellar population properties, and thus, more constant M/L profiles \citep{mn15}. Thus, we do not expect a systematic bias in the BH masses due to the stellar population properties of the host galaxies. We interpret our results as a direct connection between the central BH and the star formation history of galaxies. More massive BHs would have formed earlier and in denser regions of the Universe, feeding more active AGNs, and thus quenching the star formation more quickly. This scenario leads to older and more $\alpha$-enhanced stellar populations. As the BH mass and the AGN feedback decrease, galaxies would form later, creating stars over more extended periods of time, leading to lower [Mg/Fe] and younger ages. For galaxies above L$^*$, like those studied in this work, the effect of stellar feedback even in the early stages of galaxy formation is expected to be negligible. However, a natural prediction of this AGN-driven quenching is that the differences between over- and under-massive galaxies would start vanishing for objects below L$^*$. Is then the chemical enrichment of massive galaxies entirely determined by the AGN activity in the early Universe? The abundance pattern of a galaxy depends on two factors: the formation time-scale of its stellar populations and the number of massive stars responsible for the chemical enrichment, i.e., the stellar initial mass function (IMF). Consequently, an enhanced [Mg/Fe] can result from a short star-formation event or from a more extended star-formation history but with a flat (giant-dominated) IMF \citep{vazdekis96,thomas99}. While our analysis at fixed $\sigma$ shows an enhanced [Mg/Fe] for over-massive BH galaxies, therefore supporting a connection between AGN and the abundance pattern, the IMF might also be playing an important role in establishing the [Mg/Fe]--$\sigma$ relation. In particular, it has been shown that a time-varying IMF, which is flatter at earlier epochs, is necessary to reconcile the chemical properties of nearby massive galaxies and their apparently non-universal IMF \citep{Ferreras15,weidner:13,mn16}. Numerical simulations have also supported the idea of a flat IMF during the early formation of massive galaxies \citep{Calura,Arrigoni,Fontanot}. Thus, the [Mg/Fe]--$\sigma$ relation is potentially driven by a combination of the two processes, AGN-related quenching plus a non-universal IMF. Irrespective of the origin of the abundance pattern in galaxies, {\it our results demonstrate, observationally, a strong correlation between the black hole masses and the star formation histories of galaxies, which we interpret as AGN feedback directly driving the star formation history of massive galaxies}. | 16 | 9 | 1609.05899 |
1609 | 1609.05311_arXiv.txt | The angular resolution ($\sim$10$''$) achieved by the Herschel Space Observatory $\sim$3.5\,m telescope at FIR wavelengths allowed us to roughly separate the emission toward the inner parsec of the galaxy (the central cavity) from that of the surrounding circumnuclear disk (the CND). The FIR spectrum toward Sgr~A$^*$ is dominated by intense [O\,{\sc iii}], [O\,{\sc i}], [C\,{\sc ii}], [N\,{\sc iii}], [N\,{\sc ii}], and [C\,{\sc i}] fine-structure lines (in decreasing order of luminosity) arising in gas irradiated by the strong UV field from the central stellar cluster. The high-$J$ CO rotational line intensities observed at the interface between the inner CND and the central cavity are consistent with a hot isothermal component at $T_{\rm k}$$\approx$10$^{3.1}$\,K and $n$(H$_2$)$\approx$10$^4$\,cm$^{-3}$. They are also consistent with a distribution of lower temperatures at higher gas density, with most CO at $T_{\rm k}$$\approx$300\,K. The hot CO component (either the bulk of the CO column density or just a small fraction depending on the above scenario) likely results from a combination of UV and shock-driven heating. If \mbox{UV-irradiated} and heated dense clumps do not exist, shocks likely dominate the heating of the hot molecular gas component. Although this component is beam diluted in our FIR observations, it may be resolved at much higher angular resolution. An ALMA project using different molecular tracers to characterize UV-irradiated shocks in the innermost layers of the CND is ongoing. | 16 | 9 | 1609.05311 |
||
1609 | 1609.00534_arXiv.txt | {After the loss of a second reaction wheel the \Kepler mission was redesigned as the K2 mission, pointing towards the ecliptic and delivering data for new fields approximately every 80 days. The steady flow of data obtained with a reduced pointing stability calls for dedicated pipelines for extracting light curves and correcting these for use in, \eg, asteroseismic analysis.} {We provide corrected light curves for the K2 fields observed until now (campaigns 0--4), and provide a comparison with other pipelines for K2 data extraction/correction. } {Raw light curves are extracted from K2 pixel data using the ``K2-pixel-photometry'' (\ktpt) pipeline, and corrected using the KASOC filter.} {The use of \ktpt allows for the extraction of the order of $90.000$ targets in addition to $70.000$ targets proposed by the community --- for these, other pipelines provide no data. We find that \ktpt in general performs as well as, or better than, other pipelines for the tested metrics of photometric quality. In addition to stars, pixel masks are properly defined using \ktpt for extended objects such as galaxies for which light curves are also extracted.} {} | \label{sec:intro} During May of 2013 a second of four on-board reaction wheels of the \Kepler spacecraft was lost and with it the ability to maintain 3-axis pointing stability of the spacecraft. This led to the redesigned mission ``K2'' where fields towards the ecliptic are observed for a duration of approximately 80 days \citepads{2014PASP..126..398H}. The specific challenges with data quality, combined with the high and steady flow of data from the K2 mission calls for dedicated data analysis pipelines to deliver data to the community. We here report on the release of light curves extracted from raw pixel data from K2's Campaigns (C) 0--4 using masks defined by the \ktpt (K2-Pixel-Photometry) pipeline presented in \citetads[][]{2015ApJ...806...30L}, hereafter L15. Corrections of the resulting raw light curves are made using the KASOC pipeline by \citetads[][]{2014MNRAS.445.2698H}, hereafter HL14. This paper will serve as a data release note, describing the characteristics of the data and the reduced products that have been made available via the KASOC database\footnote{\url{http://kasoc.phys.au.dk/}}. Our paper is structured as follows. In Sections~\ref{sec:dataext} and \ref{sec:datproc} we briefly describe the concept of the \ktpt pipeline, and the KASOC pipeline which removes systematic artefacts. Here we also report on the properties of the pipeline segment pertaining to defining masks and estimating magnitudes. \sref{sec:datchar} reports on characteristics of the extracted light curves, focusing on noise properties. We detail in \sref{sec:datprod} the data products that have been made available on KASOC and summarise in \sref{sec:dis} with an outlook on future potential updates to the pipeline. | \label{sec:dis} We have presented characteristics of light curves from K2 campaigns 0--4 extracted using the \ktpt pipeline --- these light curves, and their power spectra, will be made available on the KASOC database. In terms of the data extraction the \ktpt pipeline performs very well, quantified by an addition of ${\sim}90.000$ extra light curves from untargeted stars for which data would not have been available otherwise. Concerning the definition of pixel masks a correlation as expected is obtained between mask sizes and target brightness, and contrary to other pipelines, masks are properly defined even for extended objects such as galaxies. The use of \ktpt light curves would thus increase the likelihood of detecting signals from supernovas and AGNs in these extragalactic targets. The extracted light curves are corrected using the KASOC Filter pipeline, and we find that these overall have lower photometric variability than those from other pipelines --- this could impact the detectability of, for instance, seismic signals. For \ktpt light curves a median drop in our proxy for white noise (see metric 5 in \sref{sec:datchar}) by a factor of ${\sim}10$ between C0 and C3 for \Kpt$\approx9-11$, which should positively affect the detection of oscillations from red giants. For future light curve processing we note that the use of house-keeping data from the \Kepler spacecraft could improve light curve corrections, because this would allow for a complete mapping between CCD position and apparent movement on the CCD without the need for computing stellar centroids. We find that the concept of \ktpt holds great potential for use with the upcoming NASA TESS mission (Transiting Exoplanet Survey Satellite; \citeads{2014SPIE.9143E..20R}). TESS will deliver full frame images of a $24^{\circ}\times 96^{\circ}$ field-of-view (FOV) with a cadence of ${\sim}30$ min for a duration of 27 days per field --- here an automatic and robust definition of pixels masks for targets in the FOV will be needed for the optimal utilisation of TESS data. | 16 | 9 | 1609.00534 |
1609 | 1609.05916_arXiv.txt | The recent detections of the binary black hole mergers GW150914 and GW151226 have inaugurated the field of gravitational-wave astronomy. For the two main formation channels that have been proposed for these sources, isolated binary evolution in galactic fields and dynamical formation in dense star clusters, the predicted masses and merger rates overlap significantly, complicating any astrophysical claims that rely on measured masses alone. Here, we examine the distribution of spin-orbit misalignments expected for binaries from the field and from dense star clusters. Under standard assumptions for black-hole natal kicks, we find that black-hole binaries similar to GW150914 could be formed with significant spin-orbit misalignment only through dynamical processes. In particular, these heavy-black-hole binaries can only form with a significant spin-orbit \emph{anti}-alignment in the dynamical channel. Our results suggest that future detections of merging black hole binaries with measurable spins will allow us to identify the main formation channel for these systems. | \label{sec:level1} The gravitational-wave detections GW150914 and GW151226 are the first direct evidence of the formation and merger of stellar-mass binary black holes (BBHs) in the local universe \citep{Abbott2016a,Abbott2016b}. Although many channels have been explored for the formation of such systems, most proposals fall into two categories: the ``field'' channel, in which BBHs are formed from isolated stellar binaries, usually involving either a common-envelope phase \cite[e.g.,][]{Voss2003,Dominik2012,Dominik2013,Belczynski2016} or chemically-homogeneous evolution due to rapid stellar rotation \cite[e.g.][]{DeMink2016TheLIGO,Mandel2016MergingBinaries,Marchant2016}, or the ``dynamical'' channel, in which BBHs are created though three-body encounters in dense star clusters \citep[e.g.,][]{Sigurdsson1993,PortegiesZwart2000,Downing2010,Downing2011,Ziosi2014,Rodriguez2015a,Rodriguez2016a}. Unfortunately, the masses and merger rates predicted by these models often significantly overlap, making it difficult to discriminate between different formation channels for BBHs even with multiple detections. However, masses and merger rates are not the only observable predictions from BBH formation models. In particular, the distribution of BH spin orientations are expected to depend heavily on the binary formation mechanism. For BBHs from the field, it is expected that the individual BH spins should be mostly aligned with the orbital angular momentum \citep{Kalogera2000}, with any misalignment arising from the momentum ``kick'' imparted to the orbit during core collapse. For dynamically-formed BBHs, both the spin and orbital angular momenta should be randomly distributed on the sphere. These spin-tilt misalignments produce relativistic precession of the orbit, which can be detected through the amplitude modulations in the gravitational waveform as the binary changes its orientation with respect to the detector \citep{Apostolatos1994,Vitale}. In this letter, we compare the expected distributions of spin-tilt misalignments for binaries formed from isolated binary stellar evolution to those formed from dynamical encounters in dense star clusters. We find that, for sufficiently massive systems (such as GW150914), measurements of the BBH spin-tilt will allow LIGO to discriminate between dynamically- and field-formed binaries. In addition, we find that dynamics provides the best route to forming binaries with a significant component of the spins anti-aligned with the orbital angular momentum. Since Advanced LIGO can best constrain the component of the spin angular momentum that is aligned with the orbital angular momentum \cite[][and references therein]{TheLIGOScientificCollaboration2016} we suggest that this may represent the best way to differentiate these BBH populations. | In this letter, we explore the spin-tilt distributions of BBHs from different formation channels. We have shown for heavy BBH systems, such as GW150914, the allowed range of spin-orbit misalignments that can be produced by BH NKs is limited. Only under the extreme case where BHs of all masses can recieve NKs comparable to NSs, can isolated stellar evolution produce spin-tilt misalignment greater than $90^{\circ}$. On the other hand, BBHs formed through dynamical processes in dense star clusters are expected to produce isotropically-distributed spin-tilt misalignments, which easily allow for the formation of BBHs with significantly anti-aligned spin and orbital angular momenta. Since any model of BH formation that allows for full-NS NKs results in a predicted BBH merger rate below the 90\% lower-limit observed by Advanced LIGO, we conclude that any sufficiently-massive BBH merger ($\mathcal{M}_c \gtrsim 10-15M_{\odot}$, depending on the driving mechanism of the NK) that shows a negative $\chi_{\rm{eff}}$ was most likely formed through dynamical processes. There are many additional facets of the BBH spin problem to be considered: first, although 50\% of dynamically-formed binaries will have $\chi_{\rm{eff}}<0$ (assuming non-zero component spins), this does \emph{not} mean that 50\% of binaries detected by LIGO from clusters will have clearly discernible $\chi_{\rm{eff}}<0$. Systems with $\chi_{\rm{eff}}\gg 0$ are detectable at greater distances than systems with $\chi_{\rm{eff}}\ll 0$ \citep{Ajith,Dominik2014}. Furthermore, systems with large spins in the plane of the orbit (the most probable configuration for dynamically-formed binaries) will precess, producing amplitude modulations that can further decrease detectibility of rapidly-spinning binaries. Given that dynamics preferentially forms BBHs with spins lying in the orbital plane, such precessional effects may offer the best chance for identifying dynamically-formed BBHs. Although precession has not been observed in the two BBHs detected so far, improvements in the lower-frequency limit of the LIGO instrument will increase the number of precessional periods a binary experiences while in the LIGO band, significantly improving the ability to measure the in-plane component of the BH spins. Studies to fully characterize the detection rate and distinguishability of these two astrophysical populations \citep[similar to][]{Vitale2016,Stevenson2016} are currently underway. | 16 | 9 | 1609.05916 |
1609 | 1609.08834_arXiv.txt | We study the conditions for the onset of Thermal Instability in the innermost regions of compact galactic nuclei, where the properties of the interstellar environment are governed by the interplay of quasi-spherical accretion onto a supermassive black hole (SMBH) and the heating/cooling processes of gas in a dense nuclear star cluster. Stellar winds are the source of material for radiatively inefficient (quasi-spherical, non-magnetised) inflow/outflow onto the central SMBH, where a stagnation point develops within the Bondi type accretion. We study the local thermal equilibrium to determine the parameter space which allows cold and hot phases in mutual contact to co-exist. We include the effects of mechanical heating by stellar winds and radiative cooling/heating by the ambient field of the dense star cluster. We consider two examples: the Nuclear Star Cluster (NSC) in the Milky Way central region (including the gaseous Mini-spiral of Sgr~A*), and the Ultra-Compact Dwarf galaxy M60-UCD1. We find that the two systems behave in different ways because they are placed in different areas of parameter space in the instability diagram: gas temperature vs. dynamical ionization parameter. In the case of Sgr~A*, stellar heating prevents the spontaneous formation of cold clouds. The plasma from stellar winds joins the hot X-ray emitting phase and forms an outflow. In M60-UCD1 our model predicts spontaneous formation of cold clouds in the inner part of the galaxy. These cold clouds may survive since the cooling timescale is shorter than the inflow/outflow timescale. | The composition and state of interstellar gas and dust in galaxies vary across different morphological types and evolutionary stages \citep{binney1998,swamy2005}. New stars form if the building material is available but the process of star-formation can be quenched by shock-heating and lack of supplies as galaxies evolve in the course of cosmological history \citep{kennicutt98,tacchella2015}. The environmental aspects are particularly complex in the central regions of galaxies, where strong tidal fields as well as effects of intense irradiation arise in the sphere of influence of the supermassive black hole (SMBH). The latter usually resides within a dense Nuclear Star Cluster (NSC) that may or may not be permeated by the dusty gaseous environment, depending on the specific conditions of a given source \citep{cole2015}. Our Milky Way's centre is a prominent example of a NSC that hosts both a SMBH and a large amount of material forming new stars even in its recent past \citep{eckart2005,genzel2010}. The physics of NSCs in galaxies, namely, their origin, history and the composition of their interstellar environment has a close resemblance on smaller scales to the properties of globular clusters \citep{degrijs2010}. Unlike nuclei of galaxies, typical globular clusters lack SMBHs in their cores; also, they are generally unable to retain any significant amount of gas and dust \citep{frank76,moore11}. However, the category of Ultra-Compact Dwarf galaxies \citep{mieske2013,mieske2014} appears to be a suitable type of object that can help us to explore the physics and evolution of NSCs with a central SMBH, and to compare them with the properties of the NSC in our Galaxy. The mechanism of cooling and heating of the interstellar medium (ISM) has been the object of detailed studies for some time \citep{dyson1980,kennicutt1998}. The microscopic processes that govern the gas dynamics are well understood, but nevertheless we still lack a detailed understanding of the chemical composition of the dusty plasma and of the energy input from stars. Such processes in galactic cores are complicated further by the unusually high density of the NSC \citep{genzel2010,schodel2014,fritz2016}, the effect of accretion onto SMBH and possible feedback in the form of a jet \citep{moscibrodzka13,yuan2014}, vigorous starburst activities, as well as the role of interactions and mergers \citep{kennicutt2012}. In this paper, we consider length-scales deep inside the NSC, where radiation and outflows from stars as well as energetic emission from the accretion flow, govern the physical properties of the system \citep{dopita2003}. The complexity of the gas dynamics in such a situation was described by \cite{silich2008} in their spherically symmetric picture. Very close to the center the material flows in, and accretes onto the supermassive black hole. Far out the material has enough energy to escape in a transonic outflow, leading to a continuous loss of gas. If the radiative cooling is inefficient, the inflow/outflow regions are separated by a stagnation radius. The relevant solutions have been found by \citet{quataert2004}. However, if plasma cooling is efficient, instead of a simple stagnation radius a whole region forms with no stationary solution \citep{silich2008}. A multi-phase medium develops where cold (relatively dense) clouds can coexist together with the hot, diluted gas \citep{rozanska14}. Pressure is the same in both phases. Therefore, density and temperature can span a broad range of values. The fate of the cold phase is determined by the characteristic length \citep{field1965,defouw1970,begelman1990}, \begin{equation} \lambda_{\rm F}=\left(\frac{\kappa T}{\Lambda n^2}\right)^{1/2}, \end{equation} where $\kappa$ is the thermal conductivity of the medium, $T$ -- temperature, $n$ -- density number, and $\Lambda$ is the total cooling rate \citep{draine1984}. Clouds of size less than $\lambda_{\rm F}$ tend to evaporate (heat conduction dominates), whereas larger clouds can be stabilized by radiative losses in the hot ambient medium (external heating vs.\ radiative cooling define the equilibrium of large clouds). Additional processes, such as turbulence and magnetic fields can further modify the basic scenario (small-scale magnetic fields induce anisotropy by inhibiting heat transport across the tangled field lines), but for the purpose of this paper we do not take them into account. Here we consider a local development of Thermal Instability (TI), although larger-scale global instabilities may also be important for the evolution of the system as a whole \citep{ciotti2001}. We study the above-mentioned type of TI, paying attention to the description of the heating/cooling processes of matter with the use of the photoionization code {\sc cloudy} \citep{ferland1996,ferland2013}. A simple parametrization of the gas cooling rate from \cite{plewa1995} was employed by \citet{silich2008}, while we add a more detailed description of the system. In particular, we include the spectral shape of the incident radiation from NSC. Here, we consider two special cases. The first example concerns the dense NSC near the Galactic Center (GC) SMBH. In addition to our previous work \citep{czerny2013b,czerny2013c,rozanska14} where we have taken into account the role of radiation heating by accretion flow, now we also include the role of energy input by radiation and wind outflows generated by hot stars. The second example falls within the category of Ultra-Compact Galaxies (UCDs) as an extreme case of NSCs where the outer part of the galaxy is missing, possibly due to interaction. In particular, the proto-typical M60-UCD1 \citep{mieske2013,mieske2014} serves as an exploratory case. For their extreme properties -- compact dimensions and enhanced mass-to-light ratio -- UCDs fit somewhere in between the NSC of the Galactic centre on one side and globular clusters on the other. With respect to conditions for the TI, we expect different results for UCDs than for the GC of the Milky Way because of their old stellar populations. By examining a sample of UCDs in the Virgo Cluster, \citet{zhang2015} concluded that these are a qualitatively different type of object from luminous (otherwise ``normal'') globular clusters. \citet{seth2014} has shown that the dynamical mass of M60-UCD1's black hole reaches $2.1\times10^7M_\odot$ while its nuclear star-cluster half-light radius is only $\sim 24$~pc. We illustrate the main differences of the plasma distribution in these type of objects from the case of our GC. The structure of this paper is as follows. In Sec.~\ref{sec:mo} we introduce the basic equations and present the full set-up of our model. All results are shown in Sec.~\ref{sec:res}, where we discuss two examples: Sgr~A* in the centre of the Milky Way, and UCD1 associated with M60 galaxy. Various aspects of the TI mechanism and potential ways to generalize our scenario are discussed in Sec.~\ref{sec:dis}. Finally, Sec.~\ref{sec:con} contains the main conclusions. | \label{sec:con} We studied the conditions for the onset of the Thermal Instability in compact stellar systems with a supermassive black hole residing in the core. As the Thermal Instability develops, it can help cold clumps to survive in the surrounding hot medium and drive them toward the central SMBH, thus enhancing the mass accretion rate during episodes of clumps disruption and inflow. The Nuclear Star Cluster in the centre of the Milky Way and the Ultra-Compact Dwarf galaxy UCD1 near M60 galaxy represent prototypical systems with a small half-light radius and large mass-to-light ratio, suggesting that an interplay between gravitational, radiative, and hydrodynamic influences leads to an interesting richness of the evolutionary tracks of the accreting SMBH. A large number of UCDs have been discovered in the last decade, however the presence of SMBHs at the centres of UCDs remains an open question. Sgr~A* is the best-resolved extreme example of a galactic nucleus with a Nuclear Star Cluster in addition to a SMBH. To explore the possibility of TI as a driver that triggers variability via accretion episodes, we discussed an appropriate definition of the ionization parameter $\Xi$ and studied the position of different systems with respect to the S-curve in the instability diagram. In addition to the effect of X-ray irradiation from the core we also took the cooling effect of ambient stellar radiation and mechanical heating from colliding winds into account, and we considered the presence of stagnation radius $R_{\rm st}$ in the Bondi-like hot inflow/outflow. We showed that Thermal Instability indeed operates under suitable conditions while it can be suppressed in other parts of the parameter space during the evolution of the system. Cold clouds can thus remain within the surrounding hot diluted medium for a relatively long period. A more complete multi-wavelength picture of these systems can help to constrain the state of their ISM in the future. Current evidence for the presence of a SMBH at the centre of M60-UCD1 arises from dynamical modeling of adaptive optics kinematic data \citep{seth2014}. However, apart from a tentative detection in X-rays, there is very little information about the SED of the central black hole. As we have seen in Section 3.2, the shape of the SED of the central black hole influences the formation of TI close to the SMBH. Follow-up observations in the X-ray and radio continuum can help to detect signatures of accretion in the central black hole and provide a more realistic SED. Observations in the infrared can also reveal the presence of dust/gas in the central regions to get a better estimate of the properties of the ISM in those objects. | 16 | 9 | 1609.08834 |
1609 | 1609.04701_arXiv.txt | Utilizing the all-sky imaging capabilities of the LWA1 radio telescope along with a host of all-sky optical cameras, we have now observed 44 optical meteor counterparts to radio afterglows. Combining these observations we have determined the geographic positions of all 44 afterglows. Comparing the number of radio detections as a function of altitude above sea level to the number of expected bright meteors we find a strong altitudinal dependence characterized by a cutoff below $\sim$ 90 km, below which no radio emission occurs, despite the fact that many of the observed optical meteors penetrated well below this altitude. This cutoff suggests that wave damping from electron collisions is an important factor for the evolution of radio afterglows, which agrees with the hypothesis that the emission is the result of electron plasma wave emission. | Recently \citet{Obenberger14} discovered that bright meteors will occasionally produce a radio afterglow at the high frequency (HF; 3 - 30 MHz) and very high frequency (VHF; 30 - 300 MHz) radio bands. Since then, afterglows have been regularly observed using the all-sky imaging capabilities of the first station of the Long Wavelength Array (LWA1), a 10 to 88 MHz radio telescope comprised of 256 dual polarization dipole antennas spread over a diameter of 100 meters \citep{Ellingson13}. The afterglows have little to no polarization, last from tens to hundreds of seconds, and have a broad spectrum, which appears to follow a steep power law, getting brighter at lower frequencies \citep{Obenberger15b,Obenberger16}. An upper frequency cutoff has not been detected in any event, but the radiated power drops below the LWA1 sensitivity above 60 MHz, for most events. We believe the emission to be intrinsic to meteor events and not the result of reflection. It is well established that meteors create ionization trails that can reflect man-made or or natural radio emission. Reflected signals are generally narrowband, polarized, and irregular, which is in contrast to the properties of the radio afterglows that we observe with the LWA1. There are no known radio sources that are bright enough and have sufficient bandwidth to produce reflected signals similar to our observations. With nearly 20,000 hours of data collected between April 2012 and April 2016, 154 radio transients have been detected by the LWA1, the majority of which appear to be radio afterglows from meteors. \citet{Obenberger15b} proposed the hypothesis that the afterglows could be the result of radiated electron plasma waves, occurring across a range of plasma frequencies found in the turbulent trail. This hypothesis was based on the fact that the emission is broadband, and appears to trace the expected range of plasma frequencies of the trail, where the plasma frequency is related to the electron density, $n_{e}$, by, \begin{equation} \omega_{pe} = \sqrt{\frac{n_{e} e^{2}}{m \epsilon_{0}}} \end{equation} where, $e$ is the electric charge, $m$ is the mass of the electron, and $\epsilon_{0}$ is the permittivity of free space. The electron plasma wave hypothesis has several challenges. Electron collisions with neutrals and ions would damp the waves much faster than the long timescales over which the afterglows are observed, requiring energy to be continuously injected into the trail in order to drive waves. Furthermore, electrostatic electron plasma waves would need to somehow be converted into electromagnetic waves, but steep density gradients within meteor trails would certainly aid the process. This is likely analogous to stimulated electromagnetic emissions (SEE) observed in the ionospheric F-region, where Langmuir waves are driven near the center frequency of high power transmitters and are then converted to electromagnetic waves \citep{Leyser01}. If radio afterglows are indeed caused by electron plasma waves, there should be an altitudinal dependence on the occurrence and brightness features. Electron plasma waves can only occur at altitudes where the electron collision frequency with both neutrals and ions is lower than the plasma frequency. More importantly, collisions would act as a damping agent to the wave growth. Currently, the best way to measure the altitudes of radio afterglows is by triangulating the position of optical counterparts. This is possible using the many all-sky fireball-searching cameras located in New Mexico or Arizona that share visible sky with the LWA1. The NASA All-Sky Fireball Network \citep{Cooke12} operates two cameras in southeast NM and three in south central AZ. Likewise the Sky Sentinel LLC (http://goskysentinel.com), operates two cameras near Albuquerque, NM. The authors of this paper operate one camera at Sevilleta National Wildlife Refuge, NM. Most of the cameras are all well over 100 km away from the LWA1, meaning that many events that occur above the LWA1 are near or below the observable horizon. Furthermore, light pollution (man-made and from the Moon) along with cloudy nights prevent many LWA1 events from being seen by the cameras. Despite these difficulties, between April 2012 and June 2016 we detected 44 meteor radio afterglows with measured optical counterparts. Statistical analysis of these events are presented in this paper. | Using coordinated optical and radio observations, we have found an altitude dependence on the occurrence of meteor radio afterglows. This dependence is characterized by a cutoff below 90 km. Such a cutoff agrees with our hypothesis that meteor radio afterglows are the result of electron plasma waves emission from turbulent meteor trails, though the cause may indeed be unrelated. | 16 | 9 | 1609.04701 |
1609 | 1609.06474_arXiv.txt | We report the discovery of a new \kep\/ first-overtone RR Lyrae pulsator, \obj. The pulsation shows large, 0.1\,d amplitude, systematic phase variations that can be interpreted as light travel-time effect caused by orbital motion in a binary system, superimposed on a linear pulsation-period decrease. The assumed eccentric ($e=0.47$) orbit with the period of $\approx 2$\,yr is the shortest among the non-eclipsing RR Lyrae binary candidates. The binary model gives a lowest estimate for the mass of the companion of 8.4\,$\mathfrak{M}_{\odot}$, that places it among black hole candidates. Beside the first-overtone pulsation, numerous additional non-radial pulsation frequencies were also identified. We detected an $\approx 47$-d Blazhko-like irregular light-curve modulation. | Past decades showed that the pulsation period of many RR Lyrae stars undergo long-term variations that cannot be explained by simple evolutionary effects. Beside abrupt changes \citep[see e.g.][]{lacluyze2004,sodor2007}, many stars show well documented cyclic years-to-decades-long period variations in the Galactic field \citep[e.g.][]{firmanyuk1982}, but mainly in globular clusters \citep[see e.g.][]{jurcsik2011,szeidl2011}. These variations often resemble the Light Travel-time Effect (LiTE), the consequence of orbital motion in combination with the finite speed of light. The investigation of period changes is the most efficient method for revealing RR Lyrae binary candidates, because typical RR Lyrae characteristics, mainly their evolutionary stadium and luminosity, disadvantage other available methods \citep[see e.g. discussions by][]{richmond2011,skarka2016}. Recently, several studies based on time-delay analysis introducing a few tens of binary candidates were published \citep[][]{li2014,guggenberger2015,hajdu2015,liska2016b,dePonthiere2016JAVSO..44...18D}. The most promising star, showing distinct, well-defined cyclic changes, is TU~UMa \citep[for a detailed study see][]{liska2016a}. Unfortunately, none of the candidates has yet been fully confirmed spectroscopically\footnote{An ongoing spectroscopic campaign on several candidates takes place right now \citep{guggenberger2016}.}, and the only confirmed RR Lyrae-like variable in eclipsing system turned out not to be a classical RR Lyrae, but the product of evolution in a close binary system \citep{pietrzynski2012,smolec2013}. Therefore, firm identification of an RR Lyrae in binary system supported by spectroscopic observations is still of extremely high importance favouring candidates with the shortest proposed, year-long, orbital periods. In this research note, we present one such candidate. We identified \obj\ as a previously unknown first-overtone RR Lyrae-type variable (RRc)\footnote{After identification, we found a Planet Hunters blog entry from Oct. 2012 on the suspected RRc nature at {\tt http://bit.ly/28Ip1Nc}}. As detailed light-curve analysis of only four \kep\ RRc stars has been published to date \citep{moskrrc}, this itself makes \obj\ an interesting target. However, our analysis revealed that this star might be a binary with the shortest know orbital period among non-eclipsing RR Lyrae binary candidates. In this research note, we analyse the \oc\/ variations in the context of hypothetical binarity, and present a concise analysis of the pulsation of \obj. We also present pro and con arguments of the binary explanation, and discuss the further observations necessary to confirm or reject the binary hypothesis. | \subsection{Pulsation} \label{sect:pulsdisc} KIC\,2831097 appears to be a typical first-overtone RR Lyrae pulsator. It shows a wide variety of pulsational phenomena that were already found in the other four investigated \kep\ RRc stars by \cite{moskrrc}. These are: \begin{itemize} \item A secondary pulsation frequency, $f_2$ with $f_1/f_2=0.612$ ratio to the first-overtone pulsation frequency, $f_1$. \item Half-integer multiples (subharmonics) of $f_2$. \item Linear combinations of $f_1$ with $f_2$ and its subharmonics. \item All peaks are broadened in the periodogram of the time-transformed data. \item Strong phase variations and weak, irregular amplitude changes on the order of $\pm$10 per cent. \item Additional, non-radial pulsation modes. \item Many Blazhko-modulation-like frequency components around the harmonics of $f_1$. \end{itemize} Blazhko-modulation-like side peaks around the pulsation harmonics ($kf_1+jf_\mathrm{m}$) can be found up to $j=5$. These peaks are equidistant, but broadened. The broadening indicates that the modulation is not strictly periodic. The wiggles visible in the residual \oc\/ variations (3rd panel of Fig.~\ref{fig:orb}), especially in the first half of the data, show an $\approx47$-d periodicity corresponding to $f_\mathrm{m}$. An interesting feature of the Fourier spectrum of \obj\ is the periodic pattern visible in Fig.~\ref{fig:sp1}. The overall distribution of the peaks is quite regular: 1\,--\,4 broadened peaks precede each pulsation harmonic with equidistant spacing of $f_1-1/2 f_2 = 0.48$\,\cd. This regular spacing has a simple arithmetic origin, as the linear-combination labels in the top part of the figure indicate. \subsection{Binarity} According to our orbital solution to the \oc\/ variations, the binary system has an eccentric orbit with quite high eccentricity of 0.47 and orbital period of 753\,d (2.06\,yr). This is the shortest known orbital period non-eclipsing RR Lyrae binary candidate \citep[see the up-to-date RRLyrBinCan database\footnote{http://rrlyrbincan.physics.muni.cz/},][]{liska2016b}. The orbital parameters and an adopted mass of the RR Lyrae component of $\mathfrak{M}_{1} = 0.6$\,$\mathfrak{M}_{\odot}$ predicts a very high mass for the possible companion; $\mathfrak{M}_{2} = 8.4$\,$\mathfrak{M}_{\odot}$, that places it among black hole candidates, due to evolutionary reasons. Beside the high mass of the companion, the rate of the linear period change is also extraordinary. Parameter $\beta$ with $-46.7$\,d\,Myr$^{-1}$ is almost 62 times higher than for the star SW~Psc with record value of period shortening ($\beta = -0.756(61)$\,d\,Myr$^{-1}$) among the field RR Lyrae stars \citep{leborgne2007}. All in all, there are several arguments both in favour and against the binary hypothesis. \begin{itemize} \item [] Pro arguments are: \item [+] Almost two complete, repetitive orbital cycles can be followed in the \oc\/ diagram. \item [+] The phase variations are not accompanied by correlated amplitude variations that would suggest Blazhko modulation. \item [+] Deviations from the orbital \oc\/ curve appear to follow a different periodicity of around 900\,d (see Fig.~\ref{fig:orb}) \vskip2mm \item []Con arguments are: \item [--] If \obj\ is a binary, the significant residual \oc\/ variations still require a different explanation. \item [--] Long-period RRc stars often show strong \oc\/ variations \citep{moskrrc}, even in a periodic fashion \citep{Derekas2004MNRAS.354..821D}. \item [--] This is the second long-pulsation-period RRc binary candidate appear to orbit a black hole companion after BE~Dor \citep{Derekas2004MNRAS.354..821D}, which is at least suspicious. \end{itemize} The \kep\ data in itself is insufficient to decide the question of binarity. An important goal of this research note is to facilitate further observations on this object both spectroscopically and photometrically. We already initiated a ground-based photometric campaign to follow-up \oc\/ variations to extend the time base. Considering the relatively short predicted orbital period and large predicted gamma velocity amplitude, several short spectroscopic observing campaigns with 4-m class telescopes in the following 2\,--\,4 observing seasons must be decisive on this matter. Our new \oc\/ data will help timing these spectroscopic follow-up observations. On the other hand, if \obj\ would prove to be a non-binary RR Lyrae star, it will be a warning that even single RR Lyrae can produce \oc\ curves that can be satisfactorily modelled with the combination of orbital light delay and linear period change, although the orbital parameters might be physically less plausible \citep[see also][]{Derekas2004MNRAS.354..821D}. This might be especially true for objects with less precise and less densely sampled \oc\ curves than the excellent \kep\/ data on our target. | 16 | 9 | 1609.06474 |
1609 | 1609.08143_arXiv.txt | \label{sec:intro} Weak gravitational lensing of the cosmic microwave background (CMB)~\cite{blanchard87, bernardeau97, zaldarriaga98, lewis06} is now a highly significant feature, seen in both the power spectra~\cite{calabrese08, reichardt09, keisler11, sievers13, story13, planck13parameters,planck15parameters} and the higher-order statistics~\cite{smith07, hirata08, Das:2011ak, vanEngelen:2012va, polarbear14, story15, planck15lensing}. Depending on the question of interest, CMB lensing can be either a nuisance or a tool. For instance, the sum of the neutrino masses can be measured from the reconstruction of the lensing potential~\cite{Kaplinghat:2003bh}. For some other parameters, error bars improve when the effect of lensing is removed from the power spectra (delensing). Delensing the $B$-mode polarization to search for primordial gravitational waves is one example that has been studied in great detail~\cite{Knox:2002pe, Kesden:2002ku, Seljak:2003pn, Smith2010, Sherwin:2015baa}, but delensing is a more broadly useful tool that has been explored to a much smaller extent in temperature ($T$) and $E$-mode polarization ($E$). Recently the delensing of the small-scale temperature field was demonstrated on \planck CMB data using \planck maps of the cosmic infrared background~\cite{Larsen:2016wpa}. In this paper we present a computation of the delensed small-scale CMB power spectra to all orders in the lensing potential, calculate the associated covariance matrices of delensed power spectra, and forecast parameter constraints from upcoming CMB surveys when analyzing the delensed spectra. One of the motivations for studying delensing in this regime is for future measurements of the effective number of neutrino species, $\Neff$. Free streaming radiation, such as neutrinos, is known to induce a phase shift in the acoustic peaks of the primary CMB~\cite{Bashinsky:2003tk,Follin:2015hya,Baumann:2015rya}. Lensing is known to smooth the acoustic peaks~\cite{Seljak:1995ve, Zaldarriaga:1998ar} which, in turn, reduces the accuracy of the measurements of the peak locations. In fact, the benefit of delensing is quite analogous to BAO reconstruction~\cite{Eisenstein:2006nk}, as illustrated in Figure~\ref{fig:BAO_analogy}. For this reason, forecasts for future CMB experiments show that unlensed spectra lead to better measurements of $\Neff$~\cite{Baumann:2015rya}. In reality, delensing is an imperfect procedure and therefore any proper treatment of forecasting or analysis should predict the delensed, rather than unlensed, spectra. One of the great technical simplifications of CMB lensing is that the process is local in the observed direction. In the flat sky limit, \beq \tilde T(\x) = T(\x+\va(\x)) \simeq T(\x) + \va(\x)\cdot \vec \nabla T(\x) + \ldots \ . \eeq where $\tilde T$ ($T$) is the lensed (unlensed) temperature map, $\vec \alpha = \vec \nabla \phi$ is the deflection angle, and $\phi$ is the lensing potential. Given an observed temperature map ($\To$) and lensing map ($\vao$), we can certainly imagine a perturbative approach to delensing where \beq \Td(\x) \approx \To(\x) - \vao \cdot \vec \nabla \To(\x) \ , \eeq where $\Td$ is the delensed temperature map. In practice, modeling lensing of the CMB power spectra requires more accuracy than the simple perturbative description. Fortunately, $\phi$ is Gaussian to good approximation, which makes an all-orders description of the lensed spectra calculable~\cite{Seljak:1995ve, Zaldarriaga:1998ar}. One would therefore expect that delensing could be treated by a similar all-orders procedure to predict the delensed power spectra (see also~\cite{Larsen:2016wpa} for a related discussion), given a non-perturbative description of the method for delensing. In this paper, we will provide an all-orders description of delensing for both temperature and polarization. We will first describe a non-perturbative approach to delensing that reproduces the unlensed CMB in the limit of no noise. This procedure is naturally generalized to account for the noise in the temperature, polarization, and lensing maps. We are careful to use filtered maps as part of the delensing procedure, which we show is necessary for improving parameters constraints. In principle, one can then produce the all-orders delensed spectra. In practice, the exact expressions are difficult to calculate due to the non-local relationship between the observed data and the true location of the underlying lenses. Fortunately, on the scales of interest, the lensing potential varies slowly compared to the CMB maps and these non-local effects can be neglected or included in a perturbative expansion. This will allow us to provide simple expressions for the delensed power spectra that we also implement numerically. The most immediate application of these all-orders results is for forecasting future CMB experiments. We include forecasts covering a range of possible experimental configurations to illustrate the impact of delensing on $\Neff$ and other cosmological parameters. Our goal is to understand to what degree forecasts using unlensed spectra are achievable given realistic noise levels in the lensing map. This is especially important for forecasts of $\Neff$ for CMB Stage IV, which are tantalizingly close to the theoretical threshold of $\Delta \Neff = 0.027$ (see e.g.~\cite{Brust:2013xpv,Salvio:2013iaa,Kawasaki:2015ofa,Chacko:2015noa,Adshead:2016xxj,Baumann:2016wac} for discussion). We will also show that delensing reduces the covariance between the lensing power spectrum and the observed temperature and polarization spectra. Proper forecasting must thus account for both the delensed spectra and covariance matrix~\cite{BenoitLevy:2012va,Schmittfull:2013uea}. \begin{figure}[t!] \begin{center} \includegraphics[width=0.75\textwidth]{temp_corr_func_lensing_combined} \caption{The effect of lensing and delensing on the temperature two-point correlation function, $C_T(r)$. The top panel shows the lensed and unlensed curves, as well as the delensed curves for various experimental noise configurations using the tools developed in this work. Specifically, the Stage II, III, and IV experiments contain noise levels of 10, 5, and 1 $\mu$K-arcmin respectively. The bottom panel shows the change relative to the unlensed correlation function. We see that lensing smoothes the BAO feature in the CMB and is restored by delensing, much like what is done with BAO-reconstruction at lower redshifts~\cite{Eisenstein:2006nk}.} \label{fig:BAO_analogy} \end{center} \end{figure} This paper is organized as follows. In Section~\ref{sec:theory}, we present the theoretical framework for computing the delensed CMB spectra. We apply these results in Section~\ref{sec:sims} to show the numerically computed spectra and covariance matrices. In Section~\ref{sec:params}, we use these results in forecasts for future CMB experiments. We highlight the impact of delensing by comparing forecasts with lensed, unlensed, and delensed spectra. We conclude in Section~\ref{sec:concl}. The main text is supplemented by six appendices. Appendix~\ref{app:grad} explores the validity of our expansion in gradients of $\phi$. We compute the optimal filters in Appendix~\ref{app:filters} for both the temperature and polarization spectra in various limits and explain the choice of filters used in the main text. Appendix~\ref{app:numpol} gives the expressions for efficient numerical computation of the delensed polarization spectra. In Appendix~\ref{app:covmat}, we show how to calculate the delensed covariance matrix. In Appendix~\ref{app:info}, we explore the effect of delensing on the Fisher information. We argue that, as long as the lensing potential is included in the likelihood, one should gain information by delensing. Appendix~\ref{app:exact} explores an alternate all-orders approach to delensing that is exact in the limit of no noise. We will use the following conventions throughout: we define Stage II, III, and IV to be 1 arcmin resolution experiments with 10, 5, and 1 $\mu$K-arcmin temperature noise respectively. The lensing noise for these experiments is determined assuming the minimum variance quadratic estimator~\cite{Hu:2001kj}, which combines information in the lensed temperature and polarization fields, including the improvement from iterative delensing with the $EB$ reconstruction~\cite{Smith2010}. We typically show power spectra in terms of ${\mathcal D}_\ell \equiv \ell (\ell+1) C_\ell / (2\pi)$. We will use $\vl$ to label harmonics of the CMB temperature and polarization but we use $\vL$ for the harmonics of the lensing potential. | \label{sec:concl} In this paper, we have shown that future CMB experiments will be sufficiently sensitive to CMB lensing that the delensing of all of the spectra (and not just $B$ modes) can meaningfully improve the constraints on cosmological parameters. Delensing sharpens in the acoustic peaks, improving the measurement of peak locations and any cosmological parameters that affect the acoustic structure. Delensing also removes the lens-induced covariances for the modes measured with high significance. We have shown how to compute the predictions for the delensed spectra and covariances to all orders in the lensing potential. We used these results to model the impact of delensing on cosmological parameters of interest. The most notable improvements occurred for parameters sensitive to peak locations and associated parameters that would otherwise be degenerate. In $\Lambda$CDM, the most dramatic improvements occurred for $\theta_s$ which is directly a measurement of the peak locations. When $Y_p$ and $\Neff$ are both free, the phase shift due to $\Neff$ breaks the degeneracy between these two parameters and delensing is seen to substantially improve error bars, showing an improvement of roughly 20\% for both parameters with a Stage IV experiment when compared to forecasts with lensed spectra. More generally, we show that when the residual lens-induced covariances are included, Fisher information always increases when using delensed, rather than lensed, spectra. Looking forward, delensed spectra will ultimately be necessary not just for forecasting but also for any likelihood analysis with delensed data. However, unlike lensed or unlensed spectra, the theoretical predictions depend also on the experimental noise. The analysis presented here computes these spectra for more idealized experiments. In principle, the approach taken here will generalize to any experiment, but real data may violate some of the technical assumptions needed to simplify our analytic predictions. More optimistically, we did not fully solve the problem of how to optimize our filters to maximize the Fisher information and one might imagine even more information may yet be available. As delensing of the CMB becomes more commonplace, these and other extensions of this work will deserve further exploration. \vskip23pt \paragraph{Acknowledgements} We thank Daniel Baumann, Raphael Flauger, Marcel Schmittfull, Neelima Sehgal, Blake Sherwin, and Kendrick Smith for helpful discussions. D.G.~and J.M.~also thank Daniel Baumann and Benjamin Wallisch for collaboration on related work that inspired this project. D.G.~was supported by an NSERC Discovery Grant and the Canadian Institute for Advanced Research. J.M.~was supported by the Vincent and Beatrice Tremaine Fellowship. \newpage \appendix | 16 | 9 | 1609.08143 |
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1609 | 1609.08972_arXiv.txt | We studied the physical parameters of a sample comprising of {\it all} {\it Spitzer/IRS} public spectra of Seyfert galaxies in the mid-infrared (5.2-38\,$\umu$m range) under the active galactic nuclei (AGN) unified model. We compare the observed spectra with $\sim10^6$ {\sc clumpy} model spectral energy distributions, which consider a torus composed of dusty clouds. We find a slight difference in the distribution of line-of-sight inclination angle, $i$, requiring larger angles for Seyfert 2 (Sy\,2) and a broader distribution for Seyfert 1 (Sy\,1). We found small differences in the torus angular width, $\sigma$, indicating that Sy\,1 may host a slightly narrower torus than Sy\,2. The torus thickness, together with the bolometric luminosities derived, suggest a very compact torus up to $\sim$6\,pc from the central AGN. The number of clouds along the equatorial plane, $N$, as well the index of the radial profile, $q$, are nearly the same for both types. These results imply that the torus cloud distribution is nearly the same for type 1 and type 2 objects. The torus mass is almost the same for both types of activity, with values in the range of $M_{tor}\sim$10$^{4}-$10$^{7}\rm M_{\odot}$. The main difference appears to be related to the clouds' intrinsic properties: type 2 sources present higher optical depths $\tau_V$. The results presented here reinforce the suggestion that the classification of a galaxy may depend also on the intrinsic properties of the torus clouds rather than simply on their inclination. This is in contradiction with the simple geometric idea of the unification model. | According to the unified model, the energy from active galactic nuclei (AGN) is powered by the accretion of matter into a supermassive black hole (SMBH) \citep{lynden,beg84}. The unification scheme suggests that the different AGN types are explained by the line-of-sight (LOS) orientation of an obscuring material, which surrounds the central source and is arranged in an axisymmetric/toroidal geometry and composed primarily of gas and dust. Under edge-on views, it obscures the radiation from the accretion disk and broad line region (BLR). Such an object is classified as a type 2 AGN. When viewed face-on, the central engine can be observed directly. These galaxies are classified as type 1 AGNs \citep{ant93, urr95}. The unified model was firstly supported through spectropolarimetric observations of the Seyfert 2 (Sy\,2) galaxy NGC\,1068 \citep{am85}, revealing the polarized broad emission lines, and followed by other polarized broad line observations in type 2 AGNs \citep[e.g., by][]{tran92, tran95}. This hidden type 1 emission can be visible via light scattering in the ionizing cones, which corresponds to ionizing radiation that is collimated by the torus opening angle, providing additional indirect evidence for the unified model \citep[e.g.,][]{pogge88, thaisa91,thaisa92}. The dusty structure of the AGN unified model is responsible for absorbing short wavelength light from the active nucleus and re-emitting it mainly in the infrared (IR) wavelengths, leading to a peculiar signature in the spectral energy distribution (SED) of a galaxy. In specific, the silicate feature at \hbox{9.7\,$\umu$m} in the mid-infrared (MIR) is frequently found in absorption in type 2 and is also expected to appear in emission in type 1. However, in most type 1 objects this feature is either mild or absent \citep{hao07,wu09}. In addition, there are some cases where silicate emission is detected in type 2 \citep[e.g., in Sy\,2 NGC\,2110 by][]{mason09,sturm06}. Consequently, the MIR spectral range hosts fundamental features necessary to study the putative torus required in the Unified Model for AGNs. The recent significant advances in observational facilities, such as ALMA and VLTI, now allow us to resolve the central parsec scales in nearby AGNs. So far, only a few VLBI observations achieve sufficient spatial resolution to isolate the emission of these obscured structures. For instance, the cases of NGC\,1068 \citep{gra15,jaffe04,lop14} and Circinus \citep{tri07,tri14}. Very recently, \citet{santi16} and \citet{ima16} presented the first resolved images of the torus of NGC\,1068, the former using the continuum and the CO(6-5) emission observed with ALMA Band\,9 and the latter using HCN(3-2) and HCO$\rm ^{+}$(3-2) emission lines. These cases are successful precedents for forthcoming ALMA observations intended to study molecular gas in the torus and its surrounding \citep{net15}. While there are no plenty of data with such detailed observations, the optimal way to probe the physical processes related to the torus is understanding the radiation reprocessing mechanisms responsible for the singular behaviour of the AGN SEDs. In the last two decades, several models have been developed in order to understand the torus emission. For example, \citet{kro88} proposed that the torus should constitute of a large number of optically thick dusty clouds, otherwise the dust grains would be destroyed by the high AGN energy luminosity. Their presumption is reinforced by VLTI interferometric observations in the N-band range (\hbox{8--13\,$\umu$m}) performed by \citet{tri07} in the nucleus of the Circinus galaxy, providing strong evidence of a clumpy and dusty structure. Due to computational issues in modelling a clumpy medium, some studies have explored the effect of a dusty uniform distribution in a toroidal geometry \citep{pier92, gra94, efs95, dul05, fri06}. However, to explain the low resolution ($>$1'') observed SEDs and IR spectra in such homogeneous descriptions, the models force the torus size to be at scales of $\gtrsim$100\,pc. With the advent of high-spatial resolution using 8$m$-class telescopes, it was demonstrated that the surrounded dusty environment is much more compact, with sizes of a few parsecs \citep{jaffe04, tristram09, burtscher09}. Nevertheless, in the last few years, some efforts have been made to handle a clumpy formalism and they can naturally explain the problem with the silicate issue mentioned above \citep{nkv02,honig06,nkv08a,nkv08b,scha08,sta12}. Among them, the {\sc clumpy} models presented by \citet{nkv02,nkv08a,nkv08b} are, to date, some of the most successful models for representing the re-processed MIR torus emission and allowing us to constrain some torus properties. They consist of a large database of theoretical SEDs resulting from a 1D radiative transfer code \citep[{\sc dusty},][]{ive99} taking into account the continuum emission from clumpy media with shadowed individual clouds. One of the advantages of a clumpiness formalism is that they can reproduce more realistic MIR spectra. This is because they have a wide range of dusty cloud temperatures at the same radius from the central source and even distant clouds can be directly illuminated by the AGN, contrary to the smooth density distributions. The {\sc clumpy} models have been used by several works to study the torus properties, for example, in a sample of 26 quasar by \citet{mor09}, in a analysis of 27 Sy\,2 by \citet{lir13} and in modest to small samples of Seyfert galaxies \citep[e.g.][]{ichi15} and the works from \citet{ah11,ram09,ram11}, hereafter, AH11, RA09 and RA11, respectively. One of the main differences between our work and AH11 and RA11 is the use of near infrared (NIR) data for all the galaxies in their analysis and our much larger sample. We investigated the torus properties of 111 Seyfert galaxies using data archive from Infrared Spectrograph \citep[IRS,][]{houck04} aboard the {\it Spitzer Space Telescope} in the \hbox{5.2--38\,$\umu$m} spectral range. We compared the sample with the {\sc clumpy} theoretical SEDs from \citet{nkv02,nkv08a,nkv08b} using two different approaches: the $\chi_{red}^2$ test as well as bayesian inference \citep[{\sc BayesClumpy},][]{ase09}. Section 2 characterizes the sample and data reduction. In section 3 we describe the {\sc clumpy} models, the PAH's decontamination from the SEDs and the different approaches utilized to fit the data. Main results and the discussion are summarized in Section 4 and the contribution of the NIR data is exploited in Section 5. Our conclusions are presented in Section 6. \section[]{The Data} We have performed an analysis on a sample of 111 nearby galaxies classified as Seyfert galaxies that were available in the {\it Spitzer Heritage Archive}. The sample consists of 84 galaxies that have been presented in previous works \citep{gal10,wu09}, 14 galaxies from \citet{sal10} and another 13 objects available in the Spitzer archive (presented here for the first time). The galaxies were observed with the IRS using two low spectral resolution (R$\sim$60-127) modules: Short-Low (SL) and Long-Low (LL), covering a wavelength range from 5.2 to \hbox{38\,$\umu$m} in the MIR. The SL module has an image scale of 1.8''/pixel and the LL module 5.1''/pixel. Both are sub-divided in order 1 and 2. \begin{figure*} \begin{center} \includegraphics[width=172mm]{sample.eps} \caption{Characteristics of the 111 AGN samples. The solid line histograms show the properties for Seyfert 1 galaxies while the dashed lines represent the Seyfert 2 sources. Morphological classification and distances were obtained from the NED - {\it NASA/IPAC Extragalactic Database} or from \citet{whi92}. In the left panel, we gathered all morphological types into 7 mean classes: irregular (Irr), compact (Comp), peculiar (Pec), elliptical (E), spiral (S), lenticular (S0) and barred spiral (SB). The references for L$_{IR}$ and L$_{X}$ can be founded in Table~\ref{obs:tab1}.} \label{samp} \end{center} \end{figure*} With the exception of 7 galaxies whose spectra are available from the SINGS Legacy program\footnote{The IRS data from the SINGS Legacy Project are available at http://irsa.ipac.caltech.edu/data/SPITZER/SINGS/. The nuclear spectra were extracted over a 50''$\times$33'' aperture.} \citep[PID 159,][]{sings}, all other data were processed using the Basic Calibration Data (BCD) pipeline\footnote{For more details, please see the IRS Instrument Handbook.} (version 18.18). The BCD pipeline manages the raw data through basic processing, such as the detection of cosmic rays, the removal of saturated pixels, dark current and flat-field subtraction and droop correction. For the sample presented in \citet{gal10}, 78 objects have the spectral mapping mode available, while the other 6 present the mapping mode only in LL and SL observations in the staring mode (NGC\,526A, NGC\,4941, NGC\,3227, IC\,5063, NGC\,7172 and NGC\,7314). The mapping mode observations were processed by employing the CUbe Builder for IRS Spectra Maps \citep[{\sc CUBISM},][]{cubism07} to construct the data cubes. Sky subtraction were evaluated from an average spectra of the off-source orders: e.g. while the source is centred in the first order, the second order is pointed at the sky in an offset position. We used a 3.9$\times$11.1\,pixel extraction (equivalent to a 10'' circular radius aperture centred on the brightest source) to extract the spectra. In a few cases the extractions showed a mismatch between the modules or their orders that was corrected by scaling the spectra as recommended by \citet{pahfit07}. For the remaining 27 objects the data are available in staring mode and the calibrated spectra were obtained from the Cornell Atlas of Spitzer/IRS Sources \citep[CASSIS,][]{cassis11}. CASSIS\footnote{CASSIS products are available at \newline http://cassis.astro.cornell.edu/atlas} provides optimal extractions and diagnostic tools to guarantee the most accurate background subtraction, especially for faint sources. In most cases, the optimal CASSIS extraction pointed to sky subtraction through the off-order method. However, in a few cases, CASSIS indicated the subtraction by nod positions as the best spectral extraction. Furthermore, the majority of CASSIS products were established as point-like sources\footnote{The optimal CASSIS extractions equivalent to extended sources are Mrk\,471, Mrk\,609, Mrk\,993, NGC\,5695, NGC\,5782, NGC\,7679 and NGC\,7682.}. Our final sample is composed of 45 Sy~1 and 65 Sy~2 galaxies with redshifts between 0.002\,$\le$\,$z$\,$\le$\,0.079. The AGNs are preferentially found in host galaxies with barred spiral, lenticulars or in spiral morphological types. The mean values for the IR luminosities are L$\rm _{IR}$(Sy1)= 4.64$\times$10$^{10} \rm L_{\odot}$ for Sy\,1 and L$\rm _{IR}$(Sy2)= 5.44$\times$10$^{10} \rm L_{\odot}$ and for the hard X-ray luminosities are L$_{\rm 2-10Kev}$(Sy1)= 1.59$\times$10$^{43}$ and L$_{\rm 2-10Kev}$(Sy2)= 1.19$\times$10$^{43}$ erg $\rm s^{-1}$. The sample properties are summarized in Figure~\ref{samp} and listed in Table~\ref{obs:tab1}. \subsection[]{Removing the PAH Contamination}\label{pahremove} Since the IRS {\it Spitzer} spectra were extracted in a 20'' circular diameter aperture, corresponding to $\sim$1-20\,Kpc of the galaxies (except for z=0.79, Mrk478 which represents $\sim$33\,Kpc), the host galaxy contribution is unavoidable in our sample. In order to minimize the effects from star formation and to isolate the AGN emission of the galaxy, we have adopted a similar method as that used in \citet{lir13}. They remove the stellar contribution by subtracting templates developed by \citet{pahfit07}, when the MIR is dominated by polycyclic aromatic hydrocarbons (PAHs) emission of star forming regions. Instead of fitting star formation templates, we chose to follow another approach in order to attenuate the PAH's contribution (and therefore, that of the host galaxy) in the spectra. We applied the {\sc pahfit} tool developed by \citet{pahfit07}. This code decomposes the emission lines of the low resolution IRS {\it Spitzer} spectra, modelling them as the sum of starlight continuum, thermal dust continuum, and emission lines (pure rotational lines of H$_2$, fine structure lines, and dust emission features). All flux intensity components are affected by dust extinction, quantified by the optical depth \citep[for more details, see][]{pahfit07}. \begin{figure} \begin{center} \includegraphics[width=86mm]{pah_contribution.eps} \caption{Typical examples of the subtraction of the PAH and ionic line components from the spectra. The black lines represent the observed spectra, while the dotted/dashed orange and dashed pink lines show the resulting adjusted spectra created by fitting the PAH emission and ionic and hydrogen lines, respectively, using the {\sc pahfit} tool. In the dotted red lines are the subtracted spectra that were handled in our analysis. In the top panel the results for NGC\,1365 are shown, characterizing a galaxy with strong PAH emission. On the other hand, the middle panel shows little contribution from this feature for NGC\,1275. An example of a deep silicate absorption and PAH emission is presented in the bottom panel for the Sy\,2 NGC\,7172.} \label{pah} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics[width=86mm]{compare_paper.eps} \vspace{-0.5cm} \caption{We show a comparison of the low resolution {\it Spitzer} IRS spectra and the ground based nuclear emission observations. The top panel shows the spectrum of Mrk\,3 from Michelle while the middle and bottom panels present the data from T-ReCs for NGC\,1386 and NGC\,7213, respectively. The black lines represent the IRS data, the dotted red lines the starburst subtracted spectra and the dashed blue lines the high resolution spectra. Except in the case of Mrk\,3, the subtracted spectra appear to well represent the emission from the active nucleus.} \label{high} \end{center} \end{figure} Since the continuum from our Seyfert sample is not only due to dust and stellar components, but also to the AGN power-law continuum, we decided to subtract only the emission lines from the H$_{2}$ and the molecular features of PAH emission from the observed spectra. It is, however, worth mentioning that most of the PAH contribution lies in 5-15\,$\mu$m, where the stellar emission is more prominent. For longer wavelengths, the host galaxy emission is very difficult to distinguish from the AGN continuum, and unfortunately, the current spectral decomposition codes are unable to separate each contribution for $\lambda\gtrsim$20\,$\mu$m \citep[e.g.,][]{pahfit07,her15}. This trend might overestimate AGN emission at longer wavelengths, which could bias the outputs of the CLUMPY models towards extended and broader tori, due to the cooler dust that peaks in the far-infrared range. Nonetheless, recently \citet{ful16} separated the AGN and PAH components using the full wavelength coverage of the {\it Spitzer}/IRS spectra of 11 Seyfert galaxies. They used the templates provided by \citet{her15} and then compared the AGN resulting spectra with the 31.5\,$\mu$m imaging photometry from the Stratospheric Observatory For Infrared Astronomy (SOFIA), finding that most of the sources are AGN dominated at 31.5\,$\mu$m. In Figure~\ref{pah} we present some representative examples of this approach\footnote{In Appendix B we present the adjust for all the objects in the sample. The decomposed spectra files are available upon request, please contact the authors.}. Shown is a case with strong PAH emission and second with little PAH feature contribution (Sy\,1 NCG\,1365 and Sy\,2 NGC\,1275 respectively). Also, we selected an example of deep silicate absorption in 9.7\,$\mu$m for NGC\,7172, which is surrounded by PAH emission. As can be seen, the effect of the molecular emission features is more prominent at shorter wavelengths and can alter the shape of the spectrum. The majority of galaxies (about 80\% of the sample) exhibit a substantial star forming contribution \citep[see also][]{sal10}. Recently, some other studies have been supporting this star forming subtraction methodology. For instance, in \citet{rus14} there is no PAH emission detected using high resolution nuclear spectra from T-ReCs when compared with IRS observations of NGC\,7213 and NGC\,1386. Also, no PAH emission bands were detected in the nuclear region ($\sim$200\,pc) of Mrk\,3, a Compton-thick Sy~2, using Michelle/Gemini spectrograph \citep{sal14}. \citet{dav12} argued that the PAH molecules can not survive in a radius smaller than 50\,pc, a value corresponding to a region larger than that of the torus extension \citep[parsec scale,][]{tran92}. However, in some cases, e.g. in T-ReCs observations of NGC1808, the aromatic component was detected at 8.6 and 11.3$\umu$m in the galaxy centre ($\sim$26 pc) up to a radius of 70 pc from the nucleus \citep{sal13}. To illustrate the effect of the starburst subtraction method, we show in Figure~\ref{high} the high resolution data from Michelle and T-ReCs of the galaxies Mrk\,3, NGC\,1386 and NGC\,7213, compared to the IRS spectra. Also shown is the final spectra resulting from the subtraction of the PAH components. The clean IRS spectra tends to better approximate the nuclear spectra from high resolution observations, except for the Mrk\,3. This is possibly due to the fact that this galaxy is a Compton-thick object and has a heavy absorbed dust/gas component \citep[$N_{H}\sim 1.1\times 10^{24} \rm cm^{-2}$,][]{sal14} obscuring the nucleus, leading to a higher continuum in the {\it Spitzer} observation. Moreover, the fact of this galaxy has a small starburst contribution may explain why we see almost no differences between the IRS spectra and the subtracted one. However, in the cases of NGC\,1386 and NGC\,7213, we believe that the PAH subtraction approach represents a good approximation of the nuclear emission. Thus, the spectral decomposition methodology was applied to all the objects used in our study. \section[]{Modelling the SED in the MIR} \subsection[]{{\sc clumpy} Torus Models} A clumpy medium provides a natural explanation for the silicate absorption feature that was expected to be observed in emission in type 1 sources but is frequently mild or even flat, since it requires at least a clump obscuring the radiation at the observer's LOS. The most successful and up to date clumpy models are those of the Kentucky group. \citet{nkv02,nkv08a,nkv08b} developed a formalism to handle a clumpy media, considering point-like dusty clouds distributed in a toroidal geometry around the central AGN. The {\sc clumpy} models are a large database ($\sim$10$^6$) of theoretical SEDs resulting from the radiative transfer treatment through the {\sc dusty} code \citep{ive99}. The dust grains follow the MNR size distribution \citep{mnr77} and are composed by the standard Galactic mixture of 47\% graphite with optical constants and 53\% cold silicates. While the graphite grains are the responsible for the IR emission at $\lambda\gtrsim 1\umu$m, the 9.7\,$\umu$m and 18\,$\umu$m emission and absorption features are attributed to silicate grains \citep[e.g.][]{bar87,pier92,gra94,sie04}. The {\sc clumpy} models assume that the torus is formed by dusty clumps constrained by the following parameters: (i) the number of clouds, $N_0$ , in the torus equatorial radius; (ii) $\tau_{V}$, the optical depth of each cloud defined at 0.55\,$\umu$m band; (iii) the radial extension of the clumpy distribution, $Y=R_{o}/R_{d}$, where $R_o$ and $R_d$ are the outer and inner radius of the torus, respectively; (iv) the radial distribution of clouds as described by a power law $r^{-q}$; (v) the torus angular width, $\sigma$, constrained by a Gaussian angular distribution width and (vi) the observers viewing angle $i$. The grid of these model parameters are listed in Table~\ref{obs:tab2}. \begin{table} \centering \begin{minipage}{86mm} \caption{Parameters values adopted in fitting} \begin{scriptsize} \begin{tabular}{@{}lcl@{}} \hline \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{Sampled Values} & \multicolumn{1}{c}{Description} \\ \hline \noalign{\smallskip} \multicolumn{3}{c}{{\sc clumpy} Models }\\ \noalign{\smallskip} \hline $i$ & 0-90 steps of 10$^\circ$ & Observer's viewing angle \\ $N$ & 1-15 steps of 1 & Clouds along the equatorial plane \\ $q$ & 0-3 steps of 0.5 & Power law index of the radial distribution \\ $\tau_{V}$ & 5,10,20,30,40,60,80,100,150 & Optical depth of individual clouds \\ $\sigma$ & 15-70 steps of 5 & Torus angular width \\ $Y$ & 5, 10-100 steps of 10 & Torus thickness\\ \hline \hline \noalign{\smallskip} \label{obs:tab2} \end{tabular} \end{scriptsize} \end{minipage} \end{table} The model geometry also allow us to determine other parameters that are crucial to understand the obscuration effects of the central source. They are the number of clouds along the LOS, $N_{los}$, described by almost a Gaussian distribution along the equatorial plane ($N$), which depends on the inclination, $\beta=\pi/2 -i$, and angular width, $\sigma$, parameters \begin{equation} N_{los}(\beta)=N exp^{- {\left ( \frac{\beta}{\sigma} \right )}^2} \label{numlos} \end{equation} and the total optical depth of the torus along the LOS, product of the number of clouds and the optical depth of each cloud, or, the visual extinction: \begin{equation} A_{V}=1.086 N_{los} \tau_{V}% \label{averm} \end{equation} One of the characteristics of Nenkova et al. models is that the SEDs reproduced are not exclusively sensitive to the inclination angle, as established by the only orientation dependent unification schemes. The continuum shape and behaviour of the silicate features also have a strong dependence with the optical properties, characterized by the optical depth \hbox{$\tau_{V}$}, and the number of clouds along radial rays, specifically at the equatorial plane, $N$. In the latter, $N$ must be sufficient large, \hbox{$N\sim$5--10}, to assure the attenuation of X-rays in type 2 sources while the former one was constrained to values \hbox{$\tau_{V}\gtrsim$60} to ensure the probability of photon escape. The explanation for many problems faced by the smoothly distribution handling are answered by the clumpiness nature of the toroidal structure and, therefore, the {\sc clumpy} models constitute a powerful tool to probe the torus physical properties proposed by the AGN's Unified Model. \subsection[]{Fitting Procedure} Once we applied the procedure to isolate the nuclear emission, we performed two different approaches to compare the MIR resulting spectra from IRS observations with Nenkova's theoretical models. In the following sections we describe the techniques employed. \subsubsection[]{$\chi^2_{red}$ test} We developed a code to compare each spectrum with all $10^6$ {\sc clumpy} models SEDs. The routine searches for the parameters which minimizes the equation: \begin{equation} {\chi_{red}}^2 = \frac{1}{N} \sum_{i=1}^N {\left ( \frac{F_{obs,\lambda_{i}} - F_{mod, \lambda_{i}}}{\sigma_{\lambda_i}} \right )}^2 \label{chi2} \end{equation} where N is the number of data points in the spectrum, $F_{obs,\lambda_{i}}$, and $F_{mod, \lambda_{i}}$, are the observed and theoretical fluxes at each wavelength and $\sigma_{\lambda_i}$ are the uncertainties in $F_{obs,\lambda_{i}}$. Both $F_{obs,\lambda_{i}}$ and $F_{mod, \lambda_{i}}$ were normalized to unit at 28.0$\mu$m for all the galaxies in the sample, with the uncertainties correctly propagated. The ``decontaminated" nuclear spectrum was compared to the clumpy theoretical SEDs and we test the results for the best fit, e.g., the minimum $\chi^2_{red}$ and 5, 10, 15 and 20 per cent its deviation fractions, using a similar approach of \citet{nik09} and \citet{sal13}. In this work, we choose to represent the best fit and 10\% of deviation solutions. \subsubsection[]{BayesCLUMPY Technique} \begin{figure*} \begin{center} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{IC4329A_bestMAP_JY.eps} \end{minipage} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{Mrk3_bestMAP_JY.eps} \end{minipage} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{NGC1275_bestMAP_JY.eps} \end{minipage} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{NGC1365_bestMAP_JY.eps} \end{minipage} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{NGC1386_bestMAP_JY.eps} \end{minipage} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{NGC4507_bestMAP_JY.eps} \end{minipage} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{NGC6860_bestMAP_JY.eps} \end{minipage} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{NGC7172_bestMAP_JY.eps} \end{minipage} \begin{minipage}{0.325\textwidth} \includegraphics[width=\textwidth]{NGC7213_bestMAP_JY.eps} \end{minipage} \caption{Examples of adjusts for the best fit using ${\chi_{red}}^2$ and the maximum-a-posteriori distribution from BayesCLUMPY. Best torus fitting to the spectrum is represented by yellow dashed line for the former and by blue dotted-dashed line in the latter case. The observed spectra and the SED models are normalized at 28$\mu$m.} \label{adjust} \end{center} \end{figure*} We apply the Bayesian inference tool BayesCLUMPY \citep{ase09} in order to achieve the best fitting parameters for the observed nuclear SEDs. The technique consists to perform a Markov Chain Monte Carlo method to investigate the parameter space defined by the first 13 eigenvectors. These values result from the combination of the principal component analysis and the artificial neural network that provides a interpolation in the database of the model grid from the theoretical {\sc clumpy} models ($\sim 10^{6}$ models). This approach allows to obtain the marginal posterior distribution for each model parameter, taking into account all a-priori constrains and the information from the observations. To assure the stability of the solution, we performed consecutive runs of the algorithm. It is important to emphasize that fitting clumpy torus models to the spectra is an intrinsically degenerate problem, as we can obtain the same observable effect for different sets of parameters. \subsubsection[]{Final Fitting} An example of fitting for some galaxies is presented in Figure~\ref{adjust} and the individuals fittings are presented in the Appendix C. The yellow dashed line shows the model fitted for the minor ${\chi_{red}}^2$ value, e.g., the best fit, and blue dotted-dashed line represents the correspondent best $\chi^2$ solution for BayesCLUMPY inference, the maximum-a-posteriori (MAP) values. The derived mean parameters for both $\chi^2_{red}$ and the Bayesian method are very similar, and in general the $\chi^2_{red}$ solution is the most approximated to the observed spectrum (besides that it provides a solution within the models base). The goodness of both fitting procedures can be quantified by the values derived for the $\chi^2_{red}$. We also account an additional quality indicator, the {\it adev}, which gives the percentage mean deviation over all fitted wavelengths \citep{cid13}: \begin{equation} {adev} = \frac{1}{N} \sum_{i=1}^N \frac{|F_{obs,\lambda_{i}} - F_{mod, \lambda_{i}}|}{F_{obs,\lambda_i}} \end{equation} In Figure~\ref{adev} we present the distribution of the {\it adev} and the minimum $\chi^2_{red}$ values derived for all the sample (except for the galaxies Mrk 3, NGC 1097, NGC 1566, NGC 4594, NGC 5033 and NGC 7679 that present values $\chi^2_{red}$ and MAP$>$50). For more than 50\% of the adjusted models we found $\chi^2_{red}$ values less than 5, which can be classified as satisfactory adjustments. Also, the deviation between the observation and the best model fitted is less than {\it adev}$\lesssim 20$\% for the majority of objects. In general, the Figures~\ref{adjust} and \ref{adev} indicate that the $\chi^2_{red}$ method provides more satisfactory adjusts than the MAP using the BayesCLUMPY. This is the reason we have chosen to only discuss the $\chi^2_{red}$ results in the next sections. \begin{figure} \begin{center} \includegraphics[width=86mm]{ADEV_CHI.eps} \vspace{-0.5cm} \caption{We show the values derived for the $\chi^2_{red}$ ({\it top panel}) and the {\it adev} ({\it bottom panel}) that quantify the goodness of the $\chi^2_{red}$ and the BayesCLUMPY fitting techniques. The orange filled histograms represent the values derived using the $\chi^2_{red}$ technique while the blue dashed lines are the distribution of the MAP values derived using the BayesCLUMPY method.} \label{adev} \end{center} \end{figure} \section[]{Comparison between type 1 and type 2 sources} In order to compare the two fitting methodologies, we decided to consider the best solution of the ${\chi_{red}}^2$ test and the MAP provided by the BayesCLUMPY method. However, it is important to notice that the model interpolations performed in BayesCLUMPY allows for a grid of parameters different from the ones provided by the clumpy torus models and listed in Table~\ref{obs:tab2}. \subsection{Direct Parameters} Both fitting methodologies allows for the determination of parameters within the models set, what we call {\it direct parameters}. The values obtained for those parameters are presented in frequency histograms (Figure~\ref{direct}) as well as, the obtained mean parameters are listed in Table~\ref{obs:tabmean}. We have chosen to discuss the results obtained with the ${\chi_{red}}^2$ methodology, however, for completeness we will keep in all the histograms the results obtained with the BayesCLUMPY MAP mode. Below we discuss the results of each parameter individually. It can be seen from Figure~\ref{direct} that the inclination angle relative to the observer's LOS, $i$, appears to be larger for Sy\,2 ($\rm \bar{i}(Sy2)=64.5^\circ \pm 28.3^\circ$) than for Sy\,1 ($\rm \bar{i}(Sy1)=50.6^\circ \pm 31.4^\circ$). This parameter was studied in previous works, with controversial results. RA11 studying a sample of 7 Sy\,1 and 14 Sy\,2 galaxies and from the 13 objects presented in AH11 sample, found no significant differences in this parameter and suggested that type 2 objects could be seen in any orientation if there is at least one cloud obscuring the observers LOS. On the other hand, \citet{mor09} studied 26 type 1 PG quasars using Spitzer data found $\bar{i}$=33$^{\circ}$ while \citet{lir13} obtained a typical value of i $\gtrsim$40 for a sample of 27 Sy\,2 with about half of their sample requiring values $i\sim$70-90$^\circ$. Our mean results for this parameter suggest that Sy\,1 do present a slightly lower value for $i$ than Sy\,2s, supporting the viewing angle orientation requirement for the AGN's Unified Model. \begin{table} \centering \begin{minipage}{86mm} \caption{Mean parameters derived from the ${\chi_{red}}^2$ and MAP of {\sc CLUMPY} models fitting} \begin{scriptsize} \begin{tabular}{@{}lcc@{}} \hline \hline \multicolumn{1}{c}{Parameter} & \multicolumn{1}{c}{$\chi^2_{red}$} & \multicolumn{1}{c}{MAP} \\ \noalign{\smallskip} \multicolumn{1}{c}{} & \multicolumn{1}{c}{{\sc sy 1} --- {\sc sy 2}} & \multicolumn{1}{c}{{\sc sy 1} --- {\sc sy 2}} \\ \hline \noalign{\smallskip} \multicolumn{3}{c}{{\sc Direct}} \\ \noalign{\smallskip} \hline i & 50.6$\pm$31.4 --- 64.5$\pm$28.3 & 57.1$\pm$32.7 --- 51.6$\pm$35.3\\ $\sigma$ & 36.4$\pm$19.2 --- 43.7$\pm$20.5 & 44.7$\pm$19.8 --- 50.7$\pm$17.6\\ N & 9.0$\pm$5.0 --- 10.0$\pm$4.0 & 8.0$\pm$5.0 --- 11.0$\pm$5.0\\ Y & 53.7$\pm$34.9 --- 46.1$\pm$34.1 & 54.5$\pm$34.9 --- 53.1$\pm$38.3\\ $\tau_V$ & 77.3$\pm$57.0 --- 110.9$\pm$49.2 & 69.5$\pm$52.2 --- 93.0$\pm$52.1\\ q & 0.8$\pm$0.8 --- 0.9$\pm$0.7 & 1.0$\pm$0.8 --- 0.8$\pm$0.8\\ \hline \noalign{\smallskip} \multicolumn{3}{c}{{\sc Indirect}} \\ \noalign{\smallskip} \hline N$_{los}$ & 3.0$\pm$4.0 --- 7.0$\pm$5.0 & 4.0$\pm$4.0 --- 6.0$\pm$5.0\\ A$_V$ & 287$\pm$595 --- 899$\pm$829 & 241$\pm$509 --- 671$\pm$799\\ log($N_{H}/ \rm cm^{-2}$) & 23.7$\pm$24.1 --- 24.2$\pm$24.2 & 23.7$\pm$24.0 --- 24.1$\pm$24.2\\ P$_{esc}$ & 0.3$\pm$0.3 --- 0.1$\pm$0.2 & 0.2$\pm$0.3 --- 0.1$\pm$0.2\\ C$_T$ & 0.7$\pm$0.2 --- 0.8$\pm$0.2 & 0.8$\pm$0.2 --- 0.9$\pm$0.2\\ $M_{tor}(M_{\odot})$ & 2.1$\pm$3.9$\times$10$^6$ --- 2.7$\pm$5.5$\times$10$^6$ & 2.4$\pm$3.7$\times$10$^6$ --- 3.5$\pm$6.0$\times$10$^6$\\ \hline \noalign{\smallskip} \label{obs:tabmean} \end{tabular} \end{scriptsize} \end{minipage} \end{table} \begin{figure} \begin{center} \includegraphics[width=86mm]{hist_chi_bayes.eps} \vspace{-0.5cm} \caption{The frequency histograms distribution for direct parameters, $\rm i$, $\rm \sigma$, $\rm N$, $\rm Y$, $\rm \tau_V$ and $\rm q$, derived from the {\sc clumpy} models fitting. The brown filled histograms represent the MAP distributions resulting from the employing of the BayesCLUMPY task and the stepped blue distribution shows the results of the best solution applying the $\chi^2_{red}$ test. In all panels, the distributions for the 46 Sy\,1 are plotted at the left side and for the 65 Sy\,2 at the right side. The lined-dotted lines indicate the mean value of the MAP distribution and the hatched area delineate the mean values from the $\chi^2_{red}$ and the uncertainties around the average.} \label{direct} \end{center} \end{figure} Accordingly the {\sc clumpy} models, the dusty clouds follow a Gaussian like distribution along the equatorial ray characterized by a torus angular width ($\sigma$). Our results show that there is no significant differences for the mean $\sigma$ values in the different types of activity, being $\rm \bar{\sigma}(Sy1)=36.4^{\circ}\pm19.2^{\circ}$ and $\rm \bar{\sigma}(Sy2)=43.7^{\circ}\pm20.5^{\circ}$. Taking only the mean values into account, these results may indicate that the torus hosted by Sy\,1s is biased towards smaller values than those found in Sy\,2s. In fact, these values agree with those found by RA11 and are further supported by the findings of \citet[][$\sigma >$ 40, for 70\% of their Sy\,2]{lir13} and \citet[][$\bar{\sigma}=34$, for their type 1 sources]{mor09}. Regarding the number of clouds along the LOS, we found that both types are well represented by $\sim$ 10 clouds ($\rm \bar{N}(Sy1)=9\pm5$ and $\rm \bar{N}(Sy2)=10\pm4$). In the case of quasars this number seems to be smaller ($\sim$5)than in the case of Seyfert galaxies \citep[e.g][]{mor09,lir13}. Thus, our findings reinforce the scenario proposed by AH11 in which the number of clouds might be in an evolutionary stage of a receding torus. Besides the above parameters, other fundamental parameter is the torus thickness, $Y$, which is calculated as the ratio of the outer $\rm R_o$ and inner radius $\rm R_d$, $\rm Y=R_{o}/R_{d}$, where $\rm R_d$ is set as being the distance from the central source where dust sublimates and according to \citet{bar87} can be obtained by \begin{center} \begin{equation} R_{d}=0.4 {\left ( \frac{L_{AGN}}{10^{45} \rm erg^{-1}} \right ) }^{0.5} {\left ( \frac{1500 \rm K}{T_{sub}} \right ) }^{2.6} ~~\rm pc \label{rsub} \end{equation} \end{center} with $\rm T_{sub}$ being the dust sublimation temperature and $L_{AGN}$ is the AGN bolometric luminosity. The values we derived for the torus thickness do not present any significant distinction on average values and also for the shape of the distribution, as it can be seeing in Figure~\ref{direct}. For both classes, we can find solutions at the edges of the distribution, indicating that the majority of objects requires or a very large value of Y or a compact torus. In this case, the mean values derived ($\rm \bar{Y}(Sy1)=53.7\pm34.9$ and $\rm \bar{Y}(Sy2)=46.1\pm34.1$) do not represent the sample. In fact, as pointed out by \citet{nkv08b}, when $q=2$ the IR fitting leads to a poor constrain on the torus extension, since the clouds are distributed close to $R_d$. Therefore RA11 and AH11 have chosen to restrict this parameter accordingly with observations that suggest smaller values for the torus radial extension \citep[ Y$\sim$10-20,][]{jaffe04,tri07,raban}. We also performed our MIR fitting using the same constrain of Y[5,30] adopted in AH11 and still our findings do not imply significant changes on the other parameters distribution. Hence, we decided to maintain the original $Y$ parameter space since this bi-modality found in our results can be attributed to a better constrain on $\gtrsim$20\,$\mu$m which are not included to the SEDs in the AH11 and RA11 sample. Indeed, \citet{ful16} shows that the inclusion of SOFIA photometric data in the 30-40\,$\mu$m wavelength range helps to better constrain $Y$. This is because the outer radius $R_o$ is more sensitive to the cooler dust that peaks in the far-IR, providing information about the torus size. Due to computational limitations, the {\sc clumpy} models assume that all dust clouds have the same optical depth, $\tau_{V}$ \citep[see][for details]{nkv08b}. It is clear from Figure ~\ref{direct} that the distribution of individual clouds optical depths points is centred in high values of $\tau_{V}$. Also, approximately 60\% of the solutions for Sy\,2 galaxies require $\tau_{V} \sim 140$\,mag, presenting an average value of $\rm \bar{\tau_{V}}(Sy2) = 111 \pm 49$\,mag for type 2 sources, while for Sy\,1 we found a smaller value for $\rm \bar{\tau_{V}}(Sy1) = 77 \pm 57$\,mag. Both results are in agreement with the high optical depth condition ($\rm \tau_{V} \gtrsim 60$) of the {\sc clumpy} models, which requires such values to ensure that we do have optically thick clouds and a finite photon escape probability. However, for this parameter, our results differ from those found in the literature, which derive lower values of $\tau_V$ for Sy\,2 galaxies, for example, for the 14 Sy\,2 sample of RA11 the typical values derived are $\tau_V \sim 30$\,mag and for the 27 Sy\,2 from \citet{lir13}, the best solutions in general assume lower values ($\tau_{V} \lesssim 25$\,mag). We also tested for a possible correlation with $\tau_V$ and the galaxy inclination and no correlation was found. In the {\sc clumpy} model the clouds distribution is described by a power law with form $ r^{-q}$. The histograms with the indexes ($q$) distribution for both types of activity show that the solutions are found to be more likely within lower values for this parameter, generally between $0<q<1$. Values of $q\sim0$ indicate a constant distribution, revealing that the number of clouds presents a weak dependence on the distance to the central AGN, while values $q\sim 1$ point to a distribution following a $1/r$ relation. The average values derived for both classes are quite similar for both types of activities, being $\rm \bar{q}(Sy1)=0.8$ and $\rm \bar{q}(Sy2)=0.9$. Our results follow the same trend as found by \citet[][$ \bar{q} = 1$]{mor09} and also by \citet[][$\rm q \sim 0$]{lir13}, since the distribution for this parameter is quite spread as can be seen in the histograms in Figure~\ref{direct}, where more than 30\% of the sample present values of $q =0$. \begin{table} \centering \begin{minipage}{86mm} \setlength{\tabcolsep}{15pt} \caption{The K-S test for the parameters distribution of Sy1 and Sy2} \begin{tabular}{ccc} \hline \hline \noalign{\smallskip} {\sc Parameter Distribution} & {\sc D} & {\sc p-value} \\ \noalign{\smallskip} \hline \noalign{\smallskip} i & 0.44 & 0.25 \\ $\sigma$ & 0.18 & 0.99 \\ N & 0.33 & 0.31 \\ Y & 0.20 & 0.97 \\ $\tau_V$ & 0.27 & 0.59 \\ q & 0.17 & 0.99 \\ \hline \noalign{\smallskip} \label{ks_tab} \end{tabular} \end{minipage} \end{table} We also performed a two-sample Kolmogorov-Smirnov (K-S) test \citep{mises} in order to verify the results discussed above and quantify the differences between the parameters distribution for both activity types. The K-S test determine if the Sy\,1 and Sy\,2 parameters have the same distribution and the values derived for $D$, i.e. the supremum of the cumulative distribution functions (CDFs) of the Sy\,1 and Sy\,2 for each {\sc clumpy} parameter, and $p$-$value$ are shown in Table~\ref{ks_tab}. As we can see, the inclination $i$ presents a significant discrepancy between the CDFs since the $D$ value is the most considerable among the other {\sc clumpy} parameters, followed by $N$ and $\tau_V$. Since in both activity types we found $N\sim$10, the main parameters to classify a Sy\,1 or a Sy\,2 rely on a combination of $i$ and $\tau_V$: it depends on the observers' LOS orientation as well on the obscuring properties of the clouds. On the other hand, the $p$-$value$ for $\sigma$, $Y$ and $q$ suggest that Sy\,1 and Sy\,2 populations are drawn from the same distribution, e.g., we can not distinguish whether a distribution of the geometrical parameters $\sigma$, $Y$ and $q$ is from a Sy\,1 or a Sy\,2. Some objects in our sample are common to previous works of RA09 (9 objects), AH11 (14 objects), RA11 and \citet{lir13} (20 objects). In general, our mean results are in good agreement with the literature, although the individual solutions may be quite different. We attribute these differences to the fact that each study used distinct approaches (for example, wavelength coverage, resolution, parameter constrains, methodology). For instance, that may also explain the differences in the reported parameters for the same galaxy in different papers by the same authors. In addition, our results in general tend to be more consistent with those presented by \citet{lir13}. As pointed out by the latter, there are very significant differences in the results found between RA11 and AH11 attributed to the inclusion of the 10\,$\mu$m spectroscopic observations. Since the silicate at 9.7\,$\mu$m is a important dust feature, the inclusion of detailed spectral information around this feature is crucial to properly describe the physical parameters from the SEDs. In order to illustrate a mean SED and torus physical representation, we present a sketch in Figure~\ref{torus} that shows the mean theoretical SEDs from {\sc clumpy} to create a representative SED for each type of activity. There we combine the mean parameters derived in Table~\ref{obs:tabmean}. We also illustrate a schematic cross section view of the tori for both activity types, in order to highlight the differences in the torus physical properties, for instance, the slightly larger radial thickness for Sy\,1 and the wider angular width in Sy\,2, consequently, (given the Gaussian distribution) increasing the number of clouds in this type. These results are in agreement with the results of RA11 who found that the tori of Sy~1's are narrower and with fewer clouds than those found in Sy~2's. Furthermore, the mean SEDs do not present a turnover of the torus emission, predicted to occur between 30 - 50\,$\mu$m. This result is in agreement with those found by \citet{ful16}, where no turnover was observed below 31.5\,$\mu$m. Further nuclear far-IR observations would be essential to determine the peak of the IR emission, giving insight into the torus outskirts. \begin{figure} \begin{center} \includegraphics[width=86mm]{SED_torus.eps} \vspace{-0.4cm} \caption{Combination of the mean parameters from {\sc clumpy} theoretical SEDs, represented by the dashed purple line for Sy\,1 and the dotted-dashed blue lines for Sy\,1. A schematic torus cross section is also illustrated in order to feature the main differences between the torus physical properties.} \label{torus} \end{center} \end{figure} \subsection{Indirect Parameters} As mentioned before, the model geometry enable us to estimate other important parameters that may help us to understand the physical properties of the putative torus required by the unified model. The distribution derived for the indirect parameters are described below and presented in Figure~\ref{indirect} as well as the information about mean values are summed up in Table~\ref{obs:tabmean} and described in the text. It is worth mentioning that all these indirect parameters where obtained using the results of the best direct parameters described in the previous section. \begin{figure} \begin{center} \includegraphics[width=86mm]{hist_chi_bayes_others.eps} \vspace{-0.5cm} \caption{The frequency histograms distribution for indirect parameters, $N_{los}$, $ A_V$, $N_{H}$, $P_{esc}$ and $C_T$, derived from the {\sc clumpy} models fitting. The brown filled histograms represent the MAP distributions resulting from the employing of the BayesCLUMPY tool and the stepped blue distribution shows the results of the fit best solution applying the ${\chi_{red}}^2$ method. The panels follow the same scheme listed in Figure~\ref{direct}. } \label{indirect} \end{center} \end{figure} Since we are dealing with a clumpy media one of the most important parameters in describing the torus is the number of clouds blocking our LOS ($N_{los}$). By using the model clouds distribution (with a Gaussian like form), centred at the equatorial plane, we can compute the number of clouds along any specific direction, thus if we choose the LOS direction we can compute $N_{los}$ (Equation~\ref{numlos}). The $N_{los}$ distribution is shown in the top panel of Figure~\ref{indirect}, by inspecting this figure, it is clear that the number of clouds along the observer's LOS presents a sharp peak in its distribution for Sy~1 (centred at $\sim$3), while a spread distribution is found for Sy~2 ($\bar{N_{los}}=7$). At the same level of importance, is the extinction of the light caused by the material composing the LOS clouds. Once $N_{los}$ is know the total optical depth along the LOS is obtained with Equation~\ref{averm}. The distribution of A$_V$ is well defined for Sy~1, with small values, while in Sy~2 it is flat. In addition, the determination of $N_{los}$ is also related with the X-ray columnar hydrogen density which can be derived using the standard Galactic ratio and the foreground extinction from \citet{boh78} via $N_{H}/A_{V}$=1.9$\times$10$^{21} \rm cm^{-2}$. In agreement with the two previous indirect parameters, the $N_{H}$ is well defined for the Sy~1 galaxies ($\bar{N_{H}}=5\times10^{23}cm^{-2}$) and with a not so centred distribution for Sy~2's ($\bar{N_{H}}=1.6\times10^{24} cm^{-2}$). These results together with the fact that we are not finding significant difference in the observers viewing angle for the different classes, point to the fact that the most important parameter in determining if a galaxy is classified as a type 1 or 2 object is if there are clouds able to block the radiation from the BLR and central engine. This suggests that the fundamental requirements of the unified model for AGNs depends more on the intrinsic parameters of the torus than on its geometry. In fact, our results are still supported by the finding of RA11 found significant differences in the torus angular size for the different classes. However, in contradiction with our results, they do find lower optical depth in Sy2 when compared with Sy~1. One of the fundamental requirements of the unification schemes is if a photon generated in the accretion disk is able to scape through the torus. Thus, a fundamental parameter that can be derived from \citet{nkv08b} formalism is the escape probability, $P_{esc}$. This parameter can work as a estimator whether an object is type 1 or type 2, since the putative large viewing angles in the latter is associated with the probability to have more clouds blocking the AGN radiation, leading to a finite but small probability of direct view to the AGN. When the condition $\tau_{V}\gg$1 is achieved $P_{esc}$ can be estimated as: \begin{equation} P_{esc} \cong e^{-N_{los}} \label{pesc} \end{equation} The frequency histograms showing the $P_{esc}$ are presented in Figure~\ref{indirect}. The results agree with the predictions (i.e. lower probabilities are expected in type 2 objects). We found mean values of $\rm \bar{P}_{esc}(Sy2)=0.1$ and $\rm \bar{P}_{esc}(Sy1)=0.3$ indicating that, on average, a photon originated in the central source has a $\sim$30\% chance to escape from the torus without being absorbed. The individual clouds emission, as adopted in the {\sc clumpy} models formalism, plays a fundamental role to understand the emerging IR torus radiation. It can be originated by clouds directly illuminated by the AGN photons plus the reprocessed radiation from the shaded side of clouds which are heated by the emission of more internal clouds. Thus, what is observed is a sum of the radiation emitted by the torus and the photons generated in the accretion disc that are able to scape (i.e. $P_{esc}$), therefore knowing $P_{esc}$ is fundamental to determine the whole SED emission. \begin{figure} \begin{center} \includegraphics[width=86mm]{pescape.eps} \caption{The figure illustrates the distribution of $P_{esc}$, the photon escape probability, in function of the torus width, $\sigma$ and the complementary viewing angle, $\beta$=$\pi/2-i$, related by Equation~\ref{pesc}. In agreement with the unified model premise, which expect that Sy\,2 galaxies more likely on the left side and Sy\,1 on the center of the graph and higher $P_{esc}$ values, we found Sy\,2 more concentrated at lower probabilities, except for some objects. As a representative value for our sample, we utilized $N$=10 to plot the $P_{esc}$ curves.} \label{pescape} \end{center} \end{figure} \begin{figure*} \begin{center} \includegraphics[width=172mm]{NxSig10_test.eps} \vspace{-1.5cm} \caption{The graph represents the distribution of $N$ and $\sigma$ and their correlation with the covering factor, $C_{T}$. Covering factors curves are present for values from 0.2 to 0.9 according to Equation~\ref{cov}. The closed diamonds represent the Sy\,1 objects and the circles show the Sy\,2 types. The histograms for $N$ and $\sigma$ are attached at the top and right side of the main plot, respectively, for both activity types. As argued in \citet{eli12}, the Sy\,2 galaxies are more likely drawn from the distribution of higher covering factors than Sy\,1 types.} \label{covfactor} \end{center} \end{figure*} Once $P_{esc}$ is a non-linear function of $\sigma$, $\beta$ and $N$ we used the results we obtained with our Spitzer data fittings for $\sigma$ and $\beta$ and adopted a value for $N$=10 in order to determine $P_{esc}$ curves in the $\sigma \times \beta$ plane. The results are shown in Figure~\ref{pescape}, for display purposes for this figure we used a 10\% of $\chi^2_{red}$ deviations as described in \citet{sal13}. It emerges from this figure that most of the Sy\,2 galaxies present $P_{esc}\lesssim$10\%. The distribution of $P_{esc}$ is quite broad for Sy\,1, that may be a reflect of the fact that both $\sigma$ and $\beta$ do present a variety of values in this class (see Figure~\ref{direct}). This parameter was also studied by RA11 and AH11, our results are in good agreement with those found by these authors, in the sense that there is a significant difference between both types of activities. However, while we find almost the same fraction for Sy~1s, we find larger values for Sy~2s than the values found by these authors. We attribute this difference (in type 2 objects, $P_{esc}^{we}$=10\% and $P_{esc}^{they}$=0.1\%) to the fact they restricted the torus thickness (5$\leq$ Y $\leq$ 30) and we allow it to take all the possible values. Another parameter provided by the model is the geometrical covering factor that can be understood as the sky fraction at the AGN centre which is being obscured by the dusty clouds. This parameter can be determined by integrating the $P_{esc}$ over all orientations, following the equation \citep{nkv08a}: \begin{equation} C_{T}= 1 - \int_{0}^{\pi/2}P_{esc}(\beta)\cos(\beta)d\beta \label{cov} \end{equation} The distribution of the derived values for $C_T$ are presented in Figure~\ref{indirect}. We found slightly larger $C_T$ values for type~2 sources ($\rm \bar{C}_{T}(Sy2)=0.8\pm0.2$) than for type~1 galaxies ($\rm \bar{C}_{T}(Sy1)=0.7\pm0.2$). Our values are in agreement with literature in the sense that there is a difference between both activities, however, while RA11 find typical values of 0.5 for for the Sy\,1 in their sample, these authors find almost the same values we found for the Sy~2 in their sample. \citet{mor09} also found an even smaller ($\sim$0.3) mean value in their type 1 PG quasars sample. Accordingly to \citet{nkv08a} the definition of $C_{T}$ arises from the geometry and probabilistic nature of a {\sc clumpy} medium and can be interpreted as the fraction of randomly distributed observers whose view to the central source is blocked, or as the fraction of type 2 objects in a random sample. The covering factor can be also decisive into AGN classification, because an AGN with a larger covering factor has a higher probability to be viewed as type 2. Many questions are still opened concerning the definition of the intrinsic covering factor, if the geometrical one is related with the ``dust'' covering factor proposed by \citet{maio07} (defined as the ration between the thermal component and the AGN contributions). Since the covering factor measures the fraction of AGN luminosity captured by the torus and converted to infrared, the AGN IR luminosity is $C_{T}L_{bol}$, where $L_{bol}$ is its bolometric luminosity \citep{eli12}. Thus, it is expected that type 2 AGNs have intrinsically higher IR luminosities than type 1. However, in disagreement with earlier expectations of a strong anisotropy at $\lambda\lesssim 8\umu$m, Spitzer observations present very similar IR fluxes of type 1 and 2 as shown by \citet{lutz,bucha}, which can be partly explained by a clumpy torus distribution. The geometrical $C_{T}$ can be interpreted as the ``true" torus covering factor because it is independent on $i$. However, on the other hand, as can be noted from Equation~\ref{cov} $C_T$ depends on N and $\sigma$, thus to investigate this relation we show in Figure~\ref{covfactor} the results of the models fits\footnote{For display purposes we adopted the mean values of each parameter for the 10\% deviation of the best $\chi^2_{red}$.} in the $N$--$\sigma$ plane together with the contour plots of $C_T$. We found that type~2 objects do preferentially lie on the top right of the figure, or in other words they do have large $C_{T}$ values. However, in the case of type~1 objects (where low $C_{T}$ values are expected, since the BLR emission should be observable) we found that they are spread over the whole plane. AH11 and RA11 suggest that type 1 and type 2 AGNs preferentially are located in different regions on the plane (with type 1 having lower values than type 2), however we do not see this trend in our work because, despite the same results for the $\sigma$, we derived larger values for the number of clouds, $N$, and therefore it is expected more clouds obscuring the central source. Since $C_T$ is very sensitive to $N$ and $\sigma$, our results always point to higher values than those found in their sample. We would also like to emphasize that our sample consist in a statistically representing sample, and this trend may be biased since the other works have a smaller sample or due to the restrictions in the parameter space adopted by the authors. \subsection{Torus mass and size} Beside the above torus parameters, the {\sc clumpy} formalism also allows to determine the mass of the emitting hot dust, as well as to set some constrains on the torus size. From the adjustment of the theoretical SEDs {\sc clumpy} model, the bolometric luminosity of the AGN, $ L_ {AGN} $, can be found from the scale factor ($\Theta$) of the model to the observation, by solving the equation: \begin{equation} \lambda_{obs} F_{obs,\lambda} = \Theta \frac{\lambda_{mod} F_{mod, \lambda}}{F_{AGN}} \end{equation} We can derived $L_{AGN}$ applying the distance relation $ L_{AGN} = 4 \pi D^2 \Theta $ and once it is calculated Equation~\ref{rsub} can be used to estimate the inner radius, assuming a sublimation temperature for the silicate grains (we used $ T_{sub}=1500$\,K). The torus dimension is estimate by the relation Y=$R_{o}/R_{d}$, where $Y$ is taken from the best fit. In order to test the $L_{AGN}$ values derived from the scaling of the {\sc clumpy} models, we can compare them with those reported in the literature for the X-rays by applying the bolometric correction of $\sim$20 \citep{elvis} and the comparison between the fitted and literature $L_{AGN}$ is shown in Figure~\ref{lagn}. As can be seen from the one-to-one line the observed and calculated values do agree well. \begin{figure} \begin{center} \includegraphics[width=86mm]{lx-lagn.eps} \caption{Comparison between the bolometric luminosities, $L_{AGN}$, derived from the {\sc clumpy} models with those reported on the literature for the hard X-ray luminosities, $L_X$, applying the bolometric corrections of \citet{elvis}. The diamonds represent the Sy\,1 objects while the circles indicate the Sy\,2 types and the dashed line indicates the identity line.} \label{lagn} \end{center} \end{figure} Figure~\ref{lumR} shows histograms for the distributions of $ L_{AGN}$ and $ R_{o}$. No significant differences between type 1 and type 2 galaxies are seen. In general, the estimated values of the AGN bolometric luminosity range between $42<log(L_{AGN})<46$, and the average values in both classes are typically $L_{AGN}\sim 10^{44}$. For the sublimation radius we find averages $\rm R_d (Sy1) =$0.12\,pc for Sy\,1 galaxies and $\rm R_d(Sy2) = $ 0.16\,pc for Sy\,2, which lead to average torus sizes very close to those found in the literature \citep[RA09, AH11, RA11,][]{lir13}, with typical values of $R_o\lesssim$6\,pc. These results are further supported by observational evidences. For instance, previous works using MIR interferometric observations provide information of a relatively compact torus, with a few parsecs scale \citep[][]{jaffe04,tri07, tristram09, burtscher09}. \begin{figure*} \begin{center} \includegraphics[width=172mm]{lum_rout.eps} \caption{The histograms show the distribution of the AGN bolometric luminosities (left panel), torus sizes, $R_o$, in the middle panel and the torus masses, $M_{tor}$ at the right. Histograms filled in purple represent the distributions for Sy\,1 and dashed lines in blue indicate the distributions for Sy\,2.} \label{lumR} \end{center} \end{figure*} By adopting some approximations for the torus geometry and size, we can also estimate its total mass. Considering the mass of a single cloud as $m_{H}N_{H,c}A_{c}$, where $N_{H,c}$ is its column density and $A_c$ its cross sectional area, the total mass in clouds is given by $M_{tor}=m_{H}{N_{H}}^{1}\int \eta_{c}(r,\beta)dV$, where $\eta_{c}(r,\beta)$ indicates the clouds distribution profile. For simplicity, assuming a sharp-edge angular distribution, $M_{tor}$ can be analytically calculated \citep{nkv08b}: \begin{equation} M_{tor}= 4 \pi m_H sin(\sigma) {N_{H}}^{(eq)} R_{d}^2 Y I_{q}(Y) \label{mtorus} \end{equation} where $Y_{q}=$1, $Y/(2lnY)$ and $Y/3$ for $q=$2,1 and 0, respectively, and ${N_{H}}^{(eq)}$ is the mean overall column density in the equatorial plane. The latter can be estimated by multiplying the number of clouds along the equatorial ray $N$ by a single cloud columnar density $N_{H,c}$ $\sim$10$^{22}$--10$^{23}\rm cm^{-2}$. Finally, since $N\sim$ 5--15,${N_{H}}^{(eq)}$ assumes typical values of $\sim$10$^{23}$--10$^{24}\rm cm^{-2}$. We found that $M_{tor}$ ranges from $\rm 10^4 M_\odot$ to $\rm 10^7 M_\odot$ in both activities with mean values typically with $\rm 10^6 M_\odot$ (Figure~\ref{lumR}), in agreement with the estimating by \citet{lir13} and \citet{mor09} using the {\sc clumpy} model formalism to derive $M_{tor}$. A recent work from \citet{garcia} was able to constrain $M_{tor}$ derived from {\sc clumpy} models fitting with the mass of molecular outflow observations in NGC\,1068 using ALMA observations in band 7 and 9. They estimate $M_{tor}\sim2\times10^5 M_{\odot}$, consistent to the estimated molecular gas mass detected inside the central aperture (r=20\,pc) derived from the CO(3-2) emission. | 16 | 9 | 1609.08972 |
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1609 | 1609.05688_arXiv.txt | Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare predictions of mean-field dynamo models to observational data on magnetic pitch angle and the strength of the mean magnetic field. We demonstrate that a standard $\alpha^2\Omega$ dynamo model produces pitch angles of the regular magnetic fields of nearby galaxies that are reasonably consistent with available data. The dynamo estimates of the magnetic field strength are generally within a factor of a few of the observational values. Reasonable agreement between theoretical and observed pitch angles generally requires the turbulent correlation time $\tau$ to be in the range $10$--$20\Myr$, in agreement with standard estimates. Moreover, good agreement also requires that the ratio of the ionized gas scale height to root-mean-square turbulent velocity increases with radius. Our results thus widen the possibilities to constrain interstellar medium (ISM) parameters using observations of magnetic fields. This work is a step toward systematic statistical tests of galactic dynamo theory. Such studies are becoming more and more feasible as larger datasets are acquired using current and up-and-coming instruments. | \label{sec:intro} Spiral galaxies contain magnetic fields that are coherent on scales larger than the outer scale of turbulence, the so-called large-scale, or mean magnetic fields \citep{Beck+Wielebinski13,Beck15b}. Mean-field turbulent dynamo theory is the leading theory to explain the prevalence and properties of large-scale magnetic fields in galaxies \citep{Ruzmaikin+88,Beck+96,Brandenburg+Subramanian05a,Klein+Fletcher15}. The galactic dynamo theory has proved to be successful in explaining the overall large-scale magnetic properties of a generic spiral galaxy as well as those of a selection of nearby galaxies. Dynamo models contain a number of parameters that are poorly constrained by theory and observations as they require detailed knowledge on the size and shape of the galactic ionized layers, the magnitude and spatial distribution of the turbulent speeds and scales, as well as their variations with galactic azimuth and radius \citep[e.g.,][]{Brandenburg+93,SS98,Moss98,Rohde+99,Moss+07}. Statistical studies of the large-scale magnetic fields in samples of galaxies are limited by the fact that they require observations of synchrotron emission and Faraday rotation at sensitivity and resolution currently achievable only for a modest number of nearby galaxies (\citealt{Fletcher10}, \defcitealias{Vaneck+15}{VBSF}\citealt[][(hereafter \citetalias{Vaneck+15})]{Vaneck+15}, \citealt{Tabatabaei+16}). The radio telescopes of a new generation would significantly expand the observational database \citep[e.g.,][]{GBF04} to make such comparisons feasible. However, approaches to such comparisons of theory with observations need to be developed now, but \citetalias{Vaneck+15} demonstrated that correlations between individual parameters of spiral galaxies (such as the rotational shear rate) and their magnetic fields are not easy to detect because even the simpler properties of the global magnetic structures are sensitive to a relatively large number of diverse galactic parameters. As a result, the scatter between the remaining parameters hides the expected correlation. In addition, the observational data need to be reduced in a coherent and systematic manner to admit comparison with theory. Therefore, a statistical comparison of dynamo theory with observations requires, apart from a suitable reduction of the observational data \citepalias[as suggested by][]{Vaneck+15}, a careful approach. Another obstacle in observational verifications of galactic dynamo theory is that interstellar random magnetic fields usually exceed the mean field in strength \citep{Ruzmaikin+88,Beck+96}, so that dedicated techniques are required to deduce the parameters of the global magnetic structures observed. Moreover, galactic magnetic fields, despite being dominated by an axisymmetric structure (in agreement with predictions of the dynamo theory) are further modified by the spiral arms and various asymmetries of the host galaxies. Therefore, careful identification of the underlying axially symmetric magnetic field in the observations is required before the theory can be meaningfully compared with observations. Among approaches suggested to quantify the large-scale structures in the observed distributions of synchrotron emission and Faraday rotation are the expansion of the azimuthal patterns in Faraday rotation into Fourier series in azimuthal angle \citep{SSK92,Berkhuijsen+97,Fletcher+04,Fletcher+11} and wavelet analysis \citep{Frick+00,Patrikeev+06}. In this paper we compare predictions of galactic dynamo theory with the pitch angles of the large-scale magnetic fields in those galaxies where observational data have been interpreted appropriately. The pitch angle of the mean magnetic field is defined as $p=\arctan(\mbr/\mbp)$, with $-90^\circ<p\le90^\circ$, where $(r,\phi,z)$ are cylindrical polar coordinates with the $z$-axis parallel to the galactic angular velocity $\bfOmega$, and $\meanv{B}$ is the regular magnetic field. This is the acute angle between the mean magnetic field and the tangent to the circumference in the galactic plane, and its negative values signify a trailing spiral. There are several advantages in using the magnetic pitch angle to test the galactic dynamo theory \citep{Baryshnikova+87,Krasheninnikova+89}. Firstly, $p$ is readily predicted by the standard non-linear mean-field dynamo theory, with the need to fix the values of only a small number of parameters \defcitealias{Chamandy+14b}{CSSS}\defcitealias{Chamandy+Taylor15}{CT} (\citealt{Sur+07b},\citealt{Chamandy+14b} (hereafter \citetalias{Chamandy+14b}), \citealt{Chamandy+Taylor15} (hereafter \citetalias{Chamandy+Taylor15})). Secondly, the closely related position angle of the polarized synchrotron emission is directly observable, though it must be corrected for Faraday rotation. In contrast, the \textit{strength} of the mean magnetic field depends on additional parameters involving less certain physics. Its observational determination relies on the questionable assumption of an energy or pressure equipartition between cosmic rays and magnetic fields \citep{BK05,Stepanov+14} when deduced from the synchrotron intensity, or the implicit assumption of the statistical independence of the magnetic, thermal-electron and cosmic-ray density fluctuations when obtained from Faraday rotation \citep{Beck+03}. As a result, the regular magnetic field magnitude $\mean{B}$ determined from observational data is arguably less reliable than its inferred pitch angle. Moreover, $\mean{B}$ is sensitive to details of the dynamo non-linearity and the extent to which the dynamo is supercritical, to which $p$ is less sensitive. \citet{Fletcher10} (see also \citealt{Klein+Fletcher15}), briefly assessed the ability of dynamo theory to explain some features of galactic magnetic fields, but they restricted the comparison to the kinematic, or linear regime of dynamo action where magnetic field still grows exponentially. Nearby galaxies definitely have the dynamo action saturated since the energy density of the large-scale magnetic field is comparable to the turbulent energy density, so nonlinear, steady-state solutions of the dynamo equations are more relevant in such comparisons. As pointed out by \citet{Elstner05} and studied in detail by \citetalias{Chamandy+Taylor15}, magnetic pitch angles are predicted to be smaller in magnitude in the saturated state than in the kinematic regime. \citetalias{Vaneck+15} expanded the database compiled by \citet{Fletcher10} and performed a statistical analysis of the data, including an assessment of the level of agreement between the data and solutions of a simple analytical non-linear dynamo model. The magnetic pitch angles predicted by the dynamo model used by \citetalias{Vaneck+15} had magnitudes much too small to explain observations, confirming concerns voiced previously \citep{Elstner05}. \citetalias{Chamandy+Taylor15} explored the parameter space of the dynamo models more extensively to find magnetic pitch angles comparable to those observed can be obtained in standard dynamo models but not with the canonical, solar-neighborhood parameter values used by \citetalias{Vaneck+15}. Our goal here is to develop further such a comparison using essentially the same dynamo model as \citetalias{Chamandy+Taylor15} (with a few refinements). Given the deliberate simplicity of the galactic dynamo models used, the incompleteness of the galactic dynamo theory in general, and imperfections in the observational data, it is unrealistic to expect an agreement between the theory and observations at the level of rigorous statistical tests, and such comparisons would necessarily remain qualitative at least until more extensive, homogeneous and reliable observational data become available. The paper is organized as follows. In Section~\ref{sec:data}, we briefly discuss the data set. We then present dynamo solutions in Section~\ref{sec:model} illustrating both numerical and analytical results in various regions of the parameter space. Sections~\ref{sec:data} and \ref{sec:model} present only a brief discussion, and the reader is referred to \citetalias{Vaneck+15} and \citetalias{Chamandy+Taylor15} for more detail. A discussion of the galactic model used as input to the model can be found in Section~\ref{sec:input}. Section~\ref{sec:output} presents the main results, comparing the magnetic pitch angles obtained in the dynamo theory and observations, while Section~\ref{sec:variations} explores effects of varying model parameters. We discuss the implications of our results and the significance of the remaining discrepancies between the theory and the data in Section~\ref{sec:discussion}. We formulate our conclusions in Section~\ref{sec:conclusions}. \begin{table*} \begin{center} \caption{\label{tab:B_data}Large-scale magnetic fields observed in the sample galaxies: the galactocentric radius, magnetic pitch angle $p$, and strength of the axisymmetric component of the mean magnetic field $\mean{B}$ are given in Columns $2$--$4$ \citepalias[][and references therein]{Vaneck+15}. Columns $5$--$7$ refer to saturated solutions of our fiducial numerical model (`fid') with $\tau=14\Myr$ and exponentially flared disks (see Figures~\ref{fig:p}, \ref{fig:B}, and \ref{fig:growth_time} for a graphical representation of $p$, $B$, and $T_3$, respectively.) The quantity $T_3$ is the $10^3$-folding time of the mean magnetic field in the kinematic (linear) regime. Column $8$ shows results for $p$ for the model for which $\tau$ is allowed to vary from galaxy to galaxy (`$\tau$ var.'), discussed in Section~\ref{sec:variable_tau}: $\tau=10\Myr$ for M31, $14\Myr$ for M33, $20\Myr$ for M51, $30\Myr$ for M81, $16\Myr$ for NGC~253, $19\Myr$ for NGC~1097, $12\Myr$ for NGC~1365, $10\Myr$ for NGC~1566, $14\Myr$ for NGC~6946, and $11\Myr$ for IC~342. Column $9$ refers to the model with $h=\const=0.4\kpc$ (`$h$ const.'), which is discussed in Section~\ref{sec:constant_h}. Finally, columns $10$ and $11$ respectively show results for the models which have no outflow (`$U\f=0$'), and for which the outflow of the fiducial model was multiplied by $10$ (`$U\f=10\times$'), both of which are discussed in Section~\ref{sec:outflows}. These differ from the fiducial model only for galaxies for which data were available to estimate the outflow velocity: M31, M33, M51, NGC~253, and NGC~6946. } \begin{tabular}{@{}ccccccccccc@{}} \hline \hline (1) &(2) &(3) &(4) &(5) &(6) &(7) &(8) &(9) &(10) &(11)\\ Galaxy &Radial range &$p$ &$\mean{B}$ &$p$ &$\mean{B}$ &$T_3$ &$p$ &$p$ &$p$ &$p$ \\ & &(obs.)&(obs.) &(fid.)&(fid.) &(fid.) &($\tau$ var.)&($h$ const.) &($U\f=0$) &($U\f=10\times$) \\ &$[\!\kpc]$ &$[^\circ]$ &$[\!\mkG]$ &$[^\circ]$ &$[\!\mkG]$ &$[\!\Gyr]$ &$[^\circ]$ &$[^\circ]$ &$[^\circ]$ &$[^\circ]$ \\ \hline M31 &$6$--$8$ &$-13\pm4$ &$4.8$ &$-28.7$ &$0.9$ &$1.1$ &$-19.9$ &$-17.4$ &$-27.6$ &$-31.5$ \\ &$8$--$10$ &$-19\pm3$ &$5.6$ &$-18.6$ &$1.1$ &$1.2$ &$-13.2$ &$-16.0$ &$-17.8$ &$-20.3$ \\ &$10$--$12$ &$-11\pm3$ &$4.7$ &$-15.3$ &$1.1$ &$1.7$ &$-10.9$ &$-18.4$ &$-14.7$ &$-16.5$ \\ &$12$--$14$ &$-8\pm3$ &$4.9$ &$-13.7$ &$0.8$ &$2.5$ &$-9.8$ &$-23.0$ &$-13.2$ &$-14.6$ \\[7pt] M33 &$1$--$3$ &$-51\pm2$ &$0.7$ &$-56.0$ &$1.2$ &$5.4$ &$-56.0$ &$-19.6$ &$-55.4$ &$-59.1$ \\ &$3$--$5$ &$-41\pm2$ &$0.3$ &$-26.0$ &$1.1$ &$3.2$ &$-26.0$ &$-24.0$ &$-25.5$ &$-27.2$ \\[7pt] M51 &$2.4$--$3.6$ &$-20\pm1$ &$1.2$ &$-12.5$ &$6.4$ &$0.19$ &$-18.2$ &$-4.8$ &$-11.8$ &$-13.2$ \\ &$3.6$--$4.8$ &$-24\pm4$ &$1.5$ &$-15.3$ &$4.8$ &$0.29$ &$-22.4$ &$-7.9$ &$-14.5$ &$-16.2$ \\ &$4.8$--$6.0$ &$-22\pm4$ &$2.5$ &$-17.6$ &$3.8$ &$0.54$ &$-25.9$ &$-12.0$ &$-16.7$ &$-18.6$ \\ &$6.0$--$7.2$ &$-18\pm1$ &$2.5$ &$-13.5$ &$2.8$ &$0.71$ &$-19.6$ &$-12.3$ &$-12.8$ &$-14.4$ \\[7pt] M81 &$6$--$9$ &$-21\pm7$ &-- &$-7.8$ &$1.7$ &$0.96$ &$-17.0$ &$-11.9$ &$-7.8$ &$-7.8$ \\ &$9$--$12$ &$-26\pm6$ &-- &$-4.6$ &$0.8$ &$2.1$ &$-9.9$ &$-16.1$ &$-4.6$ &$-4.6$ \\[7pt] NGC~253 &$1.4$--$6.7$ &$-25\pm5$ &$4.4$ &$-21.8$ &$2.8$ &$0.40$ &$-25.3$ &$-10.0$ &$-20.6$ &$-24.7$ \\[7pt] NGC~1097 &$1.25$--$2.50$ &$-34\pm2$ &$1.4$ &$-8.1$ &$7.7$ &$0.12$ &$-11.2$ &$-2.1$ &$-8.1$ &$-8.1$ \\ &$2.50$--$3.75$ &$-36\pm4$ &$1.1$ &$-11.4$ &$5.9$ &$0.16$ &$-15.7$ &$-3.4$ &$-11.4$ &$-11.4$ \\ &$3.75$--$5.00$ &$-23\pm2$ &$1.9$ &$-22.0$ &$3.9$ &$0.27$ &$-31.5$ &$-7.4$ &$-22.0$ &$-22.0$ \\[7pt] NGC~1365 &$2.625$--$4.375$ &$-34\pm2$ &$0.8$ &$-46.9$ &$2.4$ &$0.93$ &$-37.3$ &$-11.0$ &$-46.9$ &$-46.9$ \\ &$4.375$--$6.125$ &$-17\pm1$ &$0.8$ &$-28.9$ &$3.6$ &$0.40$ &$-24.2$ &$-9.2$ &$-28.9$ &$-28.9$ \\ &$6.125$--$7.875$ &$-31\pm1$ &$0.7$ &$-29.6$ &$3.1$ &$0.78$ &$-24.8$ &$-11.3$ &$-29.6$ &$-29.6$ \\ &$7.875$--$9.625$ &$-22\pm1$ &$1.2$ &$-29.9$ &$2.5$ &$1.5$ &$-25.0$ &$-13.7$ &$-29.9$ &$-29.9$ \\ &$9.625$--$11.375$ &$-37\substack{+6\\-1}$ &$1.1$ &$-28.6$ &$1.9$ &$2.7$ &$-24.0$ &$-15.9$ &$-28.6$ &$-28.6$ \\ &$11.375$--$13.125$ &$-29\pm11$ &$0.7$ &$-28.0$ &$1.1$ &$5.8$ &$-23.5$ &$-18.9$ &$-28.0$ &$-28.0$ \\ &$13.125$--$14.875$ &$-33\pm6$ &$0.4$ &$-27.8$ &$0.5$ &$25.$ &$-23.4$ &$-22.8$ &$-27.8$ &$-27.8$ \\[7pt] NGC~1566 &$2.7$--$8.0$ &$-20\pm5$ &-- &$-28.2$ &$3.4$ &$0.88$ &$-19.4$ &$-12.7$ &$-28.2$ &$-28.2$ \\[7pt] NGC~6946 &$0$--$6$ &$-27\pm2$ &-- &$-29.4$ &$3.1$ &$0.55$ &$-29.4$ &$-11.9$ &$-28.2$ &$-31.0$ \\ &$6$--$12$ &$-21\pm2$ &-- &$-12.6$ &$0.8$ &$2.9$ &$-12.6$ &$-24.5$ &$-12.0$ &$-14.7$ \\ &$12$--$14$ &$-10\pm6$ &-- &$-7.1$ &$0.4$ &$6.2$ &$-7.1$ &$-40.0$ &$-6.5$ &$-9.8$ \\[7pt] IC~342 &$5$--$9$ &$-21\pm2$ &-- &$-26.4$ &$1.8$ &$1.8$ &$-20.2$ &$-16.1$ &$-26.4$ &$-26.4$ \\ &$9$--$13$ &$-18\pm2$ &-- &$-23.6$ &$0.6$ &$9.7$ &$-18.2$ &$-29.9$ &$-23.6$ &$-23.6$ \\ \hline\hline \end{tabular} \end{center} \end{table*} \begin{table*} \begin{center} \caption{\label{tab:input_data}Observational data used as input into the model to calculate the configuration of the mean magnetic field. Data from columns 2--6 are taken from \citetalias{Vaneck+15}. Column~3 gives the magnitude of the angular velocity $\Omega$ averaged over the radial range shown in column~2. Column~4 gives the shear parameter $q=-S/\Omega$ averaged over the radial bin, where the radial shear $S$ is taken from \citetalias{Vaneck+15}. Columns~5 and 6 refer to the HI and star formation rate surface densities, respectively (if the data were not available, the entry reads `--'). The corrected value of $d_{25}=2r_{25}$ is taken as the mean of LEDA (column~7) and NED (column~8) database entries. Those values denoted with `$*$' in the outermost radial bin of NGC~6946 are extrapolations assuming exponential profiles for $\Sigma_I$ and $\Sigma_\mathrm{*}$. } \begin{tabular}{@{}cccccccc@{}} \hline \hline (1) &(2) &(3) &(4) &(5) &(6) &(7) &(8)\\ Galaxy &Radial range &$\Omega$ &$q$ &$\Sigma_I$ &$\Sigma_\mathrm{*}$ &$\log(2r_{25})$ &$\log(2r_{25})$ \\ & & & & & &LEDA &NED \\ &$[\!\kpc]$ &$[\!\kmskpc]$ & &$M_\odot\pc^{-2}$ &$M_\odot\pc^{-2}\Gyr^{-1}$ &$[0.1']$ &$[0.1']$ \\ \hline M31 &$6$--$8$ &$38.4$ &$0.75$ &$1.47$ &$0.443$ &$3.28$ &$3.31$ \\ &$8$--$10$ &$31.1$ &$0.99$ &$2.17$ &$0.621$ & & \\ &$10$--$12$ &$25.1$ &$1.07$ &$3.64$ &$0.794$ & & \\ &$12$--$14$ &$21.1$ &$1.02$ &$4.05$ &$0.227$ & & \\[7pt] M33 &$1$--$3$ &$40.7$ &$0.62$ &$11.3$ &$9.64$ &$2.80$ &$2.87$ \\ &$3$--$5$ &$24.9$ &$0.84$ &$9.43$ &$3.99$ & & \\[7pt] M51 &$2.4$--$3.6$ &$86.5$ &$1.13$ &$5.20$ &$20.7$ &$2.15$ &$2.05$ \\ &$3.6$--$4.8$ &$58.1$ &$1.05$ &$5.97$ &$13.5$ & & \\ &$4.8$--$6.0$ &$46.7$ &$0.87$ &$8.98$ &$18.0$ & & \\ &$6.0$--$7.2$ &$38.1$ &$1.05$ &$6.63$ &$7.92$ & & \\[7pt] M81 &$6$--$9$ &$31.7$ &$1.24$ &$3.33$ &-- &$2.36$ &$2.44$ \\ &$9$--$12$ &$19.8$ &$1.49$ &$2.32$ &-- & & \\[7pt] NGC~253 &$1.4$--$6.7$ &$50.9$ &$0.97$ &$3.28$ &$35.1$ &$2.40$ &$2.45$ \\[7pt] NGC~1097 &$1.25$--$2.50$ &$182$ &$1.20$ &$3.00$ &-- &$2.03$ &$1.98$ \\ &$2.50$--$3.75$ &$94.5$ &$1.43$ &$2.95$ &-- & & \\ &$3.75$--$5.00$ &$62.1$ &$1.00$ &$3.13$ &-- & & \\[7pt] NGC~1365 &$2.625$--$4.375$ &$71.3$ &$0.58$ &$3.39$ &-- &$2.08$ &$2.05$ \\ &$4.375$--$6.125$ &$52.4$ &$0.95$ &$4.31$ &-- & & \\ &$6.125$--$7.875$ &$39.3$ &$1.05$ &$6.89$ &-- & & \\ &$7.875$--$9.625$ &$30.9$ &$1.11$ &$9.50$ &-- & & \\ &$9.625$--$11.375$ &$25.1$ &$1.19$ &$10.8$ &-- & & \\ &$11.375$--$13.125$ &$20.9$ &$1.22$ &$9.58$ &-- & & \\ &$13.125$--$14.875$ &$17.7$ &$1.21$ &$8.26$ &-- & & \\[7pt] NGC~1566 &$2.7$--$8.0$ &$38.2$ &$0.96$ &$9.69$ &-- &$1.86$ &$1.92$ \\[7pt] NGC~6946 &$0$--$6$ &$48.1$ &$0.86$ &$6.30$ &$20.2$ &$2.19$ &$2.22$ \\ &$6$--$12$ &$19.6$ &$1.05$ &$4.08$ &$2.50$ & & \\ &$12$--$14$ &$13.4$ &$1.02$ &$3.05^*$ &$0.620^*$ & & \\[7pt] IC~342 &$5$--$9$ &$28.1$ &$1.05$ &$6.41$ &-- &$2.62$ &$2.65$ \\ &$9$--$13$ &$17.7$ &$0.95$ &$6.53$ &-- & & \\ \hline\hline \end{tabular} \end{center} \end{table*} | \label{sec:conclusions} We have used a simple, mean-field dynamo model to calculate the strength and direction of the axisymmetric large-scale (or regular) magnetic field in nearby disk galaxies for which sufficient data are available. We obtain a fairly reasonable level of overall agreement between model solutions and observations for the magnetic pitch angle $p=\arctan(\mbr/\mbp)$ for the galaxies M31, M51, M81, NGC~253, NGC~1566, NGC~6946, and IC~342. For M33, large pitch angle magnitudes comparable with observed values are obtained, but detailed agreement is lacking. For the two barred galaxies in the sample, NGC~1097 and NGC~1365, our model does worse, which is expected as their gas flows and magnetic fields deviate strongly from axial symmetry. However, agreement for these galaxies is better at larger galactocentric distance, where effects of the bar are less important. For the regular magnetic field strength, our model agrees with the data to within a factor of a few. The field strength is less precisely determined than the magnetic pitch angle, both observationally and theoretically. We confirm that it is possible to explain large pitch angle magnitudes in galaxies by appealing to parameter values different from standard (solar neighborhood) estimates. Specifically, large pitch angles require a relatively small ratio of disk semi-thickness to turbulent speed $h/u$ and/or a relatively large correlation time $\tau$, compared to standard estimates of $\sim40$--$50\Myr$ and $10\Myr$, respectively. To obtain locally growing solutions for the mean magnetic field in the kinematic dynamo regime for all radii in all galaxies in the sample, we require that the standard estimate for the kinetic $\alpha$ effect be enhanced by a factor of about $2$. This suggests that standard estimates for the $\alpha\kin$ effect may be too small. We obtain strong evidence that the ratio $h/u$ tends to increase with galactocentric radius within galaxies. Assuming, as we have done, that $u$ is approximately constant with radius, this result implies that the ionized disk within which dynamo action occurs is flared. Our model produces good agreement with observation when we choose the turbulent correlation time to lie somewhere within the range $\tau\sim10$--$20\Myr$, which is consistent with standard estimates. The specific value of $\tau$ is, however, likely to vary from galaxy to galaxy. Extending the present work will require better and more homogeneous magnetic field and kinematics data for nearby galaxies, as well as refinements to the dynamo model to incorporate additional physical effects. Further, a detailed investigation of the possible connections between spiral arms and magnetic pitch angles is still needed. While our main objective was to make progress toward better tests of dynamo theory, the present work also demonstrates the promise of inverting the problem to probe ISM physics using magnetic fields. | 16 | 9 | 1609.05688 |
1609 | 1609.07158_arXiv.txt | We have developed a maximum likelihood source detection method capable of detecting ultra-faint streaks with surface brightnesses approximately an order of magnitude fainter than the pixel level noise. Our maximum likelihood detection method is a model based approach that requires no {\it a priori} knowledge about the streak location, orientation, length, or surface brightness. This method enables discovery of typically undiscovered objects, and enables the utilization of low-cost sensors (i.e., higher-noise data). The method also easily facilitates multi-epoch co-addition. We will present the results from the application of this method to simulations, as well as real low earth orbit observations. | \label{sec:introduction} Satellites and near earth objects (NEOs) appear as streaks in the images of sidereal tracking surveys. There is evidence that the NEOs and satellites (including space debris) follow an inverse power law luminosity function with there being many more fainter objects than brighter objects \cite{Schildknecht:2001ks, Schildknecht:2004kr, NAP12842}. Thus going fainter provides the best return on object characterization and actionable information. Additionally, algorithms that can detect streaks as faint as possible can enable the use of lower cost telescopes and detectors. Astronomical surveys of local solar system or Earth orbiting objects typically fall into two broad categories: object tracking and sidereal tracking. In the case of object tracking, the object of interest will appear as a point source convolved with the atmospheric/optic point spread function (PSF) and the stars or other objects moving at a different angular velocity will appear as streaks. In the case of sidereal tracking, the stars will appear as PSF's and satellites and NEOs will appear as streaks of varying lengths. Sidereal tracking surveys have the advantage of enabling easy discrimination of satellites and NEOs from galactic and extra-galactic sources, which significantly outnumber the satellites and NEOs. This comes at the price of making detection of satellites and NEOs more challenging due to extending their signal spatially and increasing the noise floor as a function of the angular velocity of the source \cite{Krugly:2004ca}. We will introduce a maximum likelihood detection method as a statistically rigorous extension of a signal-matched-filter \cite{woodward1953probability,turin1960} that is capable of maximizing the detectability of satellites and NEOs in both categories of surveys while maintaining high purity. | \label{sec:discussion} Signal-matched filters have been used extensively in astronomical image detection algorithms to detect faint, low surface brightness, sources. In this conference proceeding we have outlined how signal-matched filters can be incorporated into a maximum likelihood statistical formalism. This formalism has a number of advantages. It accounts for spatially-varying source models, image noise, and PSFs. In addition, it enables easy epoch co-addition that is absent of the systemics associated with varying PSFs and the processing of data on a pixel grid. In addition to outlining the maximum likelihood detection method we have demonstrated it on a number of simulated images, as well as an image of a real LEO object observed during the STARE proof of concept survey. We have also demonstrated how the method enables us to detect and deblend multiple ultra-faint streaks, with varying properties, in a single image. The ability of the maximum likelihood method to recover all of the information in a given image, and combine the information from multiple epochs in a statistically rigorous manner, enables the detection of ultra-faint sources. Furthermore, the probabilistic basis of the maximum likelihood detection method enables detection of multiple objects in a given image (including blended sources), and initial estimates of the detected object properties, including uncertainties that can be consistently propagated to downstream estimates (e.g., orbit parameter estimates; see \cite{SchneiderDawson}). It is for these reasons that ultra-faint, low signal-to-noise, sources can still result in actionable information. | 16 | 9 | 1609.07158 |
1609 | 1609.00064_arXiv.txt | Recent studies have shown that outflows in at least some broad absorption line (BAL) quasars are extended well beyond the putative dusty torus. Such outflows should be detectable in obscured quasars. We present four WISE selected infrared red quasars with very strong and peculiar ultraviolet Fe\,{\sc ii} emission lines: strong UV Fe\,{\sc ii} UV arising from transitions to ground/low excitation levels, and very weak Fe\,{\sc ii} at wavelengths longer than 2800\AA. The spectra of these quasars display strong resonant emission lines, such as C\,{\sc iv}, Al\,{\sc iii} and Mg\,{\sc ii} but sometimes, a lack of non-resonant lines such as C\,{\sc iii}], S\,{\sc iii} and He\,{\sc ii}. We interpret the Fe\,{\sc ii} lines as resonantly scattered light from the extended outflows that are viewed nearly edge-on, so that the accretion disk and broad line region are obscured by the dusty torus, while the extended outflows are not. We show that dust free gas exposed to strong radiation longward of 912\AA~ produces Fe\,{\sc ii} emission very similar to that observed. The gas is too cool to collisionally excite Fe\,{\sc ii} lines, accounting for the lack of optical emission. The spectral energy distribution from the UV to the mid-infrared can be modeled as emission from a clumpy dusty torus, with UV emission being reflected/scattered light either by the dusty torus or the outflow. Within this scenario, we estimate a minimum covering factor of the outflows from a few to 20 percent for the Fe\,{\sc ii} scattering region, suggesting that Fe\,{\sc ii} BAL quasars are at a special stage of quasar evolution. | Outflows are ubiquitous among quasars. They manifest themselves as blue-shifted broad and narrow absorption lines in UV and X-rays (e.g., Boksenberg et al. 1978; Turnshek et al. 1980; Weyman et al. 1991). The broad absorption lines (BALs) with widths of around a few thousands to a few ten thousands \kms~appear in 15-25\% of all quasars (e.g.,Weymann et al. 1991; Knigge et al. 2008), and intrinsic narrow absorption lines (NALs) with widths around hundreds to one thousand \kms~in 40-50\% of quasars (Nester et al. 2008). Almost all known BAL QSOs show broad high ionization absorption lines, such as \civ, \nv (Weymann et al. 1991; cf, Mrk 231, Veilleux et al. 2013), while only a small fraction (about 25\%) of BAL QSOs display also low ionization broad absorption lines (LoBALs, Weymann et al. 1991; Zhang et al. 2010; c.f. Urrutia et al. 2009), commonly \mgii. A yet smaller subset of LoBAL QSOs ($<1$\% of all quasars) exhibit broad \feii~absorption lines (hereafter, FeLoBALs; Trump et al. 2006; c.f., Dai et al. 2012). There are two different scenarios for BAL and non-BAL quasars or for a subclass of BAL QSOs. In the first scenario, the presence or the absence of BALs, or more generally, the manifestation of different subclasses of BALs, are attributed to the different viewing angles of the same intrinsic population (Weymann et al. 1991). While in the second scenario, LoBAL and non LoBAL QSOs are at different evolutionary stages (Boroson \& Meyers 1992; Voit et al. 1993; Hall et al. 2002). In other words, only a small fraction of quasars possess low-ionization outflows. Early studies showed that the emission lines and broad-band spectral energy distributions (SED) are very similar for HiBAL and non BAL quasars (Weymann et al. 1991), suggesting the unification scheme. Hamann, Korista \& Morris (1993) constrained the global covering factor to less 20\% from the fraction of resonant scattering light. However, systematic trends in the SED and emission lines have been revealed with a large sample of BAL, LoBAL in particular, and a non-BAL quasar sample from SDSS (e.g., Zhang et al. 2010; Baskin, Laor \& Hamann 2013; Farrah et al. 2010; Wang et al. 2013; and reference therein; c.f., Lazarova et al. 2012), suggesting that the global covering factor and properties of LoBALs depend on the intrinsic properties of the system. Feedback through these outflows is now widely believed to be a key physical process in the formation of massive galaxies (Fabian 2012). However, the mass loss rate and kinetic power, as well as the size, of outflows are still poorly constrained for the majority of BAL quasars (Lucy et al. 2014). To estimate these parameters from absorption lines, one needs to know the global covering factor, column density and the gas density or distance. The gas column density can be inferred from the column densities of a set of ions through photoionization modeling. However, the gas density diagnostics for absorption lines are available for only a rare subset of BAL QSOs with measured absorption lines from low-lying excitation levels of heavy elements (de Kool et al. 2001; Korista et al. 2008; Dunn et al. 2012). Previous measurements of density in a dozen of BALs, mostly FeLoBALs, quasars, indicate that BAL region (BALR) is extended from 100 parsec to several kpc from quasars (de Kool et al. 2001; Korista et al. 2008; Borguet et al. 2013; Chamberlain et al. 2015). The large size implies a very large mass outflow rate ($10^{2-3}$ M$_\sun$~yr$^{-1}$) and large kinetic power (a few to 10 percent of the total luminosity) if the outflows cover a substantial fraction of the sky. However, absorption lines can only probe the gas on the line of sight, so the global covering factor of absorbing gas is virtually unknown in an individual object. Because these quasars are so rare, the average global covering factor must be very small, according to the unification scheme, but if they are at a special evolution stage, on the other hand, the covering factor can be substantial. Interestingly, Liu et al. (2015) detected extended outflow components in two low z AGNs on the physical sizes consistent with those inferred from ultraviolet absorption lines. In this paper, we report four quasars, including one that was noted already by Ross et al. (2015), with peculiar ultraviolet \feii spectra. They were discovered during the course of studying a sample of heavily obscured quasars in WISE: $W1-W4>8.0$. We perform an analysis of the emission lines and the broad band SED, and present evidence that the \feii emission lines in these objects are dominated by continuum fluorescence pumping in the extended outflows, so they can be used to constrain the covering factor and size of BALR of LoFeBAL. The paper is organized as follows. In section 2, we present an analysis of the optical spectra and broad band SED. In section 3, we discuss the nature of \feii emission and continuum emission, and a brief conclusion is given in section 4. Spectral models of fluorescent Fe~II emission are presented in an appendix. | We presented an analysis of four quasars with peculiar UV \feii spectra. They had extremely strong UV1,3,4,62,63 and very weak \feii at wavelengths longer than 2800. Their SEDs rise very steeply from the optical to the mid-infrared, suggesting they are obscured. The obscurer is most likely the dusty torus, since that also provides a self-consistent explanation for the infrared emission although other alternatives cannot be ruled out. The characteristics of the \feii spectra can be understood as due to resonant scattering in an extended outflow since the size of the scattering region must be outside the obscuring torus and its \feii spectrum similar to absorption spectrum of FeLoBALs. Our fluorescent models can successfully produce the observed UV \feii band ratios and the weakness of \feii lines at wavelengths longer than 2800\AA with a low ionizing photon fluxes. This is because the strong UV lines are excited by continuum pumping within gas that is too cool for collisional excitation to be significant. Strong \aliii and weak \ciii] and Si {\sc iii} emission may be explained as resonant scattering, as is observed in FeLoBAL QSOs. The obscuration of the direct continuum also explains the very large equivalent widths of \feii, \mgii and \aliii lines. These objects are misaligned FeLoBALs. By considering the amount of scattered light we set a lower limit on the covering factor of FeLoBALs to be 5\% to 20\% in three objects, supporting the scenarios that FeLoBAL QSOs are a special stage of quasar evolution. | 16 | 9 | 1609.00064 |
1609 | 1609.02061_arXiv.txt | { The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2-point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is genuinely geometrical (e.g. non-degenerate with a boost) and reflects in the structure of the off-diagonal correlators. At lowest order in this effect, the temperature and polarisation correlation matrices have non-vanishing diagonal elements, as usual, and all the off-diagonal terms are excited. This particular signature of a local void model allows one, in principle, to disentangle geometrical effects from local kinematical ones in CMB observations.} | In the standard lore of the construction of a cosmological model~\cite{pu-book,Ruth_book} the universe on large scale is assumed to be spatially homogeneous and isotropic. In this framework a class of privileged fundamental observers is naturally identified. This class of reference observers is a theoretical construct and any (real) observer should be able to (1) identify this privileged cosmological reference frame and (2) determine his peculiar velocity with respect to this frame, using his observations. This has probably been best achieved with the analysis of the cosmic microwave background (CMB). In the standard interpretation, the observed large amplitude of the CMB temperature dipole is interpreted as the Doppler effect associated to our motion with respect to the CMB rest frame, assumed to coincide with the one of the fundamental observers. Assuming that the whole CMB dipole is of Doppler origin (i.e. it arises from the boost of the CMB monopole), one concludes~\cite{kogut93,fixsen96,hinshaw09} that our velocity is $v=(369\pm0.9)~\rm{km}\cdot{\rm s}^{-1}$ in the direction $(l,b)=(263^{\rm o}.99\pm0^{\rm o}.14,48^{\rm o}.26\pm0^{\rm o}.03)$. Besides this dominant effect, a boost induces other observable effects on the CMB: (1) a {\em modulation}, which gives rise to an amplification of the apparent temperature in the direction of the motion (similar to the dipole as a boosting of the monopole); (2) an {\em aberration} effect, which shifts the apparent position of fluctuations toward the velocity direction and changes the angular scale, hence shrinking the anisotropy on one half of the sky and stretching it on the other half; (3) a quadrupole induced by the dipole~\cite{KK03}. Finally (4) a boost affects polarization since it generates $B$-modes from $E$-modes. Both modulation and aberration also induce couplings among neighboring multipoles. Indeed, the observed temperature $\tilde \Theta$ can be related to the one in the CMB frame $\Theta$ by~\cite{CvL02} \be\label{primiere} \tilde \Theta({\tilde{\bm n}}) = \frac{\Theta({{\bm n}})}{\gamma\left(1-\tilde{\bm n}\cdot{\bm v}/c \right)}\,, \ee with $\gamma=(1-\beta^2)^{-1/2}$ and $\beta=v/c$. The multiplicative factor in eq. (\ref{primiere}) has the effect of inducing couplings on all scales between neighboring multipoles of the correlation function. The detectability of these effects, was discussed in Refs.~\cite{Kosowsky:2010jm,BR06,Amendola:2010ty} and the effects were shown to be observable by the {\em Planck} satellite. Such a measurement was later performed by {\em Planck} \cite{Aghanim:2013suk} and the result confirmed this standard kinematic interpretation. Despite this strong case for a Doppler interpretation, the possibility that the \emph{anomalous} amplitude of the dipolar modulation might have a non-kinematical origin has been considered, raising the more fundamental question that a Doppler-like modulation can in fact have a geometrical origin, i.e. that it would originate from our universe not being spatially homogeneous and/or isotropic, e.g. because of the existence of a local void. Indeed, in full generality one expects that both effects (i.e. the kinematical and the geometrical ones) have to be considered and ideally one should be able to disentangle them from CMB observations. In particular, the idea that the CMB dipole can arise from a large scale isocurvature perturbation was considered in Ref.~\cite{Langlois:1995ca}. Such a perturbation was modeled by considering a spherically symmetric spacetime of the Lema\^{\i}tre-Tolman-Bondi (LTB) family as a perturbation of a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime. More recently, Ref.~\cite{Roldan:2016ayx} argued that a large scale dipolar gravitational potential could mimic a Lorentz boost. In particular, because of lensing such a gravitational potential can induce mode couplings similar to aberration and modulation. Anyway this requires both a fine-tuning of the radial profile of the potential and a primordial dipolar potential.\\ The goal of this article is to fully characterize the effect of kinematics (local boost) and geometry (local void) on temperature and $E$-, $B$-modes of polarization. To that purpose, we consider two models: \begin{itemize} \item a standard model in which the universe is described by a FLRW spacetime, allowing for a boost of the observer with respect to the cosmological frame. As emphasized earlier, this has been extensively studied but it will serve as a reference for comparison. In this analysis the small parameter in which analytical results are expanded is the boost velocity $\beta$; \item a model of universe consisting of a spherical void with an overdense central region described by a Kottler spacetime and embedded in a FLRW universe. This construction is known as a Swiss-cheese model~\cite{ES45a,ES45b,Fleury:2014gha,Fleury:2013sna}. The Kottler spacetime is the generalization of the Schwarzschild (\emph{Sch}) spacetime to the case of a non-vanishing cosmological constant. For simplicity, when deriving analytic expressions, we shall assume that at late time the universe is fully matter dominated and we will thus describe the void by a \emph{Sch} spacetime. We shall not assume the observer to seat at the center of symmetry so that he will observe an axially symmetric spacetime. The last scattering surface is described as a constant time hypersurface lying in the FLRW region. In this analysis, two small parameters come into play: (1) the ratio between the radial displacement of the observer from the center of the void $D$ and the radius of the void $\chi_h$ (noted $\hat D$) and (2) the ratio between the radii of the void and of the last scattering surface ($\chi_h/\chi_{\text{LSS}}$) which we show to be proportional to $\sqrt{\hat r_S} \equiv \sqrt{r_S/\chi_h}$ where $r_S$ is the Schwarzschild radius ($r_S\equiv 2GM$) of the \emph{Sch} region. \end{itemize} In both cases our goal is to compute the 2-point angular correlation functions and the off-diagonal correlators. In particular, we shall compute analytically all the effects induced on the CMB (temperature and polarisation) related to the off-center position of an observer in the void. For an observer who does not seat at the center of symmetry, light deflection generates $B$-modes from $E$-modes at first order in lensing.\footnote{On the other hand, for a spherically symmetric situation, $B$-modes are generated from $E$-modes as a coupling between the lensing potential and CMB polarisation. This is considered as a second order effect, but also linear in the lensing.} This was already investigated in Ref.~\cite{Goto:2011ru}, an analysis that will be refined in our study. \\ Technically, while the first model has been studied in various works, the second requires to go through a series of technical steps. \begin{enumerate} \item First, we have to describe the geometry of the void and how it is matched to the outside FLRW region. Among the matching conditions, we find that the radius of the boundary $r_h(t)$ seen from the void is expanding with the cosmological scale factor $a(t)$ as \be r_h(t) = a(t) \chi_h\,, \ee where $\chi_h$ is the constant comoving radius of the void as seen from the FLRW region. \item Second, the geodesic equation for an off-center observer needs to be solved and the resulting trajectory expressed in terms of the angle $\theta_{\text{obs}}$ between the off-center direction and the direction of observation. Two main effects have to be considered: (1) the bending of the geodesic and more generally its deformation due to the propagation in the \emph{Sch} region. This has the effect of deforming the last scattering surface located in the FLRW region in two ways: an orthoradial displacement similar to lensing, and a radial displacement similar to time-delay or Shapiro potential effect; (2) the modification of the energy of the emitted photons which adds to the Sachs-Wolfe effect, located on the last scattering surface. Both the deformation of the photon trajectory and energy modulation are non-local effects. If the local velocity of the observer is carefully chosen, we find that there is no effect at order $\sqrt{\hat r_S}$. Furthermore at order $\hat r_S$ there is no additional energy modulation, and only the effects of lensing-like deflection and radial displacement come into play. The lensing-like effect is the dominant contribution and its leading order term when expanded in powers of $\hat D$ is \be\label{MainResult} \theta_{\text{LSS}} - \theta_{\text{obs}} \simeq \frac{\hat r_S}{\hat D} \tan \frac{\theta_{\text{obs}}}{2}\,. \ee \item Finally, by taking into account this dominant effect, we are able to find analytic expressions for angular power spectra of temperature and $E$- and $B$-modes of polarization, as well as for the off-diagonal correlators. For instance, we find that the off-diagonal correlator of the observed temperature anisotropy field $\tilde{\Theta}$ has non-vanishing matrix elements of the form \be \langle \tilde{\Theta}_{\ell m}\tilde{\Theta}_{\ell+L\,m+M}^* \rangle\,, \ee with no restriction on the value of $L$, due to the off-center position of the observer inside the local void. As a consequence of eq. (\ref{MainResult}), the ratio between these off-diagonal correlators and the isotropic diagonal correlators $C_\ell$ (which are the usual correlators generated in a perturbed FLRW geometry) are typically proportional to the geometrical factor $\hat r_S/\hat D$. This has to be compared with the kinematical effect of a local boost which generates correlators of these types only for $L=1$ at lowest order in the boost parameter $\beta$. \end{enumerate} The paper is organized as follows. Light propagation in the void model is detailed in section \ref{geometry}. In particular, in section \ref{geometrys} we describe the geometry of our void model, in section \ref{geodesic2} we detail the general method to solve for the geodesic, and in \ref{geodesic3} we present an analytic method to determine the emission point on the last scattering surface (LSS) given the reception time and direction. In section \ref{numerics} the results of the analytic analysis are compared with the numerical resolution. In section \ref{boost} we calculate the contributions of the lensing-like deflection and radial modulation, together with the energy modulation, at order ${\hat r_S}^{1/2}$ and $\hat{r}_S$. Separating the contribution which is non-degenerate with the effect of a boost, so as to isolate geometrical contributions from kinematical ones, we show that no geometrical contributions are present at order ${\hat r_S}^{1/2}$. The explanation of this result is discussed in section \ref{discussion physics}. In section \ref{CMBoff} we analyze the CMB sky seen by an off-center observer in the void and we calculate the temperature and polarization correlation functions, still focussing on contributions non-degenerate with the effects of a boost of the observer. Conversely, in section \ref{Boost} we turn to a FLRW model and we calculate correlation functions of CMB observables for an observer whose reference frame is in motion with respect to the CMB rest frame. To facilitate the reading, several technical details and intermediate calculations are relegated in the appendices. | This article fully characterizes the effect of the local void on the temperature and $E$, $B$- polarization modes measured by an off-centered observer. We have considered a universe consisting of a spherical void, described by a Kottler spacetime, embedded in a FLRW universe and a static observer into the void, displaced with respect to the center of symmetry. We have introduced a perturbation scheme which allowed us to analytically calculate the 2-point angular correlation functions and the off-diagonal correlators for both temperature and polarization at leading order and next-to leading order in the perturbation parameter $\hat{r}_S^{1/2}$. We found that the energy shift can be suppressed by a proper choice of the observer velocity, while the lensing-like effect remains. This last effect is a genuinely geometrical effect (non-degenerate with the effect of a boost), which reflects in the structure of the off-diagonal correlators. Indeed the structure of the correlation matrix is quite complex: at linear order in lensing the correlation matrix has non-vanishing diagonal elements and all the off-diagonal terms are excited, i.e. at linear order in lensing we get corrections among all the multipoles $\ell \leftrightarrow \ell \pm L$, $\forall L$. We have explicitly computed the off-diagonal structure of the correlation matrix for $M=m=0$: the correlation is mildly stronger for closer multipoles (i.e. small $L$) and it slowly decreases going away from the diagonal, as can be seen on Fig. \ref{FlmLM}. As a second model we have considered a FLRW universe, allowing for a boost of the observer with respect to the CMB rest frame and we have calculated the correlation function of temperature and polarization for such an observer. For this model, the results for the CMB correlators are standard, but we re-derived them to make a direct comparison with the results of the void model. In this analysis, the small parameter that allows us to expand the analytic results is the boost velocity $\beta$. At linear order in $\beta$ all the diagonal terms of the correlation matrices are vanishing. Off-diagonal correlators are non-vanishing only for $L=1$, i.e. we have only correlation among $\ell\leftrightarrow \ell\pm 1$ multipoles. If we repeat the calculation of the correlators up to order $\beta^2$, we get non vanishing diagonal correlators and off-diagonal terms of the correlation matrix at order $\beta^2$ non-vanishig for $L=2$. In fact this result can be generalized: at a generic order $\beta^n$, we would get off-diagonal terms of the correlation matrix at order $\beta^n$ non vanishing for $L=n$. The fact that in the void model, at first order in lensing, we get correlations among all the multipoles is an extremely interesting signature of the void model, which in principle would allow one to distinguish in CMB observations geometrical effects (coming e.g. from the presence of an overdense region) from kinematical effects. This work puts for the first time the discussion of the possible geometrical origin of the CMB dipole on a firm ground. The next step would be to refine our toy-model for the void, considering e.g. an LTB geometry to describe an overdense region. We expect that the results found in this analysis would stay qualitatively the same for the case of a LTB void model.\\ \noindent {\bf Acknowledgements:} GC is particularly grateful to Prof. Ruth Durrer for having encouraged her to start working in this direction. The work of GC is supported by the Swiss National Science Foundation. The work CP and JPU was supported by French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02. \vspace{3cm} \newpage \appendix | 16 | 9 | 1609.02061 |
1609 | 1609.07969_arXiv.txt | We propose a new mechanism to generate a lepton asymmetry based on the vacuum CP-violating phase transition (CPPT). This approach differs from classical thermal leptogenesis as a specific seesaw model, and its UV completion, need not be specified. The lepton asymmetry is generated via the dynamically realised coupling of the Weinberg operator during the phase transition. This mechanism provides a connection with low-energy neutrino observables. \\[2.5mm] Keywords: leptogenesis, Weinberg operator, phase transition | The origin of the matter-antimatter asymmetry is one of the most important mysteries of our Universe. One popular mechanism to explain this asymmetry is baryogenesis via leptogenesis. The classic examples of high-scale leptogenesis \cite{Fukugita:1986hr} introduce right-handed neutrinos, $N$, which are Majorana in nature and therefore break lepton number. The decay of the right-handed neutrinos provides a departure from equilibrium and their couplings to leptonic doublets, $\ell$, violate CP. A lepton asymmetry, produced from the preferential decays of $N$, is subsequently converted to a baryon asymmetry by $B-L$ conserving sphaleron processes \cite{Khlebnikov:1988sr}. In addition to fulfilling Sakharov's criterion \cite{Sakharov:1967dj}, this scenario of leptogenesis provides a natural explanation of small neutrino masses via the seesaw mechanism. The origin and energy scale of CP violation is still unknown and remains a widely studied theoretical issue. There is a rich programme of neutrino experiments such as LBNF/DUNE \cite{DUNE} and T2HK \cite{T2HK} that aim to measure leptonic CP violation. In conjunction, these experiments will investigate the correlations between leptonic observables. The interrelation between mixing angles and phases will play a crucial role in determining the fine structure of leptonic mixing. The observed pattern may be the result of an underlying flavour symmetry which could be continuous, $U(1)$ \cite{Froggatt:1978nt}, $SU(3)$, $SO(3)$ \cite{Alonso:2013nca}, or a non-Abelian, discrete symmetry such as $A_4$, $S_4$ \cite{King:2014nza}, {\it et al}. In these models, SM-singlet scalars (flavons) acquire vacuum expectation values that lead to the breaking of the flavour symmetry and results in the observed mixing structure and CP violation. The source of CP violation can arise \emph{spontaneously} or \emph{explicitly}. Spontaneous CP violation refers to the scenario in which CP conservation is imposed on the Lagrangian but is spontaneously broken by the vacuum \cite{Branco:2011zb, deMedeirosVarzielas:2011zw} whilst explicit CP violation results from complex Yukawa couplings. Unlike conventional high-scale leptogenesis, where CP is explicitly violated above the seesaw scale, in this work we investigate the possibility CP violation occurs below such a scale. In this paper, we propose a new mechanism for generating a lepton asymmetry based on a CP-violating phase transition (CPPT). This mechanism allows a connection between the baryon asymmetry, neutrino oscillation experiments and leptonic flavour mixing. CPPT differs from conventional scenarios of high-scale leptogenesis in several key aspects: we apply an effective field theory approach, which does not constrain the study to a particular model of neutrino mass generation and consequently CP violation occurs below this energy scale. We simply assume that neutrino masses are generated by the Weinberg operator, the coefficients of which are dynamically realised during CPPT. The lepton asymmetry is produced via the interference of Weinberg operators at different times. To perform the calculation we utilise the closed-time-path (CTP) formalism \cite{Schwinger:1960qe, Keldysh:1964ud}. We focus on the generation of initial asymmetry at the constant temperature, $T$, and defer a more complete calculation of the final lepton asymmetry, accounting for evolution, to future work \cite{future}. | We have proposed a novel mechanism based on CPPT to generate the matter-antimatter asymmetry. It differs from conventional high-scale leptogenesis scenarios as we assume CP is broken below the scale of neutrino mass generation and apply an effective theory approach which permits model independence. Moreover, this mechanism allows for a connection between leptonic flavour structure and the baryon asymmetry. The essential requirements of this approach are a CP-violating phase transition and the Weinberg operator. We assume the complex coefficients of this operator are dynamically realised. During the phase transition, the lepton asymmetry is generated from the interference of the Weinberg operator at different times. In order to generate the observed baryon asymmetry, the temperature scale of CPPT is approximately $T_\text{CPPT} \sim 10^{11}$ GeV. | 16 | 9 | 1609.07969 |
1609 | 1609.05477_arXiv.txt | We investigate the matter distribution of a spiral galaxy with a counter-rotating stellar core, SDSS J1331+3628 (J1331), independently with gravitational lensing and stellar dynamical modelling. By fitting a gravitational potential model to a quadruplet of lensing images around J1331's bulge, we tightly constrain the mass inside the Einstein radius $R_\text{ein}=(0.91\pm0.02)''$ $(\simeq1.83\pm0.04~\text{kpc})$ to within 4\%: $M_\text{ein} = (7.8\pm0.3) \times 10^{10} \text{M}_\odot$. We model observed long-slit major axis stellar kinematics in J1331's central regions by finding Multi-Gaussian Expansion (MGE) models for the stellar and dark matter distribution that solve the axisymmetric Jeans equations. The lens and dynamical model are independently derived, but in very good agreement with each other around $\sim R_\text{ein}$. We find that J1331's center requires a steep total mass-to-light ratio gradient. A dynamical model including an NFW halo (with virial velocity $v_{200} \simeq 240 \pm 40~\text{km s}^{-1}$ and concentration $c_{200} \simeq 8 \pm 2$) and moderate tangential velocity anisotropy ($\beta_z \simeq -0.4 \pm 0.1$) can reproduce the signatures of J1331's counter-rotating core and predict the stellar and gas rotation curve at larger radii. However, our models do not agree with the observed velocity dispersion at large radii. We speculate that the reason could be a non-trivial change in structure and kinematics due to a possible merger event in J1331's recent past. | \label{sec:intro} Determining the overall mass distribution of galaxies and separating the dark matter (DM) from the stellar mass components is a crucial step in better understanding the structure and formation of galaxies and the nature of DM. Cosmological simulations suggest that cold DM forms cuspy halos following a Navarro-Frenk-White (NFW) profile \citep{1996ApJ...462..563N}. However, the existence of central DM density cusps in massive galaxies depends strongly on the stellar mass-to-light ratio (e.g., \citealt{2011MNRAS.416..322D}), and DM dominated dwarf galaxies even favour DM halos with cores (e.g., \citealt{1994Natur.370..629M,2001ApJ...552L..23D}). This discrepancy, known as the core-cusp problem, might be resolved by galaxy formation processes such as mergers and outflows (e.g., \citealt{2001ApJ...560..636E,2012MNRAS.421.3464P}). Especially the influence of mergers on the DM and baryonic structure of galaxies is currently an active field of research (e.g., \citealt{2009ApJ...697L..38J,2010ApJ...712...88L,2012MNRAS.425.3119H,2015MNRAS.453.2447D}). The mass distribution of massive galaxies can be measured in completely independent fashions by gravitational lensing and dynamical modelling. Combining these two methods allows for valuable cross-checking opportunities to disentangle the galactic stellar and DM content. Massive galaxies can act as gravitational lenses, deflect the light of background sources, and give rise to multiple images. This strong gravitational lensing tightly constrains the projected total mass of the lens galaxy inside $\sim 1''$ (e.g., \citealt{2010ARA&A..48...87T}). The mass profile at larger galactocentric radii can be probed by gas rotation curves that directly measure the galaxy's circular velocity profile (e.g., \citealt{1980ApJ...238..471R}). However, due to its dissipative nature gas motions are very sensitive to disturbances by, e.g., spiral arms and bars (e.g., \citealt{2004dad..book.....S}). Because stars are dissipationless dynamical tracers and present almost everywhere in the galaxy, stellar dynamical modelling can complement mass constraints from lensing at small and gas motions at large radii. As stellar motions are complex---a bulk rotation around one principal axis combined with random motions in all coordinate directions---\citep{2008gady.book.....B}, full dynamical modelling of rotation, dispersion, and velocity anisotropies is needed to deduce the matter distribution. The Sloan WFC Edge-on Late-type Lens Survey (SWELLS, WFC = Wide field camera) \citep{SWELLSI,SWELLSII,SWELLSIII,SWELLSIV,SWELLSV,SWELLSVI} is dedicated to finding and investigating spiral galaxies, which are (i) strong gravitational lenses and (ii) observed almost edge-on, such that rotation curves can be easily measured. By combining lensing and dynamical modelling, degeneracies inherent in both methods can be broken. One of the SWELLS galaxies is the massive spiral SDSS J1331+3628, to which we refer as J1331 in the remainder of this work. It has bluish spiral arms and a large reddish bulge (see Figures \ref{fig:F450W} and \ref{fig:F814W}), which is superimposed by a quadruplet of extended bluish images approximately at a distance of $1''$ from the galaxy center (see Figure \ref{fig:lens_just_imgpos}). The lensed object might be a star-forming blob of a background galaxy. J1331 stands out of the SWELLS sample because of its large counter-rotating core (see Figure \ref{fig:kinematics}), which might be an indication that J1331 underwent a merger in its recent past. J1331 is therefore of special interest and a convenient candidate to investigate observationally if and how a merger might have modified the DM and stellar distribution of a massive spiral galaxy. This requires in particular a precise disentanglement of stellar and DM components in the galaxy's inner regions. J1331 has already been the subject of several studies: \citet{SWELLSI} confirmed that J1331 is a strong gravitational lens, measured its apparent brightness, and estimated the stellar masses of disk and bulge. The lensing properties of J1331 were first analysed by \citet{SWELLSIII}. \citet{SWELLSV} measured the gas and stellar kinematics along the major axis, and deduced J1331's mass profile from the gas rotation curve at large radii and total mass inside the Einstein radius from gravitational lensing, focusing mostly on the outer regions of J1331. The goal of this work is now the in-depth analysis of the matter distribution in J1331's inner regions. This will complement the previous studies of J1331 and is an important step in understanding J1331's merger-modified mass structure. We use stellar dynamical modelling in addition to lensing constraints, similar to a study of the Einstein Cross by \citet{GlennEC}. We attempt to disentangle the stellar and DM components and test if employed axisymmetric Jeans models work also in the presence of a counter-rotating core. This paper is organized as follows: Section \ref{sec:data} summarizes the data, Section \ref{sec:Modelling} gives an overview of the modelling techniques used in this work, and Section \ref{sec:Results} presents our results on the surface photometry of J1331 using Multi-Gaussian expansions (Section \ref{sec:MGE_results}), constraints from lensing (Section \ref{sec:results_lensing}) and Jeans modelling based on the surface brightness only (Section \ref{sec:results_JAM_SB}) and including an NFW DM halo (Section \ref{sec:results_JAM_NFW}). Finally, Section \ref{sec:Discussion} uses these results to discuss J1331's possible merger history, stellar mass-to-light ratio, central kinematics, and starting points for future work. \begin{figure*} \centering \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=.9\linewidth]{first_glimpse_450.ps} \caption{J1331 in the F450W filter.} \label{fig:F450W} \end{subfigure}% \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=.9\linewidth]{first_glimpse_814.ps} \caption{J1331 in the F814W filter.} \label{fig:F814W} \end{subfigure} \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=.9\linewidth]{lens_imgpos.ps} \caption{Lensing images around the galaxy center.} \label{fig:lens_just_imgpos} \end{subfigure}% \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=.9\linewidth]{stellar_kinematics_data.ps} \caption{Stellar kinematics by \citet{SWELLSV}.} \label{fig:kinematics} \end{subfigure} \caption{Hubble Space Telescope (HST) images and stellar kinematics of the galaxy SDSS J1331+3628 (J1331), which has a large counter-rotating core and whose bulge acts as a strong lens for a bluish background source. \emph{Panel (a) and (b):} HST/WFPC2/WFC3 images of J1331 by \citet{SWELLSI} in two filters, F450W in panel (a) and F814W in panel (b). The black solid line in panel (b) shows the orientation of the major axis. Its length is $10''$ and it marks approximately the region within which we carry out the dynamical modelling. \emph{Panel (c):} Lensing images in the central region of J1331. An IRAF \emph{ellipse} model was fitted to and then subtracted from the galaxy's F450W surface brightness in panel (a). The (smoothed) residuals within the white square in panel (a) are shown in panel (c). The four bright blobs (A, B, C, and D), which are visible in the residuals, are arranged in a typical strong lensing configuration around the center of the galaxy (G). (The configuration of the two additional blobs which lie approximately on a line with A, B, and G does not suggest that these blobs are a lensing doublet. They might rather be star-forming regions of a background galaxy.) \emph{Panel (d):} Stellar kinematics along the galaxy's major axis as measured by \citet{SWELLSV}. Shown are line-of-sight rotation velocity $v_\text{rot}$ (top), line-of-sight velocity dispersion $\sigma$ (middle) and the root mean-square (rms) velocity $v_\text{rms} = \sqrt{v_\text{rot}^2 + \sigma^2}$ (bottom). The dashed line indicates the galaxy's effective half-light radius (in the F814W filter), $R_\text{eff} = 2.6'' \hat{=} 5.2~\text{kpc}$. The $v_\text{rot}$ curve reveals that J1331 has a counter-rotating core within $R_\text{eff}$.} \label{fig:specialJ1331} \end{figure*} | \label{sec:Discussion} We have presented different dynamical models for the central region of J1331. Some of them capture the observed kinematics, but none of them work at both small and large radii. In the following we try to resolve some of the ambiguities by discussing possible reasons, by comparing our results to previous work and by hazarding some guesses on the true nature of J1331's matter distribution, which should be easily testable by future observations. \begin{table*} \centering \caption{Total $I$-band luminosity, stellar mass, and mass-to-light ratio, calculated from the $I$-band AB magnitudes and stellar masses found for J1331's bulge and disk by \citet{SWELLSI} (their table 2) for comparison with this work. The transformation from AB magnitudes to the Johnson-Cousins $I$-band used the relation $I[\text{mag}] = I[\text{ABmag}] - 0.309$ from \citet{FG1994} (their table 2). For the conversion from apparent magnitude to total luminosity the redshift $z=0.113$ \citet{SWELLSIII} was turned into a luminosity distance using the WMAP5 cosmology by \citet{WMAP5cosm}. } \begin{tabular}{cccccc} \hline\hline & & \multicolumn{2}{c}{Chabrier IMF} & \multicolumn{2}{c}{Salpeter IMF}\\ & $L$ [$10^{10}L_{\odot}$] & $M_*$ [$10^{10}\text{M}_\odot$] & $\Upsilon_\text{I,*}^\text{chab}$ & $M_*$ [$10^{10}\text{M}_\odot$] & $\Upsilon_\text{I,*}^\text{sal}$ \\\hline bulge & $3.10 \pm 0.15 $ & $7.8 \pm 1.8$ & $2.5 \pm 0.6$ & $14.5 \pm 3.7 $ & $4.7 \pm 1.2$ \\ disk & $2.35 \pm 0.11 $ & $2.9 \pm 0.7$ & $1.2 \pm 0.3$ & $5.2 \pm 1.1$ & $2.2 \pm 0.5$ \\ total & $5.45 \pm 0.19$ & $10.6 \pm 1.9$& & $19.7 \pm 3.9$&\\\hline \end{tabular} \label{tab:previousresults} \end{table*} \subsection{On J1331's possible merger history} \label{sec:discussion_merger} J1331 has a large counter-rotating stellar core within $\sim 2''$. This suggests a process in J1331's past in which two components with angular momenta oriented in opposite directions were involved. Accretion of gas on retrograde orbits and subsequent star formation could lead to a younger and counter-rotating stellar population. However, to form enough stars such that the net rotation of the large and massive core is retrograde, a very large amount of gas would have had to be accreted by J1331---which is not very likely. Galaxy mergers are another possible scenario. Major mergers can form kinematically decoupled cores (KDCs) (e.g., \citealt{2011MNRAS.414.2923K,2015ApJ...802L...3T}), if they include large amounts of gas \citep{2010ApJ...723..818H}. During a minor merger, the dense nucleus of a satellite galaxy on a retrograde orbit could survive the dissipationless accretion and spiral to the galaxy's core due to tidal friction (e.g., \citealt{1984ApJ...287..577K,1988ApJ...327L..55F}). Usually ellipticals and the bulges of massive spirals appear reddest in their center and get increasingly bluer with larger radii. Mergers can reverse this behaviour by inducing the creation of young stellar populations in the remnant's center. Major mergers can trigger star formation bursts (e.g., \citealt{2008gady.book.....B}, \S 8.5.5). After a minor merger the satellite's stellar population now residing in the remnant's core is in general younger than the massive progenitor's bulge \citep{1996AJ....112..839C,2010MNRAS.404.1775T}. The different stellar populations in a merger remnant can be associated with different $\Upsilon_*$ and in rare cases they even show up as a reverse colour gradient within the bulge in photometry \citep{1990ApJ...361..381B, 1997ApJ...481..710C}. Even though investigation of the photometry of J1331 did not reveal a distinct blue core in J1331, we cannot fully exclude the possibility that J1331 has such a $\Upsilon_*$ gradient (see discussion in Sections \ref{sec:results_JAM_SB_MfL} and \ref{sec:results_JAM_SB_gradient}). Spatially resolved stellar population analysis based on integral-field spectroscopy of J1331's bulge could provide further information on the true $\Upsilon_*(R')$. Another way how galaxy encounters can modify the structure of galaxies is the excitation of warps \citep{1991wdir.book.....C,2013pss5.book..923S}. Warps lead to a twist in the projected kinematic major axis with radius, which is then also misaligned with the photometric major axis (\citealt{1998gaas.book.....B}, \S 8.2.4). From kinematics along the photometric major axis only it can however not be determined if such a twist or misalignment is present in J1331, but it should be immediately visible in a 2D kinematic map. \subsection{On J1331's central stellar mass-to-light ratio} \label{sec:MLdiscussion} Some of the ambiguities in recovering J1331's matter distribution could be resolved by learning more about stellar populations with different IMFs in J1331. In particular, a sophisticated guess for the stellar mass-to-light ratio in the bulge could be compared to our very reliable measurement of the total mass-to-light ratio inside the Einstein radius $\Upsilon_\text{I,tot}^\text{ein} = 5.56 \Upsilon_{I,\odot}$. This would then either support or contradict the presence of a significant amount of DM in the bulge. Traditional choices for the IMF are the bottom-heavy IMF by \citet{Salpeter1955}, $\xi(m) \propto m^{-x}$ with $x=2.35$, where $\xi(m) \diff m$ is the number of stars with mass $m$ in $[m,m+\diff m]$, and the IMFs by \citet{2002Sci...295...82K} and \citet{Chabrier2003}, which are in agreement with each other and predict less low-mass stars. In the following we discuss why we think---based on our results and previous analyses---that J1331's bulge has an IMF slightly less bottom-heavy than the Salpeter-like IMF. \emph{(i) Indications for a slightly less bottom-heavy Salpeter-like IMF in J1331's bulge:} \citet{Ferreras} found a relation between the central stellar velocity dispersion $\sigma_0$ in early-type galaxies and the IMF slope $x$, where a higher $\sigma_0$ suggests a more bottom-heavy IMF. For a unimodal (Salpeter-like) IMF and $\sigma_0 \simeq 200~\text{km s}^{-1}$ in J1331 (see Figure \ref{fig:kinematics}), this relation predicts $x \approx 2.33$, which is close to the standard Salpeter slope, also supported by \citet{2014MNRAS.438.1483S}. When assuming a bi-modal (Kroupa-equivalent-like) IMF, \citet{Ferreras} predict $x \approx 2.85$ for J1331's central velocity dispersion. This is more bottom-heavy than the standard \citet{2002Sci...295...82K} IMF. Overall, the central velocity dispersion suggests a rather bottom-heavy IMF in J1331's bulge and therefore large stellar mass-to-light ratio. \citet{SWELLSI} estimated J1331's stellar bulge mass given a Salpeter IMF and measured the $I$-band AB magnitude of the bulge. Transformed to a stellar $I$-band mass-to-light ratio, their results would correspond to $\Upsilon_\text{I,*}^\text{sal} = 4.7 \pm 1.2$ (see Table \ref{tab:previousresults}). This is not too far from $\Upsilon_\text{I,*} = 4.2 \pm 0.2$ (see Table \ref{tab:modelB4_bestfit}), which we found when including an NFW halo in the JAM modelling. \emph{(ii) Indications for and arguments against a Chabrier-like IMF in J1331's bulge:} When \citet{SWELLSI} assumed a Chabrier IMF, their result translates to $\Upsilon_\text{I,*}^\text{chab} = 2.5 \pm 0.6$ (see Table \ref{tab:previousresults}). In Section \ref{sec:results_JAM_SB_gradient}, we created a dynamical model from only the surface brightness distribution and an increasing mass-to-light ratio profile without additional DM halo and without velocity anisotropy. We found that such a model would be perfectly consistent with the Einstein mass, predict a total $\Upsilon_\text{I,tot}(R'\sim0) = 2.53$---being consistent with the Chabrier IMF estimate by \citet{SWELLSI}---and rise quickly to $\Upsilon_\text{I,tot}(R'\gtrsim R_\text{ein}) \gtrsim 6$. This rise in $\Upsilon_\text{I,*}(R')$ could be either due to a cuspy DM halo (see Section \ref{sec:results_JAM_NFW}) or a very strong gradient in $\Upsilon_\text{I,*}$ (see Section \ref{sec:discussion_merger}). However, we rule out that a DM cusp is the sole reason because a cuspy and therefore overall massive DM halo does not match the kinematics in J1331's outer regions. We also rule out that a very strong $\Upsilon_\text{I,*}$ gradient is the only reason, because---as mentioned in Section \ref{sec:discussion_merger}---photometry did not reveal the clear existence of a blue population in the very center of J1331's bulge. Also, our modelling attempts allowing for velocity anisotropy (Sections \ref{sec:results_JAM_SB_MfL} and \ref{sec:results_JAM_NFW}) suggest that we do need some moderate $\beta_z<0$ to explain the central $v_\text{rms}$ dip. And lastly---as laid out in the previous paragraph---J1331's central velocity dispersion suggests a more bottom-heavy IMF. Overall it is therefore not very likely that the central regions of J1331 have such a low $\Upsilon_\text{I,*}^\text{chab} \sim 2.5$. \emph{(iii) Arguments against an IMF more bottom-heavy than the Salpeter IMF in J1331's bulge:} We also compare our results from Section \ref{sec:results_JAM_NFW} with the study by \citet{SWELLSV}. They found that the bulge of J1331 has an IMF \emph{more} bottom-heavy than the Salpeter IMF. Our fitting attempt---using more data within $\sim 3.5''$ than \citet{SWELLSV}---in Section \ref{sec:results_JAM_NFW} gave $\Upsilon_\text{I,*} = 4.2 \pm 0.2$ as best fit (see Table \ref{tab:modelB4_bestfit}), which indicates a \emph{less} bottom-heavy IMF than the Salpeter IMF. In Section \ref{sec:discussion_kinematics}, we will argue why we do not think that the \cite{SWELLSV} model is a good model for the central regions of J1331. \subsection{On J1331's kinematics} \label{sec:discussion_kinematics} Overall, the kinematics of the merger remnant J1331 are peculiar. In particular, there are two features in the $v_\text{rms}$ curve that are hard to explain with standard modelling techniques. The first feature, the deep central $v_\text{rms}$ dip, was studied in detail in this work. The second feature, the drop and rise in $v_\text{rms}$ around $R'\sim6''$, is even harder to explain; below we will speculate about possible reasons that could cause such a signature. \emph{(i) The central $v_\text{rms}$ dip within $R'\lesssim1''$:} First, we will compare our modelling results with the modelling results by \citet{SWELLSV} within $R_\text{eff}$. \citet{SWELLSV} fitted a stellar mass model and NFW halo to (i) the Einstein mass and (ii) gas kinematics at larger radii $\gtrsim8''$. Figure \ref{fig:vcirc_comparison} compares the circular velocity curve found by \citet{SWELLSV} with a mass-follows-light model scaled to fit our Einstein mass (by multiplying the light distribution in Table \ref{tab:MGEF814W} by $\Upsilon_\text{I,tot}^\text{ein} = 5.56$, analogous to Figure \ref{fig:lenscomparelight}). Within $0''.5 < R < 5''$ they agree with each other. The models in this work used more than just the Einstein mass to constrain the matter distribution at small radii: The lens mass model constrained also the shape of the mass distribution within the lensing image configuration at $R_\text{ein} \sim 1''$. The dynamical models used stellar kinematics inside $R' \simeq 3.5''$. We compare the lens mass model's $v_\text{circ}$ (for $\alpha=1.0\pm 0.1$) with the NFW JAM model (Table \ref{tab:modelB4_bestfit}) in Figure \ref{fig:vcirc_comparison} as well. Within and around $R_\text{ein}$ they are consistent with each other, even though they were independently derived. They do not agree with the mass-follows-light-like result by \citet{SWELLSV} and in Section \ref{sec:results_JAM_SB_MfL} we showed that ``mass-follows-light'' is not a good model for J1331. \begin{figure} \centering \includegraphics[width=0.9\linewidth]{B4_jam_profiles_errors_short_vcirc.ps} \caption{Comparison of the circular velocity curve of J1331's inner regions for different models: (i) JAM model with NFW DM halo from Section \ref{sec:results_JAM_NFW_results} and Figure \ref{fig:modelB4_models} (green). (ii) Lens model from Section \ref{sec:results_lensing_bestfit} and Figure \ref{fig:JAM_modelL} with $\alpha = 1.1$ (red dashed line), $\alpha = 1$ (red solid line) and $\alpha=0.9$ (red dash-dotted line). (iii) Mass-follows-light model, which uses the F814W surface brightness in Table \ref{tab:MGEF814W} and the mass-to-light ratio in the Einstein radius, $\Upsilon^\text{ein}_\text{I,tot} = 5.56$, to generate a mass distribution, as in Figure \ref{fig:lenscomparelight} (orange line). (iv) Model from gas kinematics and Einstein mass found by \citet{SWELLSV} (their Figure 2, best model with 68\% confidence region) (blue lines).} \label{fig:vcirc_comparison} \end{figure} Because we used more data constraints in the center than \citet{SWELLSV}, we think that our model for J1331's bulge is more reliable. In conclusion, we suspect that the most likely model for J1331's central bulge is a moderate DM contribution in the center (Section \ref{sec:results_JAM_NFW_results}) with some tangential anisotropy (Sections \ref{sec:results_JAM_SB_MfL} and \ref{sec:results_JAM_NFW}, which would be also consistent with the counter-rotation in the bulge) and an overall $\Upsilon_\text{*,I}$ in the bulge which is slightly lower than that of a Salpeter-like IMF (Section \ref{sec:MLdiscussion}). Different stellar populations inside the bulge due to the merger (Section \ref{sec:discussion_merger}) with different $\Upsilon_{*}$ could add to an overall rising $\Upsilon_\text{tot}(R')$ profile (Sections \ref{sec:results_lensing_compare} and \ref{sec:results_JAM_SB_gradient}). \emph{(ii) The drop and rise of the $v_\text{rms}$ curve around $R'\sim 6''$:} The drop in $v_\text{rms}$ around $R'\sim4''$ (Figure \ref{fig:kinematics}) is most likely due to the transition from red bulge to blue disk (compare bulge size in Figures \ref{fig:F450W} and \ref{fig:F814W}). A mix of different stellar populations in the disk could make the modelling difficult: The smooth light distribution was derived from the F814W filter and is therefore dominated by older stars, while the measured light-weighted stellar kinematics in the disk are dominated by luminous young stars with their lower velocity dispersion. As the merger could have caused a warp in J1331's disk, it is possible that bulge and disk have different inclination angles and a kinematic twist. The latter could have lead to a misalignment of the long-slit and the galaxy's kinematic major axis at larger radii, therefore to measurements of lower $v_\text{rot}$ and consequently to a stronger underestimation of the true $v_\text{circ}$, which would add to the drop in $v_\text{rms}$. Around $R'\sim7''$ the rotation curve and dispersion show some wiggles which lead to a spontaneous rise of the $v_\text{rms}$. As the spiral arms with their non-circular motions and patchy star-forming regions cross the major axis around this radius, we suspect they cause this disturbance of the axisymmetric kinematics. \emph{(iii) The profile of the DM halo at $R'\gtrsim 5''$:} The DM halo should start to dominate the kinematics at larger radii. \cite{SWELLSV}, who fitted an NFW halo to the gas kinematics in the outer regions, found lower halo masses ($v_\text{circ,halo}(5'') \sim 120~\text{km s}^{-1}$ according to their Figure 2) than we did ($v_\text{circ,halo}(5'') \sim 200~\text{km s}^{-1}$, Figure \ref{fig:vcirc_comparison}). As we did not fit the outer regions and only used a prior for $v_\text{200}$, their result in this regime is more reliable. Given our findings that an NFW halo does not fit the kinematics at both small and large radii, we suspect that the true halo has a profile that deviates strongly from an NFW halo, possibly as a result of the merger. All of these speculations should be easily testable with 2D kinematics. \subsection{Future work} J1331's merging history and peculiar kinematics make it a valuable and exiting target to study merger remnants and a challenge for dynamical modelling techniques. We found however that the existing data alone---photometry and major axis kinematics---is not sufficient to resolve all the ambiguities we encountered in our modelling. The main future work would be therefore getting high-resolution integral-field spectroscopy for J1331. High spatial resolution would be required to clearly identify J1331's presumably complex kinematic structure. High spectral resolution would be important to be able to reliably measure the low velocity dispersion in the outer regions of J1331. Specifically 2D kinematics should help to answer the following questions: Is the drop in $v_\text{rms}$ around $R' \sim 3-6~\text{kpc}$ real? Did the long slit spectrograph maybe miss the major axis of the disk? And most importantly: Are the kinematics asymmetric? Is it possible that there even exists a kinematic twist due to the merger in J1331's past? In the latter two cases we would need to apply non-axisymmetric Jeans models to J1331 as the assumption of axisymmetry of this work would not be valid anymore. Furthermore, learning more about different stellar populations in J1331 would lead to valuable constraints for the modelling. While a quick investigation of the photometric colour profile did not reveal obvious colour gradients in J1331's bulge, there could be still stellar $\Upsilon_{I,*}$ variations due to age or metallicity differences. Existing major axis spectroscopy and/or future IFU data could be employed (i) to investigate absorption line indices to confirm (or contradict) the existence of $\Upsilon_{I,*}$ gradients and (ii) to perform stellar population analyses to constrain $\Upsilon_{I,*}$ reliably and independently of kinematics. Future modelling approaches should fit dynamics (stellar and gas kinematics) simultaneously with the gravitational lensing (image positions, shape and even flux ratios) in a similar fashion to \citet{SWELLSIV}. To also model the extent, shape and flux of the lensing images, the method by \citet{2004ApJ...611..739T,2003ApJ...590..673W} could be employed, which models the surface brightness distribution of the images and source on a pixelated grid. For this to work, a good model for the galactic extinction would be needed---but 2D spectroscopy could also help with this. All of the above would lead to a much better understanding of J1331's structure and mass distribution and therefore answer questions on how mergers might modify spiral galaxies. \subsection{Summary} We constrained the matter distribution of the massive spiral galaxy J1331, which has a large counter-rotating core, probably due to a merger in its past, and acts as a strong gravitational lens for a background source. We used two independent methods to model J1331: gravitational lensing and dynamical Jeans modelling. We focused on the bulge region of J1331 to complement previous studies of J1331 by \citet{SWELLSIII} and \citet{SWELLSV}. The mass constraints from lensing and dynamics agree very well with each other within $R_\text{eff}$. In our lensing approach we fitted a scale-free galaxy model to the lensing image position. This constrained the Einstein radius to within 2\% [$R_\text{ein}=(0.91\pm0.02)'' \hat{=}(1.83\pm0.04)~\text{kpc}$], and the Einstein mass to within 4\% ($M_\text{ein} = (7.8\pm0.3) \times 10^{10} \text{M}_\odot$), consistent with results by \citet{SWELLSIII}. A MGE fit to J1331's surface brightness in the F814W filter in HST imaging by \citet{SWELLSI} helped us determining the effective radius, $R_\text{eff} \simeq 2.6'' \hat{=} 5.2~\text{kpc}$, and total $I$-band luminosity of the galaxy, $L_\text{I,tot} \simeq 5.6 \times 10^{10} L_\odot$. Axisymmetric JAM modelling allowed a comparison between model predictions for the second velocity moment given a tracer and mass distribution and the observed stellar kinematics from major axis long slit spectroscopy by \citet{SWELLSV}. The independent JAM model of the lens mass model was consistent with observed kinematics within $R_\text{eff}$. We also fitted mass models with and without NFW halo to the stellar kinematics within $R'=3.5~\text{kpc}$. From this we deduced that a mass-follows-light model (even with velocity anisotropy) is not a good model for J1331's inner regions. This ruled out the previous findings of \citet{SWELLSV} for J1331's bulge. We discussed that, to describe the observed stellar kinematics, we most likely require a moderate contribution of a DM halo already in the bulge, moderate tangential velocity anisotropy, $\beta_z \simeq -0.4\pm0.1$, and possibly even a varying stellar mass-to-light ratio, which could be the result of the previous merger event. We argue that we expect the total stellar mass-to-light ratio within the bulge to be $\Upsilon_\text{I,*}\simeq 4.2\pm0.2$, which is slightly less bottom-heavy than a Salpeter IMF ($\Upsilon_\text{I,*}^\text{sal}\sim 4.7$). We also showed that it is possible to construct a model which includes the counter-rotating core and fits the rotation curve at large radii. While both our independent mass models are consistent with each other within $\sim R_\text{eff}$, they do not describe the data at large radii very well. We speculate how a merger could have modified the kinematic structure and/or mass distribution of J1331. To resolve the ambiguities in J1331's mass distribution two-dimensional kinematic maps of J1331 from integral-field unit spectroscopy are needed. | 16 | 9 | 1609.05477 |
1609 | 1609.02311_arXiv.txt | We have investigated the effect of group environment on residual star formation in galaxies, using \textsl{\textsc{Galex}} NUV galaxy photometry with the SDSS group catalogue of \citet[][]{Yang:2007aa}. We compared the \nuvr\ colours of grouped and non-grouped galaxies, and find a significant increase in the fraction of red sequence galaxies with blue \nuvr\ colours outside of groups. When comparing galaxies in mass matched samples of satellite (non-central), and non-grouped galaxies, we found a $>4\sigma$ difference in the distribution of \nuvr\ colours, and an \nuvr\ blue fraction $>3\sigma$ higher outside groups. A comparison of satellite and non-grouped samples has found the NUV fraction is a factor of $\sim2$ lower for satellite galaxies between $10^{10.5}M_{\astrosun}$ and $10^{10.7}M_{\astrosun}$, showing that higher mass galaxies are more able to form stars when not influenced by a group potential. There was a higher \nuvr\ blue fraction of galaxies with lower S\'ersic indices ($n < 3$) outside of groups, not seen in the satellite sample. We have used stellar population models of \citet[][]{Bruzual:2003aa} with multiple burst, or exponentially declining star formation histories to find that many of the \nuvr\ blue non-grouped galaxies can be explained by a slow ($\sim2$ Gyr) decay of star formation, compared to the satellite galaxies. We suggest that taken together, the difference in \nuvr\ colours between samples can be explained by a population of secularly evolving, non-grouped galaxies, where star formation declines slowly. This slow channel is less prevalent in group environments where more rapid quenching can occur. | Large galaxy surveys have revealed the colour bimodality of galaxy populations, with the evolution of stellar masses in each population suggesting that these galaxies transition between a blue and red population. Colour bimodality is a generalisation of the result of \citet[][]{Visvanathan:1977aa} who found elliptical galaxies in a tightly constrained colour--magnitude red sequence, with only small metallicity and age differences \citep[][]{Kodama:1998aa}. While initially found in clusters \citep[e.g.][and references therein]{Bower:1992aa}, this red sequence has been seen in populations of galaxies in large surveys \citep[e.g.][]{Blanton:2003aa, Baldry:2004aa}. Conversely, a star forming population is seen in the so called `blue cloud' -- a lower mass, broadly blue area of the colour--magnitude diagram, where young stars dominate the flux of a galaxy. It is common to use the optical colour of a galaxy to discriminate between galaxies with different mean stellar ages, and likely different star formation histories \citep[e.g.][]{Strateva:2001aa, Hogg:2003aa, Baldry:2004aa, Balogh:2004aa, Stott:2007aa, van-den-Bosch:2008aa}. While the optical bands give an indication of galaxy mean stellar age, alternative wavelengths can improve measurements of the current and recent star formation of a galaxy. One of the most direct measures of star formation comes from using ultraviolet light (UV), which is known to directly trace even low levels of star formation \citep[$<1M_{\astrosun}/\rm{year}$,][]{Salim:2007aa} using stars of a lifetime of $10^{8.5}$ years \citep[][]{Martin:2005aa}. Even in the absence of evidence of star formation in optical photometry, the near UV (NUV) band can detect young stellar populations that have formed within $\sim1$ Gyr \citep[e.g.][]{Ferreras:2000aa, Yi:2005aa}. This sensitivity to low levels of star formation causes the NUV-optical colour--magnitude diagram to lose the clear bimodal structure seen in optical colour--magnitude diagrams \citep[][]{Wyder:2007aa}. Instead a third population, the green valley, resides between the larger red sequence and blue cloud, suggesting differences in star formation levels unable to be distinguished in optical photometry \citep[][]{Wyder:2007aa, Salim:2014aa}. Galaxies in the green valley have shown intermediate specific star formation rates (log(sSFR)$\sim-11$), red optical colours, and intermediate masses ($M_{\astrosun} \sim 10^{10.8}$), indicating that they are in the process of moving between the blue cloud and the red sequence \citep[][]{Salim:2007aa, Schiminovich:2007aa, Salim:2014aa}. It is this breaking of the optical colour bimodality that shows several different stages of evolution may be present within a single broad colour population. One example of the several stages of evolution within a single broad population comes from \citet[][]{Schawinski:2014aa}, who found that splitting the green valley by morphological type will separate different transition paths. The green valley can be separated into two evolutionary paths, with elliptical galaxies predominantly found at the low mass end, and spirals at the high mass end. This indicates that the green valley contains two populations: one dominated by ellipticals, having ceased star formation quickly (a rapid quench, with a characteristic time of $<250$ Myr) and joining the red sequence at low mass; the other containing slowly evolving discs, which are undergoing a secular quenching of star formation (i.e. with times much greater than a dynamical timescale, which we define as $>1$Gyr), and joining the red sequence at higher masses \citep[][]{Kormendy:2004aa}. The rapid quenching may have a similar evolution to early-type galaxies with signs of recent star formation \citep[][]{Yi:2005aa}. Such galaxies generally have elliptical morphologies and red optical colours, but have an excess of blue \nuvr\ colours, beyond that of old stellar populations \citep[][]{Kaviraj:2007aa, Schawinski:2007aa, Rawle:2008aa}. This blue NUV colour is thought to indicate the presence of a burst of recent star formation, most likely originating after a merger \citep[][]{Kaviraj:2007aa, Kaviraj:2011aa}, however there is little preference for location both within clusters, and in local density \citep[][]{Schawinski:2007aa, Yi:2011aa}. The origin of the young galaxy population is likely a merger induced burst of extra star formation, preceding a completely passive red sequence galaxy. The second group of green valley galaxies are populations of spiral galaxies that are undergoing a slow decline in star formation \citep[][]{Schawinski:2014aa}. This population of slowly quenching spirals shows similarities to optically red, passive spiral galaxies \citep[e.g.][]{Wolf:2009aa, Bonne:2015aa, Fraser-McKelvie:2016aa}. These galaxies have spiral morphologies, but optical colours which suggest little widespread star formation \citep[][]{Masters:2010aa}. They also have lower star formation rates \citep[][]{Tojeiro:2013aa}, and appear in higher density regions than the blue, star forming counterparts \citep[][]{Skibba:2009aa, Bamford:2009aa}. They are found to still have residual NUV \citep[][]{Crossett:2014aa} and FUV fluxes \citep[][]{Moran:2006aa}, with star formation histories suggesting they may be the progenitors of large cluster S0 and elliptical galaxies \citep[][]{Mahajan:2009aa}. These red spiral galaxies likely form through interactions with group and cluster potentials, rather than with other galaxies, by truncating star formation without disturbing the typically fragile disc structure \citep[][]{Wolf:2009aa}. These results describe a transition from blue/star forming to red/passive that can occur in two broad ways; one dominated by fast morphological transformations and a quick cessation of star formation, and a slower process of mass growth and star formation decline, which may involve a group/cluster potential. The interaction between galaxy and environment therefore plays a key role in the evolution of its star formation. It is known that galaxies in denser regions have lower specific star formation rates \citep[e.g.][]{Lewis:2002aa, Gomez:2003aa}, redder colours \citep[][]{von-der-Linden:2010aa}, and generally more elliptical shapes \citep[][]{Dressler:1980aa} than those in less dense environments. These trends with density are more evident at small separations \citep[$<1$ Mpc,][]{Kauffmann:2004aa, Wilman:2010aa} typical of galaxy group scales. Galaxies in these more dense group environments also have their properties linked to those of their host central \citep[e.g.][]{Weinmann:2006aa, Prescott:2011aa}. The mechanisms in which groups can influence infalling members include: stripping the cold or warm gas supply in galaxies, \citep[][]{Gunn:1972aa, Quilis:2000aa, Balogh:2000aa}, tidal interactions and harassment between neighbours \citep[][]{Farouki:1980aa, Moore:1996aa}, and galaxy-galaxy mergers. In this work we examine the processes occurring within these transition populations. To do so we look at optically red galaxies with blue \nuvr\ colours, such that the galaxy has a large old stellar population (from red optical colours), but an additional small population of young stars due to the presence of NUV \citep[][]{Yi:2005aa, Schawinski:2007aa}. These colour selections best isolate galaxies with low levels of recent star formation, with $\sim1\%$ of mass in young stars \citep[a residual amount of star formation, $<1M_{\astrosun}/\rm{year}$, ][]{Kaviraj:2007aa, Salim:2007aa}. If this \nuvr\ blue population of galaxies is indeed a result of the effects of group environment or neighbours, then looking at group properties would help disentangle the different pathways for these galaxies with residual star formation. The different group properties (central vs satellite, grouped vs ungrouped) can discriminate if falling into a larger halo does cause the excess of NUV flux. We use the group catalogue of \citet[][]{Yang:2007aa} to look at the NUV in the process of a galaxy transitioning. In an idealised scenario, the quenching of a disc dominated system will require a long time-scale where the morphology does not change, whereas a burst of star formation is more likely merger driven. While these simplified scenarios do not account for extra gas infall onto ellipticals, or for any subtle effects of harassment/ram pressure, it can still be used as a basis for this investigation. In Section \ref{Section:Sample} we describe the Group catalogue by \citet[][]{Yang:2007aa}, and the \textsl{\textsc{Galex}} data employed for this study, as well as the use (and validity) of the selections made. In Section \ref{Section:Results} we present some primary results from this study, with \nuvr\ blue fractions used to compare the residual star formation within different populations of galaxies. In Section \ref{Section:Discussion} we discuss the roles of fast and slow quenching in different environmental samples as a way of explaining the results, before summarising in Section \ref{Section:Conclusion}. Throughout this work, we us AB magnitudes, and assume a flat cosmology with values of $H_0 = 71 {\rm km s^{-1} Mpc^{-1}}$ and $\Omega_M = 0.23.$ | \label{Section:Discussion} In the previous sections, we have investigated the residual star formation of red sequence galaxies within groups from SDSS, and whether differences in group and non-group populations infer different mechanisms that cause the presence of star formation at the $\sim1\%$ by mass level. We have used \nuvr\ blue fractions to quantify the amount of residual star formation in our sample, finding the fraction to be $\sim 12\%$ of our total red sequence sample. We find there is a significant difference in the residual star formation between group and non-group galaxies, with the latter containing a fraction of galaxies with \nuvr\ residual star formation of $\sim 16 \%$, compared to satellite galaxies with only $\sim 9\%$. Previous studies have found little density change for \nuvr\ fraction \citep[e.g. ][]{Schawinski:2007aa, Yi:2011aa}, but do not specifically probe group halo environment, preferring a local density measure instead. The results do broadly match the idea of environment quenching of star formation \citep[e.g. ][]{Peng:2010aa}, with colour fractions inside and outside groups similar to that of \citet[][]{van-den-Bosch:2008aa}. A higher blue fraction of comparatively low ($n<2.5$) S\'ersic index red sequence galaxies is also seen outside of groups, compared to satellites. These galaxies may form part of the class of red spirals seen elsewhere \citep[e.g. ][]{Masters:2010aa, Bonne:2015aa} with the red optical colours caused by the large underlying old stellar population \citep[][]{Cortese:2012aa}. Red spirals are known to have higher star formation rates than similar mass red ellipticals \citep[][]{Tojeiro:2013aa} so are more likely to contain residual star formation, and thus are a potential candidate for our low S\`ersic population. The scenario presented matches that of \citet[][]{Schawinski:2014aa}, whereby disc-like galaxies move onto the red sequence in a different pathway to elliptical galaxies. The smaller residual star formation fraction for both disc galaxies and high mass galaxies inside groups, compared to those outside of groups indicates quenching is likely to have occurred early on in the mass evolution due to environment. The non-grouped galaxies will move onto the red sequence later in their mass evolution, and retain lower S\'ersic indices at higher mass. We use \ur\ and \nuvr\ colour-colour diagrams with \citet[][]{Bruzual:2003aa} stellar population models, to test different formation scenarios of the blue \nuvr\ colour. These tracks are analogous to those of \citet[][]{Schawinski:2014aa} and \citet[][]{Smethurst:2015aa}, who found longer decay timescales to be more common in morphologically selected spiral galaxies. Our study finds a similar result, that galaxies undergoing these slower quenches are preferentially non-grouped, and have low S\'ersic indices. Our satellite sample has an evolution similar to that of \citet[][]{Wetzel:2013aa}, where galaxies once falling into groups have a short ($<0.8$ Gyr) quench time, however differs from that of \citet[][]{Skibba:2009ab}, whose models show longer quenches are preferred in groups, taking $>2$ Gyr. The model design however, dictates that these galaxies move onto the red sequence at high mass. This differs from our red sequence satellites, which show a lower fraction of residual star formers at high mass. These results indicate that the excess of residual star formation outside group environments must be due to a long, slow quench in star formation. In contrast, the same stellar population tracks do not represent the majority of the satellite galaxy population. These galaxies have instead fully quenched, which has stopped any residual star formation from occurring. This shows that star formation on residual levels can be due to environmental effects, such that residual star formation in galaxies within groups will be quenched on short timescales, compared to those outside. \citet{Rasmussen:2012aa} hypothesize that star formation quenching in galaxies from group accretion would be larger than the typical crossing time of a group ($1.1-1.6$ Gyr), suggesting a longer timescale quenching than our results. This finding agrees with simulations of ram pressure in group environments from \citet{Steinhauser:2016aa} showing the migration of galaxies on the \ur\ \nuvu\ colour-colour diagram from blue to red would take $> 1$ Gyr due to ram pressure, consistent with other ram pressure models \citep[e.g. ][]{Tonnesen:2007aa}. \citet{Rasmussen:2012aa} suggests that tidal interactions between galaxies could speed up this quenching process, and would present a short lived enhancement of star formation. Our satellite sample is therefore likely quenching due to a combination of these processes, with ram pressure alone insufficient. However, our red sequence sample eliminates galaxies many star formation enhancement signatures to test this theory further. Our results demonstrate that the blue \nuvr\ colours of our group galaxies are best explained solely by the rapid quenching of galaxies. Mechanisms such as the `strangulation' process, where the group/cluster medium starves a galaxy of gas and star formation on scales of several Gyr \citep[][]{Larson:1980aa, Balogh:2000aa, Peng:2015aa}, are therefore not the dominant mode of residual star formation quenching of our satellite sample. Instead, processes such as ram pressure stripping \citep[][]{Gunn:1972aa} that act on timescales of $<500$ Myr \citep[][]{Bahe:2015aa}, appear more likely to cause the decline in star formation. The spread of S\'ersic indices suggest that morphology may also be altered. S\'ersic profiles of post-merger galaxies are generally higher \citep[n$\sim4$, ][]{Aceves:2006aa}, with processes such as tidal interactions \citep[][]{Barnes:1991aa} and harassment \citep[][]{Moore:1996aa} also potential candidates for the truncation of the grouped galaxies. A merger induced burst of a red galaxy is also possible instead of a quench, but models in Fig \ref{fig:multiplot} (a) suggest this is transition is short-lived, so a less likely candidate. The lack of slow quenching provides more evidence of the importance of a group environment on the rapid transformation of star forming galaxies once truncation starts \citep[][]{Wetzel:2012aa, Wetzel:2013aa}. By contrast, the non-grouped sample shows colours consistent with a mix of rapid and slow quenching events. Many of the non-grouped galaxies are thus likely undergoing a secular ($>1$ Gyr timescale) form of evolution. \citet[][]{Pan:2014aa} found that late-type green valley galaxies with \nuvr\ blue disks are likely to have formed from secular processes, matching this result. Many of the excess galaxies are therefore likely to be secularly evolving, disk and pseudobulge galaxies, with secular processes common in pseudobulge galaxies \citep[][]{Kormendy:2004aa}, and pseudobulge galaxies known to have red optical colours \citep[][]{Fernandez-Lorenzo:2014aa}. While many of the galaxies in the non-group sample are best suited to a long decay model, other sources have colours that can be traced by a fast decay. These could be the result of the larger scale environment, with processes acting on the galaxy outside the local halo environment \citep[e.g. ][]{Bahe:2013aa}. These processes are not able to be looked at without knowledge of the wider structure, so are left unknown in this study. Another possible contaminant in the non-grouped sample are leftover remnants of fossil groups \citep[e.g. ][]{Ponman:1994aa, Jones:2003aa}. These galaxies would have undergone a rapid quench, or a merger induced burst of star formation, leaving the result appearing to be alone within a single halo, but still a result of direct environmental processes. Further analysis of the haloes could help isolate this possible scenario, but is left as a future endeavour. | 16 | 9 | 1609.02311 |
1609 | 1609.09832_arXiv.txt | We focus on understanding the beaming of gravitational radiation from gamma ray bursts (GRBs) by approximating GRBs as linearly accelerated point masses. For accelerated point masses, it is known that gravitational radiation is beamed isotropicly at high speeds, and beamed along the polar axis at low speeds. Aside from this knowledge, there has been very little work done on beaming of gravitational radiation from GRBs, and the impact beaming could have on gravitational wave (GW) detection. We determine the following: (1) the observation angle at which the most power is emitted as a function of speed, (2) the maximum ratio of power radiated away as a function of speed, and (3) the angular distribution of power ratios at relativistic and non-relativistic speeds. Additionally the dependence of the beaming of GW radiation on speed is essentially the opposite of the beaming of electromagnetic (EM) radiation from GRBs. So we investigate why this is the case by calculating the angular EM radiation distribution from a linear electric quadrupole, and compare this distribution to the angular gravitational radiation distribution from a GRB. | Binary neutron stars, binary black holes and neutron star-black hole pairs are the most likely source of gravitational waves. Emissions from these compact binaries are expected to be short gamma ray bursts (GRBs), which are very short bursts of large amounts of electromagnetic energy. GRBs are divided into two types based on the signal's duration and spectral hardness: ``short'' and ``long'' GRBs$^1$. The origin of ``short'' GRBs is thought to be from compact binaries coalescence (CBC). If gravitational waves are detected by advanced LIGO from CBCs, we can further distinguish between the signals produced by different binary systems. ``Long'' GRBs mostly originate from stellar collapses and are not that relevant here. An overly simplistic equation used to compute the so-called ``isotropic'' energy due to a GRB is given as$^2$: \begin{equation} E_{iso} = \frac{4\pi(BC){D_{L}}^{2}f}{1+z} \label{e_iso} \end{equation} where $E_{iso}$ refers to the energy due to the GRB that is emitted in all directions equally, $z$ is the redshift, $D_L$ is the luminosity distance to the source, $f$ is the fluence measured in the High Energy Transient Explorer (HETE-2) waveband, and BC is the bolometric correction for this waveband for GRBs. $E_{iso}$ is taken to be ~$10^{-2} M_{sun}c^2$. However it is not certain that the CBC sources in LIGO's sensitivity range will emit GRBs isotropically. In fact if the bursts are at lower speeds, they will be beamed along the polar axis, which might present a better chance of detection. However it has been determined that if the GWs are beamed along the polar axis, the power due to these signals would have been underestimated by the factor $u$: \begin{equation} u=1+\frac{11x}{16}+\frac{11x^2}{16}+\frac{x^3}{16}+\frac{x^4}{16} \end{equation} where $x$ = $\cos\psi$ and $\psi$ is the opening angle around the normal into which the bursts are beamed$^3$. And if GRBs are emitted isotropicly, they might not be strong enough to be detected, since $E_{iso}$ varies among order of magnitudes for different known GRBs$^4$. So we need to determine what proportion of this variable amount of power is actually detectable. Additionally, we know that gravitational waves are the result of a time-varying quadrupole moment of a source, but there exists a fundamental difference in the way that electromagnetic radiation from an accelerated point charge behaves at relativistic speeds compared to gravitational radiation from an accelerated point mass at relativistic speeds: \begin{equation} \frac{ dE}{d\Omega d\omega} = \frac{e^2}{4\pi^2 c}\beta^2 \gamma^2\frac{\sin^2\theta}{(1-\beta\cos\theta)^2} \label{em_beam} \end{equation} \begin{equation} \frac{dE}{d\Omega d\omega} = \frac{Gm^2}{4\pi c^2}\beta^4\gamma^2\frac{\sin^4\theta}{(1-\beta\cos\theta)^2} \label{gw_beam} \end{equation} Here $\frac{dE}{d\Omega d\omega}$ is the energy emitted per solid angle $\Omega$ per angular frequency $\omega$, $\theta$ is the observation angle, and the rest of the variables carry their usual meanings. At relativistic speeds, equations \ref{em_beam} and \ref{gw_beam} indicate that EM radiation is beamed and that GW radiation is not (it is in fact isotropic). We investigate why this fundamental difference occurs by accelerating a linear electric quadrupole (two dipoles back-to-back) and calculating its power distribution. There has been work done on calculating the electric and magnetic fields of a dipole in motion, and the corresponding power distributions as a function of $\theta$, the observation angle$^5$. In this case, the power distribution of a linearly accelerating dipole is even more beamed than for an accelerated point charge. However, no such calculation has been done for a linear electric quadrupole in motion, nor has an angular power distribution ever been computed. | Based on figure \ref{pow_vs_spd}, only a small fraction (12\%-15\%) of power from a GRB per unit solid angle is received by us even if we are observing it from the optimal angle. Additionally a GRB emitted directly at us at $\beta=0.999$ will not yield the greatest ratio of power ($\theta_{max}\approx48^{\circ}$). We have also seen that the angle at which we will see the most power decreases at higher speeds. Gravitational wave detection is hindered by the angular distribution of accelerated point masses: we therefore believe that radiation from bursts will be harder to see in most scenarios. Even in the best case scenario (at the optimal viewing angle), only around 15\% of the total power per unit solid angle will reach us. The event will need to be very strong and emitted at the optimal angle to be seen. Figures \ref{leading_order} and \ref{beta_0_1} show that the quadrupole moment is probably not responsible for the differing EM and GW angular power distributions. This is because the EM radiation due to an accelerating electric quadrupole at relativistic speeds is beamed along the observation axis, and the radiation is isotropic at lower speeds. Gravitational radiation from an accelerated point mass behaves exactly opposite to this. We recognize that a better quadrupole to use would have been a square of charge in two dimensions centered at the origin, since it does not have the higher-order multipoles that a linear electric quadrupole does. We think this calculation would yield more insight into the reasons why changing quadrupole moments drive gravitational wave emission. | 16 | 9 | 1609.09832 |
1609 | 1609.00907_arXiv.txt | We entertain the possibility that primordial black holes of mass $\sim (10^{26}$--$10^{29})$~g, with Schwarzschild radii of $\ord{\text{cm}}$, constitute $\sim 10\%$ or more of cosmic dark matter, as allowed by various constraints. These black holes would typically originate from cosmological eras corresponding to temperatures $\ord{10-100}$~GeV, and may be associated with first order phase transitions in the visible or hidden sectors. In case these small primordial black holes get captured in orbits around neutron stars or astrophysical black holes in our galactic neighborhood, gravitational waves from the resulting ``David and Goliath (D\&G)" binaries could be detectable at Advanced LIGO or Advanced Virgo for hours or more, possibly over distances of $\ord{10}$~Mpc encompassing the Local Supercluster of galaxies. The proposed Einstein Telescope would further expand the reach for these signals. A positive signal could be further corroborated by the discovery of new particles in the $\ord{10-100}$~GeV mass range, and potentially also the detection of long wavelength gravitational waves originating from the first order phase transition era. | 16 | 9 | 1609.00907 |
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1609 | 1609.09826_arXiv.txt | As the sample of white dwarfs with signatures of planetary systems has grown, statistical studies have begun to suggest our picture of compact debris disk formation from disrupted planetary bodies is incomplete. Here we present the results of an effort to extend the preferred dust disk model introduced by \citet{jur03} to include elliptical geometries. We apply this model the observed distribution of fractional infrared luminosities, and explore the difference in preferred parameter spaces for a circular and highly elliptical model on a well-studied dusty white dwarf. | To date, several dozen white dwarfs with compact circumstellar dust disks have been confirmed via the detection of infrared radiation in excess of their stellar photospheres. The observed excess offers the chance to constrain a handful of properties of the dust, including rough orbital parameters. The favored model for the origin of the dust was introduced by \citet{jur03}, wherein an asteroid on an initially highly eccentric orbit is tidally shredded, and the resulting dust settles into a compact optically thick and vertically thin disk. The orbits of the dust resulting from the tidal disruption are then expected to be constrained within two physical boundaries: the outer edge should be broadly consistent with the tidal disruption radius, beyond which asteroids are expected to survive their flyby encounters, while the inner edge should be able to extend to the sublimation radius of the dust, within which no dust can survive the intense radiation of the white dwarf. The \citet{jur03} model has seen great success in it's ability to explain both the abundance patterns seen in the material accreted onto the white dwarf surface, and to reproduce the observed infrared excess. The inner and outer radii of best-fitted models of the infrared excess are broadly consistent with the expected physical boundaries and, despite extensive searches, no evidence for a substantial amount of dust existing beyond the the tidal disruption radius has been found \citep{far16}. | 16 | 9 | 1609.09826 |
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1609 | 1609.07185_arXiv.txt | Among the most studied approaches to introduce the breaking of Lorentz symmetry, the generic approach is one of the most frequently used for phenomenology, it converges on the modification of the free particle dispersion relation. Using this approach in the photon sector, we have calculated the squared probability amplitude for vacuum Cherenkov radiation and photon decay by correcting the QED coupling at tree level and first order in LIV parameters. For the lower order energy correction we calculate the emission and decay rate for each process. | Cosmic rays are the most energetic phenomena known so far, reaching energies of several decades of EeV \cite{XMAX,GZK}. Among the many particulars their study and understanding reveal, they also provide an energy window to test fundamental physics. Such is the case of the search for signatures of Lorentz Invariance Violation (LIV), mainly motivated by Quantum Gravity theories and string theories \cite{QG1,QG2, QG3, QG4}. Due the the nature of this symmetry, the derived physics from LIV tends to be unique and energy dependent \cite{DIS2, DIS1}. Therefore, its consequences at the highest energies and very long distances could be identified in the current observatories and experiments. Following this spirit, in this paper we present a generic approach and a phenomenological first order correction to the production rates of two processes that could have a significant impact on cosmic particle propagation. The generic mechanism for introducing LIV, often found in the literature \cite{DIS2,DIS1, DIS3,DIS4, GUNTER-PH, VCR, GUNTER-PD, LIV-proc}, is summarized in an explicit not Lorentz invariant (LI) term added to the free particle Lagrangian density that will converge into the following generic correction to the dispersion relation: \begin{equation}\label{eq_S} S_{a} = E_a^2 - p_a^2 = m_a^2 \pm \alpha_{a,n}A^{n+2}, \end{equation} where $E_a$ and $p_a$ stand for the four-momenta associated with an $a$ particle species. Additionally, for particular models, $A$ can take the form of $E$ or $p$, however, for the ultra relativistic limit where $m_a\ll\{E, p \} $, any particular choice of $A$ will be equivalent. The coefficient $\alpha_{a,n}$ in Eq.~(\ref{eq_S}), parametrizes the particle species dependent LIV correction, where $n$ expresses the correction order to the mass shell. It is common to associate a generic $\alpha_{n} \approx E_{QG}^{-n}$, where $E_{QG}$ is the scale of Quantum Gravity or the scale of the expected new physics beneath. Several methods are used in the search for LIV signals, some of them can lead to lower limits to $E_{QG}$ \cite{HESS-LIV,FERMI-LIV,GRB-LIV, HAWC-LIV}, which is expected to be close to $10 ^ {19}$~GeV~. In the next section, we have applied the generic correction shown in Eq.~(\ref{eq_S}) for photons to derived the LIV corrected square amplitude at tree level from the diagrams in figure 1. It is worth stressing that such processes are forbidden in the standard theory by energy-momentum conservation, but under the LIV hypothesis they can be possible. Both of them are used in the search for LIV evidence. The first one is the emission of a single photon by a charged particle that propagates in vacuum and it is frequently named vacuum Cherenkov radiation \cite{GUNTER-PH,VCR}. The second is LIV photon decay \cite{GUNTER-PH, GUNTER-PD}, and it is motivated by the LIV extra term in Eq.~(1) that can be read as an effective photon mass and it will depend on the LIV coefficients; the simplest process will produce an electron - positron pair. Once the corrected square amplitude has been derived, we used it to find the process rates. | We have found a generic first order LIV correction to the emission and decay rates for vacuum Cherenkov radiation and LIV photon decay. Both processes, kinetically forbidden in a LI theory, can be possible under LIV hypothesis. The possible consequences of both processes decrease while the LIV photon coefficient $\alpha_{1} \rightarrow 0$. Both processes can lead to different expected physics at the most energetic scenarios, such as cosmic rays, but we will present such an analysis in a future work. \ack This work was partially supported by Conacyt grant No. 237004. | 16 | 9 | 1609.07185 |
1609 | 1609.05978_arXiv.txt | { Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the {\py FAST-PT} framework (McEwen {\it et al.}, 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at \url{https://github.com/JoeMcEwen/FAST-PT}.} \newcommand{\Pl}{P_\text{lin}} \newcommand{\LegP}{{\cal P}} \newcommand{\dq}[1]{\frac{d^3 \bm{q}_{#1}}{(2\pi)^3}} \newcommand{\dqn}[1]{d^3\bm{q}_{#1}} \newcommand{\thet}[2]{\theta({\bm{#1}_{#2}})} \newcommand{\theto}[2]{\theta^{(1)}({\bm{#1}_{#2}})} \newcommand{\thett}[2]{\theta^{(2)}({\bm{#1}_{#2}})} \newcommand{\delt}[2]{\delta({\bm{#1}_{#2}})} \newcommand{\delto}[2]{\delta^{(1)}({\bm{#1}_{#2}})} \newcommand{\deltt}[2]{\delta^{(2)}({\bm{#1}_{#2}})} \newcommand{\bisp}[3]{\left\langle #1 #2 #3 \right\rangle} \newcommand{\sovast}{Sov. Astron.} \newcommand{\mnras}{Mon. Not. R. Astron. Soc.} \newcommand{\aj}{Astron. J.} \newcommand{\aap}{Astron. Astrophys.} \newcommand{\apjl}{Astrophys. J. Lett.} \newcommand{\jcap}{J. Cosmo. Astropart. Phys.} \newcommand{\pasj}{Proc. Astron. Soc. Japan} \newcommand{\physrep}{Phys. Rep.} \newcommand{\prd}{Phys.~Rev.~D} \newcommand{\physreps}{Phys. Rep.} \newcommand{\apj}{Astrophys. J.} \newcommand{\apjs}{Astrophys. J. Supp.} \newcommand{\nat}{Nature} \begin{document} | \label{sec:intro} Observational cosmology has entered a new era of precision measurement. Current and upcoming surveys \cite{Levi:2013gra,BOSS2013AJ....145...10D,EUCLID2011arXiv1110.3193L,WFIRST2013arXiv1305.5422S,Abbott:2016ktf} are enabling us to probe large-scale structure in more detail and over larger volumes, and hence to better constrain the underlying cosmological model. A parallel effort is underway to understand the astrophysical effects that are both signals and contaminants in these measurements. For example, weak gravitational lensing has become a powerful and direct probe of the dark matter distribution \cite{Bartelmann:1999yn,Mellier:1998pk}, but it also suffers from systematic uncertainties, such as galaxy intrinsic alignments (IA), which must be mitigated in order to make use of high-precision measurements. Similarly, connecting observable tracers (\eg in spectroscopic surveys) with the underlying dark matter requires a description of the bias relationship \cite{Seljak:2004sj,McDonald:2006mx,2009JCAP...08..020M,Baldauf:2011bh,2012JCAP...03..004S} and the effect of redshift-space distortions (RSDs) \cite{1987MNRAS.227....1K,Scoccimarro:2004tg,Taruya:2010mx}. Developments in CMB measurements provide another illustration, as the range of observables has expanded from early initial detections of temperature anisotropies by COBE \cite{1992SvAL...18..153S,Smoot:1992td,Kovac:2002fg,Readhead:2004xg,Bennett:2012zja,Crites:2014prc,Naess:2014wtr,Ade:2013hjl,Ade:2015tva}. Current and future measurements \cite{Adam:2015rua,2011JCAP...07..025K,2009arXiv0906.1188B,2014SPIE.9153E..1LL,Andre:2013afa,Andre:2013nfa} will be able to investigate more subtle effects, such as the kinetic Sunyaev-Zel'dovich (kSZ) \cite{1972CoASP...4..173S,Carlstrom:2002na} and CMB spectral distortions \cite{Chluba:2011hw,Khatri:2012tw}. While modern cosmology has advanced significantly using our understanding from linear perturbation theory, nonlinear contributions become significant at late times and at smaller scales. In the quasi-linear regime, many relevant cosmological observables are usefully described using perturbation theory at higher order. Significant effort has been devoted to understanding structure formation via a range of perturbative techniques (\eg \cite{Bernardeau:2001qr,Sugiyama:2013mpa,Crocce:2005xy,McDonald:2006hf,McDonald:2014dxa,2011JCAP...10..037A,Baumann:2010tm,Carrasco:2012cv,Pajer:2013jj,Hertzberg:2012qn,Blas:2015qsi}). In this work, we consider integrals in standard perturbation theory (SPT), although the methods and code we develop have a broader range of applications. The next-to-leading-order (``1-loop'') corrections in these perturbative expansions are typically expressed as two-dimensional mode-coupling convolution integrals, which are generically time consuming to evaluate numerically. Recent algorithmic developments have dramatically sped up these computations for {\em scalar} quantities -- those with no dependence on the direction of the observer, such as the matter density or real-space galaxy density. The new algorithms \cite{McEwen:2016fjn,Schmittfull:2016jsw} take advantage of the locality of evolution in perturbation theory, the scale invariance of cold dark matter (CDM) structure formation, and the Fast Fourier Transform (FFT); and work is underway to apply them to 2-loop power spectra as well \cite{Schmittfull:2016yqx}. In a previous paper, we introduced the {\py FAST-PT} implementation of these methods in Python \cite{McEwen:2016fjn}. However, there are many interesting 1-loop convolution integrals for {\em tensor} quantities -- those with explicit dependence on the observer line of sight, such as those arising for redshift-space distortions. In this case, we need convolution integrals with ``tensor'' kernels:\footnote{The kernel $K$ can be expressed as a sum of polynomials in the relevant dot products. ``Tensor'' refers to the general transformation properties of the cosmological quantities being considered under a symmetry operation -- in this case, rotations in SO(3). For instance, the momentum density is a rank 1 tensor (a vector) while the IA field is a rank 2 tensor. The scalar case (rank 0) considered in \cite{McEwen:2016fjn} is thus a specific application of this more general framework.} \begin{equation} I(k) = \int\dq{1}K(\hat{\bm{q}}_1\cdot\hat{\bm{q}}_2,\hat{\bm{q}}_1\cdot\hat{\bm{k}},\hat{\bm{q}}_2\cdot\hat{\bm{k}},q_1,q_2)P(q_1)P(q_2)~, \label{eq:tensor_int} \end{equation} where $K(\hat{\bm{q}}_1\cdot\hat{\bm{q}}_2,\hat{\bm{q}}_1\cdot\hat{\bm{k}},\hat{\bm{q}}_2\cdot\hat{\bm{k}},q_1,q_2)$ is a tensor mode-coupling kernel, $\bm{k}=\bm{q}_1+\bm{q}_2$, $k=\vert\bm{k}\vert$, and $P(q)$ is the input signal -- typically the linear matter power spectrum -- logarithmically sampled in $q$. Due to the dependence on the direction of $\bm{k}$, the decomposition of these kernels is more complicated than in the scalar case. In this work, we generalize our {\py FAST-PT} algorithm to evaluate these tensor convolution integrals, achieving $\mathcal{O}(N\log N)$ performance as in the scalar case. This paper is organized as follows: in \S\ref{sec:method} we provide the mathematical basis for our method (\S\ref{subsec:theory}), introduce our algorithm (\S\ref{subsec:algorithm}), and discuss divergences that may arise and how they are resolved (\S\ref{subsec:div}). In section \S\ref{sec:example} we apply our method to several examples: the quadratic intrinsic alignment model (\S\ref{subsec:quadratic_IA}); the Ostriker-Vishniac effect (\S\ref{subsec:OV}); the kinetic polarization of CMB (\S\ref{subsec:kP}); and the 1-loop redshift-space power spectrum (\S\ref{subsec:RSD}). Section \S\ref{sec:summary} summarizes the results. An appendix contains derivations of the relevant mathematical identities. The Python code implementing this algorithm and the examples presented in this paper is publicly available at \url{https://github.com/JoeMcEwen/FAST-PT}. | \label{sec:summary} In this paper we have extended the {\py FAST-PT} algorithm to treat 1-loop convolution integrals with tensor kernels (explicitly dependent on the direction of the observed mode). The generalized algorithm has many applications -- we have presented quadratic intrinsic alignments, the Ostriker-Vishniac effect, kinetic CMB polarizations, and a sophisticated model for redshift space distortions. Our algorithm and code achieve high precision for all of these applications. We have tested the output of the code to high wavenumber ($k=10~h/$Mpc), although we reiterate that the smaller scales considered are beyond the range of validity of the underlying perturbative models. The reduction in evaluation time is similar as for the scalar {\py FAST-PT}. For instance, execution time is $\sim 0.1$ seconds for 600 $k$ values in all our examples. In the results shown here, the input power spectrum was sampled at 100 points per $\log_{10}$ interval. We find that much of the noise (in comparisons with the conventional method) is driven by the exact process by which the CAMB power spectrum is interpolated before it is used in {\py FAST-PT}. There are underlying physical concepts and symmetries that make the efficiency of this algorithm possible. For example, the locality of the gravitational interactions allows us to separate different modes in configuration space. Since the structure evolution under gravity only depends on the local density and velocity divergence fields, in Fourier space the 1-loop power spectra of the matter density as well as its tracers (assuming local biasing theories) must be in form of Eq.~(\ref{eq:tensor_int}), where the kernels can always be written in terms of dot products of different mode vectors. Without this locality, it may not be possible to write the desired power spectrum as a sum of terms that can be calculated with this algorithm. The scale invariance of the problem also indicates that we should decompose the input power spectrum into a set of power-law spectra and make full use of the FFT algorithm. There are also rotational symmetries that allow us to reduce the 3-dimensional integrals to 1-dimension. This algorithm, and implementations of the examples presented here, are publicly available as a Python code package at \url{https://github.com/JoeMcEwen/FAST-PT}. | 16 | 9 | 1609.05978 |
1609 | 1609.00593_arXiv.txt | This work presents the first characterization of the internal structure of overpressured steady superfast magnetosonic relativistic jets in connection with their dominant type of energy. To this aim, relativistic magnetohydrodynamic simulations of different jet models threaded by a helical magnetic field have been analyzed covering a wide region in the magnetosonic Mach number - specific internal energy plane. The merit of this plane is that models dominated by different types of energy (internal energy: hot jets; rest-mass energy: kinetically dominated jets; magnetic energy: Poynting-flux dominated jets) occupy well separated regions. The analyzed models also cover a wide range of magnetizations. Models dominated by the internal energy (i.e., hot models, or Poynting-flux dominated jets with magnetizations larger than but close to 1) have a rich internal structure {characterized by a series of recollimation shocks} and present the largest variations in the flow Lorentz factor {(and internal energy density)}. Conversely, in {kinetically dominated} models there is not much internal nor magnetic energy to be converted into kinetic one and the jets are featureless, with small variations in the flow Lorentz factor. The presence of a significant toroidal magnetic field threading the jet produces large gradients in the transversal profile of the internal energy density. {Poynting-flux dominated models with high magnetization} ($\approx 10$ or larger) are prone to be unstable against magnetic pinch modes, which sets limits to the expected magnetization in parsec-scale AGN jets {and/or constrains their magnetic field configuration}. | How relativistic jets are launched, accelerated, and collimated is probably one of the most important questions related to AGN jet physics and other astrophysical systems involving black hole accretion, such as $\gamma$-ray bursts (GRBs) or tidal disruption flares (TDFs). It is thought that dynamically important helical magnetic fields twisted by the differential rotation of the black hole's accretion disk or ergosphere play an important role \citep{BZ77,BP82,MB09,TN11,ZC14}. As the jet propagates, part of the magnetic energy of the plasma is converted into kinetic energy, accelerating the jet while maintaining a parabolic shape (see, e.g., \citealp{KB07}, and references therein for theoretical approaches to the problem; see \citealp{NA13}, for an investigation of the parabolic jet structure in M87). For initially relativistic hot jets, thermal acceleration can also play a role \citep[see, e.g.,][] {GM95,GM97}. Simultaneous multi-wavelength and Very Long Baseline Interferometry (VLBI) observations of AGN jets suggest that the acceleration and collimation of the jet takes place in the innermost $10^{4-6}$ Schwarzschild radii { from the central black hole}, upstream of the millimeter VLBI (mm-VLBI) core \citep{MJ08}, defined as the bright compact feature in the upstream end of the observed VLBI jet. The simultaneity of multi-wavelength flares (from radio to $\gamma$-ray energies) with the passage of a new superluminal component through the mm-VLBI core has led to the suggestion that this corresponds to a strong recollimation shock \citep[e.g.,][]{MJ08,MJ10,CG15a,CG15b}. {Moreover, in sources as CTA~102, in which this coincidence has not been proven, the presence of a stationary feature close to the VLBI core was claimed to explain the spectral evolution of a radio-flare \citep{FP11}. Multifrequency VLBI observations showed evidence in this direction \citep{FR13a,FR13b}}. The interaction of the moving shock associated with the superluminal component and the standing shock at {or close to} the mm-VLBI core would produce the particle acceleration and burst in particle and magnetic energy densities required to produce the multi-wavelength flares. It should be noted that this association of the mm-VLBI core with a recollimation shock {would not be} in contradiction with the predictions from the Blandford \& K\"{o}nigl jet model \citep{BK79} that establishes the VLBI core as the location at which the jet becomes optically thin, as long as this transition at {\it centimeter} wavelengths takes place {\it downstream} of the mm-VLBI core. Relativistic (magneto)hydrodynamical simulations have shown that pressure mismatches between the jet and ambient medium lead to the formation of a pattern of recollimation shocks \citep[e.g.,][]{Wi87,DM88,DP93,GM95,GM97,GL16,MA09,PK15,MG15}. It is therefore natural to expect that if the mm-VLBI core corresponds to a recollimation shock other similar standing VLBI features would be observed downstream of its location. Indeed, although some stationary features have been found at hundreds of parsecs from the central engine \citep[e.g.,][]{RG10}, most of the stationary components observed in AGN jet appear in the innermost jet regions, close to the VLBI core \citep[e.g.,][]{JM05,CM14,GL16}. Hence, obtaining a better characterization of recollimation shocks is of special relevance not only for the interpretation of the observed VLBI structure in AGN jets, but also to obtain a better understanding of the nature of the mm-VLBI core and its connection with the emission mechanisms at X and $\gamma$-ray energies often observed from these sources. Recollimation shocks have been previously studied through relativistic hydrodynamic and magnetohydrodynamic numerical simulations \citep[e.g.,][]{GM95,GM97,KF97,MM12,PK15,KP15,MG15,FP16}. In this paper we present the first systematic study of the resulting jet structure in connection with the dominant type of energy in the jet, namely internal, kinetic, or magnetic, through relativistic magnetohydrodynamical simulations of overpressured superfast-magnetosonic jets { propagating through a homogeneous ambient medium. The effect of a pressure-decreasing atmosphere in the structure of jets, particularly in the properties of recollimation shocks, and the jet energy conversion will be the subject of future research}. {The paper is organized as follows. In Section~2, we define the parameter space of our study. Axisymmetric jet models are injected into the two-dimensional numerical grid in transversal equilibrium to minimize radial perturbations. In Section~3 we describe the transversal structure of the injected models. Section~4 is devoted to describe the setup of the simulations, whereas in Section~5 we present and discuss the results on the internal structure of jets. Finally, in Section~6 we summarize our main conclusions.} | The internal structure of eight superfast magnetosonic, overpressured jet models has been analyzed. The injection parameters of these models have been chosen to cover a wide region in the magnetosonic Mach number - specific internal energy plane. The merit of this plane is that models dominated by different kind of energies (internal energy: hot jets; rest-mass energy: kinetically dominated jets; magnetic energy: Poynting-flux dominated jets) occupy well separated regions. The analyzed models also cover a wide range of magnetizations. The rest of injection parameters (the rest-mass density, the jet overpressure factor, the flow Lorentz factor, and the flow azimuthal velocity -equal to zero-) are kept constant. Jets are injected in internal transversal equilibrium to minimize the sideways perturbations once immersed in the ambient medium and to obtain an internal structure as clean as possible. The transition between the jet and the ambient medium is smoothed by means of a shear layer of different widths to stabilize the models against the growth of magnetic pinch instabilities. The conclusions of our analysis are listed below. \begin{enumerate} \item The models with a richer internal structure are those dominated by the internal energy, i.e., those in the {hot jets} region or its neighbourhood (i.e., Poynting-flux dominated jets with magnetizations larger than but close to 1). In these cases, the models have a substantial amount of internal energy which is efficiently converted into kinetic energy at jet expansions and back to internal energy at { recollimation} shocks. These models present the largest variations in flow Lorentz factor { and internal energy density along the axis}. \item Conversely, in the {kinetically dominated jet} models there is not much internal nor magnetic energy to be converted into kinetic one, {the jets} have no internal structure and the flow Lorentz factor is constant. Despite the large difference in magnetization, kinetically dominated models with the same magnetosonic Mach number have very similar overall structure (jet oscillation, amplitude of variations, local jet opening angles,...). \item As a consequence of the magnetic pinch exerted by the toroidal magnetic field, {models with large magnetizations} concentrate most of their internal energy in a thin hot spine around the axis. The width of this spine is related with the location of the maximum toroidal field across the jet. \item {Poynting-flux dominated models with high magnetization} are prone to be unstable against magnetic pinch modes. \item All the models present a jet oscillation with a characteristic wavelength that follows definite trends with specific internal energy, magnetosonic Mach number and magnetization. \item The { change in (average) magnetic pitch angle} is limited to few degrees around the average value. However, large local radial variations in the pitch angle can be expected from almost $0^\circ$ close to the axis to values larger than the average at some intermediate radius. \item Despite the fact that the studied models are injected with pure axial flow velocities, all develop {small azimuthal velocities} (of the order of 2\% of the speed of light or smaller) as a result of the Lorentz force in axisymmetric converging/diverging flows. These speeds tend to be larger in those models where the jet oscillation has a larger amplitude. \end{enumerate} Despite its limitations, the present study is the first attempt to identify the structural ingredients (including the properties of { recollimation} shocks) that characterize hot, Poynting-flux dominated and kinetically dominated, relativistic jets. Our study is of special relevance in the interpretation of parsec-scale AGN jets. On one hand, our simulations confirm the correlation between the Mach angles, the angles of the conical shocks and the separation between them (in models with internal structure) and allow us to estimate the magnetosonic Mach numbers of parsec-scale jets with stationary components. {It should be noted, however, that our simulations are two-dimensional and that imperfect azimuthal symmetry of the ambient medium would disrupt the coherence of the standing shock pattern after few jet oscillations.} On the other hand, our study reveals that the presence of a significant toroidal component of the magnetic field in these objects produces a complex transversal structure with a central spine (extending up to the radius of the maximum of the toroidal field) where the thermal pressure (and hence the plasma internal energy) is close to its maximum. {A layer with milder (magnetic, thermal) pressure profiles that extends up to the outer jet/ambient-medium transition layer wraps the central spine}. This complex profile in the thermal energy distribution and the magnetic pitch angle {must} leave their imprints in the total and polarized emission, which will be the subject of a forthcoming paper. In that work we shall {analyze in detail the emission properties of these models,} paying special attention to the relative intensity of the components associated to the shocks as a function of the viewing angle, to the tranversal structure of the jet and, in general, to the signatures of the magnetic field structure in the polarized emission. {Our results prove the stabilization effect of shear layers for the CDI in Poynting-flux dominated jets.} More interestingly, the stability of Poynting flux dominated jets against pinch oscillations (and, in particular, the role of the shear layer in the stabilization of these flows) merits further exploration as a way to constrain the magnetization parameter { and/or the magnetic field configuration} in parsec-scale AGN jets. Additional parameters should be explored, specially the overpressure factor ({related with the formation of Mach disks}) and the magnetic field pitch angle, as well as new strategies to generate the steady models. In a recent paper, \cite{KP15} describe a simple numerical approach to study the structure of steady axisymmetric superfast-magnetosonic jets by means of one-dimensional time dependent simulations by using $z$ (the axial cylindrical coordinate) as the time coordinate. Although subject to a number of approximations, the approach works well and could be used to generate approximate steady solutions in a wider space of parameters. | 16 | 9 | 1609.00593 |
1609 | 1609.03522.txt | Massive stars are key players in the evolution of galaxies, yet their formation pathway remains unclear. In this work, we use data from several galaxy-wide surveys to build an unbiased dataset of $\sim$\,700 massive young stellar objects (MYSOs), $\sim$\,200 giant molecular clouds (GMCs), and $\sim$\,100 young ($\textless$\,10 Myr) optical stellar clusters (SCs) in the Large Magellanic Cloud. We employ this data to quantitatively study the location and clustering of massive star formation and its relation to the internal structure of GMCs. We reveal that massive stars do not typically form at the highest column densities nor centers of their parent GMCs at the $\sim$\,6 pc resolution of our observations. Massive star formation clusters over multiple generations and on size scales much smaller than the size of the parent GMC. We find that massive star formation is significantly boosted in clouds near SCs. Yet, whether a cloud is associated with a SC does not depend on either the cloud's mass or global surface density. These results reveal a connection between different generations of massive stars on timescales up to 10 Myr. We compare our work with Galactic studies and discuss our findings in terms of GMC collapse, triggered star formation, and a potential dichotomy between low- and high-mass star formation. | Massive stars dominate the structure and energy budget of the interstellar medium of galaxies through intense radiation fields, stellar winds, and supernova explosions. Yet, the pathway that leads to their formation remains unclear, as the process is notoriously difficult to probe because of large distances, crowding, high levels of obscuration, and short lifetimes. In general, star formation studies have seen dramatic progress in the past decade, which can largely be attributed to the {\em Spitzer} space telescope and the {\em Herschel} space observatory. These missions opened up the mid-to-far infrared (IR) sky at high resolution, allowing us to peek into star forming cradles that are deeply embedded within giant molecular clouds (GMCs). The internal structure of GMCs reveal infrared dark clouds (IRDCs) and filaments (up to tens of pc), clumps ($\sim$\,1 pc) and cores ($\sim$\,0.1 pc). It is now largely understood that there is an intimate connection between filaments and the formation of low-mass prestellar cores \citep{konyves_2010,andre_2010,andre_2014}. In contrast, studying high-mass clumps and cores has proven to be difficult despite numerous attempts targeting the earliest stages of massive star formation \citep{motte_2007,tackenberg_2012,ragan_2012, schneider_2012}. Recent large surveys of the Galactic plane yield promising results by detecting {\em candidate} massive star forming clumps \citep[e.g.,][]{svoboda_2015}. Still, confusion and distance ambiguity will inherently complicate studies of massive star formation in the Galaxy and its connection to larger-scale structures in the interstellar medium, e.g., the parent GMCs. Leaving aside the difficulties in probing Galactic massive star formation, there is no theoretical consensus as to the exact physical process that ultimately leads to a (cluster of) massive stars \citep{tan_2014}. In this respect, it has long been debated that low-mass stars and high-mass stars may not form alike: whereas low-mass cores and stars may form `spontaneously' through hierarchical fragmentation within GMCs \citep{andre_2014}, the formation of high-mass stars may be `triggered' \citep{elmegreen_1998} by an external mechanism, although the exact nature and/or importance of triggering has remained controversial \citep[see][and references therein]{dale_2015}. In this work, we present a galaxy-wide study of massive star formation and its relation with GMCs in the Large Magellanic Cloud (LMC). The LMC provides us with an excellent opportunity to study the formation of massive stars in a wide range of evolutionary stages, since its face-on orientation minimizes confusion and distance ambiguities, while being close enough to resolve individual clouds and stars ($\sim$\,50 kpc; \citealt{pietrzynski_2013}). By combining several galaxy-wide surveys, we create a unique view of massive young stellar objects (MYSOs), GMCs, and optical stellar clusters (SCs) in the LMC. The multi-facetted nature and sheer size of the data traces massive star formation as a function of environment and evolutionary state, and the overarching goal of this study is to exploit this unique dataset to quantify the location, clustering, and propagation of massive star formation within GMCs. In Sec. \ref{sec:observations}, we present the observations. In Sec. \ref{sec:catalogue}, we build our catalogue of MYSOs, the completeness of which is tested in Sec. \ref{sec:completeness}. We describe the dust fitting and creation of column density maps and subsequent cloud decomposition in Sec. \ref{sec:mapandcloud}. The distribution of MYSOs within GMCs and its relation to SCs is presented in Sec. \ref{sec:results}. We compare our results with studies performed in the Galaxy, an discuss our findings in relation to recent numerical and analytical studies of collapsing molecular clouds in Sec. \ref{sec:discussion}. We conclude in Sec. \ref{sec:conclusions}. | \label{sec:conclusions} We have studied massive star formation in GMCs of the LMC using an unbiased sample of $\sim$\,700 MYSOs, $\sim$\,200 GMCs, and $\sim$\,100 SCs. Unhindered by confusion or luminosity uncertainties that typically hamper Galactic studies, we were able to study the location, clustering, and propagation of massive star formation within GMCs. Our main results are as follows: \begin{enumerate} \item[-] Our MYSO catalogue is complete for Stage 1 MYSOs of mass $M$\,$\textgreater$\,8 $M_\m{\odot}$, provided that they have mid-IR counterparts (Sec. \ref{sec:completeness}). \item[-] We find ongoing massive star formation (i.e., over the past $\sim$\,10$^5$ yr) in 33\% or 48\% of the LMC GMCs, depending if we consider `clouds' or `islands' (Sec. \ref{sec:dendrogram}). We substantiate the classification scheme from \citet{kawamura_2009} by revealing that Type 1 GMCs are (mostly) devoid of massive star formation (Tab. \ref{tab:mysos}). \item[-] We find that massive stars do not form at the peak column densities within GMCs at the $\sim$\,6 pc resolution of our observations (Figs. \ref{fig:postage} and \ref{fig:histogram}). Specifically, half of our sample of MYSOs/VMYSOs/DCs are located $\textgreater$\,10 pc from $N_\m{max}$ (Fig. \ref{fig:cumulative}). We have excluded completeness or feedback as a cause for this result (Sec. \ref{sec:results}). \item[-] By means of angular correlation functions (Eqs. \ref{eq:auto} \& \ref{eq:cross}; Fig. \ref{fig:clustering}), we have demonstrated that MYSOs/VMYSOs/DCs are strongly clustered on scales much smaller than the size of CO islands and clouds. The auto-correlations show very similar results compared to their respective cross-correlations with SCs, indicating that massive star formation is clustered over different generations on timescales up to 10 Myr. \item[-] We find that the rate of massive star formation is significantly elevated in clouds near SCs (Fig. \ref{fig:triggering}). At the same time, the rate of massive star formation in these clouds appears unrelated to the global cloud properties $M_\m{cloud}$ and $\mean{\Sigma_\m{cloud}}$. The relative increase in massive star formation becomes less pronounced at larger distances from the SCs. \end{enumerate} We argue that massive star formation is a local process within GMCs. It appears that the initial conditions leading to massive star formation do not necessarily occur in the densest, most opaque regions of GMCs. Our results reveal a close connection between different generations of massive stars on timescales up to 10 Myr, which may provide further support for triggering as a key mode for massive star formation, which in its turn could proceed very differently compared to their lower mass counterparts. | 16 | 9 | 1609.03522 |
1609 | 1609.04379_arXiv.txt | We present an updated global model of the solar corona, including the transition region. We simulate the realistic tree-dimensional (3D) magnetic field using the data from the photospheric magnetic field measurements and assume the magnetohydrodynamic (MHD) Alfv\'en wave turbulence and its non-linear dissipation to be the only source for heating the coronal plasma and driving the solar wind. In closed field regions the dissipation efficiency in a balanced turbulence is enhanced. In the coronal holes we account for a reflection of the outward propagating waves, which is accompanied by generation of weaker counter-propagating waves. The non-linear cascade rate degrades in strongly imbalanced turbulence, thus resulting in colder coronal holes. The distinctive feature of the presented model is the description of the low corona as almost-steady-state low-beta plasma motion and heat flux transfer along the magnetic field lines. We trace the magnetic field lines through each grid point of the lower boundary of the global corona model, chosen at some heliocentric distance, $R=R_{b}\sim1.1\ R_\odot$ well above the transition region. One can readily solve the plasma parameters along the magnetic field line from 1D equations for the plasma motion and heat transport together with the Alfv\'en wave propagation, which adequately describe physics within the heliocentric distances range, $R_{\odot}<R<R_{b}$, in the low solar corona. By interfacing this threaded-field-lines model with the full MHD global corona model at $r=R_{b}$, we find the global solution and achieve a faster-than-real-time performance of the model on $\sim200$ cores. | Observations from Hinode and Solar Dynamics Observatory (SDO) (\cite{dupo08} and \cite{mcintosh11}) raised the estimate for the \alf wave energy in the SC. About $10\div20\%$ of this outward propagating energy is adequate to heat the SC and accelerate the solar wind in IH. Therefore, several three-dimensional (3-D) solar wind (\cite{usma00}, \cite{suzu05}, \cite{verd10}, \cite{osman11}, {\color{cyan}{\it Lionello et al.} (2014a, 2014b)}) and coronal heating (\cite{tu97}, \cite{hu00}, \cite{ dmit02}, \cite{Habb03} and \cite{cran10}) models that included, or were exclusively driven by, \alf wave turbulence became increasingly popular and paved the road for the development of even more advanced \alf wave driven models. Although popular, this physics-based approach to modeling the solar environment is not the only way to model the solar corona and the solar wind. Semi-empirical descriptions of the solar wind, like the widely used Wang-Sheeley-Arge (WSA) model \cite[] {arge00} is also attractive because of their simplicity and ability to predict the solar wind speed in the IH. In addition, the WSA formulae can be easily incorporated into global 3-D models for the SC and IH \cite[see ][]{cohen07} via a varying polytropic index distribution as proposed by \cite{roussev03b}. Similarly, instead of the \alf wave turbulence dissipation mechanism to heat the corona, one can use well established models with semi-empirical heating functions, such as those presented by {\color{cyan}{\it Lionello et al.} (2001, 2009)}, \cite{rile06}, \cite{tito08} and \cite{downs10}. This method leads to reasonably good agreements with observations in EUV, X-rays and white light. The agreement looks particularly impressive for the PSI predictions about the solar eclipse image. An important limitation of the semi-empirical models is that they depend on free parameters that need to be determined for various solar conditions. This fact makes it complicated to use them in an integrated modeling approach describing the Solar Corona (SC) and Inner Heliosphere (IH) system with very few free parameters. In the presented research, the \alf wave turbulence is treated as the only energy source to heat the SC and to power and accelerate the solar wind. From the model for the quiet-time SC and IH the {\it ad hoc} elements were eliminated by \cite{sok13}. In the Alfv\'en-Wave-driven SOlar Model (AWSoM) the plasma is heated by the dissipation of the Alfv\'en wave turbulence, which, in turn, is generated by the nonlinear interaction between oppositely propagating waves \cite[]{hollw86}. Within the coronal holes there are no closed magnetic field lines, hence, there are no oppositely propagating waves. Instead, a weak reflection of the outward propagating waves locally generate sunward propagating waves as quantified by \cite{vanderholst13}. The small power in these locally generated (and almost immediately dissipated) inward propagating waves leads to a reduced turbulence dissipation rate in coronal holes, naturally resulting in the bimodal solar wind structure. Another consequence is that coronal holes look like cold black spots in the EUV and X-rays images, the closed field regions are hot and bright, and the brightest are active regions, near which the wave reflection is particularly strong (see \cite{sok13}, \cite{oran13} and \cite{vanderholst13}). The described global models simulate the steady state of the solar terrestrial environments, which serves as a background for {\it space weather}. Space weather describes the dynamic state of the Earth's magnetosphere-ionosphere system, which is driven by the solar wind and solar ionizing radiation. The greatest disturbances in space weather are geomagnetic storms, the most severe of which are caused by coronal mass ejections (CMEs) (see \cite{gosling1993}). While there are many models of CME initiation by magnetic free energy, these simulations are often performed in a small Cartesian box \cite[e.g.][]{torok2005}, or using global models with no solar wind (e.g. \cite{antiochos1999} and \cite{ fan2004}). So far there have only been a few magnetically driven Sun-to-Earth CME simulations through a realistic interplanetary medium using 3-D MHD (cf. {\color{cyan} {\it Manchester et al.} (2004a, 2004b, 2005)}, \cite{lugaz07} and \cite{toth2007}). The MHD simulation of \cite{toth2007} was able to match the CME arrival time to Earth within 1.8 hours and reproduce the magnetic field magnitude of the event. A simple but convenient way to simulate a magnetically-driven CME is to superimpose a \cite{gibson98} (GL) or \cite{titov99} (TD) magnetic flux-tube configuration onto the background state of the SC. Specific examples of such CME simulations using the AWSoM model for the SC and IH with a superimposed GL magnetic configuration include \cite{manchester2012} and \cite{jin13,Jin:2017a,Jin:2017b}. The GL magnetic configuration describes an erupting magnetic filament filled with excessive plasma density. That filament becomes an expanding flux rope (magnetic cloud) in the ambient solar wind while evolving and propagating outward from the Sun, thus allowing the simulation of the propagation to 1 AU of a magnetically driven CME. In a similar way, by superimposing multiple TD configurations, \cite{linker16} have recently modeled the July 2000 CME eruption. Here we present the development of the AWSOM. A distinctive feature of the presented model is the description of the low SC as almost-steady-state low-beta plasma motion along the magnetic field lines, the heat fluxes also being aligned with the magnetic field. The Low Solar Corona model which ranges from the upper chromosphere to the heliocentric distances about $\sim 1.1\ R_{\odot}$ and includes the transition region at $R_\odot<R<1.03\ R_\odot$, is the heart of the global models. In the low SC the Alfv{\'e}n waves pass from the chromosphere to the solar corona, the plasma temperature increases by two orders of magnitude (from ten thousand to million K), and this is also a place where the solar wind originates. The multi-wavelength observations (in EUV and X-rays) from several satellite locations (SDO, STEREO A,B) may be used to validate the simulation model. Therefore, any global model must account for the processes in this region. On the other hand, for the simulation model to explain the space weather and also have a predictive capability, it should be capable of simulating the dynamic processes faster than they proceed in real time, and the low SC appears to be a bottleneck limiting the computational efficiency and performance. In numerical simulations of the solar corona, both for the ambient state and especially for dynamical processes, the greatest number of computational resources is spent for maintaining the numerical solution in the low SC and in the transition region, where the temperature gradients are sharp and the magnetic field topology is complicated. The degraded computational efficiency is caused by the need for the highest resolution as well as the use of a fully three-dimensional implicit solver for electron heat conduction. The need to find a numerical method, which would allow us to gain in the computational efficiency, motivates the research presented here. We benefit from the observation that although the simulations of the low SC are computationally intense, the physical nature of the processes involved is rather simple as long as the heat fluxes and slow plasma motional velocities are mostly aligned with the magnetic field. The Alfv\'en wave turbulence, is characterized by the wave Poynting flux, which is also aligned with the magnetic field. Therefore, the plasma state at any point within the low SC is controlled by the plasma, particle, and Alfv\'en wave transport along the magnetic field line, which passes through this point. This physical property is typical for a variety of magnetized plasmas in different astrophysical and laboratory environments and may be used as the base of a new numerical method, which solves the state of plasma in each grid point in the computational domain depth in the following way: (1) by passing the magnetic field line ('thread') through this point and connecting it with the domain boundaries (e.g., with chromosphere and with the global solar corona domain, once the method is applied to the low SC) and (2) by solving a set of one-dimensional transport equations to relate the grid point value to the boundary conditions. We trace the magnetic field lines through all grid points of the lower boundary of the global coronal model chosen at some heliocentric distance $R=R_b\sim1.1\ R_\odot$ well above the transition region. One can readily solve the plasma parameters along the magnetic field line from effectively 1D equations for the plasma motion and heat transfer together with the Alfv\'en wave propagation, which adequately describe physics within the heliocentric distance range, $R_\odot<R<R_b$, i.e. in the low solar corona. By interfacing this Threaded-Field-Line Model (TFLM) for the low corona with full MHD global corona model at $R=R_b$ we find the global solution and achieve faster-than-realtime performance of the model with moderate computational resources. Due to the latter feature we call the newly developed model AWSoM-R (AWSoM-Realtime). | The AWSoM-R model presented here extends the earlier developed AWSoM (\cite{sok13} and \cite{vanderholst13}) with the TFLM description for the transition region and Low Solar Corona. It allows us to simulate the Solar-Earth environments on realistic 3D grids faster than real time and with no loss in the results quality. | 16 | 9 | 1609.04379 |
1609 | 1609.01289_arXiv.txt | \noindent We investigate the early Universe production of sterile neutrino Dark Matter by the decays of singlet scalars. All previous studies applied simplifying assumptions and/or studied the process only on the level of number densities, which makes it impossible to give statements about cosmic structure formation. We overcome these issues by dropping all simplifying assumptions (except for one we showed earlier to work perfectly) and by computing the full course of Dark Matter production on the level of non-thermal momentum distribution functions. We are thus in the position to study all aspects of the resulting settings and apply all relevant bounds in a reliable manner. We have a particular focus on how to incorporate bounds from structure formation on the level of the linear power spectrum, since the simplistic estimate using the free-streaming horizon clearly fails for highly non-thermal distributions. Our work comprises the most detailed and comprehensive study of sterile neutrino Dark Matter production by scalar decays presented so far. | 16 | 9 | 1609.01289 |
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1609 | 1609.03559_arXiv.txt | We here present the first spatially-resolved study of the IMF in external galaxies derived using a dynamical tracer of the mass-to-light ratio. We use the kinematics of relaxed molecular gas discs in seven early-type galaxies (ETGs) selected from the \atlas\ survey to dynamically determine mass-to-light ratio (M/L) gradients. These M/L gradients are not very strong in the inner parts of these objects, and galaxies that do show variations are those with the highest specific star formation rates. Stellar population parameters derived from star formation histories are then used in order to estimate the stellar initial mass function function (IMF) mismatch parameter, and shed light on its variation within ETGs. Some of our target objects require a light IMF, otherwise their stellar population masses would be greater than their dynamical masses. In contrast, other systems seem to require heavier IMFs to explain their gas kinematics. Our analysis again confirms that IMF variation seems to be occurring within massive ETGs. We find good agreement between our IMF normalisations derived using molecular gas kinematics and those derived using other techniques. Despite this, we do not see find any correlation between the IMF normalisation and galaxy dynamical properties or stellar population parameters, either locally or globally. In the future larger studies which use molecules as tracers of galaxy dynamics can be used to help us disentangle the root cause of IMF variation. | The stellar initial mass function function (IMF) is one of the most fundamental, and hotly debated, observational topics in astrophysics. Observations of stars within our own Milky Way suggest that the gravitational collapse of molecular clouds leads to star formation, and the birth of a population of stars whose masses can be well described by a single mass function \citep{1955ApJ...121..161S,2001MNRAS.322..231K,2003PASP..115..763C}. This mass function appears to be universal across the range of environments which we are able to probe within our own Galaxy \citep{2002Sci...295...82K,2010ARA&A..48..339B}. In the early universe, and in other extragalactic environments, however, conditions can be very different than those found locally. Understanding if the IMF is universal in these places, or if it varies (and why) is crucial to allow interpretations of observations, impacting almost all areas of astrophysics. For instance calibrations that allow estimation of star formation rates, stellar mass loss return rates and even total stellar masses rely intimately on an assumed IMF \citep[e.g.][]{2016arXiv160305281C}. Recently, evidence for the non-universality of the stellar IMF of the most massive early-type galaxies (ETGs) has begun to mount. This evidence comes from three independent techniques which can probe the IMF in the unresolved stellar populations of ETGs, based on the modelling of stellar kinematics (e.g.~\citealt{2012Natur.484..485C,2013MNRAS.432.2496D,2013ApJ...765....8T}); utilising strong gravitational lensing \citep[e.g.][]{2010ApJ...709.1195T,2010ApJ...721L.163A}; or via gravity-sensitive spectroscopic features in galaxy spectra (e.g.~\citealt{2003MNRAS.339L..12C,2010Natur.468..940V,2012ApJ...760...71C,2013MNRAS.429L..15F}). Stellar kinematic and lensing studies are sensitive to the stellar M/L, and the major uncertainty in such studies relates to the contribution of the dark matter halo to the potential of galaxies. Spectroscopic constraints are mostly sensitive to the ratio between giant and dwarf stars, and its primary uncertainty is degeneracy between the IMF parameters and those of the underlying stellar populations, most notably the effect of variations in the individual elemental abundances. Studies utilising these techniques seem to agree that a variation in the IMF is occurring, with more massive ETGs having heavier IMFs. These studies disagree, however, on what the primary driving mechanism for such a variation is, with some studies favouring galaxy velocity dispersion \citep[e.g.][]{2012Natur.484..485C,2013MNRAS.433.3017L,2015MNRAS.446..493P}, others metallicity \citep[e.g.][]{2015ApJ...806L..31M} or (alpha-)element abundances \citep[e.g.][]{2012ApJ...760...71C}. Some authors have suggested that these studies lack internal consistency, with different analyses of the same objects finding different IMF slopes \citep{2014MNRAS.443L..69S}. The water has muddied further with the discovery that dwarf elliptical galaxies also seem to have non universal IMFs, spanning a similar range of giant galaxies, while having vastly different properties \citep{2015arXiv150908462T}. In this work we introduce a new complementary technique to probe the IMF in galaxies. We use the kinematics of the cold molecular gas reservoirs in massive early-type galaxies to constrain their mass profiles. By combining these profiles with observations of the galaxies' stellar luminosity profile (and stellar population parameters) we are able to derive mass-to-light ratios, and constrain the IMF in a radially resolved manner. Studies of the radial variation of the IMF within individual objects are relatively new (see e.g. \citealt{2015arXiv150908250L,2015MNRAS.452..597Z}), but have significant diagnostic power to determine the astrophysics behind IMF variation. For instance \cite{2015MNRAS.447.1033M} find significant IMF gradients in two massive ETGs, while a lower mass object showed little variation. If confirmed, this could imply that the enhanced fraction of low mass stars causing IMF variation is only present in galaxy bulges which formed violently at high redshift. In Section \ref{sample} of this paper we present details of our sample selection and the properties of the target objects. Section \ref{newdata} details the observation parameters and reduction for the new data used in this work. In Section \ref{method} we present details of the method we use to constrain the IMF. We then present our results in Section \ref{results}, and discuss them in Section \ref{discuss}, before concluding in Section \ref{conclude}. \begin{table*} \caption{Properties of the ETGs included in this study} \begin{tabular*}{0.85\textwidth}{@{\extracolsep{\fill}}l r r r r r r r r} \hline Name & Distance & M$_{Ks}$ & $\sigma_{e}$ & R$_e$ & R$_{\rm max}$/R$_e$ & log$_{10}$(M$_{\rm gas}$/M$_*$) &$\alpha_{\rm dyn}$ (C+12) \\ & (Mpc) & (mag) & (\kms) & (kpc) & & \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8)\\ \hline NGC0524 & 23.3 & -24.71 & 220 & 4.9 & 0.49 & -3.43 & 0.60\\ NGC3607 & 22.2 & -24.74 & 206 & 4.1 & 0.21 & -2.84 & 0.72\\ NGC3665 & 33.1 & -24.92 & 216 & 5.0 & 0.51 & -2.44 & 0.96\\ NGC4429 & 16.5 & -24.32 & 177 & 3.3 & 0.52 & -2.78 & 0.92\\ NGC4459 & 16.1 & -23.89 & 158 & 2.8 & 0.13 & -2.67 & 0.70\\ NGC4526 & 16.4 & -24.62 & 208 & 3.5 & 0.35 & -2.65 & 0.94\\ IC0719 & 29.4 & -22.70 & 128 & 1.8 & 1.11 & -2.29 & $^*$2.06 \\ \hline \end{tabular*} \parbox[t]{0.85\textwidth}{{ \textit{Notes:} Column 1 lists the name of each source. Column 2 to 5 are the distance, $Ks$-band absolute magnitude, velocity dispersion within one effective radius, and effective radius of each object. These are reproduced from \cite{2011MNRAS.413..813C} and \cite{2013MNRAS.432.1709C}. Column 6 contains the ratio of R$_{\rm max}$ (the radius at which the rotation profile becomes flat; these figures taken from \citealt{2014MNRAS.444.3427D}) to the effective radius R$_e$. Column 7 lists the gas fraction (molecular plus atomic) within the inner regions of these objects, as described in \cite{2014MNRAS.444.3427D}. The stellar mass used here is the dynamical mass derived from jeans modelling in \cite{2013MNRAS.432.1709C}. Column 8 contains the $\alpha_{\rm dyn}$ value derived by \cite{2012Natur.484..485C}. A star denotes values of $\alpha_{\rm dyn}$ considered unreliable by \cite{2012Natur.484..485C} due to the presence of strong population gradients.}} \label{proptable} \end{table*} | \label{conclude} In this paper we present the first spatially-resolved study of the IMF in external galaxies derived using a dynamical tracer of the mass-to-light ratio. We do this using molecular gas kinematics in seven early-type galaxies selected from the \atlas\ survey. We compare these measurements to stellar population parameters derived from star formation histories in order to estimate the IMF-mismatch parameter, and shed light on the variation of the IMF within early-type galaxies. We find that the mass-to-light ratio gradients in the inner parts of our target objects are not very strong (independent of the method used to derive them). Several objects do show modest M/L$_{\rm CO}$ gradients, while other have smaller M/L$_{\rm CO}$ variations at individual radii, which relate to specific features in their gas distribution. The objects that do seem to show M/L$_{\rm CO}$ variations are also those with the highest specific star formation rates. The majority of these slight gradients are also present in the stellar population analyses, but not all are. We confirm that the IMF appears to vary when comparing different massive ETGs. Some of our target objects require a light IMF, otherwise their stellar population masses would be greater than their dynamical masses. In contrast, other systems seem to require heavier IMFs to explain their gas kinematics. We find good agreement between our IMF normalisations derived using molecular gas kinematics and those derived by \atlas\ using stellar kinematics. This provides an independent check on the stellar kinematic results, suggesting that if a problem exists in current analyses it is more likely to lie in the stellar population modelling, rather than in the dynamics. We note that this agreement occurs despite our objects being the hardest to model using stellar methods (due to their strong discs of gas and dust). Thus with this technique we can, in principle, extend studies of the IMF normalisation to more gas-rich systems. We do not see strong variation of the IMF normalisation with galaxy dynamical or stellar population properties in this work, either locally or globally. This study allows us to remove potential biases due to aperture effects that were faced by previous studies. By considering the local variations in both IMF and stellar populations we find no evidence for a correlation between IMF and stellar populations, consistent with the weak or absent correlations reported in \cite{2014ApJ...792L..37M}. In this work alone we also do not find a convincing connection between galaxy dynamics and the IMF. Future works of this type will be required to show if the lack of observed correlations is real, or due to low number statistics. In the future larger studies of molecular gas kinematics can help to disentangle the cause of IMF variation. This method provides an independent check on the conclusions of other dynamical methods, and in addition can provide dynamical information on IMF gradients within individual galaxies. Projects such as the CARMA-EDGE survey \citep{2015IAUGA..2257914U} and the MASSIVE survey \citep{2014ApJ...795..158M}, which combine IFU kinematics with resolved molecular gas observations should allow extension of this technique to large samples of galaxies across the Hubble sequence. \vspace{0.5cm} \noindent \textbf | 16 | 9 | 1609.03559 |
1609 | 1609.04465_arXiv.txt | We present photometry and time-series spectroscopy of the nearby type Ia supernova (SN Ia) SN\,2015F over $-16$ days to $+80$ days relative to maximum light, obtained as part of the Public ESO Spectroscopic Survey of Transient Objects (PESSTO). SN\,2015F is a slightly sub-luminous SN Ia with a decline rate of $\dmB=1.35\pm0.03$\,mag, placing it in the region between normal and SN\,1991bg-like events. Our densely-sampled photometric data place tight constraints on the epoch of first light and form of the early-time light curve. The spectra exhibit photospheric \ion{C}{ii} $\lambda 6580$ absorption until $-4$\,days, and high-velocity \ion{Ca}{ii} is particularly strong at $<-10$\,days at expansion velocities of $\simeq$23000\kms. At early times, our spectral modelling with \textsc{syn++} shows strong evidence for iron-peak elements (\ion{Fe}{ii}, \ion{Cr}{ii}, \ion{Ti}{ii}, and \ion{V}{ii}) expanding at velocities $>14000$\kms, suggesting mixing in the outermost layers of the SN ejecta. Although unusual in SN Ia spectra, including \ion{V}{ii} in the modelling significantly improves the spectral fits. Intriguingly, we detect an absorption feature at $\sim$6800\,\AA\ that persists until maximum light. Our favoured explanation for this line is photospheric \ion{Al}{ii}, which has never been claimed before in SNe Ia, although detached high-velocity \ion{C}{ii} material could also be responsible. In both cases the absorbing material seems to be confined to a relatively narrow region in velocity space. The nucleosynthesis of detectable amounts of \ion{Al}{ii} would argue against a low-metallicity white dwarf progenitor. We also show that this 6800\,\AA\ feature is weakly present in other normal SN Ia events, and common in the SN\,1991bg-like sub-class. | \label{sec:introduction} The uniformity of type Ia supernova (SN Ia) light curves allows them to be used as reliable distance indicators, providing crucial evidence for the accelerated expansion of the universe \citep{riess98, perlmutter99}. Despite many years of research and the general agreement that the progenitor stars of SNe Ia are accreting carbon-oxygen (CO) white dwarfs in binary systems, the nature of the companion star \citep{2014ARA&A..52..107M}, and the detailed physics of the explosion, remain uncertain. The study of the outer layers of SN Ia ejecta can, in principle, provide important clues about the progenitor white dwarf and explosion physics by tracing the extent and amount of any unburnt material and the metallicity of the progenitor star \citep{hoflich98, lentz00, walker12, maguire12, foley13, mazzali14}. In particular, early ultraviolet (UV) spectra are sensitive to the abundance of iron-group elements in the outermost layers, and can place important constraints on progenitor metallicity \citep{hachinger13, maguire12, foley13, mazzali14}. Any carbon detected in the outermost layers is particularly important, as carbon is the only element that could not be the result of thermonuclear burning, and can be directly associated with the original composition of the CO white dwarf. The amount and distribution of carbon can place strong constraints on the extension of the burning front and the degree of mixing during the explosion \citep{branch03, thomas07, parrent12}. These outer layers can only be studied with early spectroscopic observations. The unburned material can be detected as absorption lines of \ion{C}{ii} in the optical \citep{parrent11, thomas11b, folatelli12, silverman12, maguire14, cartier14}, and of \ion{C}{i} in the near-infrared \citep[NIR; ][]{hoflich02, marion06, marion09, hsiao13, hsiao15, marion15}. Recent studies have shown that at least 30 per cent of SNe Ia possess \ion{C}{II} absorption lines prior to maximum light \citep{thomas11b, folatelli12, silverman12, maguire14}. Early spectra of SNe Ia also commonly exhibit `high-velocity' (HV) features. These spectroscopic features correspond to absorption lines with expansion velocities much higher than the photospheric velocity, and usually greater than 15000\kms, sometimes reaching 30000\kms\ or higher at the earliest phases. The most common HV features are of \ion{Ca}{II}, which seem to be a ubiquitous phenomenon at early stages \citep{mazzali05, childress14, maguire14, silverman15}. HV features of \ion{Si}{II} are rarer \citep[see][]{marion13, childress13, silverman15}, and HV features of other ions (\ion{S}{II}, \ion{Fe}{II}, \ion{C}{II}, \ion{O}{I}) have also been claimed \citep{fisher97, hatano99, mazzali01, branch03, garavini04, nugent11, marion13, cartier14}. Such high expansion velocities suggest that HV features are produced in the outermost layers of the SN ejecta. Therefore, it is reasonable to hypothesize that their origin is tightly linked to the progenitor system and/or the physics of the burning in the outermost layers of the white dwarf. HV features are ubiquitous in SN Ia spectra at about a week prior to maximum light \citep{mazzali05, marion13, childress14, maguire14, silverman15, zhao15}, and decrease in strength with time \citep{maguire14, silverman15, zhao15}. Possible explanations for HV features include density enhancements from swept-up \citep{gerardy04} or distant \citep{tanaka06} circumstellar material, abundance enhancements in the outermost layers of the ejecta \citep{mazzali05}, or variations of the ionization state in the outer layers due to non `local thermodynamic equilibrium' (LTE) effects \citep{blondin13}. Their origin remains a puzzle. The advent of high-cadence wide-area sky surveys over the last ten years has meant that the quality and quantity of early SN discoveries has increased, and with it has come a wealth of early SN Ia spectroscopy. In this paper, we present spectroscopy and photometry of the nearby SN Ia SN\,2015F. In Section~\ref{observations_sec}, we introduce SN\,2015F and describe the photometry and spectroscopy, beginning at $-16.30$\,d relative to peak brightness and extending to $+75.5$\,d past peak. We also estimate the distance to the host of SN\,2015F (NGC 2442), the rise time, and the epoch of first light. In Section~\ref{analysis_sec}, we analyse the spectroscopic data, and in Section \ref{spec_mod_sec} we model the spectra using the {\sc syn++} code. We discuss our results in Section~\ref{discusion_sec}, and summarize in Section~\ref{conclusions_sec}. Throughout, we assume a value for the Hubble constant of $H_0=70$\,km\,s$^{-1}$\,Mpc$^{-1}$. | \label{discusion_sec} The previous sections have presented a high-quality time-series of spectra and photometry of the nearby type Ia SN\,2015F. Our data make it one of the best observed SNe Ia at early times, and the early spectroscopic coverage have allowed us to study the outer layers of the SN ejecta in detail. In particular, these data provide evidence for either photospheric \ion{Al}{ii} or high-velocity \ion{C}{ii}, as well as iron-peak elements in the outer layers. We discuss these in turn. \subsection{Photospheric Aluminium} \label{sec:aluminium} Our favoured explanation of the $\sim6800$\,\AA\ spectral feature in SN\,2015F is photospheric \ion{Al}{ii} (see Section~\ref{spec_mod_sec}), expanding at a velocity of $\sim 13000$\kms\ (Fig.~\ref{ions_velplot_fig}). The \ion{Al}{ii} material has to be confined in a relatively narrow range of velocity, as the $\sim 6800$\,\AA\ feature does not appear to evolve in velocity over 16 days (Fig.~\ref{cii_velplot_fig}). However, we caution that the feature is quite weak and is affected by telluric absorption; a definitive statement about the velocity evolution is difficult to make. Aluminium in SNe Ia has not been commonly reported in the literature. To our knowledge, the only previous claim was in the peculiar `.Ia' \citep{2007ApJ...662L..95B} candiate SN\,2010X \citep{kasliwal10}. $^{27}$\ion{Al}{} is the only stable aluminium isotope, which according to nucleosynthesis calculations is $\sim 10^{3}$ more abundant than the radioactive $^{26}$\ion{Al}{} isotope \citep{iwamoto99,seitenzahl13}. However, the expected mass fraction of $^{27}$\ion{Al}{} in SNe Ia is relatively low, only $10^{-3}$ to $10^{-2}$ times the total mass of $^{28}$\ion{Si}{} \citep{iwamoto99,seitenzahl13}, the latter being the most abundant silicon isotope in SNe Ia. Given this low predicted abundance of Al, strong \ion{Al}{ii} features seem unexpected. The yield of $^{27}$Al obtained from the W7 \citep{nomoto84} nucleosyntheis models of \citet{iwamoto99}, and the three-dimensional N100 delayed-detonation models of \citet{seitenzahl13}, predict a strong dependence of the abundance of $^{27}$\ion{Al}{} on metallicity. A change from zero to solar metallicity in the progenitor white dwarf produces an increase of an order of magnitude in the yield of $^{27}$Al by mass. As a comparison, the abundances of $^{12}$C and $^{28}$Si remain essentially flat as function of progenitor metallicity. Thus a relatively metal-rich progenitor may help to explain the presence of Al in SN\,2015F. In Section \ref{sec:comp-other-supern} we noted the common presence of the $\sim6800$\,\AA\ feature in SN\,1991bg-like SNe. This class appears to explode in more massive, higher metallicity galaxies; we also note the non-detection of this feature in SN\,2011fe which seems to be the result of a sub-solar metallicity progenitor \citep[see][]{mazzali14}. As SN\,1991bg-like SNe exhibit lower photospheric temperatures than normal SNe Ia, in principle, the presence of the \ion{Al}{ii} lines could be explained by a temperature effect and not as a metallicity effect. However, in the case of SN\,2015F a temperature effect can be ruled out by the simultaneous detection of the $\sim6800$\,\AA\ feature with \ion{Si}{iii} lines, which are a signature of a hot SN ejecta, and are strong at -6\,d and -4\,d (see Section \ref{sec:comparison-with-sn}). \subsection{Carbon material} \label{sec:carbon-material} A second explanation for the $\sim6800$\,\AA\ feature is high-velocity (HV) \ion{C}{II} $\lambda 7234$; photospheric \ion{C}{II} is clearly detected. This suggests that the outermost layers ($\gtrapprox$18000\kms) of SN\,2015F are mostly unburned, consistent with the \citet{mazzali14} model for SN\,2011fe, in which the outermost layers of the SN ejecta (\textgreater$19400$\kms) are unburned, and are composed mainly of carbon. The fact that SN\,2015F has a faster decline rate than SN\,2011fe, and is thus a dimmer/cooler event, suggests a less efficient burning, and perhaps an even larger amount of unburned material in the outer layers than in SN\,2011fe. In recent delayed-detonation models \citep{seitenzahl13}, the outermost layers of the ejecta ($v_{exp}$ \textgreater $20000$ \kms) are mostly composed of carbon and oxygen, and this may explain any HV \ion{C}{ii}. Nevertheless, we do not see a correspondingly strong HV \ion{O}{i} line in SN\,2015F. In \citet{seitenzahl13}, carbon could also be present down to about $10000$\kms, which may explain photospheric \ion{C}{ii} in SN\,2015F \citep[but see also][]{mazzali14}. Under the assumption that the 6800\,\AA\ absorption feature corresponds to HV \ion{C}{ii} $\lambda 7234$, we show its velocity evolution in Figs.~\ref{ions_velplot_fig} and \ref{cii_velplot_fig}. The first spectrum of SN\,2015F has lower signal-to-noise ratio implying a larger uncertainty in the minimum of the feature, located at $\simeq$16900\kms\ ($6828$\,\AA). The feature evolves getting weaker and moving to redder wavelengths with time. We measured the minimum of this absorption feature at phases $<-6$\,d (note the measurement is affected by telluric on the red side; see Fig.~\ref{cii_velplot_fig}), and we show its expansion velocity in Fig.~\ref{ions_velplot_fig}. The feature appears confined to a narrow range in velocity space from $\simeq$18700\kms\ to $\simeq$17000\kms, but is persistent, and is still present in the spectrum at $+2$\,d. The feature is also observed in SN\,2007af at slightly higher velocities until $-4$\,d, and then disappears. The possibility that the HV features of \ion{C}{II} and \ion{Ca}{II} are produced close in velocity space may suggest a common origin for the HV material (see Fig.~\ref{ions_velplot_fig}). HV \ion{Ca}{ii} features exhibit a plateau in their velocity evolution between $-10$ and $-4$\,d (Fig.~\ref{ions_velplot_fig}). At the same phase, the velocity measured for the possible HV \ion{C}{II} $\lambda 7234$ feature is similar, but slightly lower. \subsection{Iron-group elements in SN\,2015F} \label{sec:iron-group-elements} Using \textsc{syn++} to model the spectra of SN\,2015F (see Section~\ref{spec_mod_sec}), we have identified lines of \ion{Ti}{ii}, \ion{V}{ii}, \ion{Cr}{ii}, and \ion{Fe}{II} expanding at $\simeq$14800\kms. This implies a non-negligible amount of iron-group elements in the region between $15000$ to $20000$\kms of the SN ejecta. \citet{hatano99} reported strong \ion{Fe}{ii} absorptions in the $-12$\,d spectrum of SN\,1994D at $\sim$4300 and $\sim$4700\,\AA, and included in their \textsc{synow} model a HV \ion{Fe}{II} component extending from $22000$\kms\ to $29000$\kms, to reproduce these features. Strong and broad lines of iron-peak elements at such high-expansion velocities are generally unexpected in SNe Ia, since the pre-expansion suffered by the layers at higher velocities than $10000$ to $13000$ \kms\ will decrease the density too much to burn the material to iron-peak elements. Only in the case of a rapid transition in the burning speed front, from a sub-sonic deflagration to a super-sonic detonation, would the flame burn the outermost layers ($v_{\mathrm{exp}}$ \textgreater $13000$ \kms) to iron-peak elements, yielding mainly radioactive $^{56}$Ni and not enough IMEs to reproduce the characteristic spectral features of normal SNe Ia. The decay of $^{56}$Ni mixed in the outermost layers can then heat the ejecta, producing strong lines of doubly-ionized species such as \ion{Fe}{iii} and \ion{Si}{iii} as in the brightest SNe. In the earliest spectra of SN\,2015F ($<-12$\,d), this is not observed; by contrast, SN\,2015F exhibits a spectrum dominated mainly by singly-ionized species (\ion{Fe}{ii}, \ion{Si}{ii}, \ion{S}{ii}, \ion{Ca}{ii}), consistent with a normal or relatively low ejecta temperature. At later phases, from about $-11$\,d, SN\,2015F begins to exhibit \ion{Si}{iii} $\lambda 4560$ and \ion{Si}{iii} $\lambda 5540$ lines, now suggesting heating from the decay of radioactive material mixed in the outer layers of the SN ejecta. The absorption features produced by iron-group elements in the very early spectra of SNe Ia could be explained by iron-peak elements synthesized during the SN explosion and mixed to the outermost layers of the SN ejecta, or as absorptions of iron-peak elements present in the white dwarf surface at the moment of the explosion \citep[see][]{lentz00} -- or a combination of both. Recent three-dimensional delayed detonation models predict that freshly synthesized iron-peak elements are located mainly at intermediate velocities \citep[$\sim$3000 to 10000\kms;][]{seitenzahl13}, the latter not corresponding with the observations of SN\,2015F. However, \citet{seitenzahl13} remark that models with a strong (turbulent) deflagration phase, which are rather symmetric under rotation on large scales, exhibit strong inhomogeneities in the burning products on small scales. This may explain pockets of iron-peak material, observed at high-velocity, mixed in the outermost layers as in the case of SN\,2015F. To disentangle the metallicity of the progenitor from the fraction of freshly synthesized iron-group elements mixed to the outermost layers would require a detailed modelling using the abundance tomography technique \citep{stehle05, mazzali05, tanaka11, hachinger13, mazzali14}. This is beyond the scope of this paper, and will be the subject of a future article. % | 16 | 9 | 1609.04465 |
1609 | 1609.08966_arXiv.txt | {Stellar activity and convection-related surface structures might cause bias in planet detection and characterization that use these transits. Surface convection simulations help to quantify the granulation signal.} {We used realistic three-dimensional (3D) radiative hydrodynamical (RHD) simulations from the \textsc{Stagger} grid and synthetic images computed with the radiative transfer code {{\sc Optim3D}} to model the transits of three prototype planets: a hot Jupiter, a hot Neptune, and a terrestrial planet.} {We computed intensity maps from RHD simulations of the Sun and a K-dwarf star at different wavelength bands from optical to far-infrared that cover the range of several ground- and space-based telescopes which observe exoplanet transits. We modeled the transit using synthetic stellar-disk images obtained with a spherical-tile imaging method and emulated the temporal variation of the granulation intensity generating random images covering a granulation time-series of 13.3 hours. We measured the contribution of the stellar granulation on the light curves during the planet transit.} {We identified two types of granulation noise that act simultaneously during the planet transit: (i) the intrinsic change in the granulation pattern with timescale (e.g., 10 minutes for solar-type stars assumed in this work) is smaller than the usual planet transit ($\sim$hours as in our prototype cases), and (ii) the fact that the transiting planet occults isolated regions of the photosphere that differ in local surface brightness as a result of convection-related surface structures. First, we showed that our modeling approach returns granulation timescale fluctuations that are comparable with what has been observed for the Sun. Then, our statistical approach shows that the granulation pattern of solar and K-dwarf-type stars have a non-negligible effect of the light curve depth during the transit, and, consequentially on the determination of the planet transit parameters such as the planet radius (up to 0.90$\%$ and $\sim0.47\%$ for terrestrial and gaseous planets, respectively). We also showed that larger (or smaller) orbital inclination angles with respect to values corresponding to transit at the stellar center display a shallower transit depth and longer ingress and egress times, but also granulation fluctuations that are correlated to the center-to-limb variation: they increase (or decrease) the value of the inclination, which amplifies the fluctuations. The granulation noise appears to be correlated among the different wavelength ranges either in the visible or in the infrared regions.} {The prospects for planet detection and characterization with transiting methods are excellent with access to large amounts of data for stars. The granulation has to be considered as an intrinsic uncertainty (as a result of stellar variability) on the precise measurements of exoplanet transits of planets. The full characterization of the granulation is essential for determining the degree of uncertainty on the planet parameters. In this context, the use of 3D RHD simulations is important to measure the convection-related fluctuations. This can be achieved by performing precise and continuous observations of stellar photometry and radial velocity, as we explained with RHD simulations, before, after, and during the transit periods.} | \begin{table*} \centering \begin{minipage}[t]{\textwidth} \caption{3D RHD simulations from \textsc{Stagger} grid.} % \label{simus} % \centering % \renewcommand{\footnoterule}{} \begin{tabular}{c c c c c c c c c} % \hline\hline % $<T_{\rm{eff}}>$\footnote{Horizontal and temporal average of the emerging effective temperatures from \cite{2013A&A...557A..26M}} & [Fe/H] & $\log g$ & $x,y,z$-dimensions & $x,y,z$-resolution & $\rm{M}_{\star}$ & $\rm{R}_{\star}$ & granule size\footnote{approximate granulation size from \cite{2014arXiv1405.7628M} divided by the stellar radius. See also Fig.~\ref{mu1}} & Number of tiles \footnote{$N_{\rm{tile}} = \frac{\pi \cdot \rm{R}_\star}{x,y\rm{-dimension}}$} \\ $[\rm{K}]$ & & [cgs] & [Mm] & [grid points] & [$\rm{M}_\odot$] & [$\rm{R}_\odot$] & [$10^{-3}$] & over the diameter\\ \hline 5768 (Sun) & 0.0 & 4.4 & 7.76$\times$7.76$\times$5.20 & 240$\times$240$\times$240 & 1.0 & 1.00 & 4.5 & 286\\ 4516 (K~dwarf) & 0.0 & 4.5 & 4.00$\times$4.00$\times$3.17 & 240$\times$240$\times$240 & 0.7\footnote{Fig.~1 of \cite{2013A&A...557A..26M}} & 0.78 & 5.1 & 427\\ \hline\hline % \end{tabular} \end{minipage} \end{table*} Among the different methods used to detect exoplanets, the transit method is a very successful technique: 1147 planets and 3787 transit candidates have been confirmed with it \citep[as of November 2015 from http://exoplanets.org, ][]{2011PASP..123..412W}. A transit event occurs when the planet crosses the line of sight between the star and the observer, thus occulting part of the star. This creates a periodic dip in the brightness of the star. The typical stellar light blocked is $\sim1\%$, 0.1$\%$, and 0.01$\%$ for Jupiter-, Neptune- and Earth-like planets transiting in front of a Sun-like star, respectively \citep{1984Icar...58..121B}, making the detection very challenging, in particular for Earth-like planets. During the transit, the flux decrease is proportional to the squared ratio of planet and stellar radii. For sufficiently bright stars, the mass can also be measured from the host star's radial velocity semi-amplitude \citep{2012A&A...538A...4M}. When the mass and radius of an exoplanet are known, its mean density can also be deduced and provide useful information for the physical formation processes. Today and in the near future, the prospects for planet detection and characterization with the transiting methods are excellent with access to a large amount of data coming, for instance, from the NASA missions Kepler \citep{2010Sci...327..977B} and TESS \citep[Transit Exoplanet Survey Satellite,][]{2010AAS...21545006R}, or from the ESA missions PLATO 2.0 \citep[PLAnetary Transits and Oscillation of stars,][]{2014ExA...tmp...41R} and CHEOPS \citep[CHaracterizing ExOPlanet Satellite, ][]{2013EPJWC..4703005B}. \\ Space- and ground-based telescopes used for transit photometry require high photometric precision to provide accurate planetary radii, masses, and ages. Moreover, transit photometry also needs continuous time series data over an extended period of time. Earth-sized planets are the most challenging targets: if the radius of the Earth is approximately 1/100 that of the Sun, then a transit of the Sun by Earth blocks $\sim10^{-4}$ of the solar flux, in addition to the challenge of the limited number of photons arriving from a faint star. For all these reasons, it is necessary to go to space to monitor the target fields continuously with minimal interruptions.\\ However, with improved photometric precision, additional sources of noise that are due to the presence of stellar surface inhomogeneities such as granulation, will become relevant, and the overall photometric noise will be less and less dominated by pure photon shot noise. The Sun's total irradiance varies on all timescales relevant for transit surveys, from minutes to months \citep{2004A&A...414.1139A}. In particular, granulation analysis of SOHO quiet-Sun data shows that the photometric variability ranges from 10 to 50 part-per-million (ppm) \citep{2002ApJ...575..493J,1997SoPh..170....1F}. The granulation was observed for the first time on the Sun by \cite{1801RSPT...91..265H}, but \cite{1864MNRAS..24..161D} coined the term granules. The granulation pattern is associated with heat transport by convection, on horizontal scales on the order of a thousand kilometers \citep{2009LRSP....6....2N}. The bright areas on the stellar surfaces, the granules, are the locations of upflowing hot plasma, while the dark intergranular lanes are the locations of downflowing cooler plasma. Additionally, the horizontal scale on which radiative cooling drives the convective motions is linked with the granulation diameter \citep{1990A&A...228..155N}. Stellar granulation manifests either on spatially resolved (e.g., images of the solar disk) or unresolved observables such as spectral line profiles in terms of widths, shapes, and strengths. The best observational evidence comes from unresolved spectral lines because they combine important properties such as velocity amplitudes and velocity-intensity correlations, which produce line broadening. This is interpreted as the Doppler shifts arising from the convective flows in the solar photosphere and solar oscillations \citep{2000A&A...359..729A,2009LRSP....6....2N}. Similarly, correlations of velocity and temperature cause characteristic asymmetries of spectral lines as well as net blueshifts for main-sequence stellar types \citep{1987A&A...172..211D,2005oasp.book.....G}. The purpose of this work is to study the impact of stellar granulation on the transit shape and retrieved planetary parameters (e.g., radius). We considered three prototypes of planets with different sizes and transit time lengths corresponding to a hot Jupiter, a hot Neptune, and a terrestrial planet. We used theoretical modeling of stellar atmospheres where the multidimensional radiative hydrodynamic equations are solved and convection emerges naturally. These simulations take surface inhomogeneities (i.e., the granulation pattern) and velocity fields into account in a self-consistent manner. They cover a substantial portion of the Hertzsprung-Russell diagram \citep{2013A&A...557A..26M,2009MmSAI..80..711L,2013ApJ...769...18T}, including the evolutionary phases from the main sequence over the turnoff up to the red giant branch for low-mass stars. \begin{figure} \centering \begin{tabular}{c} \includegraphics[width=0.9\hsize]{images/image_mu_1.0_7500_7700_band7_Sun.ps} \\ \hspace*{-2.96cm} \includegraphics[width=0.45\hsize]{images/image_mu_1.0_7500_7700_band7_Kdwarf.ps} \end{tabular} \caption{Intensity maps computed at [7620-7640] $\AA$ (Table~\ref{wavelengths}) of the 3D RHD simulations of Table~\ref{simus} and for the vertical direction ($\mu=1.0$). The intensity ranges from [$1.56$--$2.76]\times10^6$\,erg\,cm$^{-2}$\,s$^{-1}$\,{\AA}$^{-1}$ for the Sun (top) and from [$0.68$--$1.10]\times10^6$\,erg\,cm$^{-2}$\,s$^{-1}$\,{\AA}$^{-1}$ for the K~dwarf (bottom). The size ratio between the two images corresponds approximatively to the numerical box sizes.} \label{mu1} \end{figure} | We used 3D RHD surface convection simulations with the \textsc{Stagger} code to provide synthetic stellar-disk images to study the background granulation during planet transits of three prototype planets: a hot Jupiter, a hot Neptune, and a terrestrial planet. We analyzed the effect of convection-related surface structures at different wavelengths ranging from the optical region to the far-infrared. These wavelength bands cover the range of several ground- and space-based telescopes observing planet transits and are sensitive to molecules that can give important hints on the planetary atmosphere composition. We modeled the transit light curves using the synthetic stellar-disk images obtained with the spherical-tile imaging method that was previously explained and applied in \cite{2010A&A...524A..93C,2012A&A...540A...5C,2014A&A...567A.115C,2015A&A...576A..13C}. We emulated the temporal variation of the granulation intensity, which is $\sim$10 minutes \citep{2002A&A...396.1003N} for the Sun, generating random images that cover a granulation time-series of 13.3 hours. We used the data (size, flux, and duration of the transit) of three prototype planets with the purpose of studying the resulting noise caused by the granulation on the simulated transits. From the synthetic light curves, our statistical approach shows that the granulation pattern of solar and K-dwarf-type stars have a non-negligible effect on the light-curve depth during the transit for small and large planets. This intrinsic uncertainty affects the determination of the planet transit parameters such as the planet radius (up to 0.90$\%$ and $\sim0.47\%$ for terrestrial and gaseous planets, respectively), particularly for planets with small diameters. The consequences of the granulation noise on the radius are non-negligible. The full characterization of the granulation is essential to determine the degree of uncertainty on the planet parameters. In this context, the use of 3D RHD simulations is important to estimate the amplitude of the convection-related fluctuations. This can be achieved by performing precise and continuous observations of stellar photometry and radial velocity, explained with RHD simulations, before, after, and during the transit periods. We identified two types of noise that act simultaneously during the planet transit: the intrinsic change in the granulation pattern with timescale (e.g., 10 minutes for solar-type stars assumed in this work) is smaller than the usual planet transit ($\sim$hours as in our prototype cases), and the noise caused by transiting planet occulting isolated regions of the photosphere that differ in local surface brightness because of convection-related surface structures. We showed that the RMS caused by the granulation pattern changes in the stellar irradiation during the transit of the terrestrial planet (between 3.5 and 2.7 ppm for the Sun and K~dwarf, respectively) is close to what has been found by \cite{2002ApJ...575..493J} and \cite{1997SoPh..170....1F}: 10 to 50 ppm. This indicates that our modeling approach is reliable. We also showed that different orbital inclination angles with respect to transits at $inc=$90$^{\circ}$ (planet crossing at the stellar center) display a shallower transit depth, and longer ingress and egress times, as expected, but also RMS values correlated to the center-to-limb variation: granulation fluctuations increase for $inc$ different from 90$^\circ$. Finally, the granulation noise appears to be correlated among the different wavelength ranges in the visible and the infrared regions, at least for the spectral resolution used in this work. Three-dimensional RHD simulations are now established as realistic descriptions for the convective photospheres of various classes of stars. They have recently been employed to explain the transit of Venus in 2004 \citep{2015A&A...576A..13C}. Chiavassa and collaborators showed that in terms of transit depth and ingress/egress slopes as well as the emerging flux, a 3D RHD simulation of the Sun is well adapted to interpret the observed data. Their light-curve fit was supported by the fact that the granulation pattern changes would affect transit depth. Modeling the transit light curve of exoplanets is crucial for current and future observations that aim to detect planets and characterize them with this method. The good and time-dependent representation of the background stellar disk is mandatory. In this context, 3D RHD simulations are useful for a detailed quantitative analysis of the transits. | 16 | 9 | 1609.08966 |
1609 | 1609.01595_arXiv.txt | We started a photometric survey using the WFC3/UVIS instrument onboard the Hubble Space Telescope to search for multiple populations within Magellanic Cloud star clusters at various ages. In this paper, we introduce this survey. As first results of this programme, we also present multi-band photometric observations of NGC~121 in different filters taken with the WFC3/UVIS and ACS/WFC instruments. We analyze the colour-magnitude diagram (CMD) of NGC~121, which is the only "classical" globular cluster within the Small Magellanic Cloud. Thereby, we use the pseudo-colour C$_{F336W,F438W,F343N}=(F336W-F438W)-(F438W-F343N)$ to separate populations with different C and N abundances. We show that the red giant branch splits up in two distinct populations when using this colour combination. NGC~121 thus appears to be similar to Galactic globular clusters in hosting multiple populations. The fraction of enriched stars (N rich, C poor) in NGC~121 is about 32\%$\pm$3\%, which is lower than the median fraction found in Milky Way globular clusters. The enriched population seems to be more centrally concentrated compared to the primordial one. These results are consistent with the recent results by Dalessandro et al. (2016). The morphology of the Horizontal Branch in a CMD using the optical filters $F555W$ and $F814W$ is best produced by a population with a spread in Helium of $\Delta Y$=0.025$\pm$0.005. | \label{sec:intro} A nearly ubiquitous property of ancient globular clusters (GCs) so far studied is that they host multiple populations in the form of internal chemical abundance variations in light elements \citep[see e.g.][for a review]{Gratton12}. So far, Ruprecht 106 and IC~4499 seem to be the only exceptions (see \citealt{Villanova13} and \citealt{Walker11}). Interestingly, these variations, which are not observed among field stars of the same metallicity, show correlated patterns in certain elements, e.g. the prominent Na-O anti-correlation \citep[e.g.][]{Carretta09} or the C-N anti-correlation \citep[e.g.][]{Cannon98}. These chemical anomalies are not only detected in Milky Way GCs but also in old clusters in nearby dwarf galaxies, like in the Fornax dwarf spheroidal galaxy \citep{Larsen14}, the Sagittarius dwarf galaxy \citep{Carretta10a, Carretta14} or the Large Magellanic Cloud \citep[LMC,][]{Mucciarelli09}. The Na-O and C-N anti-correlations are ideal tracers of the multiple populations in GCs. These can be detected by spectroscopic analysis of individual stars in a cluster \citep[e.g.][]{Carretta09, Carretta15, Marino16} down to the main sequence \citep[e.g.][]{Harbeck03, D'Orazi10}. \citet{Marino08} in their study of the GC M4, combined spectroscopic and photometric data and showed that there is a direct relation between the broadening of the red giant branch (RGB) in the colour-magnitude diagram (CMD) and the spectroscopically determined populations with varying Na and O abundances (see \citealt{Dalessandro14} and \citealt{Mucciarelli16} for a similar study on NGC~6362). The different element abundances within the stars influence the colour of the stars in certain filter bands and can therefore result in a broadening or splitting of the various stellar evolutionary stages in the CMD, like the RGB, sub-giant branch (SGB) and the main sequence (MS). With the photometric precision of the Hubble Space Telescope (HST) combined with the usage of ultraviolet filters it is possible to trace the multiple populations throughout the entire CMD down to the lowest magnitudes \citep[e.g.][]{Milone15a, Piotto15}. As multiple populations are even observed along main sequence stars indicates that the formation mechanism must have acted already at early stages of the cluster's life. As the observed multiple populations clearly contradict our view of star clusters as simple stellar populations, several scenarios have been put forward to explain this phenomenon in recent years. Most of them involve the formation of more than one generation of stars where the younger stars form out of a mix of pristine gas and the enriched ejected material from stars of the older generations. The different scenarios propose various types of polluter stars: interacting massive binaries \citep{deMink09}, fast rotating massive stars \citep[e.g.][]{Decressin09, Krause13} and asymptotic giant branch (AGB) stars \citep[e.g.][]{D'Ercole08}. Alternatively, \citet{Bastian13a} proposed the early disk accretion scenario where the accretion disks of low-mass pre-MS stars sweep up enriched material ejected by rotating massive stars of the same generation. However, all proposed scenarios have severe difficulties accounting for the breadth of observations \citep[see e.g.][]{Bastian15a, Renzini15}. In order to produce the observed anti-correlations in certain elements and the fraction of enriched stars, the GCs must have been at least one order of magnitude more massive at birth in scenarios invoking multiple star formation epochs \citep[e.g.][]{D'Ercole08, Bekki11}. This is referred to as the "mass-budget problem" (see e.g. \citealt{Larsen12}, \citealt{BastianLardo15} and \citealt{Cabrera-Ziri15} for a discussion). Additionally, none of the proposed sources of enriched material is able to reproduce consistently the extent of the observed abundance patterns in GCs \citep{Bastian15b}. As the proposed theories do not require any specific conditions for the formation of multiple populations, they should also be present in younger clusters with comparable observed properties to ancient GCs. Several studies aimed to find indications of multiple populations or multiple star formation events in such clusters. However, up to now no clear evidence is found for either of these indicators in young clusters. \citet{Bastian13b} did not detect any signs of ongoing star formation in a sample of 130 massive ($10^4$ - $10^8$~M$_{\sun}$) clusters with ages between 10~Myr and 1~Gyr. Also numerous searches for age spreads in extragalactic young massive clusters remain without any detection \citep[e.g.][]{Larsen11, BastianSilvaVilla13, Cabrera-Ziri14, Niederhofer15, Cabrera-Ziri16a}. In order to form a second generation of stars, a cluster either has to retain gas that is left over from the first star formation event or (re-)accrete fresh gas from its surroundings. But young clusters seem to remove the gas very efficiently already at young ages \citep[e.g.][]{Bastian14, Hollyhead15} and no clusters have been detected with an associated gas reservoir sufficient for a subsequent period of star formation \citep[e.g.][]{Cabrera-Ziri15, BastianStrader14, Longmore15} In a series of papers, \citet{Mucciarelli08, Mucciarelli11, Mucciarelli14} spectroscopically studied RGB stars in the intermediate-age (1-3~Gyr) LMC clusters NGC 1651, NGC~1783, NGC~2173, NGC~1978 and NGC~1806, as well as in the $\sim$200~Myr old cluster NGC~1866, in large part motivated by the search for multiple populations. Among their sample of stars they did not detect any significant spread in light element abundances. \citet{Davies09} analyzed two Scutum Red Supergiant Clusters in the Milky Way, RSGC1 and RSGC2 ($\sim$2$\times$10$^4$~M$_{\sun}$) and found that they are chemically homogeneous. Similarly, \citet{Cabrera-Ziri16b} found that the young ($\sim$15~Myr) massive ($\sim$10$^6$~M$_{\sun}$) cluster NGC~1705:~1 shows [Al/Fe] abundances comparable to those of Small Magellanic Cloud (SMC) field red supergiant stars at the same metallicity, while an Al enhancement is generally observed in GCs showing multiple populations, although the authors could not rule out that small Al spreads were present. The above-mentioned results challenge the interpretation that young massive clusters form the same way as GCs and may suggest that correlated anomalies in light elements are exclusively found in old GCs. However, due to the still small number of studies the hypothesis that young massive clusters are real counterparts of ancient GCs can not conclusively be discarded. We recently started a photometric survey of star clusters spanning a wide range of masses and ages within the Magellanic Clouds using the HST WFC3/UVIS instrument. This survey will help to answer the open question as to whether the age or the mass of a cluster is the critical parameter that determines if a cluster can host multiple populations. We included in our sample also NGC~121, the only "classical" GC in the SMC with an age $>$10~Gyr \citep{Glatt08a} as a benchmark object to test our methods. Note that, although NGC~121 is indeed the oldest SMC cluster, its age of about 10.5~Gyr is substantially younger than that of typical Milky Way or LMC globulars. In this paper, we report on the ability of the combination of the $F336W$, $F343N$, and $F438W$ filters to separate populations with different chemical abundances in the CMD. Furthermore, we apply our method to NGC~121 which is shown to host multiple populations as well \citep{Dalessandro16}. The paper is structured as follows: In $\S$ \ref{sec:survey} we introduce our survey of Magellanic Cloud clusters. We describe the observations of NGC~121 and the data reduction procedure in $\S$ \ref{sec:obs}. The analysis of the data and the results are shown in $\S$ \ref{sec:analysis}. In $\S$ \ref{sec:conclusions} we discuss our results and draw final conclusion. | \label{sec:conclusions} Using a combination of three blue/ultraviolet filters we were able to detect two distinct stellar populations in the RGB of the SMC cluster NGC~121 (however, more populations might be present). The brighter/bluer sequence corresponds to a population with a pristine chemical abundance whereas the fainter/redder sequence is composed of chemically enriched stars. Our findings are in agreement with the recent results by \citet{Dalessandro16}. They found that the RGB is broader than expected from photometric errors in the $m_{F336W}$ vs $m_{F336W}-m_{F438W}$ CMD. Using a combination of the filters $F336W$, $F438W$ and $F814W$, they detected a splitting in the RGB, as well. We find that the fraction of the second population stars is 32\%, consistent with the results from \citet{Dalessandro16} who found a fraction of enriched stars of 35\%, , using the pseudo-color $C_{F336W,F438W,F814W}$. This, however, is much smaller than the expected median value found in Galactic GCs. \citet{BastianLardo15} collected a sample of 33 GCs and found that the fraction of enriched stars is never smaller than 50\% with median value of 68\%$\pm$7\%. Moreover, this fraction seems to be independent of the cluster mass, metallicity or distance to the centre of the Galaxy. The data set presented in this study is mainly based on spectroscopic data that only probe the outer regions of the clusters. Thus, the result refers to the fraction measured at larger radii. Given our results, the fraction of enriched stars appears to vary from cluster to cluster, much more than reported by \citet{BastianLardo15}. This is consistent with the results of Lardo et al. (in prep.) who found larger variations in Galactic GCs using photometric surveys. Their data are based on much larger statistical samples of stars within individual clusters and also sample the inner regions of GCs. The data sets of \citet{BastianLardo15} and Lardo et al. (in prep.) therefore sample different regions of clusters with different properties and possibly varying ratios of first and second population stars. Even though the relative number of enriched stars we find in NGC~121 is low, it is still in tension with scenarios that invoke strong cluster mass loss to go from initial fractions of enriched stars of $\sim$5\% to higher values by preferentially removing stars with primordial chemical composition. If we assume that only first population stars have been removed it follows that NGC~121 must have lost $\sim$90\% of its initial mass in order to get to the observed fraction of 32\% enriched stars. This is, however, only a lower limit as we assume that only stars with a primordial composition have been lost. This high number, however, seems to be unlikely given the weak tidal field of the SMC and the present-day mass of NGC~121 (log(M/M$_{\sun}$)=5.57, \citealt{McLaughlin05}). It is expected that the time it takes to dissolve a star cluster is longer for more massive clusters and in weaker tidal fields \citep[see e.g.][and references therein, for a discussion]{BastianLardo15}. Quite extreme assumptions have to be made for the cluster and its environment in order to allow for such high dissolution rates (see \citealt{D'Ercole08}). Such high cluster dissolution rates are also in tension with observations of the Fornax Dwarf Spheroidal galaxy \citep{Larsen12}. In contrast, \citet{Kruijssen15} showed in his model for the origin and evolution of GCs that typically, GCs could have only been, on average, at the most a factor of three more massive at birth. Additionally, we analyzed the radial distribution of the two populations. We found that up to a radius of 300 pixels (12$\arcsec$), which is approximately the core radius of NGC~121, the two populations are distributed the same. Only at larger distances, the second population stars seem to be more centrally concentrated than the primordial stars. In the self enrichment scenario where a second generation of stars forms within a cluster out of a mixture of processed stellar material and pristine gas, it would be expected that this second generation is formed in the centre of the cluster as the gas densities are highest there. A more centrally concentrated second population would be in agreement with the prediction from this scenario. Other studies from the literature do not provide definitive answers regarding the relative radial distributions of populations in different clusters. Using ground-based photometry or spectroscopy measurements, the enriched populations are generally found to be more concentrated \citep[e.g.][]{Carretta10b, Beccari13, Larsen14, Li14}. But due to the crowding in the inner regions these studies usually avoid the central parts of the clusters. Recently, \citet{Larsen15} analyzed the GC M15 using HST/WFC3 data and found that stars with primordial chemical composition are more centrally concentrated than stars with enhanced N abundances, taking also the central parts of the cluster into account. This trend, however, seems to invert at larger radii \citep{Lardo11}. \citet{Dalessandro11} studied the radial distributions of the two populations found in the SGB and the RGB of NGC~6362, but did not find any significant difference along the two populations across the extent of the cluster. Similarly, \citet{Nardiello15} found that the populations of the red and blue MS in the two GCs NGC~6752 and NGC~6121 (M4) show no difference in their radial distributions. The results in this paper along with the findings of \citet{Dalessandro16} add the SMC to the list of galaxies (including the Milky Way, e.g. \citealt{Gratton12}, the LMC, \citealt{Mucciarelli09} and the Fornax dwarf spheroidal galaxy, \citealt{Larsen14}) harbouring a GC with multiple populations. Therefore, it appears that this is a ubiquitous property of old GCs independent of environment or galaxy type. However, it is not clear yet what parameter controls whether a star cluster is able to host multiple populations. The scenarios that invoke self-enrichment and multiple episodes of star formation require the clusters to have high masses at birth in order to retain the processed stellar ejecta. As NGC~121 is relatively young, compared to Milky Way GCs, formation scenarios that include Pop III stars can already be ruled out. In forthcoming papers we will continue the study of a variety of massive clusters with a range of different ages and masses within the Magellanic Clouds aiming to constrain the parameter that is responsible for the formation of multiple populations in star clusters. In the present work, we introduced an ongoing photometric survey using the HST searching for multiple populations in LMC/SMC clusters spanning a large range of ages. We presented, as first results of this survey, the detection of two populations in the RGB of the 10.5~Gyr old SMC cluster NGC~121 as well as evidence of an He spread from the morphology of its HB. In the future, our survey will be capable to provide important observational constraints on the origin of multiple populations by helping to constrain the range of ages and/or masses where they are present. | 16 | 9 | 1609.01595 |
1609 | 1609.01130_arXiv.txt | The dynamics of colliding wind binary systems and conditions for efficient particle acceleration therein have attracted multiple numerical studies in the recent years. These numerical models seek an explanation of the thermal and non-thermal emission of these systems as seen by observations. In the non-thermal regime, radio and X-ray emission is observed for several of these colliding-wind binaries, while gamma-ray emission has so far only been found in $\eta$ Carinae and possibly in WR 11. Energetic electrons are deemed responsible for a large fraction of the observed high-energy photons in these systems. Only in the gamma-ray regime there might be, depending on the properties of the stars, a significant contribution of emission from neutral pion decay. Thus, studying the emission from colliding-wind binaries requires detailed models of the acceleration and propagation of energetic electrons. This in turn requires a detailed understanding of the magnetic field, which will not only affect the energy losses of the electrons but in case of synchrotron emission also the directional dependence of the emissivity. In this study we investigate magnetohydrodynamic simulations of different colliding wind binary systems with magnetic fields that are strong enough to have a significant effect on the winds. Such strong fields require a detailed treatment of the near-star wind acceleration zone. We show the implementation of such simulations and discuss results that demonstrate the effect of the magnetic field on the structure of the wind collision region. | Massive, luminous stars of spectral type O and B and also Wolf-Rayet (WR) stars are known to drive mass-loaded and fast stellar winds. In systems containing two such luminous stars the supersonic winds interact with each other, thereby forming a wind-collision region (WCR) enclosed by two strong shock waves \citep[see, e.g.][]{Usov1992ApJ389_635}. These shocks have the potential to accelerate particles to sufficiently high energies that the WCR becomes visible in non-thermal radiation \citep[see, e.g.,][]{EichlerUsov1993ApJ402_271,DoughertyWilliams2000MNRAS319_1005, DoughertyEtAl2003AnA409_217, NiemelaEtAl1998AJ115_2047}. The relevant emission channels of non-thermal radiation are synchrotron emission in the radio regime \citep[see, e.g.,][]{DoughertyEtAl2005ApJ623_447,WilliamsEtAl1997MNRAS289_10,Pittard2010MNRAS403_1633}, inverse Compton emission in the X-ray regime \citep[see, e.g.][]{PittardEtAl2010MNRAS403_1657} and both inverse Compton and pion decay processes at higher energies \citep[see, e.g.][]{BenagliaRomero2003AnA399_1121,ReimerEtAl2006ApJ644_1118,ReitbergerEtAl2014ApJ789_87}. For an overview of observations of colliding-wind binaries (CWBs) at different energies see \citet{DeBecker2013AnA558A_28}. Apparently, a large fraction of the non-thermal photons result from energy-loss processes of electrons accelerated at the shock fronts. The acceleration and energy losses of these electrons strongly depend on the strength and direction of the magnetic field in and near the WCR. The majority of the recent modeling efforts, however, was based on hydrodynamical modeling of the interacting stellar winds. In these cases, the magnetic field was prescribed analytically: \citet{DoughertyEtAl2003AnA409_217,PittardDougherty2006MNRAS372_801} assumed the magnetic energy density to be proportional to the thermal pressure, while \citet{ReitbergerEtAl2014ApJ782_96,ReitbergerEtAl2014ApJ789_87} used an analytical description for the magnetic field from each individual star. Such prescriptions, however, are rather simplified. Apart from that, no direction of the magnetic field can be inferred from these approaches. Thus, neither an acceleration efficiency depending on the obliquity of the shocks nor a consistent treatment of the polarization of synchrotron emission can be taken into account. \citet{FalcetaGoncalvesAbraham2012MNRAS423_1562} introduced the first magnetohydrodynamical models of a CWB system. In these simulations, a dipole field with a polar field strength of $B \sim 10^{-4}$ Tesla for each star was prescribed, and the magnetic field in the stellar wind plasma was evolved consistently in time. Such a comparatively weak field is transported passively with the flow of the stellar winds without having a relevant back reaction on the wind evolution. Observations, however, indicate that magnetic fields of early type stars might be significantly stronger than that \citep[see, e.g.,][]{AuriereEtAl2007AnA475_1053,PetitEtAl2013MNRAS429_398,ChevrotiereEtAl2014ApJ781_73, FossatiEtAl2015AnA574A_20,FossatiEtAl2015AnA582A_45,WadeEtAl2016MNRAS456_2}. However, there is also a wide range of stars for which only upper limits could be determined. With regard to stars in particle-accelerating CWB systems no such strong fields have been observed, yet. For several such systems \citet{NeinerEtAl2015AnA575A_66} find upper limits for the polar magnetic-field strength on the order of 0.02 Tesla. This discussion shows that it is certainly worthwhile to investigate CWB systems with polar magnetic fields stronger than $\sim10^{-4}$ Tesla. In this case the change of the stellar wind outflow due to the presence of the magnetic field has to be taken into account. This is particularly important for the acceleration region of the wind near the stellar surface. Correspondingly, we investigate magnetohydrodynamical models of such systems with surface magnetic fields on the order of 0.01 Tesla. For this we introduce a multi-step procedure that assures the consistent treatment of magnetic field and wind acceleration near the stellar surface. In the next section we present this method together with the description of the numerical model used in this study. In Sec. \ref{SecResults} we then discuss the results and implications of our study of a range of models of magnetized CWBs. Finally, we summarize our findings in Sec. \ref{SecConclusion}. | \label{SecConclusion} In this study we detailed a numerical method for the investigation of colliding-wind binary systems that are subject to sufficiently strong stellar magnetic fields such that the structure of the stellar wind outflows is clearly affected by the presence of these fields. Our method is a multi-step process, where we first make sure that the wind acceleration near the stellar surface is consistently simulated by performing near-star simulations for each star individually. These simulations are then injected into a large-scale simulation of the colliding-wind binary system. For the magnetic field strengths investigated in this paper we found a significant impact on the structure of the WCR when the polar field strengths of the B star yields a magnetic confinement parameter $\eta > 0.1$. For stronger fields a nose-like structure emerges at the WCR connected to the higher mass-loss rate near the magnetic equator of the B star. This nose structure -- that becomes ever sharper with increasing strength of the surface magnetic field of the B star -- is unstable and decays, leaving one side of the WCR in a turbulent state. Apparently, this affects mainly the contact discontinuity, leaving the shock fronts mostly undisturbed -- at least for the simulations with stellar separation smaller than 2880\,$R_{\Sun}$. This disturbance only becomes relevant, when the dipole axis of the B-star is normal to the line of centers between the stars. Thus, the specific setups of the dipole axes are very important for the structure of the WCR. Together with the dynamics of such a system, this might lead to WCRs becoming more turbulent during short episodes of the stellar orbit. In this study we only investigated a limited amount of configurations. Especially for magnetic fields near or even exceeding a magnetic confinement parameter $\eta\ge 1$, considerably higher spatial resolution will be necessary to be able to study the impact of the ever thinner region with increased mass loss around the magnetic equator. Thus, the present study is only a starting point showing that the impact of the presence of the magnetic field is very relevant and should be taken into account in future investigations. Apart from the impact of the magnetic field on the structure of the WCR also the direction of the magnetic field relative to the shock fronts is relevant for particle acceleration. We show the first analysis of the obliqueness of the shocks in the WCR. The most important parameter in this context is the stellar separation, where in our model an increasing separation leads to a larger region where the shock is quasi parallel. However, stronger turbulence in the WCR can also have an effect on the shock-fronts possibly leading to very localized and dynamical changes in shock obliqueness. This might only be revealed in higher-resolution simulations. Such an analysis of the shock obliqueness allows for a consideration of different acceleration efficiencies in future simulations of particle acceleration in magnetized colliding-wind binaries. This also shows the importance of a correct treatment of the magnetic field in the interpretation of observed high-energy emission patterns from these binary systems. | 16 | 9 | 1609.01130 |
1609 | 1609.03135_arXiv.txt | We present high resolution numerical simulations of the colliding wind system $\eta$ Carinae, showing accretion onto the secondary star close to periastron passage. Our hydrodynamical simulations include self gravity and radiative cooling. The smooth stellar winds collide and develop instabilities, mainly the non-linear thin shell instability, and form filaments and clumps. We find that a few days before periastron passage the dense filaments and clumps flow towards the secondary as a result of its gravitational attraction, and reach the zone where we inject the secondary wind. We run our simulations for the conventional stellar masses, $M_1=120 \rmModot$ and $M_2=30 \rmModot$, and for a high mass model, $M_1=170 \rmModot$ and $M_2=80 \rmModot$, that was proposed to better fit the history of giant eruptions. As expected, the simulations results show that the accretion processes is more pronounced for a more massive secondary star. | \label{sec:intro} The binary system $\eta$ Carinae is composed of a very massive star, hereafter -- the primary (\citealt{Damineli1996, DavidsonHumphreys1997}) and a hotter and less luminous evolved main sequence star (hereafter -- the secondary). The system is unique in several aspects, such as a highly eccentric orbit (\citealt{Daminelietal1997}; \citealt{Smithetal2004}), and strong winds (\citealt{PittardCorcoran2002}; \citealt{Akashietal2006}), that together leads to a strong interaction every 5.54 years during periastron passage, known as the spectroscopic event. During the event many bands and spectral lines show fast variability (e.g., \citealt{Smithetal2000}; \citealt{DuncanWhite2003}; \citealt{Whitelocketal2004}; \citealt{Stahletal2005}; \citealt{Nielsenetal2007}, \citealt{Daminelietal2008a},\citeyear{Daminelietal2008b}; \citealt{Martinetal2010}; \citealt{Mehneretal2010},\citeyear{Mehneretal2011},\citeyear{Mehneretal2015}; \citealt{Davidson2012}; \citealt{Hamaguchietal2007},\citeyear{Hamaguchietal2016}), and the x-ray intensity drops for a duration of a few weeks (\citealt{Corcoranetal2015} and references therein). Observations of spectral lines across the 2014.6 event indicate weaker accretion onto the secondary close to periastron passage compared to previous events, hinting at a decrease in the mass-loss rate from the primary star \citep{Mehneretal2015}. \cite{Soker2005b} suggested that clumps of size of $>0.1$ per cent the binary separation will be accreted onto the secondary near periastron passages. Accretion was then used to model the spectroscopic events (\citealt{Akashietal2006}; \citealt{KashiSoker2009a}). \cite{KashiSoker2009b} performed a more detailed calculation, integrating over time and volume of the density within the Bondi-Hoyle-Lyttleton accretion radius around the secondary, and found that accretion should take place close to periastron and the secondary should accrete $\sim 2 \times 10^{-6} \rmModot$ each cycle. Other papers referred to a ``collapse'' of the colliding winds region at the spectroscopic event. This term remained ambiguous since it was first suggested by \cite{Daminelietal2008a}, and could be interpreted either as accretion, shell-ejection event \citep{Falcetaetal2005}, or other possibilities (see \citealt{Teodoroetal2012}). \cite{Parkinetal2009} did however consider a collapse on to the surface of the secondary star, and developed a model that gives accretion of $\sim 7 \times 10^{-8} \rmModot$ per cycle. \cite{Parkinetal2011} performed AMR simulations of the colliding winds, but did not obtain accretion. However, when performing stationary colliding winds simulations at the time of periastron, their results showed unstable wind, mainly as a result of the non-linear thin shell instability \citep{Vishniac1994}, and clumps were formed and reached up to a very close distance from the secondary. They also suggested that obtaining clumps that fall towards the secondary is resolution-dependent. \cite{Akashietal2013} conducted 3D hydrodynamical numerical simulations using the \texttt{VH-1} code to study accretion in $\eta$ Car. They found that a few days before periastron passage clumps of gas are formed due to instabilities in the colliding winds structure, and some of these clumps flow towards the secondary. The clumps came as close as one grid cell from the secondary wind injection zone, implying accretion. In their simulations, however, although the gravity of the secondary star was included, self-gravity of the wind was not included, and the resolution was too low to see the accretion itself. \cite{Maduraetal2013} used SPH simulation to model the colliding winds. Though suggesting that a collapse may occur, their results never showed any collapse or accretion. Recent numerical simulation of the periastron passages (e.g., \citealt{Maduraetal2015}; \citealt{Clementeletal2015a}, \citeyear{Clementeletal2015b}) were interested in other aspects, and did not find accretion to take place near periastron passages. In this work we take a step forward, and use one of the best numerical tools available and run advances simulations in order to test whether accretion takes place, and to what extent. In section \ref{sec:simulation} we describe the numerical simulation. Our results, showing accretion, are presented in section \ref{sec:results} followed by a summary and discussion in section \ref{sec:summary}. | \label{sec:summary} We performed detailed \texttt{FLASH} simulations of the \etc colliding winds system close to periastron passage. The colliding wind region is prone to instabilities that lead to a non-linear formation of clumps and filaments that were accreted onto the secondary star. The formation of filaments and clumps can occur without self-gravity, as a result of e.g., thermal instability. The free-fall (collapse) time of each clump as a result of self-gravity is much longer than the duration of the clump formation, indicating self-gravity does not have a significant role in the formation of the clumps. Comparing to the simulations of \cite{Akashietal2013} we get a more clumpy flow. This is a result of better resolution and modeling of radiative cooling. It is important to emphasize that solving the colliding winds and accretion problem requires high resolution to resolve the colliding wind structure and the clumps that form and then flow towards the accretor (the secondary star in our case). A delicate treatment of the runaway numerical cooling is essential, otherwise there is a risk of a runaway cooling (see section \ref{sec:simulation}). The periastron-accretion model advocates for the formation of dense blobs (clumps) in the post-shock primary wind layer of the winds colliding region \citep{Soker2005a, Soker2005b}. Based on these early suggestions, there have been a few interpretations of observations of spectral lines accross the periastron passage of \etc as being emitted or absorbed by blobs in the winds colliding region, (e.g, \citealt{KashiSoker2009c}; \citealt{Richardsonetal2016}). Our simulations confirmed that the dense clumps are crucial to the onset of the accretion process. X-ray observations of \etc show flares each cycle when the two stars approach to periastron passage (\citealt{Davidson2002}; \citealt{Corcoran2005}; \citealt{Corcoranetal2010},\citeyear{Corcoranetal2015}). \cite{MoffatCorcoran2009} suggested that the flares are the result of that clump formation in the post-shocked primary wind, interacting with the colliding winds region, and compressing the hot gas in the post-shocked secondary wind. We find that accretion occurs even for smooth primary (and secondary) wind, without creating artificial clumps numerically. The colliding winds region is compressed in some regions by the instabilities, and that may be the cause for the flares. Seeding clumps in the primary wind would have also made accretion occur easier. However, we showed here that even for `rough' conditions -- smooth primary wind and no artificial shut-down of the secondary wind -- accretion does occur. Accretion is obtained both for the high mass model $(M_1,M_2)=(170 \rmModot, 80 \rmModot)$ and the conventional mass model $(M_1,M_2)=(120 \rmModot, 30 \rmModot)$. For the high mass model it is easier to obtain accretion, as the stronger secondary gravity attracts the clumps more easily, and does not let the secondary wind drive them away. We note that had we turned off the secondary wind in response to clumps reaching the secondary wind injection cells, accretion rate would have increased, until long after periastron passage. As the orbital separation increases, accretion rate decreases \citep{KashiSoker2009b}, and the secondary wind is expected to resume. Since accretion occurs for the parameters present-day \etc, it let alone occurred during the 1840's Great Eruption, when the mass loss rate from the primary was larger by orders of magnitude. The results therefore strengthen the accretion model for the Great Eruption (\citealt{Soker2001,KashiSoker2010}). When running preliminary further simulations for the conventional mass model, we found that from the beginning of the accretion phase, up to 50 days after periastron $\approx 10^{-7} \rmModot$ reach the injection zone of the secondary wind. The amount of mass that is accreted is difficult to estimate, as it requires \emph{modeling} the response of the secondary to the mass that is being accreted. Specifically, how the secondary wind is affected by accretion. The number stated above for the accreted mass was derived assuming minimal response. Obviously, as we know from observations that the x-ray radiation shuts down, this means that the secondary wind is reduced significantly. We would therefore expect the accreted mass to be larger than the value above, and possibly closer to the results of \cite{KashiSoker2009b}. In this paper, however, we do not assume anything about the response of the secondary to accretion, and present pure hydrodynamical results which by themselves show that accretion does occur. In a future paper we intend to use simulations to model the response of the secondary to the gas accreted onto it. Doing so will allow us to quantify the accreted mass, and its dependence on the primary mass loss rate and other parameters. This will hopefully lead to a better understanding of observations of \etc during the spectroscopic event, and the differences between the last events. | 16 | 9 | 1609.03135 |
1609 | 1609.07136_arXiv.txt | In recent work done by \citeauthor{2014ApJ...792...54S}, the color variation of quasars, namely the bluer-when-brighter trend, was found to be timescale-dependent using SDSS $g/r$ band light curves in the Stripe 82. Such timescale dependence, i.e., bluer variation at shorter timescales, supports the thermal fluctuation origin of the UV/optical variation in quasars, and can be well modeled with the inhomogeneous accretion disk model. In this paper, we extend the study to much shorter wavelengths in the rest frame (down to extreme UV), using {\it GALaxy Evolution eXplorer} (\GALEX) photometric data of quasars collected in two ultraviolet bands (near-UV and far-UV). We develop Monte-Carlo simulations to correct possible biases due to the considerably larger photometric uncertainties in \GALEX{} light curves (particularly in far-UV, comparing with SDSS $g/r$ bands), which otherwise could produce artificial results. We securely confirm the previously discovered timescale dependence of the color variability with independent datasets and at shorter wavelengths. We further find the slope of the correlation between the amplitude of color variation and timescale however appears even steeper than that predicted by the inhomogeneous disk model, which assumes that disk fluctuations follow damped random walk process. In line with the much flatter structure function observed in far-UV comparing with that at longer wavelengths, this implies deviation from DRW process in the inner disk where rest frame extreme UV radiation is produced. | \label{sect:intro} As a defining feature of quasars and active galactic nuclei (AGNs), variability starts to gain more attention because it holds otherwise inaccessible information of them. The energy source of these shinning sources is widely accepted to be dominated by the thermal radiation from the accretion disk \citep{1973A&A....24..337S}. As suggested by the reverberation mapping projects \citep{2004ApJ...613..682P}, variability should be traced back to the inner parts of AGNs, including the accretion disk, which contributes optical and UV photons, and the presumed corona, which dominates over the X-ray band. The corona is generally assumed to work as a light bulb above the disk and modulates radiation from the disk, encoding information about sizes and distances in the form of time lags between light curves in different photometric bands. This is the famous X-ray reprocessing model \citep{1991ApJ...371..541K}, and has been tested in great details with nearby Seyferts \citep{2005ApJ...622..129S,2014MNRAS.444.1469M,2015ApJ...806..129E,2016ApJ...821...56F,2016MNRAS.456.4040T}. The correlation analysis of inter-bands (X-ray/UV/optical) light curves typically results in lags less than a few days (for a short review, see \citealt{2012MNRAS.423..451L}), likely corresponding to light travel time. However, it should be kept in mind that X-ray only contributes to a small fraction of AGNs' total bolometric luminosity, especially for brighter ones \citep{2005AJ....130..387S,2010A&A...512A..34L,2010ApJS..187...64G}, thus could be insufficient to produce the observed UV/optical variation \citep{2008RMxAC..32....1G}. Different mechanisms are involved to explain the observed UV/optical variation in AGNs. These include changes in global accretion rates \citep{2006ApJ...642...87P,2008MNRAS.387L..41L,2011ApJ...731...50S,2012ApJ...758..104Z,2013A&A...554A..51G}, and the instability of the accretion disk \citep{1998ApJ...504..671K,2003MNRAS.342.1222C,2013A&A...560A.104M} with large temperature fluctuations \citep{2011ApJ...727L..24D,2012ApJ...744..147S,2014ApJ...783..105R,2014ApJ...792...54S}. Recent progresses on the UV/optical variability of AGNs show that it can be modeled by damped random walk (DRW) process \citep{2009ApJ...698..895K,2010ApJ...708..927K,2010ApJ...721.1014M,2013ApJ...765..106Z} or even more complicated ARMA (autoregressive moving average) model \citep{2014ApJ...788...33K}. Furthermore, it is revealed that the variability behavior is wavelength dependent in the sense that the variation in bluer bands is stronger than that in redder ones. As a result, AGNs appear bluer when they get brighter. Such bluer-when-brighter (BWB) trend has been confirmed for both nearby AGNs \citep{2010ApJ...711..461S} and quasars \citep{1985ApJ...296..423C,1990ApJ...354..446W,1991ApJ...366...64C,1999MNRAS.306..637G,2000ApJ...540..652W,2001ApJ...551..103T,2002ApJ...564..624T,2004ApJ...601..692V,2005ApJ...633..638W,2011A&A...525A..37M,2011A&A...527A..15W,2011ApJ...731...50S,2012ApJ...744..147S,2012ApJ...758..104Z,2012ApJ...759...88B,2014ApJ...783..105R,2014ApJ...792...54S,2016ApJ...822...26G}. The two aforementioned disk-related mechanisms for the origin of UV/optical variability can both explain such BWB trend. A third explanation involves the contamination from the host galaxy or other more stable components \citep{2003MNRAS.344..492H,2010ApJ...711..461S}. Using SDSS photometric monitoring of 9258 spectroscopic confirmed quasars in Stripe 82, \citet{2014ApJ...792...54S} discovered that the color variability (the BWB trend) is more prominent on shorter timescales than on longer ones, which was coined as timescale-dependent color variability. Given the fact that neither the changing accretion rate nor contamination from host galaxy can produce timescale-dependent behavior, an inhomogeneous disk with temperature fluctuations should step in. Based on the original model proposed by \citet{2011ApJ...727L..24D}, \citet[][hereafter Cai16]{2016ApJ...826....7C} developed a revised inhomogeneous accretion disk model, and found that such model can well explain the observed timescale-dependent color variability in \citet{2014ApJ...792...54S}, primarily focusing on the slope of the relation between the amplitude of color variation and the timescale. The underlying physics is the inner and hotter zones of the accretion disk fluctuate at shorter timescales, and thus produce faster and bluer variations. Studying the variation of quasars at different timescales therefore provides an approach to probe the accretion disk in a spatially resolved manner. The UV light curves of quasars recorded by \GALEX{} enable us to extend the study of \citet{2014ApJ...792...54S} to shorter wavelengths, and probe the fluctuation at the inner most accretion disk. Using quasar light curves from \GALEX{} GR5, \citet{2011A&A...527A..15W} presented the ensemble near-UV (NUV) and far-UV (FUV) structure functions of quasars in the observed frame. They demonstrated that variation in FUV is stronger than that in NUV and they both triumph over the amplitudes of optical variability, also supporting the BWB diagram. Is such BWB trend revealed by \GALEX{} similarly timescale-dependent? To address this question, the contents of this work are orchestrated as follows: Section~\ref{sect:data} describes the data collected from \GALEX{} archive and Section~\ref{sect:method} makes use of the method introduced by \citet{2014ApJ...792...54S} to check the timescale dependence of color variability. We also present Monte-Carlo simulations to correct possible bias due to the large photometric uncertainties in the light curves. In Section~\ref{sect:diss}, we give the timescale-dependent color variation in different redshift bins and comparisons with the inhomogeneous model developed by Cai16. Conclusions are listed in Section~\ref{sect:conc}. | \label{sect:conc} Making use of FUV and NUV light curves of SDSS spectroscopically confirmed quasars collected from \GALEX{}, we confirm that the BWB trend of quasars is timescale-dependent, even in the rest frame EUV bandpass. We show that one can use the structure functions in various bands as an indirect approach to explore the timescale dependence of color variability. To better understand the cause of timescale-dependent color variability, the whole sample is divided into three redshift bins and we find clear timescale dependence of the BWB trend in all three bins. However, the observed timescale-dependent trends appear too steep to be fitted with the inhomogeneous disk model based on DRW process. Together with the much flatter structure function observed in \GALEX{} FUV (than in NUV and optical bands), these results suggest that the inner most accretion disk, where rest frame EUV radiation is emitted, fluctuates differently from DRW. Studying the rest frame EUV variability, which is more or less similar to X-ray variation in PSD slopes at timescales discussed in this work, could be highly rewarding as it probes the physics in the inner most regions of the nuclei. | 16 | 9 | 1609.07136 |
1609 | 1609.05305_arXiv.txt | The enormous velocities of the so called hypervelocity stars (HVSs) derive, likely, from close interactions with massive black holes, binary stars encounters or supernova explosions. In this paper, we investigate the origin of hypervelocity stars as consequence of the close interaction between the Milky Way central massive black hole and a passing-by young stellar cluster. We found that both single and binary HVSs may be generated in a burst-like event, as the cluster passes near the orbital pericentre. High velocity stars will move close to the initial cluster orbital plane and in the direction of the cluster orbital motion at the pericentre. The binary fraction of these HVS jets depends on the primordial binary fraction in the young cluster. The level of initial mass segregation determines the value of the average mass of the ejected stars. Some binary stars will merge, continuing their travel across and out of the Galaxy as blue stragglers. | \label{sec:intro} Hypervelocity Stars (HVSs) are stars escaping the Milky Way (MW) gravitational well. Whereas \citet{hil88} predicted theoretically their existence, HVSs were observed for the first time only $17$ years later by \citet{brw05}. About $20$ HVSs have been found at velocities up to $\approx 700$ km s$^{-1}$ in the outer MW halo (between $50$ and $120$ kpc) by the Multiple Mirror Telescope (MMT) spectroscopic survey \citep{brw10,brw14}. This survey targets stars with magnitudes and colors typical of $2.5-4\ \mathrm{M}_{\odot}$ late B-type stars. As consequence of the target strategy, the MMT stars could be either main sequence B stars, evolved blue horizontal branch stars or blue stragglers \citep{brw14}. Recently, astronomers have started to investigate low-mass HVS candidates \citep{li15,zie15}. Being a MMT spectroscopic survey, HVS data suffer from the lack of tangential velocity measurements. The astrometric European satellite \textit{Gaia} (http://www.cosmos.esa.int/web/gaia) is expected to measure proper motions with an unprecedented precision, providing a larger and less biased sample of HVSs (allegedly $\approx 100$ in a catalogue of $\approx 10^9$ stars). Moreover, \textit{Gaia}'s sensitivity is good enough to search for multi-planet systems around massive stars and to reveal their architectures and three-dimensional orbits, giving the possibility of spotting some planetary transits around HVSs \citep*{gin12,frg16}. The Hills' mechanism \citep{hil88} involves the tidal breakup of a binary that passes close to the Milky Way Black Hole (BH) \citep*{gil06,gil07,loc08,oll08,sar09}, but the physical mechanism responsible for the production of the observed HVSs is still debated. Other possible origins have been advanced \citep{brw15}, such as the interaction of a BH binary with a single star \citep{yut03}, the interaction of star clusters and BHs \citep{cap15,fra16}, supernova explosions \citep*{zub13,tau15}, tidal disruption of a dwarf galaxy passing through the Galactic Center (GC) \citep{aba09} and the dynamical evolution of a thin and eccentric disk orbiting around a massive BH \citep{sub14,haa16,sub16}. The extreme velocities of HVSs indicate they may derive from a strong dynamical interaction with BHs in the GC or in a nearby galaxy \citep*{she08}. The importance of HVSs is that they can provide information on the environment where they were born \citep{gou03}. In particular, they can discriminate between a single and a binary BH in the GC \citep*{ses07}. Since their orbits are determined by the MW potential, HVS kinematics can be used to probe the Galactic potential's triaxiality \citep*{gne05,yum07} and discriminate among different Galactic mass distributions \citep*{pee09,gne10,frl16}. As \citet{cap15} and \citet{fra16} have shown, a relevant mechanism to accelerate stars to high or even hyper velocities is that due to the close interaction of a single or binary massive black hole and a passing-by massive stellar cluster \citep*{arc16}. In the cited works the analysis was done for an evolved globular cluster-like object. The aim of this paper is, instead, that of investigating a possible origin of HVSs which involves a Young Star Cluster (YSC) that, during its orbit, has had the chance to pass close to the MW central super massive black hole (SMBH). When the YSC passes by the SMBH, some of its stars can be stripped from the cluster and ejected with high velocities \citep{cap15,fra16}. The outline of the paper is as follows. In Section 2, we describe the method we use to study the consequences of YSC-BH interaction. In Section 3, the results are presented and discussed. Finally, in Section 4, we summarize our main conclusions. | \label{sec:con} In this paper we investigated the origin of HVSs as a consequence of the close passage of a YSC around the Milky Way's central SMBH. During the close encounter, some stars are stripped from the cluster and may be ejected with high velocities \citep{cap15,fra16}. We focussed our attention on the stars lost by the system and ejected at hyper velocities after the interaction with the BH, examining the role of the cluster initial binary fraction and mass segregation. We found that this mechanism produces single and binary HVSs in a burst-like event (when the cluster is at the orbital pericenter), nearly in the initial cluster orbital plane and in the direction of the cluster orbital motion. The binary fraction of these HVSs jets depends on the initial fraction of binaries in the progenitor cluster. On the other side, the initial mass segregation affects the mass of ejected stars: the smaller the initial segregation fraction, the larger the average mass of HVSs. Moreover, we found that also the top-heaviness of the IMF and the total mass of the cluster affects the mass distribution of HVSs: a top-heavy IMF and a large cluster mass increase the average mass of HVSs. We also quantified how many binary stars survive at hypervelocities. Applying the \citet{kro95b} eigenevolution formulas we found that $\approx 7$\% of binary HVSs will merge to become, eventually, blue straggler HVSs. Both binary and blue stragglers HVSs have been observed. \citet{ede05} observed a star moving with a velocity of at least $530$ km s$^{-1}$ in the Galactic rest frame. According to stellar atmosphere fits the star is a 9 M$_{\odot}$ main-sequence star $50$ kpc away. The lifetime of this star is several times shorter than its flight time from the Milky Way, suggesting an LMC origin \citep{gua07} or a blue straggler origin \citep{per09}. The latter channel suggest that the progenitor was likely a binary system ejected from the Milky Way at $\gtrsim 800$ km s$^{-1}$ \citep{brw15}. Recently, \citet{nem16} have spotted the first binary HVS candidate $\approx 5.7$ kpc far from the GC travelling at $\approx 571$ km s$^{-1}$. \citet{brw08} showed that HVSs are clustered in the direction of the constellation Leo. \citet*{brw12} proposed that the HVS anisotropy could reflect the anisotropy of the Galactic potential. Our model predicts that the anisotropy of HVSs is a natural consequence of cluster motion at the pericentre. This is natural if most stars form in clusters \citep{kro05}. \citet*{paw12} showed that the MW is surrounded by a disk of mostly coorbiting satellite galaxies, the vast polar structure (VPOS) \citep*{ktb05}. Is the disk of stars around the super massive BH of the MW, and/or some gaseous disk there, oriented as the VPOS? The known HVSs do correlate with the VPOS \citep*{paw13} and if the innermost accretion disk or circum-nuclear disk of the super massive BH is aligned with the VPOS, then results showed in this paper may nicely explain the anisotropy of the flux of HVSs: a moderate embedded cluster forms in the gaseous disk and falls towards the super massive BH and produces the HVS flux. This is similar to the dwarf-galaxy picture \citep{aba09}, but is more plausible since stars form in embedded clusters, also in the inner Galaxy, and the youth of the HVSs is then also less of a problem \citep{brw14}. HVSs are powerful tools to investigate the physics of the GC, being in an accessible region of the sky, and also to study the dark sector of our Galaxy \citep{per09,frl16}. When a star cluster passes near the SMBH, it produces HVSs as a consequence of the strong interaction with the SMBH tidal field. If HVSs are generated through the process presented in this paper, by studying their spatial and velocity distribution, it is possible to constrain the physical properties of clusters that have infallen onto the central SMBH, over the course of the Milky Way's history, including their binary and mass composition. | 16 | 9 | 1609.05305 |
1609 | 1609.02713_arXiv.txt | Typical solar flares display two quasi-parallel, bright ribbons on the chromosphere. In between is the polarity inversion line (PIL) separating concentrated magnetic fluxes of opposite polarity in active regions (ARs). Intriguingly a series of flares exhibiting X-shaped ribbons occurred at the similar location on the outskirts of NOAA AR 11967, where magnetic fluxes were scattered, yet three of them were alarmingly energetic. The X shape, whose center coincided with hard X-ray emission, was similar in UV/EUV, which cannot be accommodated in the standard flare model. Mapping out magnetic connectivities in potential fields, we found that the X morphology was dictated by the intersection of two quasi-separatrix layers, i.e., a hyperbolic flux tube (HFT), within which a separator connecting a double null was embedded. This topology was not purely local but regulated by fluxes and flows over the whole AR. The nonlinear force-free field model suggested the formation of a current layer at the HFT, where the current dissipation can be mapped to the X-shaped ribbons via field-aligned heat conduction. These results highlight the critical role of HFTs in 3D magnetic reconnection and have important implications for astrophysical and laboratory plasmas. | 16 | 9 | 1609.02713 |
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1609 | 1609.05844_arXiv.txt | The Crab Pulsar has been recently detected at very high energies (VHE) with its pulsed VHE emission reaching up to $1.5$ TeV. The VHE peaks appear synchronised with the peaks at GeV energies and show VHE spectra following hard power-law functions. These new findings have been interpreted as evidence for a gamma-ray production that happens very close to the light cylinder. Motivated by these experimental results we consider the efficiency of magnetocentrifugal particle acceleration in the magnetosphere of the Crab Pulsar, reexamining and extending results obtained in a previous work \citep{or09}. It is shown that efficient magnetocentrifugal acceleration close to the light cylinder could provide the required electron Lorentz factors of $5\times 10^6$ and that the resulting inverse Compton (IC) scattering off thermal photons might explain the enigmatic TeV emission of the pulsar. We estimate the corresponding VHE luminosity and provide a derivation of its spectral characteristics, that appear remarkably close to the observational results to encourage further studies. | Rotating neutron stars are today known to be accompanied by pulsed non-thermal high- and very high energy (VHE) gamma-ray emission \citep[e.g.,][]{abdo,lem}. While these observations point to the presence of highly energetic charged particles in the pulsar environment, the origin of these particles is still an open question \citep[see e.g.,][]{ahar2,bednarek12,hirotani14,harding15,mochol15}. According to the standard theory of pulsars, primary particles are uprooted from the star's surface by means of strong longitudinal (along the magnetic field line) electrostatic fields \citep{rud} and efficiently accelerated in a region between the surface and the light cylinder (LC) area (a hypothetical zone where the linear velocity of rotation matches the speed of light). In order to produce VHE emission up to TeV energies, as e.g. seen in the case of the Crab Pulsar, electrons would need to achieve high Lorentz factors of the order of $\sim 10^6-10^7$ \citep[e.g.,] []{aliu,magic}. It is still not known which mechanism of acceleration is responsible for that and where in the magnetosphere this process may take place. In the framework of e.g. polar cap models longitudinal electrostatic fields are presumed to allow significant particle acceleration along open magnetic field lines close to the neutron star \citep[e.g.,][]{arons,michel}. However, the acceleration efficiency is usually found to be too strongly limited by curvature and/or Inverse Compton radiation processes \citep{daugherty,dermer} in order to account for the production of TeV particles. To overcome these difficulties, alternative (so-called outer gap) models might be invoked \citep[e.g.,][]{cheng,chiang,hirotani}, where particles are accelerated in the outer parts of the magnetosphere. Yet the anticipated radiation reaction forces along with the relatively short gap sizes still impose severe constraints on maximum attainable particle energies. A number of different approaches have been considered to improve on these problems. \cite{usov} for example, have examined the intermediate formation of an electron-positron bound state that could possibly prevent an early screening of the gap electric field. \cite{muslim}, on the other hand, have extended the pulsar's electrodynamics by taking into account general relativistic effects. Although these mechanisms allowed to slightly increase the gap size and thus led to more energetic particles, the corresponding energies are still not high enough when put in the context of recent VHE observations. In general, the pulsar magnetosphere is characterized by extremely strong magnetic fields, which in the case of the Crab Pulsar are believed to be of the order of $4\times 10^{12}$G close to star's surface. This in turn means that charged particles very efficiently emit synchrotron radiation with an associated cooling timescale $t_{syn}\sim\gamma m_0c^2/P_{syn}$ (where $\gamma$, $m_0$ is the electron's Lorentz factor and mass, respectively, $c$ is the speed of light, $P_{syn}\approx 2e^4\gamma^2B^2/3m_0^2c^3$ is the single particle synchrotron power and $e$ is the electron's charge) that is by many orders of magnitude smaller than the kinematic timescale $P$, where $P$ is the rotation period, i.e. $P\approx 0.0334$ sec in the case of the Crab Pulsar \citep[e.g.,][]{lyne}. Hence, charged particles injected into the magnetosphere will quickly transit to the ground Landau level and start sliding along the magnetic field lines. As the field lines co-rotate with the star, the particle dynamics is then expected to be strongly influenced by the effects of centrifugal acceleration and the synchrotron losses do not impose constraints on the maximum attainable energies of particles. It is clear that these effects might be extremely efficient close to the LC zone. In the context of the Crab, the possible role of the centrifugal mechanism to generate the pulsar's emission has been examined by \cite{gold}. In particular, he has argued that the co-rotation of plasma particles in the pulsar's magnetosphere could "create" an efficient energy transfer channel from the rotator into the kinetic energy of plasma particles. Motivated by this, a simplified model of centrifugal acceleration was developed by \cite{macrog}, who considered a rectilinear rotating channel with a body, freely sliding inside it. In the framework of special relativity they showed for the first time that the incorporation of relativistic effects of rotation can lead to radial deceleration, which is at first sight a rather uncommon phenomenon, yet already known from general relativity \citep{abram}. Since then, centrifugal particle acceleration has been studied in a variety of contexts and used to e.g., predict the location to frequency mapping in the case of multi-second pulsars \citep{gang1,gang2} or to analyse the origin of the variable high energy emission from the rotating jet base in active galactic nuclei (AGN) \citep[e.g.,][]{ganglesch,riegman,Xu02,orb07,ghis09}. The results illustrated amongst other the particular role of inverse Compton scattering on the efficiency of centrifugal acceleration. In a direct application of centrifugal acceleration to Crab-like pulsars we have shown that close to the LC area electrons could achieve Lorentz factor up to $\gamma\sim 10^7$ \citep[][]{or09}. The analysis of different radiation processes suggested that inverse Compton scattering in the Crab Pulsar's magnetosphere could lead to detectable pulsed VHE emission in the TeV band. Based on the MHD approximation, a detailed investigation of magneto-centrifugal acceleration of plasma bulk motion close to the light cylinder has been recently presented by \cite{bog1}, extending an earlier approach developed in \cite{bog2}. The results are of particular interest as they lead to very similar expectations in the case of the Crab Pulsar. In that approach the dynamics of the particles has been investigated for different 3dim-configuration of magnetic field lines and it was shown that close to the LC area particles can achieve extremely high Lorentz factor following a scaling as previously employed. The aforementioned works are especially interesting in the context of the latest results by the MAGIC Collaboration reporting the detection of pulsed VHE emission up to 1.5 TeV from the Crab Pulsar, the highest ever detected \citep{magic}. The VHE pulse profiles revealed two narrow peaks P1 (located at a phase close to $1$) and P2 (located at a phase close to $0.4$) that appear synchronised with those seen by Fermi-LAT in the GeV domain. Their detection significance (in $\sim 320$h of data) is different, though, with only P2 being significantly detected ($>5\sigma$) at energies above $400$ GeV. The phase-folded pulse spectra are compatible with power-law functions over a range of $\sim70$ GeV up to $1.5$ TeV, with photon indices $\alpha = 3.5 \pm 0.1$ (for P1) and $\alpha = 3.0 \pm 0.1$ (for P2), and TeV flux levels $E^2dN/dEdAdt$ $\lppr 5\times 10^{-14}$ TeV cm$^{-2}$s$^{-1}$ (P1) and $\left(9\pm3\right) \times 10^{-14}$ TeV cm$^{-2}$s$^{-1}$ (P2), respectively. It is worth noting that this is the first clear detection of a pulsed emission component from the Crab in the TeV regime. Unpulsed (steady) TeV emission, attributed to its nebula, has been detected quite some time ago \cite[e.g.,][]{weekes89,ahar1} whereas early evidence for pulsed gamma-ray emission (above a few tens of GeV) has been related to an inverse Compton (IC) origin in the pulsar wind zone some tens of light cylinder radii away \citep{ahar2}. In this paper we reconsider the role of the magneto-centrifugal acceleration for the Crab Pulsar in the light of the latest VHE findings, applying and extending results previously obtained \citep{or09}. We show that the agreement with observations is successfully close to encourage further modelling. The paper is organized in the following way. In section~II, basic results of centrifugal acceleration are recaptured and discussed. Section~III then presents an application to the Crab Pulsar, while conclusions are summarised in section~IV. \section[]{Centrifugal acceleration} \subsection{Energy-Position Dependence} In this section we consider the dynamics of centrifugally accelerated particles close to the LC surface. As noted above, synchrotron losses will ensure that a charge particle quickly transits to the ground Landau level and starts to slide along the field line. Under such conditions it can be shown that the Lagrangian of a single relativistic massive particle (with rest mass $m_0$) moving along a co-rotating field line located in the equatorial plane can be written as \citep{rijmpd} \begin{equation}\label{L} L = -m_0\left(1-\upsilon_r^2-\upsilon_{\phi}^2\right)^{1/2}, \end{equation} where ($c\equiv1$), $\upsilon_r = \dot{r}$ and $\upsilon_{\phi} = \Omega r+\dot{r}B_{\phi}/B_{r}$ are respectively the radial and tangential components of velocity, $\Omega = 2\pi/P$ is the pulsar's angular velocity of rotation, and $B_{r}$ and $B_{\phi}$ are the corresponding components of the magnetic field, respectively. Since the Lagrangian is not explicitly time-dependent, the related Hamiltonian $H=\dot{r} P - L$, where $P=\partial L/\partial \dot{r}$ is the generalized momentum, is a constant of motion (Noether's theorem). Using Eq.~(\ref{L}) one finds \begin{equation}\label{H} H = \gamma m_0\left(1-\Omega r\upsilon_{\phi}\right) = \rm{const}, \end{equation} Accordingly, in the presence of a dominant radial field, the radial behaviour of the Lorentz factor for a particle injected at $r_0$ with initial Lorentz factor $\gamma_0$ becomes \citep{rijmpd} \begin{equation}\label{gr} \gamma(r) = \gamma_0\,\frac{(1-r_0^2/r_L^2)}{(1-r^2/r_L^2)}, \end{equation} where $r_L=c/\Omega$ denotes the light cylinder radius. A charged particle following the field will thus dramatically increase its Lorentz factor upon approaching the light cylinder ($r\rightarrow r_L$). Using eq.~(\ref{gr}) and the general definition of $\gamma$, the characteristic acceleration timescale can be expressed as \begin{equation}\label{tacc} t_{\rm acc}(\gamma) = \frac{\gamma}{\dot{\gamma}} \simeq \frac{\gamma_0^{1/2} (1-r_0^2/r_L^2)^{1/2}r_L}{2 \gamma^{1/2} c} \propto 1/\sqrt{\gamma} \end{equation} In principle, the Lorentz factor dependence, eq.~(\ref{gr}), can also be obtained within the fluid dynamical framework of the MHD approximation. As shown recently by \cite{bog1}, the relativistic dynamics of particles following a rotating field line with a general 3d-shape in a plasma satisfying the frozen-in condition obeys the equation \begin{equation}\label{b1} \frac{1}{\gamma}\frac{\partial\gamma}{\partial R}=\frac{2R}{1-R^2}+ \frac{\upsilon_r\left(\upsilon^2\cos\psi+R\left(1-R^2\right)\frac{\partial\cos\psi} {\partial R}\right)}{\left(1-R^2\right)\left({\bf e_re_{_B}}\right)\left(1-\upsilon_d^2\right)}, \end{equation} where $R = r/r_{L}$ is the dimensionless radial coordinate, $\upsilon$ is the total particle velocity, ${\bf e_r}$ and ${\bf e_{_B}}$ are the unit vectors along the radial coordinate and along the direction of the magnetic field line, respectively, $\psi$ is the angle between ${\bf e_r}$ and ${\bf e_{\phi}}$, ${\bf e_{\phi}}$ is the unit tangential vector, $\upsilon_d = {\bf E\times B}/B^2$ is the drift velocity and ${\bf E}$ and ${\bf B}$ are the electric and magnetic field vectors, respectively. As discussed by \cite{bog1}, on approaching the LC ($R = 1$) the second term of the right-hand side of Eq. (\ref{b1}) remains finite, while the first term diverges. Therefore, the aforementioned equation reduces to \begin{equation}\label{b2} \frac{1}{\gamma}\frac{\partial\gamma}{\partial R}=\frac{2R}{1-R^2}, \end{equation} which no longer depends on the concrete shape of the field line (as long as it is positively twisted) and has the solution expressed in eq.~(\ref{gr}). Identifying possible sites in numerical simulations and adopting parameters characteristic for the Crab Pulsar, \cite{bog1} found that Lorentz factor up to $ \sim 5\times 10^7$ (at the Alfv\'enic surface) could be achieved by magnetocentrifugal acceleration. \subsection{Trajectories - the Archimedean spiral as attractor} On crossing the light cylinder, magnetic field lines frozen into the plasma are generally expected to approach an Archimedean spiral shape with the plasma flowing in it at constant Lorentz factor, i.e. the Archimedean spiral becomes an attractor \citep{bog1}. This compares well with the analysis of \cite{grg} who, in an extension of the work by \cite{macrog}, examined curved rotating channels in the equatorial plane and studied the relativistic dynamics of a particle sliding inside this channel. As seen by a laboratory observer, the effective angular velocity of a particle can be written as \citep{grg} \begin{equation}\label{omef} \Omega_{ef} = \Omega+\phi'(r)\upsilon_r, \end{equation} where the shape of the channel is given in polar coordinates in terms of $\phi$. On the other hand, since we observe plasma particles escaping the inner magnetosphere, the particle dynamics is expected to tend to the force-free regime. As a consequence the effective angular velocity has to vanish eventually and the particle's radial velocity should saturate. This in turn means that the physically interesting "trajectories" are those with $\phi(r) = ar$, where $a$ is a constant. Together with $\Omega$ this explicitly defines the asymptotic velocity as \begin{equation}\label{vas} \upsilon_{as}=-\frac{\Omega}{a}. \end{equation} Obviously, if the initial velocity of the particle coincides with $\upsilon_{as}$, its dynamics will be force-free from the very beginning. It seems interesting to study what happens if the initial velocities are different. For this purpose one can consider the metric tensor on the Archimedean field lines \citep{grg} \begin{equation}\label{ds} ds^2 = g_{00}dt^2+2g_{01}dtdr+g_{11}dr^2, \end{equation} where \begin{equation} \label{gab} g_{\alpha\beta} = \left(\begin{array}{ccc} -\left(1-\Omega^2r^2\right), \;\;\; & a\Omega r \\ a\Omega r , \;\;\; & 1+a^2r^2 \\ \end{array}\right), \end{equation} with indices $\alpha,\beta = {0,1}$ and using $c\equiv 1$. Then, by introducing the Lagrangian of a particle \citep[e.g.,][]{shapiro} \begin{equation} \label{lag} L_A = -m_0 \left(g_{\alpha\beta}\frac{dx^{\alpha}}{d\tau}\frac{dx^{\beta}}{d\tau}\right)^{1/2}, \end{equation} one can see that $t$ is a cyclic parameter for which the associated conjugate momentum is conserved. Therefore, one can show that the proper energy of the particle (per unit rest mass) given by \begin{equation} \label{ener} E_A = -\frac{g_{00}+g_{01}\upsilon_r}{\left(-g_{00}-2g_{01}\upsilon_r- g_{11}\upsilon_r^2\right)^{1/2}}, \end{equation} is a conserved quantity. Here we have employed the fact that based on the normalisation of the 4-velocity, the Lorentz factor of the particle in terms of the radial velocity is given by $\gamma(r) =\left(-g_{00}-2g_{01}\upsilon_r-g_{11} \upsilon_r^2\right)^{-1/2}$. Equation~(\ref{ener}) then leads to the following relation for the radial velocity \begin{eqnarray} \label{vr} \upsilon_r&=&{\frac{\sqrt{g_{00}+E_A^2}}{g_{01}^2+E_A^2g_{11}}}\nonumber \\ &\times&{\left[-g_{01}\sqrt{g_{00}+E_A^2} \pm E_A \sqrt{g_{01}^2-g_{00}g_{11}} \right]}. \end{eqnarray} \begin{figure} \resizebox{\hsize}{!}{\includegraphics[angle=0]{fig1.eps}} \caption{Characteristic dependence of the Lorentz factor on the radial coordinate for different initial Lorentz factors $\gamma_0$. For illustration the calculations are done for an Archimedean spiral with small (asymptotic) Lorentz factor $\gamma_{as} = 7$. All particles are launched from $r_0 = 0$. As it is evident from the plot, the curve $\gamma = \gamma_{as}$ "attracts" all other curves.} \label{fig1} \end{figure} In Fig. \ref{fig1} the characteristic behaviour of $\gamma(r)$ is shown for different initial conditions. For illustration and in order to facilitate a comparison with \cite{bog1}, a small (asymptotic) Lorentz factor $\gamma_{as} = 7$ has been employed for the Archimedean spiral. As can be seen, even if the particles are initially not in the force-free regime, they asymptotically tend to it. A similar investigation but for 3-dim geometry has been recently performed by \cite{guda}. In \cite{bog1} it has been argued that efficient magnetocentrifugal acceleration occurs close to the Alfv\'enic region (an area where the Alfv\'enic velocity equals that of plasma particles). By estimating the corresponding distance in the case of the Crab Pulsar and using eq.~(\ref{gr}) a maximum attainable value for the Lorentz factor, $\gamma_{max}\sim 5\times 10^7$ has been inferred. As discussed in \cite{or09} and considered in more detail in the following, the aforementioned value could in principle be slightly reduced by means of energy losses. \section[]{Emission characteristics} In the envisaged scenario, centrifugal particle acceleration can occur as long as the inertia of the plasma particles does not counteract efficient co-rotation with the magnetic field. This is satisfied if the magnetic field energy density $B^2/8\pi$ exceeds the plasma energy density, $\gamma n_{_{GJ}}Mm_0c^2$, where $n_{_{GJ}} =\Omega B\cos\alpha/(2\pi ec)$ is the Goldreich-Julian number density \citep{gj} close to the star, i.e. the number density of primary particles, $M\approx\gamma/\gamma_0$ is the multiplicity factor \citep{or09} and $\alpha$ is the inclination angle between the axis of rotation and the magnetic dipole. For the Crab Pulsar one has $P=2\pi/\Omega= 0.033$ sec, a nominal light cylinder scale $r_{L}=c P/2\pi=1.58\times 10^8$ cm, an effective radial distance $r_l=r_{L}/\sin\alpha$ and a surface magnetic field $B_0\simeq 4 \times 10^{12}$ G. For a dipolar field approximation, the magnetic field then scales as $B(r_l) \simeq 1.5 \times 10^6\sin^3\alpha$ G in the LC area. For these parameters, the requirement of efficient co-rotation leads to a constraint on the maximum Lorentz factor of \begin{equation} \label{gcor} \gamma_{max}^{cor}\approx 2 \times 10^7 \left(\frac{\gamma_0}{10^4}\right)^{1/2}\left(\frac{\sin^{3}\alpha} {\cos\alpha}\right)^{1/2}, \end{equation} where the initial injection Lorentz factor has been normalized on $10^4$ \citep[e.g.,][]{melrose}. \begin{figure} \centering \resizebox{5cm}{!}{\includegraphics[angle=0]{fig2.eps}} \caption{Sketch of the magnetospheric-centrifugal Pulsar model. Charged particles following co-rotating magnetic field lines will be radially decelerated while moving outwards but attain a large azimuthal velocity component close to light cylinder (LC) surface. A suitably aligned observer will see a strong (beamed) high-energy emission pulse for a short fraction of the period.} \label{fig2} \end{figure} It is generally assumed that the high energy emission is generated by particles sliding along open field lines. In the framework of the present model, these field lines are almost straight in a sense that their curvature radius exceeds the nominal light cylinder radius. Yet, in the laboratory frame of reference particles will almost rigidly rotate on the LC surface \citep{gold}. Therefore, curvature emission \citep[e.g.,][]{och} could be of significance in limiting the maximum attainable energies. For Lorentz factor of the order of $\gamma \sim 10^7$ the characteristic peak frequency, $\nu_{cur}\approx 3c\gamma^3/(4\pi R_c)$, with $R_c\simeq r_L$, in the case of the Crab Pulsar becomes \begin{equation} \label{nuc} \nu_{cur}\approx 5\times 10^{22}\times\left(\frac{\gamma}{10^7}\right)^3 ~{\rm Hz}, \end{equation} which corresponds to photon energies of the order of $0.2 \left(\gamma/10^7\right)^3$ GeV. Hence curvature emission could in principle lead to a detectable, pulsed GeV contribution. Note that in principle some mild variation in curvature radii $R_c$ may occur that could be determined within a more detailed approach \citep[e.g.,][]{gang2}. We may estimate achievable energies in the presence of curvature losses by equating the associated cooling time scale $t_{cur} = \gamma mc^2/P_{cur}$, where $P_{cur} =2e^2c\gamma^4/(3r_L^2)$ is the single particle curvature energy loss rate, i.e. \begin{equation} \label{tc} t_{cur}\approx 4.5\times 10^{18}\times\frac{1}{\gamma^3}~{\rm sec}, \end{equation} with the acceleration timescale (i.e., eq.~[\ref{tacc}] with $r_L$ replaced by $r_l$) as applied to the Crab Pulsar, \begin{equation} \label{tac} t_{\rm acc}\approx \frac{2.6\times 10^{-3}}{\sin\alpha}\times\left(\frac{\gamma_0}{\gamma}\right)^{1/2} ~{\rm sec}, \end{equation} yielding maximum attainable Lorentz factor \begin{equation} \label{gc} \gamma_{max}^{cur}\approx 5\times 10^7\sin^{2/5}\alpha, \end{equation} where we have employed $\gamma_0\approx 10^4$. Since $\gamma_{max}^{cor}<\gamma_{max}^{cur}$, the relevant constraint is thus essentially imposed by the requirement of co-rotation and not by curvature losses. In the approach described here, efficient particle acceleration is thus taking place in the LC zone, the energisation being mediated by centrifugal effects and not magnetic field-aligned electric fields \citep[cf. also][]{hirotani14}. In the considered framework, the high energy radiation is generated in a thin shell of thickness \begin{equation}\label{d} d\sim \gamma_0 r_L/\gamma \end{equation} close to the LC surface \citep{or09}. For a quasi-monoenergetic particle distribution the total luminosity could be approximated by $L_{cur}^{GeV} \sim 2 n_{_{GJ}} M\Delta VP_{cur}$, where $\Delta V\sim \chi \left(\delta l\right)^2 d$ is the corresponding volume, $\chi\lppr1$ is a dimensionless factor depending on the topology of magnetic field lines, $\delta l \sim r_L \theta$ is the azimuthal length scale involved in this process, $\theta \sim \Omega P/10$ is the corresponding angle, where $P/10$ is an approximate value for the pulse duration inferred from the light curve observed \citep{magic}, and where we have taken into account that the pulsar emits in two channels. Combining the noted values, the pulsed luminosity generated due to curvature emission at energy $h\nu_{cur}$ in the GeV band would be of the order of \begin{equation} \label{Lc} L_{cur}^{GeV}\simeq 2\times 10^{34} \left(\frac{\gamma}{10^7}\right)^4 \chi\cos\alpha\,\sin^3\alpha\;~{\rm erg/sec}\,. \end{equation} The specific amount and the spectral shape will depend on the real (space-energy) distribution of particles and the range of curvature radii involved, and will need detailed modelling. Given the magnitude of eq.~(\ref{Lc}) and the fact that the emission is expected to be significantly focused (beamed; see also below), curvature radiation is likely to be of prime relevance for understanding the origin of the $\gamma$-ray emission as seen by Fermi-LAT \citep{abdo0,magic}. Given the generic constraints for curvature emission (e.g., eq.~[\ref{nuc}]), it is usually believed that inverse Compton (IC) scattering is responsible for the VHE emission in millisecond pulsars \cite[e.g.,][]{lyutikov13,harding15,magic}. To this, in principle a variety of soft photons fields could contribute, e.g. the thermal emission of the neutron star or secondary synchrotron emission. As shown in \cite{or09}, in the centrifugal-type approach following \cite{gold}, the contribution of the star's thermal photon field to the IC process becomes of relevance as the particle-soft photon interaction angle is not negligible but of order $\sim \pi/2$. For the Crab pulsar, the surface temperature is of the order of $T \simeq 1.2\times 10^6$ K \citep[e.g.,][]{weisskopf}, corresponding to photon energies of $2.8 kT\sim 0.3$ keV. IC up-scattering of thermal photons to the VHE regime will thus occur in the Klein-Nishina regime. One could verify that the associated electron inverse Compton losses will not impose further restrictions on the maximum attainable energies by recourse to the single particle emission power \citep[e.g.,][]{blum} \begin{equation} \label{PKN} P_{KN}\simeq\frac{\sigma_T\left(mckT\right)^2}{16\hbar^3}\left(\ln \frac{4\gamma kT}{mc^2}-1.981\right)\left(\frac{r_s}{r_l}\right)^2\,, \end{equation} where $\sigma_T\approx 6.65\times 10^{-25}$cm$^2$ is the Thomson cross section, $\hbar\approx 1.05\times 10^{-27}$ erg-sec is the Planck constant, $k= 1.38\times 10^{-16}$ erg/deg(K) is the Boltzmann constant and $r_s\approx 11.5$ km is the neutron star's radius \citep{lat}. To first order the corresponding cooling timescale $t_{_{IC}}=\gamma mc^2/P_{KN}$ thus increases and becomes less constraining with Lorentz factor $\gamma$, whereas in contrast the acceleration timescale, eq.~(\ref{tacc}), decreases as $1/\gamma^{1/2}$. The noted IC scattering is thus not expected to impose constraints on the acceleration efficiency. Up-scattering of thermal photons could, however, lead to pulsed $\gamma$-ray emission in the VHE domain as pointed out in \cite{or09}. The scattered photons could well reach energies of the order of $\epsilon\approx \gamma mc^2\sim 5\left(\gamma/10^7 \right)$ TeV. The MAGIC experiment has recently reported pulsed VHE emission with an energy flux level for the higher peak P2 of $F=\left(9\pm 3\right)\times 10^{-14}$TeV cm$^{-2}$s$^{-1}$ in the interval $\left[965,1497\right]$ GeV \citep{magic}, corresponding to an isotropic equivalent (spectral) luminosity of $L_{TeV} \simeq (5-10)\times 10^{31}$ erg/s at a distance of $d\simeq 2$ kpc. In the considered framework, this emission would be generated by relativistic particles with Lorentz factors $\sim (2-3)\times 10^6$. We may again roughly estimate the possible order of magnitude for the spectral IC luminosity at $\sim1$ TeV expected in the centrifugal model by multiplying the single particle power $P_{KN}$, eq.~(\ref{PKN}), with the relevant particle number $N\simeq 2n_{GJ} M \Delta V$ (two channels) to obtain \begin{eqnarray} L_{IC}^{TeV}\simeq 1.4\times 10^{31} \left(\frac{B}{10^6\rm{G}}\right) \left(\frac{T}{1.2\times 10^6\rm{K}}\right)^2 \chi \cos\alpha \sin^2\alpha ~\frac{\rm{erg}}{\rm{s}}\,.\hspace*{-1cm}\nonumber\\ \label{LTEV} \end{eqnarray} One could use this expression to evaluate the degree of focusing and estimate a fiducial solid angle for the corresponding IC emission cone of $\Delta \Omega \sim L_{IC}^{TeV}/(d^2F) \sim 2.6 \chi\sin^2\alpha \cos\alpha$ sr if a dipolar field scaling $B(r_l) \propto \sin^3 \alpha$ close to the LC surface is employed. In Fig.~\ref{fig2} a sketch of the magnetospheric-centrifugal Pulsar model is shown. Following the approach developed by \cite{gold} centrifugally accelerated particles in the LC zone have large azimuthal velocities and thus approximately emit along a tangent to the LC surface. It seems evident that in this approach the peaks in the light curves are in phase for all energy regimes that are rotationally produced sufficiently close to the LC area. \noindent A priori, the radiating particle distribution is not expected to be mono-energetic, but instead to have some distribution in energy. This is a complicated issue and, amongst others, likely to be sensitive on the magnetic field topology, the injection spectrum and radiation reaction effects. Nevertheless, one can still evaluate some simple characteristics: Suppose electrons are injected (by inner gap-type processes) into the magnetosphere at a rate $Q$ with some Lorentz factor $\gamma_0$ and centrifugally accelerated along a magnetic field line until co-rotation breaks down and they escape further acceleration by crossing the LC surface. Then to first order, the differential particle density distribution $n(\gamma)$ along a field line in the steady state can be approximated by \citep{riegaha08} \begin{equation}\label{neq} n(\gamma) \simeq \frac{Q\,t_{acc}}{\gamma}~ H(\gamma-\gamma_0) \propto \gamma^{-3/2} \end{equation} using that $t_{acc} \propto \gamma^{-1/2}$, eq.~(\ref{tacc}). Particles with higher $\gamma$ are located closer to the LC surface and occupy a thinner shell of width $d \propto \gamma_0/\gamma$, eq.~(\ref{d}), compared to those at lower energies. An observer will thus see the integrated emission produced by an effective particle number $N=\int N(\gamma) d\gamma = \int n(\gamma)d\gamma dV = \int n(\gamma) \Delta V d\gamma$, i.e., by an effective differential number of electrons $dN_{e}= N_{e}(\gamma)\,d\gamma$ with a power-law distribution \begin{equation}\label{neff} N_{e}(\gamma)=n(\gamma)\Delta V \propto \gamma^{-5/2}\,, \end{equation} noting that $\Delta V \propto d \propto 1/\gamma$. Up-scattering of a thermal black body distribution by a power law electron distribution with power index $p$ in the KN limit will produce a photon spectrum \citep{blum} \begin{equation} \frac{dN_{\gamma}}{d\epsilon_{\gamma} dt} \propto \epsilon_{\gamma}^{-(p+1)} \left(\ln\frac{\epsilon_{\gamma} kT}{m^2c^4}+1+C(p)\right) \end{equation} for photon energies $\epsilon_{\gamma} \ll \gamma_{max} m_e c^2$, where $C(p=2.5)\simeq -2.4$. The corresponding spectral characteristics resulting from the power law electron distribution $p=2.5$ of eq.~(\ref{neff}) turns out to be surprisingly close to the VHE measurements by MAGIC, reporting photon indices $\alpha = 3.5 \pm 0.1$ (for P1) and $\alpha = 3.0 \pm 0.1$ (for P2). This is illustrated in Fig.~\ref{fig3}. It is likely that modifications in, for example, the magnetic field topology and a detailed treatment of the particle particle injection and transport, aberration and travel time effects will lead to some index variation around this main spectral value but full modelling would be required to infer its plausible range. \begin{figure} \resizebox{\hsize}{!}{\includegraphics[angle=0]{fig3.eps}} \caption{Illustration of the spectral VHE characteristics expected in the magneto-centrifugal Pulsar model as a result of inverse Compton scattering of thermal photons in the KN regime. The spectral points are the MAGIC (phase-folded) VHE measurements for the main pulse P1 and the interpulse P2, respectively \citep{magic}.} \label{fig3} \end{figure} | The recent detection of pulsed VHE emission from the Crab Pulsar \citep[][]{magic} has opened new avenues in pulsar research. The apparent synchronisation of the pulse profile at GeV and TeV energies suggests a common property such as a very similar location of production, the transparency for $\gamma$-ray photons hints to an outer magnetospheric region, while the expected IC origin points to the presence of very energetic particles with Lorentz factors of at least $\gamma\sim 5\times 10^6$. Such characteristics are challenging to accommodate in traditional emission models. In the present paper we have argued that magneto-centrifugal particle acceleration may offer an interesting means to account for the noted characteristics. In this framework, efficient particle acceleration takes place in the vicinity of the light cylinder, with the high-energy $\gamma$-ray emission related to curvature radiation and the VHE emission (above some tens of GeV) generated by inverse Compton (IC) upscattering in the Klein-Nishina regime. The model assumes the occurrence of pair cascades as conventionally treated to provide the seed particles for injection. A simple analysis of the anticipated VHE spectral characteristics suggests a power-law index remarkably close to that actually observed. In the present model the slight spectral difference reported for the pulses P1 and P2 in the VHE regime could be related to two different magnetospheric locations with varying field topology along with possible variations in the injection spectrum. A full treatment of the corresponding particle transport and radiation properties, aberration and travel time effects seems required, however, to elucidate its most plausible range and to eventually help us understand particle acceleration processes in pulsar magnetospheres. Given the promising potential of magneto-centrifugal particle acceleration for understanding the origin of the observed VHE emission, this seems a program worth doing. The current MAGIC results rely on an analysis that combined many periods ($\sim 320$h, spread from 2007 to 2014) with different sensitivities and energy thresholds, in which the pulse $P1$ is detected with a moderate significance level of $\leq2.8\sigma$. Updated VERITAS results (based on $\sim200$h of data) find a phase-averaged differential spectrum for the Crab Pulsar compatible with the MAGIC results, but did not yet manage to establish pulsed emission above 400 GeV \citep{nguyen}. Further observations with current and future (CTA) instruments \citep[e.g.,][]{cta}, establishing a homogeneous data set, and refined analysis will thus be important to better characterise its spectral evolution and extension, and thereby eventually help us to understand the origin of the high-energy emission in young pulsars. | 16 | 9 | 1609.05844 |
1609 | 1609.05075_arXiv.txt | { We present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region in response to rapid heating events. In the coupled corona, transition region and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation). However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux \lq jumps\rq\ across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved one-dimensional model, we present field-aligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both one-dimensional hydrodynamic and three-dimensional magnetohydrodynamic simulations are discussed. } | } \indent The interaction between the solar corona and chromosphere is central to understanding the observed properties of magnetically closed coronal loops. It is well known that if the corona is heated impulsively (by for example, a flare, microflare or nanoflare), both the temperature and density increase and then decline, with the time of peak temperature preceding that of the peak density. The changes in density can only be accounted for by mass exchange between the corona and chromosphere, mediated by the transition region (TR). \\ \indent Recognising the role of the TR is essential for developing reliable models of impulsive heating. For a static equilibrium loop with steady heating, the TR is defined as the region extending from the top of the chromosphere to the location where thermal conduction changes from an energy loss to a gain \citep[e.g.][]{paper:Veseckyetal1979}. The full TR occupies roughly 10\% of the total loop length, the radiation from it is roughly twice that from the corona, and the temperature at its top is of order 60\% the temperature at the loop apex \citep{paper:Cargilletal2012a}. The energy balance in the TR is approximately between downward thermal conduction and optically thin radiation (for a loop in thermal equilibrium). \\ \indent The change in coronal density in response to impulsive heating arises because the increased coronal temperature implied by the heating gives rise to an excess downward heat flux that the TR is unable to radiate \citep{paper:Klimchuketal2008,paper:Cargilletal2012a}. The outcome is an enthalpy flux from chromosphere, through the TR, to the corona, often called (chromospheric) \lq evaporation\rq\ \citep[e.g.][]{paper:Antiochos&Sturrock1978}. The location of the TR moves downward in the atmosphere, and the evaporation process actually heats chromospheric material to coronal temperatures. The process is reversed after the density peaks when the TR requires a larger heat flux than the corona can provide, and so instead an enthalpy flux from the corona is set up, which both drains the corona and powers the TR radiative losses \citep{paper:Bradshaw&Cargill2010a, paper:Bradshaw&Cargill2010b}. The TR now moves upwards as the chromosphere is replenished. \\ \indent While straightforward in principle, this heating and upflow followed by cooling and downflow cycle poses major challenges for computational modelling, with conductive cooling being the most severe. For a loop in static equilibrium, in the TR one has an approximate energy equation that equates, \begin{align} \hspace{2cm} \kappa_0 T^{7/2}/ L_T^2 \sim (P/2k_B)^2 \Lambda(T)/T^2, \end{align} where $L_T$ is the temperature length scale (see Eq. \eqref{eqn:1d_L_T} for the definition) and the radiative loss function $\Lambda(T)$ decreases as a function of temperature above $10^5$K. Thus, one finds $L_T^2 \sim T^{11/2} / \Lambda(T)$, assuming the pressure is constant. Since $T$ decreases in the TR, $L_T$ must also decrease rapidly. For a static loop with peak temperature 1.75MK and density 0.25$\times 10^{15}$m$^{-3}$, $L_T \sim 30$km at $10^5$K. When impulsive heating occurs, $L_T$ is even smaller. This leads to the familiar difficulty with computational models of loop evolution: how to implement a grid that resolves the TR. Good resolution is essential in order to obtain the correct coronal density \citep[][hereafter BC13]{paper:Bradshaw&Cargill2013}, otherwise the downward heat flux jumps over an under-resolved TR to the chromosphere where the energy is radiated away. BC13 showed that major errors in the coronal density were likely with lack of resolution. \\ \indent Since the conductive timescale across a grid point has real physical meaning for the problems at hand, an explicit numerical method is to be preferred (implicit solvers require matrix inversion with no guarantee of convergence). One option is to use brute force on a fixed grid with a large number of grid points. This is slow, since numerical stability of an explicit algorithm requires $ \Delta t \leq\textrm{min}( k_B n (\Delta z)^2 / (2\kappa_0 T^{5/2}) ) $ (where $\Delta z$ is the cell width and the timestep is the minimum over the whole grid), so that a lot of time is wasted computing in the corona where $L_T$ is large and high spatial resolution is not required. A non-uniform fixed grid, with points localised at the TR is an option, but since the TR moves (see above), there is no guarantee that high resolution will be where it is required. Instead, modern schemes use an adaptive mesh which allocates points where they are needed \citep[][BC13]{paper:Bettaetal1997, paper:Bradshaw&Mason2003}. The time step restriction is the same as for a uniform grid, but effort is no longer wasted computing highly resolved coronal solutions. \\ \indent Thus far we have not distinguished between the common one-dimensional (1D) hydrodynamic (field-aligned) modelling and multi-dimensional MHD simulations. It is straightforward for a 1D code with an adaptive mesh and a large computer to model a single heating event, and, with patience, to model a nanoflare train lasting several tens of thousands of seconds \citep{paper:Cargilletal2015}. However, ensembles of thousands of loop strands heated by nanoflares pose more severe computational challenges. This has led to the development of zero-dimensional field-aligned hydrodynamical models \citep[e.g.][] {paper:Klimchuketal2008,paper:Cargilletal2012a, paper:Cargilletal2012b,paper:Cargilletal2015} that provide a quick and accurate answer to the coronal response of a loop to heating. \\ \indent The implementation of field-aligned loop plasma evolution into multi-dimensional MHD models poses much more serious challenges due to the number of grid points that can be used, so that 3D MHD simulations run in a realistic time. This is of the order of $500^3$ at the present time. If one desires to resolve the TR with a fixed grid, one needs several thousand points in one direction, so that there will be a loss of resolution elsewhere as well as a potentially crippling reduction of the time step. \\ \indent The second difficulty is that while an adaptive mesh can still be used in the TR, with commensurate computational benefits, there can be other parts of such simulations that have equally pressing requirements for high resolution, such as current sheets, and, once again, an adaptive mesh does not eliminate the time step problem. \\ \indent Artificially low coronal densities is the main consequence of not resolving the TR (BC13) and this has significant implications for coronal modelling. The purpose of this paper is to present a physically motivated approach to deal with this problem by using an integrated form of energy conservation that treats the unresolved region of the lower TR (referred to as the unresolved transition region) as a discontinuity, that responds to changing coronal conditions through the imposition of a jump condition. \\ \indent We describe the key features of the 1D field-aligned model and the definitions used to locate the unresolved transition region (UTR) in Section \ref{section:Equations and Numerical Method} and Appendix \ref{app:A}. The UTR jump condition is derived and the implementation described in Section \ref{section:Unresolved Transition Region Jump Condition}. In Section \ref{section:Results}, we present example simulations to benchmark our approach against a fully resolved 1D model. We conclude with a discussion of our new approach and the advantages of employing it, in both 1D and 3D simulations, in Section \ref{section:Discussion and Conclusions}. | } \indent The difficulty of obtaining adequate spatial resolution in numerical simulations of the corona, transition region (TR) and chromosphere system has been a long-standing problem. As pointed out by BC13, the main consequence of not resolving the TR is that the resulting coronal density is artificially low. This paper has presented an approach to deal with this problem by using an integrated form of energy conservation that essentially treats the lower TR as a discontinuity. Hence, the response of the TR to changing coronal conditions is determined through the imposition of a jump condition. When compared to fully resolved 1D models (e.g. BC13), our new approach generated improved coronal densities with significantly faster computation times than the corresponding high-resolution and fully resolved models. Specifically, our approach required at least one to two orders of magnitude less computational time than fully resolved (high-resolution) models. \\ \indent The 12 cases presented in this paper were selected to correspond to the benchmark cases presented by BC13. In all 12 cases, the evolution of the coronal density is considerably improved, compared to the same resolution run without the jump condition implemented. Crucial here, is to obtain a reasonable estimate of the (integrated) radiative losses in the unresolved part of the TR. \\ \indent We have considered only spatially uniform impulsive heating events. Simulations with the heating concentrated either at the loop base or near the loop apex will be presented in a subsequent publication. \\ \indent The advantages of this new approach are multiple. For 1D hydrodynamic simulations of the coronal response to heating \citep[see e.g.][for a review]{paper:Reale2014}, the short computation time means that (a) simulations of coronal heating events can be run quickly, permitting an extensive survey of the (large) parameter space and (b) simulations of multiple loop strands (thousands or more) that either comprise a single observed loop (e.g. a core loop), or an entire active region, can be performed with relative ease. In 3D MHD codes, the method can be included without the need for higher spatial resolution and a corresponding extended computation time. Indeed, our results suggest that good accuracy can be obtained with the order of 500 grid points, typical of what is routinely used in current 3D MHD simulations. The extension to 3D will be addressed fully in a future publication. \\ \indent The work presented here has adopted the simplest possible model for the radiation in the lower, unresolved transition region (UTR), and leads to improved coronal densities. The estimate used was motivated by the calculation of the radiation integrals for the equilibrium conditions (as shown in Fig. \ref{Fig:integrated_radiative_losses_eq}), at which the error is at most around a factor of 2 when using a uniform grid with between 125 and 2,000 grid points. On the other hand, the densities are systematically higher than those in fully resolved 1D models, which can be tracked down to the simple model underestimating the true value of the integrated radiative losses in the UTR ($R_{utr}$), at the very start of the heating phase. One can mitigate this problem by using slightly more complicated models for $R_{utr}$ at the start of the increased heating event and this will be addressed in a subsequent publication. However, for the present, the density draining phase is captured correctly which is important as this is the phase that is seen in many observations of coronal loops. We note that in Case 8, during this phase and throughout the entire evolution, the most refined uniform grid solution (Lare1D with 8,000 grid points) achieved a better agreement with the fully resolved model than the jump condition (LareJ with 500 grid points) solution but at significantly greater computational cost. \\ \indent Our emphasis here has been on obtaining an improved coronal density. This is important for interpreting observations of, for example, active region loop cores, \lq warm\rq\ loops, as well as microflare and flare coronal emission. On the other hand, by treating the lower (unresolved) TR as a discontinuity, information will be lost on detailed TR emission lines such as CIV. If the jump condition is applied close to 1 MK (i.e. between $ 5 \times 10^5$ K and 1 MK) the details of the (bright) TR will be lost, although integrated TR quantities can of course still be deduced. This loss of detail would particularly affect studies of, for example, the bright TR “moss” – bright emission at the footpoints of very hot loops \citep[see e.g.][]{paper:Flectcher&DePontieu1999}. Full numerical resolution is still required to deduce these, with the corresponding risk of serious errors in the plasma density. Model setups with smaller coronal domains (coronal heights) and or lower temperatures (say below 1-2 MK) are likely to have adequate resolution \citep[e.g.][]{paper:Zachariasetal2011, paper:Hansteenetal2015}. \\ \indent In summary, this paper has presented an approach to deal with the difficulty of obtaining the correct interaction between a downward conductive flux from the corona and the resulting upflow from the TR. A wide range of impulsive (spatially uniform) heating events was considered for both short and long loops. Our new method was used in simulations with coarse resolutions that do not resolve the lower transition region. The main result is that the method leads to (i) coronal densities comparable to fully-resolved 1D models but with significantly faster computation times, and (ii) significant improvements in the accuracy of both the coronal density and temperature temporal evolution when compared to the equivalent simulations run without this approach. | 16 | 9 | 1609.05075 |
1609 | 1609.00650_arXiv.txt | We report a detailed analysis of all regions of current star formation in the walls of the supergiant \HI shell (SGS) in the galaxy Holmberg~II based on observations with a scanning Fabry--Perot interferometer at the 6-m SAO RAS telescope. We compare the structure and kinematics of ionized gas with that of atomic hydrogen and with the stellar population of the SGS. Our deep \Ha images and archival images taken by the \textit{HST} demonstrate that current star formation episodes are larger and more complicated than previously thought: they represent unified star-forming complexes with sizes of several hundred pc rather than `chains' of separate bright nebulae in the walls of the SGS. The fact that we are dealing with unified complexes is evidenced by identified faint shell-like structures of ionized and neutral gas which connect several distinct bright \HII regions. Formation of such complexes is due to the feedback of stars with very inhomogeneous ambient gas in the walls of the SGS. The arguments supporting an idea about the triggering of star formation in SGS by the \HI supershells collision are presented. We also found a faint ionized supershell inside the \HI SGS expanding with a velocity of no greater than $10-15 \kms$. Five OB stars located inside the inner supershell are sufficient to account for its radiation, although a possibility of leakage of ionizing photons from bright \HII regions is not ruled out as well. | \begin{figure} \includegraphics[width=\linewidth]{Ha_FUV_HI_color.pdf} \includegraphics[width=\linewidth]{HoII_color_ifp_fuv_hi_zoom.pdf} \caption{False-colour image of the galaxy Holmberg~II: red, green, and blue channels correspond to H$\alpha$, FUV (GALEX) and \HI 21 cm (LITTLE THINGS) emission, respectively. The grey line denotes the area covered by our \Ha observations (both imaging and FPI) excluding the regions with optical ghosts contamination; the green line shows the area covered by \HST data we used to identify OB-stars. Bottom image shows the area of active star formation with the different brightness setup}\label{fig:colorIm} \end{figure} Irregular galaxies are widely used to study stellar feedback: radiation, stellar winds and supernovae that regulate the structure and kinematics of the interstellar medium (ISM) and might trigger new episodes of star formation. Due to the lack of spiral waves and the fact that gaseous discs are thicker than those in spiral galaxies, irregular galaxies reveal giant \HI supershells and holes with sizes as large as 1 -- 2 kpc and lifetimes up to several hundreds Myr. Giant supershells and holes in some galaxies represent the dominant feature of the ISM \citep*[see, e.g.][and references therein]{Young97, ott01, Simpson05, cannon11a, Warren11}. Such large structures are usually called supergiant shells (SGS), or giant supershells. Formation mechanisms of supergiant shells have been discussed extensively in recent decades. In the standard approach based on the \citet{weaver77} model, the cumulative action of multiple stellar winds and supernovae explosions is responsible for \HI shells formation \citep[see, e.g.][]{mccray87, tenor88, ott01}. However, it has been recognized long ago \citep[see, e.g.][]{tenor88, rhode99, kim99, Simpson05, silich06} that this scenario cannot explain the origin of giant supershells, in which the mechanical energy input from detected stellar clusters appears to be inconsistent with that required by the standard model. Several other mechanisms have been proposed: collisions of high velocity clouds with galactic discs \citep{tenor81}, fractal ISM \citep{elmegreen97}, radiation pressure from field stars \citep{elmegreen82}, ram pressure of the intergalactic medium \citep{bureau02}, \HI dissolution by UV radiation \citep{vorobyov04}, non-linear evolution of self-gravitating turbulent galactic discs \citep*{wada00, dib05} and even exotic mechanisms (see references in \citealt{silich06} and \citealt{Warren11}). The Im type (Magellanic-type irregulars) non-interacting gas-rich galaxy Holmberg~II, a member of the M81 -- NGC~2403 group, is one of the main `laboratories' for studying this phenomenon. \citet{puche92} explained the formation of SGSs and giant \HI cavities in Holmberg~II by the effect of multiple supernova explosions and stellar winds of massive stars located inside the associations. \citet{maschenko95} adopted this mechanism of SGSs formation and explained the discrepancy between the computed and observed elongation of many such shells by their mutual interaction and inhomogeneity of the ambient medium. The problem of the validity of such a `standard mechanism' in the case of Holmberg~II was first considered by \citet{rhode99} and then discussed by \citet{bureau02} and \citet{weisz09a}. The trouble with it was that many supershells lacked young stellar associations whose energy could be sufficient to produce the observed structures. By now, it is well established that high star-formation rates can be maintained for a much longer time period than previously believed: dwarf galaxies are characterized by the ability to sustain a high star-formation efficiency over several hundred Myr, and in some cases even up to 1~Gyr -- the specific (per stellar mass unit) star formation rate is high enough to exhaust gas content in $0.4-1$ Gyr \citep{mcquinn09, mcquinn10a, mcquinn10b} with local short starbursts occurring during this period. Such long periods of intense star formation provide enough energy from stellar winds and supernova explosions to drive the formation of giant cavities and supershells \citep[see, e.g.][]{weisz09b, cannon11a, cannon11b, Warren11}. \citet{weisz09a} have shown that the supershells and holes in the galaxy Holmberg~II contain multiple stellar generations and might have been formed from the energy input of these stars integrated over the lifetime of the \HI structure. A comparison of the energy of supergiant shells with the energy inflow from supernovae performed by \citet{bagetakos11} is also consistent with their formation as a result of multiple starbursts spanning a long period of time. The energetics of supergiant shells, i.e. the fraction of energy deposited in them by supernovae explosions and stellar winds, is a crucial issue for understanding their origin. It is commonly known since the first numerical studies of dynamics of supernovae remnants \citet{cox72,chevalier74} that after entering the radiative expansion stage, the total energy of the remnant decreases with a radius of $\propto R^{-2}$ to $\propto R^{-3}$, so that on a time-scale of 0.1 Myr, only around 2\% of the SN energy is available for driving the shell \citep[see more recent simulations with non-equilibrium cooling by][]{sharma14}. \citet{tomisaka81} assumed that the fraction of energy radiatively lost by a supernova might decrease, when an explosion occurs into a low density bubble produced by a stellar wind and/or previously exploded supernova(e). Within a simplistic model of sequential explosions of 20 to 100 SNe occurring at the same centre, they found qualitatively reasonable agreement with galactic superbubbles. The principal issues: the exact expansion law and the fraction of energy remained for a continuous support of growing superbubbles, have been nonetheless left beyond clear understanding. In full 3D numerical simulations of sequential SNe exploding at the same centre, \citet{sharma14} have found that even on a long time-scale (30 to 50 Myr), up to 30\% of the injected energy can retain into slow expansion of the supershell. This conclusion is valid though only in case of `coherent' SNe explosions, i.e. when the remnants overlap before entering the radiative stage \citep{nath13}. Numerical models with scattered explosions, i.e. spread through over an active volume, confirm this result: collective action of `coherent' SNe makes them more efficient in driving supershells, with a fraction of retained energy of $\sim 0.1$ on times up to 10 Myr \citep{vasiliev15,yadav16}. In all cases, the expansion sets asymptotically into a power law close to the standard $t^{3/5}$ wind regime with mechanical luminosity reduced by a factor of approximately 10, though still depending on interrelation between gas density and SN rate \citet{vasiliev15}. When the origin of supergiant shells of kpc-scales are concerned, particularly in such galaxies as Ho~II and IC 2574, where signs of merging of different superbubbles are clearly seen, numerical description becomes more challenging. However, in conditions typical of dwarf galaxies, the wind expansion law with energy reduced by a factor of 10 would be a reasonable conservative approach. Short (about 10 Myr) local starbursts, which we observed as complexes of ionized gas, are located mainly inside dense walls of giant H~{\sc i} structures in Holmberg~II. According to the modern concepts, ongoing star formation there could be triggered by the expansion and/or collision of supergiant shells. The analysis of the influence of these new sites of star formation on the evolution of supergiant shells and hence on the structure of the gaseous medium of the galaxy is of greatest interest. \medskip This work is a third in the series of our investigations of the galaxy Holmberg~II. Previously in \citet*{egorov13}, we studied the ionized gas spectra of star-forming regions in Ho~II using optical long-slit spectroscopic observations carried out with the 6-m SAO RAS telescope. We estimated oxygen, nitrogen, sulphur, neon and argon abundances in individual \HII regions and found the average metallicity in the galaxy to be either 0.1 $Z_\odot$ or 0.3 $Z_\odot$ depending on the estimation method applied. In \citet{wiebe14}, we performed a multiwavelength photometric study of star formation regions in Ho~II using archival data of GALEX, \textit{Spitzer} and \textit{Herschel} space telescopes. We have examined for the first time how the emission of star-forming regions over a wide wavelength range evolves with time. We traced the evolution of the fraction of polycyclic aromatic hydrocarbons (PAHs) and of the hot-grain properties in the galaxy. The aim of this study is to analyse the kinematics of ionized gas in all regions of star formation and of their ambient neutral gas in the most extended 2~kpc sized supergiant shell in the galaxy. We search for shell-like structures of ionized gas that reveal signs of expansion and compare them with stellar population in star-forming regions. We also try to recognize kinematic evidences for possible supernovae shocks in the eastern chain of bright emission nebulae predicted by \citet{tong95}. An analysis of gas kinematics % in the rim of an \HI SGS is of great interest, because it may help to find out how such giant structures change when affected by new local bursts of triggered star formation. When studying the supergiant \HI shell with triggered star formation located in the Irr galaxy IC~2574 \citep{egorov14}, we found for the first time an inner weak diffuse emission of ionized gas in \Ha and \SII 6717,6731 lines with kinematic evidences for expansion. We showed that such an inner giant ionized supershell must have likely be formed as a result of the action of Lyman continuum photons escaping the star-forming regions on to the neutral gas in the supergiant \HI shell. This is a new phenomenon hitherto unobserved in IC~2574, and the search of such inner shell-like \HII structures inside \HI supergiant shells in other irregular galaxies seems to be interesting. Earlier, we briefly announced the discovery of a similar giant faint ionized supershell inside the \HI SGS in Holmberg~II \citep*{egorov15}, which is seen on the bottom panel of Fig.~\ref{fig:colorIm}; here we report the results of its investigation. To avoid confusion, further we will use the SGS abbreviation to refer to the supergiant shell in Holmberg~II under consideration and will use the full term `supergiant shell' to denote the entire class of such objects. This study is based on our observations conducted with the scanning Fabry--Perot interferometer (FPI) in \Ha line and with narrow-band \Ha, \SII and \OIII filters at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS). High spatial and spectral resolutions of FPI data allows to analyze the ionized gas kinematics in superbubbles in details. A number of the studies made using this technique were published \citep*[see e.g.][and references therein]{lozinsk03, relano05, egorov10, egorov14, cf15, sc15} The observations and data reduction performed are described in Section~\ref{sec:obs}. In Section~\ref{sec:overview}, we overview the results of previous multiwavelength studies of Holmberg~II. Section~\ref{sec:shells} is devoted to the search for expanding ionized and neutral shells and supershells. In Section~\ref{sec:morphology}, we analyse the morphology of \HII complexes in the galaxy. In Section~\ref{sec:discussion}, we discuss the results obtained, including the nature of the faint ionized inner supershell inside the \HI SGS. Section~\ref{sec:summary} summarizes the main results of this study. | \begin{tabular}{cccc} \hline Shell & $V_{exp}, \kms$ & Size, pc & Age, Myr \\ \hline SE1 & 15 & 86 & 1.7\\ SE2 & 30--37 & $322\times230$ & 2.6\\ SE3 & 25--30 & $282\times188$ & 2.8\\ SE4 & 27--32 & $190\times128$ & 1.8\\ SE5 & 27 & $358\times240$ & 4.0\\ SE6 & $\simlt20$ & 74 & 1.1\\ \multicolumn{3}{c}{Age of HSK~67, 70:} & $3.8 - 4.8^*$ \\ \multicolumn{3}{c}{} & $2.5 - 4.5^{**}$ \\ \hline NE1 & 26 & $72\times50$ & 0.8\\ NE2 & 15 & $162\times104$ & 3.2\\ NE3 & 17 & $254\times224$ & 4.5\\ NE4 & 24 & $210\times168$ & 2.6\\ \multicolumn{3}{c}{Age of HSK~59, 71, 73:} & $3.5 - 4.1^*$ \\ \multicolumn{3}{c}{} & $2.5 - 4.5^{**}$ \\ \hline N1 & 22 & $362\times316$ & 4.9\\ N2 & 28 & $142\times96$ & 1.5\\ N3 & 10 & $124\times76$ & 3.7\\ N4 & 18 & $230\times203$ & 7.2\\ \multicolumn{3}{c}{Age of HSK~45:} & $3.7^*$ \\ \multicolumn{3}{c}{} & $2.5 - 3.5^{**}$ \\ \hline NW1 & 25 & $392\times312$ & 4.7\\ NW2 & 21 & $112\times70$ & 1.6\\ NW3 & 21 & $163\times102$ & 2.3\\ NW4 & 27 & 216 & 2.4\\ NW5 & $\simeq 20 $ & 226 & 3.4\\ % \multicolumn{3}{c}{Age of HSK~15, 16, 17, 20, 25:} & $4.8 - 6.2^*$ \\ \multicolumn{3}{c}{} & $4.5 - 6.3^{**}$ \\ \hline ExtNE1 & 20 & $49$ & 1.5\\ \multicolumn{3}{c}{Age of ExtNE:} & $3.5 - 4.5^{**}$ \\ \hline ExtN1 & 23 & 139 & 3.6 \\ \multicolumn{3}{c}{Age of ExtN:} & $3.5 - 4.5^{**}$ \\ \hline S1 & 40 & 120 & 1.8\\ \hline \multicolumn{4}{l}{\begin{scriptsize} $^*$Estimates made by \citet{wiebe14} using H$\beta$ equivalent width.\end{scriptsize}}\\ \multicolumn{4}{l}{\begin{scriptsize} $^{**}$Estimated by \cite{stewart00} using \Ha and FUV data. \end{scriptsize}} \\ \end{tabular} \end{table} \begin{table*} \caption{Sizes and ionization budget of complexes of ongoing star formation}\label{tab:ionization} \begin{tabular}{ccccccc} \hline Complex & Size & F(\Ha), & N(OV5) & N(OB) & $\mathrm{Q_{H\alpha}}$ & $\mathrm{Q_{stars}}$ \\ & pc & $10^{-13}$ erg s$^{-1}$ cm$^{-2}$ & & & $\mathrm{10^{50}\ s^{-1} }$&$\mathrm{10^{50}\ s^{-1} }$\\ \hline SE & $1150\times1050$ &9.3 & 56 & 35 & 8.8 &9.7\\ NE & $1400\times980$& 9.7 & 58 & 26 & 9.1 &8.3 \\ N & $1500\times1000$ &14.0 & 83 & 36 & 13.2 & 11.1\\ NW & $2450\times1600$ & 8.4 & 50 & 31 & 7.9 &7.6 \\ Int.shell (diff) & $2730\times2280$ & 0.7 & 4 & 5 & 0.7 &1.0\\ Int.shell (all) & $2730\times2280$ & 1.7 & 10 & 7& 1.6 & 1.5\\ ExtN & $1530\times1030$ & 1.1 & 7 & $8^*$ & 1.1 & $1.9^*$\\ ExtNE & $960\times700$ & 0.5 & 3 & 3 & 0.5 &1.1\\ \hline \multicolumn{6}{l}{\begin{scriptsize} $^*$Might be underestimated because of the incomplete coverage by \HST observations (see Fig.~\ref{fig:colorIm}).\end{scriptsize}}\\ \end{tabular} \end{table*} Earlier, \cite{weisz09a} identified four local \HI shells in the SGS wall with sizes of $300 - 400$~pc expanding with velocities $7-15 \kms$. These shells (\# 8, 12, 14 and 27 in Fig.~2 of their paper) are located in the immediate vicinity of the \HII HSK~70, 16, 17, and 26 regions (see fig.~\ref{fig:reg_separation}). In addition, shells \# 16 and 23 are also seen and located north of the central chain of star-forming regions which might be connected with it. We refined the location of the \HI shells associated with star-forming regions and performed search for ionized gas shells in the galaxy. Below, we report the details and results of our kinematic analysis. An expanding shell can be identified by a velocity ellipse (or a part of it) in PV diagrams or by splitting of an emission-line profile. In the case where the expansion velocity of a shell is small and spectral resolution is insufficient to resolve two components, the shell distinguishes itself by its higher velocity dispersion in the centre. We used all the above techniques to search for expanding shells and estimate their expansion velocities. Figure~\ref{fig:HI_maps} shows the \HI column density and line-of-sight velocity dispersion (second moment) maps for three areas -- SE, N and NW -- where we see increased \HI velocity dispersion. The areas of high velocity dispersion in Fig.~\ref{fig:HI_maps} correspond indeed to the expanding \HI superbubbles. This suggestion is confirmed by our analysis of PV diagrams. For example, the `velocity ellipse' might be seen at positions of $100 - 140$ , $170 - 220$ arcsec along PV diagram \# 1 (HI) and $15 - 65$ arcsec along PV diagram \# 2 (HI) in Fig.~\ref{fig:pv}, which correspond to the regions of the increased velocity dispersion in Fig.~\ref{fig:HI_maps} in the areas of N, NW and SE respectively. It was shown in many studies \citep[][see also references therein]{MunozTunon1996,ML12} that the intensity -- velocity dispersion diagrams of ionized gas ($I - \sigma$) can be successfully used to identify areas, where the increased velocity dispersion is caused by expanding shells. We fitted the \Ha line profile to a single-component Voigt profile in each pixel obtained from the FPI data cube and constructed the $I - \sigma$ diagram for the galaxy Holmberg~II (see Fig.~\ref{fig:i_sigma}). The red line in the diagram marks the intensity-weighted average velocity dispersion of ionized gas in the galaxy -- $\sigma_m = 20.4 \pm 7.1 \kms $. Identical colours in the diagram (the top panel) and map (the bottom panel) are used to highlight the characteristic areas. Thus, the horizontal strip with relatively low velocity dispersion and high surface brightness marked in blue corresponds to bright \HII regions and includes 50 per cent of the galaxy's \Ha flux. Areas of increased dispersion, which are most likely associated with spectroscopically unresolved expanding shells, are shown in green colour, whereas the red colour corresponds to shell-like structures with clear separation of the components of the \Ha line profile. The remaining areas of the increased velocity dispersion are shown in orange colour, and areas of low surface brightness, in grey colour. We performed a more bona fide search for expanding structures of ionized gas by analysing the PV diagrams that uniformly cover each region of ongoing star formation in the galaxy. Some examples of them are shown in Fig.~\ref{fig:pv}. In the areas shown in red colour in Fig.~\ref{fig:i_sigma}, we see clear evidence for gas expansion in the form of the velocity ellipse or a part of it. Subsequent fitting of the \Ha profiles by one, two or three Voigt components allowed us to estimate the expansion velocities of the corresponding structures. Our analysis of gas kinematics in the \HI and \Ha lines revealed three local neutral-gas shells associated with star-forming regions and 22 ionized gas shells. Their location is shown in grey and blue colours respectively in Fig.~\ref{fig:SE_shells} -- \ref{fig:sb_stars}. We found no signs of expansion of bright \HII regions. Despite a rather high spectral resolution of FPI, the expansion velocities of these regions proved to be low: it does not exceed $11 \kms$ (half of the instrumental FWHM of FPI used). All the expanding shells of ionized gas, which we found, represent faint filamentary features in the \Ha image and possibly reside in a medium with a relatively low density. In our earlier paper \cite{wiebe14}, we have estimated the expansion velocity of the \HII regions HSK45 and HSK73, however, it is now clear that the evidence of their expansion does not refer to bright nebulae but rather to faint shell-like ionized-gas structures around them. We estimated the kinematic ages of the identified local \HII shells in terms of \citet{weaver77} model by the following relation: \[ t=0.6 R/V_{\rm exp}, \] where $R$ is the radius in pc, $V_{\rm exp}$ -- the expansion velocity in $\kms$ and $t$ -- the age in Myr. To estimate the ages of bright \HII regions that show no signs of its expansion, in \citet{wiebe14} we used the equivalent width (EW) of the $H_{\beta}$ emission line which correlates rather well with the age of \HII regions \citep[see, e.g.][]{schaerer98, leitherer99}. The derived ages of the faint local shells found inside the \HII complexes and of bright \HII regions are summarized in Table~\ref{tab:shells_summary}. This table also lists the age estimates made by \citet{stewart00} for star-forming regions based on the results of FUV and optical observations. Because of the uncertainty in the method used for age determination, the above authors divided all \HII regions studied into four age groups: $0-3.5$ Myr, $3.4-4.5$ Myr, $4.5-6.3$ Myr and older than 6.3 Myr (see table~5 in their paper). Given the results of the search for expanding shells and the study of their kinematics, we can conclude that the observed emission structures in the four areas in the SGS walls (SE, NE, N and NW) that we identified based on morphology and in two areas outside the SGS (ExtN and ExtNE) are indeed physically connected. This means (see also Sections~\ref{sec:morphology} and \ref{sec:complexes} below) that the current star formation in the galaxy is represented by unified complexes with sizes of several hundred pc which combine several bright nebulae. \label{sec:discussion} \subsection{What triggered star formation in Ho~II?} Detailed multicolour \textit{HST} photometry of the stellar population inside each supergiant \HI shell in the Ho~II galaxy reported by \cite{weisz09a} (see also references therein) revealed stars of several age groups rather than single coeval clusters as previously believed. It stimulated a new currently widely accepted model: neutral supergiant shells were formed from several generations of stars over several hundreds million years. The main criterion of current starburst -- the H$\alpha$ emission in the neighbourhood of a newly formed cluster of young stars -- appears for $1-2$ Myr and rapidly fades (in about 10 Myr -- the main-sequence lifetime of OB stars and the time-scale of coherent existence of young star clusters \citealt{lada03}). The UV radiation of massive young stars of the cluster reaches its maximum at about 5 Myr, and FUV decays over much longer time-scale limiting the time period, when the traces of star formation remain visible to $\simeq 100 - 150$ Myr \citep{ oconnel97, stewart00}. That is why in terms of accepted model of supergiant shells formation, the H$\alpha$ emission and 24 $\mu$m IR radiation which trace the sites of current SF in Irr galaxies and, in particular, in Ho~II, do not always correlate with the location of giant \HI supershells of at least several hundred Myr old. Two questions concerning star formation processed in Irr galaxies remain to be of interest today: what actually triggers the ongoing star formation in a particular region of a galaxy? And how does the structure and kinematics of giant \HI cavities and shells change under the influence of new episodes of star formation in their walls? The analysis of the structure and kinematics of \HII regions in the walls of the SGS in the Ho~II galaxy that we perform in this study is an attempt to shed certain light on the problem. In this section, we discuss the probable mechanism responsible for initiation of the ongoing star formation in Holmberg~II. An analysis of deep $H\alpha$ images of 51 Irr and diffuse galaxies allowed \citet{hunter93} to discover a distinguishing feature of Ho~II, which consisted of the very local disposition of \HII regions. The authors formulated the question: why there are so few shell-like ionized structures despite the presence of many neutral supergiant shells which most likely have been produced by the stellar wind and SN explosions of rich OB associations? As we pointed out above, all local star-forming complexes --- the brightest emission nebulae as well as the brightest UV and IR regions --- are located in the northern wall of the most extended \HI cavity in the galaxy (see Fig.~\ref{fig:colorIm}). Such localization makes the question about the nature of ongoing star formation in Ho~II to be more intriguing -- why \HII regions are observed mostly in the north part of SGS, but not spread over it? One of possible explanation of such star formation distribution might be its occurring in the densest gaseous clouds in the galaxy. Does the locations of star-forming regions in Ho~II correlate with the gas volume density in the SGS? To answer to this question, we estimated the \HI volume density from the LITTLE THINGS data. We constructed the 21-cm line intensity map using the technique described by \citet{things} based on the \HI 21~cm line intensity distribution. To convert column density into volume density, we assumed that the scale height of the \HI disc and its inclination to be $h=400$~pc \citep{banerjee11} and $i=47^\circ$ \citep{Oh11} respectively. As a result, we establish that the distribution of \HI volume density in the SGS discussed, where regions of ongoing star formation are located, is, on the whole, uniform with $n_\mathrm{HI}$ varying from 0.3 to $0.7\ \mathrm{cm}^{-3}$. The inferred densities agree with the previous estimates of the density in the SGS: $0.5\ \mathrm{cm}^{-3}$ and $0.3\ \mathrm{cm}^{-3}$ according to \citet{bagetakos11} and \citet{puche92} respectively. The `central arc' of bright ionized nebulae in the Ho~II galaxy is indeed located in the region of the highest HI column density. However, the average column density of neutral gas at this location does not substantially exceed the density in the southern wall of the SGS which contains small separate star-forming regions but with no extended \Ha emission complexes similar to the regions in the `central arc' (see Fig.~\ref{fig:colorIm}). Moreover, star formation in galaxies may occur in environments with sufficiently low densities. Recent studies fail to reveal the so-called gas surface density threshold above which star formation begins; at lower densities, the star-formation efficiency decreases more rapidly with the decrease of gas density but does not vanish even at $\Sigma_{\rm HI+H_2}<0.5$ M$_\odot$ pc$^{-2}$ (see \citealt{bigiel08, bigiel10, zasov12, abram12} and references therein) and, apparently even at lower densities (\citealt{shi14}). Summing up, we can't explain the observed location of \HII regions in Ho~II by the gas density distribution. Our study shows that the region that separates the SGS discussed and the giant irregularly shaped northern cavity consisting of several shells adjoining each other in the sky plane is characterized by a very non-uniform structure and the greatest local variations of the neutral-gas velocity in the galaxy. The distribution of \HI velocity dispersion along the SGS discussed here shows insignificant variations -- approximately from 7 to $16 \kms$. However, it is interesting to verify whether these variations are related to ongoing star formation in the SGS rims. In order to answer this question we compared pixel-by-pixel the \HI velocity dispersion and \Ha flux that traces star formation rate. The procedure had several steps. First of all, we performed a Gaussian convolution of our \Ha image in order to obtain the same spatial resolution as for the \HI LITTLE THINGS data. We then resized the convolved \Ha image in order to obtain the same pixel scale with an \HI velocity dispersion map. After that, the pixels corresponding to the bright \HI rim of the SGS were selected for a further analysis. We constructed a 2D histogram of the \Ha flux and \HI velocity dispersion distributions among these pixels. The resulting histogram is shown in the top panel of Fig.~\ref{fig:HI_I-sigma}. We also show the mean \HI velocity dispersion and its standard deviation for each flux bin. \begin{figure} \includegraphics[width=0.97\linewidth]{HoII_HIsig_Haflux.pdf} \includegraphics[width=0.97\linewidth]{IC2574_HIsig_Haflux.pdf} \caption{2D histogram of the \Ha flux and \HI velocity dispersion along the SGS in Ho~II (top) and IC~2574 (bottom) galaxies. Black points and bars denote the mean value and standard deviation of the \HI velocity dispersion for each \Ha flux bin.}\label{fig:HI_I-sigma} \end{figure} As is evident from the constructed histogram, the \HI velocity dispersion in the SGS does not change in the areas with a very low \Ha flux. However, starting from $F(\mathrm{H}\alpha) \simeq 2\times10^{-18} \mathrm{erg\ s^{-1}\ cm^{-2}\ arcsec^{-2}}$, velocity dispersion begins to show an increasing trend. The observed dependence can be explained by two factors. First, the \HI velocity dispersion may have become higher because of the collision of the SGS with the above northern supershells resulting in ignition of star formation in this region. Second, the ongoing star formation itself may have an effect on the SGS by increasing the \HI turbulence level near bright \HII regions. In the bottom panel of Fig.~\ref{fig:HI_I-sigma}, we show the similar histogram for another supergiant shell we previously studied \citep{egorov14} located in IC~2574 galaxy. In contrast to Ho~II SGS, the morphology of a supergiant shell in IC~2574 does not reveal any signs of its interaction with neighbouring shells, and we do not see any clear correlation between the \HI velocity dispersion and the \Ha flux for that case. This allows us to prefer the first explanation of the dependence observed for the Ho~II galaxy. The above facts and considerations suggest that the last episode of star formation in the Ho~II galaxy, which we observed as areas of bright \HII regions and shells, was triggered by the collision of two above mentioned giant \HI shell-like structures (or, possibly, by the collision of multiple shells that produced them). The mechanism of star formation triggered by the collision of supergiant shells is well known \citep[see][]{chernin95}; many colliding supergiant shells with star formation have been found in the LMC (see the references in the above paper). One of the most striking examples of this process is clearly observed in the irregular Local group galaxy IC~1613, where the region of ongoing star formation is localized at the periphery of a supergiant \HI shell at the place of its collision with another supergiant shell located north of it \citep[see][]{lozinsk02}. Another example of this type can be found in the NGC~6946 galaxy: a complex of \HII regions, which is the second largest such complex in the galaxy, is located at the interface between two neutral gas cavities \#107 and \#106 identified by \cite{boomsma08}, see also \citet*{efremov11}. Note that the collision of supergiant shells by itself is, generally speaking, also a natural consequence of the interaction between the collective wind and supernovae and the ambient gas over a more extended scale length and time-scale. \subsection{Complexes of current star formation}\label{sec:complexes} Faint extended filamentary structures of ionized gas identified in this study, which connect individual bright \HII regions, have changed our understanding of the regions of triggered star formation in the galaxy. It is evident that current sites of star formation are not `chains' of bright nebulae in the walls of the HI SGS, as previously thought, but rather unified extended star-forming complexes with sizes extending up to several hundreds pc, i.e. comparable to the size of the SGS. The conclusion that the structures considered are single entities is further corroborated by our discovery of faint neutral shells surrounding the complexes SE, N and NW. The formation of such unified complexes can be understood in terms of the current view on the feedback between stars and the ambient gas given the strong inhomogeneity of gas in the SGS walls. The UV radiation of massive stars ionizes the surrounding gas and creates bright \HII regions. At the outer boundary of a dense parent cloud, the ionization front penetrates further into the tenuous medium creating `blisters' on the side of the dense cloud (a so-called `champagne effect') according to the model by \cite{tenor79}. Radiation and stellar winds form faint shell-like structures in the tenuous ambient medium. These structures resemble faint filamentary structures observed in the SE, NE, N and NW complexes. As expected in terms of this model, the observed expansion velocity of faint shell-like formations exceeds the expansion velocities of the bright and more compact nebulae (see Section~\ref{sec:shells}). Note that the age of faint extended structures should be close to that of bright and more compact structures if these are unified sites of star formation. Unfortunately, the accuracy of age determination for individual objects in these unified complexes of star formation listed in Table~\ref{tab:shells_summary} leaves a lot to be desired because of too many uncertain factors involved. We discussed the errors of age estimations based on the equivalent width of the H-beta line in our earlier paper \citet{wiebe14}. The main ones are the assumption about a single starburst in a given \HII complex and the internal extinction (see also \citealt{stasinska96}). The age determined by \citet{stewart00} should be treated as the mean age of stars in the aperture because of the fact that a single-generation model is used to interpret a flux from what is potentially a mix of populations of slightly different ages. To compensate for this uncertainty, regions are classified into four age groups. According to the authors, when comparing regions the actual age cutoffs for each group should be ignored and groups should be just thought to consist of relatively very young, young, intermediate-age or older star-forming regions. In principle, the most accurate age estimate is the kinematic age if the expansion velocity and the radius of a shell are correctly determined. However, in the case of Ho~II the spatial resolution is insufficient to construct the `velocity ellipse' in each nebula. We attempted to estimate the expansion velocity from the split of the position-velocity diagrams, however, no such evidence was revealed for bright regions. For this reason, we have estimated the expansion velocities of the nebulae from individual profiles, i.e. without any guarantee that they refer to the region of the most high-velocity motions. Furthermore, the irregular structure of the \HII regions complicates a correct determination of the shell radius. \begin{figure} \includegraphics[width=\linewidth]{SIIOIII_v1.pdf}% \caption{\SII6717,6731\AA\, to \OIII5007 emission-line ratio maps for the SE complex (left) and the \HII region at the south-west of the SGS rim (right). Isophotes correspond to the \Ha flux levels $(5, 15, 25, 35 and 45)\times10^{-17}\ \mathrm{erg\ s^{-1}\ cm^{-2} \ arcsec^{-2}}$. The regions contaminated by the foreground stars are masked.}\label{fig:IPM} \end{figure} Given these uncertainties, the ages estimated by different methods (listed in Table~\ref{tab:shells_summary}) are consistent with our conclusion about single complexes of current star formation in the galaxy, which combine several bright nebulae and the associated weak shell-like structures. In Section~\ref{sec:morphology}, we report the estimations of the amount of ionizing radiation from the young massive stars located inside the complexes. It follows from Table~\ref{tab:ionization} that it is sufficient to account for the observed \Ha flux for all the complexes. In faint external complexes the energy of stars is more than sufficient for ionizing the gas. The `extra' photons from these complexes probably leak from these low-density and high-humidity complexes. \cite{pellegrini11} proposed the method of distinguishing between density- and radiation bounded \HII regions based on the \SIIOIII\, ratio map. The main idea of the method is that for an optically thick nebula one should observe the increased \SIIOIII\, ratio at the edges of a region, while in the optically thin case the low ionization zone with the enhanced \SII emission might not appear. We have applied this method to the galaxy Holmberg~II and found that almost all regions of ionized gas show the ionization structure that is typical of optically thick \HII regions -- they exhibit the outer shell of the enhanced \SIIOIII\, ratio surrounding the \OIII dominated core corresponding to the hot regions near the ionization sources. As an example of such structures, we show the \SIIOIII\, map for the SE complex on the left panel of Fig.~\ref{fig:IPM}. Note, however, the increased contribution of \OIII emission outside the border of the northern \HII region probably caused by the ionizing radiation leakage toward the centre of the SE complex. The only optically thin region in the galaxy that does not represent such a \SII shell is the compact \HII region at the south-western part of the SGS (shown in the right panel of Fig.~\ref{fig:IPM}). Thus, we may expect large escape fraction of ionizing radiation from this region, but also we cannot rule out the possible leakage from other \HII regions due to their porosity. Strictly speaking, this method allows us to identify density-bounded regions, but the regions which look like radiation-bounded in the \SIIOIII\, maps still might be optically thin. \subsection{Internal ionized supershell in SGS.}\label{sec:superbubble} We were the first to identify a faint diffuse internal supershell of ionized gas inside the SGS which was not seen in the \textit{HST}/ACS images. The expansion velocity of the inner shell coincides with the expansion velocity of the neutral SGS. The \OIIIHb\, vs \SIIHa\, diagnostic diagram shown in Fig.~\ref{fig:BPT} suggests that the increased values of these ratios corresponding to a gas glow behind the shock front is practically not observed in the galaxy including the region inside the the SGS. It can be concluded from this that the nature of the ionized gas emission inside the SGS in the Ho~II galaxy differs from that we have discovered inside the supergiant \HI shell of the IC~2574 galaxy. Based on the observed increased \SIIHa\ and \NIIHa\ line ratios of diffuse gas in the IC~2574 SGS, we concluded \citep{egorov14} that it should be similar to those of the extra-planar diffuse ionized medium (DIG) in spiral and irregular galaxies. Owing to that similarly to the DIG, we explained the faint diffuse ionized gas emission inside the SGS in IC~2574 as a result of leakage of both the ionizing photons and mechanical energy from the bright \HII regions. In the case of Ho~II, the location of the regions corresponding to the ionized internal superbubble on the diagnostic diagram (Fig.~\ref{fig:BPT}) is indicative of the photionization mechanism of gas emission there. The analysis of the FUV morphology of the galaxy presented by \cite{stewart00} shows the large region of faint diffuse FUV emission extending to the south-west of the central arc of bright \HII complexes. This structure is clearly seen in Fig.~\ref{fig:colorIm}. The relatively bright regions of FUV emission, denoted as star-forming regions 23, 35, 36 and 37 in the list of \cite{stewart00} and selected by the above authors as areas with FUV and no H$\alpha$ emission and also fainter regions practically completely fill the inner supergiant shell (see Fig.~\ref{fig:colorIm}). However, the observed FUV emission comes from the regions, where intensive star formation occurred 20--60~Myr ago \citep{weisz09a} and hence there was a lack of ionizing Lyman quanta. What is responsible for the creation of this internal ionized supershell in SGS then? As it follows from Fig.~\ref{fig:sb_stars}, five identified OB stars are located inside the internal \Ha superbubble near its north-western edge. Their photometry shows that all of them are massive O stars. Correspondingly, these stars are most likely the main source of ionizing photons. Thus, according to Table~\ref{tab:ionization}, the amount of ionizing quanta from these stars is consistent with the value necessary to maintain the observed \Ha flux. Note that the pure diffuse component of the ionized superbubble is denoted as `Int.shell (diff)' in Table~\ref{tab:ionization}, while `Int.shell (all)' means the whole region including the compact bright \HII nebulae at the rim of the superbubble. Additional sources of ionizing radiation could be located in the south-western chain of bright compact \HII regions, for which there are no available data about their stellar population. However, a certain contribution of energy leakage to the ionization of the superbubble can not be ruled out. The latter is supported with the fact that the brightest nebula at the southern rim of the superbubble seems to be optically thin (see Fig.~\ref{fig:IPM} and Section~\ref{sec:complexes}) that might cause the high fraction of ionizing photons escape. Summing up, the ionized internal supershell was created most probably by the influence of ionizing radiation of 5 O stars located at its interior and of the additional energy leakage from nearby bright \HII complexes to the internal walls of the \HI SGS. In addition, a continuing mechanical energy input from stellar activity, winds and SNe explosions, may also act on to the internal side of the SGS and contribute to its dynamics. For instance, speaking about the SE complex shown in Fig.~\ref{fig:SE_shells}, it can be clearly seen from rough estimates that the total mechanical energy input from the stars inside the shell $\dot E_{\rm wind}\sim 10^{38}$ erg s$^{-1}$ and the shell kinetic energy consumptions $\dot E_k\sim\sum 4\pi\rho R^2v_s^3\sim 2\times 10^{38}$ erg s$^{-1}$ are marginally equal (the gas density $n\sim 0.3$ cm$^{-3}$ is assumed, see above). Shock waves from a stellar wind and SNe evacuate most of gas into the shell, so that the cavity remains filled mostly by wind and SNe ejecta with a very low density. For instance, when a supergiant shell is produced by multiple SNe explosions the remaining density might be as low as $\simlt 10^{-4}$ of the ambient density \citep{sharma14}. Even if a much less violent energy release by ionizing radiation from underlying OB stars evacuates the gas, its density within the photo-ionized bubble remains as low as $\sim 10^{-2.5}$ \citep{henney05, henney07}. One, therefore, estimates the gas density inside the bubble as $n_b\simlt 5\times 10^{-5}$ cm$^{-3}$ if the bubble is due to SNe explosions, and as $n_b\sim 10^{-3}$ cm$^{-3}$ otherwise. In these conditions, the wind generated by massive stars inside the SGS acts from the interior and transfer momentum to the supershell. The free expansion phase of the wind continues until the swept-up mass equals to the wind-blown mass \citep[see, e.g.][]{draine11} \be t_0\simeq 10^2n_b^{-1/2}\dot M_6^{1/2}v_{\rm w,8}^{-3/2}~{\rm yr}, \ee where $\dot M_6$ in units $10^{-6}M_\odot$ yr$^{-1}$, $v_{\rm w,8}$ is the wind velocity in $10^3$ km s$^{-1}$. This gives $t_0\simeq 3\times 10^4$ yr and the corresponding radius $R_0\simeq 30$ pc for a SNe produced the SGS and an order of magnitude lower $t_0$ and $R_0$ for the case of a SGS driven by ionization fronts. Accounting that the massive stars inside the supershell (marked in Fig.~\ref{fig:sb_stars}) are located at larger distances -- 100 to 400 pc, one can estimate pressure acting on to the shell as \be \label{vs} P_{\rm w}=\rho_b\dot R_b^2\simeq 10^{-8}\left({L_{36} n_b^2\over R_{\rm 1~pc}^2}\right)^{1/3}~{\rm dyn~cm^{-2}}, \ee where $L_{36}$ is the wind mechanical luminosity in units $10^{36}$ erg s$^{-1}$, $R_b$ is the radius of a wind-driven shock in the ambient medium, $R_{\rm 1~pc}$ is its value in 1 pc. When the wind-driven shock acts on to the supershell it can support the expansion with the velocity \be v_{_{\rm SGS}}\simeq \left({P_{\rm w}\over\rho_0}\right)^{1/2}\simeq 0.8\times 10^8{\left({L_{36}\over R_{\rm 1~pc}^2}\right)}^{1/6}{n_b^{1/3}\over n_0^{1/2}}~{\rm cm~s^{-1}}, \ee so that for a SNe swept-up supershell with $n_b\sim 5\times 10^{-5}$ cm$^{-3}$ a star located at $R=100$ pc (as, e.g. the brightest star in the left corner of the SE5 shell in Fig.\ref{fig:SE_shells}) would produce the velocity of the supershell of 6 km s$^{-1}$, while for $n_b=10^{-3}$ cm$^{-3}$ it would support $v{_{\rm SGS}}\simeq 13$ km s$^{-1}$. It is worth stressing that episodic wind and SNe explosions and the respective feedback during the whole evolution of the SGS can support gas density in the bubble at a level sufficient for transferring a proper momentum on its internal surface. In those cases, when OB stars lie closer than $R_0$ to the SGS edge, they act on to the supershell by the expanding wind directly without transferring momentum through the gas inside the cavity. In this case, the shell velocity supported by wind would be a factor of $(L_{36} n_0/R_{\rm 1~pc}^2 n_b^2)^{1/6}$ higher than the above estimate in Eq.~(\ref{vs}). One may expect that the similar enhancement of the action of a stellar wind on the supershell would take place, when the wind propagates through low density tunnels inside the bubble. Overall, one may think that energy release in the form of Ly-continuum photons and corpuscular winds emitted by massive stars inside the supershells does not only support their expansion, but also provides proper conditions for transferring momentum from stars to the walls and keeping them continuously expanding until star formation is exhausted. \subsection{Search for SNRs in the SGS.}\label{sec:SNe} Radio observations of the Ho~II galaxy \citep*{tong95, braun07, heald09} revealed a continuum radio emission in the region of bright emission nebulae. The synchrotron component of radio emission was identified in the eastern chain of bright nebulae by \citet{tong95} and this fact led the authors to suspect that these areas may contain supernova remnants. The detected polarized radio emission also coincides with this chain \citep{heald09}. \citet{hong13} identified the shock-ionized component via the line diagnostic diagram \OIIIHb\ vs \NIIHa\ inside the HSK~45 nebula using the high resolution \HST data. Our spectroscopic observations \citep{egorov13} did not allow us to identify the optical emission of these hypothetical supernova remnants and shock fronts by the \textsc{I([S~ii])/I(H$\alpha$)} line ratio. We used our narrow-band images in the \OIII 5007\AA, \SII 6717,6731\AA\, and \Ha lines to construct the diagnostic diagram of \OIIIHb\, vs \SIIHa\, ratios for each pixel of the galaxy. All the used line ratios were corrected by reddening using the mean value $E(B-V)=0.05$ \citep{egorov13}. We calculated the values of H$\beta$ fluxes from the H$\alpha$ flux using the theoretical ratio I(H$\alpha$)/I(H$\beta$) for $T=10000$~K \citep{osterbrock}. The result is shown in Fig.~\ref{fig:BPT}. A black curve denotes the separation line between the regions with pure photoionization and composite (with a probably significant contribution of the shocks) excitation \citep{kewley01}. As follows from this diagram, almost all emission observed in the galaxy has been excited by photoionization and do not show any signs of shocks. The points lying over the separation curve in the diagram correspond to the regions of low brightness with low signal-to-noise ratio. Nevertheless, we should note a limited implication of this method of construction of these diagnostic diagrams, because the inhomogeneous reddening may lead to incorrect results. Also the low metallicity should shift the separation line to the area of lower line ratios. But even proposing that all points corresponding to the right wing of the `seagull shape' in Fig.~\ref{fig:BPT} should lie under the curve, the collision excitation revealed by that way will be important only in the diffuse surrounding of the HSK~45 nebula. \begin{figure} \includegraphics[width=\linewidth]{BPT.pdf} \caption{Diagnostic diagram $\log(\textsc{[O iii]}5007/\mathrm{H}\beta)$ (computed by dividing the \Ha flux by 2.86) vs $\log(\textsc{[S ii]}6717,6731/\mathrm{H}\alpha)$ constructed for our narrow-band images in H$\alpha$, \SII and \OIII lines. A separation line from \citet{kewley01} between regions of pure photoionization excitation and of significant contribution of the shocks is shown by a black line.}\label{fig:BPT} \end{figure} If shock waves from possible SNe and/or stellar winds play an important role in the excitation of emission lines in some regions, we should be able to reveal the corresponding kinematic signatures. In bright nebulae of the eastern chain, where radio observations suggested the presence of supernova remnants, we found no signs of high velocities typical of not too old supernova remnants. However, high-velocity components of the \Ha line (in some places having the elevated velocity dispersion) are indeed observed in the outer weakly ionized structures in the SE and NE areas and especially in the N area, where the brightest nebula, HSK 45, is located (see Figs.~\ref{fig:SE_shells}, \ref{fig:NE_shells} and \ref{fig:N_shells}). We currently can not say firmly whether these high-velocity motions are associated with the inflow of kinetic energy from supernova explosions or from the winds of O type stars. Note, however, that when shock waves from supernovae propagate in an inhomogeneous (cloudy) medium, all typical shock manifestations -- via emission, morphology or kinematics, become amorphous \citep{korolev15}. Hence, given that the region under study has been a subject of repeated exposure of strong perturbing factors (ionization fronts, wind flows) over long time, the absence of clear signs of supernovae can be explained by the inhomogeneity of the gaseous environment. A detailed analysis of the structure and kinematics of all bright \HII complexes of ongoing star formation in the walls of the supergiant shell of neutral gas in the Ho~II galaxy is performed based on the observations carried out at the SAO RAS 6-m telescope with a scanning Fabry--Perot interferometer in the \Ha line combined with direct images taken in the H$\alpha$, \SII and \OIII lines. We also used the {\it HST} archival images. The kinematics of ionized gas is compared to that of neutral gas based on the data of VLA observations in the 21-cm radio line taken from the LITTLE THINGS survey archive \citep{littlethings} and to the stellar population of the area. The observed data sheds certain light on the process of evolution of giant \HI structures under the action by ionizing radiation and inflow of mechanical energy from local bursts of star formation in the walls of these structures. The following results have been obtained: \begin{enumerate} \item We found 22 faint expanding ionized superbubbles in star formation complexes of the galaxy and estimated their expansion velocities and kinematic ages using the results of the ionized gas kinematics analysis. Also 3 local expanding \HI shells tied with star formation complexes in the SGS rim were identified. \item % We showed that current star formation episodes in the SGS were more extensive and complex than previously thought: they represent not `chains' of separate individual bright nebulae in the walls of the \HI SGS but rather unified star-forming complexes with sizes of several hundred pc. The formation of such unified complexes is due to the stellar feedback given the strong inhomogeneity of the gas in the SGS walls. Given the large errors of different methods, the inferred age of faint extended and bright more compact structures is consistent with the assumption that they are unified complexes of ongoing star formation. \item We suggest that the last episode of star formation in the galaxy that we observe as areas of bright \HII regions and shells in the northern wall of the SGS was triggered by its collision with giant shell-like \HI structures located north of the SGS. \item We discovered a faint ionized supershell inside the neutral SGS. % The origin of this weak \Ha emission somewhat differs from that of the faint inner ionized supershell that we earlier found in the SGS in IC~2574 galaxy, where the leakage of ionizing photons from bright \HII regions in the walls of the SGS is proposed as a main ionization source \citep{egorov14}. In Ho~II, five OB stars located inside the ionized supershell can explain its emission; however, we do not also rule out the leakage of ionizing photons from bright \HII regions. \item We have not been found any clear kinematic signatures of the effect of shock waves associated with supernova remnants in the eastern chain of bright nebulae earlier suspected of the synchrotron component of the radio emission. \end{enumerate} | 16 | 9 | 1609.00650 |
1609 | 1609.03379_arXiv.txt | Observations of galaxies in the local Universe have shown that both the ionized gas and the stars of satellites are more metal-rich than of equally massive centrals. To gain insight into the connection between this metallicity enhancement and other differences between centrals and satellites, such as their star formation rates, gas content, and growth history, we study the metallicities of $>$3600 galaxies with $\mstar > 10^{10}\, \msun$ in the cosmological hydrodynamical \eagle{} 100 Mpc `Reference' simulation, including $\sim$1500 in the vicinity of galaxy groups and clusters ($\mvir \geq 10^{13} \msun$). The simulation predicts excess gas and stellar metallicities in satellites consistent with observations, except for stellar metallicities at $\mstar \lesssim 10^{10.2} \msun$ where the predicted excess is smaller than observed. The exact magnitude of the effect depends on galaxy selection, aperture, and on whether the metallicity is weighted by stellar mass or luminosity. The stellar metallicity excess in clusters is also sensitive to the efficiency scaling of star formation feedback. We identify stripping of low-metallicity gas from the galaxy outskirts, as well as suppression of metal-poor inflows towards the galaxy centre, as key drivers of the enhancement of gas metallicity. Stellar metallicities in satellites are higher than in the field as a direct consequence of the more metal-rich star forming gas, whereas stripping of stars and suppressed stellar mass growth, as well as differences in accreted vs.~in-situ star formation between satellites and the field, are of secondary importance. | \label{sec:introduction} The internal properties of galaxies in dense environments are known to differ systematically from isolated galaxies, for example their colour (e.g.~\citealt{Peng_et_al_2010}), star formation rate (e.g.~\citealt{Kauffmann_et_al_2004, Wetzel_et_al_2012}), morphology (\citealt{Dressler_1980}) and atomic hydrogen content (e.g.~\citealt{Fabello_et_al_2012, Hess_Wilcots_2013}). Processes associated with galaxies becoming satellites have emerged as the primary driver of these trends \citep{Peng_et_al_2012}, with satellites in more massive haloes generally exhibiting greater differences from centrals. However, a detailed understanding of the physics responsible for the differences between centrals and satellite galaxies has so far proved elusive, although a large number of mechanisms have been proposed that could play a role: ram pressure stripping of galactic gas in the cold (\citealt{Gunn_Gott_1972}) or hot phase (\citealt{Larson_et_al_1980}), tidal forces (e.g.~\citealt{Moore_et_al_1996}), or galaxy--galaxy `harrassment' (\citealt{Moore_et_al_1996, Moore_et_al_1998}). A promising way to make progress from the observational side is to better constrain the evolutionary history of satellite galaxies. Because the long timescales of galaxy evolution preclude direct observations of changes in individual galaxies, this requires recourse to indirect methods such as comparing galaxy populations at different cosmic epochs or analysing tracers that encode a record of a galaxy's history. One example is the ages of individual stars, knowledge of which allows the star formation history of a galaxy to be reconstructed \citep{Weisz_et_al_2014, Weisz_et_al_2015}. However, this method is limited to galaxies in the immediate vicinity of the Milky Way due to its requirement for high spatial resolution. An alternative tracer, which is observable to much larger distances, is the elemental composition or `metallicity' of a galaxy: this reflects both the star formation history (because stars synthesize new heavy elements), as well as gas inflows that supply fresh, metal-poor gas \citep{White_Rees_1978} and outflows, which remove metal-enriched material from the galaxy (e.g.~\citealt{Larson_1974, Dekel_Silk_1986}). Metallicities can typically be measured for two particular components of a galaxy: its ionized gas, where individual elements such as oxygen and hydrogen lead to prominent emission lines (e.g.~\citealt{Brinchmann_et_al_2004, Tremonti_et_al_2004}), and from absorption lines in stellar atmospheres \citep{Gallazzi_et_al_2005}. Over the last decades, observations have shown that metallicity correlates with other galaxy properties. Early reports of an increased metallicity in more massive galaxies by e.g.~\citet{Lequeux_et_al_1979} were confirmed by analyses of the Sloan Digital Sky Survey (SDSS): \citet{Tremonti_et_al_2004} showed that the gas-phase metallicity of star forming galaxies in SDSS increases strongly with the stellar mass, and interpreted this as evidence for the efficiency of outflows in removing metals from lower-mass galaxies, while \citet{Gallazzi_et_al_2005} reached a similar conclusion from an analysis of stellar metallicities in SDSS. \citet{Lara-Lopez_et_al_2010} and \citet{Mannucci_et_al_2010} demonstrated an additional (inverse) dependence of metallicity on the star formation rate of galaxies, which has since been studied by many other authors (e.g.~\citealt{Andrews_Martini_2013, Lara-Lopez_et_al_2013}; see also \citealt{Bothwell_et_al_2013}) and interpreted as the effect of metal-poor gas inflows boosting star formation and diluting metallicity at the same time (see also \citealt{Ellison_et_al_2008a, Finlator_Dave_2008, Zhang_et_al_2009}). In addition, mounting evidence indicates that metallicity is also affected by a galaxy's external environment at fixed stellar mass. \citet{Cooper_et_al_2008} demonstrated that (gas) metallicity is enhanced in dense environments, while \citet{Ellison_et_al_2008b} found that the opposite is true for galaxies in close pairs. Making use of the SDSS group catalogue of \citet{Yang_et_al_2007}, which splits galaxies into centrals and satellites, \citet[hereafter P10]{Pasquali_et_al_2010} found that satellite galaxies have higher stellar metallicity, as well as older stellar ages, than centrals of the same stellar mass, and that this difference increases towards lower stellar mass and higher host halo mass. These authors suggested stripping of stars, and the resulting reduction in stellar mass at constant metallicity, as an explanation for the stellar metallicity excess in satellites. In a similar way, \citet[hereafter P12]{Pasquali_et_al_2012} demonstrated the existence of a metallicity excess in the ionised gas of star-forming satellites relative to centrals. Although simple chemical evolution models can give some insight into the physical origin of these metallicity relations (e.g.~\citealt{Garnett_2002, Tremonti_et_al_2004, Peng_Maiolino_2014, Lu_et_al_2015}), a robust interpretation requires recourse to more sophisticated calculations. \citetalias{Pasquali_et_al_2010} compared their observational results to predictions from the semi-analytic galaxy formation model of \citet{Wang_et_al_2008}, and found that the model could reproduce the age difference between centrals and satellites as a consequence of star formation quenching after a galaxy becomes a satellite, which typically happens earlier in more massive haloes. However, they found that the \citet{Wang_et_al_2008} model predicts stellar metallicities in satellites that are nearly equivalent to those of centrals, in contrast to their observations. \citetalias{Pasquali_et_al_2010} concluded that this failure might point to an oversimplified treatment of environmental processes such as tidal stripping of stars in the model. Cosmological hydrodynamical simulations are potentially a more powerful tool to understand the physics behind the elevated metallicities in satellites, because they self-consistently model the formation of galaxies and their environment, including the baryonic component, without explicitly distinguishing between centrals and satellites. Coupled with increasingly realistic `sub-grid' physics prescriptions to describe unresolved processes like radiative cooling, star formation, and feedback, such simulations have now evolved to the point where the modelled galaxy populations resemble observations in several key properties such as their stellar mass, star formation rate, and metallicity \citep{Vogelsberger_et_al_2014, Schaye_et_al_2015}. In a recent study, \citet{Genel_2016} used the Illustris simulation \citep{Vogelsberger_et_al_2014} to gain insight into the elevated gas-phase metallicities in satellite galaxies (see also \citealt{Dave_et_al_2011, DeRossi_et_al_2015}, who reported excess metallicity in satellites compared to centrals in earlier simulations). The Illustris simulation was found to qualitatively reproduce the observational result of \citetalias{Pasquali_et_al_2012}, the elevated metallicity in satellites being driven by differences in the radial distribution of star-forming gas as well as different star formation histories of satellites \citep{Genel_2016}. In this paper, we perform an analysis of the \eagle{} simulation (\citealt{Schaye_et_al_2015, Crain_et_al_2015}) to gain further insight into the nature of satellite metallicities. Our aim is twofold: on the one hand, we want to test whether \eagle{} -- which differs from Illustris in several key aspects including the hydrodynamics scheme and implementation of feedback from star formation -- is able to reproduce the observed metallicity differences between satellites and centrals. This is an important test of the model, and also serves to establish whether the agreement with observations in terms of gas-phase metallicity reported by \citet{Genel_2016} is primarily a consequence of the specific model used for Illustris, or rather a more generic success of modern cosmological simulations. Secondly, we will use the detailed particle information and evolutionary history of the simulated galaxies from \eagle{} to study the origin of this metallicity enhancement. While \eagle{} has been calibrated to match the masses and sizes of observed present-day galaxies, the metallicities were not explicitly constrained, and can hence be regarded as a prediction of the simulation. This is in contrast to Illustris, where the metallicity of outflowing gas is reduced by means of an adjustable parameter in order to match the normalisation of the observed mass-metallicity relation \citep{Vogelsberger_et_al_2013}. As shown by \citet{Schaye_et_al_2015}, the observed mass--metallicity relation for both star forming gas and stars is nevertheless broadly reproduced for massive ($\mstar > 10^{10}\, \msun$) galaxies in the largest-volume \eagle{} simulation, while at lower masses, the predicted metallicities are systematically too high. This discrepancy is eased in higher-resolution \eagle{} simulations -- in which the gas metallicities are consistent with observations for $\mstar \gtrsim 10^{8.5} \msun$, although stellar metallicities are still somewhat higher than observed \citep{Schaye_et_al_2015} -- but because these are computationally much more challenging, they were restricted to a relatively small box with side length of 25 comoving Mpc, and hence lack the massive haloes whose satellites we wish to study. For this reason, we here mostly restrict our analysis to the study of satellites with $\mstar > 10^{10} \msun$, for which the offset between different resolution runs is $\lesssim 0.15$ dex. The remainder of this paper is structured as follows. In \S \ref{sec:eagle}, we briefly review the relevant characteristics of the \eagle{} simulation and describe our galaxy selection and method for tracing galaxies between different snapshots. Predictions for the gas-phase and stellar metallicities of satellite galaxies are presented and compared to both observations and alternative theoretical models in \S \ref{sec:trends}. \S \ref{sec:origin_zgas} illuminates the nature of differences in the gas-phase metallicity, highlighting gas stripping and suppressed gas inflows as the two dominant mechanisms responsible. We then investigate the action of indirect effects such as stellar mass stripping on stellar metallicities in \S \ref{sec:origin_zstar}, and demonstrate a direct connection between the excess in gas-phase and stellar metallicities in \eagle{}. Our results are summarized and discussed in \S \ref{sec:summary}. Throughout the paper, we use a flat $\Lambda$CDM cosmology with parameters as determined by \citet{Planck_2014} (Hubble parameter $h \equiv $ H$_{0}/(100\,{\rm km}\,{\rm s}^{-1}{\rm Mpc}^{-1}) = 0.6777$, dark energy density parameter $\Omega_\Lambda = 0.693$ (dark energy equation of state parameter $w=-1$), matter density parameter $\Omega_{\rm M} = 0.307$, and baryon density parameter $\Omega_{\rm b} = 0.04825$). The solar metallicity and oxygen abundance are assumed to be Z$_\odot$ = 0.012 \citep{Allende-Prieto_et_al_2001} and 12+log(O/H) = 8.69 \citep{Asplund_et_al_2009}, respectively. Unless specified otherwise, all masses and distances are given in physical units. In our plots, dark shaded regions denote $1\sigma$ uncertainties calculated as explained in Section \ref{sec:zgas}, while light shaded bands (where shown) indicate galaxy-to-galaxy scatter (central 50 per cent, i.e.~stretching from the 25th to the 75th percentile), unless explicitly stated otherwise. | \label{sec:summary} Motivated by observational reports that satellite galaxies in groups and clusters have metallicities that are higher than those of central galaxies of the same stellar mass, we have compared the gas-phase and stellar metallicities of $> 3600$ field and group/cluster satellite galaxies (host halo mass $\log_{10} (\mvir/\msun) = 10^{13}$--$10^{14.5}$, galaxy stellar mass $\log_{10} (\mstar/\msun) > 10^{10}$) in the 100 cMpc \eagle{} `Reference' simulation (Ref-L100), and have also compared to alternative theoretical models. After confirming that \eagle{} broadly reproduces the observed environmental difference in both gas and stellar metallicities, we have tested several mechanisms that could cause this effect, including gas stripping, suppression of gas inflows, differing stellar age, stripping of stars, and differences in accretion of stars from other galaxies. The main results of our study may be summarised as follows: \begin{enumerate} \item The \eagle{} simulation generally reproduces the observed enhancement of metallicity in both the star-forming gas and the stellar components. For gas metallicity, an approximate match to the observational galaxy selection (specific star formation rate sSFR $\equiv$ SFR/$\mstar > 10^{-10.5}$ yr$^{-1}$), fibre size ($R_\text{2D} \leq 3$ pkpc), and weighting (by star formation rate) leads to quantitative agreement within the statistical uncertainties (Fig.~\ref{fig:gasz}). The stellar metallicity enhancement of satellites with $\mstar \gtrsim10^{10.5} \msun$ is also matched quantitatively if simulated metallicities are weighted by stellar mass, while weighting by luminosity underpredicts the observed excess. At lower masses, the simulations predict a smaller stellar metallicity excess than observed regardless of the weighting scheme, which is only partly ameliorated at higher resolution (Fig.~\ref{fig:stars.total-zmet}). \item The stellar metallicity enhancement is sensitive to the subgrid efficiency of star formation feedback, with alternative \eagle{} models (which produce galaxies that are too compact) generally predicting a larger excess than the Reference implementation, in particular for satellites in galaxy clusters (Fig.~\ref{fig:subgridcomp}). A comparison to other simulations taken from the literature has shown qualitative agreement on enhanced gas and stellar metallicity in satellites, but with significant differences at a quantitative level (Fig.~\ref{fig:modelcomp}). \item Satellites in \eagle{} show evidence of a significant removal of star-forming gas from their outskirts. This explains the elevated level of metallicity of the star-forming gas only partly, however: even at fixed radius ($r \lesssim 15$ pkpc), satellites are metal-enriched compared to the field. This is predominantly the result of suppressed metal-poor inflows, but to a lesser extent also of enhanced enrichment due to a larger relative contribution of recycled stellar outflows, from more metal-rich stars (Figs.~\ref{fig:gas_profiles} and \ref{fig:gas_zmet_histograms}). \item As observed, the stellar metallicity enhancement in \eagle{} satellites is less strong amongst star-forming galaxies than the general population. Furthermore, our analysis predicts a significantly stronger enhancement for transitional galaxies (sSFR $\approx 10^{-11}$ yr$^{-1}$) compared to those with higher star formation rates. This suggests a tight causal link between star formation quenching and metallicity enhancement in satellite galaxies (Fig.~\ref{fig:zstar_ssfr}). \item Stellar mass loss through e.g.~tidal forces cannot account for the stellar metallicity offset, because galaxies surviving until $z = 0.1$ have typically only lost $< 0.05$ dex in stellar mass since reaching their maximum $\mstar$. Taking into account the missed stellar growth in satellites as a consequence of star formation quenching, this difference increases to only $\lesssim 0.2$ dex even for galaxies of $\mstar \approx 10^9 \msun$ in clusters. Mass loss of $\sim$0.4 dex would be required to explain the metallicity offset, both in \eagle{} and in the observations of \citet{Pasquali_et_al_2010} (Fig.~\ref{fig:mstar_diff}). \item \eagle{} satellites accrete a smaller fraction of their stars from other galaxies than field galaxies (3 per cent vs.~7 per cent at $\mstar \approx 10^9 \msun$; Fig.~\ref{fig:accreted_fraction}). Taking this difference into account by comparing stellar populations in centrals and satellites that were formed at the same time in galaxies of the same stellar mass, satellites show no increase in metallicity for stars formed at $z \gtrsim 2$ (Fig.~\ref{fig:zmet_mbirthmatched}). \item A metallicity offset due to `direct' environmental contributions remains for stars born at $z \lesssim 2$; this increases towards later star formation times when a larger fraction of satellites had already fallen into their host halo (Fig.~\ref{fig:censat}). We confirm that, in \eagle{}, this is due to excess metallicity in satellites compared to the field even at $z=2$ (Fig.~\ref{fig:gas_redshift}). \end{enumerate} The salient conclusion of this analysis is that the excess stellar and gas-phase metallicities in satellite galaxies are both directly linked to environmental star formation quenching, and are not symptoms of two different physical processes, as was suggested by \citet{Pasquali_et_al_2012}. Stellar metallicities in satellites are raised predominantly because they formed from relatively highly metal-enriched gas. In turn, this excess gas enrichment results from the removal of relatively metal-poor gas from galaxy outskirts -- likely due to ram pressure stripping -- and suppression of metal-poor gas inflows, which is plausibly a consequence of the removal of less dense gas from the galaxy halo. A testable prediction of this scenario is that the stellar metallicity of transitional galaxies (sSFR $\approx 10^{-11}$ yr$^{-1}$, which are likely in the process of being quenched) should be significantly raised in satellites compared to the field. The key problem of this general picture is its prediction of, and indeed reliance upon, an enhancement of satellite gas-phase metallicity not only at $z \approx 0$, but also at earlier epochs, at least as far back as $z \approx 0.5$ when a significant fraction of the stars making up present-day galaxies were yet to form. What limited observational evidence is available on this topic instead suggests that any difference between the metallicity of satellites and centrals is insignificant \citep{Kacprzak_et_al_2015,Maier_et_al_2016}, with some studies even presenting evidence for a \emph{lower} metallicity in satellites \citep{Valentino_et_al_2015, Wuyts_et_al_2016}. Our analysis suggests that environmental differences in gas metallicity are highly sensitive to both galaxy selection and analysis details such as aperture and weighting scheme, and that observations may significantly underestimate the `true' metallicity enhancement of satellites. While it is unclear at present to what extent this conclusion is also applicable to $z \gg 0$, it nevertheless highlights the need for careful like-with-like comparisons tailored to the characteristics of a given observation to draw meaningful conclusions about the success or failure of theoretical galaxy formation models in this respect. A second potential discrepancy between not just \eagle{}, but also the Illustris simulation and the \citet{Henriques_et_al_2015} semi-analytic galaxy formation model and observations, is their collective failure to reproduce the strong rise in satellite stellar metallicity enhancement with decreasing stellar mass at $\mstar \lesssim 10^{10.5} \msun$ \citep{Pasquali_et_al_2010}. Although the severity of this discrepancy cannot be authoritatively assessed without recourse to larger high-resolution hydrodynamical simulations that adequately sample the satellite galaxy population, it is nevertheless interesting to speculate on two potential causes. First, it might hint at some physical process whose importance is \emph{fundamentally} underestimated in current theoretical models, for example thermal conduction, (physical) viscosity, or magnetic fields. Alternatively, it is at least possible that the effect is actually overestimated in the observational data: its primary driver is not an actual rise of satellite metallicity, but rather a strong decline in the stellar metallicity of central galaxies. As discussed by \citet{Gallazzi_et_al_2005}, estimating stellar metallicities from absorption lines in SDSS spectra requires prior subtraction of (often much stronger) emission lines, which has a larger impact on star forming than passive galaxies. Towards lower mass, most field galaxies are star forming, but a significant fraction of satellites are not (e.g.~\citealt{Wetzel_et_al_2012}), which might lead to subtle biases in the derived metallicities of these two populations. The fact that \citet{Pasquali_et_al_2012} demonstrate a lack of strong stellar metallicity enhancement in \emph{star-forming} low-mass satellites is consistent with this hypothesis, but would also arise naturally from a causal connection between star formation quenching and metallicity enhancement in satellites, as advocated by \eagle{}. We note that a recent study of \citet{Peng_et_al_2015} reports only a small environmental difference between the stellar metallicities of \emph{passive} galaxies in SDSS, which indicates that a varying star-forming fraction is indeed the main driver behind the metallicity excess observed in the overall satellite population \citepalias{Pasquali_et_al_2012}. Another important area of progress from the observational side is the ability to measure metallicity across entire galaxies, as opposed to only the innermost few kpc, with integral-field-units (IFUs) such as CALIFA \citep{Sanchez_et_al_2013}, MaNGA \citep{Bundy_et_al_2015}, and MUSE \citep{Bacon_et_al_2010}. IFU observations of a representative number of group/cluster galaxies in the local Universe will be able to directly test our prediction that the metallicity of star forming gas is enhanced in satellites even after accounting for the removal of low-metallicity gas from the galaxy outskirts. Furthermore, combining such data with planned large \hi{} surveys such as \textsc{Apertif} or eventually the SKA could directly link the stripping of low-density gas with the enhancement of metallicity in the remaining dense, star forming gas, and thus shed new light onto the effects of environment on galaxy evolution. | 16 | 9 | 1609.03379 |
1609 | 1609.06595_arXiv.txt | The only well-studied red nova progenitor (V1309 Sco) was a contact binary with a 1.4-day period. The prospects for searching for similar systems, as well as stellar merger candidates in general, are explored in this work. The photospheric temperatures of 128 variables with periods $P=1.1-1.8$\,d classified as W UMa-type binaries are calculated using their colors listed in the SDSS catalog. A selection of 15 contact binaries with similar temperatures and periods as the V1309 Sco progenitor is thus compiled. The Kepler Eclipsing Binary Catalog is used to analyse systems with eclipse timing variations (ETV) possibly caused by changes of the orbital period. Out of the 31 systems with parabolic ETV curves listed by Conroy et al. (2014, AJ, 147, 45) two could be contact binaries with a decreasing period and, therefore, potential stellar merger candidates. Out of the 569 contact binaries in the OGLE field analysed by Kubiak et al. (2006, AcA, 56, 253) 14 systems have periods longer than 0.8\,d and a statistically significant period decrease. | 16 | 9 | 1609.06595 |
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1609 | 1609.04303_arXiv.txt | {Gaia Data Release 1 (Gaia DR1) contains astrometric results for more than 1~billion stars brighter than magnitude 20.7 based on observations collected by the Gaia satellite during the first 14~months of its operational phase.} {We give a brief overview of the astrometric content of the data release and of the model assumptions, data processing, and validation of the results.} {For stars in common with the Hipparcos and Tycho-2 catalogues, complete astrometric single-star solutions are obtained by incorporating positional information from the earlier catalogues. For other stars only their positions are obtained, essentially by neglecting their proper motions and parallaxes. The results are validated by an analysis of the residuals, through special validation runs, and by comparison with external data.} {For about two million of the brighter stars (down to magnitude $\sim$11.5) we obtain positions, parallaxes, and proper motions to Hipparcos-type precision or better. For these stars, systematic errors depending for example on position and colour are at a level of $\pm 0.3$~milliarcsecond (mas). For the remaining stars we obtain positions at epoch J2015.0 accurate to $\sim$10~mas. Positions and proper motions are given in a reference frame that is aligned with the International Celestial Reference Frame (ICRF) to better than 0.1~mas at epoch J2015.0, and non-rotating with respect to ICRF to within 0.03~mas~yr$^{-1}$. The Hipparcos reference frame is found to rotate with respect to the Gaia DR1 frame at a rate of 0.24~mas~yr$^{-1}$.} {Based on less than a quarter of the nominal mission length and on very provisional and incomplete calibrations, the quality and completeness of the astrometric data in Gaia DR1 are far from what is expected for the final mission products. The present results nevertheless represent a huge improvement in the available fundamental stellar data and practical definition of the optical reference frame.} | This paper describes the first release of astrometric data from the European Space Agency mission Gaia \citep{2016GaiaP}. The first data release \citep{2016GaiaB} contains provisional results based on observations collected during the first 14 months since the start of nominal operations in July 2014. The initial treatment of the raw Gaia data \citep{2016GaiaF} provides the main input to the astrometric data processing outlined below. The astrometric core solution, also known as the astrometric global iterative solution (AGIS), was specifically developed to cope with the high accuracy requirements, large data volumes, and huge systems of equations that result from Gaia's global measurement principle. A detailed pre-launch description was given in \citetads{2012A&A...538A..78L}, hereafter referred to as the AGIS paper. The present solution is largely based on the models and algorithms described in that paper, with further details on the software implementation in \citetads{2011ExA....31..215O}. Nevertheless, comparison with real data and a continuing evolution of concepts have resulted in many changes. One purpose of this paper is to provide an updated overview of the astrometric processing as applied to Gaia Data Release 1 (Gaia DR1). A specific feature of Gaia DR1 is the incorporation of earlier positional information through the Tycho-Gaia astrometric solution (TGAS; \citeads{2015A&A...574A.115M}). It is important to emphasise the provisional nature of the astrometric results in this first release. Severe limitations are set by the short time period on which the solution is based, and the circumstance that the processing of the raw data -- including the image centroiding and cross-matching of observations to sources -- had not yet benefited from improved astrometry. Some of the known problems are discussed in Sect.~\ref{sec:problems}. These shortcomings will successively be eliminated in future releases, as more observations are incorporated in the solution, and as the raw data are re-processed using improved astrometric parameters, attitude, and modelling of the instrument geometry. | } \centering \small \setlength{\tabcolsep}{7pt} \vspace{-2mm} \begin{tabular}{lrrrrrrrl} \hline\hline \noalign{\smallskip} & \multicolumn{3}{c}{All primary sources} && \multicolumn{3}{c}{Hipparcos subset} \\ Quantity & 10\% & 50\% & 90\% && 10\% & 50\% & 90\% & Unit\\ \noalign{\smallskip} \hline \noalign{\smallskip} Standard uncertainty in $\alpha$ ($\sigma_{\alpha*}=\sigma_{\alpha}\cos\delta$) & 0.147 & 0.254 & 0.601 && 0.158 & 0.224 & 0.391 & mas \\ Standard uncertainty in $\delta$ ($\sigma_{\delta}$) & 0.140 & 0.233 & 0.530 && 0.150 & 0.218 & 0.378 & mas \\ Standard uncertainty in $\varpi$ ($\sigma_{\varpi}$) & 0.242 & 0.322 & 0.644 && 0.229 & 0.283 & 0.499 & mas \\ Standard uncertainty in $\mu_{\alpha*}$ ($\sigma_{\mu\alpha*}$) & 0.500 & 1.132 & 2.671 && 0.035 & 0.064 & 0.129 & mas~yr$^{-1}$ \\ Standard uncertainty in $\mu_\delta$ ($\sigma_{\mu\delta}$) & 0.441 & 0.867 & 1.957 && 0.031 & 0.056 & 0.109 & mas~yr$^{-1}$ \\ Semi-major axis of error ellipse in position ($\sigma_\text{pos,\,max}$) & 0.203 & 0.319 & 0.753 && 0.196 & 0.263 & 0.475 & mas \\ Semi-major axis of error ellipse in proper motion ($\sigma_\text{pm,\,max}$) & 0.715 & 1.322 & 3.189 && 0.038 & 0.069 & 0.137 & mas~yr$^{-1}$ \\ Excess source noise ($\epsilon_i$) & 0.299 & 0.478 & 0.855 && 0.347 & 0.572 & 1.185 & mas \\ Number of field-of-view transits input to the solution ($N$) & 8 & 15 & 25 && 7 & 14 & 25 & \\ Number of good CCD observations AL used in the solution ($n_\text{good}$) & 57 & 99 & 185 && 51 & 93 & 180 & \\ Fraction of bad CCD observations AL ($n_\text{bad}/(n_\text{good}+n_\text{bad})$) & 0.0 & 0.0 & 2.0 && 0.0 & 0.0 & 1.8 & \% \\ Normalised difference to Hipparcos proper motion ($\Delta Q$) & -- & -- & -- && 0.33 & 2.35 & 11.32 & \\ Magnitude in Gaia's unfiltered band ($G$) & 9.27 & 11.04 & 12.05 && 6.84 & 8.28 & 9.70 & mag \\ \noalign{\smallskip} \hline \end{tabular} \tablefoot{ Columns headed 10\%, 50\%, and 90\% give the lower decile, median, and upper decile of the quantities for all 2\,057\,050~primary sources, and for the subset of 93\,635 sources in common with the Hipparcos catalogue \citepads{2007ASSL..350.....V}. See footnote~\ref{footnote:downweighting} for the definition of good and bad CCD observations. } \end{table*} \begin{figure*} \resizebox{\hsize}{!}{% \includegraphics{tgasSourceDensityLogEquHp6an.pdf} \includegraphics{tgasNGoodObsAlLogEquHp6an.pdf} \includegraphics{tgasExcessSourceNoiseLogEquHp6an.pdf} } \caption{Summary statistics for the 2~million sources in the primary data set of Gaia DR1: (\textbf{a}) density of sources; (\textbf{b}) number of good CCD observations per source; (\textbf{c}) excess source noise. The maps use an Aitoff projection in equatorial (ICRS) coordinates, with origin $\alpha=\delta=0$ at the centre and $\alpha$ increasing from right to left. The mean density ({\bf a}) and median values ({\bf b} and {\bf c}) are shown for sources in cells of about 0.84~deg$^2$. A small number of empty cells are shown in white.} \label{fig:stats1} \end{figure*} \begin{figure*} \resizebox{\hsize}{!}{% \includegraphics{tgasSourceDensityLogGalHp6an.pdf} \includegraphics{tgasNGoodObsAlLogGalHp6an.pdf} \includegraphics{tgasExcessSourceNoiseLogGalHp6an.pdf} } \caption{Summary statistics for the 2~million sources in the primary data set of Gaia DR1: (\textbf{a}) density of sources; (\textbf{b}) number of good CCD observations per source; (\textbf{c}) excess source noise. These maps use an Aitoff projection in Galactic coordinates, with origin $l=b=0$ at the centre and $l$ increasing from right to left. The mean density ({\bf a}) and median values ({\bf b} and {\bf c}) are shown for sources in cells of about 0.84~deg$^2$. A small number of empty cells are shown in white.} \label{fig:stats2} \end{figure*} \subsection{Primary data set} \label{sec:results_primary} For each source the primary solution gives the five astrometric parameters $\alpha$, $\delta$, $\varpi$, $\mu_{\alpha *}$, and $\mu_\delta$ together with various statistics indicating the quality of the results. The most important statistics are \begin{itemize} \item the standard uncertainties of the astrometric parameters: $\sigma_{\alpha *}=\sigma_{\alpha}\cos\delta$, $\sigma_{\delta}$, $\sigma_\varpi$, $\sigma_{\mu\alpha *}$, and $\sigma_{\mu\delta}$; \item the ten correlation coefficients among the five parameters: $\rho(\alpha,\delta)$, $\rho(\alpha,\varpi)$, etc.; \item the number of field-of-view transits of the source used in the solution: $N$; \item the number of good and bad CCD observations% \footnote{As described in Sect.~5.1.2 of the AGIS paper, an observation is never rejected but is downweighted in the solution if it gives a large residual. $n_\text{bad}$ is the number of CCD observations for which the downweighting factor $w_l < 0.2$. According to Eq.~(66) in the AGIS paper this means that the absolute value of the residual exceeds $3\ln 5\simeq 4.83$ times the total uncertainty of the residual, computed as the quadratic sum of the formal standard uncertainty of the observation ($\sigma_l$), the excess attitude noise, and the excess source noise. $n_\text{good}$ is the number of CCD observations for which $w_l \ge 0.2$ (absolute residual less than 4.83 times the total uncertainty); $n_\text{good}+n_\text{bad}$ is the total number of CCD observations of the source.\label{footnote:downweighting}} of the source: $n_\text{good}$, $n_\text{bad}$; \item the excess source noise: $\epsilon_i$. This is meant to represent the modelling errors specific to a given source, i.e.\ deviations from the astrometric model in Eq.~(\ref{eq:source1}) caused, for example, by binarity (see Sect.~3.6 in the AGIS paper). Thus, it should ideally be zero for most sources. In the present primary solution nearly all sources obtain significant excess source noise ($\sim$0.5~mas) from the high level of attitude and calibration modelling errors. An unusually large value of $\epsilon_i$ (say, above 1--2~mas) could nevertheless indicate that the source is an astrometric binary or otherwise problematic. \end{itemize} Additional statistics can be calculated from the standard uncertainties and correlation coefficients. These include the semi-major axes of the error ellipses in position and proper motion. Let $C_{00}=\sigma_{\alpha *}^2$, $C_{11}=\sigma_{\delta}^2$, and $C_{01}=\sigma_{\alpha *}\sigma_{\delta}\rho(\alpha,\delta)$ be elements of the $5\times 5$ covariance matrix of the astrometric parameters. The semi-major axis of the error ellipse in position is \begin{equation}\label{eq:sigmaPos} \sigma_\text{pos,\,max} = \sqrt{\frac{1}{2}(C_{00}+C_{11}) + \frac{1}{2}\sqrt{(C_{11}-C_{00})^2+4C_{01}^2}} \, , \end{equation} with a similar expression for the semi-major axis of the error ellipse in proper motion, $\sigma_\text{pm,\,max}$, using the covariance elements $C_{33}$, $C_{44}$, and $C_{34}$.% \footnote{The semi-minor axis is obtained by taking the negative sign of the inner square root in Eq.~(\ref{eq:sigmaPos}). The position angle of the major axis (in the range $-90^\circ$ to $90^\circ$) is obtained as $\theta=\text{atan2}(2C_{01}, C_{11}-C_{00})/2$.} For the subset in common with the Hipparcos catalogue one additional statistic is computed: $\Delta Q$, which measures the difference between the proper motion derived in the primary (TGAS) solution and the proper motion given in the Hipparcos catalogue.% \footnote{The quantity $\Delta Q$ was introduced by \citetads{2014A&A...571A..85M} in the context of the HTPM project, but the present definition differs from the one in that paper in that only the proper motion differences are considered here.} It is computed as \begin{equation}\label{eq:DeltaQ} \Delta Q = \begin{bmatrix} \Delta\mu_{\alpha *} & \Delta\mu_{\delta} \end{bmatrix} \left(\vec{C}_\text{pm,\,T}+\vec{C}_\text{pm,\,H}\right)^{-1} \begin{bmatrix} \Delta\mu_{\alpha *} \\ \Delta\mu_{\delta} \end{bmatrix} \, , \end{equation} where $\Delta\mu_{\alpha *}=\mu_{\alpha *\text{T}}-\mu_{\alpha *\text{H}}$ and $\Delta\mu_{\delta}=\mu_{\delta\text{T}}-\mu_{\delta\text{H}}$ are the proper motion differences, with T and H designating the values from respectively TGAS and the Hipparcos catalogue. $\vec{C}_\text{pm,\,T}$ is the $2\times 2$ covariance submatrix of the TGAS proper motions and $\vec{C}_\text{pm,\,H}$ the corresponding matrix from the Hipparcos catalogue. The new reduction of the raw Hipparcos data by \citetads{2007ASSL..350.....V} was used, as retrieved from CDS, with covariances computed as described in Appendix~B of \citetads{2014A&A...571A..85M}. For the calculation in Eq.~(\ref{eq:DeltaQ}) the Hipparcos proper motions were first transformed to the Gaia DR1 reference frame by means of Eq.~(\ref{eq:align3}) and then propagated to epoch J2015.0, assuming zero radial velocity. $\Delta Q$ is therefore sensitive to all deviations from a purely linear tangential proper motion, including perspective effects. If the proper motion errors in TGAS and in the Hipparcos catalogue are independent and Gaussian with the given covariances, then $\Delta Q$ is expected to follow a chi-squared distribution with two degrees of freedom, i.e.\ $\text{Pr}(\Delta Q > x)=\exp(-x/2)$. \begin{landscape} \begin{figure} \resizebox{\hsize}{!}{\includegraphics[angle=0]{suCorr.pdf}} \caption{Summary statistics for the 2~million sources in the primary data set. The five maps along the main diagonal show, from top-left to bottom-right, the standard uncertainties in $\alpha$, $\delta$, $\varpi$, $\mu_{\alpha*}$, $\mu_\delta$. The ten maps above the diagonal show the correlation coefficients, in the range $-1$ to $+1$, between the corresponding parameters on the main diagonal. All maps use an Aitoff projection in equatorial (ICRS) coordinates, with origin $\alpha=\delta=0$ at the centre and $\alpha$ increasing from right to left. Median values are shown in cells of about 0.84~deg$^2$.} \label{fig:statSigmaCorr} \end{figure} \end{landscape} The primary solution gives astrometric results for about 2.48~million sources. Unreliable solutions are removed by accepting only sources with \begin{equation}\label{eq:formal1} \sigma_\varpi < 1~\text{mas} \quad \text{and} \quad \sigma_\text{pos,\,max} < 20~\text{mas} \, . \end{equation} Here $\sigma_\varpi$ is the standard uncertainty in parallax from Eq.~(\ref{eq:infl}), and $\sigma_\text{pos,\,max}$ is the semi-major axis of the error ellipse in position at the reference epoch (J2015.0). The second condition removes a small fraction of stars with extremely elongated error ellipses. Applying the filter in Eq.~(\ref{eq:formal1}) results in a set of 2\,086\,766~sources with accepted primary solutions. However, for a source to be included in Gaia DR1 it must also have valid photometric information. The primary data set therefore gives astrometric parameters for 2\,057\,050~sources together with their estimated standard uncertainties, correlations among the five parameters, and other quality indicators. A statistical summary is presented in Table~\ref{tab:statSummary}. Separate statistics are given for the subset of Hipparcos sources, which have rather different uncertainties in proper motion owing to the more accurate positions at the Hipparcos epoch. Figures~\ref{fig:stats1}--\ref{fig:statSigmaCorr} show the variation of some statistics with celestial position. The distribution of $\Delta Q$ for the Hipparcos subset is discussed in Appendix~\ref{sec:hipparcos}. In the primary data set, the standard uncertainties of the positions at epoch J2015.0 and of the parallaxes are dominated by attitude and calibration errors in the Gaia observations. They therefore show little or no systematic dependence on magnitude. For the proper motions, on the other hand, the dominating error source is usually the positional errors at J1991.25 resulting from the Hipparcos and Tycho-2 catalogues. The uncertainties in proper motion therefore show a magnitude dependence mimicking that of the positional uncertainties in these catalogues. To preserve the statistical integrity of the data set, no filtering was applied based on the actual values of the astrometric parameters. Thus, the primary data set contains 30\,840 (1.5\%) negative parallaxes. The most negative parallax is $-24.82\pm 0.63$~mas, but even this provides valuable information, e.g.\ that there are parallaxes that are wrong by at least 40~times the stated uncertainty. However, owing to a technical issue in the construction of the initial source list, several nearby stars with high proper motion are missing in the Hipparcos subset of Gaia DR1. In particular, the 19 Hipparcos stars with total proper motion $\mu>3500$~mas~yr$^{-1}$ are missing, including the five nearest stars HIP~70891 (Proxima Cen), 71681 ($\alpha^2$~Cen), 71683 ($\alpha^1$~Cen), 87937 (Barnard's star), and HIP~54035. ($\alpha^{1}$ and $\alpha^{2}$~Cen would in any case have been rejected because they are too bright.) \begin{table*} \caption{Statistical summary of the 1141~million sources in the secondary data set of Gaia DR1. \label{tab:statSummarySecondary}} \centering \small \setlength{\tabcolsep}{8pt} \vspace{-2mm} \begin{tabular}{lrrrrrl} \hline\hline\noalign{\smallskip} Quantity && 10\% & 50\% & 90\% && Unit\\ \noalign{\smallskip} \hline \noalign{\smallskip} Standard uncertainty in $\alpha$ ($\sigma_{\alpha*}=\sigma_{\alpha}\cos\delta$) && 0.285 & 1.802 & 12.871 && mas \\ Standard uncertainty in $\delta$ ($\sigma_{\delta}$) && 0.257 & 1.568 & 11.306 && mas \\ Semi-major axis of error ellipse in position ($\sigma_\text{pos,\,max}$):\\ \hspace{5mm} $G<16$ (7\% of the secondary data set) && 0.106 & 0.255 & 4.118 && mas \\ \hspace{5mm} $G=16{-}17$ (7\%) && 0.182 & 0.484 & 11.105 && mas \\ \hspace{5mm} $G=17{-}18$ (13\%) && 0.284 & 0.761 & 11.534 && mas \\ \hspace{5mm} $G=18{-}19$ (22\%) && 0.501 & 1.444 & 13.027 && mas \\ \hspace{5mm} $G=19{-}20$ (31\%) && 0.986 & 2.816 & 16.314 && mas \\ \hspace{5mm} $G=20{-}21$ (20\%) && 2.093 & 7.229 & 21.737 && mas \\ \hspace{5mm} all magnitudes (100\%) && 0.349 & 2.345 & 15.699 && mas \\ Excess source noise ($\epsilon_i$) && 0.000 & 0.594 & 2.375 && mas \\ Number of field-of-view transits input to the solution ($N$) && 7 & 13 & 26 && \\ Number of good CCD observations AL used in the solution ($n_\text{good}$) && 41 & 71 & 157 && \\ Fraction of bad CCD observations AL ($n_\text{bad}/(n_\text{good}+n_\text{bad})$) && 0.0 & 0.0 & 2.0 && \% \\ Magnitude in Gaia's unfiltered band ($G$) && 16.49 & 19.02 & 20.32 && mag \\ \noalign{\smallskip} \hline \end{tabular} \tablefoot{ Columns headed 10\%, 50\%, and 90\% give the lower decile, median, and upper decile of the quantities for the 1\,140\,662\,719 secondary sources. See footnote~\ref{footnote:downweighting} for the definition of good and bad CCD observations. } \end{table*} \begin{figure*} \resizebox{\hsize}{!}{% \includegraphics{secondaryAllSourceDensityLogEquHp6an.pdf} \includegraphics{secondaryIgslSourceDensityLogEquHp6an.pdf} \includegraphics{secondaryNewSourceDensityLogEquHp6an.pdf} } \caption{Density of sources in the secondary data set of Gaia DR1: (\textbf{a}) all 1141~million sources in the secondary data set; (\textbf{b}) the 685~million sources in common with the IGSL; (\textbf{c}) the 456~million new sources. These maps use an Aitoff projection in equatorial (ICRS) coordinates, with origin $\alpha=\delta=0$ at the centre and $\alpha$ increasing from right to left. Mean densities are shown for sources in cells of about 0.84~deg$^2$. } \label{fig:secondaryEqu} \end{figure*} \begin{figure*} \resizebox{\hsize}{!}{% \includegraphics{secondaryAllSourceDensityLogGalHp6an.pdf} \includegraphics{secondaryIgslSourceDensityLogGalHp6an.pdf} \includegraphics{secondaryNewSourceDensityLogGalHp6an.pdf} } \caption{Density of sources in the secondary data set of Gaia DR1: (\textbf{a}) all 1141~million sources in the secondary data set; (\textbf{b}) the 685~million sources in common with the IGSL; (\textbf{c}) the 456~million new sources. These maps use an Aitoff projection in Galactic coordinates, with origin $l=b=0$ at the centre and $l$ increasing from right to left. Mean densities are shown for sources in cells of about 0.84~deg$^2$. } \label{fig:secondaryGal} \end{figure*} \subsection{Secondary data set} \label{sec:results_secondary} The secondary solution gives approximate positions for more than 2.5~billion entries, including more than 1.5~billion ``new sources'' created in the process of cross-matching the Gaia detections to the source list \citep[see Sect.~4 in][]{2016GaiaF}. Many of the new sources are spurious, and a suitable criterion had to be found to filter out most of the bad entries. On the other hand, for uniformity of the resulting catalogue, it is desirable that the very same criteria do not reject too many of the solutions using observations cross-matched to the initial source list. By comparing the distributions of various quality indicators for the two kinds of sources, the following criterion was found to provide sensible rejection of obviously spurious sources while retaining nearly all solutions for sources in the initial source list: \begin{equation}\label{eq:formal2} N \ge 5 \quad \text{and} \quad \epsilon_i < 20~\text{mas} \quad \text{and} \quad \sigma_\text{pos,max} < 100~\text{mas} \, . \end{equation} $N$ is the number of field-of-view transits used in the solution, $\epsilon_i$ is the excess source noise (Sect.~\ref{sec:results_primary}), and $\sigma_\text{pos,max}$ the semi-major axis of the error ellipse in position at the reference epoch. The excess source noise is essentially a measure of the astrometric consistency of the $N$ transits. The first two conditions therefore mean that the source should have been detected at least five times at positions consistent within some 20~mas. This limit is large enough to accommodate attitude and calibration modelling errors as well as source modelling errors for many unresolved binaries, while rejecting the much larger mismatches that are typically found for spurious detections. The limit on the size of the error ellipse in position removes very faint sources with large photon-noise uncertainties and some sources with extremely elongated error ellipses. That Eq.~(\ref{eq:formal2}) provides a reasonable selection was checked in several selected areas by superposing the positions of accepted and rejected sources on images obtained with the ESO VLT Survey Telescope (VST) for the Gaia ground based optical tracking (GBOT) project \citepads{2014SPIE.9149E..0PA} and, for some very high-density areas in the Baade's window region, with the HST Advanced Camera for Surveys (ACS/WFC). These checks indicate that the above criterion is even conservative in the sense that very many real sources detected by Gaia are not retained in the present preliminary selection. Applying the selection criterion in Eq.~(\ref{eq:formal2}) results in accepted positional solutions for 1467~million entries, of which 771~million are in the IGSL and 695~million are new sources. A large number of entries in the IGSL were found to be redundant, resulting in nearly coinciding positional solutions. The secondary data set of Gaia DR1 consists of the 1\,140\,622\,719 non-redundant entries that also have valid photometric information. The leftmost maps in Fig.~\ref{fig:secondaryEqu} shows the total density of sources in the secondary data set; the other two maps show the densities of the IGSL and new sources. Imprints of the ground-based surveys used in the construction of the IGSL are clearly seen in the latter two maps (as over- and under-densities in Fig.~\ref{fig:secondaryEqu}b and c, respectively). These are largely absent in the total density map (Fig.~\ref{fig:secondaryEqu}a), which however still shows features related to the scanning law of Gaia (cf.\ Fig.~\ref{fig:stats2}b). Figure~\ref{fig:secondaryGal} shows the same densities in Galactic coordinates. The secondary data set contains only positions, with their estimated uncertainties and other statistics, but no parallaxes or proper motions. Some statistics are summarised in Table~\ref{tab:statSummarySecondary}. The standard uncertainties in position are calculated using the recipe in \citetads{2015A&A...583A..68M}. This provides a conservative estimate based on a Galactic model of the distribution of the (neglected) parallaxes and proper motions. | 16 | 9 | 1609.04303 |
1609 | 1609.01526_arXiv.txt | Uniformity in thickness and electronic properties of superconducting niobium titanium nitride (NbTiN) thin films is a critical issue for upscaling superconducting electronics, such as microwave kinetic inductance detectors for submillimeter wave astronomy. In this article we make an experimental comparison between the uniformity of NbTiN thin films produced by two DC magnetron sputtering systems with vastly different target sizes: the Nordiko 2000 equipped with a circular \diameter100 mm target, and the Evatec LLS801 with a rectangular target of 127 mm $\times$ 444.5 mm. In addition to the films deposited staticly in both systems, we have also deposited films in the LLS801 while shuttling the substrate in front of the target, with the aim of further enhancing the uniformity. Among these three setups, the LLS801 system with substrate shuttling has yielded the highest uniformity in film thickness ($\pm $2\%), effective resistivity (decreasing by 5\% from center to edge), and superconducting critical temperature ($T_{\mathrm{c}}$ = 15.0 K - 15.3 K) over a \diameter100 mm wafer. % However, the shuttling appears to increase the resistivity by almost a factor of 2 compared to static deposition. Surface SEM inspections suggest that the shuttling could have induced a different mode of microstructural film growth. % | Superconducting niobium titanium nitride (NbTiN) thin films are used for highly demanding circuits that operate in the frequency range of 1 GHz - 1000 GHz. Having a gap frequency of $F_{\mathrm{gap}}\sim$1100 GHz, NbTiN is being used in transmission lines for astronomical instruments that operate at frequencies above the gap frequency of Nb ($F_{\mathrm{gap}}\sim$700 GHz) \cite{deGraauwHIFI,Jackson2006}. Aside from the high $F_{\mathrm{gap}}$, NbTiN is known to exhibit little microwave phase noise \cite{Barends2010noise} and microwave loss \cite{Barends2010Loss,Bruno2015}, making it a good material for photodetectors \cite{Janssen2013eff} and circuit quantum electrodynamic experiments \cite{vanWoerkom:2015jt}. Furthermore, NbTiN is also being used as the material for narrow band filters \cite{Endo2013}, and microwave parametric amplifiers \cite{Eom2012}. In the above-mentioned applications, the typical size of each chip has been on the order of 0.1 mm - 10 mm. However, recent applications of NbTiN have a rapidly growing degree of on-chip multiplexing, demanding the chip size to grow to 100 mm and beyond. For example, upcoming submillimeter astronomical instruments such as A-MKID \cite{Baryshev2014} and DESHIMA \cite{Endo2012SPIE} demand $10^3$-$10^4$ of NbTiN/Al hybrid microwave kinetic inductance detectors (MKIDs) \cite{Janssen2013eff}, which fill the entire surface of one or more \diameter 100 mm wafers. % Such large-scale devices have a dramatically higher demand in the uniformity of critical film properties over a large surface area, and often d.c. magnetron sputtering methods that have been designed for small devices cannot easily meet the requirements. Here we investigate how the uniformity in thickness and physical properties of NbTiN films changes, when: (1) we adopt a sputtering target that is much larger than a \diameter 100 mm wafer (especially in one direction), and (2) shuttle the wafer under the target during deposition (Fig. $\ref{Target}$). Using a larger sputter system enables us to scale deposition parameters from the smaller system to allow for a relatively easy transition between the two deposition systems \cite{bos}. Other techniques to obtain a better homogeneity, such as confocal sputtering, result typically in a strong reduction in deposition speed which can have additional complications such as increased impurity concentrations and a different film growth. In this paper we will especially focus on the parameters that are relevant for large arrays of MKIDs. In a typical MKID chip, $\sim$1000 MKIDs can be read out simultaneously with a bandwidth of 2 GHz \cite{vanRantwijk2016}, relying on the assumption that the resonance frequencies follow the design with a precision of no worse than $\sim$2 MHz. While the physical length of each resonator can be controlled with sufficient precision by standard lithographic techniques, it is challenging to keep the kinetic inductance $L_\mathrm{k}$ uniform enough over the large device area to prevent the resonance features from overlapping with one another. Because $L_\mathrm{k}$ is ultimately associated to the critical temperature $T_\mathrm{c}$, resistivity $\rho$, and film thickness $t$ (see Appendix), we will investigate the uniformity of these parameters. | Enlarging the sputtering target and shuttling the substrate in front of it have both proven to be effective methods for improving the uniformity in thickness and electronic properties of superconducting NbTiN thin films. By combining the two, we have obtained a \diameter 100 mm circular film with $T_\mathrm{c}$ = 15.2 K $\pm$ 1\%, and the variations in thickness and other physical properties are also kept to within 1-2\%. This type of film is very suited for MKID applications. | 16 | 9 | 1609.01526 |
1609 | 1609.06177_arXiv.txt | A detailed search for emission and absorption lines and assessing their upper limits are performed for Suzaku data. The method utilizes a matched-filtering approach to maximize the signal-to-noise ratio for a given energy resolution, which could be applicable to many types of line search. We first applied it to well-known AGN spectra that have been reported to have ultra-fast outflows, and find that our results are consistent with previous findings at the $\sim3\sigma$ level. We proceeded to search for emission and absorption features in the two bright magnetars 4U~0142+61 and 1RXS~J1708--4009, applying the filtering method to Suzaku data. We found that neither source showed any significant indication of line features, even using long Suzaku observations and dividing their spectra into spin phases. The upper limits on the equivalent width of emission/absorption lines are constrained to be a few eV at $\sim$ 1~keV, and a few hundreds of eV at $\sim$ 10~keV. This strengthens previous reports that persistently bright magnetars do not show proton cyclotron absorption features in soft X-rays and, even if they exist, they would be broadened or much weaker than below the detection limit of X-ray CCD. | \label{intro} X-ray diagnosis of emission and absorption lines have been playing a great role in deriving elemental composition, density and degree of ionization of gas, and velocities or kinematic of the X-ray emitting/obscuring matter. Such narrow features are commonly seen in addition to a smooth continuum spectrum; such as thermal radiation from a black body, comptonization, or bremsstrahlung. A frequently-used way to assess the significance of the line detection is to fit a theoretical model to an observed spectrum by minimizing the $\chi^{2}$ value, and evaluating the goodness of fit using the $F$-test. However, the method is sensitive to the choice of the fitting range because the fit tends to minimize the global structure of $\chi^{2}$ while a weak and narrow feature does not always contribute significantly to the $\chi^{2}$ value even if such a narrow structure really exists. In this sense, searching for an unknown line in an objective manner could be rather dependent on the way of fitting. To avoid the arbitrariness, many statistical methods have been proposed, such as the likelihood ratio test combined with the $F$-test, Bayesian posterior predictive probability \citep{Protassov2002}, and a Monte Carlo (MC) test after ``matched filter'' smoothing \citep{Rutledge2003}. Among them, the method using MC simulation with matched filter smoothing is known to be quick and robust when searching for unknown lines and finding their confidence ranges. It was first applied to the X-ray afterglows of Gamma Ray Bursts (GRBs) and showed that the emission line proposed by \citet{Reeves2002} is not statistically significant. The advantage of this method is that it does not rely on global fitting over the entire energy range but on deviation from the local continuum, and maximizes the signal-to-noise ratios by adopting a gaussian filter with a width equal to the energy resolution. The method returns a deviation from an assumed smooth continuum, making line searches possible in an unbiased way. It is also straightforward to constrain the upper limits of the emission/absorption feature. In this paper, we apply the MC simulation with matched filtering method to Active Galactic Nuclei (AGN) and magnetar \citep{Thompson1995} spectra obtained with Suzaku. We first apply it to the famous AGNs Mrk~766 and Ark~120, and examine the existence of Ultra-fast Outflows (UFOs), an AGN outflow with a velocity close to the speed of light. The observational evidence of UFOs relies on highly blue-shifted absorption lines mostly found around the Fe K band \citep{Tombesi2010}. The features are suitable to test and verify if the MC method is applicable to Suzaku data. The results are found to be consistent with those reported in \citet{Gofford2013}. We then proceeded to look into two persistently bright magnetars, 4U~0142+61 and 1RXS~J1708--4009, and searched for cyclotron features from both time-averaged and phase-resolved spectra. The upper limits of these features for both sources are evaluated using the MC method. We describe the methodology of the filtering in section 2 and the observational condition in section 3. The results of AGNs and magnetars are presented in sections 4 and 5, respectively. Section 6 contains the discussion and summary. Errors in this paper refer to 90\% confidence range unless otherwise stated. | \label{discussion} We implemented the Gaussian convoluting filter method for Suzaku XIS spectral analysis in order to quantitatively evaluate the significance of detection of emission or absorption line features. One advantage of this method is that it is not necessary to assume the existence of lines in advance of model fitting being performed. For verification of our implementation, we applied this method to the iron absorption features to AGN Mrk~766 and Ark~120 already studied by \citet{Gofford2013}. As the result of our simulation, two significant (both $>4\sigma$) absorption lines at 6.7 and 7.0~keV were detected from Mrk~766, while no features over the 3$\sigma$ level were seen in Ark~120. This result is consistent with \citet{Gofford2013}. We searched for absorption features, expected from proton cyclotron resonance, in magnetar spectra of the prototypical sources 4U~0142+61 and 1RXS~J1708--4009. The total exposures of $\sim$350 and $\sim$120~ks (sum of four and two observations) were used in the 0.9--10~keV XIS analysis for 4U~0142+61 and 0.7--10~keV for 1RXS~J1708--4009, respectively. 1RXS~J1708--4009 has been reported to show a phase dependent absorption line at $\sim$8.1~keV with $\sigma= 0.4$~keV and EW = 460~eV from the BeppoSAX observations in 1999 and 2001 \citep{Rea2003}. RXTE observed 4U~0142+61 six times during outbursts from 2006 to 2007, and detected three significant emission lines at $\sim$4, $\sim$8, and $\sim$14~keV \citep{Gavriil2011} or three absorption lines at $\sim$4, $\sim$6.5, and $\sim$11~keV \citep{Chakraborty2016} from short burst spectra. However, because these features have not been reported afterwards, proton cyclotron resonance features (CRSFs) may depend on the burst activity. In our search, a few potential lines show significance with $\sim$4$\sigma$ level in the phase-averaged analysis. As an analogy of the canonical accretion-powered pulsars with electron cyclotron resonances, the line feature is expected to be much clearer when performing phase-resolved analysis. However, no absorption feature was significantly detected in our phase-resolved spectra due to reduced statistics. Thus, we cannot conclude that this absorption is an intrinsic feature. There are several possibilities for our non-detection of the proton CRSF. The present two targets, 4U~0142+61 and 1RXS~J1708-4009, are persistently bright magnetars which provide prototypical observational properties for this class. Firstly, the absorption is much weaker than the detection limit achieved by the XIS. We derived the upper limit of the broad absorption in Figure \ref{0142-limits} for 4U~0142+61, e.g., at an optical depth of 0.03 and 0.2 at 1 and 7~keV, respectively. This XIS upper limit is comparable to that from XMM-Newton/EPIC \citep{Rea2007}, while Chandra/HETGS shows higher dependency on the energy (\cite{Juett2002}, \cite{Patel2003}). Such differences could originate from detector response, e.g., CCD vs. grating. From a theoretical viewpoint, it is also pointed out that the vacuum polarization and mode conversion may strongly suppress proton CRSF in a strong magnetic field \citep{Ho2003}. As a second possibility for the non-detection, the actual magnetic field on the magnetar surface is thought to be stronger than that derived from the $P-\dot{P}$ method when a simple dipole magnetic field configuration is assumed. The surface dipole magnetic fields were derived from the $P-\dot{P}$ method to be $B_{d} = 1.3$ and $4.7 \times 10^{14}$~G for 4U~0142+61 and 1RXS~J1708--4009, respectively. These correspond to the first Landau level transition at $\sim 0.8$~keV and $\sim 3$~keV, which are well inside the XIS energy range. However, some observational studies suggest stronger magnetic fields on the stellar surface. \citet{Gavriil2011} and \citet{Chakraborty2016} reported that the surface magnetic field of 4U~0142+61 is stronger than the dipolar one. Moreover, there are reports of proton CRSFs from two low-magnetic-field sources, SGR~0418+5279 \citep{Tiengo2013} and Swift~J1822.3-1606 \citep{Castillo2016}. Phase-dependent absorption energies are from 0.5 to 5~keV and 3 to 12~keV for SGR~0418+5279 and Swift~J1822.3-1606, respectively. Supposing these absorptions as proton CRSFs, the corresponding magnetic field becomes $>2 \times 10^{14}$~G and $(6 - 25) \times 10^{14}$~G for SGR~0418+5279 and Swift~J1822.3-1606, respectively. These measured values are much stronger (e.g., ten times stronger) than the dipolar fields, $B_{d} = 6\times10^{12}$~G and $B_{d} = 3.4\times10^{13}$~G, respectively. Contribution of higher-order multiples on the surface could explain such a difference. Therefore, if the surface magnetic fields of 4U~0142+61 and 1RXS~J1708--4009 are actually much stronger than the $P-\dot{P}$ values, the absorption features should appear at energies exceeding 10~keV. The microcalorimeter SXS onboard Hitomi will soon start high energy-resolution observations. The SXS has more than 20 times greater energy resolution than the XIS, and the method we have used for magnetars in this paper would be an efficient way to search for spectral lines. \ \par We are grateful to the Suzaku team for their long term observation of 4U~0142+61 and 1RXS~J1708--4009. S.Y and T.E. are supported by JSPS KAKENHI, Grant-in-Aid for JSPS Kakenhi 15H05438/15H00785 and 15H00845, respectively. | 16 | 9 | 1609.06177 |
1609 | 1609.03936.txt | We present a multi-wavelength polarimetric and spectral study of M87 jet obtained at sub- arcsecond resolution between 2002 and 2008. The observations include multi-band archival VLA polarimetry data sets along with the HST imaging polarimetry. These observations have better angular resolution than previous work by factors of 2-3 and in addition, allow us to explore the time domain. These observations envelope the huge flare in HST-1 located at 0.$\arcsec$86 from the nucleus \citep{2007ApJ...663L..65C, 2009ApJ...699..305H, 2009AJ....137.3864M, 2011ApJ...743..119P}. The increased resolution enables us to view more structure in each knot, showing several resolved sub-components. We also see apparent helical structure in the polarization vectors in several knots, with polarization vectors turning either clockwise or counterclockwise near the flux maxima in various places as well as show filamentary undulations. Some of these characteristics are correlated with flux and polarization maxima while others are not. We also examine the total flux and fractional polarization and look for changes in both radio and optical since the observations of \citet{1999AJ....117.2185P} and test them against various models based on shocks and instabilities in the jet. Our results are broadly consistent with previous spine-sheath models and recollimation shock models, however, they require additional combinations of features to explain the observed complexity, e.g. shearing of magnetic field lines near the jet surface and compression of the toroidal component near shocks. In particular, in many regions we find apparently helical features both in total flux and polarization. We discuss the physical interpretation of these features. | \indent M87 hosts one of the nearest (d=16 Mpc, translating to a scale of $\approx$78 pc per arcsecond) relativistic jets. The kpc scale jet is under observation in X-rays with \textit{Chandra}, optical-ultraviolet with \textit{HST}, and in radio with \textit{VLA} and \textit{VLBA}. During the last decade, a major flare was seen in knot HST-1, located 0.$''$86 from M87's nucleus. This flare, which featured an increase in optical and X-ray flux of more than a factor of 100, was observed extensively in the optical \citep{2009AJ....137.3864M, 2011ApJ...743..119P}, X-rays \citep{2006ApJ...640..211H}. \citet{2007ApJ...663L..65C} suggest that HST-1 was also the site of a TeV flare observed around the same time by the H.E.S.S. experiment, however there are other views about the origin of the TeV emission. While \citet{2011ApJ...743..177H} think that both the nucleus as well as HST-1 can be sources of TeV emission, \citet{2005ApJ...634L..33G} suggest that the 2005 TeV flare originated from the nucleus. The current facilities do not have enough angular resolution in TeV to comment on the origin of these flares and the time resolution of the observations is insufficient to discriminate as well \citep{2012ApJ...746..151A}. \\ \indent The jet morphology at all wavelengths appear broadly similar \citep{1996ApJ...473..254S, 2005ApJ...627..140P}. The observed differences can be accounted for by highly polarized synchrotron radiation at all wavelengths and a nearly constant radio-optical spectral index throughout the jet \citep{2001ApJ...551..206P}. The jet has typical fractional polarization 10\% to 20\% in most regions \citep{1990ApJ...362..449O,1999AJ....117.2185P}. Radio polarization maps on large scale show large Faraday rotations in the direction of the 2 kpc radio lobes ranging from 350 rad m$^{-2}$ in the jet to 8000 rad m$^{-2}$ in the eastern radio lobes. In a more recent study, \citet{2016ApJ...823...86A} report rotation measures of a few hundreds of rad m$^{-2}$ over the most of the jet region along with some higher values of $\sim$1000 rad m$^{2}$ in knot C, the values which are in agreement with \citet{1990ApJ...362..449O}. They fit RM with two Gaussian, one for higher values in knot C and another one for the rest of the jet, with similar standard deviation, $\sigma_{RM}$ $\sim$ 120-180 rad m$^{2}$, (see their Fig.3). The observed polarization and high rotation measure suggests that the rotation is taking place in a Faraday screen in front of the radio emitting plasma. \citet{2016ApJ...823...86A}'s results suggest this screen is much closer to the jet vicinity and most likely associated with the sheath of the jet.\\ \indent Polarimetry can reveal the configuration of the magnetic field in the emitting region, and is thus a very useful diagnostic for jets. Many knot regions show high polarization ($\approx40\%-50\%$, close to the theoretical maximum for optically thin synchrotron emission) suggesting a highly ordered magnetic field. Previous radio and optical polarization images show the magnetic field is mostly parallel to the direction the of jet except in the shock-like knot regions, HST-1, knots A and C, where it becomes perpendicular to the jet axis (\citet{1999AJ....117.2185P}, hereafter P99). \\ \indent \citet{2001ApJ...551..206P} observed changes in the spectral indices of other knots in the jet, particularly D and F, which when combined with the MFPA vector morphology at 0.$''$2 resolution, suggest high energy synchrotron emitting particles may represent a very different population than those that emit in radio. P99 proposed a ``stratified" jet model to explain the differences seen in the radio and optical flux and polarization morphology. The model suggests that the radio and optical electrons may originate from different locations within the jet (P99, Fig. 7). According to their model, the observed radio emission is coming from the outer layer or ``strata" of the jet, shown by dotted lines in the figure; whereas the optical emission is coming from the central region close to the axis of the jet shown by solid lines. \\ \indent We describe the details of the polarimetry observations used for this study and the error analysis carried out in $\S$ \ref{sec:observations}. In $\S$ \ref{sec:compare_pol}, we discuss the general trends in flux and polarization structure along the jet, and compare the observed features of the individual knots with the previous studies. In $\S$ \ref{sec:variability}, we analyze the flux and polarization variability seen over the period of observations. Finally, we discuss our findings in the $\S$ \ref{sec:discussion} and conclude our discussion in $\S$ \ref{sec:concl}. %%table 1 - {\IT VLA} observations \begin{deluxetable*}{cccccccccc} \scriptsize \tablewidth{0pt} \tablecaption{\textit{VLA} and \textit{HST} Polarimetry Observations} %\tablenum{1} \tablehead{\multicolumn{2}{c}{Project ID} & \multicolumn{2}{c}{Telescope Configuration} & \multicolumn{2}{c}{Energy Band} & \multicolumn{2}{c}{Date of observation}\\ \hline \\ \colhead{\textit{VLA}} & \colhead{\textit{HST}} & \colhead{\textit{VLA}} & \colhead{\textit{HST}} & \colhead{\textit{VLA}} & \colhead{\textit{HST}} & \colhead{\textit{VLA}} & \colhead{\textit{HST $ ^\dagger$}}} \startdata AH295 & 9705 & VLA:C:1 & ACS/HRC & X, Q & F606W & 19-Oct-02 & Dec 07 2002~ (1)\\ (J. Biretta) & (E. Perlman) & \nodata & \nodata & \nodata & \nodata & \nodata & Dec 10 2002~ (2)\\ AH822 & 9829 & VLA:A:1 & ACS/HRC & X,U,K & F606W & 02-Jun-03 & Nov 29 2003~ (3)\\ (D.E.Harris) & 10133 & \nodata & \nodata & \nodata & \nodata & 03-Jun-03 & Nov 28 2004~ (4)\\ \nodata & (J. Biretta) & \nodata & \nodata & \nodata& \nodata & 24-Aug-03$^ \ast$ & Dec 26 2004~ (5)\\ \nodata & \nodata & VLA:B:1 & \nodata & X,U,K,Q & \nodata & 16-Nov-03 & Feb 09 2005~ (6) \\ \\ AH862 & \nodata & VLA:A:1 & ACS/HRC & X,U,K & F606W & 15-Nov-04 & Mar 27 2005~ (7)\\ (D.E.Harris) & \nodata & \nodata & \nodata & \nodata & \nodata & 31-Dec-04 & May 09 2005 ~(8)\\ \nodata & \nodata & VLA:B:1 & \nodata & X,U,K,Q & \nodata & 03-May-05 & Jun 22 2005 ~(9) \\ \\ AH885 & \nodata & VLA:A:1 & ACS/HRC & X,U,K & F606W & 15-Feb-06 & Aug 01 2005~(10)\\ (D.E.Harris) & 10617 & VLA:B:1 & \nodata & X & \nodata & 07-May-06 & Nov 29 2005~(11)\\ \nodata & (J. Biretta) & \nodata & \nodata & X,U,K & \nodata & 08-May-06 & Dec 26 2005~(12)\\ \nodata & \nodata & \nodata & \nodata & X,U,K,Q & \nodata & 31-Jul-06 & Feb 08 2006~(13)\\ \nodata & \nodata & \nodata & \nodata & \nodata & \nodata & 01-Aug-06$^ \ast$ & Mar 30 2006~(14) \\ \\ AC843 & \nodata & VLA:A:1 & ACS/HRC & X,U,K & F606W & 11-Jun-07 & May 23 2006~(15)\\ (D.E.Harris) & 10910 & \nodata & \nodata & \nodata & \nodata & 12-Jun-07 & Nov 28 2006~(16)\\ \nodata & (J. Biretta) & \nodata & \nodata & \nodata & \nodata & 10-Aug-07$^ \ast$ & Dec 30 2006~(17)\\ \nodata & 11216 & \nodata & \nodata & \nodata & \nodata & 11-Aug-07$^ \ast$ & Nov 25 2007~(18) \\ \nodata & (J. Biretta) & VLA:B:1 & \nodata & X,U,K,Q & \nodata & 19-Jan-08 & \nodata &\\ \enddata \\ \tablenotetext{$^\ast$}{\textit{VLA} observations on these dates were not used due to the bad weather.} \tablenotetext{$^\dagger$}{\textit{HST} observations sequence numbers are taken from \citet{2011ApJ...743..119P}.} \label{tbl-obs_data} \end{deluxetable*} %table 2 - flux and polarization values for all knots (using combined Stokes I, Q and U images of 22 GHz) \begin{deluxetable*}{cccccc} \tablewidth{0pt} \tablecaption{Radio Flux and Polarization Data} %\tablenum{2} \tablehead{\colhead{Region}& \colhead{X$^{\dagger}$} & \colhead{Y$^{\dagger}$} & \colhead{Flux Density (mJy)}& \colhead{Polarization (\%)}& \colhead{Position Angle (deg)}} \startdata Nucleus & 769-781 & 429-441 & 4358.4 $\pm$ 0.9 & 1.3 $\pm$ 0.2 & 3 $\pm$ 1 \\ HST-1 & 803-813 & 445-455 & 89.8 $\pm$ 0.8 & 8.1 $\pm$ 0.2 & -7 $\pm$ 4 \\ D-E & 869-897 & 469-479 & 62.4 $\pm$ 1.2 & 23.6 $\pm$ 0.2 & 20 $\pm$ 3 \\ D-M & 905-923 & 473-489 & 28.4 $\pm$ 1.2 & 32.1 $\pm$ 0.2 & 18 $\pm$ 5 \\ D-W & 919-931 & 485-497 & 19.9 $\pm$ 0.9 & 19.5 $\pm$ 0.2 & 13 $\pm$ 9 \\ E & 973-1033 & 499-535 & 78.0 $\pm$ 3.3 & 11.4 $\pm$ 0.6 & 28 $\pm$ 13 \\ F & 1075-1133 & 537-585 & 137.8 $\pm$ 3.7 & 17.9 $\pm$ 0.7 & 17 $\pm$ 6 \\ I & 1175-1213 & 571-607 & 99.3 $\pm$ 2.6 & 8.6 $\pm$ 0.5 & 35 $\pm$ 10 \\ A-shock & 1223-1251 & 585-629 & 600.1 $\pm$ 2.5 & 22.7 $\pm$ 0.5 & 41 $\pm$ 1 \\ A & 1221-1295 & 581-643 & 1291.4 $\pm$ 4.7 & 10.3 $\pm$ 0.9 & -36 $\pm$ 1 \\ B1 & 1313-1341 & 617-657 & 337.8 $\pm$ 2.4 & 26.4 $\pm$ 0.4 & 32 $\pm$ 1 \\ B2 & 1367-1397 & 625-679 & 149.5 $\pm$ 2.8 & 31.5 $\pm$ 0.5 & -31 $\pm$ 2 \\ C1 & 1431-1471 & 687-729 & 320.1 $\pm$ 2.9 & 24.4 $\pm$ 0.5 & 30 $\pm$ 1 \\ C2 & 1479-1505 & 681-741 & 50.4 $\pm$ 2.8 & 56.7 $\pm$ 0.5 & 33 $\pm$ 3 \\ G1 & 1475-1531 & 753-771 & 64.0 $\pm$ 2.3 & 28.5 $\pm$ 0.4 & -11 $\pm$ 5 \\ G2 & 1527-1559 & 725-759 & 105.4 $\pm$ 2.3 & 37.1 $\pm$ 0.4 & -39 $\pm$ 2 \enddata \tablenotetext{$^\dagger$}{Box coordinates (X, Y) are in pixels. The jet is at $\sim$ 20.5$^{\circ}$ north from the x axis, with a scale of 0.''025 pixel$^{-1}$.} \label{tbl-rad-poln-flux_data} \end{deluxetable*} %table 3 - flux and polarization values for all knots (using combined Stokes I, Q and U images of F606W) \begin{deluxetable*}{cccccc} \tablewidth{0pt} \tablecaption{Optical Flux and Polarization Data} %\tablenum{3} \tablehead{\colhead{Region}& \colhead{X$^{\dagger}$} & \colhead{Y$^{\dagger}$} & \colhead{Flux Density ($\mu$Jy)}& \colhead{Polarization (\%)}& \colhead{Position Angle (deg)}} \startdata Nucleus & 769-781 & 429-441 & 630.9 $\pm$ 0.1 & 3.1 $\pm$ 1.1 & -17 $\pm$ 3 \\ HST-1 & 803-813 & 445-455 & 562.7 $\pm$ 0.0 & 27.1 $\pm$ 1.0 & -15 $\pm$ 3 \\ D-E & 869-897 & 469-479 & 42.0 $\pm$ 0.1 & 5.1 $\pm$ 6.7 & -33 $\pm$ 3 \\ D-M & 905-923 & 473-489 & 14.3 $\pm$ 0.1 & 20.5 $\pm$ 4.0 & -17 $\pm$ 3 \\ D-W & 919-931 & 485-497 & 11.3 $\pm$ 0.1 & 26.5 $\pm$ 3.3 & -31 $\pm$ 3 \\ E & 973-1033 & 499-535 & 43.2 $\pm$ 0.2 & 10.8 $\pm$ 6.4 & -27 $\pm$ 3 \\ F & 1075-1133 & 537-585 & 94.3 $\pm$ 0.2 & 12.8 $\pm$ 5.6 & -38 $\pm$ 3 \\ I & 1175-1213 & 571-607 & 36.9 $\pm$ 0.2 & 22.0 $\pm$ 3.0 & -26 $\pm$ 3 \\ A-shock & 1223-1251 & 585-629 & 33.4 $\pm$ 0.2 & 182.0 $\pm$ 2.1 & -3 $\pm$ 3 \\ A & 1221-1295 & 581-643 & 839.6 $\pm$ 0.3 & 20.0 $\pm$ 1.0 & 19 $\pm$ 3 \\ B1 & 1313-1341 & 617-657 & 203.2 $\pm$ 0.2 & 15.9 $\pm$ 1.2 & -14 $\pm$ 3 \\ B2 & 1367-1397 & 625-679 & 149.0 $\pm$ 0.2 & 22.6 $\pm$ 1.5 & 10 $\pm$ 3 \\ C1 & 1431-1471 & 687-729 & 215.6 $\pm$ 0.2 & 8.0 $\pm$ 2.7 & -9 $\pm$ 3 \\ C2 & 1479-1505 & 681-741 & 52.0 $\pm$ 0.2 & 15.6 $\pm$ 4.1 & -33 $\pm$ 3 \\ G1 & 1475-1531 & 753-771 & 29.8 $\pm$ 0.1 & 21.9 $\pm$ 3.2 & 18 $\pm$ 3 \\ G2 & 1527-1559 & 725-759 & 15.8 $\pm$ 0.2 & 26.9 $\pm$ 9.5 & 7 $\pm$ 3 \enddata \tablenotetext{$^\dagger$}{Box coordinates (X, Y) are in pixels. The jet is at $\sim$ 20.5$^{\circ}$ north from the +X axis, with a scale of 0.''025 pixel$^{-1}$.} \label{tbl-opt-poln-flux_data} \end{deluxetable*} | \label{sec:concl} \indent The overall flux and polarization of the M87's jet shows striking differences as compared to the older observations of P99. We discussed what things are different in terms of resolution and the possibility of a few real sub-structures emerging on the sub-parsec scales near the nucleus and knot HST-1. As described in \S\ref{sec:shocks}, the structure is changing suddenly beyond the recollimation shock at knot HST-1, which compresses the local magnetic field \citep{2014ApJ...785..152N, 2006MNRAS.370..981S} and forces the field lines to become perpendicular to the flow. Further downstream, the interaction between a strongly magnetised relativistic plasma outflow and non-relativistic collimating magnetohydrodynamic winds can give rise to more shocks. As a result, the particles in these regions can be accelerated to relativistic speeds and move out from the knot forming new super-luminal sub-components seen in {\it VLBA} images \citep{2007ApJ...663L..65C}, which are likely to be responsible for the flaring behavior. A more recent study by \citet{2016MNRAS.tmpL..44T}, suggest that the presence of undulations in this region may have caused due to the successive compression and stretching of the local toroidal magnetic field resulting in the spinning of the magnetic field lines. While we see helical undulations in our data, we do not have enough resolution to comment if these components are moving out or are stationary features in the jet. \\ \indent In \S\ref{sec:trends} we described a few common features of the radio and optical jet that are observed in our images. We see that the optical jet is slightly narrower than the radio with the optical emission being more defined and concentrated closer to the center. This trend appear to be consistent with the previous model of a layered or stratified jet of P 99 (see their Fig. 7). They explain this in terms of origin of radio and optical electrons being very different. In this model, the more energetic optical electrons are probably located near the center whereas the lower energy radio electrons are from the outer layer of the jet. The differences in the flux morphology in the two bands also apparently indicate that the jet follow the ``spine-sheath'' model of \citep{2007ApJ...668L..27K}, in which they suggest (similar to P99) that the higher energy photons originate from the center of the jet while the lower energy photons originate from near the surface. \\ \indent Our results do not necessarily follow the stratified jet or ``spine sheath'' models. The similarities in the flux and polarization structure that we see as explained in \S~\ref{sec:trends}, are mainly due to the higher resolution of our data as compared to the previous data of P99. We see a lot more flux as well as polarization structure that was not seen in their images. As a result their model of stratified jet does not necessarily apply to each component in the jet. The newer flux details in the inner jet knots such as HST-1, D and F, were not see in old images of P99, as a result their model does not hold true in these regions. The flux and polarization structure in these regions show quite many similarities which does not support the stratified jet model. However,the stratified jet model can still hold in general for the outer jet components i.e. A, B, C and G, where we clearly see the differences in the radio and optical flux and polarization structure. \\ \indent Another striking difference is in the polarization morphology of the jet in two bands, especially in the inner jet, the nucleus, HST-1 and knot D. Our optical images show the predominant perpendicular MFPA features in the jet. The radio MFPA, on the other hand, stays mostly parallel to the jet direction. These differences can be explained either by arguing that the direction of local magnetic field is changing, or that the radio wavelengths are being Faraday rotated. At the location of perpendicular shock, the magnetic field lines can get squeezed and forced to turn in the direction perpendicular to the direction of jet plasma. The magnetic field lines may turn back to parallel downstream of the shock. This can cause the rapid changes in the in the directions of local magnetic field. If the shock lies in the interior of the jet i.e. closer to the jet axis, this may affect optical electrons only, lying closer to the axis of the jet, and not so much on the radio electrons closer to the surface of the jet. P99, \citet{1996ApJ...467..597B, 1989ApJ...340..698O} suggested these changes can cause instabilities (like Kelvin-Helmholtz) which in turn can cause shearing of field lines near the boundary between the jet surface and interstellar medium (ISM). This may cause the increased polarization near the surface as observed in fractional polarization images in radio. \\ \indent In general, the flux as well as polarization structure in the inner jet and intermediate jet as well as the outer jet, show quite different characters in fractional polarization, which point toward the fact that structure of the magnetic field and its effects on the jet environments are completely different in each of these regions. These internal changes in the magnetic field can also affect the particle acceleration and emission mechanisms in respective regions, which we can clearly see from our radio and optical images. The effect of kink instability (as described in \S\ref{sec:helical}) on the kpc scales, away from the central engine, may play important role in defining the polarization structure in the outer jet and beyond. A more thorough followup observations of radio polarimetry and optical proper motions along the jet at higher resolution will help us gain further understanding of these processes. \\ \indent ESP and SSA acknowledge support from STScI through grants HST-GO-13759.003, 13676.003 and 13764.001. ESP and MG acknowledge support from NASA ASAP grant NNX15AE55G. %%%%%%%%%%% Add acknowledgements %%%%%%%%% | 16 | 9 | 1609.03936 |
1609 | 1609.03939_arXiv.txt | There exists a class of ultralight Dark Matter (DM) models which could form a Bose-Einstein condensate (BEC) in the early universe and behave as a single coherent wave instead of individual particles in galaxies. We show that a generic BEC-DM halo intervening along the line of sight of a gravitational wave (GW) signal could induce an observable change in the speed of GWs, with the effective refractive index depending only on the mass and self-interaction of the constituent DM particles and the GW frequency. Hence, we propose to use the deviation in the speed of GWs as a new probe of the BEC-DM parameter space. With a multi-messenger approach to GW astronomy and/or with extended sensitivity to lower GW frequencies, the entire BEC-DM parameter space can be effectively probed by our new method in the near future. | \label{sec:1} Although the existence of Dark Matter (DM) constituting about 27\% of the energy budget of our Universe~\cite{Ade:2015xua} is by now well established through various cosmological and astrophysical observations, very little is known about its particle nature and interactions. While the standard $\Lambda$CDM model with collisionless cold DM (CDM) successfully explains the large-scale structure formation by the hierarchical clustering of DM fluctuations~\cite{Blumenthal:1984bp, Davis:1985rj}, there are some unresolved issues on galactic and sub-galactic scales, such as the core-cusp~\cite{Moore:1994yx, Flores:1994gz, Moore:1999gc, deBlok:2009sp}, missing satellite~\cite{Kauffmann:1993gv, Klypin:1999uc, Moore:1999nt, Bullock:2010uy}, and too big to fail~\cite{BoylanKolchin:2011de, BoylanKolchin:2011dk, Papastergis:2014aba} problems. All these small-scale structure anomalies can in principle be resolved if the DM is made up of ultralight bosons that form a Bose-Einstein condensate (BEC), i.e. a single coherent macroscopic wave function with long range correlation; for a review, see e.g.,~Ref.~\cite{Suarez:2013iw}. There are two classes of BEC-DM, depending on whether DM self interactions are present or not. Without any self interactions, the quantum pressure of localized particles is sufficient to stabilize the DM halo against gravitational collapse only for a very light DM with mass $m\sim 10^{-22}$ eV~\cite{Sahni:1999qe, Hu:2000ke, Sin:1992bg, Matos:2008ag, Lee:2008jp, Lora:2011yc}, whereas a small repulsive self-interaction can allow a much wider range of DM masses up to $m\lesssim 1$ eV~\cite{Peebles:2000yy, Goodman:2000tg, Arbey:2003sj, Eby:2015hsq, Fan:2016rda}.\footnote{BEC configurations with heavier DM and/or an attractive self-interaction are usually unstable against gravity~\cite{Khlopov:1985jw} and more likely to form local dense clumps such as Bose stars~\cite{Tkachev:1986tr, Colpi:1986ye, Tkachev:1991ka, Kolb:1993zz, Lee:1995af}, unless the thermalization rate is faster than the Hubble rate to overcome the Jeans instability.} Concrete particle physics examples for BEC-DM are WISPs (Weakly Interacting Slim Particles)~\cite{Ringwald:2012hr}, which include the QCD axion or axion-like particles~\cite{Sikivie:2009qn, Mielke:2009zza, Erken:2011dz, Saikawa:2012uk, Davidson:2013aba, Berges:2014xea, Davidson:2014hfa, Guth:2014hsa, Banik:2015sma} and hidden-sector gauge bosons~\cite{Nelson:2011sf, Arias:2012az, Pires:2012yr, Soni:2016gzf} ubiquitous in string theories, but our subsequent discussion will be generically applicable to any BEC-DM with a repulsive self-interaction, which is necessary to obtain long-range effects~\cite{Guth:2014hsa}.\footnote{Although the simplest models, where the scalar potential has an approximate symmetry to ensure the radiative stability of the ultralight scalar, usually give rise to an attractive self-interaction in the non-relativistic limit, it is possible to have realistic models with repulsive self-interaction~\cite{Fan:2016rda, Berezhiani:2015bqa}.} The observational consequences on structure formation mentioned above cannot distinguish a BEC-DM from an ordinary self-interacting DM~\cite{Spergel:1999mh}. Existing distinction methods include enhanced integrated Sachs-Wolfe effect~\cite{Sikivie:2009qn}, tidal torquing of galactic halos~\cite{Banik:2015sma, RindlerDaller:2011kx, Banik:2013rxa}, and effects on cosmic microwave background matter power spectrum~\cite{Ferrer:2004xj, Velten:2011ab}. We propose a new method to probe the BEC-DM parameter space using gravitational wave (GW) astronomy, inspired by the recent discovery of transient GW signals at LIGO~\cite{Abbott:2016blz, Abbott:2016nmj}. We show that if GWs pass through a BEC-DM halo on their way to Earth, the small spacetime distortions associated with them could produce phononic excitations in the BEC medium which in turn induce a small but potentially observable change in the speed of GWs, while the speed of light remains unchanged. This approach is very effective if any of the future multi-messenger searches for gamma-ray, optical, $X$-ray, or neutrino counterparts to the GW signal become successful. On the contrary, a lack of any observable deviation in the speed of GWs will put stringent constraints on the BEC-DM scenario. In fact, we find that even with the current LIGO sensitivity, it might be possible to partly rule out the BEC-DM parameter space otherwise preferred by existing cosmological data. Future GW detectors such as eLISA~\cite{Seoane:2013qna} with extended sensitivity to lower GW frequencies will be able to completely rule out the cosmologically preferred region. The rest of the paper is organized as follows: in Section~\ref{sec:2}, we calculate the change in the speed of GWs due to energy loss inside the BEC medium. In Section~\ref{sec:3}, we apply this result to derive constraints on the BEC-DM parameter space. In Section~\ref{sec:4}, we discuss the effect of gravitational lensing. Our conclusions are given in Section~\ref{sec:5}. | \label{sec:5} We have proposed a new method to probe BEC-DM using GW astronomy. We have shown that GWs passing through a BEC-DM halo will get appreciably slowed down due to energy loss in collective phononic excitations. The effective refractive index depends only on the mass and quartic coupling of the DM particles, apart from the frequency and amplitude of the propagating GW. Thus, an observable deviation $\delta c_g$ in the speed of GW can be used to put stringent constraints on the BEC-DM parameter space, as demonstrated in Figure~\ref{fig:1}. The physically interesting region of BEC-DM parameter space satisfying all existing constraints can be completely probed by this new method for $\delta c_g \leq 10^{-37}$ in the LIGO frequency range and $\delta c_g \leq 10^{-24}$ in the eLISA frequency range, which is soon achievable in a multi-messenger approach to GW astronomy. % | 16 | 9 | 1609.03939 |
1609 | 1609.08506_arXiv.txt | According to the compuations results obtained by Bisikalo et al.~(2013b) for the gas-dynamical effect of stellar winds on exoplanet atmospheres, three types of gaseous envelopes can form around hot Jupiters: closed, quasi-closed, and open. The type of envelope that forms depends on the position of the frontal collision point (where the dynamical pressure of the wind is equal to the pressure of the surrounding atmosphere) relative to the Roche-lobe boundaries. Closed envelopes are formed around planets whose atmospheres lie completely within their Roche lobes. If the frontal collision point is located outside the Roche lobe, the atmospheric material begins to flow out through the Lagrangian points \Lp1 and \Lp2, which can result in the formation of quasi-closed (if the dynamical pressure of the stellar wind stops the outflow through \Lp1) or open gaseous envelopes. The example of the typical hot Jupiter HD\,209458\,b is considered for four sets of atmospheric parameters, to determine the mass-loss rates for the different types of envelopes arising with these parameters. The mass-loss rates based on the modeling results were estimated to be $\dot{M} \leq 10^{9}$\,\gs\ for a closed atmosphere, $\dot{M} \simeq 3 \times 10^{9}$\,\gs\ for a quasi-closed atmosphere, and $\dot{M} \simeq 3 \times 10^{10}$\,\gs\,for an open atmosphere. The matter in the closed and quasi-closed atmospheres flows out mainly through \Lp2, and the matter in open envelopes primarily through \Lp1. | ``Hot Jupiters'' --- exoplanets with masses comparable to Jupiter's mass but with orbital semi-major axes no greater than 0.1\,AU --- have a number of unique properties due to their proximity to their parent stars. Some of these properties, such as an increase in their atmospheric temperatures due to intense heating by the stellar radiation, are obvious. However, others do not have such a clear origin, as they are associated with a more complicated series of physical processes. For example, proximity to the star may lead to the outflow of some matter from the planetary atmosphere toward the star. Moreover, a small distance to the star results in a high orbital velocity for the planet; when the planet moves faster than the local speed of sound, a bow shock forms in front of the planet, appreciably changing the character of the interaction between the gaseous atmospheric envelope and the stellar-wind gas. Observations of hot Jupiters using the Hubble Space Telescope~\citep{Vidal-Madjar-2003, Ben-Jaffel-2007} indicated that Ly$\alpha$ absorption during the transit of the exoplanet HD\,209458\,b reached 9--15\%, while the decrease in the stellar brightness due to occultation of the planetary disk was only 1.8\%. A similar effect was also observed later in the C, O, and Si lines~\citep{Vidal-Madjar-2004, Ben-Jaffel-2010, Linsky-2010}. These observations led to the conclusion that the planet was surrounded by an extensive gaseous envelope. Similar results were obtained for the planets HD\,189733\,b and WASP-12\,b. Moreover, a transit observation of WASP-12\,b using the Hubble Space Telescope in 2009 revealed that the transit ingresses and egresses in different spectral ranges did not coincide, clearly indicating the presence of dense matter ahead of the planet at a distance of four or five planetary radii~\citep{Fossati-2010}. Explaining available and planned observations of hot Jupiters requires a clear understanding of which physical phenomena predominate in the binary systems analyzed. A gas-dynamical model for investigating the interaction between the stellar wind and exoplanetary atmospheres was proposed in~\citep{Bisikalo-2013a, Bisikalo-2013b}. The results of calculations indicated that the solutions for typical hot-Jupiters moving in orbits with supersonic velocities are affected appreciably by the bow shock that is formed in front of the atmosphere. In particular, it was shown in~\citep{Bisikalo-2013b} that the type of gaseous envelope around the exoplanet depends on the position of the frontal collision point (FCP), where the dynamical wind pressure is equal to the atmospheric pressure of the exoplanet, resulting in the separation of matter flows incident on the atmosphere relative to the Roche lobe boundaries. Planets whose FCPs lie inside their Roche lobes have almost spherical envelopes characteristic of a classical atmosphere, only slightly distorted due to influence of the star and the interaction with the stellar-wind gas. When the FCP is beyond the Roche lobe of the planet, matter begins to outflow from the planetary atmosphere through the vicinities of the Lagrangian points \Lp1 and \Lp2, giving rise to a strongly asymmetric envelope. This type of object can also be divided into two types. If the dynamical pressure of the stellar-wind gas is high enough to stop the more powerful outflow through the inner Lagrangian point \Lp1, a quasi-closed stationary envelope with a complicated shape is formed in the binary system, as was first indicated in~\citep{Bisikalo-2013a}. If the wind cannot stop the flow through \Lp1, an open envelope is formed. To determine the atmospheric properties of hot Jupiters, it is necessary to accurately determine the mass-loss rates for these different types of envelopes. This will enable us not only to estimate the characteristic lifetime of the gaseous envelope of a particular exoplanet, but also to impose specific constraints upon possible observational appearances of the envelopes that form. We have perfored numerical calculations for all three types of hot-Jupiter envelopes to determine the mass-loss rates from their atmospheres ($\dot{M}$). We have also analyzed the gas-dynamical properties of the flow structure arising due to the atmospheric mass loss of hot Jupiters. Section 2 briefly describes the numerical model, Section 3 provides the results of our numerical calculations, and Section 4 summarizes the main conclusions of this work. | \label{4} We have estimated the mass-loss rates for three possible types of envelopes around hot Jupiters~\citep{Bisikalo-2013b}: closed, quasi-closed, and open. 3D gas-dynamical modeling of the interaction between a typical hot-Jupiter with the parameters of HD\,209458\,b and the stellar wind was performed, and four models corresponding to the latest estimates of the atmospheric parameters for this planet were considered~\citep{Koskinen-2013}. We chose the model parameters so as to obtain all three types of atmospheres, while remaining within the range of known estimates. The solutions obtained for Models~1 and 2 correspond to systems with closed envelopes; there is a small outflow of matter from the vicinity of \Lp2 in Model~2. The upper limit for the mass-loss rates from these atmospheres is $10^9$\,\gs. The envelope becomes quasi-closed in Model~3; however, the outflow from the neighborhood of the inner Lagrangian point \Lp1 is stopped by the stellar wind and does not propagate farther than several radii \Rpl, and matter is lost mainly through the vicinity of \Lp2 on the leeward side. The mass-loss rate in Model~3 is $3 \times 10^9$\,\gs, only slightly higher than the corresponding values for the closed envelopes. In Model~4, the atmosphere becomes open and most of the matter is lost due to outflow through \Lp1, which cannot be stopped by the stellar wind. According to our estimates, the mass-loss rate for the open atmosphere is $3\times10^{10}$\,\gs. The estimates of mass-loss rates obtained for the closed and quasi-closed enevelopes correspond well to values derived from observations of HD\,209458\,b \citep{Shematovich-2010, Murray-Clay-2009, Koskinen-2010, Garcia Munoz-2007}. Note that the solutions we have obtained enable us to conclude with confidence that large non-spherical envelopes can exist around hot Jupiters. Regardless of the fact that the sizes of these envelopes appreciably exceed the Roche lobe of the planet, the mass-loss rates can remain low enough to ensure a stationary atmosphere and a long lifetime for the planet. This possibility for hot Jupiters to have stationary, aspherical envelopes fundamentally changes widespread approaches used to analyze observational data for exoplanetary atmospheres. | 16 | 9 | 1609.08506 |
1609 | 1609.04805_arXiv.txt | The average star formation rate (SFR) in galaxies has been declining since redshift of 2. A fraction of galaxies quench and become quiescent. We constrain two key properties of the quenching process: the quenching time scale and the quenching rate among galaxies. We achieve this by analyzing the galaxy number density profile in NUV$-u$ color space and the distribution in NUV$-u$ v.s. $u-i$ color-color diagram with a simple toy-model framework. We focus on galaxies in three mass bins between $10^{10}$ and $10^{10.6} {\rm M_{\odot}}$. In the NUV$-u$ v.s. $u-i$ color-color diagram, the red $u-i$ galaxies exhibit a different slope from the slope traced by the star-forming galaxies. This angled distribution and the number density profile of galaxies in NUV$-u$ space strongly suggest that the decline of the SFR in galaxies has to accelerate before they turn quiescent. We model this color-color distribution with a two-phase exponential decline star formation history. The models with an e-folding time in the second phase (the quenching phase) of 0.5 Gyr best fit the data. We further use the NUV$-u$ number density profile to constrain the quenching rate among star-forming galaxies as a function of mass. Adopting an e-folding time of 0.5 Gyr in the second phase (or the quenching phase), we found the quenching rate to be 19\%/Gyr, 25\%/Gyr and 33\%/Gyr for the three mass bins. These {are} upper limits of quenching rate as the transition zone could also be populated by rejuvenated red-sequence galaxies. | In many large-scale surveys, the bimodal distribution of galaxy population has been found in color-magnitude and color-mass diagrams (e.g., \citealt{strateva2001,baldry2004}). In these diagrams, galaxies located between the blue and red populations were often called `green valley galaxies'. In addition to colors, many other properties of the green valley galaxies also exhibit intermediate value between the two main populations, such as spectral indices \citep{kauffmann2003} and morphological parameters \citep{driver2006,pan2013}. Therefore, the green valley galaxies were considered to represent the transition population from the blue star-forming to red-sequence galaxies \citep{bell2004,faber2007,mendez2011,goncalves2012}. However, some studies reported that dusty star-forming galaxies may also exhibit intermediate colors and potentially contaminate the transition population \citep{brammer2009,salim2009}. {In addition, by differentiating the morphology of green valley galaxies based on Galaxy Zoo project, \citet{scha2014} and \citet{smethurst2015} argued multiple evolution pathways of galaxies through the green valley zone, with early-type galaxies quenching and late-type galaxies stalling. That conclusion could be sensitive to the exact definition (choice of color and range) of the green valley, and is made under the assumption of unchanging morphology. It is also possible that some of the green valley galaxies may come from the red sequence due to rejuvenated star formation. But we expect this fraction to be small \citep{fang2012} and we expect galaxies going from green valley to the blue cloud to be even rarer, although not impossible.} Studies about the evolution of luminosity (or stellar mass) function of different galaxy types with redshift support this transition scenario. From $z$=1 to 0, the number density of red galaxies have increased significantly by a factor of 2 or more \citep{blanton2006,brown2007,faber2007} while that of blue galaxies decreased slightly or barely changed \citep{faber2007,ramos2011,moustakas2013}. This differential evolution of luminosity function with galaxy types suggests that many blue galaxies have ceased their star formation and evolved into red sequence during this time period. The rarity of green valley population implies that the transition timescale must be short \citep{faber2007,martin2007,balogh2011}. For example, post starburst galaxies were considered to be the one of the possible candidates of galaxies that are transiting from blue to red population {\citep{yange2008, wong2012}}. Their spectra show strong Balmer absorption lines but negligible \oii\ or \ha\ emission lines, suggesting a violent shutdown of star formation in the recent past with a large amount of A stars still present. However, the small fraction of post-starburst galaxies means they can only account for a small fraction of the increase in the number density profile of red galaxies. The majority of galaxies may have ceased their SF more smoothly. Before turning quiescent, the star formation rate (SFR) in galaxies have been gradually declining since redshift of 2 \citep{madau2014}. This gradual decline of SFR introduces the cosmic evolution of main-sequence relation (i.e. mass-SFR relation \citealt{daddi2007,elbaz2007,noeske2007a}). In this work, concerning the quenching process, the problems we would like to address are: (1) how fast do galaxy SFR have to decline to turn quiescent? Does it have to be much faster than the long term decline? (2) What is the quenching rate (the fraction of quenching in a given period) among galaxies? {For the evolution speed during quenching, \citet{wetzel2012,wetzel2013} examined the star formation histories of local satellite galaxies and obtained a short quenching e-folding time ($<0.8$ Gyr) using a cosmological $N$-body simulation. Based on EAGLE cosmological hydrodynamical simulation, \citet{trayford2016} found the time scale to cross the green valley to be less than 2 Gyrs.} Recently, based on the {\em GALEX} and SDSS data, \citet{scha2014} investigated the green valley galaxies in NUV$-u$ v.s. $u-i$ color-color diagram and found that early-type green valley galaxies evolve much faster than the late-type ones with a shorter e-folding time. However the analysis based on morphology-separated populations may introduce bias in the result because the galaxy morphology may change significantly along with the transition from blue to red galaxies. In this work, we revisit the UV$-$optical color-color diagrams to answer how fast the SFR has to decline when a galaxy evolves through the transition (or green valley) zone (\textsection3). In terms of the quenching rate, \citet{moustakas2013} obtained it as a function of stellar mass and redshift by comparing the stellar mass function of star-forming and passive galaxies at different redshift. {They measured the stellar mass function from $z$=0-1 based on large galaxy sample from PRism MUlti-object Survey for intermediate-$z$ and SDSS for low-$z$. However, the quenching rate determined in this way rely on how well the stellar mass function is measured which may be limited by sample variance and observation accurancy at high redshift. Also, systematical errors may be hard to avoid , although they did really careful work to addresss it, when perform comparison between the two large surveys. Using simply divided star-forming and passive populations, the information of transition population in between is neglected.} {In this work, we go beyond simple SFR/color cuts to examine the nature of full color distribution.} Throughout this paper, we adopted the cosmological parameters with $H_0=70\, {\rm km s^{-1} Mpc}^{-1}$, $\Omega_{\Lambda}=0.73$ and $\Omega_{\rm m}=0.27$. All magnitudes in this paper are given in the AB photometric system. | In this work, we investigated the evolution speed of galaxies in the quenching stage and the quenching fraction of star-forming galaxies. We select a local galaxy sample from SDSS with {redshift} in [0.02, 0.05] and target a sub-sample of them with stellar mass in [$10^{10}$, $10^{10.6}$]${\rm M_{\odot}}$. To reproduce their UV$-$optical colors we use stellar population synthesis models. For simplicity, we adopt a model SFH of two-phase exponential decline which corresponds to the secular star-forming stage and the rapid quenching stage. In the NUV$-u$ v.s. $u-i$ color-color diagram, we find a clear turn along with a dramatic number density drop which strongly support the two-phase evolution scenario. To constrain the e-folding time of quenching stage, we compare the model tracks with the transition galaxy distribution in NUV$-u$ v.s. $u-i$ color-color diagram. For the quenching stage, the e-folding time should be statistically within [0.2, 1] Gyr while an e-folding time of 0.5 Gyr best matches the observed galaxy distribution. Adopting this best-fitting e-folding time, the crossing time $T$ of the transition zone in NUV$-u$ color is about 1.5 Gyr. The galaxy number density profile in NUV$-u$ color space provide critical insights into the quenching fraction during the past period $T$. Using a simple approach and a complicated but more accurate approach we have found consistent results for the quenching fraction among star-forming galaxies. In the three mass bins, the quenching fraction are found to be 28\%/35\%/45\%. Adopting an e-folding time of 0.5 Gyr for the quenching stage which corresponds to a crossing time $T$ of 1.5 Gyr, we further derive an quenching rate of 19\%/Gyr, 25\%/Gyr, and 33\%/Gyr for star-forming galaxies in the three mass bins. {We also examine different definitions of transition zone and found our result is insensitive to slight changes of the transition zone definition.} Compared to the quenching rate derived by \citet{moustakas2013} based on stellar mass function of star-forming and passive galaxies from $z\sim1$ to 0, our results are broadly consistent within uncertainties but systematically higher. This discrepancy, to our knowledge, is possibly due to the passive galaxies with rejuvenated star formation in transition zone and potential inaccuracies in derived e-folding time at the quenching stage. Therefore our results could be upper limits of quenching rate. | 16 | 9 | 1609.04805 |
1609 | 1609.09500_arXiv.txt | The chemical tagging technique proposed by \cite{2002ARA&A..40..487F} is based on the idea that stars formed from the same molecular cloud should share the same chemical signature. Thus, using only the chemical composition of stars we should be able to re-group the ones that once belonged to the same stellar aggregate. In \cite{2015A&A...577A..47B}, we tested the technique on open cluster stars using iSpec \citep{2014A&A...569A.111B}, we demonstrated their chemical homogeneity but we found that the 14 studied elements lead to chemical signatures too similar to reliably distinguish stars from different clusters. This represents a challenge to the technique and a new question was open: Could the inclusion of other elements help to better distinguish stars from different aggregates? With an updated and improved version of iSpec, we derived abundances for 28 elements using spectra from HARPS, UVES and NARVAL archives for the open clusters M67 and IC4651, and we found that the chemical signatures of both clusters are very similar. | The chemical composition of a star provides an invaluable source of information about its history, the stellar aggregate were it was born (in some cases, still gravitationally bounded), the molecular cloud from which it was formed and, finally, the characteristics of that region and time of the Galaxy. It is accepted that most of the stars are born in groups and, if we assume that the original giant molecular cloud was homogeneous and well-mixed, then we can expect that the stars born together share a common chemical fingerprint that may be different from other stellar aggregates (born in different places and times). The chemical tagging technique \citep{2002ARA&A..40..487F} consists in identifying stars that were born together by only looking into their chemical abundances, thus, re-construct the history of our Galaxy. In \cite{2015A&A...577A..47B}, we designed and executed an experiment using open clusters (most of them with solar metallicities) to test the limits of the chemical tagging technique. We compiled a large dataset of high-resolution stellar spectra from stars in clusters, then we treat each of them as individual isolated stars, we homogeneously derived the chemical abundances for 14 elements and we tried to re-group the stars based only on their chemical information. We found that, given the level of precision that we obtained because of to the spectra quality and the limits of the methods, the differences between different open clusters for the selected elements were not significant enough to correctly disentangle their stars. In this study, we concentrated our efforts in only two clusters (M67 and IC4651) and we explore the possibility of using more elements to overcome the problems we found in \cite{2015A&A...577A..47B}. Additionally, we developed a new spectroscopic pipeline that takes advantage of the latest improvements implemented in iSpec\footnote{\href{http://www.blancocuaresma.com/s/}{http://www.blancocuaresma.com/s/}} \citep{2014A&A...569A.111B}. | We showed how a chemical signature composed of 28 different elements with a general precision better than 0.05 dex does not seem enough to chemically separate stars from the open clusters M67 and IC4651. Is this result still challenging the chemical tagging technique or these two cluster do have a common past? Both clusters are located towards the galactic anti-center at a similar distance from the Sun, although they are separated by more than $100^{\circ}$. Additionally, some studies found that M67 is several Gyr\footnote{1 Gyr represents $10^9$ years.} older than IC4651 \citep{2006MNRAS.371.1641P}. Could these clusters be born from the same molecular cloud but at different moments? This would required the cloud to be fragmented in two without triggering star formation and remaining chemically unaltered during a long time. Another possibility would be that it is common to have different molecular clouds with very similar compositions, which could mean that both were enriched in the same measure by different past events. The similarities between these two clusters should be further studied. \begin{figure}[ht!] \centering \includegraphics[width=0.8\textwidth,clip]{Images/together_all_not_strict_median_M67_No164_M67_No1194_paper} \caption{Individual differential chemical abundances with M67 No164 and M67 No1194 as reference for giants and dwarfs, respectively. The abundances correspond to individual stars from the open clusters M67 (black) and IC4651 (transparent red). All the abundances are respect to iron (i.e. [E/Fe]), except iron which is represented in respect to hydrogen (i.e. [Fe/H]).} \label{blancocuaresma:fig2} \end{figure} | 16 | 9 | 1609.09500 |
1609 | 1609.07492_arXiv.txt | The $Gaia$-ESO survey recently reported on a large sample of lithium (Li) abundance determinations for evolved stars in the rich open cluster Trumpler 20. They argue for a scenario where virtually all stars experience post main sequence mixing and Li is preserved in only two objects. We present an alternate explanation, where Li is normal in the vast majority of cluster stars and anomalously high in these two cases. We demonstrate that the Li upper limits in the red giants can be explained with a combination of main sequence depletion and standard dredge-up, and that they are close to the detected levels in other systems of similar age. In our framework, two of the detected giants are anomalously Li-rich, and we propose that both could have been produced by the engulfment of a substellar mass companion of $16^{+6}_{-10}\,\mathrm{M_J}$. This would imply that $\sim5\%$ of $1.8\,\mathrm{M_\odot}$ stars in this system, and by extension elsewhere, should have substellar mass companions of high mass that could be engulfed at some point in their lifetimes. We discuss future tests that could confirm or refute this scenario. | When stars enter their red giant branch (RGB) evolution, they go through some important changes: the energy production changes from the core to a shell surrounding it and the envelope of the stars expands. Also, the surface composition changes due to the first dredge-up (FDU), the deepening of the convective layer that brings nuclear-processed material from the stellar interior to the surface. If the element is depleted in the stellar interior, its surface abundance will be diluted during the FDU. This is the case of lithium (Li). If stars enter the RGB with a solar system meteoritic abundance of $\mathrm{A(Li)}$\footnote{$\mathrm{A(Li)}=log(N_{Li}/N_{H})+12.00$, where $N_x$ is the number of atoms of element ``$x$"}$=3.3$, the Li abundance post-FDU should be $\mathrm{A(Li)}<1.5$. After FDU, no further abundance changes are expected according to standard models. However, it is well documented observationally that there is an extra-mixing process that changes the surface abundance of giants triggered after the RGB bump \citep[e.g.,][]{gratton00, lind09}. Also, although they are uncommon, Li-rich giants do exist \citep[e.g.,][]{wallersteinsneden82,brown89}. Some explanations have been proposed for these atypical Li-rich giants. One of these is internal production through the Cameron-Fowler chain \citep{cameronfowler71}, which additionally requires extra-mixing mechanisms to transport the freshly produced Li into cooler regions of the star, preventing it from burning by proton capture. Other possibilities are external to the star. These include the accretion by the star of a planet or brown dwarf \citep{alexander67}, which have not burned Li during their lifetimes, or mass transfer from an evolved AGB star, where Li can be produced by hot bottom burning under convective conditions and thus get transported to the outer layers \citep{sackmannboothroyd92}. A key piece of information for distinguishing among mechanisms of Li enhancement is the evolutionary phase of the enriched giants. Recent observations indicate that Li-rich giants are found all along the RGB \citep[e.g.,][]{lebzelter12}, as well as the clump \citep{kumar11,SA14, monaco14, reddylambert16}, so there seems that Li-rich giants are not restricted to a particular evolutionary phase. Unfortunately, the exact mass and evolutionary stage of giants can be tricky to obtain when they are located in the field and have no parallax or asteroseismic data, as it is the case for most of the known Li-rich giants. This difficulty can be partially overcome in clusters, where the giants have similar masses, and, since the cluster members share the same original composition, distance, and age, differences in giants' surface abundances are tied to internal processes acting inside stars. Open clusters have an additional advantage over globular clusters, as they do not present evidence of multiple populations so far. In a recent work, \citet{smiljanic16} (S16 hereafter) studied the Li abundance of giants in the open cluster Trumpler 20, in the context of the $Gaia$-ESO Survey \citep{randichgilmore13}. S16 find two giants with a high Li abundance when compared to the rest of the cluster. Thus, this sample offers a great opportunity to study extra-mixing and the Li-enrichment phenomenon. This letter is organized as follows. In Section 2 we re-analyze the Trumpler 20 data published by S16, and critically discuss their interpretation and its implications. We offer an alternative explanation based on our earlier work on planet/brown dwarf engulfment \citep{AG16} in Section 3, concluding in Section 4. | Trumpler 20 presents a great opportunity to study the problem of Li-rich giants in a sample of stars with the same age and very similar post turn-off masses. S16 have published atmospheric parameters and Li abundances for 40 giants, finding that 2 of them are Li-rich. Our interpretation of the same evidence is that most of the giants are consistent with MS depletion and standard dilution produced by FDU. We conclude that both Li-rich giants are unusual in nature and have been enriched in Li, possibly by the engulfment of substellar mass companions of $16^{+6}_{-10}\,\mathrm{M_J}$. We cannot exclude the presence of mixing on the RGB, as most of the stars in the cluster only have Li upper limits, but this extra-mixing is not needed to explain the Li abundance pattern of the cluster. Other authors have found samples where the Li-rich giants are thought to be produced by planet engulfment. \citet{casey16} present an interesting sample to study, although we are not certain that all of those giants are first ascent RGB and we think that the lack of close-in planets around subgiants is not a strong enough argument to point to planet engulfment, as it would predict a much larger amount of Li-rich giants before the bump. The fraction of Li-rich giants in Trumpler 20, corresponding to $5\%$ is rather high compared to what is usually found (from $1\%$ to $2\%$). This fraction may indicate how many dwarfs of $1.8\,\mathrm{M_\odot}$ should have close-in substellar mass companions of high mass during the MS. Further abundance measurements of these and other stars in this cluster, most preferably subgiants and turn-off stars, would allow a better study of the phenomenon producing the Li enrichment. | 16 | 9 | 1609.07492 |
1609 | 1609.07989_arXiv.txt | We study the dependence of the coronal activity index on the star's rotation rate. This question was considered earlier for 824 late-type stars on the basis of a consolidated catalogue of the soft X-ray fluxes. We carry out a more refined analysis separately for G, K and M dwarfs. They distinctively exhibit two modes of activity. The first one is the saturation mode, it is characteristic of young stars and is practically not related to their rotation. The second one refers to the solar-type activity the level of which strongly depends on the rotation period. We show that the transition from one mode to another takes place at the rotation periods of 1.1, 3.3 and 7.2 days for the stars of spectral types G2, K4 and M3 respectively. In the light of the discovery of superflares on G and K stars on the {\itshape Kepler} spacecraft there arises a question of how these objects differ from other active late-type stars. We analyse the location of superflare stars relative to the stars observed by {\itshape Kepler} on the ``amplitude of rotational brightness modulation (ARM) -- rotation period'' diagram. The value of ARM reflects the relative spots area on a star and characterises the activity level in the whole atmosphere. It is shown that G and K superflare stars are basically fast rotating young objects, but some of them belong to the stars with the solar type of activity. | Introduction} The modern solar-stellar physics is characterised by obtaining observational data not on single objects, but on large numbers of stars. First of all this refers to the study of the phenomena in stellar photospheres by spacecrafts such as {\itshape CoRoT}, {\itshape Kepler} etc., which provide us with the information on tens and hundreds thousand objects. Some effects, such as bimodality of the rotation velocities distribution of stars, are now confidently revealed. This effect is distinctly manifested in M dwarfs which can be subdivided to the stars with the activity saturation and more quiet stars with the activity level close to that of the Sun (McQuillan et~al.~2014). Obviously, the main factor determining the level of activity is the rotation velocity. This applies to the activity in the chromosphere and the corona. Active processes develop approximately in the same way on all the low-mass stars possessing subsurface convective zones. However the dependence of the level and character of the activity on the spectral type is pronounced somewhat weakly in F, G, K and M dwarfs so that only recently has it become possible to detect this dependence. Here we consider this question in regard to the X-ray emission of stars. Massive exploration of the stellar coronal activity has become possible due to the creation of the catalogue of active F-M stars constructed on the basis of X-ray observations onboard the {\itshape Einstein}, {\itshape ROSAT}, {\itshape XMM-Newton} spacecrafts by Wright et~al.~(2011). They derived the dependence of the coronal activity index $R_\mathrm{X} = \lg L_\mathrm{X}/L_\mathrm{bol}$ on the rotation velocity and reliably showed that there exist two groups of stars. First, a large group with the activity saturation where $R_\mathrm{X}$ is close to $10^{-3}$ and practically does not depend on the rotation period. This group includes fast rotating stars. Second, a group of less active stars which demonstrate clear dependence of $R_\mathrm{X}$ on the rotation period. We will call the activity of these stars ``solar-type activity''. This is the magnetic activity which is characterised by the formation of spots, active regions and flares. We assume that regular cycles form within this type of activity. In more detail the evolution of the activity is considered by Katsova \& Livshits (2011) and Katsova et~al.~(2015). The stars in the second group obey Skumanich law $v \sim \sqrt{t}$, where $v$ is the rotation velocity, $t$ is the age of the star. Thus, the decrease of $R_\mathrm{X}$ with period (i. e. increase of $R_\mathrm{X}$ with the rotation velocity) can be related to the increase of the age, the fact that underlies gyrochronology --- the estimation of the age on the basis of the activity level (Mamajek \& Hillenbrand 2008). Based on the dependence of the chromospheric and coronal activity indices on the rotation period, this method has been developed for stars of different ages in the lower part of the main sequence without a separate analysis of the influence of the difference in spectral types. First evidence of the difference of the surface activity level among dwarfs of different spectral types are found by Messina et~al.~(2003) who analyse the rotational modulation of the stellar optical radiation related to the spots and consider the radiation of the coronae. The subsequent comparison of the chromospheric and coronal activity of late-type stars showed that the method of gyrochronology cannot be based on a single parameter --- such as the rotation period --- but instead should take into account the difference in spectral types (Katsova \& Livshits 2011). Recently there appeared a new approach to the analysis of X-ray data on stellar coronae. The catalogue by Wright et~al.~(2011) with minor refinements was used by Reiners et~al.~(2014). They looked for the dependence of $L_\mathrm{X} / L_\mathrm{bol}$ on the combination of the rotation period and radius of the form $R^\alpha P^\beta$ and found that for the stars with solar-type activity the data are best described by the model with $\alpha=-4$, $\beta=-2$. Taking approximately $T_\mathrm{eff} \sim R^{1/2}$ for G-M dwarfs the bolometric luminosity scales with the radius approximately as $L_\mathrm{bol} \sim R^4$. Thus, the aforementioned dependency reduces to the law $L_\mathrm{X} \sim P^{-2}$, earlier obtained by Pizzolato et~al.~(2003). The results of Reiners et~al.~(2014) has become an argument in favour of that the axial rotation rate of a star is indeed the main factor determining the activity level of different layers of the atmosphere. However in the aforementioned papers (Wright et~al.~2011; Reiners et~al.~2014) late-type stars were considered together, without subdivision in to spectral types. The main goal of our work is to extract the information on the dependence of the activity on the spectral type from the same data. We carry out an investigation analogous to that of Reiners et~al.~(2014), but separately for G, K and M stars. Further we discuss the effect of bimodality of the rotation periods distribution and its relation to the features of the stars where superflares were detected (the properties of these stars are studied by Shibayama et~al.~2013; Notsu et~al.~2015). In conclusion, we discuss our results from the point of view of changes in physical conditions in the corona which accompany the transition from a fast rotating star to slower rotating ones. | So far the consideration of the dependence of the coronal activity index on the rotation period was performed on the basis of the catalogue created by Wright et~al.~(2011). Reiners et~al.~(2014) proposed a more adequate method for describing the obtained relation; this method allowed to analyse the behaviour of $\lg L_\mathrm{X} / L_\mathrm{bol}$ in more detail. However this analysis incorporated the dataset of low-mass late-type stars as a whole. In order to obtain new information we have developed the ideas of Reiners et~al.~(2014). This allowed us to investigate the aforementioned relation separately for three spectral types using the same data. The method we used allowed us to find the rotation period at which the activity mode changes from the saturation to the solar type. For the G2, K4 and M3 stars these periods appeared to be 1.1, 3.3 and 7.2 days respectively. This means that the coronae of red dwarfs longer (up to the periods of about 10 days) exist in the saturation mode. Warmer stars exit the saturation mode earlier. In other words the coronae of red dwarfs at the period of 10 days still remain dense and hot which can be related to the predominant role of local magnetic fields on M stars. This can serve as an argument in favour of a known mechanism of the heating of the red dwarfs coronae due to numerous microflares. The investigation presented here points that in the rotation period range from several to approximately 20 days there exist stars with both modes of activity. This is beyond the frame of the one-parametric gyrochronology and points at the existence of additional factors which affect the activity level. First of all the difference between the activity levels in the chromosphere derived from $\mathrm{H}_\alpha$ line analysis and in the corona are apparently caused by different spottedness. On the Sun such difference appears when one or several large spots emerge in the active region. In open clusters with more or less confident age estimation stars which have already braked and a number of still fast rotating stars are present. These two populations are studied in detail by Barnes~(2003) (see Fig.~2 therein) who revealed their features. The most of the stars in the cluster demonstrate monotonic growth of the rotation period from F to M stars and subsequently settle at a constant period corresponding to the gyroage of the cluster. The rotation periods of the second (slowly rotating) cluster population with the age of tens of million years gradually decrease from G to M stars. The fraction of such fast rotating stars abruptly falls down in clusters older than 200 Myr. The difference between the rotation periods corresponding to the transition from one activity mode to another among stars of different spectral types can be related to the difference in mass and consequently the internal structure of these stars. First of all this applies to the convective zone. The depth of the convective zone increases from F to M dwarfs, and this changes the operation of the dynamo mechanism. One can suppose that the disclosed dependence of the point of change of the activity mode on the spectral type is associated with the gradual change of the role of large and small scale magnetic fields in the formation of the activity. Let us make a remark on one of the results concerning the stars with fundamental parameters close to those of the Sun. We have shown that G stars change the activity mode at the rotation period slightly longer than 1 day. In fact the activity of such a G star substantially exceeds all the acceptable values for the modern Sun at the highest maximum of the cycle. We use the conventional name ``young Sun'' as applied to a G dwarf with the rotation period of about 10 days (or with the age of 1 Gyr) which can already possess the activity of solar type with an established regular cycle. There pass of order 500 Myr from the saturated mode of activity until the solar-type activity sets. It is these stars with the rotation periods from 1 to 10 days where non-stationary processes with the energy and character unconceivable on the modern Sun can take place. We have analysed the location of the superflare stars on the ARM -- rotation period diagram relative to a large sample of stars observed by {\itshape Kepler} and have concluded that G and K superflare stars are mainly fast rotating young objects, but some of them belong to the stars with the solar type of activity. It is worth noting that the data we have used in Section~\ref{main} are a compilation of many researches (see Wright et~al.~2011). Unfortunately, we have little data, especially for M dwarfs with the solar-type activity. Obviously the emergence of vast homogenious data on the X-ray luminosity of low-mass stars will allow to come to more definitive conclusions on the problem under discussion. | 16 | 9 | 1609.07989 |
1609 | 1609.08260_arXiv.txt | Parker's magnetostatic theorem extended to astrophysical magnetofluids with large magnetic Reynolds number supports ceaseless regeneration of current sheets and hence, spontaneous magnetic reconnections recurring in time. Consequently, a scenario is possible where the repeated reconnections provide an autonomous mechanism governing emergence of coherent structures in astrophysical magnetofluids. In this work, such a scenario is explored by performing numerical computations commensurate with the magnetostatic theorem. In particular, the computations explore the evolution of a flux-rope governed by repeated reconnections in a magnetic geometry resembling bipolar loops of solar corona. The revealed morphology of the evolution process – including onset and ascent of the rope, reconnection locations and the associated topology of the magnetic field lines – agrees with observations, and thus substantiates physical realisability of the advocated mechanism. | The astrophysical plasmas in general, and the solar corona in particular, are described by the non-diffusive limit of magnetohydrodynamics (MHD). The reason for such description is the large length scales and high temperatures, inherent to such plasmas which make the Lundquist number ($S=v_aL/\eta$, in usual notations) extremely high. For example, the Lundquist number for the solar corona, having a typical length scale $L\approx 10^7$m and magnetic diffusivity $\eta\approx 1\rm{m}^2s^{-1}$ {\citep{aschwanden}}, is in the orders of $10^{13}$. In such high-$S$ plasmas, the Alfv\'{e}n's theorem of flux-freezing {\citep{frozen}} is satisfied, thus predicting magnetic field lines (MFLs) to remain tied with fluid parcels during an evolution. With MFLs under coevolution with fluid parcels, a magnetic flux surface (MFS)---made by the loci of MFLs---once identified with a fluid surface, will maintain the identity throughout the evolution. As demonstrated by recent numerical simulations {\citep{sanjay-pap, complexity-pap}}, such coevolution spontaneously develop current sheets (CSs); i.e., two dimensional surfaces of intense volume current density across which the MFLs flip sign. These simulations attribute the appearance of CSs to favorable contortions of MFSs, generic to the high-$S$ magnetofluids dynamics. Noteworthy in the simulations is the development of a quasi steady state, approximately concurrent with the growing CSs. This is expected as the favorable contortions bring anti-parallel field lines in proximity and thereby increase local magnetic pressure which in turn, opposes further contortions. In the ideal scenario of $\eta=0$, the quasi steady state corresponds to a steady state where magnetic field is discontinuous across a CS. The above findings are in conformity with Parker's magnetostatic theorem {\citep{parker-72, parker-88, parker-book, parker-ppcf}}. The theorem states that the development of CSs is ubiquitous in an equilibrium magnetofluid with infinite electrical conductivity and complex magnetic topology. The development is due to a general failure of spatially continuous magnetic field in achieving local equilibrium while preserving its topology. Generalization of the theorem to a magnetofluid undergoing topology-preserving evolution then naturally favors inevitable onset of CSs when the fluid relaxes toward a steady state. Here, the inevitability is due to unbalanced forces, which under flux-freezing have a constrained evolution that develop sharp gradients in the magnetic field {\citep{parker-book}}. In presence of an otherwise negligible magnetic diffusivity, the CSs provide sites where the Lundquist number is locally reduced. The flux-freezing is destroyed and the locally diffusive magnetofluid undergoes magnetic reconnections (MRs) where magnetic energy is converted into energy of mass flow and heat. With reconnection, the CSs are dissipated, and MFLs being tied to fluid parcels are expunged from the reconnection sites along with the mass flow. These expunged field lines push onto other MFLs and, under favorable conditions, may lead to further reconnections. Importantly, a single reconnection can initiate consecutive secondary MRs, intermittent in space and time, which may shape up the dynamics of high-$S$ magnetofluids. In a recent computational study \citep{dinesh-2015} a scenario was explored, where repeated reconnections were identified as a cause for generating various magnetic structures, some duplicating magnetic antics of the Sun. Toward realizing the above scenario in solar corona, we note that hard X-ray coronal sources are standardly accepted as signatures of magnetic reconnection in solar flares \citep{krucker2008}. High resolution measurements show multiple peaks of non-thermal nature in flare's time profile, which suggest the corresponding energy releases and hence, the underlying reconnections, to be episodic \citep{bhuwan2013}. Recent observations at multiple channels (hard X-ray and extreme ultraviolet) reveal intense localized brightening to occur below an ascending flux-rope \citep{kushwaha2015}. The spatio-temporal correlation between intermittent energy release and ascent of an overlying flux-rope imply a causal connection between magnetic reconnections and the ascent \citep{cho2009, cheng2011}. In the above perspective, this paper numerically demonstrates the evolution of a flux-rope in terms of its creation from initial bipolar field lines and continuous ascent, mediated via the common process of repeated spontaneous reconnections. The corresponding manifestations of magnetic topology---in likes of MRs occurring at a height, reconnections being localized below the rope and development of dips at the bottom part of the rope---are in general harmony with observations. This contrasts with the contemporary simulations of flux-ropes that judiciously precondition rope evolution---either by specifying preexisting twisted magnetic structures that emerge from below the photosphere {\citep{fan2001,fan&gibson2003,fan2010,fan2011,chatterjee2013,fan2016}}, or by forcing magnetic reconnections inside a sheared arcade with select (shearing and/or converging) initial flows {\citep{van&martens,choe1996,amari1999,amari2003,aulanier2010,xia2014}}. While the present work also explores MRs inside sheared arcades, the computations being in agreement with the magnetostatic theorem generate spontaneous reconnections which provide an autonomous mechanism to govern dynamics of any high-$S$ magnetofluid. The novelty of this work is in its approach to establish creation and activation of a physically realizable flux-rope as a consequence of the autonomous mechanism. Introspectively, such a rope has the flavor of a self-organized state \citep{kusano1994}. To make numerical simulations agree with the theory of CS formation, the requirement is the satisfaction of flux-freezing to high fidelity between two successive MRs, while enabling local diffusion of MFLs co-located and concurrent with the developing CSs. These two requirements are achieved through the following numerical scheme. Viscous relaxation \citep{low-bhattacharyya,sanjay-pap,dinesh-2015,complexity-pap} of a thermally homogeneous, incompressible magnetofluid with infinite electrical conductivity is employed to evolve the fluid under the flux-freezing till CSs develop. To focus on the idea, the relevant Navier-Stokes MHD equations are \begin{eqnarray} \label{stokes} & & \frac{\partial{\bf{v}}}{\partial t} + \left({\bf{v}}\cdot\nabla \right) {\bf{ v}} =-\nabla p +\left(\nabla\times{\bf{B}}\right) \times{\bf{B}}+\frac{\tau_a}{\tau_\nu}\nabla^2{\bf{v}} ~~~,\\ \label{incompress1} & & \nabla\cdot{\bf{v}}=0 ~~~, \\ \label{induction} & & \frac{\partial{\bf{B}}}{\partial t}=\nabla\times({\bf{v}}\times{\bf{B}}) ~~~, \\ \label{solenoid} & &\nabla\cdot{\bf{B}}=0 ~~~, \end{eqnarray} in usual notations. The equations (\ref{stokes})-(\ref{solenoid}) are written in dimensionless form, with all variables normalized according to \begin{eqnarray} \label{norm} & &{\bf{B}}\longrightarrow \frac{{\bf{B}}}{B_0} ~~~,\\ & &{\bf{v}}\longrightarrow \frac{\bf{v}}{v_a}~~~,\\ & & L \longrightarrow \frac{L}{L_0}~~~,\\ & & t \longrightarrow \frac{t}{\tau_a} ~~~,\\ & & p \longrightarrow \frac{p}{\rho {v_a}^2}~~~. \end{eqnarray} Here, the constants $B_0$ and $L_0$ are generally arbitrary, but can be fixed by the magnetic field strength and size of the system. Furthermore, $v_a \equiv B_0/\sqrt{4\pi\rho_0}$ is the Alfv\'{e}n speed and $\rho_0$ is the constant mass density. The constants $\tau_a$ and $\tau_\nu$ have dimensions of time, and represent Alfv\'{e}n transit time ($\tau_a=L_0/v_a$) and viscous diffusion time scale ($\tau_\nu= L_0^2/\nu$) respectively, with $\nu$ being the kinematic viscosity. The pressure $p$ satisfies the elliptic partial differential equation \begin{equation} \label{pressure} \nabla^2\left(p+\frac{v^2}{2}\right)=\nabla\cdot\Big[(\nabla\times{\bf{B}})\times{\bf{B}}-(\nabla\times{\bf{v}})\times{\bf{v}}\Big] \end{equation} \noindent generated by imposing the incompressibility (\ref{incompress1}) on the momentum transport equation (\ref{stokes}); see \citep{low-bhattacharyya} for discussion. If released from an initial non-equilibrium state, the above fluid evolves by converting magnetic energy into the energy of mass flow while the latter gets dissipated by viscosity. The terminal state is then expected to be static where the pressure gradient is balanced by the Lorentz force as MFLs cannot get diffused because of the flux-freezing. In simulations however, only a quasi-steady state is achieved, maintained by a partial balance of Lorentz force, pressure gradient and viscous drag; details of the energetics can be found in \citep{low-bhattacharyya, sanjay-pap, dinesh-2015, complexity-pap}. The CSs develop as the fluid relaxes to the terminal state. As thickness of the developing CSs falls below the selected grid resolution, scales become under-resolved and numerical artifacts such as spurious oscillations are generated through employed numerical techniques. These under-resolved scales can be removed by utilizing an apt numerical diffusivity of non-oscillatory finite volume differencing. In literature, such calculations relying on the non-oscillatory numerical diffusivity are referred as Implicit Large Eddy Simulations (ILESs) \citep{grinstein-2007}. The computations performed in this work are in the spirit of ILESs where simulated MRs, being intermittent in space and time, mimic physical reconnections in high-$S$ fluids. The rest of the paper is organized as follows. In section II we construct the initial magnetic field and discuss the numerical model. Section III is dedicated to results and discussions. In section IV, we summarize results and highlight important findings. | The presented simulations start from a select motionless state with magnetic field congruent to a gauge-invariant form of linear force-free field having translational symmetry. These simulations identify repeated magnetic reconnections as an autonomous mechanism for creating a flux-rope from initially bipolar field lines and, subsequently, for triggering and maintaining its ascent via reconnections that occur below the rope. The computations being commensurate with the requirements of magnetostatic theorem, the reconnections are spontaneous and inherent to the evolving fluid. The computational commensuration with the Parker's theorem is achieved by viscous relaxation of an incompressible, thermally homogeneous high-$S$ magnetofluid maintaining the condition of flux-freezing. During the relaxation, sharpening of magnetic field gradient is unbounded, ultimately leading to MRs at locations where separation of non-parallel field lines approaches grid resolution. The MR process per se is underresolved, but effectively regularized by locally adaptive dissipation of MPDATA, in the spirit of ILES subgrid-scale turbulence models. In effect, the post-reconnection condition of flux-freezing is restored, and field lines tied to the reconnection outflow push other sets of MFLs, leading to secondary MRs. The whole process is replicated in time to realize repetitive reconnections. The simulated relaxation process comprises three distinct phases. In the first phase, a combination of incompressibility and the initial Lorentz force deforms initial field lines such that the field gradient sharpens in a direction implied by the initial condition (herein $x$). Further push eventuates in reconnection and development of a $X$-type neutral point along with a detached flux-rope. Repeated reconnections around the $X$-type null generate more detached field lines which contribute to the rope. Moreover, being frozen to the outflow, the rope ascends vertically. Because the reconnections are localized below the evolving rope, the scenario is in general agreement with observations. As the magnetofluid relaxes to a quasi-steady state, the process enters the second phase of the relaxation with the $X$-type null being squashed to generate two $Y$-type nulls along with an extended CS beneath the rope. In the third phase the extended CS decay, resulting in an increase in the kinetic energy of mass flow. Because of the corresponding decrease in magnetic intensity near the decaying CS, MFLs from all side of the CS are stretched into the field depleted region. The rope becomes dipped at the bottom and a new $X$-type null is generated which ascends with the rope. Continued further in time, the flux-rope reconnects internally and loses its structure. Fully three dimensional simulations are also performed to verify the robustness of repeated spontaneous MRs in creation and ascent of a rope accordant to a more realistic evolution. Importantly, the three dimensional simulations document the intensity of CSs developed over respective PILs to be non-uniform---a feature expected in realistic ropes developed via reconnections. Altogether the computations extend Parker's magnetostatic theorem to the scenario of evolving magnetic fields which can undergo magnetic reconnection. Notably, the theorem in absence of magnetic diffusivity leads to CSs, having true mathematical singularities in magnetic field which are end states of any evolution. But in presence of small but non-zero magnetic diffusivity, as in astrophysical plasmas, the theorem opens up the possibility of spontaneous generation of secondary CSs and subsequent MRs that may contribute to the dynamics of the plasma. The computations confirm the contribution to be meaningful as it can generate observed magnetic structures and govern their dynamics which, in this case, is the evolution of a flux-rope in terms of its generation and ascent in a magnetic topology relevant to the solar corona. Additionally, in context of the standard flare model, the simulations imply a direct involvement of magnetic reconnection in the activation of flux-ropes. | 16 | 9 | 1609.08260 |
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