A Galaxy Redshift Survey Near HST/COS AGN Sight Lines

The COS GTO galaxy redshift survey was designed to obtain redshifts for all galaxies with g < 20 that are within 20' of each of the 40 AGN sight lines targeted by the HST/COS GTO team. We successfully observed galaxies near 38 of these sight lines, whose names, positions, and redshifts are listed in Table 1 along with the color excess along the line of sight as measured by Schlafly & Finkbeiner (2011) and the abbreviations used to identify the sight lines in the supplementary data products. The two sight lines that were observed by the HST/COS GTO team, but not included in this survey, are (1) PKS 0003+148, which was hard to access from the southern hemisphere when we were observing sight lines with similar RAs, and (2) PKS 0405–123, which has extensive galaxy survey results to fainter magnitudes already in the literature (e.g., Chen & Mulchaey 2009; Prochaska et al. 2011; Johnson et al. 2013).

Whenever possible, we used photometry and photometric redshifts (z_phot) from the SDSS (Alam et al. 2015) to choose our spectroscopic targets (see below). SDSS z_phot values have typical uncertainties of σ_phot = 0.025 (Beck et al. 2017) and catastrophic failure rates (differences in spectroscopic and photometric redshift determinations that exceed 3σ_phot) of ≈1.6% (see Beck et al. 2017 for a detailed discussion). When SDSS imaging was unavailable (primarily in the southern hemisphere) we obtained our own images of the sight lines using the MOSAIC imagers of the Blanco 4 m telescope at Cerro Tololo Inter-American Observatory⁷ (40' × 40' field of view) and the WIYN 0.9 m telescope at Kitt Peak National Observatory⁸ (60' × 60' field of view).

These observations are detailed in Table 2, which lists the sight line name, telescope, observation date, and exposure time in the SDSS g, r, i filters, respectively. While the imaging depth achieved depends on the observing conditions, typical limiting magnitudes for point sources in Blanco data are 23.9, 24.2, and 24.2 in g-, r-, and i-band, respectively. In WIYN 0.9 m data we typically reach 22.1 mag in g-band, 22.3 mag in r-band, and 21.9 mag in i-band.

Spectroscopic targets were identified by generating a list of all galaxies with g < 20 located within 20' of the AGN sight line and removing those galaxies with known redshifts. The remaining targets were assigned priority levels based on their brightness and photometric redshift (when available). Bright galaxies with g < 18 were given highest priority, regardless of photometric redshift. Fainter galaxies with 18 < g < 20 were given lower priority, and only targeted if their photometric redshifts were no more than σ_phot larger than the AGN redshift. The lowest priority targets were those that fell outside our completeness goals (i.e., galaxies with g > 20 and/or positions >20' from the AGN sight line) and were only targeted if their photometric redshifts were no more than σ_phot larger than the AGN redshift. We observed objects with known redshifts, or with photometric redshifts above our thresholds, as "extra" targets in a configuration only when no higher-priority galaxies could be accommodated. In fields where photometric redshifts from SDSS are unavailable, spectroscopic target selection was based solely on apparent g-band magnitude and proximity to the QSO sight line.

MOS for this survey was performed with the HYDRA spectrograph on the WIYN 3.5 m telescope at Kitt Peak National Observatory (Barden et al. 1993; Bershady et al. 2008) or the AAΩ spectrograph on the 3.9 m Anglo-Australian Telescope at Siding Springs Observatory (Sharp et al. 2006). Table 3 lists the sight-line name, telescope, observation date(s), and exposure time per fiber configuration for our spectroscopic observations.

At WIYN/HYDRA, we used the 600@10.1 grating centered at 5200 Å with the blue cables and the Bench Camera, yielding a spectral resolution of ${ \mathcal R }\approx 1200$ over the wavelength range 3800–6600 Å. While the S/N achieved generally decreases as the galaxy's apparent magnitude increases, the relationship is not straightforward due to variations in observing conditions and galaxy surface brightness. The S/N of spectra obtained with this instrument is ${11}_{-5}^{+8}$ per pixel, and the g-band magnitude of targeted galaxies is ${19.4}_{-0.7}^{+0.5};$ quoted values are medians, and ranges indicate the 16th and 84th percentile values.

At AAT/AAΩ, we used the 580V and 385R gratings centered at 4800 and 7250 Å, respectively, yielding a spectral resolution of ${ \mathcal R }\approx 1300$ over the wavelength range 3700–8800 Å. The S/N of spectra obtained with this setup is ${6}_{-3}^{+10}$ per pixel, and the galaxy g-band magnitude range is ${19.9}_{-1.3}^{+0.7}$.

With both instruments, we chose our wavelength coverage to ensure we were sensitive to Ca ii H & K absorption from z ≈ 0 galaxies. Most redshifts in this survey were obtained with WIYN/HYDRA, so the wavelength of Hα is not usually covered, and direct measurement of galaxy star formation rate is not possible.

The galaxy group survey was designed to support HST/COS observations of AGNs that probe SDSS-selected galaxy groups (Stocke et al. 2017). These groups have modest numbers of SDSS galaxies (N = 3–10), so we have designed a survey aimed at increasing the number of group members to N ≳ 20 per group. This allows various observed (e.g., group velocity dispersion) and inferred (e.g., group halo mass) group properties to be well-constrained (J. T. Stocke et al. 2018, in preparation). The 10 sight lines observed as part of this study are listed in Table 4, along with their positions, redshifts, color excesses, and the abbreviations used for the sight lines in the supplementary data products.

Unlike the COS GTO galaxy redshift survey, this survey was not designed to be complete around the AGN sight line. Instead we placed fibers on galaxies with unknown redshift near the SDSS group centers. Bright galaxies (g < 18) within 20' of the group center were given highest priority regardless of their photometric redshift, followed by fainter galaxies (18 < g < 20) with photometric redshifts within 2σ of the SDSS group redshift, and then galaxies with g < 20 that were located 20'–30' from the group center and had photometric redshifts within 2σ of the group redshift. We observed fewer configurations per sight line for this survey because our goal was not high completeness, but rather a fair sampling of potential group members. We were not concerned with identifying all possible group members so long as we found enough so that the group is well-characterized.

MOS for this survey was performed with WIYN/HYDRA and MMT/Hectospec (Fabricant et al. 2005). A journal of our observations is shown in Table 5, which lists the sight line name, telescope, observation date(s), and exposure time per fiber configuration. Four of the ten sight lines in this survey were observed with both WIYN/HYDRA and MMT/Hectospec.

At WIYN/HYDRA we again used the 600@10.1 grating centered at 5200 Å (${ \mathcal R }\approx 1200$ from 3800 to 6600 Å); the S/N of these spectra is ${9}_{-3}^{+5}$ per pixel, and the galaxy g-band magnitude range is ${19.4}_{-0.7}^{+0.5}$. At MMT/Hectospec, we used the 270 gpm grating to achieve ${ \mathcal R }\approx 1000$ from 3700 to 9100 Å; the S/N of these spectra is ${7}_{-3}^{+6}$ per pixel, and the galaxy g-band magnitude range is ${19.8}_{-0.8}^{+0.7}$. As before, we chose our wavelength coverage to ensure sensitivity to Ca ii H & K absorption at z ≈ 0.

Galaxy redshifts are assigned from a by-eye verification and correction of initial automated redshifts. The automated routine takes three approaches. The first is a cross-correlation with SDSS spectral templates,¹⁴ but this was generally found to be an ineffective method due to the poor spectrophotometry of the spectra, particularly near the bandpass edges. More effective are the two line-search methods, the first of which looks for emission lines (Mg ii 2799 Å, [O ii] 3728 Å, Hβ, [O iii] 4959/5007 Å, Hα) and the second of which looks for absorption lines (Ca ii H & K, G-band, Mg i b, Na i D). An à trous wavelet (wavelet "with holes"; i.e., edge avoiding; Starck et al. 1997) is applied to the spectra, with parameters optimized on a training set for our resolution and lines of interest. Cuts are made to find lines above the S/N. The routine searches for doublet lines (Ca ii H & K, [O iii] 4959/5007 Å), and searches for line identifications that maximize other detected lines matching to known lines. Consistent redshifts from several lines together are given higher probability, as are stronger lines.

This approach is generally effective for good S/N galaxies, particularly those with emission lines. However, its accuracy is not enough to enable the raw use of the automated results. Sometimes lines are present, beneath our S/N threshold, or the automated guess for the strongest line was mistaken. Noise vectors are also sometimes incorrect. The results of the automated routine are thus verified and corrected by eye, with the program's guesses for each method (cross-correlation, emission lines, and absorption lines) presented to the user to accept or correct. If the redshift needed correction, the user would correct a known line to its proper location, and the program would center on this line.

The final object redshift estimates are made by using whichever method was verified as "good," combining emission and absorption redshifts if they were both good and agreed with each other to within δz = 0.002. If they disagreed, emission redshifts were preferred. Uncertainty was estimated from agreement of all lines, with an additional 15 km s⁻¹ added in quadrature to account for wavelength calibration uncertainty.

Table 6 lists basic and derived information for the nearly 9000 galaxies observed as part of the COS GTO or galaxy group redshift surveys for which we have redshift determinations. The basic information includes the galaxy name, sky position, redshift, and apparent g-, r-, and i-band magnitudes. In addition, the galaxy's luminosity, virial radius, halo mass, stellar mass, and impact parameter with respect to the QSO sight line are listed. We are disseminating all of the individual galaxy spectra we have acquired (see doi:10.17909/T9XH52) as a MAST High-Level Science Product.¹⁵

The galaxy name is a combination of the sight line abbreviation (Tables 1 and 4), the galaxy's position angle with respect to the sight line (in degrees), and the galaxy's angular distance from the sight line (in arcsec).¹⁶ The tabulated luminosities are calculated in the rest-frame g-band (${M}_{g}^{* }=-20.3;$ Montero-Dorta & Prada 2009) using K-corrections from Chilingarian et al. (2010) and Chilingarian & Zolotukhin (2012). A galaxy's virial radius and halo mass are estimated from its rest-frame g-band luminosity using the prescription of Stocke et al. (2013), and the stellar mass is calculated from the galaxy's rest-frame i-band luminosity using Equation (8) of Taylor et al. (2011).

For the luminosity calculations, the apparent magnitudes in Table 6 are corrected for the effects of Galactic foreground extinction using the sight line color excesses (Tables 1 and 4) and the reddening law of Fitzpatrick (1999) with R_V = 3.1. The analytic K-corrections of Chilingarian et al. (2010) are only defined for z < 0.5, so the rare objects in Table 6 at larger redshift have their K-corrections evaluated at z = 0.5 and should be treated with caution. We also constrain the galaxy colors to the range −0.1 ≤ g−r ≤ 1.9 and 0 ≤ g−i ≤ 3 (in the observed frame) when evaluating the K-corrections and −0.2 ≤ g−i ≤ 1.6 (rest-frame) when determining the stellar mass to ensure that we are not extrapolating beyond the color range used to define the relationships.

The final column of Table 6 can be used to determine whether a galaxy is near a COS absorption-line system: a value of 3 indicates that a galaxy is the closest known galaxy within 20' of an IGM H i absorber; a value of 2 indicates that it is the closest galaxy in Table 6 to an absorber, but a closer galaxy is known from SDSS or other sources; a value of 1 indicates that a galaxy is within 1000 km s⁻¹ of an absorber but is not the closest galaxy to that absorber; and a value of 0 indicates that a galaxy is not within 1000 km s⁻¹ of any absorber. Absorption-line redshifts are taken from the HST/COS IGM survey of Danforth et al. (2016) and the galaxy groups analysis of (J. T. Stocke et al. 2018, in preparation). Three-dimensional galaxy-absorber distances, D, are calculated using a reduced-Hubble-flow model with v_red = 400 km s⁻¹, and the "closest" galaxy is defined to be the galaxy within 20' and 1000 km s⁻¹ of the absorber that has the smallest D/R_vir (see Section 4.1 for details).

Despite our efforts to avoid stars when conducting our galaxy redshift surveys, they were occasionally observed. In Table 6 we assume that any object with z < 0.001 is a star, in which case we set the final column to −1 and do not calculate any of the derived galaxy quantities (luminosity, virial radius, halo mass, stellar mass, or impact parameter).

Finally, one of the GTO sight lines included in our galaxy redshift survey (SDSS J1439+3932) was never observed with COS. We include the redshift measurements for these galaxies in Table 6, but set the final column to −2 since the absorber locations are unknown.

While the formal redshift uncertainties listed in Table 6 and described above are the only method we have to assign uncertainty to individual redshift determinations, additional estimates are possible using aggregates of galaxies with similar properties. We perform both internal and external validations of the redshifts provided in Table 6 using galaxies that we observed multiple times and galaxies that have SDSS redshift measurements, respectively.

3.2.1. Internal Consistency

There are two reasons that individual galaxies were observed multiple times in our program. The first is that faint galaxies (g > 19) were sometimes assigned to multiple configuration files to increase their S/N. The second reason is that a single configuration file was sometimes observed multiple times due to weather or instrument problems with the first observation, or because a particular sight line was preferentially positioned during an available observation window.

All told, our surveys include 2153 galaxies that were observed twice or more (the maximum number of observations for a single galaxy is six). After removing any observations that did not result in a redshift determination, we calculated the velocity difference (Δv = c Δz) between individual redshift measurements and sorted them by telescope/instrument combination. Next, the duplicate spectra were visually classified as emission-line galaxies with strong emission and little to no absorption, absorption-line galaxies with strong absorption and little to no emission, or composite galaxies that show evidence of significant emission and absorption. Finally, we calculated the average and standard deviation of the velocity offsets for each instrument and type of galaxy. Table 7 displays the results of our analysis.

Table 7.  Redshift Comparisons for Duplicate Observations

Sample	Absorption-line Galaxies			Composite Galaxies			Emission-line Galaxies
	N	$\overline{{\rm{\Delta }}v}$	σv	N	$\overline{{\rm{\Delta }}v}$	σv	N	$\overline{{\rm{\Delta }}v}$	σv
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
AAT	24	13 ± 47	197 ± 45	35	20 ± 13	78 ± 11	7	4 ± 13	32 ± 14
MMT	71	12 ± 12	101 ± 10	202	4 ± 3	54 ± 3	46	11 ± 8	52 ± 6
WIYN	253	−9 ± 5	92 ± 4	544	−2 ± 4	87 ± 3	71	6 ± 7	60 ± 5
Combined	348	−4 ± 5	100 ± 4	781	0 ± 3	81 ± 2	124	10 ± 5	57 ± 4
WIYN + MMT	37	−49 ± 20	118 ± 18	60	−39 ± 10	76 ± 7	20	−12 ± 10	43 ± 10
External (SDSS)	154	−9 ± 4	60 ± 3	94	−10 ± 5	50 ± 4	12	−8 ± 3	13 ± 3

Note. The mean velocity offset, $\overline{{\rm{\Delta }}v}$, and standard deviation, σ_v, are given in units of km s⁻¹.

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Sight lines in the COS GTO survey were never observed with more than one spectrograph (Table 3). This means that redshift comparisons for these sight lines primarily characterize the consistency of our redshift measurement procedure (Section 3.1). The first three rows of Table 7 are for data taken with AAT/AAΩ, MMT/Hectospec, and WIYN/HYDRA, respectively. They show that none of the instruments have a large characteristic offset between repeated redshift measurements of any galaxy type, with typical values of $| \overline{{\rm{\Delta }}v}| \lt 10\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Further, the velocity distributions for emission-line galaxies (σ_v ∼ 50 km s⁻¹) are consistently narrower than the distributions for absorption-line galaxies (σ_v ∼ 100 km s⁻¹), with the composite galaxies having intermediate values. There are hints of differences in characteristic widths between the instruments, but the small sample sizes of the AAT and MMT data sets preclude us from drawing firm conclusions.

The fourth row of Table 7 shows the results of combining the previous three rows to maximize the sample size for any galaxy type. The distribution of velocity offsets for this combined sample is shown in Figure 3 for each galaxy type. The overlaid Gaussians are not fits to the data, but rather expectations based on the measured means and standard deviations if the data are normally distributed (i.e., the only free parameters are mean, $\overline{{\rm{\Delta }}v}$, and standard deviation, σ_v; the amplitude is proportional to ${\sigma }_{v}^{-1}$). In all cases, the Gaussian expectations from Table 7 are a reasonable description of the data.

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Some of our galaxy group sight lines were observed with both WIYN and MMT (Table 5), allowing us to search for systematic offsets in redshifts derived from HYDRA and Hectospec spectra that may arise due to varying wavelength coverage and S/N. The fifth row of Table 7 shows the results for ∼120 galaxies that have redshift determinations from both WIYN and MMT. The widths of the velocity distributions for each type of galaxy are very similar to what we found in our single-instrument analyses, but there is a 20–50 km s⁻¹ characteristic difference (2–4σ significance) between the two measurements. There is no clear cause for this discrepancy, but the instrumental setups do differ; with our chosen gratings (Section 2), WIYN/HYDRA has a wavelength coverage of 3800–6600 Å (notably, this means that we rarely observe Hα emission) and resolution ${ \mathcal R }\approx 1200$, while MMT/Hectospec covers 3700–9100 Å at somewhat lower resolution (${ \mathcal R }\approx 1000$).

3.2.2. External Validation

As described in Section 2, we allowed galaxies with known SDSS redshifts to be observed as "extra" targets in our configurations if no additional objects with unknown redshift could be accommodated in the configuration design. This choice now gives us the opportunity to externally validate our redshift measurements with SDSS. To gather the largest possible sample, we entered the galaxy positions from Table 6 into the SDSS CrossID tool¹⁷ and then cleaned the results to remove spurious matches.

This resulted in 260 galaxies with measurements in both SDSS and Table 6. The last row of Table 7 shows how our redshift measurements compare to the SDSS values for absorption-line, emission-line, and composite galaxies. The galaxy classification was performed exactly as before (i.e., from visual inspection of our spectra) to minimize systematic biases. Approximately 1/3 of the galaxies with SDSS redshifts are in regions surveyed only by WIYN, ∼1/4 are in regions surveyed only with MMT, and ∼40% are near sight lines surveyed with both telescopes.

Our redshift measurements show excellent agreement with the SDSS values, as shown in Figure 4. The average velocity offset between them is ∼10 km s⁻¹ for all three galaxy types, which is small enough to be consistent with zero in all cases. As with our internal comparison, we find that the widths of the velocity distributions are narrower for emission-line galaxies than absorption-line galaxies, with composite galaxies having intermediate values.

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Interestingly, the standard deviations between our redshifts and the SDSS values are smaller than the standard deviations from our internal consistency checks for all galaxy types. This is probably because galaxies with SDSS spectra are brighter (r < 17.8; Strauss et al. 2002) than the typical galaxies we surveyed. Thus their redshift estimates are more precise by virtue of having high S/N. Conversely, our internal consistency comparisons (Section 3.2.1) include fainter objects with lower S/N and less precise redshift measurements.

In this section, the completeness of these observations and this survey are discussed using several different measures. The first two measures ("observational completeness" and "targeting completeness") describe how efficiently redshifts were determined from the spectra obtained and how efficiently each sight line was observed for galaxies, respectively. Many observational variables affect these two completeness measures, including transparency, seeing, total integration time obtained, galaxy central surface brightness, and galaxy spectral classification (emission, absorption, or composite; see Section 3.2). These values provide an indication about whether re-observing fields with low completeness values would be important or not. The third measure, "overall completeness," is the important number for users of this survey, as it provides a quantitative measurement of the likelihood that all or nearly all galaxies that are potentially associated with an absorber have been identified. These values are generally quite high (>80%), excepting for the sight lines that targeted nearby galaxy groups where the overall completeness typically exceeds 60% by design.

Table 8 lists several measures of completeness for each sight line surveyed. The first is the observational completeness, or the fraction of all observed galaxies for which we were able to determine a redshift, regardless of their apparent brightness or location with respect to the QSO sight line. These values are generally quite high, with ∼25% of the sight lines being 100% complete and ∼75% having observational completenesses >90%. Only two sight lines (4%) have observational completenesses <60%. Northern hemisphere sight lines tend to have higher observational completeness than southern hemisphere ones. We attribute this to the fact that we were granted more observing time in the northern hemisphere, which enabled us to re-observe sight lines that experienced poor weather or instrumental problems in their initial observations. Thus the root cause of the lower observational completeness in southern hemisphere sight lines is lower S/N in the data (see Section 2).

The second measure of completeness in Table 8 is the targeting completeness, or the fraction of all targeted galaxies located within 20' of the QSO sight line with g < 20 that were observed. Recall that our target lists exclude galaxies with known redshifts from SDSS or other sources (Section 2). Approximately 2/3 of the sight lines have targeting completeness >80%, and no sight line has <40%. The 10 sight lines that were observed as part of the galaxy group survey (Section 2.2) have lower targeting completenesses than those observed as part of the COS GTO survey (Section 2.1). This difference is by design (see Section 2.2 for details), but it is clear that the targeting completeness for the galaxy group sight lines is large enough to achieve their goal of a fair sampling of potential group members.

The third completeness measure in Table 8 is the overall completeness, which is defined as the fraction of all galaxies with g < 20 located within 20' of the sight line that have known redshifts from Table 6, SDSS, or other published sources. To be consistent with our configuration design requirements (Section 2), we also require that galaxies have photometric redshifts (when available) no more than σ_phot larger than the AGN redshift for inclusion in the overall completeness calculation. In non-SDSS fields where photometric redshifts were unavailable, the overall completeness is based solely on apparent g-band magnitude and proximity to the QSO sight line. The overall completeness has a larger spread of values than the observational and targeting completenesses; nevertheless, >85% (41/48) of the sight lines have overall completeness >70% and only one sight line has a value <50%.

These overall completeness values are conservative in the sense that they are likely lower limits on the actual completeness in any one sight line, or in the survey overall. This is because we have used photometric redshifts for some galaxies proximate to the sight lines. We include galaxies without spectroscopic redshifts but whose photometric redshifts are consistent with being foreground to the AGN (see above) as adding to the incompleteness of the survey. In non-SDSS fields, no photometric redshifts are used so that the incompleteness is overestimated even more.

Any single number is a crude measure of the completeness of a survey. Thus we provide two additional estimates of the survey completeness around our sight lines. One measure is found in the Appendix, which provides tables for individual sight lines listing overall completeness values in bins of magnitude and impact parameter from the QSO sight line. The other measure searches for regions surrounding each sight line where the overall completeness is >90% for angular separations of θ ≤ θ_lim and apparent g-band magnitudes of g ≤ g_lim. When performing this search, we prioritized complete to fainter magnitudes (larger g_lim) over complete to larger impact parameters, and we required the search volume to contain at least 10 galaxies. The values of g_lim, θ_lim, and the limiting (overall) completeness in this region are listed in Columns 5–7 of Table 8, respectively.

Unfortunately, four of our sight lines (3C 57, H 1821+643, Mrk 421, and PKS 2005–489) do not reach the limiting completeness threshold for any combination of g_lim and θ_lim in our data. On the other hand, there are 11 sight lines (23%) that have >90% completeness all the way to the edge of the survey region (i.e., g_lim = 20.0 and θ_lim = 20'), and an additional 21 sight lines (44%) that are complete to g_lim = 20.0 with θ_lim ranging from 38 to 189. Thus 2/3 of the sight lines are >90% complete to galaxies with g < 20 over some region of the survey volume.

The COS GTO survey was designed to be complete to L ≲ 0.1 L* galaxies at z ≤ 0.1 located within 1 Mpc of the sight line. A completeness limit of g_lim = 20.0 corresponds to L ≈ 0.15 L* at z = 0.1 (Montero-Dorta & Prada 2009), and 1 Mpc is equivalent to θ_lim = 90 at z = 0.1. A total of 24 of the 38 sight lines in the COS GTO survey (63%) are >90% complete to at least these thresholds; if we restrict our analysis to the northern hemisphere, 20/29 WIYN sight lines (69%) meet the design goals.

Of the remaining value-added columns in Table 6, the "absorption flag" in the final column is particularly interesting. It encodes the results of comparing the positions and redshifts of 8230 galaxies (all of the galaxies in Table 6 with z_gal > 0.001 located near one of the 47 sight lines with HST/COS observations) with the redshifts of 1565 H i absorbers from HST/COS (Danforth et al. 2016; J. T. Stocke et al. 2018, in preparation). The galaxy redshifts are in the range 0.00113 ≤ z_gal ≤ 0.90909, while H i absorbers have redshifts in the range 0.00165 ≤z_abs ≤ 0.68278 and column densities in the range 12.10 ≤log N_{H I} ≤ 19.23.

Absorption flags equal to zero (3781 galaxies) indicate that a galaxy is not within 1000 km s⁻¹ of an absorber, while a value of one (3699 galaxies) indicates that a galaxy is within 1000 km s⁻¹ of an absorber but is not the closest galaxy to that absorber. All velocity comparisons are done in the rest frame of the absorber (i.e., Δv = c(z_gal−z_abs)/(1 + z_abs)) and the "closest" galaxy to an absorber is defined as the one with the smallest value of D/R_vir, where D is the three-dimensional distance between the galaxy and the absorber. The galaxy-absorber distance along the line of sight, D_z, is calculated using a reduced-Hubble-flow model where D_z = 0 if $| {\rm{\Delta }}v| \,\leqslant 400\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and ${D}_{z}=(| {\rm{\Delta }}v| -400\,\mathrm{km}\,{{\rm{s}}}^{-1})/H(z)$ otherwise. The three-dimensional distance is then found by summing D_z and the impact parameter, ρ, in quadrature.

Absorption flags larger than one imply that a galaxy is, at a minimum, the closest galaxy in Table 6 to an absorber, in the sense described above. A value of two (179 galaxies) indicates that a closer galaxy is known from SDSS or other sources (e.g., Prochaska et al. 2011). A value of three (571 galaxies) indicates that a galaxy is the closest known galaxy within 20' and 1000 km s⁻¹ of an absorber.

However, this closest galaxy determination is not always unique (i.e., the closest galaxy to an absorber in Table 6 may also have a redshift from SDSS or elsewhere). We find 67 of these coincidences, such that 504/571 (88%) of the galaxies with absorption flag values of three were not known to be the closest galaxy to an absorber before this work. Similarly, of all the galaxies with absorption flags of two or three, indicating that they are the closest galaxies in Table 6 to an absorber, 504/750 (67%) represent newly discovered galaxy-absorber associations. This finding, in conjunction with the completeness analysis in Sections 3.3 and Table 8, suggests that the GTO and group surveys presented in Sections 2 and 3 are deeper than other galaxy redshift surveys near the majority of these QSO sight lines.

The absorption flags in Table 6 do not address ambiguity in the closest galaxy associations. A choice must often be made between associating an absorber with a low-luminosity galaxy with a small impact parameter or a higher luminosity galaxy that is somewhat farther away. This motivated our decision to divide by the estimated virial radius of each galaxy and associate the absorber with the galaxy with the smallest D/R_vir in this and previous works (e.g., Stocke et al. 2013; Keeney et al. 2017). While this does not remove the ambiguity altogether, it at least provides an objective discriminator.

Keeney et al. (2017) studied the properties of 45 galaxies located within 2 R_vir of low-z H i absorbers, including measurements of properties (inclination, star formation rate, gas-phase metallicity) that we cannot measure for all galaxies in Table 6. They also provided indicators of how unique each absorber-galaxy association is by examining the ratios of the impact parameters and galaxy-absorber velocity differences for the nearest and next-nearest galaxies (see Figure 16 and 17 of Keeney et al. 2017). This analysis found that the galaxy-absorber associations are robust at D ≲ 1.4 R_vir and more questionable, particularly in velocity, at larger values (see Section 7.2 in Keeney et al. 2017).

When calculating three-dimensional galaxy-absorber distances, we adopt a reduced-Hubble-flow velocity of 400 km s⁻¹ because it corresponds to the maximum rotation velocities in the most massive star-forming galaxies and the largest velocity dispersions in passive galaxies. However, this value is assumed, not derived, so it creates some ambiguities in assigning individual galaxy-absorber associations. For example, if galaxy redshifts are varied by ±1σ_z from their nominal values, then 6/96 galaxy-absorber associations with D ≤ 1.4 R_vir change. Because a single galaxy can be associated with more than one absorber, only five galaxies are responsible for these changes; three of these galaxies had initial galaxy-absorber velocity differences >300 km s⁻¹ and the other two had large redshift uncertainties of cσ_z/(1 + z_gal) >400 km s⁻¹. At larger distances (D > 1.4 R_vir), where Keeney et al. (2017) found that associations with an individual galaxy are not conclusive, ≈95/1075 (9%) of all galaxy-absorber associations change when the galaxy redshifts are varied by ±1σ_z.

Figure 6 displays galaxy-absorber properties for the 571 galaxies in Table 6 identified as the closest known galaxy to an absorber. The data are displayed as in the bottom panel of Figure 5, where the contour levels are drawn at the 1σ and 2σ levels with respect to the galaxy density, data inside the 2σ contour are galaxy density, and data outside the 2σ contour are individual data points. Solid blue lines indicate the median value of each property, and the dashed lines in the bottom panel indicate our reduced-Hubble-flow velocity.

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The typical galaxy-absorber association in Table 6 is between an ∼L* galaxy located ∼8 R_vir from an absorber with log N_{H I} ∼ 13.4. No trend of galaxy luminosity as a function of D/R_vir is evident. The same can be said for the H i column density for the data inside the contours; however, at D ≲ 3 R_vir there is a correlation between higher H i column densities and closer galaxy-absorber separations. This trend is supported by the analysis of Stocke et al. (2013; see their Figure 5). All of the closest galaxy-absorber associations have $| {\rm{\Delta }}v| \,\lt 400\,\mathrm{km}\,{{\rm{s}}}^{-1}$ because we do not impose any line of sight corrections on the three-dimensional galaxy-absorber distance, D, until $| {\rm{\Delta }}v|$ exceeds this threshold. A more complete analysis of nearest-neighbor statistics for close galaxy-absorber separations, particularly as it relates to the spread of metals in the IGM, can be found in Pratt et al. (2018).

Using the current survey, it is also possible to calculate H i Lyα covering fractions for galaxy-absorber associations. To do so, we searched for galaxies within 4 R_vir of absorbers with 0.042 ≤ z_abs ≤ 0.135. The maximum redshift is chosen such that g = 20 corresponds to L ≤ 0.3 L*, and the minimum redshift is chosen such that 20' corresponds to ρ ≥ 1 Mpc. We also set a luminosity limit of L ≤ 3 L* (i.e., R_vir < 250 kpc) to ensure that we are sensitive to all galaxies with D < 4 R_vir that are within 1 Mpc of the QSO sight line.

To investigate the H i Lyα covering fractions in this galaxy sample, we have employed the procedure used in Stocke et al. (2013) by which the redshift of each galaxy within 4 R_vir of the sight line is used as a marker to search for H i absorption at N_{H I} ≥ 10¹³ cm⁻². If H i absorption is present above this threshold, this constitutes a "hit" (H); if no absorption is present, this constitutes a "miss" (M). The covering fraction is simply C = H/(H + M). Spectral regions not sensitive enough for the above limit to be detectable are not used in this analysis (e.g., locations of Galactic metal-line absorption or strong absorption at another redshift; Stocke et al. 2013).

Figure 7 displays the results of this analysis. The top panel compares the Lyα covering fractions as a function of D/R_vir for galaxies with L ≥ L* (red) and L < L* (blue). The number of galaxies in each subsample is listed in parentheses, and the shaded regions show the 68% confidence Poisson uncertainties for each bin (Gehrels 1986). While the uncertainties overlap in most of the radial bins, the covering fraction for L < L* galaxies are flatter than for more luminous galaxies.

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These results differ slightly from the finding of Stocke et al. (2013; see their Figure 7), with the largest difference being a (∼2σ) larger covering fraction (C = 0.7 compared to 0.5) for sub-L* galaxies, but it should be noted that the absorber and galaxy samples used for the covering fractions also differ from what Stocke et al. (2013) used. Nevertheless, both Figure 7 and Stocke et al. (2013) find that galaxies with L ≳ 0.1 L* have H i covering fractions >50% out to 4 R_vir and that the covering fraction for L > L* galaxies is very high, consistent with unity inside R_vir.

The COS-Halos project Werk et al. (2013) finds a similarly high covering fraction for star-forming galaxies inside an impact parameter of 0.5 R_vir, while Wakker & Savage (2009) found unity H i covering fractions out to ∼R_vir for massive galaxies. Chen et al. (2001) and Liang & Chen (2014) also found high Lyα covering fractions around nearby galaxies. Similarly, covering factors close to unity are found at z = 2–3 by Rudie et al. (2012; see their Table 6) with these high covering factors extending to much greater impact parameters at comparable column densities (log N_{H I} ≥ 13) to this study and Wakker & Savage (2009). The Rudie et al. (2012) covering fractions for log N_{H I} ≥ 14, which may be a more appropriate comparison between high- and low-z, are nearly identical to what is shown in Figure 7 and in Wakker & Savage (2009) in showing a very slow decline out to several virial radii.

The bottom panel of Figure 7 compares the covering fractions for absorption-line galaxies (red) and emission-line and composite galaxies (blue). We use these observationally defined samples as proxies for the star-forming and passive galaxy populations, since it is not always possible to determine specific star formation rate using the current spectra because (1) for most WIYN/HYDRA spectra, Hα is not included in the observing band; and (2) more distant galaxies are not well-resolved in our images and so have only poorly determined sizes. We use the absorption-line galaxies, which show no sign of emission lines from star formation, as proxies for passive galaxies; all galaxies with emission-line and composite spectra are assumed to be star-forming.

The covering fraction for emission-line and composite (star-forming) galaxies is slightly higher than that of absorption-line (passive) galaxies at all radii, although the uncertainties in the radial bins overlap. Despite showing no significant difference in covering fraction in the binned data shown in Figure 7, taken altogether the emission-line and composite galaxies have $C=113/155={0.73}_{-0.05}^{+0.04}$ within 4 R_vir, while the absorption-line galaxies have $C=53/88={0.60}_{-0.07}^{+0.06}$. The covering fraction for passive galaxies in our sample is therefore ∼2σ lower than that of star-forming galaxies. Since the data in the top panel of Figure 7 include some absorption-line galaxies, it is probable that all star-forming galaxies with L ≥ 0.3 L* have a near-unity covering fraction inside their virial radius.

The other interesting new result is that the absorption-line galaxies show a rather flat covering fraction of ∼60% out to 4 R_vir (∼750 kpc for an L* galaxy). Previous hints of a flat covering fraction for passive galaxies come from Keeney et al. (2017), whose sample included a few passive galaxies at impact parameters >R_vir, and from (J. T. Stocke et al. 2018, in preparation), who find Lyα and O vi absorption far enough away from individual bright passive galaxies that these authors ascribe the absorption to an intra-group medium, not to an individual galaxy. Lower overall covering fractions that are rather constant with impact parameter argue in favor of a more extensive, but clumpy, medium in systems of passive galaxies like dense groups of galaxies.

Figure 8 is analogous to Figure 7, except that it shows the Lyα covering fractions as a function of physical distance, D, rather than normalized distance, D/R_vir. The top panel shows covering fractions for galaxies of different luminosities and has no information for L < L* galaxies in the outermost bin because those distances correspond to D > 4 R_vir. To within the (largely overlapping) uncertainties, this plot shows a smooth, shallow decline in covering fraction with increasing distance for galaxies of all luminosities.

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The bottom panel of Figure 8 shows the covering fractions for star-forming and passive galaxies, defined by their spectral classification as above. The uncertainties are once again large, but there are hints of an intriguing trend whereby star-forming galaxies have higher covering fractions than passive galaxies at D ≲ 400 kpc, the two samples have comparable covering fractions when D ∼ 400–800 kpc, and then passive galaxies have larger covering fractions at D ≳ 800 kpc. Larger sample sizes are required to determine whether this trend is robust.