arXiv subjects

Ting Xiao

Publications and source records attributed to Ting Xiao.

At least 55 records · Page 3Linked to original sources

arXiv2019

Linking bar- and interaction-driven molecular gas concentration with centrally-enhanced star formation in EDGE-CALIFA galaxies

We study the spatially resolved star formation history and molecular gas distribution of 58 nearby galaxies, using integral field spectroscopy from the CALIFA survey and CO $J=1\rightarrow 0$ intensity mapping from the CARMA EDGE survey. We use the 4000 Å break (D$_n$4000), the equivalent width of the H$δ$ absorption line (EW H$δ_A$), and the equivalent width of the H$α$ emission line (EW H$α$) to measure the recent star formation history (SFH) of these galaxies. We measure radial profiles of the three SFH indicators and molecular gas mass surface density, from which we measure the level of centrally enhanced star formation and the molecular gas concentration. When we separate our galaxies into categories of barred (17 galaxies), unbarred (24 galaxies), and merging/paired (17 galaxies) we find that the galaxies which have centrally-enhanced star formation (19/58) are either barred (13/19) or in mergers/pairs (6/19) with relatively high molecular gas concentrations. A comparison between our barred galaxies and a snapshot of a hydrodynamic $N$-body simulation of a barred galaxy shows that the current theory of bar formation and evolution can qualitatively reproduce the main features of the observed galaxies in our sample, including both the sharp decrease of stellar age in the galactic center and the gradual decrease of age with increasing distance from center. These findings provide substantial evidence for a picture in which cold gas is transported inward by a bar or tidal interaction, which leads to the growth and rejuvenation of star formation in the central region.

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arXiv2018

The Effect of Galaxy Interactions on Molecular Gas Properties

Galaxy interactions are often accompanied by an enhanced star formation rate (SFR). Since molecular gas is essential for star formation, it is vital to establish whether, and by how much, galaxy interactions affect the molecular gas properties. We investigate the effect of interactions on global molecular gas properties by studying a sample of 58 galaxies in pairs and 154 control galaxies. Molecular gas properties are determined from observations with the JCMT, PMO, CSO telescopes, and supplemented with data from the xCOLD GASS and JINGLE surveys at $^{12}$CO(1-0) and $^{12}$CO(2-1). The SFR, gas mass ($M_\mathrm{H_{2}}$), and gas fraction ($f_{gas}$) are all enhanced in galaxies in pairs by $\sim$ 2.5 times compared to the controls matched in redshift, mass, and effective radius, while the enhancement of star formation efficiency (SFE $\equiv$ SFR/$M_{H_{2}}$) is less than a factor of 2. We also find that the enhancements in SFR, $M_{H_{2}}$ and $f_{gas}$ increase with decreasing pair separation and are larger in systems with smaller stellar mass ratio. Conversely, the SFE is only enhanced in close pairs (separation $<$ 20 kpc) and equal-mass systems; therefore most galaxies in pairs lie in the same parameter space on the SFR-$M_{H_{2}}$ plane as controls. This is the first time that the dependence of molecular gas properties on merger configurations is probed statistically with a relatively large sample and with a carefully-selected control sample for individual galaxies. We conclude that galaxy interactions do modify the molecular gas properties, although the strength of the effect is merger configuration dependent.

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arXiv2018

JINGLE, a JCMT legacy survey of dust and gas for galaxy evolution studies: I. Survey overview and first results

JINGLE is a new JCMT legacy survey designed to systematically study the cold interstellar medium of galaxies in the local Universe. As part of the survey we perform 850um continuum measurements with SCUBA-2 for a representative sample of 193 Herschel-selected galaxies with M*>10^9Msun, as well as integrated CO(2-1) line fluxes with RxA3m for a subset of 90 of these galaxies. The sample is selected from fields covered by the Herschel-ATLAS survey that are also targeted by the MaNGA optical integral-field spectroscopic survey. The new JCMT observations combined with the multi-wavelength ancillary data will allow for the robust characterization of the properties of dust in the nearby Universe, and the benchmarking of scaling relations between dust, gas, and global galaxy properties. In this paper we give an overview of the survey objectives and details about the sample selection and JCMT observations, present a consistent 30 band UV-to-FIR photometric catalog with derived properties, and introduce the JINGLE Main Data Release (MDR). Science highlights include the non-linearity of the relation between 850um luminosity and CO line luminosity, and the serendipitous discovery of candidate z>6 galaxies.

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arXiv2018

SDSS-IV MaNGA: Star formation cessation in low-redshift galaxies I. Dependence on stellar mass and structural properties

We investigate radial gradients in the recent star formation history (SFH) using 1917 galaxies with $0.01<z<0.14$ and integral-field spectroscopy from the ongoing MaNGA survey. For each galaxy, we obtain two-dimensional maps and radial profiles for three spectroscopically-measured parameters that are sensitive to the recent SFH: D$_n$(4000) (the 4000Å break), EW(H$δ_A$) (equivalent width of the H$δ$ absorption line), and EW(H$α$) (equivalent width of the H$α$ emission line). We find the majority of the spaxels in these galaxies are consistent with models with continuously declining star formation rate, indicating that starbursts occur rarely in local galaxies. We classify the galaxies into three classes: fully star-forming (SF), partly quenched (PQ) and totally quenched (TQ), according to the fraction of quenched area within 1.5 times the effective radius, $f_Q(1.5R_e)$. We find that galaxies less massive than $10^{10}$M$_{\odot}$ present at most weak radial gradients in all the diagnostic parameters. In contrast, galaxies with stellar mass above $10^{10}$M$_{\odot}$ present significant gradients in all the three diagnostic parameters if classified as SF or PQ, but show weak gradients in D$_n$(4000) and EW(H$δ_A$) and no gradients in EW(H$α$) if in the TQ class. This implies the existence of a critical stellar mass, at $\sim10^{10}$M$_{\odot}$, above which the star formation in a galaxy gets shutdown from the inside out. Galaxies tend to evolve synchronously from inner to outer regions before their mass reaches the critical value. We have further divided the sample at fixed mass by both bulge-to-total luminosity ratio and morphological type, finding that our conclusions hold regardless of these factors: it appears that the presence of a central dense object is not a driving parameter, but rather a byproduct of the star formation cessation process.

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arXiv2018

SDSS IV MaNGA: Dependence of Global and Spatially-resolved SFR-M* Relations on Galaxy Properties

Galaxy integrated Hα star formation rate-stellar mass relation, or SFR(global)-M*(global) relation, is crucial for understanding star formation history and evolution of galaxies. However, many studies have dealt with SFR using unresolved measurements, which makes it difficult to separate out the contamination from other ionizing sources, such as active galactic nuclei and evolved stars. Using the integral field spectroscopic observations from SDSS-IV MaNGA, we spatially disentangle the contribution from different Hα powering sources for ~1000 galaxies. We find that, when including regions dominated by all ionizing sources in galaxies, the spatially-resolved relation between Hα surface density (ΣHα(all)) and stellar mass surface density (Σ*(all)) progressively turns over at high Σ*(all) end for increasing M*(global) and bulge dominance (bulge-to-total light ratio, B/T). This in turn leads to the flattening of the integrated Hα(global)-M*(global) relation in the literature. By contrast, there is no noticeable flattening in both integrated Hα(HII)-M*(HII) and spatially-resolved ΣHα(HII)-Σ*(HII) relations when only regions where star formation dominates the ionization are considered. In other words, the flattening can be attributed to the increasing regions powered by non-star-formation sources, which generally have lower ionizing ability than star formation. Analysis of the fractional contribution of non-star-formation sources to total Hα luminosity of a galaxy suggests a decreasing role of star formation as an ionizing source toward high-mass, high-B/T galaxies and bulge regions. This result indicates that the appearance of the galaxy integrated SFR-M* relation critically depends on their global properties (M*(global) and B/T) and relative abundances of various ionizing sources within the galaxies.

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arXiv2017

Resolved star formation and molecular gas properties of green valley galaxies: a first look with ALMA and MaNGA

We study the role of cold gas in quenching star formation in the green valley by analysing ALMA $^{12}$CO (1-0) observations of three galaxies with resolved optical spectroscopy from the MaNGA survey. We present resolution-matched maps of the star formation rate and molecular gas mass. These data are used to calculate the star formation efficiency (SFE) and gas fraction ($f_{\rm~gas}$) for these galaxies separately in the central `bulge' regions and outer disks. We find that, for the two galaxies whose global specific star formation rate (sSFR) deviates most from the star formation main sequence, the gas fraction in the bulges is significantly lower than that in their disks, supporting an `inside-out' model of galaxy quenching. For the two galaxies where SFE can be reliably determined in the central regions, the bulges and disks share similar SFEs. This suggests that a decline in $f_{\rm~gas}$ is the main driver of lowered sSFR in bulges compared to disks in green valley galaxies. Within the disks, there exist common correlations between the sSFR and SFE and between sSFR and $f_{\rm~gas}$ on kpc scales -- the local SFE or $f_{\rm~gas}$ in the disks declines with local sSFR. Our results support a picture in which the sSFR in bulges is primarily controlled by $f_{\rm~gas}$, whereas both SFE and $f_{\rm~gas}$ play a role in lowering the sSFR in disks. A larger sample is required to confirm if the trend established in this work is representative of green valley as a whole.

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arXiv2017

Mid-infrared flare of TDE candidate PS16dtm: dust echo and implications for the spectral evolution

PS16dtm was classified as a candidate tidal disruption event (TDE) in a dwarf Seyfert 1 galaxy with low-mass black hole ($\sim10^6M\odot$) and has presented various intriguing photometric and spectra characteristics. Using the archival WISE and the newly released NEOWISE data, we found PS16dtm is experiencing a mid-infrared (MIR) flare which started $\sim11$ days before the first optical detection. Interpreting the MIR flare as a dust echo requires close pre-existing dust with a high covering factor, and suggests the optical flare may have brightened slowly for some time before it became bright detectable from the ground. More evidence is given at the later epochs. At the peak of the optical light curve, the new inner radius of the dust torus has grown to much larger size, a factor of 7 of the initial radius due to strong radiation field. At $\sim150$ days after the first optical detection, the dust temperature has dropped well below the sublimation temperature. Other peculiar spectral features shown by PS16dtm are the transient, prominent FeII emission lines and outflows indicated by broad absorption lines detected during the optical flare. Our model explains the enhanced FeII emission from iron newly released from the evaporated dust. The observed broad absorption line outflow could be explained by accelerated gas in the dust torus due to the radiation pressure.

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arXiv2017

The peculiar filamentary HI structure of NGC 6145

In this paper, we report the peculiar HI morphology of the cluster spiral galaxy NGC 6145, which has a 150 kpc HI filament on one side that is nearly parallel to its major axis. This filament is made up of several HI clouds and the diffuse HI gas between them, with no optical counterparts. We compare its HI distribution with other one-sided HI distributions in the literature, and find that the overall HI distribution is very different from the typical tidal and ram-pressure stripped HI shape, and its morphology is inconsistent with being a pure accretion event. Only about 30% of the total HI gas is anchored on the stellar disk, while most of HI gas forms the filament in the west. At a projected distance of 122 kpc, we find a massive elliptical companion (NGC 6146) with extended radio emission, whose axis points to an HI gap in NGC 6145. The velocity of the HI filament shows an overall light-of- sight motion of 80 to 180 km/s with respect to NGC 6145. Using the long-slit spectra of NGC 6145 along its major stellar axis, we find that some outer regions show enhanced star formation, while in contrast, almost no star formation activities are found in its center (less than 2 kpc). Pure accretion, tidal or ram-pressure stripping is not likely to produce the observed HI filament. An alternative explanation is the jet-stripping from NGC 6146, although direct evidence for a jet-cold gas interaction has not been found.

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arXiv2017

Bar-induced central star formation as revealed by integral field spectroscopy from CALIFA

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 4000Å break (D$_n$(4000)), and the equivalent width of H$δ$ absorption (EW(H$δ_A$)) and H$α$ emission (EW(H$α$)). 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 D$_n$(4000), and most of them correspondingly show a central upturn in EW(H$δ_A$) and EW(H$α$). 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.

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arXiv2017

SDSS IV MaNGA: Discovery of an $H_α$ blob associated with a dry galaxy pair -- ejected gas or a `dark' galaxy candidate?

We report the discovery of a mysterious giant $H_α$ blob that is $\sim 8$ kpc away from the main MaNGA target 1-24145, one component of a dry galaxy merger, identified in the first-year SDSS-IV MaNGA data. The size of the $H_α$ blob is $\sim$ 3-4 kpc in radius, and the $H_α$ distribution is centrally concentrated. However, there is no optical continuum counterpart in deep broadband images reaching $\sim$26.9 mag arcsec$^{-2}$ in surface brightness. We estimate that the masses of ionized and cold gases are $3.3 \times 10^{5}$ $\rm M_{\odot}$ and $< 1.3 \times 10^{9}$ $\rm M_{\odot}$, respectively. The emission-line ratios indicate that the $H_α$ blob is photoionized by a combination of massive young stars and AGN. Furthermore, the ionization line ratio decreases from MaNGA 1-24145 to the $H_α$ blob, suggesting that the primary ionizing source may come from MaNGA 1-24145, likely a low-activity AGN. Possible explanations of this $H_α$ blob include AGN outflow, the gas remnant being tidally or ram-pressure stripped from MaNGA 1-24145, or an extremely low surface brightness (LSB) galaxy. However, the stripping scenario is less favoured according to galaxy merger simulations and the morphology of the $H_α$ blob. With the current data, we can not distinguish whether this $H_α$ blob is ejected gas due to a past AGN outburst, or a special category of `ultra-diffuse galaxy' (UDG) interacting with MaNGA 1-24145 that further induces the gas inflow to fuel the AGN in MaNGA 1-24145.

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arXiv2017

A Ringed Dwarf LINER 1 Galaxy Hosting an Intermediate-mass Black Hole with Large-scale Rotation-like Hα Emission

We report the discovery of a 20-kpc-sized Hα emission in SDSS J083803.68+540642.0, a ringed dwarf galaxy (M$_V$ = -17.89 mag) hosting an accreting intermediate-mass black hole at z=0.02957. Analysis of the HST images indicates that it is an early-type galaxy with a featureless low-surface brightness disk (μ0 = 20.39 mag arcsec$^{-2}$ in the V band) and a prominent, relatively red bulge (V - I = 2.03, Re = 0.28 kpc or 0."48) that accounts for ~81% of the total light in the I band. A circumgalactic ring of a diameter 16 kpc is also detected, with a disperse shape on its south side. The optical emission lines reveal the nucleus to be a broad-line LINER. Our MMT longslit observation indicates that the kinematics of the extended Hα emission is consistent with a rotational gaseous disk, with a mean blueshifted velocity of 162 km s$^{-1}$ and mean redshifted velocity of 86 km s$^{-1}$ . According to our photoionization calculations, the large-scale Hα emission is unlikely to be powered by the central nucleus or by hot evolved (post-AGB) stars interspersed in the old stellar populations, but by in situ star formation; this is vindicated by the line-ratio diagnostic of the extended emission. We propose that both the ring and large-scale Hα-emitting gas are created by the tidal accretion in a collision-and then merger-with a gas-rich galaxy of a comparable mass.

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arXiv2015

SDSS-IV/MaNGA: Spectrophotometric Calibration Technique

Mapping Nearby Galaxies at Apache Point Observatory (MaNGA), one of three core programs in the Sloan Digital Sky Survey-IV (SDSS-IV), is an integral-field spectroscopic (IFS) survey of roughly 10,000 nearby galaxies. It employs dithered observations using 17 hexagonal bundles of 2 arcsec fibers to obtain resolved spectroscopy over a wide wavelength range of 3,600-10,300A. To map the internal variations within each galaxy, we need to perform accurate {\it spectral surface photometry}, which is to calibrate the specific intensity at every spatial location sampled by each individual aperture element of the integral field unit. The calibration must correct only for the flux loss due to atmospheric throughput and the instrument response, but not for losses due to the finite geometry of the fiber aperture. This requires the use of standard star measurements to strictly separate these two flux loss factors (throughput versus geometry), a difficult challenge with standard single-fiber spectroscopy techniques due to various practical limitations. Therefore, we developed a technique for spectral surface photometry using multiple small fiber-bundles targeting standard stars simultaneously with galaxy observations. We discuss the principles of our approach and how they compare to previous efforts, and we demonstrate the precision and accuracy achieved. MaNGA's relative calibration between the wavelengths of H$α$ and H$β$ has a root-mean-square (RMS) of 1.7%, while that between [NII] $λ$6583A and [OII] $λ$3727A has an RMS of 4.7%. Using extinction-corrected star formation rates and gas-phase metallicities as an illustration, this level of precision guarantees that flux calibration errors will be sub-dominant when estimating these quantities. The absolute calibration is better than 5% for more than 89% of MaNGA's wavelength range.

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arXiv2015

An HI View of Galaxy Conformity: HI-rich Environment around HI-excess Galaxies

Using data taken as part of the Bluedisk project we study the connection between neutral hydrogen (HI) in the environment of spiral galaxies and that in the galaxies themselves. We measure the total HI mass present in the environment in a statistical way by studying the distribution of noise peaks in the HI data cubes obtained for 40 galaxies observed with WSRT. We find that galaxies whose HI mass fraction is high relative to standard scaling relations have an excess HI mass in the surrounding environment as well. Gas in the environment consists of gas clumps which are individually below the detection limit of our HI data. These clumps may be hosted by small satellite galaxies and\or be the high-density peaks of a more diffuse gas distribution in the inter-galactic medium. We interpret this result as an indication for a picture in which the HI-rich central galaxies accrete gas from an extended gas reservoir present in their environment.

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arXiv2015

P-MaNGA: Full spectral fitting and stellar population maps from prototype observations

MaNGA (Mapping Nearby Galaxies at Apache Point Observatory) is a 6-year SDSS-IV survey that will obtain resolved spectroscopy from 3600 $Å$ to 10300 $Å$ for a representative sample of over 10,000 nearby galaxies. In this paper, we derive spatially resolved stellar population properties and radial gradients by performing full spectral fitting of observed galaxy spectra from P-MaNGA, a prototype of the MaNGA instrument. These data include spectra for eighteen galaxies, covering a large range of morphological type. We derive age, metallicity, dust and stellar mass maps, and their radial gradients, using high spectral-resolution stellar population models, and assess the impact of varying the stellar library input to the models. We introduce a method to determine dust extinction which is able to give smooth stellar mass maps even in cases of high and spatially non-uniform dust attenuation. With the spectral fitting we produce detailed maps of stellar population properties which allow us to identify galactic features among this diverse sample such as spiral structure, smooth radial profiles with little azimuthal structure in spheroidal galaxies, and spatially distinct galaxy sub-components. In agreement with the literature, we find the gradients for galaxies identified as early-type to be on average flat in age, and negative (- 0.15 dex / R$_e$ ) in metallicity, whereas the gradients for late-type galaxies are on average negative in age (- 0.39 dex / R$_e$ ) and flat in metallicity. We demonstrate how different levels of data quality change the precision with which radial gradients can be measured. We show how this analysis, extended to the large numbers of MaNGA galaxies, will have the potential to shed light on galaxy structure and evolution.

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arXiv2015

P-MaNGA: Gradients in Recent Star Formation Histories as Diagnostics for Galaxy Growth and Death

We present an analysis of the data produced by the MaNGA prototype run (P-MaNGA), aiming to test how the radial gradients in recent star formation histories, as indicated by the 4000AA-break (D4000), Hdelta absorption (EW(Hd_A)) and Halpha emission (EW(Ha)) indices, can be useful for understanding disk growth and star formation cessation in local galaxies. We classify 12 galaxies observed on two P-MaNGA plates as either centrally quiescent (CQ) or centrally star-forming (CSF), according to whether D4000 measured in the central spaxel of each datacube exceeds 1.6. For each galaxy we generate both 2D maps and radial profiles of D4000, EW(Hd_A) and EW(Ha). We find that CSF galaxies generally show very weak or no radial variation in these diagnostics. In contrast, CQ galaxies present significant radial gradients, in the sense that D4000 decreases, while both EW(Hd_A) and EW(Ha) increase from the galactic center outward. The outer regions of the galaxies show greater scatter on diagrams relating the three parameters than their central parts. In particular, the clear separation between centrally-measured quiescent and star-forming galaxies in these diagnostic planes is largely filled in by the outer parts of galaxies whose global colors place them in the green valley, supporting the idea that the green valley represents a transition between blue-cloud and red-sequence phases, at least in our small sample. These results are consistent with a picture in which the cessation of star formation propagates from the center of a galaxy outwards as it moves to the red sequence.

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arXiv2014

Overview of the SDSS-IV MaNGA Survey: Mapping Nearby Galaxies at Apache Point Observatory

We present an overview of a new integral field spectroscopic survey called MaNGA (Mapping Nearby Galaxies at Apache Point Observatory), one of three core programs in the fourth-generation Sloan Digital Sky Survey (SDSS-IV) that began on 2014 July 1. MaNGA will investigate the internal kinematic structure and composition of gas and stars in an unprecedented sample of 10,000 nearby galaxies. We summarize essential characteristics of the instrument and survey design in the context of MaNGA's key science goals and present prototype observations to demonstrate MaNGA's scientific potential. MaNGA employs dithered observations with 17 fiber-bundle integral field units that vary in diameter from 12" (19 fibers) to 32" (127 fibers). Two dual-channel spectrographs provide simultaneous wavelength coverage over 3600-10300 A at R~2000. With a typical integration time of 3 hr, MaNGA reaches a target r-band signal-to-noise ratio of 4-8 (per A, per 2" fiber) at 23 AB mag per sq. arcsec, which is typical for the outskirts of MaNGA galaxies. Targets are selected with stellar mass greater than 1e9 Msun using SDSS-I redshifts and i-band luminosity to achieve uniform radial coverage in terms of the effective radius, an approximately flat distribution in stellar mass, and a sample spanning a wide range of environments. Analysis of our prototype observations demonstrates MaNGA's ability to probe gas ionization, shed light on recent star formation and quenching, enable dynamical modeling, decompose constituent components, and map the composition of stellar populations. MaNGA's spatially resolved spectra will enable an unprecedented study of the astrophysics of nearby galaxies in the coming 6 yr.

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arXiv2012

Gas depletion in cluster galaxies depends strongly on their internal structure

We analyze galaxies in 300 nearby groups and clusters identified in the Sloan Digital Sky Survey using a photometric gas mass indicator that is useful for estimating the degree to which the interstellar medium of a cluster galaxy has been depleted. We study the radial dependence of inferred gas mass fractions for galaxies of different stellar masses and stellar surface densities. At fixed clustercentric distance and at fixed stellar mass, lower density galaxies are more strongly depleted of their gas than higher density galaxies. An analysis of depletion trends in the two-dimensional plane of stellar mass $M_*$ and stellar mass surface density $μ_*$ reveals that gas depletion at fixed clustercentric radius is much more sensitive to the density of a galaxy than to its mass. We suggest that low density galaxies are more easily depleted of their gas, because they are more easily affected by ram-pressure and/or tidal forces. We also look at the dependence of our gas fraction/radius relations on the velocity dispersion of the cluster, finding no clear systematic trend.

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arXiv2011

Dust reddening in star-forming galaxies

We present empirical relations between the global dust reddening and other physical galaxy properties including the Halpha luminosity, Halpha surface brightness, metallicity and axial ratio for star-forming disc galaxies. The study is based on a large sample of ~22 000 well-defined star-forming galaxies selected from the Sloan Digital Sky Survey (SDSS). The reddening parameterized by color excess E(B-V) is derived from the Balmer decrement. Besides the dependency of reddening on Halpha luminosity / surface brightness and gas phase metallicity, it is also correlated with the galaxy inclination, in the sense that edge-on galaxies are more attenuated than face-on galaxies at a give intrinsic luminosity. In light of these correlations, we present the empirical formulae of E(B-V) as a function of these galaxy properties, with a scatter of only 0.07 mag. The empirical relation can be reproduced if most dust attenuation to the HII region is due to diffuse interstellar dust distributing in a disc thicker than that of HII regions. The empirical formulae can be incorporated into semi-analytical models of galaxy formation and evolution to estimate the dust reddening and enable comparison with observations more practically.

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