Neutral Hydrogen in the z\sim 2.3 CGM

The Gaseous Environment of High-z Galaxies: Precision Measurements of Neutral Hydrogen in the Circumgalactic Medium of z ~ 2-3 Galaxies in the Keck Baryonic Structure Survey

Abstract

We present results from the Keck Baryonic Structure Survey (KBSS), a unique spectroscopic survey of the distant universe designed to explore the details of the connection between galaxies and intergalactic baryons within the same survey volumes, focusing particularly on scales from kpc to a few Mpc. The KBSS is optimized for the redshift range , combining S/N Keck/HIRES spectra of 15 of the brightest QSOs in the sky at with very densely sampled galaxy redshift surveys within a few arcmin of each QSO sightline. In this paper, we present quantitative results on the distribution, column density, kinematics, and absorber line widths of neutral hydrogen (H i) surrounding a subset of 886 KBSS star-forming galaxies with and with projected distances physical Mpc from a QSO sightline. Using Voigt profile decompositions of the full Ly forest region of all 15 QSO spectra, we compiled a catalog of individual absorbers in the redshift range of interest, with log(). These are used to measure H i absorption statistics near the redshifts of foreground galaxies as a function of projected galactocentric distance from the QSO sightline and for randomly chosen locations in the intergalactic medium (IGM) within the survey volume. We find that  and the multiplicity of velocity-associated H i components increase rapidly with decreasing galactocentric impact parameter and as the systemic redshift of the galaxy is approached. The strongest H i absorbers within physical kpc of galaxies have   orders of magnitude higher than those near random locations in the IGM. The circumgalactic zone of most significantly enhanced H i absorption is found within transverse distances of kpc and within km s of galaxy systemic redshifts. Taking this region as the defining bounds of the circumgalactic medium (CGM), nearly half of absorbers with log() 15.5 are found within the CGM of galaxies meeting our photometric selection criteria, while their CGM occupy only 1.5% of the cosmic volume. The spatial covering fraction, multiplicity of absorption components, and characteristic  remain significantly elevated to transverse distances of 2 physical Mpc from galaxies in our sample. Absorbers with   cm are tightly correlated with the positions of galaxies, while absorbers with lower  are correlated with galaxy positions only on Mpc scales. Redshift anisotropies on these larger scales indicate coherent infall toward galaxy locations, while on scales of physical kpc peculiar velocities of km s with respect to the galaxies are indicated. The median Doppler widths of individual absorbers within 1-3 of galaxies are larger by % than randomly chosen absorbers of the same , suggesting higher gas temperatures and/or increased turbulence likely caused by some combination of accretion shocks and galactic winds around galaxies with M M at .

Subject headings:
cosmology: observations — galaxies: high-redshift — galaxies: evolution — galaxies: formation — intergalactic medium — quasars: absorption lines

1. Introduction

Hydrogen, comprising three quarters of the baryonic mass of the universe, is the principal component of all luminous objects in the universe. It is the fuel source for stars and therefore for star formation. Thus, in order to understand the formation and evolution of galaxies, one must understand and be able to trace the inflow and outflow of this fuel.

There exist very poor observational constraints on the movement of baryons in and out of galaxies. At high redshift in star-forming systems, it has been argued that the outflow rate must be similar to the star-formation rate (Pettini et al. 2000) and that the inflow rate must be similar to the combined star-formation rate and outflow rate (Erb 2008; Finlator & Davé 2008).

Recently there has been a flurry in the theoretical literature predicting the prevalence of accretion of cold gas (log() K) onto high-z galaxies via filamentary “cold flows” (Birnboim & Dekel 2003; Kereš et al. 2005; Ocvirk et al. 2008; Brooks et al. 2009; Faucher-Giguère et al. 2011; van de Voort et al. 2011a, b). In this model, the baryons stream into galaxies along the filamentary structure of the cosmic web, accreting onto galaxies without experiencing virial shocks. A wide range of predictions has been made concerning the efficiency of the transport of this material into galaxy halos, as well as its role in fueling ongoing star formation (van de Voort et al. 2011b; Faucher-Giguère et al. 2011). Further, there may be substantial suppression of the cold accretion rate caused by galaxy-scale mass outflows, evidence for which is commonly observed in the spectra of high- star-forming systems (Pettini et al. 2001; Shapley et al. 2003; Adelberger et al. 2005a; Steidel et al. 2010). Mapping the gas distribution surrounding galaxies is critical to constraining these models (Faucher-Giguère & Kereš 2011; Fumagalli et al. 2011), and would be a significant step toward understanding and quantifying the exchange of baryons between the sites of galaxy formation and the nearby intergalactic medium (IGM).

There has been a large amount of recent theoretical examination of the nature of IGM absorbers and their relation to galaxies using simulations. Ly is believed to broadly trace the filamentary large-scale structure (Cen et al. 1994; Zhang et al. 1995; Miralda-Escudé et al. 1996; Hernquist et al. 1996; Rauch et al. 1997; Theuns et al. 1998; Davé et al. 1999; Schaye 2001) although there are indications (Barnes et al. 2011) that winds could blow spatially extended halos of gas which may have recently been observed both in absorption (Steidel et al. 2010) and in Ly emission (Steidel et al. 2011). There seems to be general agreement that galactic winds are responsible for metal absorbers in the IGM. Booth et al. (2010) suggest that mostly low mass (M M) galaxies must be responsible for the pollution, while Wiersma et al. (2010) suggest only half of the metals would originate from galaxies with M M. Wiersma et al. (2010) also studied the history of the ejection of these metals and found that half of the metals observed at redshift 2 were ejected during the time between . Using cosmological “zoom-in” simulations Shen et al. (2011) found a “Lyman Break”-type galaxy could distribute metals to 3 virial radii by . Simcoe (2011) recently considered this problem observationally, finding that indeed 50% of the metals observed in the IGM at were placed there since , i.e. in 1.3 Gyr. Oppenheimer & Davé (2008) and Oppenheimer et al. (2010) studied the fate of winds using cosmological simulations and found that while galactic winds are likely responsible for the metallic species seen in the IGM, much of the outflowing gas may be bound to galaxies and may fall back in. In their simulations the recycling timescale scaled inversely with mass because winds emanating from more massive galaxies experienced greater hydrodynamic drag due to the increased abundance of dense IGM surrounding them. Further, in these simulations the largest source of gaseous fuel for star formation after was recycled wind material.

To date, systematic attempts to jointly study high- galaxies and their intergalactic environs have been made by Adelberger et al. (2003, 2005a) (see also Crighton et al. 2011). These studies focused primarily on H i and C iv absorption in the spectra of background QSOs whose sightlines probed regions covered by Lyman break galaxy (LBG) surveys. This work allowed for a first glimpse of the distribution of diffuse gas surrounding forming galaxies at high redshift, and, perhaps more tantalizing, evidence for interactions between the IGM and galaxies during the epoch when galaxies are expected to be most active. Generally, Adelberger et al. (2003) and Adelberger et al. (2005a) found excess H i absorption out to hcomoving Mpc (cMpc) of galaxies [2 physical Mpc (pMpc) at using the cosmology adopted in this paper]. C iv systems were found to correlate strongly with the positions of galaxies suggesting a causal connection. Unfortunately, these papers could not consider physical properties of the gas such as its column density or temperature because the data were not of sufficiently high quality to perform Voigt profile analysis. As such these papers focused on the transmitted flux which could be applied to a wider range of data qualities.

In this work, we provide high-accuracy analysis of the spectral regions surrounding 886 high- star-forming galaxies as seen in absorption against the spectra of background hyper-luminous QSOs using data drawn from the Keck Baryonic Structure Survey (KBSS; Steidel et al, in prep). The KBSS was specifically designed to allow for the observation of gas absorption features surrounding high-redshift star-forming galaxies, providing unique insight into the IGM/galaxy interface at high redshift. The size and quality of the KBSS sample allow us to map the distribution and properties of gas near to individual star-forming galaxies with direct physical parameters such as the column density as opposed to proxies such as the equivalent width. This paper is the first in a series designed to study the physical properties of star-forming galaxies at high redshift using Voigt profile analysis of this data sample. The complementary analysis presented by Rakic et al. (2011b) describes the pixel statistics of the QSO spectra from the KBSS and the correlation of H i optical depth with the positions and redshifts of galaxies.

In §2 we discuss the galaxy and QSO data and present the Voigt profile analysis of the QSO spectra in §3. The distributions of H i absorbers as a function of velocity, impact parameter, and 3D distance are presented in §4. In §5 we consider the geometric distribution of the gas using the covering fraction and incidence of absorbers. §6 focuses on 2D “maps” of the absorber distribution around galaxies. In §7 we analyze the velocity widths of individual absorbers and their correlation with the proximity of galaxies. We discuss the results and their possible interpretation in §8 with a brief summary of the paper and our conclusions in §9.

Throughout this paper we assume a -CDM cosmology with km s Mpc, , and . All distances are expressed in physical (proper) units unless stated otherwise. We use the abbreviation pkpc and pMpc to indicate physical units, and ckpc or cMpc for co-moving units. At the mean redshift of the galaxy sample (), 300 pkpc is 210hpkpc (physical) or hckpc; the age of the universe is 2.9 Gyr, the look-back time is 10.9 Gyr, and 8.2 pkpc subtends one arcsecond on the sky.

2. Observations

The data presented in this paper are drawn from the Keck Baryonic Structure Survey (KBSS) and include a large sample of rest-UV (2188) and rest-optical (112) spectra of UV-color selected star-forming galaxies at . These galaxies were photometrically selected to lie in the foreground of one of 15 hyper-luminous QSOs in the redshift range for which we have obtained high-resolution, high signal-to-noise ratio (S/N) echelle spectra.

The redshift range of this survey has important significance in the history of the universe – it coincides with the peak of both universal star formation (see Reddy et al. 2008) and super-massive black hole growth (see Richards et al. 2006). Spectroscopic observations of star-forming galaxies during this epoch commonly exhibit signatures of strong outflowing winds (Pettini et al. 2001; Shapley et al. 2003; Adelberger et al. 2005a; Steidel et al. 2010). At the same time, the baryonic accretion rate onto galaxies is predicted to be near its peak at (e.g., van de Voort et al. 2011b; Faucher-Giguère et al. 2011; van de Voort et al. 2011a.) Thus, the signatures of galaxy formation within the IGM should be at their peak as well.

The redshift range offers a number of practical advantages as well: first, the rapidly-evolving  forest has thinned enough to allow measurements of individual H i systems and to enable the detection of important metallic transitions falling in the same range (notably, O vi , 1036); second, the astrophysics-rich rest-frame far-UV becomes accessible to large ground-based telescopes equipped with state-of-the-art optical spectrographs; third, the rest-frame optical spectrum is shifted into the atmospheric transmission windows in the near infrared, allowing for observations of a suite of diagnostic emission lines (H, H, [O ii] 3726,3729, [O iii]4363,4959,5007, and [S ii] 6717,6732) neatly packed into the J, H, and K bands.

Name RA Dec 16 17 range N18 S/N Ly19 S/N Ly 20
Q0100+130 (PHL957) 01:03:11.27 13:16:18.2 2.721 3133 2.0617– 2.6838  47  77 50
HS0105+1619 01:08:06.4 16:35:50.0 2.652 3230 2.1561– 2.6153  53 127 89
Q014209 (UM673a) 01:45:16.6 09:45:17.0 2.743 3097 2.0260– 2.7060  65  71 45
Q0207003 (UM402) 02:09:50.71 00:05:06.5 2.872 3227 2.1532– 2.8339  46  82 55
Q04491645 04:52:14.3 16:40:16.2 2.684 3151 2.0792– 2.6470  50  73 41
Q0821+3107 08:21:07.62 31:07:51.17 2.616 3239 2.1650– 2.5794  37  50 33
Q1009+29 (CSO 38) 10:11:55.60 29:41:41.7 2.65221 3186 2.1132– 2.6031  36  99 58
SBS1217+499 12:19:30.85 49:40:51.2 2.704 3098 2.0273– 2.6669  43  68 38
HS1442+2931 14:44:53.67 29:19:05.6 2.660 3152 2.0798– 2.6237  46  99 47
HS1549+1919 15:51:52.5 19:11:04.3 2.843 3165 2.0926– 2.8048  54 173 74
HS1603+3820 16:04:55.38 38:12:01.8 2.55122 3181 2.1087– 2.5066  37 108 58
Q1623+268 (KP77) 16:25:48.83 26:46:58.8 2.5353 3126 2.0544– 2.4999 13323  48 28
HS1700+64 17:01:00.6 64:12:09.4 2.751 3138 2.0668– 2.7138 11024  98 42
Q2206199 22:08:52.1 19:43:59.7 2.573 3084 2.0133– 2.5373  45  88 46
Q2343+125 23:46:28.30 12:48:57.8 2.5730 3160 2.0884– 2.5373  8425  71 45
Table 1KBSS Central QSOs and Foreground Galaxy Samples
Figure 1.— The redshift distribution of the 2188 galaxies in the full KBSS sample (dark shaded histogram) and of the subset of 886 galaxies used for the analysis in this paper (light shaded histogram), which are those with redshifts high enough that the corresponding wavelength of the  transition is observed in the relevant QSO spectrum, and with km s. The dark vertical line segments mark the redshifts of the 15 KBSS QSOs.
Figure 2.— The number of galaxies as a function of physical impact parameter  for the sample which has appropriate redshifts to be used in this work (light shaded histogram in Figure 1; see Table 1). The decline in the number of galaxies at   2 pMpc is due to the typical survey geometry of the KBSS fields as described in §4.2.1.

2.1. The Galaxy Sample

The KBSS galaxy sample, a subset of which is used in this paper (Figure 1), is described in detail by Steidel et al (2012); here we present a brief summary. Galaxies were selected for spectroscopy using their rest-frame UV colors (i.e., LBGs) according to the criteria outlined by Steidel et al. (2004) and Adelberger et al. (2004) for and by Steidel et al. (2003) for . In combination, these criteria have been devised to efficiently select star-forming galaxies over the redshift range . In total, the KBSS galaxy sample includes (5-10Å) rest-UV spectra of 2188 star-forming galaxies obtained at the W.M. Keck Observatory using the Keck 1 10m telescope and the blue arm of the Low Resolution Imaging Spectrometer (LRIS-B; Oke et al. 1995; Steidel et al. 2004.)

Most of the observations were conducted using a 400 lines mm grism (blazed at 3400 Å in first order) in combination with a dichroic beamsplitter sending all light shortward of Å into the blue channel, where the wavelength coverage for a typical slit location was  Å with a resolving power using 12 wide slits (Steidel et al. 2010). Some of the spectra were obtained using the d560 beamsplitter (beam divided near 5600 Å) together with a 600 lines mm grism (4000 Å blaze), typically covering  Å with a resolving power . Observations obtained after July 2007 made use of the Cassegrain Atmospheric Dispersion Corrector, thus minimizing the effects of differential atmospheric refraction over the spectral range of interest. Wavelength calibration was accomplished using Hg, Cd, Zn, and Ne lamps, with zero point corrections based on night sky emission lines on each individual exposure.26

The exposure times allocated to individual galaxies ranged from 1.5-7.5 hours depending on the number of separate masks containing the same target; typically galaxies were observed on either 1 or 2 masks, each mask receiving a total integration of 1.5 hours. Further details on the selection, observing strategy, and data reduction for KBSS galaxies are presented elsewhere (Steidel et al. 2010, Steidel et al. 2012).

The rest-UV spectra of LBGs are dominated by the continuum emission of O and B stars, over which are superposed numerous resonance absorption lines of metallic ions and H i. The H i  line at 1215.67 Å may be seen in emission or absorption (and often in both). The absorption features arise in cool interstellar gas in the foreground of the OB stars; they are most commonly observed to be blue-shifted by 100 – 800 km s with respect to the systemic velocity of the stars, as measured from either rest-frame optical nebular emission lines or stellar photospheric lines in stacked spectra (see Pettini et al. 2001; Shapley et al. 2003; Adelberger et al. 2005a; Steidel et al. 2010) or from the redshift-space symmetry of Ly absorption in the nearby IGM (Rakic et al. 2011a). Common lines observed include: O vi 1031,1036, Si ii , , Si ii+O i (blend),Si iii 1206, Si iv 1393,1402, N v 1238,1242, C ii 1334, C iii 977, and C iv 1548,1550. The profile of the Ly emission or absorption line is modulated by the optical depth of the material closest to the systemic velocity of the stars, which has been shown to correlate most significantly with the baryonic mass (Steidel et al. 2010) and the physical size (Law et al., in prep) of the galaxy.

The sample used in this study includes 886 galaxies within the redshift range where at minimum Ly and Ly are observed in the HIRES spectrum and with redshifts placing them at least 3000 km s blue-ward of the redshift of the QSO. The latter criterion was selected to avoid proximate systems that originate within material ejected from the QSO itself and/or the region affected by its ionizing radiation field.

A typical galaxy in the spectroscopic survey has a bolometric luminosity of L (Reddy et al. 2008, 2011), a star-formation rate (SFR) of M yr (Erb et al. 2006b), a stellar age of Gyr (Erb et al. 2006c), and a gas-phase metallicity of (Erb et al. 2006a). The galaxies inhabit dark matter halos of average mass M (Adelberger et al. 2005b; Conroy et al. 2008, Trainor & Steidel, in prep; Rakic et al, in prep) and average dynamical masses of M (Erb et al. 2006c) and generally exhibit dispersion-dominated kinematics (Law et al. 2009). The luminous parts of the galaxies are dominated by baryons, typically half stars and half cold gas (Shapley et al. 2005; Erb et al. 2006c), with half-light radii of pkpc (Law et al. 2011). The spectroscopic sample includes objects with apparent magnitudes , where is equivalent to m(6830 Å). At the mean redshift of the sample () the faint limit corresponds to a galaxy of 0.25L (Reddy & Steidel 2009).

The redshift distribution of the galaxy and QSO sample is presented in Figure 1, and the distribution of physical impact parameters, , between the galaxies and the QSO lines of sight is shown in Figure 2.

At present, 112 galaxies in the full KBSS sample have been observed spectroscopically in the near-IR using using NIRSPEC (McLean et al. 1998) on the Keck II telescope. 87 of these galaxies lie in our chosen redshift interval. The NIRSPEC target selection, data, and reductions are discussed in Erb et al. (2006b, c). The NIR redshifts, generally based on the H emission line, are estimated to be accurate to 60 km s or at .

2.2. Measured and Calibrated Redshifts

Because the most prominent features in the UV spectra of star forming galaxies are not at rest with respect to a galaxy’s systemic redshift, , corrections must be applied to avoid substantial systematic redshift errors. The velocity peak and centroid of the  emission line, when present, tend to be redshifted with respect to by several hundred km s, while the strong UV absorption features () tend to be similarly blue-shifted with respect to (Shapley et al. 2003; Adelberger et al. 2003; Steidel et al. 2010). These observations are generally interpreted as strong evidence for the presence of galaxy-scale outflows.

Here we adopt estimates of galaxy systemic redshifts () computed in the manner proposed by Adelberger et al. (2005a) and later updated by Steidel et al. (2010) and Rakic et al. (2011a). Adelberger et al. (2005a) and Steidel et al. (2010) analyzed the subset of the UV sample for which both rest-UV and rest-optical spectra had been obtained. They measured the average offset between redshifts defined by H emission versus  and to estimate average corrections. The H line traces the ionized gas in star-forming regions and is therefore a reasonable proxy for the systemic velocity of the stars, which are more difficult to measure due to the weakness of the UV photospheric absorption lines. Rakic et al. (2011a) used the QSO and galaxy data set presented here and calibrated velocity offsets appropriate for various classes of LBGs by insisting that the average IGM  absorption profiles should be symmetric with respect to galaxy redshifts. In both cases, the offsets represent those of the ensemble while in reality there is some scatter between individual objects even if their spectral morphology is similar. However, as we will demonstrate, the adopted must be generally quite accurate in order to produce the trends described below.

The formulae used for estimating from  and  measurements are reproduced below. For galaxies with H-based redshifts (87/886), we set . For galaxies which have measured   with or without the presence of  emission (691/886),

(1)

where

(2)

is the velocity shift needed to transform the observed redshift into its systemic value,  is the measured redshift from the centroids of interstellar absorption lines, and corresponds to the estimated systemic redshift of the galaxy.

For galaxies which have redshifts measured only from Ly in emission (90/886), we compute the redshift as

(3)

where

(4)

is the velocity shift needed to transform the observed redshift into its systemic value,  is the measured redshift from Ly, and is adopted systemic redshift.

For galaxies with measurements of both  and , we verify that . If the corrected absorption redshift is not bracketed by the two measured redshifts (18/886 galaxies)27, then we use the average of  and :

(5)

The residual redshift errors have a significant impact on our ability to interpret the kinematic information in the data; thus, their amplitude will be important to consider in the examination of the line-of-sight distribution of H i. Steidel et al. (2010) found this method generally corrects the redshifts to within km s of the systemic velocity.

2.3. QSO Observations

The 15 hyper-luminous () QSOs in the center of the KBSS fields (Table 1) were observed with the High Resolution Echelle Spectrometer (HIRES; Vogt et al. 1994) on the Keck I telescope. All available archival data for these 15 QSOs have been incorporated, including data taken with UVES (Dekker et al. 2000) on the VLT for Q2206-199 and Q2343+125. We obtained additional HIRES observations in order to reach a uniformly high S/N ratio over the spectral range of primary interest, Å. The final HIRES spectra have (FWHM km s), S/N per pixel, covering at least the wavelength range 3100 – 6000Å with no spectral gaps. The significant improvement in the UV/blue sensitivity of HIRES resulting from a detector upgrade in 2004 enabled us to observe Ly down to at least in all 15 KBSS sightlines, and to significantly lower redshifts in many (see Table 1.) The additional constraints provided by Ly (and in many cases, additional Lyman series transitions) allow for much more accurate measurements of H i for cm (see §3); this is particularly important since these column densities are typical of H i gas in the CGM at these redshifts (see §5).

The QSO spectra were reduced using T. Barlow’s MAKEE package which is specifically tailored to the reduction of HIRES data. The output from MAKEE is a wavelength-calibrated28 extracted spectrum of each echelle order, corrected for the echelle blaze function and transformed to vacuum, heliocentric wavelengths. The spectra were continuum-normalized in each spectral order using low-order spline interpolation, after which the normalized 2-D spectrograms were optimally combined into a single one-dimensional, continuum-normalized spectrum resampled at 2.8 km s per pixel.

Figure 3.— A demonstration of our treatment of the continuum surrounding damped-Ly systems. Top: In black, the continuum-normalized HIRES spectrum of Q2343+125 showing km s surrounding the DLA. The (red) dashed line corresponds to the Voigt profile of the DLA centered at with log() . Shown in the light (blue) curve is the error spectrum. Bottom: The HIRES spectrum of the same QSO with the DLA profile divided out. The new error spectrum accounting for the DLA profile division is shown by the light (blue) curve. The new continuum (with the DLA divided out) is shown in the dashed (red) curve.
Figure 4.— Example fits to the QSO data surrounding the redshifts of galaxies in our sample. Displayed in black are the continuum-normalized HIRES spectra showing the Lyman series transitions within 700 km s of the systemic redshift of 5 galaxies with redshifts as indicated. Over-plotted in color are Voigt profile decompositions for H i absorption systems within 700 km s of the galaxy redshift. Successive rows illustrate the fit to Ly, Ly, etc. Absorption in the HIRES spectra that does not appear in the colored fit corresponds to absorption from metallic species or from H i at a redshift far from that of the galaxy. Note that for all galaxies in our sample, the QSO spectra cover the Ly and Ly transitions near the galaxy redshifts, and for the higher-redshift galaxies, many more transitions in the Lyman series can be measured.

Three of the KBSS QSO spectra contain a damped Lyman (DLA) system ( cm), and three contain a sub-DLA ( cm). Special care must be taken in the continuum fit to the regions surrounding these systems, as the damping wings of the absorption lines extend for thousands of km s from line center. In these regions, we carefully fit a Voigt profile to the core of the absorber and adjusted the original continuum fit so that the Voigt profile produced a good fit to the damping wings, as shown in the top panel of Figure 3. The final Voigt profile fit is divided into the true spectrum, resulting in a new spectrum where the wings of the DLA have been removed, as illustrated in the bottom panel of Figure 3. The re-normalized spectrum can then be used to fit additional absorption systems superposed on the damping wings.

The redshifts of the QSOs are measured from rest-frame optical emission lines using lower-dispersion NIR spectra. The details of this procedure and the expected errors in the QSO redshifts are reported upon in Trainor & Steidel (2011, submitted). The precise QSO redshifts do not affect our analysis.

3. Analysis of QSO Absorption Spectra

The process of accurately measuring H i in the  forest of QSO spectra is complicated by the saturation of moderately strong absorbers and the blending of H i features with other H i or with lines of metallic species that happen to fall in the forest region.

Our analysis includes a full Voigt-profile decomposition of the Ly forest from the lowest redshift for which Ly is available in each spectrum up to   km s blue-ward of the QSO redshift; Table 1 shows the relevant redshift range used for each QSO in the sample. The cut-off at the high redshift end is to avoid H i systems which could be ejected from and/or ionized by the QSO itself; the low-redshift cut is necessary due to the high frequency of systems with cm that will be saturated in Ly29. For saturated systems, the fit to Ly is degenerate between an increase in column density or an increase in the width of the line, . The best way to resolve this degeneracy is to measure higher-order Lyman lines where decreasing oscillator strengths allow accurate  determination.

Simultaneous fits were made to as many Lyman lines as were both (1) available in the observed spectral range and (2) needed to measure an unsaturated and uncontaminated profile in the highest-order line. The exact number of higher-order Lyman lines used therefore depended upon both the redshift of the absorber and the degree of contamination in the spectral region containing the higher-order Lyman series absorption features. Higher-order lines, whether saturated or unsaturated, were used whenever doing so provided additional constraints on the overall fit.

Example Voigt profile fits to the H i absorption in regions surrounding the systemic redshift of five galaxies from our sample are shown in Figure 4. Note that for galaxies with redshifts significantly larger than , many higher-order Lyman transitions can be measured.

To facilitate the fitting of the Lyman forest, we developed a semi-automatic line-fitting code. Briefly described, the code works with km s sections of spectrum at a time30, fitting to Ly and as many higher-order lines as are accessible within the HIRES spectrum at the redshift of the H i systems being fit. The algorithm first searches for systems by cross correlating a template hydrogen absorption spectrum (i.e., a single non-saturated H i absorption component) with the HIRES spectrum. Peaks in the cross correlation are taken as initial estimates of the centroids of absorption lines. We fit Gaussians to these lines to estimate column densities and Doppler parameters. Residual absorption features (i.e., those inconsistent with ) in the Ly portion of the spectrum are assumed to be metal lines. Residual absorption in the higher-order Lyman series sections of the spectra are assumed to be lower-redshift H i systems. The fits begin with  at the high-redshift end of the range so that their higher-order Lyman absorption can be flagged as a known contaminant for fitting lower-redshift H i absorbers.

Once estimates of the locations, column densities, and Doppler parameters of all the absorption lines are complete, they are input into the minimization code VPFIT31 written by R.F. Carswell and J.K. Webb. VPFIT simultaneously fits all transitions of H i as well as the specified contaminating lines. The results are checked by eye, alterations made where the fit is inappropriate, and the process is repeated iteratively until a good fit (reduced ) is achieved. At this point, the multiple sections of spectrum are spliced together until a full fit to the forest is achieved.

It should be noted that the Voigt profile fit to a spectrum does not represent a unique solution. In this work, we fit each set of absorbers with the minimum number of components, adding additional components only when they significantly improve the . Median errors in  reported by VPFIT are 0.07 dex for absorbers with 13 ¡ log() ¡ 14 and 0.03 dex for absorbers with 14 ¡ log() ¡ 16; however in many cases the systematic errors will exceed these values. The largest source of error in our fits to low column-density systems is uncertainty in the continuum level; for high column-density absorbers, it is the possibility of unrecognized sub-component structure.

The complete decomposition of the Ly forest in these 15 lines of sight includes Voigt profile fits to distinct H i absorption systems with cm, making it the largest absorber catalog ever compiled at these redshifts. It increases by an order of magnitude the number of intermediate  absorbers measured with the additional constraint of higher-order Lyman lines.

4. Circumgalactic H i

Figure 5.— The velocity-space distribution of H i absorption systems with respect to the systemic redshift of galaxies, normalized by the number of galaxies in the sample. Absorbers with log() and within 1 pMpc of the sightline to a QSO are included. The solid histogram represents the distribution of H i around galaxies, whereas the hatched histogram represents the average absorber density near randomly-chosen redshifts drawn from our galaxy redshift distribution.

Figure 6.— As in Figure 5, where the histogram is -weighted as described in the text.

In the following sections, we discuss the statistics of individual H i absorption systems with respect to the redshifts and transverse positions of galaxies. We do not uniquely “assign” each absorber to a specific galaxy or vice versa. Instead we rely on comparisons between the absorption measured close to galaxies with that typical of “random” locations32 in the IGM. This allows us to quantify the significance of any apparent correlation with galaxies.

In principle, it would be preferable to compare absorbers found close to galaxies with those found in IGM locations known to be far from galaxies; however, because the galaxy sample is spectroscopically incomplete compared to our photometrically selected targets,33 we do not measure the redshifts of all galaxies in our survey volume. As a consequence, we do not know which locations in 3D space do not have a nearby galaxy. Thus, we can only compare locations near to galaxies with random locations in the IGM (irrespective of the positions of galaxies).

In order to reproduce the absorber distributions for a typical place in the IGM, we compiled a catalog of 15,000 random locations (in both redshift space and on the plane of the sky). The redshifts are drawn from the actual galaxy redshift list and therefore reproduce the typical IGM absorption associated with the redshift ranges covered by our galaxy sample. With each redshift, we also associate a randomly drawn QSO and an impact parameter to the QSO sightline from the real galaxy impact parameter list. We can then study the distribution of absorption systems around these 15,000 random locations and thereby understand how the presence of a galaxy alters the distributions.

Below we consider the distribution of H i surrounding galaxies: first along the line of sight, then on the plane of the sky, and finally as a function of 3D distance. These measurements are used to determine the relevant velocity and transverse scales of circumgalactic H i.

4.1. Velocity-Space Distribution of H i Near Galaxies

The properties of H i gas near galaxies in our sample can be quantified in several ways. First, we consider the line of sight velocity distribution of absorbers relative to the redshifts of galaxies. Shown in Figure 5 is the velocity distribution of all absorbers with cm within 1400 km s in redshift and 1 pMpc in projected distance from a galaxy. We define the velocity offset, , of an absorber,

(6)

where is the absorption system redshift and is the adopted systemic redshift of the galaxy from §2.2. With this definition, absorbers blue-shifted with respect to galaxies have negative .

Figure 7.— The median value of  as a function of the velocity offset of absorbers with respect to those galaxies with impact parameters 300 pkpc. Asterisks represent the median value of , dark vertical bars are the 1- dispersion in the median determined via the bootstrap method. The dark horizontal line is the median value of  in the random distribution. The light shaded boxes are the bootstrapped symmetric 1- dispersion in the median values of the samples drawn from the random distribution. The top x-axis shows the conversion between velocity offset and Hubble distance. See Equation 7 and §4.3 for further discussion.
Figure 8.—  as a function of  for absorbers with pkpc. The dashed (red) line marks the position of log() . The significance of this column density threshold is discussed in §5.
Figure 9.— The log column densities of the strongest  absorbers as a function of transverse distance. On the left we consider the max() statistic, log() of the single strongest absorber per galaxy with 700 km s. On the right is the sum() statistic, the log of the sum of the  of all the absorbers within 700 km s. Asterisks represent the median value of the considered statistic in a given bin of . Dark vertical bars are their dispersions. The horizontal position of the asterisks represent the median  of the galaxies in that bin. The number of galaxies in each bin is indicated at the bottom of the plot. The dark horizontal line is the median value drawn from the random distribution. The light shaded boxes are the bootstrapped symmetric 1- dispersion in the median values of the samples drawn from the random distribution. The bin size is 100 pkpc for absorbers with 1 pMpc and 200 pkpc for those with 1 pMpc. We increase in binning to reduce the shot noise in the bins at   2 pMpc which have fewer galaxies due to the limited field-of-view of LRIS.

We define ,) as the number of absorbers per galaxy at a given  and within the specified range of impact parameters . The solid histogram in Figure 5 represents the distribution of H i around galaxies, whereas the hatched histogram shows the average number of absorbers expected relative to randomly chosen redshifts, as described above. The number of absorbers is clearly higher near galaxies, with an excess peaking near (the galaxy systemic redshift) and confined to km s.

Figure 6 shows a similar pattern; in this case, each absorption system is weighted in proportion to log() such that high-column density systems contribute more significantly to the histogram. Each absorber with log() contributes [log() ] to the histogram, which is normalized by the number of galaxies considered. Taken together, Figures 5 and 6 indicate that there is an increase near galaxies of both the number and the column density of H i absorbers. The narrow peak of the  distribution has an apparent half-width of 300 km s, while the full excess extends to km s (most clearly shown in the right-hand panel of Figure 6).

As has been argued by Shapley et al. (2003); Adelberger et al. (2003); Steidel et al. (2010); Rakic et al. (2011a), these velocity distributions are also useful for checking our redshift calibration; their symmetry about km s is a sensitive probe of systematic errors in our galaxy systemic redshift calibration, while the width of the distribution provides an upper limit on the random errors.34 A Gaussian fit to Figure 5 yields a mean with a standard deviation of km s.

An alternative method of quantifying the column density dependence in Figure 6 is to examine the distribution of  as a function of . Figure 7 shows the median  as a function of  for all absorbers within pkpc of a galaxy35. The asterisks indicate the median value of  for each bin in velocity space. The dark vertical lines represent the dispersion in the median computed through the bootstrap method36. The value of the median column density across all velocity bins for the random distribution is shown as the dark horizontal bar; the light shaded contours are the 1- bootstrapped dispersions in the median of the random sample, where we consider samples of the same size as those from the real distribution. Note that there is an enhancement by a factor of in the median  out to   300 km s relative to galaxy redshifts. However, for   300 km s, the measurements are consistent with random places in the IGM.

Shown in Figure 8 are the individual measurement of  as a function of  for all absorbers within 1000 km s of a galaxy within pkpc of a QSO sightline. Notably, the higher- absorbers cluster strongly near the galaxy systemic redshift with a full width of km s.

In summary, Figures 5 8 clearly illustrate an enhancement in both the column density and number of absorption systems near the systemic velocities of galaxies. The most significant enhancement of column density is seen within 300 km s (Figure 7), but there is a higher number of absorbers out to at least 700 km s (Figures 5 and 6).

4.2. Transverse Distribution of Absorbers

In addition to the strong velocity alignment of absorption systems with the systemic redshift of nearby galaxies, there is also a significant increase in the column densities, , of individual absorbers with decreasing projected (or transverse) distance between the galaxy and the line of sight, . Here, we suppose that, as an ensemble, these galaxies show similar circumgalactic absorption signatures. Therefore, because galaxies fall at various discrete impact parameters from the QSO line of sight, we can combine the information from each galaxy to make a sparsely sampled map of the absorption as a function of  relative to the ensemble galaxy.

We introduce two related statistics designed to trace the change in column density as a function of . Recalling that km s encompassed the bulk of the “excess” absorption (§9), for each galaxy we define max(,700km s) to be the value of log() for the strongest absorber with 700 km s of the galaxy systemic redshift. The left panel of Figure 9 shows the median value of max(,700km s) as a function of impact parameter. A second statistic is the logarithm of the total , sum(), of all absorbers with 700 km s. The statistics of the median value of sum(,700km s) versus  is shown in the right-hand panel of Figure 9. Generally, the values of these two statistics are quite similar because the  in most velocity windows is dominated by the single highest- absorber. We consider the sum because it is most easily compared to results of numerical simulations, as it does not require the fitting of Voigt profiles to simulated data and can instead be compared to a simulation “collapsed” along the line of sight.

Figure 9 clearly demonstrates that both max() and sum() increase rapidly as one approaches a galaxy. In the bin corresponding to the smallest impact parameters, pkpc, the median value of max() is more than two orders of magnitude higher than that of a random location. Moving outwards, the median value decreases with increasing  to 300 pkpc, at which point the statistic “plateaus” and remains significantly higher than the random sample out to 2 pMpc. The plateau value in the galaxy-centric sample is max() cm, while that of the random distribution is max() cm. As we will discuss in §4.2.1, max() begins to decline for pMpc.

Figure 10.— Same as Figure 9 but for the maximum column density absorber within 300 km s. Changing the velocity interval considered with the max() statistic has little effect on the observed trends.
Figure 11.— The individual measured values of max(,300km s) for galaxies with pkpc.
Figure 12.— Ly absorption within 1000 km s of the systemic redshift of the 10 galaxies within 100 pkpc of the line of sight to the QSO. The HIRES data are in black, while the red shows our Voigt profile decomposition of the H i absorption near the redshift of the galaxy. The continuum and zero level of the spectrum are shown in dashed and dotted lines respectively. The systemic redshift of each galaxy is marked by the vertical dashed line at 0 km s. Note that the continuum is depressed in some of the spectral regions surrounding Q1442-BX333, Q1442-MD50, Q0100-BX210, and Q1442-MD84 by a DLA or sub-DLA near the galaxy redshift as described in §2.3.
Figure 13.— The max(,700km s) statistic as a function of impact parameter (different panels). The hatched histograms are the values for the random sample, the solid histograms are the values for the real sample. These histograms quantify the variation from galaxy to galaxy of the max() statistic at fixed impact parameter. P is the probability that the two max() sets were drawn from the same distribution. Notably, the last panel with the highest value of  has the least significant departure from the random distribution.

A relevant question concerns the dependence of these statistics on the size of the velocity window considered. In Figure 9 we considered the maximum column density absorber within km s of the systemic velocity of each galaxy. This corresponds to the full width of the velocity distribution shown in Figure 6. However, it is clear from Figures 6 and 7 that the majority of the excess strength of absorption falls within km s, especially for those systems with small impact parameters. Figure 10 shows max(,300km s); the trends are similar, though in the more restricted velocity window the peak on small scales is higher relative to random IGM locations–the median value in the first bin is 3 dex higher than the random redshift sample, and the extended floor of absorption is increased to at least .5 dex above the median of the random-redshift distribution. The more significant excess over random of the 300 km s version is primarily due to the exclusion of unrelated absorbers at large velocity separation; however, we note that at pkpc, the differential Hubble velocity associated with this distance along the line of sight is km s, meaning that for large  it may be more appropriate to adopt max(,700km s) as the relevant statistic. Regarding the sum statistic for the smaller velocity window (not shown), the value of the plateau and that of the random sample is dex higher for sum(,300 km s) than for max(,300 km s), similar to the variation in the statistics shown in Figure 9.

As we will argue in §5 and §8.1, the velocity and spatial scales of 300 km s and 300 kpc capture the most significant excess in both the column density and the number of absorbers near galaxies. In Figure 11 we provide the individual measurements max(, 300 km s) for all galaxies in the sample with pkpc. Note the large intrinsic scatter in max(), even at fixed impact parameter. For the 10 galaxies with the smallest impact parameters ( pkpc), the relevant portions of the QSO spectra within 1000 km s of Ly at are reproduced in Figure 12.

The large-scale distribution of H i

We now consider the larger-scale distribution H i around galaxies. Unfortunately, the sampling of galaxies with pMpc is comparatively poor in our sample due to the survey geometry of most of the KBSS fields (typically arcmin on the sky). This scale is imposed by the footprint of LRIS; with each field roughly centered on the bright QSO, the maximum observed impact parameter would be pMpc at . However, three out of 15 survey fields (see Table 1) were imaged with other instruments covering larger angular sizes and thus provide information on larger transverse scales. In Figures 9 and 10 we use wider bin sizes for absorbers with 1 pMpc in order to consider the large-scale distribution. This reduces the shot noise in the bins with 2 pMpc. Figures 9 and 10 demonstrate that max() remains higher than the global median value in the IGM (dark horizontal line) out to 2 pMpc, and then begins to decline. For larger , the data suggest column densities at or below that of random places in the IGM.

Again, considering the degree of scatter in max() at fixed impact parameter, Figure 13 shows max(,700km s) for various bins in , as indicated. The top row of panels correspond to pkpc, while the bottom two rows of panels consider larger impact parameters. Each panel shows the Kolmogorov-Smirnov probability that the two histograms are drawn from the same parent distribution. Notably, only the  pMpc bins have a distribution of max() consistent with the random sample.

Thus, we have shown that the column density of H i peaks sharply at the position of galaxies in the transverse direction, that the width of the peak is pkpc, and that there remains a significant excess of H i gas to pMpc. In §8 we discuss the implications of these results.

4.3. 3D Distribution of

The 3D distance, , is computed using the quadrature sum of the physical impact parameter () and the line-of-sight distance calculated assuming the velocity differences  are due entirely to the Hubble flow,

(7)

The 3D distance is therefore

(8)

where is given by

(9)

such that in our cosmology is

(10)

In this formalism, each absorber has a unique  with respect to a galaxy in the same field.

Figure 14.— The median column density of all absorption systems within 1400 km s of a galaxy as a function of the 3D distance between the absorber and the galaxy. The symbols have the same meaning as those in Figure 9. Note the steeply rising column densities at small  and that the median value remains above that of a random location (horizontal bar) out to 3 pMpc.

The 3D distance, due to its strong dependence on , requires that absorbers have both small  and very small values of  in order to populate bins at small values of . As a result,  has the effect of isolating those absorbers most likely to be associated with the galaxy without imposing a velocity cut.

Figure 14 shows that the median  stays above that of an average place in the universe out to   3 pMpc.37 The decline of  as a function of  is quite smooth, but again strongly peaked at the position of galaxies. The pixel analysis of the KBSS sample recently completed by Rakic et al. (2011b) studies in detail the 3D distribution of H i optical depths. There is excellent agreement between the optical depths measured in Rakic et al. (2011b) and the  trends shown in Figure 14. The smoothness of the decline is caused by the shifting of absorbers with small  and modest  into bins at larger . Thus, the signal appearing in the inner 300 pkpc in Figure 9 is distributed across a larger number of bins in  as a result of the velocity distribution of the absorbers.

The nature of the velocity width of the excess absorption will be discussed at length in §6; however, it should be noted that all measurements of  rely on the accuracy of the galaxy redshifts and in addition are affected by whatever peculiar velocities are present, whether due to random motion, inflows, or outflows.

4.4. Connection to Galaxy-Galaxy Pair Results

Steidel et al. (2010) presented a sample of 512 close angular pairs of galaxies with different redshifts (drawn primarily from the same KBSS catalogs used in the present paper), using the spectrum of the background galaxy to probe gas associated with that in the foreground. They were able to measure the strength of absorption from H i and several metallic species over a range in impact parameter pkpc. The principal advantage of this method is that it allows for probes at very small angular separation ()–obtaining statistical results for galaxies at such small separations from QSOs is difficult due both to the “glare” of the QSO and the relative rarity of QSO-galaxy pairs with very small separations (the smallest QSO sightline–galaxy separation is pkpc or ) . As such, the galaxy pair results are highly complementary to the QSO sightline study described in this paper.

Using background galaxies instead of QSOs results in two important differences between these studies: first, background galaxies have a projected “beam size” of 1 kpc at the location of the foreground galaxy, whereas background QSOs have a projected beam of order pc. As a result, the absorption seen against background galaxies measures a combination of the covering fraction of gas on kpc scales and the column density of absorbers. Further, background galaxies are faint and therefore only low-dispersion, low-S/N spectra can be obtained. Steidel et al. (2010) thus used stacks of background galaxy spectra shifted into the rest frame of the foreground galaxies to quantify the average absorption profile surrounding these galaxies. The lower-resolution spectra do not separate into individual components as would be found in individual QSO spectra. As such, the galaxy pair method allows for the measurement of equivalent widths () only. As discussed by Steidel et al. (2010) interpretation of is complicated by its sensitivity to the covering fraction and velocity extent of the absorbing material, and its relative insensitivity to ionic column density.

Steidel et al. (2010) measured of H i, C iv, C ii, Si iv, and Si ii in bins of impact parameter (). The large , particularly at pkpc, seemed to require high line-of-sight velocity spread in the gas– likely higher than could be easily explained by gravitationally-induced motions, but easily accounted for by the high velocities observed “down the barrel” in the spectra of LBGs, which typically reach km s for galaxies with properties similar to those in our sample.

Steidel et al. (2010) found that a simple geometric and kinematic model of outflows from LBGs could account simultaneously for the behavior of as a function of  as well as the shape of the blue-shifted line profiles of strong interstellar absorption features observed along direct sightlines to the same galaxies. The presence of detected C ii absorption to   pkpc was cited as evidence for a non-negligible covering fraction of H i gas having cm at such large galactocentric distances. Steidel et al. (2010) remarked that 90 kpc is very close to the expected virial radius  for LBGs similar to those in the current sample. Our max() statistic agrees well with this inference (Figure 9); in fact, we find a covering fraction % for absorbers with cm for – see § 5.2.

In addition, Steidel et al. (2010) used the same HIRES spectra as this work to show that the measured from the relevant portions of the high resolution spectra, averaged in the same way as the background galaxy spectra, are consistent with an extrapolation to   pkpc of the trend seen in the galaxy-galaxy pairs results; a similar conclusion was reached by Rakic et al. (2011b), also using equivalent width analysis of the QSO spectra, where a smooth trend was noted out to pMpc.

4.5. Comparison to previous studies at

Adelberger et al. (2003, 2005a) conducted the first systematic studies of high- galaxies and their surrounding IGM using sightline surveys of the IGM paired with large LBG surveys designed to probe galaxies in the same volume. Adelberger et al. (2003) analyzed the transmitted flux in the Ly forest of background QSOs, evaluated near the redshifts of survey galaxies. At the time, this was most easily accomplished using LBGs and background QSOs. These authors did not attempt Voigt profile decompositions (as in the present work) but focused on transmitted flux because it made for easier comparisons to theory and because the spectra covered the  transition only, making measurements of column density or optical depth difficult due to limited dynamic range for any cm. Based on 8 QSO sightlines covering , Adelberger et al. (2003) found that excess H i absorption (i.e., lower transmitted flux than the average IGM at the same redshift) was present within hcomoving Mpc (cMpc) of galaxies [1.7 physical Mpc (pMpc) at using the cosmology adopted in the present work], and an intriguing but not highly significant lack of H i very close to these galaxies (hcMpc or pkpc). C iv absorption was observed to be correlated with galaxy positions to out to 2.4hcMpc (or 800 physical kpc). The cross-correlation of C iv systems with LBGs was found to be similar to the LBG auto-correlation, suggesting that metal enriched IGM and galaxies shared the same volumes of space. The strongest C iv absorbers were so strongly correlated with LBG positions that the authors concluded that they must be causally connected to one another.

Figure 15.— The covering fraction, , of absorbers for various  thresholds (different panels) as a function of . The solid histogram represents the fraction of galaxies with an absorber of a given  or greater, within 300 km s. The hatched histogram represents  at random locations in the IGM; the horizontal dashed line marks  = 1 (100% covering). The bin size is 100 pkpc for absorbers with   1 pMpc and 200 pkpc for those with   1 pMpc.

Adelberger et al. (2005a) extended similar studies to , using a larger number of QSO sightlines and a wider range of QSO spectra for the analysis. Based once again on the transmitted flux statistics, the large-scale excess  near galaxies was consistent with the results of Adelberger et al. (2003), but the “turnover” of H i absorption on the smallest scales was not confirmed using the larger sample at somewhat lower redshift. Generally, the transmitted flux was decreasing with galactocentric distance, though it was still the case that % of the galaxies with the smallest impact parameters showed a lack of strong absorption, interpreted as evidence that the gas is clumpy. The results for C iv were extended, and it was shown that the correlation with galaxies grows increasingly strong as increases; the correlation length of cm absorption systems was similar to that of the autocorrelation length of the galaxies. The authors attempted to correlate the observed IGM properties with galaxy properties, but no significant correlations were found given the relatively small sample of galaxies at small impact parameters.

There is no overlap in the data sample used in this paper with that of Adelberger et al. (2003) which focused on higher-redshift galaxies and QSOs. Three of the fields (Q1623, HS1700, and Q2343) included in our analysis were also included in Adelberger et al. (2005a) which considered similar redshifts to this work; however, we have increased the S/N of the QSO spectra and also added many galaxy redshifts to our catalogs for these fields since the earlier analysis. The most surprising result of the Adelberger et al. (2003) sample, especially in light of the work presented here, was the reported deficit of absorption found within 0.5 cMpc or 170 pkpc of galaxies. Adelberger et al. (2005a), with a larger data set, found that 1/3 of galaxies had relatively-little H i absorption (consistent with the pixel statistics of our sample presented in Rakic et al. 2011b), but that the majority of galaxies were associated with significant absorption. In our sample, only 1/21 galaxies with 170 pkpc has a sum(, 300 km s) value less than the median of the random sample. As such we concur with the argument of Adelberger et al. (2005a) suggesting that the reported deficit was due to the small sample size presented. Further, we note that a measure of  shows that the majority of galaxies do have excess H i absorption in their surroundings.

On larger physical scales, Adelberger et al. (2003) and Crighton et al. (2011) considered the large-scale distribution of H i absorbers at while Adelberger et al. (2005a) studied that at . All found evidence for increased absorption to   5-6 cMpc or 2 pMpc. This scale is roughly consistent with our measurements of the 3D distribution of absorption presented in Figure 14, as well as with the trends in optical depth vs.  presented in Rakic et al. (2011b).

5. The Covering Fraction and Incidence of H i

Figure 16.— The incidence of H i absorbers, , as a function of impact parameter, . The solid histogram represents the mean number of absorbers per galaxy within 300 km s at the given distance, whereas the hatched histogram represents the average incidence of absorbers near randomly-chosen redshifts. The different panels show various ranges of . The bin size is 100 pkpc for absorbers with   1 pMpc and 200 pkpc for those with   1 pMpc. The incidence of absorbers exceeds the random distribution for   cm to   2 pMpc. Note that only absorbers with log() show strong association with the positions of galaxies. Table 2 gives the data values for  and P determined from these distributions.
log() range38 P P P
[cm] pMpc pMpc pMpc
13.0 13.5 1.1 0.3 -0.1 0.3 1.3 0.2 0.1 0.1 1.33 0.04 0.17 0.04
13.5 14.0 1.4 0.4 1.0 0.5 1.2 0.2 0.8 0.3 0.87 0.03 0.44 0.06
14.0 14.5 0.6 0.2 0.7 0.7 0.7 0.1 1.4 0.4 0.53 0.03 0.80 0.09
14.5 15.0 0.8 0.3 4.4 1.9 0.7 0.1 3.4 0.8 0.32 0.02 1.03 0.13
15.0 16.0 0.9 0.3 12.7 4.6 0.4 0.1 4.9 1.4 0.22 0.02 1.59 0.20
16.0 17.0 0.7 0.3 38.214.8 0.2 0.1 9.7 3.4 0.06 0.01 1.78 0.40
Table 2Absorber Incidence () and Excess Probability (P) for km s39

As discussed in §9, the scale of the strongest correlation between  and the positions of galaxies is found within 300 km s of . Adopting this value as the characteristic velocity scale for circumgalactic gas, we can examine other useful measures of the gas distribution around galaxies. The covering fraction () and the incidence of absorbers () are two ways of quantifying the geometry of the distribution as a function of both impact parameter and .

First, we define the covering fraction, (, N), as the fraction of galaxies in a bin of impact parameter, , that have an absorber within km s with   N. This is equivalent to the geometric fraction of the area of an annulus centered on the galaxy that is covered by gas with N and 300 km s. This quantity measures the variation within the sample of the decline of  as a function of .

A related quantity is the incidence of absorbers, , defined to be the number of absorbers per galaxy within a given range of  and , and with km s. Because this quantity can be greater than unity, it has larger dynamic range and so allows for a more-complete picture of the average multiplicity of absorbers at locations close to galaxies. Also, because we consider  in differential bins of , it can be used to measure the degree to which absorbers of a given  associate with galaxies.40

Figure 15 illustrates the dependence of  on  for various thresholds of  (different panels). Within 100 pkpc, even for cm. Also, every galaxy has an absorber with log() within 100 pkpc and km s. The distribution within 2.5 pMpc of lower- absorbers is relatively uniform, with 0.5. However, at larger threshold  (bottom three panels) we see that  is high () only within 200 pkpc. We will return to our measured values of  in §5.2 and §5.3 where we compare our measurements to those made at low- and also to results from numerical simulations.

Figure 16 shows the average incidence of absorbers, , as a function of distance, , and ranges of  (different panels). Notably, in all panels (i.e., at all columns densities) the average  is higher than random for 2 pMpc. For absorbers with cm (three bottom panels), there is a clear peak at small values of . No similar peak is present in the distributions of absorbers with cm (top panels). Clearly absorbers with 10 cm are more tightly correlated with the positions of galaxies than absorbers of lower column densities.

These distributions can also be used to determine the excess probability (over that of a random place in the IGM) of intersecting an absorber of a given column density, within a range of  and within some . The excess probability, P, is defined through comparison to the random distribution:

(11)

Table 2 summarizes the measured values of  and P for absorbers binned in  for the velocity window km s and three distance cuts: pkpc, pkpc, and pMpc.

Figure 17.— The incidence of absorbers, , with   10 cm as a function of impact parameter. The solid histogram represents the distribution of these high- absorbers for   300 km s. The hatched histogram represents the average incidence of the same absorbers near randomly-chosen redshifts. The vertical dotted line indicates the distance at which the incidence of the real distribution becomes comparable with that of the random distribution,   2 pMpc. The dotted horizontal line marks  .

5.1. Absorbers with   10 cm

We have shown above that absorbers with   10 cm appear to trace the positions of galaxies in our sample with high fidelity. The incidence of absorbers with   10 cm and   300 km s, as shown in Figure 17, nicely encapsulates the “shape” of the CGM. Similar to Figure 9 for   300 pkpc, one sees rising values of  as the galactocentric distance is reduced. From 300 pkpc   2 pMpc,  reaches a plateau value with   0.5 [2 pMpc = 1.4 h pMpc 4.6 h cMpc (at )]. For   2 pMpc,  drops to values consistent with the average IGM.

Recalling the quantity P(,), defined in §9 as the probability, per galaxy, of intersecting an absorber at a given  and within the specified range of , here we consider the velocity distribution of absorbers with 10 cm in bins of  as shown in Figure 18.

Fitting a Gaussian to the excess absorbers near galaxies compared to random gives a deviation () of 187 km s again suggesting that the velocity scale of the excess is 300 km s.

Integrating the distribution in the first panel of Figure 18 corresponding to   300 kpc results in an incidence averaged over 350 km s () and 300 pkpc,  . Similarly, comparing the value of  measured in the real and random distribution one infers that strong absorbers () are 4 times (P) more likely to be found within 300 kpc and km s of a galaxy in our sample, than at a random place. The parameters of the Gaussian fits in Figure 18, as well as the inferred  and P, are listed in Table 3.

In this section, we have shown that the covering fraction, , of absorbers with log() 14.5 is roughly uniform and 0.5 out to   2 pMpc, but that those with higher  only have   0.5 within   200 kpc (Figure 15). Consideration of the incidence, , indicates that absorbers with log() 14.5 are more directly related to galaxies (Figure 16). Those absorbers nicely encapsulate the “shape” of the CGM (Figure 17) and are 4 times more likely to be found within   350 km s and   300 pkpc of a galaxy in our sample than at a random place in the IGM (Figure 18).

Figure 18.— The velocity of absorbers with cm in bins of , as indicated. Note that   cm absorbers are 4 times more likely to be found within 300 km s and 300 kpc of a galaxy than at a random place in the IGM. See Table 3 for  and the excess probability for all of the panels.
41  window P
[pkpc] [km s] [km s] [km s]
   0–300   433 164 28 -350 to 350 1.700.02 4.1
 300–600 -7450 253 49 -550 to 450 1.070.01 1.19
 600–900  2949 389 49 -750 to 850 1.310.01 0.80
 900–1200 -4378 407 87 -850 to 750 1.600.01 1.14
1200–1500  6178 335 80 -650 to 750 1.200.01 0.76
1500–1800  4296 344109 -650 to 750 1.060.01 0.63
Table 3Incidence () and Excess Probability for cm 42

5.2. Covering Fractions: Comparison with Simulations

Motivated by the desire to predict the observational signatures of cold accretion streams, two recent theoretical papers have considered the covering fraction of absorbers of various  surrounding galaxies. Faucher-Giguère & Kereš (2011) consider the covering fraction of Lyman Limit (LLS, 17.2 log() 20.3) and Damped Lyman Alpha (DLA, log() 20.3) absorbers originating within cold streams near two simulated star-forming galaxies at using cosmological zoom-in simulations that do not include galactic winds. Since these authors explicitly did not consider galactic winds, their covering fractions are approximately43 a lower limit on the expected values. They considered a galaxy slightly less massive than those in our sample (M M), as well as one comparable to those in this work (M M).

For comparison, we consider the fraction of sightlines at a given  for which sum(,700 km s) falls within the specified column density range. This is most akin to the results of Faucher-Giguère & Kereš (2011) as they measure the column density of absorbers after projecting their simulated cube onto a 2D plane. Note that here we use differential bins in (17.2 log() 20.3), and since we are considering sum() rather than max(), we use  to denote the associated covering fraction (to differentiate it from the  measured earlier in this section).

Sample log() [cm] (1 ) (2 )
M M 11%
4%
M M 12% 4%
3% 1%
This work44 3014% 249%
0%45 44%
Table 4: Comparison with Faucher-Giguère & Kereš (2011)

Our measurements are compared with the Faucher-Giguère & Kereš (2011) simulation results in Table 4. Particularly in the case of LLS gas, we find times higher  within  and times higher within 2 compared with the simulations. However, if the simulations results are treated as lower limits, then clearly they are consistent with the observations.

Fumagalli et al. (2011) also considered the covering fraction of H i surrounding 6 LBG-type galaxies at using cosmological zoom-in simulations with galactic winds included (though they are relatively weak with their particular implementation). They consider absorbers within  and 2 for various thresholds in log() : , , , and cm. A comparison with the observations is given in Table 5. The models of Fumagalli et al. (2011) clearly under-predict the presence of log() gas surrounding galaxies. Similar to Faucher-Giguère & Kereš (2011), they also seem to under predict the radial extent of gas with cm.

Sample log() [cm]  (1 )  ( 2 )
Fumagalli et al. 38% 22%
16% 7%
6% 3%
3% 1%
This work46 909% 689%
3014% 289%
109% 85%
0% 44%
Table 5Covering Fraction: Comparison with Fumagalli et al. (2011)

5.3. Evolution of the CGM from to

Sample log()
[cm] pkpc km s
350 ¡330 500 72%
¿14 ¡330 500 835%
50 13 ¡300 400 96%
300 14 ¡300 400 70%
50