arXiv subjects

Dennis Zaritsky

Publications and source records attributed to Dennis Zaritsky.

At least 181 records · Page 10Linked to original sources

arXiv2014

IRAC Near-Infrared Features in the Outer Parts of S4G Galaxies

We present a catalogue and images of visually detected features, such as asymmetries, extensions, warps, shells, tidal tails, polar rings, and obvious signs of mergers or interactions, in the faint outer regions (at and outside of R_25) of nearby galaxies. This catalogue can be used in future quantitative studies that examine galaxy evolution due to internal and external factors. We are able to reliably detect outer region features down to a brightness level of 0.03 MJy/sr per pixel at 3.6 microns in the Spitzer Survey of Stellar Structure in Galaxies (S4G). We also tabulate companion galaxies. We find asymmetries in the outer isophotes in 22+/-1 per cent of the sample. The asymmetry fraction does not correlate with galaxy classification as an interacting galaxy or merger remnant, or with the presence of companions. We also compare the detected features to similar features in galaxies taken from cosmological zoom re-simulations. The simulated images have a higher fraction (33 per cent) of outer disc asymmetries, which may be due to selection effects and an uncertain star formation threshold in the models. The asymmetries may have either an internal (e.g., lopsidedness due to dark halo asymmetry) or external origin.

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arXiv2014

Ionized gas disks in elliptical and S0 galaxies at $z<1$

We analyse the extended, ionized-gas emission of 24 early-type galaxies (ETGs) at $0<z<1$ from the ESO Distant Cluster Survey (EDisCS). We discuss different possible sources of ionization and favour star-formation as the main cause of the observed emission. 10 galaxies have disturbed gas kinematics, while 14 have rotating gas disks. In addition, 15 galaxies are in the field, while 9 are in the infall regions of clusters. This implies that, if the gas has an internal origin, this is likely stripped as the galaxies get closer to the cluster centre. If the gas instead comes from an external source, then our results suggest that this is more likely acquired outside the cluster environment, where galaxy-galaxy interactions more commonly take place. We analyse the Tully-Fisher relation of the ETGs with gas disks, and compare them to EDisCS spirals. Taking a matched range of redshifts, $M_{B}<-20$, and excluding galaxies with large velocity uncertainties, we find that, at fixed rotational velocity, ETGs are 1.7 mag fainter in $M_{B}$ than spirals. At fixed stellar mass, we also find that ETGs have systematically lower specific star-formation rates than spirals. This study constitutes an important step forward towards the understanding of the evolution of the complex ISM in ETGs by significantly extending the look-back-time baseline explored so far.

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arXiv2014

Spitzer UltRa Faint SUrvey Program (SURFS UP) I: An Overview

SURFSUP is a joint Spitzer and HST Exploration Science program using 10 galaxy clusters as cosmic telescopes to study z >~ 7 galaxies at intrinsically lower luminosities, enabled by gravitational lensing, than blank field surveys of the same exposure time. Our main goal is to measure stellar masses and ages of these galaxies, which are the most likely sources of the ionizing photons that drive reionization. Accurate knowledge of the star formation density and star formation history at this epoch is necessary to determine whether these galaxies indeed reionized the universe. Determination of the stellar masses and ages requires measuring rest frame optical light, which only Spitzer can probe for sources at z >~ 7, for a large enough sample of typical galaxies. Our program consists of 550 hours of Spitzer/IRAC imaging covering 10 galaxy clusters with very well-known mass distributions, making them extremely precise cosmic telescopes. We combine our data with archival observations to obtain mosaics with ~30 hours exposure time in both 3.6$μ$m and 4.5$μ$m in the central 4 arcmin x 4 arcmin field and ~15 hours in the flanking fields. This results in 3-$σ$ sensitivity limits of ~26.6 and ~26.2AB magnitudes for the central field in the IRAC 3.6 and 4.5$μ$m bands, respectively. To illustrate the survey strategy and characteristics we introduce the sample, present the details of the data reduction and demonstrate that these data are sufficient for in-depth studies of z >~ 7 sources (using a z=9.5 galaxy behind MACSJ1149.5+2223 as an example). For the first cluster of the survey (the Bullet Cluster) we have released all high-level data mosaics and IRAC empirical PSF models. In the future we plan to release these data products for the entire survey.

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arXiv2014

The Baryonic Tully-Fisher Relationship for S$^4$G Galaxies and the "Condensed" Baryon Fraction of Galaxies

We combine data from the Spitzer Survey for Stellar Structure in Galaxies (S$^4$G), a recently calibrated empirical stellar mass estimator from Eskew et al., and an extensive database of HI spectral line profiles to examine the baryonic Tully-Fisher (BTF) relation. We find 1) that the BTF has lower scatter than the classic Tully-Fisher (TF) relation and is better described as a linear relationship, confirming similar previous results, 2) that the inclusion of a radial scale in the BTF decreases the scatter but only modestly, as seen previously for the TF relation, and 3) that the slope of the BTF, which we find to be $3.5\pm 0.2$ ($Δ$ log $M_{baryon}/Δ$ log $v_c$), implies that on average a nearly constant fraction ($\sim 0.4$) of all baryons expected to be in a halo are "condensed" onto the central region of rotationally supported galaxies. The condensed baryon fraction, $M_{baryon}/M_{total}$, is, to our measurement precision, nearly independent of galaxy circular velocity (our sample spans circular velocities, $v_c$, between 60 and 250 km s$^{-1}$, but is extended to $v_c\sim 10$ km s$^{-1}$ using data from the literature). The observed galaxy-to-galaxy scatter in this fraction is generally $\le$ a factor of 2 despite fairly liberal selection criteria. These results imply that cooling and heating processes, such as cold vs. hot accretion, mass loss due to stellar winds, and AGN driven feedback, to the degree that they affect the global galactic properties involved in the BTF, are independent of halo mass for galaxies with $10 < v_c < 250$ km/s and typically introduce no more than a factor of two range in the resulting $M_{baryon}/M_{total}$. Recent simulations by Aumer et al. of a small sample of disk galaxies are in excellent agreement with our data, suggesting that current simulations are capable of reproducing the global properties of individual disk galaxies.

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arXiv2014

Reconstructing the stellar mass distributions of galaxies using S4G IRAC 3.6 and 4.5 micron images: II. The conversion from light to mass

We present a new approach for estimating the 3.6 micron stellar mass-to-light ratio in terms of the [3.6]-[4.5] colors of old stellar populations. Our approach avoids several of the largest sources of uncertainty in existing techniques. By focusing on mid-IR wavelengths, we gain a virtually dust extinction-free tracer of the old stars, avoiding the need to adopt a dust model to correctly interpret optical or optical/NIR colors normally leveraged to assign M/L. By calibrating a new relation between NIR and mid-IR colors of GLIMPSE giant stars we also avoid discrepancies in model predictions for the [3.6]-[4.5] colors of old stellar populations due to uncertainties in molecular line opacities. We find that the [3.6]-[4.5] color, which is driven primarily by metallicity, provides a tight constraint on M/L_3.6, which varies intrinsically less than at optical wavelengths. The uncertainty on M/L_3.6 of ~0.07 dex due to unconstrained age variations marks a significant improvement on existing techniques for estimating the stellar M/L with shorter wavelength data. A single M/L_3.6=0.6 (assuming a Chabrier IMF), independent of [3.6]-[4.5] color, is also feasible as it can be applied simultaneously to old, metal-rich and young, metal-poor populations, and still with comparable (or better) accuracy (~0.1 dex) as alternatives. We expect our M/L_3.6 to be optimal for mapping the stellar mass distributions in S4G galaxies, for which we have developed an Independent Component Analysis technique to first isolate the old stellar light at 3.6 micron from non-stellar emission (e.g. hot dust and the 3.3 PAH feature). Our estimate can also be used to determine the fractional contribution of non-stellar emission to global (rest-frame) 3.6 micron fluxes, e.g. in WISE imaging, and establishes a reliable basis for exploring variations in the stellar IMF.

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arXiv2013

Unveiling the Structure of Barred Galaxies at 3.6 $μ{\rm m}$ with the Spitzer Survey of Stellar Structure in Galaxies (S$^4$G): I. Disk Breaks

We have performed two-dimensional multicomponent decomposition of 144 local barred spiral galaxies using 3.6 $μ{\rm m}$ images from the Spitzer Survey of Stellar Structure in Galaxies. Our model fit includes up to four components (bulge, disk, bar, and a point source) and, most importantly, takes into account disk breaks. We find that ignoring the disk break and using a single disk scale length in the model fit for Type II (down-bending) disk galaxies can lead to differences of 40% in the disk scale length, 10% in bulge-to-total luminosity ratio (B/T), and 25% in bar-to-total luminosity ratios. We find that for galaxies with B/T $\geq$ 0.1, the break radius to bar radius, $r_{\rm br}/R_{\rm bar}$, varies between 1 and 3, but as a function of B/T the ratio remains roughly constant. This suggests that in bulge-dominated galaxies the disk break is likely related to the outer Lindblad Resonance (OLR) of the bar, and thus moves outwards as the bar grows. For galaxies with small bulges, B/T $<$ 0.1, $r_{\rm br}/R_{\rm bar}$ spans a wide range from 1 to 6. This suggests that the mechanism that produces the break in these galaxies may be different from that in galaxies with more massive bulges. Consistent with previous studies, we conclude that disk breaks in galaxies with small bulges may originate from bar resonances that may be also coupled with the spiral arms, or be related to star formation thresholds.

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arXiv2013

An Empirical Connection between the UV Color of Early Type Galaxies and the Stellar Initial Mass Function

Using new UV magnitudes for a sample of early-type galaxies, ETGs, with published stellar mass-to-light ratios, Upsilon_*, we find a correlation between UV color and Upsilon_* that is tighter than those previously identified between Upsilon_* and either the central stellar velocity dispersion, metallicity, or alpha enhancement. The sense of the correlation is that galaxies with larger Upsilon_* are bluer in the UV. We conjecture that differences in the lower mass end of the stellar initial mass function, IMF, are related to the nature of the extreme horizontal branch populations that are generally responsible for the UV flux in ETGs. If so, then UV color can be used to identify ETGs with particular IMF properties and to estimate Upsilon_*.

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arXiv2013

Novel Probes of Gravity and Dark Energy

The discovery of cosmic acceleration has stimulated theorists to consider dark energy or modifications to Einstein's General Relativity as possible explanations. The last decade has seen advances in theories that go beyond smooth dark energy -- modified gravity and interactions of dark energy. While the theoretical terrain is being actively explored, the generic presence of fifth forces and dark sector couplings suggests a set of distinct observational signatures. This report focuses on observations that differ from the conventional probes that map the expansion history or large-scale structure. Examples of such novel probes are: detection of scalar fields via lab experiments, tests of modified gravity using stars and galaxies in the nearby universe, comparison of lensing and dynamical masses of galaxies and clusters, and the measurements of fundamental constants at high redshift. The observational expertise involved is very broad as it spans laboratory experiments, high resolution astronomical imaging and spectroscopy and radio observations. In the coming decade, searches for these effects have the potential for discovering fundamental new physics. We discuss how the searches can be carried out using experiments that are already under way or with modest adaptations of existing telescopes or planned experiments. The accompanying paper on the Growth of Cosmic Structure describes complementary tests of gravity with observations of large-scale structure.

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arXiv2013

Galaxy Cluster Baryon Fractions Revisited

We measure the baryons contained in both the stellar and hot gas components for twelve galaxy clusters and groups at z~0.1 with M=1-5e14 Msun. This paper improves upon our previous work through the addition of XMM data, enabling measurements of the total mass and masses of each major baryonic component --- ICM, intracluster stars, and stars in galaxies --- for each system. We recover a relation for the stellar mass versus halo mass consistent with our previous result. We confirm that the partitioning of baryons between the stellar and hot gas components is a strong function of M500; the fractions of total mass in stars and X-ray gas within r500 scale as M500^-0.45 and M500^0.26, respectively. We also confirm that the combination of the BCG and intracluster stars is an increasingly important contributor to the stellar baryon budget in lower halo masses. We find a weak, but statistically significant, dependence of the total baryon fraction upon halo mass, scaling as M500^0.16. For M500>2e14, the total baryon fractions within r500 are on average 18% (7%) below the Universal value from the WMAP7 (Planck) analysis. For Planck, the difference between the Universal value and cluster baryon fractions is less than the systematic uncertainties associated with M500. The total baryon fractions exhibit significant scatter, particularly at M500<2e14 Msun where they range from 60-90% (65-100%) of the Universal value for WMAP7 (Planck). The ratio of the stellar-to-gas mass within r500, a measure of star formation efficiency, strongly decreases with M500. The fact that this relation remains tight at low mass implies that the larger scatter in the total baryon fractions at these masses arises from either true scatter in the total baryon content or observational scatter in M500, rather than late-time physical processes such as redistribution of gas to beyond r500. (abridged)

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arXiv2013

X-ray nuclear activity in S4G barred galaxies: No link between bar strength and co-occurrent supermassive black hole fueling

Stellar bars can lead to gas inflow toward the center of a galaxy and stimulate nuclear star formation. However, there is no compelling evidence on whether they also feed a central supermassive black hole: by measuring the fractions of barred active and inactive galaxies, previous studies have yielded conflicting results. In this paper, we aim to understand the lack of observational evidence for bar-driven active galactic nucleus (AGN) activity by studying a sample of 41 nearby (d < 35 Mpc) barred galaxies from the Spitzer Survey for Stellar Structure in Galaxies. We use Chandra observations to measure nuclear 2--10 keV X-ray luminosities and estimate Eddington ratios, together with Spitzer 3.6um imaging to quantify the strength of the stellar bar in two independent ways: (1) from its structure, as traced by its ellipticity and boxiness, and (2) from its gravitational torque Q_b, taken as the maximum ratio of the tangential force to the mean background radial force. In this way, rather than discretizing the presence of both stellar bars and nuclear activity, we are able to account for the continuum of bar strengths and degrees of AGN activity. We find nuclear X-ray sources in 31 out of 41 galaxies with median X-ray luminosity and Eddington ratio of L_X=4.3x10^{38} erg/s and L_bol/L_Edd=6.9x10^{-6} respectively, consistent with low-luminosity AGN activity. Including upper limits for those galaxies without nuclear detections, we find no significant correlation between any of the bar strength indicators and the degree of nuclear activity, irrespective of galaxy luminosity, stellar mass, Hubble type, or bulge size. Strong bars do not favor brighter or more efficient nuclear activity, implying that at least for the low-luminosity regime, supermassive black hole fueling is not closely connected to large scale features.

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arXiv2013

On the Origin of Lopsidedness in Galaxies as Determined from the Spitzer Survey of Stellar Structure in Galaxies (S4G)

We study the m=1 distortions (lopsidedness) in the stellar components of 167 nearby galaxies that span a wide range of morphologies and luminosities. We confirm the previous findings of 1) a high incidence of lopsidedness in the stellar distributions, 2) increasing lopsidedness as a function of radius out to at least 3.5 exponential scale lengths, and 3) greater lopsidedness, over these radii, for galaxies of later type and lower surface brightness. Additionally, the magnitude of the lopsidedness 1) correlates with the character of the spiral arms (stronger arm patterns occur in galaxies with less lopsidedness), 2) is not correlated with the presence or absence of a bar, or the strength of the bar when one is present, 3) is inversely correlated to the stellar mass fraction, f_*, within one radial scale length, and 4) correlates directly with f_* measured within the radial range over which we measure lopsidedness. We interpret these findings to mean that lopsidedness is a generic feature of galaxies and does not, generally, depend on a rare event, such as a direct accretion of a satellite galaxy onto the disk of the parent galaxy. While lopsidedness may be caused by several phenomena, moderate lopsidedness ( _i + _o)/2 < 0.3) is likely to reflect halo asymmetries to which the disk responds or a gravitationally self-generated mode . We hypothesize that the magnitude of the stellar response depends both on how centrally concentrated the stars are with respect to the dark matter and whether there are enough stars in the region of the lopsidedness that self-gravity is dynamically important.

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arXiv2013

Evidence for Two Distinct Stellar Initial Mass Functions : Revisiting the Effects of Cluster Dynamical Evolution

We measure the velocity dispersions of six, galactic globular clusters using spatially integrated spectra, to test for the effects of internal dynamical evolution in the stellar mass-to-light ratios, Upsilon_*, of star clusters. In particular, we revisit whether the low values of Upsilon_* we found in our previous study, from which we concluded that there are at least two population of stellar clusters with distinct stellar initial mass functions, are artificially depressed by relaxation driven mass loss. The combination of our previous sample of five old clusters and these six now provides an order of magnitude range in cluster mass with which to explore this issue. We find no relationship between cluster mass, or relaxation time, and Upsilon_*. Because relaxation is mass dependent, we conclude that the values of Upsilon_* for these clusters are not strongly affected by dynamical effects, and so confirm the presence of the population of clusters with low Upsilon_*.

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arXiv2012

The baryon budget on the galaxy group/cluster boundary

We present a study of the hot gas and stellar content of 5 optically-selected poor galaxy clusters, including a full accounting of the contribution from intracluster light (ICL) and a combined hot gas and hydrostatic X-ray mass analysis with XMM observations. We find weighted mean stellar (including ICL), gas and total baryon mass fractions within r500 of 0.026+/-0.003, 0.070+/-0.005 and 0.096+/-0.006, respectively, at a corresponding weighted mean M500 of (1.08_{-0.18}^{+0.21}) x 10^14 Msun. Even when accounting for the intracluster stars, 4 out of 5 clusters show evidence for a substantial baryon deficit within r500, with baryon fractions (f_bary) between 50+/-6 to 59+/-8 per cent of the Universal mean level (i.e. Omega_b / Omega_m); the remaining cluster having f_bary = 75+/-11 per cent. For the 3 clusters where we can trace the hot halo to r500 we find no evidence for a steepening of the gas density profile in the outskirts with respect to a power law, as seen in more massive clusters. We find that in all cases, the X-ray mass measurements are larger than those originally published on the basis of the galaxy velocity dispersion (sigma) and an assumed sigma-M500 relation, by a factor of 1.7-5.7. Despite these increased masses, the stellar fractions (in the range 0.016-0.034, within r500) remain consistent with the trend with mass published by Gonzalez, Zaritsky & Zabludoff (2007), from which our sample is drawn.

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arXiv2012

Implications and Applications of Kinematic Galaxy Scaling Relations

Galaxy scaling relations, which describe a connection between ostensibly unrelated physical characteristics of galaxies, testify to an underlying order in galaxy formation that requires understanding. I review the development of a scaling relation that 1) unites the well-known Fundamental Plane (FP) relation of giant elliptical galaxies and Tully-Fisher (TF) relation of disk galaxies, 2) fits low mass spheroidal galaxies, including the ultra-faint satellites of our Galaxy, 3) explains the apparent shift of lenticular (S0) galaxies relative to both FP or TF, 3) describes all stellar dynamical systems, including systems with no dark matter (stellar clusters), 4) associates explicitly the numerical coefficients that account for the apparent "tilt" of the FP away from the direct expectation drawn from the virial theorem with systematic variations in the total mass-to-light ratio of galaxies within the half-light radius, 5) connects with independent results that demonstrate the robustness of mass estimators when applied at the half-light radius, and 6) results in smaller scatter for disk galaxies than the TF relation. The relation develops naturally from the virial theorem, but implies the existence of additional galaxy formation physics that must now be a focus of galaxy formation studies. More pragmatically, the relation provides a lynchpin that can be used to measure distances and galaxy masses. I review two applications: 1) the cross-calibration of distance measurement methods, and 2) the determination of mass-to-light ratios of simple stellar populations as a function of age, and implications of the latter for the stellar initial mass function.

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arXiv2012

Evidence for Two Distinct Stellar Initial Mass Functions

We present velocity dispersion measurements of 20 Local Group stellar clusters (7 < log(age [yrs]) < 10.2) from integrated light spectra and examine the evolution of the stellar mass-to-light ratio, Upsilon_*. We find that the clusters deviate from the evolutionary tracks corresponding to simple stellar populations drawn from standard stellar initial mass functions (IMFs). The nature of this failure, in which Upsilon_* is at first underestimated and then overestimated with age, invalidates potential simple solutions involving a rescaling of either the measured masses or modeled luminosities. A range of possible shortcomings in the straightforward interpretation of the data, including subtleties arising from cluster dynamical evolution on the present day stellar mass functions and from stellar binarity on the measured velocity dispersions, do not materially affect this conclusion given the current understanding of those effects. Independent of further conjectures regarding the origin of this problem, this result highlights a basic failing of our understanding of the integrated stellar populations of these systems. We propose the existence of two distinct initial mass functions, one primarily, but not exclusively, valid for older, metal poor clusters and the other for primarily, but not exclusively, younger, metal rich clusters. The young (log(age [yrs])< 9.5) clusters are well-described by a bottom-heavy IMF, such as a Salpeter IMF, while the older clusters are better described by a top-heavy IMF, such as a light-weighted Kroupa IMF, although neither of these specific forms is a unique solution. The sample is small, with the findings currently depending on the results for four key clusters, but doubling the sample is within reach.

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arXiv2012

On Dark Peaks and Missing Mass: A Weak Lensing Mass Reconstruction of the Merging Cluster System Abell 520

Merging clusters of galaxies are unique in their power to directly probe and place limits on the self-interaction cross-section of dark matter. Detailed observations of several merging clusters have shown the intracluster gas to be displaced from the centroids of dark matter and galaxy density by ram pressure, while the latter components are spatially coincident, consistent with collisionless dark matter. This has been used to place upper limits on the dark matter particle self-inteaction cross-section of order 1 cm^2/g. The cluster Abell 520 has been seen as a possible exception. We revisit A520 presenting new HST ACS mosaic images and a Magellan image set. We perform a detailed weak lensing analysis and show that the weak lensing mass measurements and morphologies of the core galaxy-filled structures are mostly in good agreement with previous works. There is however one significant difference -- we do not detect the previously claimed "dark core" that contains excess mass with no significant galaxy overdensity at the location of the X-ray plasma. This peak has been suggested to be indicative of a large self-interaction cross-section for dark matter (at least ~5 sigma larger than the upper limit of 0.7 cm^2/g determined by observations of the Bullet Cluster). We find no such indication and instead find that the mass distribution of A520, after subtraction of the X-ray plasma mass, is in good agreement with the luminosity distribution of the cluster galaxies. We conclude that A520 shows no evidence to contradict the collisionless dark matter scenario.

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arXiv2012

The Environmental Dependence of the Incidence of Galactic Tidal Features

In a sample of 54 galaxy clusters (0.04<z<0.15) containing 3551 early-type galaxies suitable for study, we identify those with tidal features both interactively and automatically. We find that ~3% have tidal features that can be detected with data that reaches a 3-sigma sensitivity limit of 26.5 mag arcsec^-2. Regardless of the method used to classify tidal features, or the fidelity imposed on such classifications, we find a deficit of tidally disturbed galaxies with decreasing clustercentric radius that is most pronounced inside of ~0.5R_200. We cannot distinguish whether the trend arises from an increasing likelihood of recent mergers with increasing clustercentric radius or a decrease in the lifetime of tidal features with decreasing clustercentric radius. We find no evidence for a relationship between local density and the incidence of tidal features, but our local density measure has large uncertainties. We find interesting behavior in the rate of tidal features among cluster early-types as a function of clustercentric radius and expect such results to provide constraints on the effect of the cluster environment on the structure of galaxy halos, the build-up of the red sequence of galaxies, and the origin of the intracluster stellar population.

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arXiv2012

The effect of the environment on the gas kinematics and the structure of distant galaxies

With the aim of distinguishing between possible physical mechanisms acting on galaxies when they fall into clusters, we study the properties of the gas and the stars in a sample of 422 emission-line galaxies from EDisCS in different environments up to z~1. We identify galaxies with kinematical disturbances (from emission-lines in their 2D spectra) and find that they are more frequent in clusters than in the field. The fraction of kinematically-disturbed galaxies increases with cluster velocity dispersion and decreases with distance from the cluster centre, but remains constant with projected galaxy density. We also studied morphological disturbances in the stellar light from HST/F814W images, finding that the fraction of morphologically disturbed galaxies is similar in all environments. Moreover, there is little correlation between the presence of kinematically-disturbed gas and morphological distortions. We also study the dependence of the Tully-Fisher relation, star formation, and extent of the emission on environment, and conclude that the gas disks in cluster galaxies have been truncated, and therefore their star formation is more concentrated than in low-density environments. If spirals transform into S0s, our findings imply that the physical mechanism transforming cluster galaxies efficiently disturbs the star-forming gas and reduces their specific star formation rate. Moreover, this star-forming gas is either removed more efficiently from the outskirts of the galaxies or is driven towards the centre (or both), helping to build the bulges of S0s. These results, in addition to the finding that the transformation mechanism does not seem to induce strong morphological disturbances on the galaxies, suggest that the physical processes involved are related to the intracluster medium, with galaxy-galaxy interactions playing only a limited role in clusters.

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