Mining Low-redshift Circumgalactic Baryons

Mining Circumgalactic Baryons in the Low-Redshift Universe

Cameron J. Liang, Hsiao-Wen Chen

Department of Astronomy & Astrophysics, and Kavli Institute for Cosmological Physics, University of Chicago, Chicago IL 60637
E-mail: jwliang@oddjob.uchicago.eduE-mail: hchen@oddjob.uchicago.edu
Abstract

This paper presents an absorption-line study of the multiphase circumgalactic medium (CGM) based on observations of , C II, C IV, Si II, Si III, and Si IV absorption transitions in the vicinities of 195 galaxies at redshift . The galaxy sample is established based on a cross-comparison between public galaxy and QSO survey data and is characterized by a median redshift of , a median projected distance of kpc to the sightline of the background QSO, and a median stellar mass of . Comparing the absorber features identified in the QSO spectra with known galaxy properties has led to strong constraints for the CGM absorption properties at . First, abundant hydrogen gas is observed out to kpc, well beyond the dark matter halo radius of individual galaxies, with a mean covering fraction of %. In contrast, no heavy elements are detected at from either low-mass dwarfs or high-mass galaxies. The lack of detected heavy elements in low- and high-ionization states suggests that either there exists a chemical enrichment edge at or gaseous clumps giving rise to the observed absorption lines cannot survive at these large distances. Considering all galaxies at leads to a strict upper limit for the covering fraction of heavy elements of % (at a 95% confidence level) over . At , differential covering fraction between low- and high-ionization gas is observed, suggesting that the CGM becomes progressively more ionized from to larger distances. Comparing CGM absorption observations at low and high redshifts shows that at a fixed-fraction of the CGM exhibits stronger mean absorption at than at and that the distinction is most pronounced in low-ionization species traced by C II and Si II absorption lines. We discuss possible pseudo-evolution of the CGM as a result of misrepresentation of halo radius, and present a brief discussion on the implications of these findings.

keywords:
galaxies:halos – galaxies: dwarf – quasars: absorption lines – intergalactic medium – survey
pagerange: Mining Circumgalactic Baryons in the Low-Redshift UniverseReferencespubyear: 2011

1 Introduction

Circumgalactic space is thought to contain a vast amount of baryons (e.g. Spitzer 1956; Fukugita 2004) that are both multiphase and dynamic (e.g. Mo & Miralda-Escudé 1996, Maller & Bullock 2004). In principle, this circumgalactic gas provides the fuel necessary for sustaining star formation in galaxies, while at the same time it is also being replenished with both newly accreted (and presumably chemically pristine) intergalactic gas and chemically enriched materials either through gas stripping due to satellite interaction or through starburst driven winds. Therefore, circumgalactic space provides a critical laboratory for studying the baryon cycle that regulates star formation and galaxy growth.

Over the past two decades, absorption spectroscopy of background QSOs have provided an effective tool for probing the otherwise unseen, diffuse gas in halos around distant galaxies. While each QSO provides a one-dimensional mapping through each single halo, observing an ensemble of close galaxy and QSO pairs leads to statistical measurements of mean halo profiles (i.e. absorption strength as a function of projected distance) averaged over the entire galaxy sample. Commonly seen transitions in circumgalactic space include hydrogen (e.g. Lanzetta et al. 1995; Chen et al. 1998, 2001a; Tripp et al. 1998; Wakker & Savage 2009; Steidel et al. 2010; Prochaska et al. 2011; Thom et al. 2012; Stocke et al. 2013; Rudie et al. 2013), the C IV  doublet (e.g. Chen et al. 2001b; Adelberger et al. 2005; Steidel et al. 2010), the Mg II  doublet (e.g. Bowen et al. 1995; Chen & Tinker 2008; Kacprzak et al. 2008; Barton & Cooke 2009; Chen et al. 2010a,b; Gauthier et al. 2010; Bordoloi et al. 2011; Werk et al. 2013), and the O VI  doublet (Chen & Mulchaey 2009; Wakker & Savage 2009; Prochaska et al. 2011; Tumlinson et al. 2011; Johnson et al. 2013). A general finding from different studies is that most galaxies are surrounded by chemically enriched gas out to kpc in projected distance. Competing scenarios for explaining the presence of heavy elements at kpc from star-forming regions include super galactic winds (e.g. Murray et al. 2011; Booth et al. 2013) and tidally disrupted satellites (e.g. Wang 1993; Gauthier 2013).

A particularly interesting absorption feature to adopt for probing the baryon content of galactic halos is the  doublet. These doublet transitions are strong and their rest-frame wavelengths, 1548.20 and 1550.77 Å, enable uniform surveys of chemically enriched gas in the optical window over a broad redshift range from redshift to .  absorbers are found to originate primarily in photoionized gas of temperature K with some contribution from shock heated gas in galaxies and galactic halos (e.g. Rauch et al. 1997; Boksenberg et al. 2003; Simcoe et al. 2004). Therefore,  absorption transitions provide an effective tracer of chemically enriched warm gas in and around star-forming regions.

A number of surveys have been carried out to characterize the statistical properties of  absorbers found along random QSO sightlines (e.g. Songaila 2001; Boksenberg et al. 2003; Simcoe 2011; Cooksey et al. 2013). While the shape of the  equivalent width frequency distribution function appears to remain the same, the total cosmic mass density in C ions is found to increase from to by a factor of 2 (e.g. Cooksey et al. 2013). The increasing  mass density together with an increasing background radiation intensity with decreasing redshift (e.g. Haardt & Madau 2012) indicate an increasing chemical enrichment level with time in the gas traced by the  absorption transitions (e.g. Oppenheimer & Davé 2008).

At the same time, only three studies have been carried out to characterize extended  gaseous halos around galaxies, two at 111Though we have recently learned that Bordoloi et al. (2014) has also been conducting a survey of  absorbers in halos around low-redshift galaxies. and one at . A clear understanding has yet to be established. At , Chen et al. (2001b) studied the incidence of  absorbing gas at projected distances kpc from a sample of 50 galaxies. These authors reported the presence of a distinct boundary at a -band luminosity-normalized projected distance of kpc, beyond which no  absorbers are detected. The lack of  absorption is based on a subsample of 35 galaxies that occur at kpc from their background QSO sightlines. In contrast, 14 of the 15 galaxies at kpc have an associated  absorber, although the rest-frame absorption equivalent width, , exhibits a large scatter between individual galaxies. At , Steidel et al. (2010) examined the mean spatial absorption profiles of 512 galaxies based on stacked spectra of background galaxies that occur at kpc. These authors found that the mean  absorption strength declines rapidly at projected distances of kpc. Comparing the observations of Chen et al. (2001b) and Steidel et al. (2010) yielded little distinction in the -traced circumgalactic medium (CGM) at low and high redshifts (Chen 2012). Both the luminosity-normalized spatial extent and mean absorption equivalent width of the CGM around galaxies of comparable mass (but with very different on-going star formation rate) have changed little over the redshift interval , although there exists a large scatter in  in the low-redshift study. Nevertheless, a lack of variation in the spatial profile of the chemically enriched CGM between two distinct epochs poses a serious challenge to the theoretical models of gas flows around galaxies (e.g. Hummels et al. 2013; Ford et al. 2013a,b).

On the other hand, Borthakur et al. (2013) targeted a sample of 20 galaxies at and were able to constrain the incidence of  absorbing gas for 17 of these galaxies. Of the 17 galaxies studied, eight occur at kpc and nine at larger distances. These authors detected  absorbers for three of the eight galaxies at kpc and three of the nine galaxies at kpc in their sample. The finding of a flat rate of  incidence with increasing projected distance is intriguing and appears to be in stark contrast to the earlier finding of Chen et al. (2001b). While Borthakur et al. attributed the detected  absorbers to starburst activity in the associated galaxies, it is not straightforward to reconcile the discrepant trend found for extended  halos between the Chen et al. and Borthakur et al. samples.

To address the discrepant trend found for extended  halos around galaxies at low redshifts and to improve the empirical understanding of how the chemically enriched CGM evolves with time, we have searched public archives to find spectroscopically identified galaxies at small projected distance to a UV bright, background QSO for which high-quality echelle/echellette spectra are already available in the Hubble Space Telescope (HST) data archive. Our search has yielded the first large sample of close QSO and galaxy pairs that enables a systematic study of extended  halos over the projected distance interval of kpc. As described below, this unique sample allows us to place unprecedented limits on the extent of chemical enrichment around low-redshift galaxies based on observations of not only the  absorption doublets but also a whole host of ionic transitions from low- and intermediate-ionization states.

Recently, Tumlinson et al. (2013) carried out a large program to use the Cosmic Origins Spectrograph (COS; Green et al. 2012) on board HST to study the CGM at kpc of 44 galaxies at . This program, known as the “COS-Halos” survey, was designed to map the multi-phase CGM using O VI and other metal-line diagnostics (Tumlinson et al. 2011; Werk et al. 2013). The low-redshift cut at was dictated by the requirement of detecting the O VI doublet using COS and the FUV channel. However, the spectral coverage of the COS FUV gratings misses the C IV doublet at , and therefore  transitions are not included in the COS-Halos analysis (e.g. Werk et al. 2013).

Our study differs from the COS-Halos program in two fundamental aspects. First, our search is designed to probe the  absorption in galactic halos for comparisons with high-redshift studies. Second, because fainter galaxies are also more numerous, it is more likely to find a faint foreground galaxy near a QSO sightline than a luminous galaxy (see the discussion is § 2). As a result, low-luminosity () and low-mass () dwarf galaxies contribute to a large fraction (%) of our random QSO and galaxy pair sample. Therefore, our study complements the COS-Halos effort both in terms of the mass regime of the galaxies and in terms of the ionization state of the CGM.

Here we report initial findings for the low-redshift CGM based on a sample of 195 galaxies for which constraints on the stellar mass are available. The available stellar mass estimate of each galaxy allows us to infer the total mass of the dark matter in which the galaxy resides (e.g. Behroozi et al. 2013; Kravtsov et al. 2014). This in turn allows us to assess the intrinsic size differences between different galaxies based on the estimated dark matter halo radius from a standard halo model. While the CGM is expected to be regulated by various complicated physical processes, including gravitational motion and star formation feedback, addressing the effects of all these processes at once is challenging. As a first step toward establishing a clear understanding of the processes that drive the observed CGM properties, we have designed our study here to account for the intrinsic size differences (driven by the gravitational potential) of individual galactic halos by normalizing the observed projected distances with the underlying halo radius. We expect that the results will facilitate future studies that consider the effect of additional processes such as star formation feedback.

This paper is organized as follows. In Section 2, we describe the selection criteria for establishing the close galaxy–QSO pair sample and summarize the properties of the galaxy members in the pair sample. In Section 3, we describe the data reduction and analysis procedures of the absorption spectra of the QSOs. In Section 4, we examine the correlation between the strengths of different ionic transitions and galaxy properties, and compare the results of our study with previous findings. Finally, we discuss the implication of our results in Section 5. Throughout the paper, we adopt the standard cosmology, , with a Hubble constant .

2 A Public Sample of Galaxy–QSO Pairs

We have assembled a large sample () of spectroscopically-identified galaxies that occur at small projected distances kpc from the sightline of a background UV bright QSO. This galaxy sample is ideal for characterizing extended gaseous halos around galaxies based on the absorption features imprinted in the spectra of the background QSOs.

We first searched the HST archive for QSOs that have been observed with either the Space Telescope Imaging Spectrograph (STIS; Woodgate et al. 1998) or the Cosmic Origins Spectrograph (COS; Green et al. 2012) as of Cycle 20. This search yielded a sample of 150 QSOs at . Next, we searched for spectroscopically identified galaxies in public archives, including the Nearby General Catalog (NGC; Sinnott 1988), the Sloan Digital Sky Survey (SDSS; York et al. 2000) spectroscopic galaxy sample, the Two Micron All Sky Survey (2MASS) galaxies (Huchra et al. 2012), and the Two Degree Field Galaxy Redshift Survey (2dFGRS; Colless et al. 2001). A galaxy and a background QSO were considered a suitable pair if they satisfied the following criteria. (1) At the redshift of the galaxy, the physical projected distance between the galaxy and the QSO sightline is kpc. (2) The galaxy must be at km s below the redshift of the QSO to avoid ambiguity between foreground absorbers and those originating in QSO outflows (e.g. Wild et al. 2008). The maximum separation limit of 500 kpc is sufficiently large to encompass the gaseous halos of galaxies known empirically (e.g. Chen et al. 1998, 2001a; Gauthier et al. 2011; Prochaska et al. 2011; Rudie et al. 2012). It is also motivated by theoretical expectations of extended halo gas out to kpc in radius from star-forming regions (e.g. Ford et al. 2013a). Therefore, including pairs separated by greater than 300 kpc allows us to explore the presence of chemically enriched gas beyond the fiducial virial radius of dark matter halos.

Finally, we formed an “isolated” galaxy and QSO pair sample by considering only galaxies without close neighbors, in order to minimize the ambiguity in associating an absorber with a galaxy. Previous studies have also shown that galaxies in group environments tend to have more extended halo gas than isolated galaxies that results in a larger scatter in the observed spatial distribution of absorption strength with projected distance (Chen et al. 2010a, Bordoloi et al. 2011a, and Gauthier & Chen 2011). In our study, a galaxy was considered an “isolated” one, if no other galaxies have been spectroscopically identified within projected separation of kpc and velocity separation of km s were present. These criteria are driven by the model expectation that an galaxy at has a virial radius of kpc and maximum circular velocity of km s. We chosen a more conservative limit to allow for uncertainties in galaxy redshifts.

Figure 1: Distribution of projected distance versus redshift for the 195 galaxies (§ 2). The top (right) panel displays the redshift (impact parameter) histograms.

Our search criteria of suitable galaxy and QSO pairs yielded a final sample of 213 “isolated” galaxies that occur at kpc from the sightline of a background QSO for studies of the low-redshift CGM. Excluding 18 galaxies that are in the COS-Dwarfs program (Bordoloi et al. 2014, in preparation) led to a total of 195 galaxies in our sample. The redshifts of the galaxies range from to with a median of , and the projected distances of the QSOs range from kpc to kpc with a median of kpc. The projected distance versus redshift distribution of the galaxies sample is shown in Figure 1, in which the top and right panels display the histograms in redshift and in projected distance, respectively.

To facilitate a detailed investigation of how the observed CGM absorption properties depend on galaxy properties, we also made use of available measurements of rest-frame UV luminosities and stellar mass from the NASA–Sloan Atlas222http://nsatlas.org/ (Blanton et al. 2005; Blanton et al. 2011). This public atlas contains 145,155 galaxies with known redshifts at . For each galaxy, it includes optical and UV photometric measurements from the SDSS Data Release 8 (Blanton et al. 2011) and GALEX Data Release 6 (Schiminovich et al. 2007), as well as derived quantities such as stellar mass () and rest-frame UV and optical absolute magnitudes computed by the K-correct code (Blanton & Roweis 2007). The rest-frame UV absolute magnitudes allows us to estimate an unobscured star formation rate (SFR) for each galaxy based on the calibration coefficient of Kennicutt & Evans (2012). The available stellar mass estimate of each galaxy allows us to infer the total mass of the dark matter halo () in which the galaxy resides (e.g. Behroozi et al. 2013; Kravtsov et al. 2014). This in turn allows us to assess the intrinsic size differences between different galaxies based on the estimated dark matter halo radius from a standard halo model (see § 4 for a more detailed discussion).

Figure 2: Observed correlation between stellar mass and rest-frame -band absolute magnitude, for 111 overlapping galaxies that are both in our pair sample and in the NASA–Sloan Atlas (dark solid points). The solid line indicates the best-fit model with and a 1- scatter of (error bar in the lower-right corner). The full NASA–Sloan catalog, which has k galaxies (grey points), is also included to contrast these 111 overlapping galaxies. The full sample displays a consistent mean relation (dashed line) and scatter between and . The consistent distribution of the two samples strongly supports that the mean relation derived using the subsample of 111 galaxies is representative of the general galaxy population at low redshifts.

Cross-matching the “isolated” galaxy sample with the NASA–Sloan Atlas resulted in 116 overlapping galaxies. We visually inspected the optical images of each galaxy and removed five objects due to erroneous photometry. This exercise resulted in a sample of 111 galaxies with accurate and star formation rate (SFR) measurements available from the NASA–Sloan Atlas. However, to utilize the full “isolated” galaxy sample for investigating how the observed CGM absorption properties depend on galaxy properties, we needed to estimate the stellar mass for each of the remaining 100 galaxies based on available photometric data. We used the subsample of 111 galaxies as a guide. Comparing the stellar mass provided by the NASA–Sloan Atlas with intrinsic luminosities in different bandpasses revealed a tight correlation between and rest-frame absolution -band magnitude, , over four orders of magnitude in (Figure 2). Based a linear regression analysis, we find that the vs.  correlation is best characterized by

(1)

with a 1- scatter of . Equation (1) enables us to obtain a stellar mass estimate and associated uncertainty for galaxies based on . In Figure 2, we also include the entire NASA–Sloan catalog, which has k galaxies (grey points), to contrast the 111 galaxies adopted for deriving Equation (1). The comparison shows that the 111 overlapping galaxies and the full NASA–Sloan catalog share a consistent mean relation and scatter between and , particularly at the high-mass end with . Equation (1) is therefore representative of the general galaxy population at low redshifts.

Figure 3: Stellar mass distribution of our galaxy sample (blue shaded histogram). The median mass is , in comparison to the characteristic mass for the field galaxies (Baldry et al. 2012; Muzzin et al. 2013). Our galaxy sample has a mass distribution that encompasses previous CGM studies at both low and high redshifts. Specifically, the COS-Halos sample at (Werk et al. 2013; red open histogram) has a median stellar mass of and the starburst sample at from Reddy et al. (2012; green open histogram) has a median stellar mass of . The number counts of the Reddy et al. sample has been reduced by a factor of 25 for presentation purpose.

We present the distribution of stellar masses of our galaxies in Figure 3. The blue shaded histogram shows the stellar mass distribution for the full sample of 195 galaxies, while the black open histogram shows the stellar mass distribution for the subsample of 102 galaxies with inferred from following Equation (1). Figure 3 shows that the galaxies in the full sample span a wide range in stellar mass, from to , with a median , which is (Baldry et al. 2012; Muzzin et al. 2013). Comparing the blue shaded and black open histograms shows that including galaxies with inferred from Equation (1) allows us to expand our CGM study to include higher-mass galaxies, covering a mass range that overlaps with the COS-Halos sample at (Werk et al. 2013; red open histogram) and the starburst sample at from Reddy et al. (2012; green open histogram)333We note that while different galaxy samples overlap in the stellar mass range, there are strong distinctions in SFR and in the knowledge of environments and redshift precisions. Specifically, the starburst sample at have a mean SFR of (e.g. Erb et al. 2006) and low-redshift galaxies have on average unobscured SFR of . In addition, while our sample only includes galaxies in an isolated environment, the environments of the high-redshift starburst sample are unknown..

In addition, examining the SFR versus correlation helps to characterize the galaxies in our pair sample in the context of the general galaxy population. Considering the 111 galaxies with both and rest-frame UV photometric measurements from the NASA–Sloan Atlas, we present in Figure 4 the specific Star Formation Rate (sSFR; SFR per unit stellar mass) and stellar mass of these galaxies (solid points) in comparison to the mean relations of star-forming main sequence galaxies (blue line) and passive, red galaxies (red) from Schiminovich et al. (2010). Recall that we measured an unobscured SFR for each galaxy based on the observed NUV flux without correcting for possible dust extinction. Therefore, our measurements likely represent lower limits to the intrinsic SFR. The tilt in the distribution of our galaxies relative to the mean relation of star-forming main-sequence galaxies can be explained by the observed correlation between dust extinction and stellar mass, namely more massive galaxies on average exhibit higher degrees of dust extinction (e.g. Zahid et al. 2013). It is clear that the majority of the galaxies in our sample are consistent with being star-forming main-sequence galaxies with a small fraction found in the red-sequence regime.

We note that while the stellar mass derived using the K-correct code may be systematically overestimated by 0.1 dex in the low mass regime of (e.g. Moustakas et al. 2013), such error translates to a systematic uncertainty of dex in , well within the scatter in the stellar-mass-to-halo-mass relation of Behroozi et al. (2013). The resulting uncertainty in is then negligible.

Of the 195 galaxies in our pair sample, 12 occur within 100 kpc in projected distance from a background QSO sightline. We summarize the properties of the galaxy sample in Table 1, which lists for each galaxy the identification, right ascension (RA) and declination (Dec), spectroscopic redshift (), unobscured SFR (when available), stellar mass (), halo mass (), halo radius (), and absolute -band magnitude .

Figure 4: Distribution of specific star formation rate (sSFR) and stellar mass based on a subsample of our galaxies with available UV photometric from the NASA-Sloan Atlas (solid points). SFR is derived based on the observed NUV flux from GALEX and therefore represents a lower limit to the intrinsic value. The blue (red) line marks the star-forming main-sequence (passive, red) galaxies from Schiminovich et al. (2010). The tilt in the distribution of our galaxies relative to the mean relation of star-forming main-sequence galaxies can be explained by more massive galaxies showing higher degrees of dust extinction (e.g. Zahid et al. 2013). Nevertheless, the majority of our galaxies are consistent with being star-forming main-sequence galaxies, and a small fraction are found in the red-sequence regime.

3 QSO UV Spectroscopy

Figure 5: Examples of galaxies with associated  absorbers from our search. For each field, we present the QSO spectrum in the left panel and the corresponding SDSS image centered at the galaxy in the right panel. In each panel, the direction to the QSO sightline is indicated by the arrow, and the horizontal bar in the upper-left corner indicates an angular scale of . The projected separation between the QSO sightline and the galaxy is shown in the lower-right corner. Absorption features due to Si III , , and at the redshifts of the galaxies are indicated by blue, dotted lines in the left panels. The absorber redshift is shown in the lower right corner of each spectrum.

Our galaxy sample contains 195 “isolated” galaxies that occur near the sightlines of 96 independent background QSOs with high-quality, far-ultraviolet echellette spectra available in the HST data archive. Of the 96 QSOs, 13 were observed using STIS and the E140M grating and 83 were observed using COS and the G130M/G160M gratings. STIS and the E140M grating offers a contiguous spectral coverage from Å to Å with a full-width-at-half-maximum resolution of km s, while COS with G130M and G160M at different central wavelengths offers a nearly contiguous spectral coverage from Å to Å with a spectral resolution of km s.

Individual flux-calibrated spectra from STIS were retrieved from the MAST server. For each QSO, individual echelle orders were continuum-normalized and co-added to form a single, stacked spectrum using our own software. The continuum was determined using a low-order polynomial fit to spectral regions that are free of strong absorption features. The mean signal-to-noise () of the combined echelle spectra of 13 QSOs have on average over the majority of the spectral regions covered by the data.

Individual one-dimensional COS spectra were retrieved from the HST archive and combined using our own software. In summary, individual spectra were first aligned using common absorption lines along each sightline, including both intervening absorbers at and known Milky Way features, such as Si III  and C II  in the G130M data and Si II  and Al II  in the G160M data. In a few sightlines, the pipeline generated individual spectra exhibit wavelength calibration errors that vary with wavelength, from Å at Å to Å at Å. We correct for the wavelength calibration errors by employing a low-order polynomial fit to the observed wavelength-dependent shift in individual spectral segment. Then the individual wavelength-corrected spectra were re-binned to a pixel resolution of km s and coadded into a single combined spectrum using our own co-addition code. The final processed and combined spectra have a median signal-to-noise of . A summary of the STIS and COS observations for each QSO is presented in Table 2, which lists from columns (1) through (5) the name, RA, Dec, emission redshift of the QSO, and the program ID under which the data were taken. We also list in columns (6) and (7) of Table 2 the median of the G130M and G160M spectra from COS and in column (8) the median of the STIS/E140M spectra.

To facilitate absorption-line measurements, we also continuum normalized each QSO spectrum using a continuum model determined from a low-order polynomial fit to spectral regions that were free of strong narrow line features. The continuum normalization included strong damping wings in each QSO spectrum due to either the Milky Way  absorption or intervening damped  absorbers. We did not attempt to fit strong emission features such as the geocoronal   and O I  lines. These narrow emission lines were instead manually masked and were not included in spectral regions for identifying absorption features.

4 Analysis

The process described in § 3 yielded high-quality, continuum-normalized UV echellette spectra of 96 QSOs. These UV spectra allow us to investigate the baryon content of the circumgalactic space within 500 kpc in projected distance of 195 independent, foreground galaxies based on the presence/absence of the corresponding absorption-line features, in particular the  doublet. In this section, we describe absorption-line constraints of individual galactic halos. In addition, we present stacked QSO spectra at the rest-frame of the galaxies, and improved absorption-line constraints afforded by the stacked spectra. We show that with much improved , these stacked spectra allow us to place unprecedented limits for the absorption properties of gaseous halos around galaxies.

4.1 Absorption Constraints of Circumgalactic Baryons

Figure 6: Relative velocity distributions of  (left) and  (right) absorbers with respect to the systemic redshift of their associated galaxies in our pair sample. We detect associated  absorbers in 125 of the 195 galaxies searched, and associated  absorbing gas in nine galaxies. The left panel shows that the velocity distributions of all  absorbers detected around galaxies at kpc (shaded histogram), around galaxies at kpc (green open histogram), and galaxies at kpc. Considering the full sample requires a double Gaussian profile to characterize the velocity distribution with a narrow component centered at km s and dispersion of km s and a broad component centered at km s and dispersion of km s (the solid curve). In contrast, the velocity distribution of  absorbing gas around galaxies can be characterized by a single Gaussian distribution of km s and km s, excluding the outlier at km s.

In order to obtain robust constraints for the baryon content in halos around our sample galaxies, we first identify and mask contaminating features associated with other strong  absorbers at along each QSO sightline, including higher-order Lyman series and ionic absorption lines. Then for each of the 195 galaxies, we search in the associated QSO spectra for the corresponding Ly absorption line within the velocity range of km s from the systemic redshifts of the galaxies. The allowed large velocity interval is guided by previous observations (e.g. Lanzetta et al. 1995) which show a velocity dispersion of km s between galaxies and their associated  absorbers. For each detected  absorber, we further examine whether associated ionic transitions, such as , C II, Si IV, S III, and Si II, are also present in the spectral range covered by the STIS/COS data. Absorption transitions considered in our study are summarized in Table 3, together with those considered by Werk et al. (2013) and Steidel et al. (2010) for comparison. We also include in Table 3 the sample size, redshift range, and stellar mass range of each galaxy sample for reference.

We detect associated  absorbers around 125 of the 195 galaxies in our survey sample, and associated  absorbing gas in nine galaxies. Roughly 30% of the detected  absorbers show multiple components within a velocity interval of 500 km s and only one of the nine detected  displays an additional secondary component at km s. No  () measurements can be made for 27 (35) galaxies due to the presence of contaminating features. This leaves 43 (151) galaxies that show no trace of  () absorbing gas at kpc and km s. Examples of the galaxies in our sample that display associated  absorbers are presented in Figure 5, which also highlights the presence of associated Si III  and in blue dotted lines.

To characterize the absorber properties, we measure the rest-frame absorption equivalent widths for all the observed transitions. We focus our current analysis on absorption equivalent width measurements in order to make direct comparisons with previous studies. A more detailed profile analysis is deferred to a future paper (Liang et al. 2014, in preparation). In cases where an absorption transition is not detected, we measure a 2- upper limit to the rest-frame absorption equivalent width over a spectral window that corresponds to the median line width (FWHM) of individual, observed components of the targeted transition from the full sample. For galaxies without associated  absorption, the upper limits of the underlying  and  absorption strengths are estimated at the systemic redshifts of the galaxies. For galaxies with associated  absorption but no detectable  features, the upper limits of the underlying  absorption strengths are estimated at the systemic velocities of the  absorbers which are the velocity centroids of the strongest components determined by the fitting routine described below.

To measure the line widths and velocity centroids of each detected absorber, we model the observed absorption profile as a collection of individual Gaussian components and consider only the minimum number of components necessary to fully describe the observed absorption features. The fitting routine returns for each component the velocity centroid, the 1- line width, and the maximum absorption depth. Considering all the individual  components observed in 125 galaxies, we measure a median component line width of km s. Considering all the individual  components observed in nine galaxies, we measure a median component line width of km s. We note that the observed median line widths are significantly larger than the line width expected of thermal broadening in a warm gas of K, which is km s for  absorbing gas. The observed line widths are therefore likely driven by the gas dynamics in galactic halos.

We present in Figure 6 the relative velocity distribution of  and  absorbers with respect to the systemic redshifts of the galaxies. Here we also adopt the velocity centroid of the strongest component found in each absorber as the systemic velocity of the absorber. The left panel of Figure 6 shows that the velocity distribution of  absorbing gas around galaxies is best represented by a double Gaussian profile with a narrow component centered at km s and dispersion of km s and a broad component centered at km s and dispersion of km s (the solid curve). Excluding the outlier at km s, the velocity distribution of  absorbing gas around galaxies can be characterized by a single Gaussian distribution of km s and km s (right panel of Figure 6).

However, we note that the sample size of  absorbing galaxies is small. It is possible that the difference seen between  and  absorbing gas in Figure 6 is driven by sampling uncertainties. To test this possibility, we randomly generated a large number of subsamples of nine  absorbers from the parent sample of 125  absorbers, and performed a Kolmogorov–Smirnov (KS) test to compare each subsample of  absorbers with the full sample of  absorbers. Roughly 1/3 of the time, the KS test gives % chance that the two samples are drawn from the same underlying parent population. Whether or not  and  absorbers share the same origin remains to be tested with a larger sample of  absorbing galaxies.

Considering the  distribution alone, we find that that the broad component is dominated by galaxies at kpc (red open histogram in the left panel Figure 6). We therefore hypothosize two different origins of the detected  absorbers: (1) halo gas associated with the galaxies contributing primarily to the narrow Gaussian distribution component and (2) intergalactic gas associated with correlated large-scale filaments dominating the broad wings. We suggest that if larger samples of CIV absorbers were found to lack a broad velocity component, that would further support this scenario.

We also repeat the search for C II , Si II , Si III , and Si IV  absorption features associated with these galaxies. The observed median line width for C II absorbing gas is km s, while the observed median line widths for silicon ions are , and 47 km s for Si II, Si III, and Si IV, respectively. We therefore adopt these velocity intervals for measuring 2- upper limits for respective ionic transitions444The velocity window adopted here for measuring upper limits of non-detections is empirically determined based on detected components, and is on average times smaller than the velocity window adopted by Werk et al. (2013) for determining their upper limits. As a result, the reported upper limits in Werk et al. (2013) are roughly 3 times higher than what we determine here.. The observed absorption properties of the gaseous halos around individual galaxies are summarized in Table 4, which we list for each galaxy the angular separation from the QSO sightline, the projected proper distance , redshift , the redshift of the associated  absorber if detected, the measured rest-frame absorption equivalent widths or 2- upper limits of different transitions.

4.2 Absorption Properties of Individual Galactic Halos

To examine the relation between the incidence and strength of CGM absorption features and galaxy properties, we present in Figure 7 the observed distribution of rest-frame absorption equivalent widths of , C II, and  versus projected distance of the associated galaxy for all galaxies in our galaxy sample. The results can be summarized as follows.

First, robust constraints in  absorption can be determined for 168 galaxies (solid points in the upper-left panel of Figure 7), 43 of which do not have a detectable  absorption feature to a sensitive upper limit (grey, solid points with arrows). All 12 galaxies at kpc exhibit a corresponding  absorber, leading to a 100% mean covering fraction of H I absorbing gas within 100 kpc of star-forming regions. Beyond kpc, the incidence of  absorption remains high with only 43 of 156 galaxies showing no corresponding  absorption features of Å, leading to a mean gas covering fraction of % over the projected distance interval of kpc from galaxies. In addition, the observed mean  absorption strength gradually declines with increasing , consistent with the mean relation reported by Chen et al. (1998, 2001a; solid line). For comparisons, we include measurements and upper limits for galaxies at from the COS-Halos program (Werk et al. 2013; open squares) and for starburst galaxies at from Steidel et al. (2010; green stars).

Second, robust constraints in C II absorption can be determined for 141 galaxies (solid points in the middle-left panel of Figure 7), 134 of which do not have a detectable C II absorption feature to a sensitive upper limit (grey, solid points with arrows). Three of the four galaxies at kpc exhibit associated C II absorption and none of the eight galaxies at kpc show a corresponding C II absorber of Å. This leads to a mean covering fraction of % in C II absorbing gas at kpc of star-forming regions and 25% at kpc. Beyond kpc, we detect C II absorption near four additional galaxies at , and 225 kpc, and the remaining galaxies do not show associated C II absorber to 2- upper limits of better than Å. The lack of observed C II absorption leads to a strong constraint on the mean C II absorbing-gas covering fraction of % over the projected distance interval of kpc from galaxies. Likewise, we include measurements and upper limits for galaxies at from the COS-Halos program (Werk et al. 2013; open squares) and for starburst galaxies at from Steidel et al. (2010; star symbols) for comparisons.

A possible explanation for a substantially lower incidence of C II absorption at kpc is an increased ionizing radiation field that offsets a larger fraction of carbon atoms into higher ionization states. We examine the incidence of  absorption features in the bottom-left panel of Figure 7, where we show that robust constraints in  absorption can be determined for 160 galaxies (solid points) and 151 of these do not have a detectable C IV absorption feature to a sensitive upper limit (grey, solid points with arrows). Of the 12 galaxies at kpc, four show a corresponding  absorber, leading to a mean covering fraction of % in  absorbing gas within 100 kpc of star-forming regions. Beyond kpc, five galaxies shows associated  absorption and the rest do not show corresponding  absorption of Å, leading to a mean  absorbing-gas covering fraction of % over the projected distance interval of kpc from galaxies. For comparisons, we include measurements and upper limits for galaxies at from (Chen et al. 2001b; open triangles) and for starburst galaxies at from Steidel et al. (2010; pluses). Note that the C IV doublets were not resolved in the stacked spectra of Steidel et al. (2010). We therefore display a possible range of  based on two extremes in the assumed line ratio (e.g. 2:1 or 1:1) between the C IV  and C IV  members.

Figure 7: Observed spatial distribution of rest-frame absorption equivalent widths of  (top), C II (middle), and C IV (bottom) in the circumgalactic space. The left panels show the variation of absorber strengths versus projected distance , while the right panels show the spatial variation as a function of halo-radius () normalized projected distance, . Galaxies with no detectable absorption are shown as 2- upper limits (points with downward arrows) that are determined based on the noise characteristics (see § 4.1). Measurements from our study are shown in solid points. Measurements for galaxies at from the COS-Halos program (Werk et al. 2013) are shown in open squares. For starburst galaxies at (Steidel et al. 2010), constraints on  and C II absorption are shown in star symbols. But because C IV doublets were not resolved in this study, a range of  is shown in vertical bars based on assumed doublet ratios of 2:1 and 1:1. The measurements at are from stacked spectra of galaxies covering a range in stellar mass (Reddy et al. 2012). Previous measurements of  absorption in the low-redshift CGM from Chen et al. (2001b) are shown in triangles. The best-fit power-law model of Chen et al. (1998, 2001a) to describe the observed versus anti-correlation is shown in solid line. Finally, mean absorption strengths determined from stacked CGM spectra of the full sample (§ 4.4) are shown in (blue) pentagons with the horizontal bars indicating the bin size.
Figure 8: Similar to Figure 6 but for the observed spatial distribution of rest-frame absorption equivalent widths of Si II (top), Si III (middle), and Si IV (bottom) in the circumgalactic space. Note that the constraints for non-detections in the COS-Halos sample appear to be worse than our typical upper limits, because the COS-Halos team adopted a much larger velocity window for measuring their upper limits (i.e.  km s adopted for the COS-Halos galaxies versus km s adopted in our study. The velocity window adopted in our study is empirically determined based on detected components, and is therefore more appropriate for constraining the presence/absence of cool, photo-ionized clouds in the circumgalactic space.

The QSO spectra also allow us to examine the spatial distribution of silicon ions in the CGM. Figure 8 displays the observed absorption strength of Si II , Si III , and Si IV  versus projected distance of the associated galaxy for all galaxies in our sample. We find that the Si II  transition appears to be contaminated for 37 galaxies, and that only three of the remaining 158 galaxies shows associated Si II absorption at , and 138 kpc. (upper-left panel of Figure 8). With the exception of one galaxy at kpc, for which no sensitive limit can be placed due to the poor quality of the data, none of the other 154 galaxies show associated Si II absorption to sensitive limits better than 0.06 Å. In addition, the Si III  transition appears to be contaminated for 62 galaxies, and eight of the remaining 135 galaxies show associated Si III absorption. Of the 10 galaxies at kpc for which constraints for Si III absorption can be obtained, four exhibit associated Si III absorption, leading to a mean Si III covering fraction of % (middle-left panel of Figure 8). At kpc, four of the 125 galaxies exhibit associated Si III, leading to a mean covering fraction of %. Finally, robust constraints in the Si IV  absorption can be determined for 150 galaxies, seven of these exhibit associated Si IV absorption with four of the detections found at kpc (bottom-left panel of Figure 8). None of the other 143 galaxies show associated Si IV absorption to sensitive limits better than 0.07 Å.

The left panels of Figures 7 & 8 display a stark contrast between the spatial distributions of hydrogen atoms and heavy elements. While hydrogen gas is observed all the way out to 500 kpc in projected distance, the same galaxies that display moderately strong H I absorption do not exhibit associated heavy elements at kpc. The lack of heavy elements at large distances persists through all ionization states examined in our study, from low-ionization species such as C and Si ions to high-ionization species such as C and Si ions. It indicates that if heavy ions are present in the outer halos, then they remain in a tenuous, hot phase in which gaseous clumps giving rise to the observed absorption lines cannot survive. Similar to Figure 7, we include previous measurements and upper limits for galaxies at from the COS-Halos program (Werk et al. 2013; open squares) and for starburst galaxies at from Steidel et al. (2010; star symbols) for comparisons.

4.3 Mass Scaling Of Extended Gaseous Halos

In addition to the distinct spatial extent between hydrogen gas and heavy ions, the left panels of Figure 7 & 8 also display significant scatter in the versus space. In particular, different galaxy samples appear to segregate in different parts of the - parameter space. Both the starburst galaxy sample and the COS-Halos sample contain primarily galaxies at kpc, which exhibit on average stronger absorption in  and in ionic transitions. Such distinction appears particularly strong in C II and Si II absorption strengths.

Recall that our galaxies span a broad range of stellar mass with 50% of the sample characterized as low-mass dwarf galaxies of , while the COS-Halos galaxies are primarily galaxies (Werk et al. 2013) and the starburst sample from Steidel et al. (2010) has a median stellar mass that lies between the COS-Halos and our samples (e.g. Reddy et al. 2012; see also Figure 3). It has been shown empirically at low redshifts that more massive galaxies on average possess more extended gaseous halos (e.g. Chen et al. 2010b). This is also expected by theoretical models (e.g. Mo & Miralda-Escudé 1996; Maller & Bullock 2004; Ford et al. 2013b). As a first step toward establishing a clear understanding of the processes that drive the observed CGM properties, it is therefore necessary to investigate whether the apparent distinction in the observed gaseous extent of different galaxy samples can be explained by the intrinsic size differences of individual galactic halos. The results will facilitate future studies that consider the effect of additional processes such as star formation feedback.

To address the possible mass-scaling of gaseous radius, we first estimate the dark matter halo mass for each galaxy based on its known stellar mass from the NASA-Sloan Atlas and the stellar mass-halo mass relation of Kravtsov et al. (2014) at . We then compute the halo radius , following the prescription of Bryan & Norman (1998)

(2)

where is the mean matter density of the Universe at , represents the overdensity over which a halo is defined, and with . The halo radius is then computed according to

(3)

Lastly, we divide the projected distance of each galaxy by its halo radius and examine how the observed absorption strengths of different transitions vary with -normalized projected distance, . The results are shown in the right panels of Figures 7 & 8.

Figure 9: Stacked QSOs spectra in different -normalized projected distance intervals from host galaxies. Galaxies at are grouped into three bins following the binning of the high-redshift starburst sample. Galaxies at are divided into two bins with roughly equal number of galaxies. The median -normalized projected distance and the number of galaxies included in each stack are indicated in each panel. The stacked spectra clearly show declining  absorption strengths with increasing projected distance, and no ionic transitions are detected with .

For comparison, we also calculate the halo radius for each COS-Halos galaxy using the published from Werk et al. (2013), normalize the galaxy projected distance by the corresponding , and include their absorption measurements in the -normalized panels. In addition, we adopt the median halo mass of for the starburst galaxies at from Reddy et al. (2012). Using a stellar mass-halo mass relation appropriate for high-redshift galaxies from Behroozi et al. (2013), we estimate a mean halo mass of and a mean halo radius of kpc555The inferred halo mass is a factor of two less than what is estimated by Steidel et al. (2010) or by Trainor & Steidel (2012) based on the observed galaxy clustering amplitude. For consistency, we adopt the halo mass estimate based on the stellar mass to halo mass relation.. Because the dispersion in as a result of dispersion in of the starburst sample is much less that the bin size adopted for , we normalize their mean projected distance by a single mean halo radius and include their measurements in the right panels of Figures 7 & 8. We cannot include the earlier  measurements of Chen et al. (2001b) because the mass of each galaxy is unknown.

After accounting for a possible mass scaling of gaseous radius, we note three important features in the right panels of Figures 7 & 8. First, the QSOs in our pair sample probe regions as close as in galactic halos to outside of galactic halos. While  absorbers are frequently observed at projected distances much beyond , no ionic transitions are found at these large radii. The few detections at kpc turn out to be associated with most massive galaxies in the sample and the QSO sightlines appear to still probe the inner halos of these galaxies. The large sample allows us for the first time to place stringent limits on the possible presence of heavy elements beyond galactic halos. We place a strict upper limit of 3% (at a 95% confidence level) on the incidence of Å metal-line absorbers over the range of projected distances from to (see § 4.5 and Figure 11 below).

Second, the COS-Halos sample probes the metal-enriched CGM over the projected distance range from to . Recall that the median mass of the COS-Halos sample at is (Werk et al. 2013), while our galaxy sample spans a broad range in stellar mass with a median . Therefore, the COS-Halos sample probes primarily the inner halos of massive galaxies and our galaxy sample extends to outer halos of lower- and high-mass galaxies. The observed absorption strengths versus -normalized projected distance from the COS-Halos observations now connect smoothly with the measurements for our sample. These include H I, C II, Si II, Si III, and Si IV. The on average stronger absorbers found around COS-Halos galaxies can therefore be explained by higher gas density in the inner halos, at least around massive galaxies. Considering our sample with the COS-Halos sample together shows that both the absorption strengths and incidence (covering fraction) of heavy elements decline steeply beyond and no heavy ions are detected beyond .

Finally, the starburst galaxy sample probes the metal-enriched CGM at over the projected distance range from to . The mean absorption strength of the metal-enriched CGM around starburst galaxies at is found to decline rapidly at beyond . In addition, the observed mean absorber strengths at a fixed remain to be stronger around these starburst galaxies than what is observed around either low-mass dwarf or high-mass galaxies at . The differential observed absorption strength versus -normalized projected distance between low- and high-redshift galaxy samples suggests for the first time that the spatial absorption profile of the CGM may have evolved since (cf. Chen 2012). However, a direct comparison between the low- and high-redshift measurements is difficult because the high-redshift measurements were made in stacked spectra which presumably includes detections and non-detections among galaxies with a broad mass range (Table 3), and there was no distinction made between independent and group galaxies. An additional uncertainty also arises due to uncertainties in halo models (Diemer et al. 2013; see further discussions in § 5.3).

4.4 Mean Absorption Profiles from Stacked CGM Spectra

Figure 10: Mean absorption profiles of  (left) and  (right) in stacked absorption spectra of galaxies in different intervals.

To further improve upon the sensitivity in searching for weak absorption features and to facilitate a more direct comparison between our study and that of Steidel et al. (2010), we experiment with co-adding the absorption spectra of individual galaxies in the rest frame. We note, however, that interpreting the comparisons between low- and high-redshift measurements is not trivial (see § 5.3 for discussion).

For each input spectrum, we first mask contaminating features due to either the Milky Way interstellar medium or other strong absorbers at redshifts different from the foreground galaxy. Then each continuum normalized QSO spectrum and its associated error spectrum are shifted to the rest frame of the foreground galaxy. To account for the velocity offset between a galaxy and its associated absorbing gas (Figure 6), the rest frame of each galaxy is set to be the redshift of the observed  absorber666We have also experimented with adopting the systemic redshift of the galaxies as the rest frame. No significant changes are seen.. For galaxies with no detected  absorbers, the rest frame is set to be the systemic redshift of the galaxy. Individual rest-frame spectra are then weighted and stacked to form a final mean spectrum. The weighting factor of each spectrum is defined as the inverse median variance which is determined using the associated error spectrum over the wavelength range from 1100 Å to 1450 Å in G130M data and from 1390 Å to 1750 Å in G160M data (e.g. columns 5 and 6 in Table 2).

We form different stacked CGM spectra for galaxies grouped in different projected distance intervals, as well as in different -normalized projected distance intervals. Given that a large fraction of detected heavy ions occur at kpc (left panels of Figures 7 & 8), we have adopted the first bin in projected distances to include galaxies at kpc and divided the remaining galaxies into three projected distance intervals with roughly equal number () of galaxies. For -normalized measurements (right panels of Figures 7 & 8), we have adopted the same binning as the high-redshift starburst galaxy sample at and divided the rest of the galaxy sample into two bins with roughly equal number () of galaxies. The stacked CGM spectra for different -normalized distance intervals are presented in Figure 9.

In each stacked CGM spectrum, we measure mean absorption strengths of different transitions. However, uncertainty estimates of the observed mean absorption strengths in stacked spectra are complicated for two main reasons. First, Figures 7 and 8 show that in each and bin there is a combination of detections and non-detections. The mean properties of each stacked spectrum are therefore likely dominated by sampling errors. In addition, we have adopted an inverse-variance weighted mean to form each stacked spectrum. The final stacks may be dominated by one or two high sightlines. To assess these sampling errors, we employ a bootstrap resampling technique.

For each subsample, we randomly sample the galaxies with replacement to construct a new subsample that contains the same number of input galaxies for stacking. We then measure the mean absorption equivalent width or a 2- upper limit if no absorption features are found in the new stack. We repeat this exercise times and examine the distribution of the resulting mean absorption measurements. We find that a convergence is reached in the distribution when . We adopt the 1- dispersion from the bootstrap resampling distribution as the uncertainties in the observed mean absorption in stacked spectra. In the case of non-detections, we quote the 95% upper bound of the distribution as the 2- upper limit to the underlying absorption strength. The measurements and associated uncertainty estimates, as well as upper limits for non-detections are included in Figures 7 and 8 as solid blue points. The results are also summarized in Tables 5 and 6, which record for each distance interval the range of projected distance (or ), median projected distance (or ), the number of galaxies included in the stack, and the mean absorption strengths in , Si III, Si II, Si IV, C II, and C IV. Both Tables 5 & 6 and Figure 9 confirm that with higher in the stacked spectra the mean  absorption strength declines steadily with increasing projected distance, while no heavy ions are detected at 95% upper limits of Å at .

The strong upper limits presented in Tables 5 and 6 for non-detections demonstrate that using stacked spectra we are indeed able to improve the constraints for the presence/absence of absorbing gas by . No ionic transitions are found outside of galactic halos to unprecedentedly sensitive limits of better than Å at the 2- level of significance. In addition, comparing the absorption-line measurements made in stacked CGM spectra confirms that massive starburst galaxies at (green symbols in the right panels of Figures 7 & 8) exhibit significantly stronger mean CGM absorption than the present-day galaxies (solid blue points). The differences are most pronounced in low-ionization species traced by C II and Si II absorption features. This is in stark contrast to the comparable mean absorption strengths of Mg II absorbers found at fixed luminosity-normalized projected distances (Chen 2012). The discrepancy is less for higher ionization species such as Si IV and C IV. Most interestingly, while we observe strong differential mean absorption strengths in different ionization states, such as between Si II and Si IV and between C II and C IV, the mean absorption strengths of different ions appear to be comparable at large distances from starburst galaxies at . The comparable strengths between low- and high-ionization transitions suggests that either the ionization condition in the high-redshift CGM is very different or the lines are saturated (in contrast to the non-saturated lines observed in our low-redshift sample) and therefore the line widths are driven by the underlying velocity field of the gas.

4.5 Gas Covering Fraction

Figure 11: Mean gas covering fraction  measured in each bin for different species. H I is shown in the left panel, Si II, Si III, and Si IV are shown in the middle panel, and C II and C IV are shown in the right panel. Gas covering fraction is computed for a detection threshold of Å. Error bars represent the 68% confidence interval. The covering fraction of  absorbing gas remains high at % outside of dark matter halos at , while the covering fraction of heavy ions is restricted to % in individual bins. Considering all galaxies at further improves the limit on the covering fraction of heavy ions to at a 95% confidence level. In inner halos (), we also find a declining mean covering fraction from high- to low-ionization species.

We have shown in § 4.4 that stacked CGM spectra enable strong limits on the possible presence of heavy elements outside of galactic halos, namely at projected distances . Within galactic halos, however, the observed mean absorption strength in a finite distance interval is the product of the spatial absorption profile and partial gas covering. Figures 7 and 8 show that not only does the absorption equivalent widths of individual absorbers decrease with increasing distance, but the fraction of detections also decreases with increasing distance. An independent measure of the gas covering fraction is therefore necessary for an accurate characterization of the spatial absorption profile of the CGM.

The large number of galaxies in our sample with sensitive limits available on the presence/absence of extended gas in individual galactic halos allows us to quantify how the covering fraction of absorbing gas varies as a function of projected distance based on an ensemble average. Here we consider galaxy subsamples defined in fixed intervals in order to obtain a global average of how the gas covering fraction depends on halo radius-normalized distance.

Following the prescription described in Chen et al. (2010a), we employ a maximum likelihood analysis to estimate for different species. First, the probability that a galaxy inside a dark matter halo of radius exhibits an absorber of rest-frame absorption equivalent width at projected distance is written as

(4)

where is the Heaviside step function with if and otherwise, and and together define the distance interval over which is calculated. The likelihood function of observing an ensemble of galaxies with associated absorbers of and galaxies with no absorbers detected to sensitive limits of can then be written as

(5)

Equation (5) is simply a binomial distribution function of a sample of objects, in which are detections, are non-detections, and  represents the mean probability of detecting an absorber that maximizes the likelihood . In the form of a likelihood function, we are able to determine the confidence level for the best fit . We evaluate  for Å by maximizing the likelihood function for different absorption transitions. Figures 7 and 8 show that the majority of the STIS and COS spectra included in our analysis all have sufficient to allow strong constraints for ruling out the presence of an absorber of Å for all transitions considered in our study. In addition, at this sensitive limit of Å, we are already probing tenuous gas of H I column density or chemically enriched CGM of C IV column density , assuming photo-ionized gas of K (e.g. Bokensenberg et al. 2003). Figure 11 shows the estimated  as a function of for different transitions. Error bars in  represent the 68% confidence interval. For non-detections, we present the 95% single-sided upper limit. The results are also summarized in Table 7.

Figure 11 clearly shows that the covering fraction of  remains high (%) outside of dark matter halos at , while the covering fraction of heavy ions is restricted to % in individual bins. Considering all galaxies at further improves the limit on the covering fraction of heavy ions to . At , low-ionization transitions display a rapidly declining covering fraction from % at to % and % at for C II and Si II, respectively. The high gas covering fraction at is consistent with measurements of % for C II and Si II from the COS-Halos sample which probes inner galactic halos at , and with Mg II observations at by Chen et al. (2010a). In contrast, the covering fraction of C IV declines from % at to % at . Combining previous results with our findings suggests that halo gas becomes progressively more ionized from to larger distances.

5 Discussion

Based on absorption spectroscopy carried out in the vicinities of 195 galaxies at , we have obtained strong constraints for the absorption properties of the CGM at low redshift. We observe distinct spatial absorption profiles between H I and heavy elements, with extended  absorbing gas found at distances far beyond the halo radius but no heavy ions detected at . Here we discuss the implications of our study.

5.1 Observed Absence of Heavy Elements at from Star-forming Regions

A particularly interesting finding from our absorption-line search is that while between 60% and 90% of the galaxies at show associated  absorbers in the QSO spectra, all but two of these  absorbers exhibit associated heavy ions to sensitive upper limits. The lack of detected heavy ions applies to both low-ionization species probed by the C II and Si II absorption transitions and high-ionization species probed by Si III, Si IV, and C IV. It implies that either the chemical enrichment in galactic halos has a finite edge at or gaseous clumps giving rise to the observed absorption lines cannot survive at these large distances.

In addition, the observed absence of heavy ions at is found around galaxies that span over four orders of magnitudes in (Figure 3). While the -normalized radial profile in principle accounts for the size-scaling between galaxies of different mass, it does not include possible variations of halo gas properties as a result of the star formation history of the galaxies. Specifically, star formation rate is known to correlate strongly with galaxy mass (e.g. Figure 4) and star formation feedback is expected to substantially alter the physical properties of halo gas (e.g. Agertz & Kravtsov 2014). At the same time, high-mass galaxies of are often found in quiescent mode with little on-going star formation (e.g. Muzzin et al. 2013), which would naturally result in a reduced absorption strength in halos around these massive galaxies (e.g. Gauthier et al. 2010).

To investigate possible variation in the -normalized radial absorption profile of the CGM, we divide the galaxy sample into low- and high-mass subsamples. Figure 12 shows the  absorption properties for low-mass galaxies of (filled and open squares) and high-mass galaxies of (filled and open circles), where (Baldry et al. 2012; Muzzin et al. 2013). Both low- and hig-mass galaxies exhibit a modest mean covering fraction of strong ( Å)  absorbers % at , and no associated  absorbers at . The sample is too small to make a strong distinction, beyond -normalization, in the extent of chemical enrichment between low- and high-mass halos in our sample.

Figure 12: -normalized radial profiles of  absorbing gas for low-mass galaxies of (filled and open squares) and high-mass galaxies of (filled and open circles), where (Baldry et al. 2012; Muzzin et al. 2013). Constraints from stacked spectra of the full sample are included for reference (pentagon points). Both low- and hig-mass galaxies exhibit a modest mean covering fraction of strong ( Å)  absorbing gas % at , and no associated  absorbers at . No significant distinction, beyond -normalization, can be made in the extent of chemical enrichment around low- and high-mass galaxies. In contrast, six of the 17 galaxies in the Borthakur et al. (2013) sample exhibit strong  absorption out to (star symbols). While the constraints for the 11 non-detections are weak, the detected  absorbers around six galaxies (four starburst and two passive galaxies) are all significantly stronger than the mean values observed in our sample.

A lack of heavy ions outside of the halos where dwarf galaxies reside provides important constraints for the amount of heavy elements that can escape these low-mass halos. Starburst driven outflows are thought to be particularly effective in removing baryons from low-mass halos because of a shallow potential well (e.g. Larson 1974; Martin 1999). Energetic outflows are also expected to suppress continuing growth of low-mass galaxies due to a reduced accretion rate (e.g. Scannapieco et al. 2001). These effects together can explain known scaling relations such as the mass-metallicity relation found in dwarf galaxies (e.g. Dekel & Woo 2003). However, model that predict enrichment levels to solar metallicity are inconsistent with the observed limits we obtain at from low-mass dwarf galaxies at . This places an important constraint on feedback models that would enrich the CGM to much higher metallicity at these distances.

Our finding of a lack of detected heavy elements beyond appears to be discrepant from the observations of Borthakur et al. (2013), who reported detections of strong  out to from massive galaxies of (star symbols in Figure 12). A possible explanation is to attribute the observed  absorbers to outflows driven by on-going star-formation activity, which indeed was part of the selection criterion of the Borthakur et al. sample. However, two of the galaxies with associated strong  absorbers are classified as quiescent galaxies with little on-going star formation since recent past.

An alternative scenario different from starburst driven outflows in explaining the presence of heavy elements at large distances is through gas stripping in an overdense group environment (e.g. Kawata & Mulchaey 2008; McCarthy et al. 2008). Such scenario can be tested with deep galaxy survey data of fields around these strong metal-line absorbers (e.g. Gauthier 2013).

To improve upon the detection limits of heavy ions in  absorbing gas, we repeat the stacking exercise discussed in § 4.4 but consider only galaxies at which exhibit associated  absorbers. The goal of this exercise is to investigate whether some constraints can be obtained on the chemical enrichment level in known gaseous clouds revealed by  absorption.

The absorption-line measurements and constraints in stacked spectra of  absorbers are summarized in Table 8. We divide the galaxies at into three subsamples, each covering different -normalized projected distance intervals. The goal is to maximize the of the stacked spectra, while searching for possible trend of chemical enrichment with distance. In this particular exercise, we also search for the presence of the N V  doublet features. Similar to the O VI absorption doublet, the N V doublet is seen in highly ionized gas and is covered in the STIS and COS FUV spectral range. Observations of the N V absorption doublet together with C IV and other low-ionization transitions, therefore, provides a measure of the ionization state of the gas (see for example Figure 32 of Thom & Chen 2008). The results of our search remains the same; namely no ionic transitions are detected in  absorbers at from galaxies in our sample. Adopting the absorption constraints for  and C IV from Table 8 and assuming typical Doppler parameters, km s (e.g. Tilton et al. 2012) and km s (e.g. Boksenberg et al. 2003), we infer a column density ratio of . In contrast, cosmological simulations that incorporate strong outflows to reproduce statistical properties of the general galaxy population in the low-redshift universe predict a column density ratio of at the virial radius of galactic halos of (Ford et al. 2013b). For photo-ionized gas, this column density ratio implies that the chemical enrichment level of  absorbing gas at cannot exceed 0.1 solar metallicity.

5.2 The Origin of a Chemical Enrichment Edge at

The distinct boundary between the presence and absence of metal-line absorbers at is seen in all ionic transitions that have been studied, including the observations of Si II, Si III, Si IV, C II, and C IV reported here and those of Mg II absorbers around galaxies (Chen et al. 2010a). It is, however, not clear whether such absorption boundary exists for highly ionized gas probed by the O VI absorption doublet. Existing observations are primarily limited to inner galactic halos at (e.g. Tumlinson et al. 2011, 2013). Other studies that extend to larger radii have only small samples of “isolated” galaxies (e.g. Chen & Mulchaey 2009; Prochaska et al. 2011) and therefore available constraints are uncertain (see Johnson et al. 2014, in preparation).

A natural explanation for the chemical enrichment edge at is the turn-around radius of starburst driven outflows, similar to a halo fountain phenomenon (cf. Bregman 1980). We note that as chemically-enriched outflowing material moves into low-density regions and mixes in with metal-poor gas, it is expected that the outflowing material would be diluted and the observed absorption strength would gradually decline. However, to produce the sharp downturn at would require a sharp decline in metallicity, which essentally indicates a finite edge of chemical enrichment and motivates the consideration of a turn-around radius of starburst driven outflows.

In this scenario, we can infer the launch speed as a function of launch radius of the outflows in individual halos. Adopting a Navarro-Frenk-White (NFW; Navarro et al. 1997) density profile for the underlying dark matter halos, we estimate the launch velocity at a launch radius following , where is the gravitational potential and is related to radius according to . For an NFW profile, is the scale radius and is the total mass enclosed within and is related to the halo mass according to .

For galaxies in halos of , which is typical of the mass range probed by our sample, we calculate a launch velocity of km s at kpc. For lower-mass galaxies in halos of , we find km s at kpc. For higher-mass galaxies in halos of , we find km s at kpc. Naturally, a larger launch speed is required in more massive halos in order to reach out to a larger distance. Because more massive galaxies on average are forming stars at a higher rate (e.g. Salim et al. 2007), it is conceivable to have a higher outflow speed from starburst driven winds in a more massive galaxy. With a larger sample, we will be able to examine whether/how the metal-line boundary depends on star formation activity.

An alternative explanation for the observed finite metal-line boundary at is the critical radius below which cool clouds can develop and stabilize in a multi-phase medium (e.g. Maller & Bullock 2004; McCourt et al. 2012). Specifically, McCourt et al. (2012) showed that hot halos can develop extended multiphase structures if the cooling time is comparable to or less than the dynamical time . Given that and , the ratio decreases rapidly with decreasing radius. While the details depend on the exact density profile of the hot halo, it is conceivable that such condition can be reached at .

Both the turn-around radius of starburst outflows and cooling radius of a hot halo can provide a physical explanation for the observed metal-line boundary. Because the former requires on-going star formation to provide the energy input, one can in principle distinguish between the two scenarios by examining whether or not the presence of a metal-line boundary depends on the star formation activity in the galaxies.

5.3 The CGM at Low and High Redshifts

When comparing a luminosity-normalized spatial extent of the CGM at different redshifts, Chen (2012) found that no distinctions can be made between low- and high-redshift galaxies that have dissimilar star formation histories. The adopted luminosity normalization was meant to account for a likely luminosity-size scaling relation commonly seen in optical disks (e.g. Cameron & Driver 2007). This approach was motivated by the expectation that the CGM is regulated by various complicated physical processes, including gravitational motion and star formation feedback. Normalizing the observed projected distance by the intrinsic luminosity offers a means of accounting for the intrinsic size differences of individual galactic halos, and represents the first step toward establishing a clear understanding of the processes that drive the observed CGM properties. The results will facilitate future studies that consider the effect of additional processes such as star formation feedback.

But while rest-frame -band luminosity () is a good proxy of mass as shown in Chen et al. (2010b), it is an indirect measure of galaxy mass. Our study presented here utilizes a sample of galaxies with known stellar masses and normalizes the observed extent of halo gas by the inferred dark matter halo radius under a simple spherical overdensity approximation (e.g. Maller & Bullock 2004).

The finding in § 4.3 is surprisingly very different from the finding of Chen (2012). Specifically, when accounting for a size-scaling based on halo mass (instead of rest-frame -band luminosity), high-redshift starburst galaxies exhibit both systematically stronger mean absorption strength at a fixed -normalized projected distance at and more extended chemically-enriched gas to than low-redshift galaxies. Furthermore, the differences in the mean absorption strengths of the low- and high-redshift CGM are most pronounced in low-ionization species traced by C II and Si II absorption lines, suggesting distinct ionization conditions between the CGM at and at high redshifts near starburst galaxies.

We note, however, that a fundamental difference between the low- and high-redshift measurements is the treatment of galaxies with close neighbors. In our study presented here, we have considered only “isolated” galaxies with no known close neighbors spectroscopically identified within 500 kpc in projected distance and km s in velocity separation. No such distinction was made in the high-redshift sample, and therefore the high-redshift CGM measurements include both isolated galaxies and those with neighbors. It has been suggested that galaxies in group environments display a more extended, chemically enrichment halo gas than galaxies in the field (e.g. Chen et al. 2010a; Bordoloi et al. 2011). At the same time, the overall cool gas content is also found suppressed in galaxy groups (e.g. Chynoweth et al. 2011). It is not clear that the more extended, strong CGM absorption around high-redshift starburst galaxies is due to a signigicant contribution of galaxies in group environments. A detailed study of the CGM in different group environments at low redshifts will be presented in a separate paper (Liang et al. 2014 in preparation).

In addition, Steidel et al. (2010) noted that the Si II absorption lines are saturated at kpc in the stacked low-resolution spectra. On the other hand, the ionic transitions observed in individual galaxies at low redshifts are not commonly saturated. Steidel et al. interpreted the observed declining absorption equivalent width (at least from to kpc) as likely due to a combination of decreasing line-of-sight velocity spread and decreasing covering fraction of the absorbing gas. In contrast, observations individual galaxies at low redshift indicate that the declining mean absorption equivalent width in stacked spectra is best explained by a declining gas covering fraction along with declining optical depth with increasing projected distance. Consequently, interpreting the observed difference between low- and hig-redshift observations becomes more complicated.

At kpc, however, Steidel et al. (2010) also pointed out that the ionic absorption lines appeared to become unsaturated around high-redshift starburst galaxies. For unsaturated lines in stacked spectra, the observed declining equivalent width is best explained by a declining gas covering fraction along with a declining optical depth, similar to the low-redshift observations. Comparisons between our means stacked spectra and those from Steidel et al. could therefore be made for observations at kpc.

Remaining caveats include redshift uncertainties. Individual spectra of these high-redshift galaxies are of low and low spectral resolution with km s. Random motions between galaxies and the absorbing gas (e.g. Figure 6) can smooth out the signal. Chen (2012) performed a simple Monte Carlo simulation to show that these uncertainties can result in an overall reduction of the absorption strength by %, increasing the discrepancy between low- and high-redshift samples. At the same time, uncertainties in sky subtraction of low spectra may also bias the continuum estimate that is difficult to assess. It is expected that these uncertainties can be resolved with absorption spectroscopy of background QSOs near individual starburst galaxies (e.g. Rudie et al. 2012; Turner et al. 2014).

Figure 13:  radial absorption profile normalized by the scale radius of the host dark matter halos (left) or by of the absorbing galaxies (right). The scale radius represents a characteristic radius where the dark matter density profile resembles an profile (Navarro et al. 1997). We also include in the left panel measurements from stacked spectra using the full galaxy sample (blue pentagons). In addition, the scaling coefficient of is not a best fit to the  data, but adopted from the best-fit coefficient of Mg II absorbers from Chen et al. (2010b). Nonetheless, the result already reveals a clear  enriched halo out to -normalized projected distance of kpc (consistent with the finding of -normalized  profile from Chen 2012). In both panels, the  radial absorption profiles at (solid points) and at (green crosses) appear to be better aligned than what is seen in the bottom right panel of Figure 7 & 8.

5.4 Uncertainties due to Pseudo-evolution of Halo Radius

We note, however, that a fundamental caveat in comparing -normalized CGM profiles at different redshifts is in how is calculated. Equations (2) and (3) outlines a commonly adopted approach to calculate halo mass and halo radius based on a spherical overdensity model. A dark matter halo is defined as a collapsed and virialized object with a mean enclosed density equal to times the mean background density at the redshift of interest. By this definition, however, as the universe expands, decreases. Consequently, both and would increase with time even for a static halo. Such pseudo-evolution of dark matter halos has been investigated by several groups, and a consistent finding in numerical simulations is that most halos of completed matter accretion by with little/no net growth in mass over the last seven billion years (e.g. Prada et al. 2006; Diemand et al. 2007; Diemer et al. 2013). Therefore, applying an normalization may impose a pseudo-evolution in the properties of galaxies residing in these low-mass halos.

Given the uncertainties in , we explore different scaling relations for an accurate comparison of the CGM absorption profiles in different epochs. In Figure 13, we present  radial absorption profile normalized by the scaled radius of the host dark matter halos (left panel) or by of the absorbing galaxies (right panel).

The scale radius represents a characteristic radius where the dark matter density profile resembles an profile (Navarro et al. 1997). The normalization is motivated by the understanding that when a halo stops accreting, the scaled radius remains constant while the halo mass and halo radius continue to increase as the universe expands and descrases. As a result, the halo concentration would also increase. Indeed, halo concentrations are found to increase rapidly for halos of at (e.g. Zhao et al. 2009).

To calculate , we adopt the mean - relation of Zhao et al. (2009), which parameterizes as a function of halo mass and redshift, . The left panel of Figure 13 shows that the -normalized  radial profile at declines rapidly at . This is consistent with observations of the sample that display a covering fraction of  absorbing gas at with % and no detections found beyond .

The agreement in the -normalized CGM absorption profiles at low and high redshifts is in stark contrast to the distinction seen in the -normalized CGM profiles presented in Figures 7 & 8. We note, however, an inherent uncertainty in as a result of the scatter in the mean - relation ( dex). Nonetheless, it underscores the fundamental difficulty in making direct comparisons of galaxies and their halo gas properties in two different epochs.

A pseudo-evolution in dark matter halo mass (and therefore halo radius ) has important implications beyond a constant CGM radial absorption profile. It would also suggest that chemical enrichment have reached out to the “edge” of the dark matter halo () or likely beyond, although a clear border for the observed metal-line absorbers outside of halo radius still implies a finite extent of chemical enrichment around galaxies. To quantify the extent of chemical enrichment, we will rely on numerical simulations as a guide for determining the physical size of the underlying dark matter halos of our galaxies. Such study is beyond the scope of this paper. We defer the analysis to a future paper (Liang et al. 2014, in preparation).

Given the uncertainty in and from dark matter halo models, we return to applying empirical properties of the galaxies for scaling halo gas properties. Instead of -band luminosity, however, we consider normalizing the projected distance of galaxies by stellar mass, . The right panel of Figure 13 shows the -normalized  radial profiles for the high- and low-redshift galaxy samples. We note that the adopted scaling coefficient of is not a best fit to the  data, but adopted from the best-fit coefficient of Mg II absorbers from Chen et al. (2010b). Nonetheless, the result already reveals a clear  enriched halo out to -normalized projected distance of kpc (in an excellent agreement with the finding of -normalized  profile from Chen 2012). Similar to the -normalized profiles in the left panel, the -normalized  radial absorption profiles at and at appear to be well aligned. With in mind the uncertainty in and the agreement in -normalized CGM radial profile, we therefore conclude that no strong evidence has been found to show a vastly different spatial distribution in the CGM absorption properties, despite a completely disparate star formation properties.

6 Summary

We have analyzed archival UV spectra of QSOs located at projected distance kpc from 195 independent galaxies in the foreground. The redshifts of the galaxies range from to with a median of , and the projected distances of the QSOs range from kpc to kpc with a median of kpc. The galaxy sample covers a broad range in stellar mass from to . The median and 1- dispersion of stellar masses in the sample are . The available UV spectra of the QSOs allow us to study the multiphase CGM based on observations of a suite of absorption features including , C II, C IV, Si II, Si III, and Si IV. Using this large QSO and galaxy pair sample, we have obtained strong constraints for the absorption properties of the CGM at . The results of our analysis are summarized as the following:

(1) We observe a stark contrast between the spatial distributions of hydrogen atoms and heavy elements. While hydrogen gas is observed all the way out to 500 kpc in projected distance with a mean covering fraction of %, the same galaxies that display moderately strong H I absorption exhibit few associated metal absorption lines at kpc. The lack of heavy elements at large distances persists through all ionization states included in the study, suggesting that either there exists a chemical enrichment edge at or gaseous clumps giving rise to the observed absorption lines cannot survive at these large distances.

(2) The distinction between chemically-enriched and metal-poor gas is further enhanced after accounting for a mass scaling of gaseous radius in galactic halos. We infer a halo mass and halo radius for each galaxy based on the known stellar mass , and find that no ionic transitions are detected at to sensitive upper limits of rest-frame absorption equivalent width Å or better. The observed absence of heavy elements at applies to both low-mass dwarfs and high-mass galaxies. Considering all galaxies at , we place a strict upper limit for the covering fraction of heavy elements of 3% (at a 95% confidence level) over the projected distance range from to .

(3) To further improve upon the sensitivity in searching for weak absorption features, we experiment with co-adding the absorption spectra of individual galaxies in the rest frame. Using stacked spectra we are indeed able to improve the constraints for the presence/absence of absorbing gas by factors of five to six. No ionic transitions are found at to unprecedentedly sensitive limits of Å or better at the 95% confidence level.

(4) Within the gaseous halo probed by our galaxy-QSO pair sample, we observe differential covering fraction between low- and high-ionization gas. The mean covering fractions of both low- and high-ionization absorbing gas remain high at % over the distance range of . At , the covering fractions of C II and Si III decline to %, while the covering fraction of  remains at %. Combining previously observed high covering fraction of low-ionization gas in inner halos () with our findings suggests that halo gas becomes progressively more ionized from to larger distances.

(5) Combining our study of outer gaseous halos of low- and high-mass galaxies with the observations of the inner halos around massive galaxies from the COS-Halos program establishes a consistent -normalized spatial absorption profile of the low-redshift CGM. Both the absorption strengths and incidence (covering fraction) of heavy elements decline steeply beyond and become vanishingly small beyond . In contrast, massive starburst galaxies at exhibit significantly stronger mean absorption than galaxies at . The differences are most pronounced in low-ionization species traced by C II and Si II absorption features, suggesting distinct ionization conditions between the CGM at low and high redshifts.

(6) We caution a potential pseudo-evolution in the CGM radial absorption profiles, when utilizing -normalized projected distances to account for the intrinsic size difference between galaxies of different halo mass. The commonly adopted spherical overdensity calculation for halo mass imposes a pseudo-evolution for static halos as the universe expands and the mean matter density decreases with time. Normalzing the observed CGM radial profile by the scale radius or by the stellar mass confirms the previous finding that no significant changes can be found between the CGM at and .

Acknowledgments

This work has benefited from valuable discussions with Benedikt Diemer, Jean-René Gauthier, Nick Gnedin, Sean Johnson, and Andrey Kravtsov. We thank Andrey Kravtsov for providing the relation during the preparation of this paper, Michael Blanton for referring us to the NASA-Sloan Atlas, and Alice Shapley and Naveen Reddy for providing a representative stellar mass distribution of the galaxy sample included in the study of Steidel et al. (2010). We also thank an annonymous referee for insightful comments that helped improve the presentation of the paper. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX13AC07G and by other grants and contracts.



Table 1: Summary of Galaxy Properties
Galaxy Name RA(J2000) Dec(J2000) (kpc)