#  HST/COS Lyman-alpha Absorbers in Cosmic Voids

William E. Watson,1 and Michael S. Vogeley,1
1Department of Physics, Drexel University, Philadelphia, PA 19104, USA
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We investigate the spatial distribution of Lyman-$\alpha$ (Ly $\alpha$)
absorbers within cosmic voids. We create a catalogue of cosmic voids in Sloan
Digital Sky Survey Data Release 7 (SDSS DR7) with the VoidFinder algorithm of
the Void Analysis Software Toolkit (VAST). Using the largest catalogue of low-
redshift (z $\lesssim$ 0.75) IGM absorbers to date, we identify 392 Ly
$\alpha$ absorbers inside voids. The fraction of Ly $\alpha$ absorbers inside
voids (65 per cent) is comparable to the volume filling fraction of voids (68
per cent), and significantly greater than the fraction of galaxies inside
voids (21 per cent). Inside voids, the spatial distribution of Ly $\alpha$
absorbers differs markedly from that of galaxies. Galaxy density rises sharply
near void edges, while Ly $\alpha$ absorber density is relatively uniform. The
radial distribution of Ly $\alpha$ absorbers inside voids differs marginally
from a random distribution. We find that lower column density Ly $\alpha$
absorbers are more centrally concentrated inside voids than higher column
density Ly $\alpha$ absorbers. These results suggest the presence of two
populations of Ly $\alpha$ absorbers: low column density systems that are
nearly uniformly distributed in the interiors of voids and systems associated
with galaxies at the edges of voids.

###### keywords:

intergalactic medium – large-scale structure of the Universe – quasars:
absorption lines

††pubyear: 2022††pagerange: HST/COS Lyman-alpha Absorbers in Cosmic
Voids–References

##  1 Introduction

The intergalactic medium (IGM) has constituted the majority of baryonic matter
throughout cosmic history. Though it remains challenging to detect in emission
(Steidel et al., 2011; Frank et al., 2012; Martin et al., 2014a, b), the IGM
has been extensively studied through absorption-line spectroscopy of distant
active galactic nuclei (AGNs), going back to the first detection by Lynds
(1971). AGN spectra display weak absorption lines blueward of the AGN frame Ly
$\alpha$ (1216 Å) emission line. This collection of discrete absorption
features, the Ly $\alpha$ forest, is produced by diffuse intergalactic
hydrogen along lines of sight to AGNs (Gunn & Peterson, 1965; Sargent et al.,
1980).

The physics underlying the Ly $\alpha$ forest has been fairly well understood
since the mid 1990s, when resolved spectral studies with the Keck telescope’s
High Resolution Echelle Spectrometer (HIRES) matched earlier results from cold
dark matter simulations (Cen et al., 1994; Hu et al., 1995). Ly $\alpha$
absorbers are highly photoionised clouds with temperature $\thicksim 10^{4}K$
(Zhang et al., 1995; Miralda-Escudé et al., 1996; Hernquist et al., 1996).
Improved understanding of intrinsic physical properties of the Ly $\alpha$
forest has furthered understanding of the IGM. The Fluctuating Gunn-Peterson
Approximation (FGPA), which relates observable Ly $\alpha$ optical depth to
intrinsic matter density (Weinberg et al., 1998; Croft et al., 1998), has been
used to determine the matter fluctuation spectrum and mean baryon density
(Rauch et al., 1997; Weinberg et al., 1997), yielding constraints on
cosmological parameters (Croft et al., 1999; Croft et al., 2002; McDonald et
al., 2000, 2006; Viel et al., 2004; Viel et al., 2008).

The Ly $\alpha$ forest has been extensively studied over an intermediate
redshift range (2 $\lesssim$ z $\lesssim$ 5), where it can be observed with
ground-based optical instruments. The Ly $\alpha$ forest is more difficult to
probe at lower redshift because it must be investigated with space-based UV
spectrographs. Notable among the latter are Copernicus (Spitzer et al., 1973),
International Ultraviolet Explorer (Boggess et al., 1978), and Far Ultraviolet
Spectroscopic Explorer (Moos et al., 2000). Additionally, the Hubble Space
Telescope (HST) has hosted a series of ultraviolet spectrographs, including
the Faint Object Spectrograph (FOS), Goddard High Resolution Spectrograph
(GHRS), Space Telescope Imaging Spectrograph (STIS), and more recently the
Cosmic Origins Spectrograph (COS). Early observations with FOS showed that the
number density of Ly $\alpha$ absorbers falls from z $=$ 2 to z $=$ 0, though
not as dramatically as originally expected (Bahcall et al., 1991; Morris et
al., 1991). Bahcall et al. (1996) proposed that low-z Ly $\alpha$ absorbers
might consitute a distinct population from high-z absorbers, with the former
tracing galaxy halos and the latter tracing the cosmic web. Against this view,
Davé et al. (1999) demonstrated that contemporaneous observations were
entirely consistent with the structure formation model of the Ly $\alpha$
forest. This established the prevailing consensus that low-z and high-z
absorbers are fundamentally the same.

Nevertheless, the Ly $\alpha$ forest changes significantly with redshift. To a
given sensitivity limit, the Ly $\alpha$ forest becomes sparser with
decreasing redshift. This results from the fact that a given overdensity
corresponds to a higher atomic hydrogen column density NHI at high-z than at
low-z (Davé et al., 1999). The redshift evolution of the Ly $\alpha$ forest is
dominated by expansion-driven decrease in mean baryon density and the decline
of quasars, the main source of metagalactic flux (Theuns et al., 1998; Haardt
& Madau, 2001). By z $\lesssim$ 2 structure formation shocks have heated
$\thicksim 50$ per cent of the IGM by mass above photoionisation temperature
into a warm-hot (WHIM) phase (Cen & Ostriker, 1999; Davé et al., 1999). At z
$\thicksim$ 0.1, Ly $\alpha$ absorption may be detectable in only 30 $\pm$ 10
per cent of the IGM by mass (Shull et al., 2012). This detection shortfall
lead to the long-standing “Missing Baryon Problem”, which appears to have been
recently resolved. The physical baryon density parameter $\Omega_{b}h^{2}$
derived from Wilkinson Microwave Anisotropy Probe (WMAP) and later Planck
observations was significantly higher than direct observation showed (Jarosik
et al., 2011; Planck Collaboration et al., 2016), until de Graaff et al.
(2017) and Tanimura et al. (2018) located so-called "missing baryons" in a
hot, diffuse phase of the IGM and the intracluster medium (ICM).

In this paper, we clarify the relationship between the low-z Ly $\alpha$
forest and the large-scale structure seen in the spatial distribution of
galaxies. As components of the IGM, Ly $\alpha$ absorbers might be expected to
trace the filaments that contain galactic groups and clusters, and to avoid
the voids that occupy $\sim 70$ per cent of the volume in the universe but
contain only $\sim 10$ per cent of galaxies. However, searches for voids in
the high-z Ly $\alpha$ forest have turned up negative (Carswell & Rees, 1987;
Ostriker et al., 1988; Pierre et al., 1988). Grogin & Geller (1998), using a
small sample 18 Ly $\alpha$ absorbers at very low redshift ($cz<10^{4}\
\textrm{km s}^{-1}$), found that absorbers do not trace galaxies, and appear
to be distributed randomly. Penton et al. (2002b) noted that voids contain
mostly low-NHI absorbers, with high-NHI absorbers tracing large-scale
structure.

More recent research at low redshift suggests that the fraction of Ly $\alpha$
absorbers inside voids significantly exceeds the fraction of galaxies inside
voids. Tejos et al. (2012) and Pan (2011) both examined HST/STIS Ly $\alpha$
absorbers in the SDSS DR7 galaxy void catalog of Pan et al. (2012). Tejos et
al. (2012) stated that 43 percent of their Ly $\alpha$ absorber sample is
inside voids. They used a void catalog based on the void finding method that
we use in this paper (see discussion of the VoidFinder algorithm in section 2
below), but to simplify their analysis, they defined each void as the largest
sphere that could fit inside an irregularly shaped void region. Pan (2011)
found 77 per cent of HST/STIS Ly $\alpha$ absorbers (Danforth & Shull, 2008)
to be inside voids, and also found evidence that the absorbers prefer the deep
interior volume of voids. Of the 92 absorbers inside voids, 34 were inside the
inner eighth of void volume, significantly greater than the 11 $\pm$ 3 that
would expected for a random distribution. These striking findings motivate the
research that we present below.

We describe the galaxy void catalog and IGM absorber catalog in Section 2
below. In Section 3, we detail the classification of Ly $\alpha$ absorbers as
being in galaxy voids or walls, and compare their properties. We characterize
the spatial distribution of Ly $\alpha$ absorbers inside voids in Section 4.
In Section 5, we discuss our findings in light of hydrodynamic simulations
that relate observables to intrinsic properties of absorbers. In Section 6, we
summarize our results.

##  2 Data

###  2.1 Galaxies

Our galaxy sample is derived from SDSS DR7 (Abazajian et al., 2009). A 2.5-m
telescope at Apache Point Observatory in New Mexico provided photometric
observations in five bands for SDSS DR7 (Fukugita et al., 1996; Gunn et al.,
1998). Images were processed and classified, and spectroscopic observations
were taken of galaxies with Petrosian r-band magnitude $r<17.77$ (Lupton et
al., 1999; Lupton et al., 2001; Strauss et al., 2002). The galaxy catalogue we
examine in this paper is Version 1.0.1 of the NASA-Sloan Atlas of Blanton et
al. (2011).

###  2.2 Ly $\alpha$ Absorbers

We use the third version of the Survey of the Low-Redshift Intergalactic
Medium with HST/COS (Danforth et al. 2016 hereafter D16), the largest and most
sensitive survey of the low-z IGM to
date111https://archive.stsci.edu/prepds/igm/. The catalog is derived from far-
UV HST/COS spectra of 82 relatively nearby AGN (zAGN$<$0.9). The COS G130M and
G160M gratings were used for 68 of the spectra, and the remaining 14 were
taken with G130M alone. The spectra have high-S/N ($\gtrsim$ 15), which allows
for identification of numerous weak absorption lines (down to
$\log{(N_{HI})}\sim 10^{12}$). As detailed in D16, a sophisticated automated
line fitting technique was used to identify Ly $\alpha$, as well as other
hydrogen, helium, and metal absorption lines in the spectra. Derived
parameters include Doppler width b, redshift zabs and atomic hydrogen column
density NHI. All absorbers are at redshift zabs $<$ 0.75, but Ly $\alpha$
absorption is only observed at z $<$ 0.47; at higher redshift, Ly $\alpha$ is
redshifted past the end of the COS/G160M detector. The catalog includes both
individual spectral components and redshift absorption systems, which are
groupings of components within a narrow velocity window ($30\ \textrm{km
s}^{-1}$ for most lines, c Wr /$\lambda_{0}$ for strong broad lines) that are
presumed to be physically associated. A discrete IGM cloud corresponds to an
absorption system, and may display multiple spectral components. Therefore, we
treat the redshift absorption systems as synonymous with Ly $\alpha$
absorbers, and only use Ly $\alpha$ components to compute the two point
correlation function in Section 4.

##  3 Large-scale Environment of Ly $\alpha$ Absorbers

Figure 1: Histogram of effective radius for VoidFinder voids in SDSS DR7 in
h-1 Mpc. By construction, all voids have $R_{v}>10$ h-1 Mpc. Error bars show
$\pm\sigma$ Poisson uncertainties.

###  3.1 Galaxy Voids in SDSS DR7

We construct a void catalog in SDSS DR7 using the VoidFinder algorithm of the
Void Analysis Software Toolkit222https://github.com/DESI-UR/VAST (VAST;
Douglass et al. 2022). VoidFinder was originally developed by Hoyle & Vogeley
(2002, 2004) based on the work of El-Ad & Piran (1997). The algorithm uses
third nearest-neighbour distances to identify probable void galaxies, which
are then removed from the sample. It then fills the cavities between the
remaining galaxies with numerous overlapping spheres of various sizes. These
empty spheres are combined into aspherical void regions. VoidFinder voids are
constructed from the union of sets of overlapping spheres, each of which
shares $\geq 50$ per cent of their volume with the largest sphere in the void.
Any void too small to contain a sphere with radius 10 h-1 Mpc is discarded.
This volume cutoff means that our void catalog is unreliable within 10 h-1 Mpc
of the boundaries of SDSS DR7, and so we do not examine Ly $\alpha$ absorbers
or galaxies in that peripheral volume. We choose the VoidFinder algorithm to
define voids because comparison with tessellation-based methods clearly
demonstrate that it is superior for the purpose of defining the void
environment of galaxies and, presumably, of IGM absorbers (Zaidouni et al.
2022, in preparation).

We compute comoving distances of galaxies and Ly $\alpha$ absorbers in h-1 Mpc
using the Planck 2018 estimates of $\Omega_{m}=$ 0.31 and $\Omega_{\Lambda}=$
0.69 (Planck Collaboration et al., 2018). We apply VoidFinder to a volume-
limited sample of SDSS DR7 galaxies (z$<$ 0.107, r-band absolute magnitude Mr
$<$ -20.09). Our void catalog consists of 995 galaxy voids, each of which is
the union of approximately 30 non-concentric overlapping spheres of various
sizes. We use Monte Carlo integration to locate the geometric center and
compute the average volume of each void. For each void, we uniformly
distribute random points inside a rectangular prism that contains the
irregularly shaped mass of nested spheres. We eliminate the points that are
outside the constituent spheres, leaving a high density sample that fills the
void. The average position of that sample is the void center. Figure 1 is a
histogram of effective void radius Rv $=$ (3V /4 $\pi$ )(1/3) for the 995
VoidFinder voids in SDSS DR7.

We also create a sample of random points (hereafter referred to as the survey
randoms) that uniformly fills most of the three dimensional comoving volume of
SDSS DR7, excluding a buffer region 10 h-1 Mpc from the boundary surfaces of
the survey, where VoidFinder cannot detect voids. We classify the survey
randoms as being in walls or voids. The fraction of survey randoms inside
voids, 68 per cent, approximates the volume filling fraction of VoidFinder
voids in SDSS DR7.

We note that our void catalogue is similar, but not identical, to that of Pan
et al. (2012). Their void catalogue was constructed from a similar sample of
SDSS DR7 galaxies to the one described in Section 2. They used an earlier
version of VoidFinder that had less stringent boundary conditions than the
VAST VoidFinder that we use for our void catalogue (see Douglass et al. 2022
for details). In the Pan et al. (2012) void catalogue, constituent spheres of
voids may extend outside the galaxy survey by as much as 50 per cent of their
volume. By contrast, the constituent spheres of voids in our catalogue cannot
have more than 10 per cent of their volume outside the SDSS DR7 volume. Note
again that our statistical analyses do not use any objects that lie within a
10 h-1 Mpc buffer near the survey boundary.

The developers of the VAST package have recently published a new void catalog
for SDSS DR7 using the newest version of VoidFinder (Douglass et al., 2022).
They used VoidFinder on the same sample of SDSS DR7 galaxies that we use, but
with a less restrictive magnitude and redshift cut on the volume-limited
sample (Mr$<$-20, z$<$0.114). As a result, their catalog has more voids and
spans a somewhat larger volume within SDSS DR7.

###  3.2 AGN Sight Lines in SDSS DR7

Figure 2: Sky projection in equatorial coordinates of the SDSS DR7 footprint
(orange), with positions of the 36 HST/COS AGN sight lines that pierce it
(crosses). Name, abbreviated name (as denoted in D16), right ascension
$\alpha$ and declination $\delta$ in degrees, and AGN redshift zAGN of sight
lines are listed in the table below.

Name | Abbr. | zAGN | $\alpha$ | $\delta$
---|---|---|---|---
SDSS J080908.13+461925 | s080908 | 0.66 | 122.28 | 46.32
PG 0832+251 | pg0832 | 0.33 | 128.9 | 24.99
PG 0844+349 | pg0844 | 0.06 | 131.93 | 34.75
Mrk 106 | mrk106 | 0.12 | 139.98 | 55.36
SDSS J092554.43+453544 | s09255b | 0.33 | 141.48 | 45.6
SDSS J092909.79+464424 | s092909 | 0.24 | 142.29 | 46.74
SDSS J094952.91+390203 | s094952 | 0.37 | 147.47 | 39.03
PG 0953+414 | pg0953 | 0.23 | 149.22 | 41.26
PG 1001+291 | pg1001 | 0.33 | 151.01 | 28.93
FBQS J1010+3003 | f1010 | 0.26 | 152.5 | 30.06
Ton 1187 | ton1187 | 0.08 | 153.26 | 35.86
1ES 1028+511 | 1es1028 | 0.36 | 157.83 | 50.89
1SAX J1032.3+5051 | 1sj1032 | 0.17 | 158.07 | 50.86
PG 1048+342 | pg1048 | 0.17 | 162.93 | 33.99
PG 1049-005 | pg1049 | 0.36 | 162.96 | 0.0
HS 1102+3441 | hs1102 | 0.51 | 166.42 | 34.43
SBS 1108+560 | sbs1108 | 0.77 | 167.88 | 55.79
PG 1115+407 | pg1115 | 0.15 | 169.63 | 40.43
PG 1116+215 | pg1116 | 0.18 | 169.79 | 21.32
PG 1121+422 | pg1121 | 0.22 | 171.16 | 42.03
SBS 1122+594 | sbs1122 | 0.85 | 171.47 | 59.17
Ton 580 | ton580 | 0.29 | 172.79 | 31.23
3C 263 | 3c263 | 0.65 | 174.99 | 65.8
PG 1216+069 | pg1216 | 0.33 | 184.84 | 6.64
PG 1222+216 | pg1222 | 0.43 | 186.23 | 21.38
3C 273 | 3c273 | 0.16 | 187.28 | 2.05
Q 1230+0115 | q1230 | 0.12 | 187.71 | 1.26
PG 1229+204 | pg1229 | 0.06 | 188.02 | 20.16
PG 1259+593 | pg1259 | 0.48 | 195.3 | 59.04
PG 1307+085 | pg1307 | 0.16 | 197.45 | 8.33
PG 1309+355 | pg1309 | 0.18 | 198.07 | 35.26
SDSS J135712.61+170444 | s135712 | 0.15 | 209.3 | 17.08
PG 1424+240 | pg1424 | 0.6 | 216.75 | 23.8
Mrk 478 | mrk478 | 0.08 | 220.53 | 35.44
Ton 236 | ton236 | 0.45 | 232.17 | 28.42
1ES 1553+113 | 1es1553 | 0.41 | 238.93 | 11.19

We restrict our investigation to AGN sight lines within the SDSS DR7
footprint, which includes 36 of the 82 AGN sight lines examined by D16 (see
Figure 2). The mean effective radius Rv of VoidFinder voids in SDSS DR7 is 16
h-1 Mpc, roughly 20 times smaller than the average comoving length of the
sight lines inside SDSS DR7. Thus, we expect each sight line to pierce
multiple void and wall regions, and we can consider the angular positions of
the AGN sight lines to be unbiased with respect to large-scale structures.
However, we have a relatively small number of sight lines along which we can
probe the IGM, so it is possible that, by chance, these sight lines do not
probe a representative sample of large-scale structures. To characterize how
these 36 sight lines intersect large-scale structure in SDSS DR7, we construct
dense a linear random distribution along the lines of sight and we determine
if each random point lies inside a VoidFinder void. We refer to this
distribution as the sight line randoms.

###  3.3 Ly $\alpha$ Absorbers and Galaxies in SDSS DR7 Voids

The sight lines in Figure 2 contain 605 absorption systems inside the redshift
limit of our void catalog (0.003 $\leq$ z $\leq$ 0.107). If an absorber lies
inside any of the constituent spherical holes of the voids, it is classified
as a void absorber. Otherwise, it is considered a wall absorber. Galaxies are
classified in the same manner. Since VoidFinder voids have a minimum radius of
10 h-1 Mpc, some of the objects we classify as being in walls actually reside
in small voids. In our classification scheme, walls encompass a wide range of
environmental conditions, from dense structures to small voids. The void
classification is stricter.

We illustrate results of our classification in Figure 3 (a), a 10 h-1 Mpc
thick slice of SDSS DR7, with wall and void galaxies from the volume-limited
sample in orange and blue, respectively. The slice midplane contains the sight
line to AGN Q1230+0115, indicated by a black line, with void and wall Ly
$\alpha$ absorbers marked as red and black bars, respectively. Figure 3 (b)
shows the same slice, with irregularly shaped blue blobs representing
VoidFinder voids. Each VoidFinder void is the union of a set of spheres (about
30 per void). Figure 3 (b) plots in grey the overlapping circular
intersections of the constituent holes with the slice midplane.

We find that Ly $\alpha$ absorbers are not preferentially found in walls,
unlike galaxies, which suggests that the spatial distribution of Ly $\alpha$
absorbers does not trace filaments and clusters in the galaxy distribution.
The fraction of Ly $\alpha$ absorbers in voids is 65 per cent, comparable to
the fraction of sight line randoms in voids, 72 per cent, which approximates
the fractional length of the AGN sight lines inside voids. In contrast, only
21 per cent of SDSS DR7 galaxies in the volume-limited sample are inside the
voids. Unsurprisingly, the galaxy void fraction is far lower than the fraction
of survey randoms inside voids, which approximates the filling fraction of
voids, 68 per cent. The small difference in void fraction of sight line
randoms and survey randoms, 72 vs. 68 per cent, reflects the finite sampling
effect discussed above in Section 3.2.

Figure 3: Top \- A 10 h-1 Mpc thick slice of SDSS DR7 in comoving Cartesian
coordinates. The vertical axis is aligned with the line of sight to AGN
Q1230+0115, indicated by the vertical line, and the slice midplane contains
the sight line. Wall and void galaxies are marked respectively in orange and
blue, while wall and void Ly $\alpha$ absorbers are black and red bars along
the sight line. The AGN itself is outside the redshift limit of SDSS DR7.
Bottom \- The same slice from SDSS DR7, showing the intersection of VoidFinder
voids with the slice midplane in blue. Axes in h-1 Mpc.

##  4 Spatial Distribution of Ly $\alpha$ Absorbers in Voids

Figure 4: Three views of the same thin slice of a void in SDSS DR7. Axes show
comoving coordinates. A simulated AGN sight line pierces the void, with Ly
$\alpha$ absorber positions marked by vertical black ticks. The origin of this
plot sits on the void’s volume-weighted centre. Left - Constituent spherical
holes of a VoidFinder void, which have circular intersections with the slice.
This void is typical of others in our catalogue in that it consists of about
30 overlapping holes. The void is the union of the holes, and its intersection
with the slice is shown in white. We emphasize that this void, like all
VoidFinder voids that consist of multiple holes, does not have a perfectly
spherical boundary. Centre - Contours of distance to the walls dw in h-1 Mpc.
We use dw to characterize the positions of void absorbers and galaxies in the
stacked density profiles shown in Figure 6. This is useful for understanding
environmental effects of proximity to walls, as dw is sensitive to the
irregular void boundary. Right - Circular annuli of scaled voidcentric
distance, r/Rv, emanating from the void centre. The dashed circle indicates
the effective radius Rv. We use r/Rv to characterize the positions of void
absorbers and galaxies in the stacked density profiles shown in Figure 8. This
helps us to understand environmental conditions of the interior of a void, but
is less useful at higher values of r/Rv, where the annuli start to collide
with the irregular void boundary.

Theoretical considerations of how physical conditions of the IGM vary with
large-scale structure suggest that we carefully examine how Ly $\alpha$
absorbers are spatially distributed. Cosmological hydrodynamic simulations
indicate that the Warm-Hot Intergalactic Medium (WHIM) becomes a more
important constituent of the IGM at z<1 (Davé et al., 2010). We expect that
the WHIM is predominantly found in and around walls, because the IGM in voids,
particularly in the deep interiors of voids, does not experience gravitational
shock-heating from structure formation. Additionally, super-Hubble expansion
inside voids should adiabatically cool and lower the density of the IGM. Thus,
Hydrogen inside voids should be cooler, less ionised, and more diffuse than in
walls. These large-scale environmental effects on the physical state of
intergalactic hydrogen affect the spatial distribution of Ly $\alpha$
absorbers. Here we examine how the density of Ly $\alpha$ absorbers varies
inside voids, from the boundaries with the walls down into the centers of
voids.

To examine enivornmental effects on IGM, we need to carefully characterize
void shape and see where absorbers reside. The left panel of Figure 4 shows
the intersection of a void and its constituent spherical holes with a plane.
This void, like others in our catalogue, has a complex, irregular geometry.
The centre and right panels compare two measures of position inside the void,
the distance from the walls dw and the scaled voidcentric distance r/Rv. At
low dw (see Figure 6), effects from shock-heating in walls should be more
prominent. Near the void centre, it is perhaps more informative and
straightforward to consider concentric shells of r/Rv. We measure the distance
outward from the volume-weighted centre of the void, and divide that distance
by the effective void radius represented by the dashed black circle. Shells of
r/Rv are spherical near the centre, but start to get cut off as they collide
with the void boundary at higher r/Rv. We keep track of which objects are
inside the void, so the absorber at upper right, which is just outside the
void but less than Rv from the centre, would not be considered when we
construct the density profiles shown in Figure 8. We note that previous
research on the void density profile (e.g. Colberg 2004) has used simple
spherical models for void shape. This slice shows that such an approach tends
to mix wall and void regions together at the void boundary.

###  4.1 Wall Distance

The IGM at the edges of voids, where they interface with dense structures, may
be shock-heated by structure formation, albeit less strongly than in the walls
themselves. Thus, the IGM near void boundaries is likely to be more highly
ionised than the IGM deeper inside voids. At the same time, the void density
profile of the IGM should behave similarly to that of the volume-limited
sample of SDSS DR7 galaxies shown in Figure 6, with a sharp increase around a
voidcentric distance of Rv. We compute the density of Ly $\alpha$ absorbers as
a function of distance dw from cosmic walls to observe the effect of variation
in IGM density and ionisation fraction on Ly $\alpha$ absorbers.

To compute the distance from cosmic walls dw to each void Ly $\alpha$
absorber, we generate a uniform distribution of random points on the irregular
boundary of each void (recall that the volume of each void is the union of
overlapping spheres of varying radius). We estimate dw as the distance from a
void Ly $\alpha$ absorber to the nearest random point on the void surface. In
the same way, we compute dw for void galaxies. Histograms of dw for void Ly
$\alpha$ absorbers and void galaxies shown in Figure 5, are markedly
different. Void galaxies are almost all within 2 h-1 Mpc of cosmic walls. The
number of void Ly $\alpha$ absorbers shows a shallower decline with dw.

To convert the measurements of dw to estimates of densities of Ly $\alpha$
absorbers and galaxies inside voids, we also compute dw for survey randoms and
sight line randoms (see Section 3) inside voids. This allows us to estimate
the available void volume as a function of dw, which we use to determine the
number density of galaxies as a function of dw for each void. We then stack
the galaxy density profiles as shown in Figure 6 (blue). We also show the
stacked density profile of Ly $\alpha$ absorbers (red). We estimate length of
AGN sight lines inside bins of dw with the sight line randoms, and use that to
construct a linear density profile of Ly $\alpha$ for the voids. In these void
density profiles, the bar height is normalized by the maximum density in
voids, so that the vertical axis $\rho_{n}$ is unitless, but still
proportional to the physical density.

Figure 5: Normalized histograms of distance to cosmic wall $d_{w}$ for Ly
$\alpha$ absorbers (red) and galaxies (blue) inside voids. There are about 50
times as many void galaxies as void Ly $\alpha$ absorbers. Error bars show
$\pm\sigma$ Poisson uncertainties.

The linear density of Ly $\alpha$ absorbers in Figure 6 (red) spikes near the
void boundary, but otherwise shows no clear trend with dw. The density peaks
at 15-16 h-1 Mpc and 17-18 h-1 Mpc are statistically insignificant, as these
bins each contain fewer than five absorbers. The volume density of void
galaxies is greatest near void-wall interfaces, but falls precipitously beyond
dw $=$ 1 h-1 Mpc and remains relatively flat thereafter.

Figure 6: Density profile of Ly$\alpha$ absorbers (red) and galaxies (blue)
inside voids as a function of distance to cosmic wall in h-1 Mpc. The
normalized density $\rho_{n}$ on the vertical axis is a unitless number
proportional to the number density along the sight lines. Profiles are stacked
for all voids, which range in effective radius from 10 to 30 h-1 Mpc.

###  4.2 Voidcentric Distance

Next we examine how the densities of Ly $\alpha$ absorbers and galaxies vary
from the centers of voids outwards. We measure these density profiles both as
a function of physical distance in h-1 Mpc and as a function of the scaled
distance from each void center. To estimate densities, we use randoms to
estimate the available volume in each bin of distance, as we did above for the
density dependence on dw. This is necessary because, as noted above, we
include only objects inside voids and volume inside voids to compute density
profiles.

Figure 7 shows the void density profiles of Ly $\alpha$ absorbers and galaxies
as functions of voidcentric distance r. The profiles are stacked for all
voids, and the bar height is normalized to eliminate physical units as before.
Note that a particular value of voidcentric distance, r, does not correspond
to a fixed value of wall distance, $d_{w}$, because voids are not spherically
symmetric. As discussed in Section 2, the geometric center of each void is
located using Monte Carlo integration. The density of galaxies increases with
voidcentric distance, with an abrupt rise between 10 and 12 h-1 Mpc. The Ly
$\alpha$ absorber density profile, by contrast, is relatively flat; the
prominent spike in the lowest bin of r is not statistically significant,
because it encompasses a very small volume and contains only two Ly $\alpha$
absorbers.

Figure 7: Radial density profile of Ly $\alpha$ absorbers (red) and galaxies
(blue) inside cosmic voids as a function of voidcentric distance, r, in h-1
Mpc. The normalized density $\rho_{n}$ on the vertical axis is a unitless
number proportional to the physical density. Profiles are stacked for all
voids, which range in effective radius from 10 to 30 h-1 Mpc. The density of
Ly $\alpha$ is relatively flat (the enhancement in the lowest bin is not
statistically significant). However, the rough statistical test summarized in
Table 1 below shows that absorbers in the lowest quartile of column density
are over-represented in the deep interiors of voids, while the highest
quartile of column density is under-represented. By contrast, the density of
galaxies is $\lesssim$ 10 per cent of the cosmic mean near void centres and
rises sharply near void edges.

To compare density profiles of voids with different sizes, we compute the
scaled voidcentric distance r/Rv for each Ly $\alpha$ absorber and galaxy
inside voids. In Figure 8, we show the void density profile of Ly $\alpha$
absorbers (red) as a function of r/Rv. Density is generally relatively flat.
The enhanced Ly $\alpha$ absorber density near the void center is of low
statistical significance. This behavior is quite distinct from that of void
galaxies (blue). Galaxy density is lowest near the void centers and rises
dramatically near void-wall boundaries. From Figure 6, we might expect an even
sharper rise of galaxy density near the void boundaries, r/Rv $\approx$ 1, but
that rise is softened, because voids are not spherical.

Figure 8: Radial density profile of Ly $\alpha$ absorbers (red) and galaxies
(blue) inside cosmic voids as a function of scaled voidcentric distance, r/Rv,
where Rv is the effective void radius. The normalized density $\rho_{n}$ on
the vertical axis is a unitless number proportional to the physical density.
Profiles are stacked for all voids, which range in effective radius from 10 to
30 h-1 Mpc. The Ly $\alpha$ density is relatively flat. The peak near the void
centre, around r/Rv $=$ 0, is not statistically significant because only 2
absorbers fall in this bin. This behavior is significantly different from the
radial density profile of void galaxies, which is lowest in the interior
volume of voids ($r/R_{v}<$ 1/2) and rises near the void edges.

####  4.2.1 Statistics of Void Ly $\alpha$ and Galaxy Spatial Distributions

To quantify the statistical significance of differences between the galaxy and
Ly $\alpha$ absorber distributions inside voids, we compute their cumulative
distributions $F_{rs}$ as functions of scaled voidcentric distance r/Rv, as
shown in Figure 9. We also compute the cumulative distribution functions of
the sight line randoms (see Section 3), as well as a random distribution of
uniform volume density. Figure 9 shows that Ly $\alpha$ absorbers (red) are
very slightly less centrally concentrated in voids than linear randoms
(green), but significantly more centrally concentrated than galaxies (blue).

We perform an Anderson-Darling test on the cumulative distribution functionss
of Ly $\alpha$ absorbers and the sight line randoms. We find a p-value of
approximately six per cent, a marginally significant result that suggests that
Ly $\alpha$ absorbers are not uniformly distributed inside voids. This
quantifies the visual impression in Figure 9 that Ly $\alpha$ absorbers are
slightly less centrally concentrated inside voids than sight line randoms.
This difference in cumulative distributionss is most apparent at scaled
voidcentric distances of $0.4$ to $0.7$.

We also carry out the Anderson-Darling test to compare galaxies with Ly
$\alpha$ absorbers, and find a statistically significant difference
(p$<$0.01); galaxies are more concentrated near the void-wall interface around
r/Rv $=$ 1, whereas the Ly $\alpha$ absorbers have a more uniform distribution
inside voids. This statistical result is further evidence that galaxies and Ly
$\alpha$ absorbers have distinct spatial distributions.

Figure 9: Cumulative distributions of Ly $\alpha$ absorbers (red), galaxies
(blue), and a Poisson distribution (green) as functions of scaled voidcentric
distance r/Rv.

####  4.2.2 Two-Point Correlation Function of Ly $\alpha$ Absorbers

We compute the two-point correlation function (2PCF) of Ly $\alpha$ lines to
characterize their small-scale clustering. This statistic was presented in D16
using an earlier version of the HST/COS low-z IGM catalog. Here, we use a
similar procedure to find the 2PCF using the latest edition of the catalog.
Individual Ly $\alpha$ absorption lines were used to compute the 2PCF, since
redshift systems group closely spaced components together and thus provide no
information about small-scale clustering. The estimator of the 2PCF is,

$\xi(\Delta v)=\frac{N_{obs}(\Delta v)}{N_{ran}(\Delta v)}-1$ (1)

where Nobs and Nran are the number of pairs of observed and simulated random
absorbers within a velocity separation $\delta v$ (Labatie et al., 2010). Thus
$\xi$ gives the probability of clustering above random. The sight line randoms
that we use to compute Nran are distributed uniformly along the AGN sight
lines. By contrast, D16 employ a more complicated procedure to distribute
random absorbers. At each resolution element $\Delta v$ in an AGN spectrum,
they compute the minimum equivalent width for detection based on the S/N of
the data to determine the probability of detection within the resolution
element. They place a random absorber within the resolution element if the
probability exceeds a random number. Notwithstanding this difference in the
randoms, our resulting 2PCF for Ly $\alpha$ absorbers, shown in 10, is nearly
identical to that presented by D16. Clustering is weak, especially for $\Delta
v>100\ {\rm km\ s}^{-1}$, which indicates that there is not significant large-
scale structure in the spatial distribution of Ly $\alpha$ absorbers. By
contrast, galaxies typically exhibit strong clustering as measured by the 2PCF
in redshift space, $\xi\approx$ 5 on scales r $<$ 10 h-1 Mpc (Li et al.,
2006).

Figure 10: The two-point correlation function $\xi$ of Ly $\alpha$ absorption
lines in the HST/COS low-z IGM survey. The lines are only weakly clustered
even over small velocity separations, so the positions of lines can be
regarded as statistically independent.

###  4.3 Doppler Parameters of Void and Wall Ly $\alpha$ Absorbers

Simulations (Cen, 2011) indicate that structure formation shock heats the
intergalactic medium in walls but not voids. This environmental effect could
be reflected in the Doppler b parameter, a measure of the width of an
absorption line, which is a function of not only absorber temperature, but
also nonthermal effects. In some cases, the COS spectral resolution may not be
fine enough to resolve component structure, particularly for strong absorption
systems. Following the example of D16, we examine the Doppler parameter of
weak (log(NHI) $<$ 13.5), single-component systems for which the b-value is
more indicative of temperature. The mean b-value is somewhat higher in voids
(mean $\bar{b}=$ 32.4 $\pm$ 1.2 km s-1, median 28.0 km s-1) than walls (mean
$\bar{b}=30.6\pm$ 1.8 km s-1, median 25.2 km s-1). This result is surprising,
given that we might expect Ly $\alpha$ absorbers in the walls to have a higher
average b-parameter because of shock heating from structure formation.
However, the difference is of modest statistical significance and the
resolution of HST/COS is predicted to limit the use of the $b$ parameter for
measuring thermal properties of the IGM in this range of line width (Davé et
al., 2010).

###  4.4 Column Density and Spatial Distribution of Void Ly $\alpha$ Absorbers

We test for dependence on the large-scale void environment of the observed
column density, NHI, of absorption systems. This distribution is of interest
because, while the void environment is characterized by lower matter density
and, therefore, structures with smaller characteristic mass, the IGM in voids
is expected to have a higher neutral fraction. The statistical distribution of
column densities reflects a complex, environmentally-sensitive interplay of
astrophysics.

Perhaps surprisingly, comparison of the means of the column density $N(HI)$ of
absorbers observed in walls and voids does not reveal a strong environmental
difference. We find that the mean $\log{N_{HI}}$ of wall absorbers, 13.59
$\pm$ 0.89, does not significantly differ from that of void absorbers, 13.43
$\pm$ 0.73.

A more detailed probe of environmental differences in the IGM is the column
density distribution (CDD) of Ly $\alpha$ absorbers, the number of absorbers
per interval of column density per unit redshift pathlength, in voids and
walls. Figure 11 is a log-log plot of the CDD of Ly $\alpha$ absorbers in
voids and walls (see Figure 5 in D16 for the CDD of the entire set of Ly
$\alpha$ absorbers). The CDD is computed as in Danforth & Shull (2008). We
correct the effective redshift path length $\Delta z$ for void and wall
absorbers using sight line randoms to estimate the fraction of sight lines in
voids and walls, respectively 72 and 28 per cent; as discussed above, the
majority of absorbers are in voids. Thus normalized, the CDDs quantify the
frequency of absorbers per unit pathlength in the separate environments. Note
that at small column densities observations of both wall and void absorbers
are limited by the the sensitivity limits of HST/COS. Correction for this
limit is important because simulations suggest that most discrete Ly $\alpha$
absorbers are low-NHI (Davé et al., 2010). Completeness correction factors at
the lower range of column density (identical for void and wall absorbers) are
based on a fifth order polynomial fit to redshift pathlengths for bins of
column density in Table 5 of D16.

The steepness of the CDD is quantified by $\beta$, where
$\partial\mathscr{N}/\partial N\partial z\propto N^{-\beta}$ (that is, the
slope in Figure 11 plus one) (Dave & Tripp, 2001). Over the full range of
column density observed, we find $\beta=$ 1.72 $\pm$ 0.03 for void absorbers,
steeper than in walls, where $\beta=$1.54 $\pm$ 0.05. Compared to voids, walls
contain a higher ratio of high to low column density systems. The shallower
slope of the wall CDD is likely connected to the fact that higher column
density systems are more closely associated with galaxies, which by definition
are primarily found in walls. For the combination of void and wall absorbers,
$\beta=$ 1.65 $\pm$ 0.02. This is matches the value obtained by D16 for the
first edition of their IGM absorber catalog. Davé et al. (2010) simulated the
CDD of Ly $\alpha$ absorbers for HST/COS and predicted a somewhat higher
value, $\beta=$ 1.70 $\pm$ 0.1.The voids dominate the statistics of the
combined distribution because they contain the majority (about 70 per cent) of
absorbers.

Our observations of the void and wall CDD contrast with simulation results of
Tonnesen et al. (2017). They compared the CDDs of Ly-$\alpha$ absorbers found
in hydrodynamic simulations of two environments: an underdense region centered
on a void and an overdense region centered on a galaxy cluster. They found a
steeper CDD in the overdense region than the underdense region over 12.5 $<$
$\log$NHI $<$14.5 (to the left of the vertical line in our Figure 11),
primarily because the overdense region had fewer high column density
absorbers. If we restrict our computation of $\beta$ to the more limited range
of column density that they examined, we find values for $\beta$ in voids and
walls (1.70 $\pm$ 0.06 and 1.63 $\pm$ 0.11 respectively) that are similar to
our findings for the full range of column density; the observed wall CDD is
shallower than the void CDD. The different findings in these simulations and
our observations may be affected by differences in classification of large-
scale environment. By including small voids in our definition of walls (recall
that VoidFinder imposes a minimum void radius of $R_{v}=10h^{-1}$ Mpc), our
wall sample may include some absorbers in underdense regions. Another
possibility is that this disagreement indicates that the two regions examined
in the simulations are not representative of typical overdense and underdense
volumes in the low-redshift universe. Perhaps the environment of the
$+1.8\sigma$ "cluster" region in the simulation suppresses absorber abundance
more than the typical overdense environment sampled by our "wall" regions.
Tonnesen et al. (2017) find that the underlying IGM clouds in their cluster
simulation region are typically at least a factor of 1.5 hotter than in the
void region. In the temperature regime $T\sim 10^{4.5}$ K, such a temperature
difference would manifest as a roughly 4 km s-1 increase in the $b$ parameter
(for purely thermal broadening, $b=12.8(T/10^{4}\,\mathrm{K})^{1/2}$ km s-1),
but our measurement of Doppler $b$ parameters for wall and void absorbers does
not yield evidence of such a shift (note again that the measured $b$
parameters are also substantially broadened by the spectroscopic resolution of
HST/COS). Our CDD is less affected by cosmic variance in the void and wall
environments, because we examined Ly $\alpha$ absorbers in a much larger
volume, including hundreds of voids.

Figure 11: Column density distribution (CDD) of HST/COS Ly $\alpha$ absorbers
in walls (black) and voids (red). This function, the number of absorbers per
logarithmic interval of column density per unit redshift pathlength, is
shallower in walls because they contain relatively more high column density
systems. For the sake of comparison, the upper limit of the range of column
density examined in Figure 2 of Tonnesen et al. (2017) is marked with a
vertical bar.

Next we test for variation with column density of the location of absorbers
within voids. We might expect lower column density absorbers to be more
prevalent in the deep interiors of voids, where the IGM is isolated from shock
heating from structure formation in dense regions. To test for that effect, we
split the 392 void absorbers into quartiles of column density and perform a
very simple test: What fraction of absorbers are found at less than half the
void radius? For each quartile, we count the number of Ly $\alpha$ absorbers
in the inner eighth of void volume, Nobs (r/ Rv < 1/2). The total number of
objects N in voids is compared with Nobs (r/ Rv < 1/2), the number inside the
inner eighth of void volume, and Nran (r/ Rv < 1/2), the number expected from
Poisson statistics.

Thus, we find suggestive evidence that low-NHI absorbers are more centrally
concentrated in voids and that the highest column density absorbers are less
centrally concentrated, as summarized in Table 1. In other words, there is a
trend for lower column density absorbers to be overrepresented in the central
regions of voids. This accords with the observation that low-NHI absorbers are
the least strongly correlated with galaxies, which are most sparse in the void
interiors.

Table 1: A summary of our simple statistical test of the central concentration of absorbers and galaxies in voids. The total number of objects N in voids is compared with Nobs (r/ Rv < 1/2), the number inside the inner eighth of void volume (within half the void radius), and Nran (r/ Rv < 1/2), the number expected from the fractions of sight line randoms and survey randoms inside a scaled voidcentric distance of 1/2. Our set of 36 AGN sight lines samples a higher fraction of the interior void volume. This is why the expected fraction of void absorbers in each quartile is higher than 1/8. Void galaxies are significantly less centrally concentrated than expected for a random distribution. For void absorbers we observe that the lowest column density quartile Q1 is more centrally concentrated, with the lowest quartile of column density being overrepresented in void centers compared to a random distribution. Conversely, the highest column density absorbers are underrepresented in void centers. | Gal. | Ly $\alpha$ | Q1 | Q2 | Q3 | Q4
---|---|---|---|---|---|---
N | 26,951 | 392 | 98 | 98 | 98 | 98
Nobs (r/ Rv < 1/2) | 1117 | 72 | 31 | 19 | 14 | 8
Nran (r/ Rv < 1/2) | 3369 $\pm$ 58 | 84 $\pm$ 20 | 21 $\pm$ 5 | 21 $\pm$ 5 | 21 $\pm$ 5 | 21 $\pm$ 5

###  4.5 Galaxy Association of Void Ly $\alpha$ Absorbers

To probe interactions between galaxies, the CGM, and the IGM, we find the
distance, dg, of each Ly $\alpha$ absorber to the nearest SDSS DR7 galaxy in
both volume-limited and apparent-magnitude limited samples. Following the
procedure in Keeney et al. (2018), we compute the velocity separation $\Delta
v$ between a galaxy and absorber to find distance along the line of sight

$D_{z}=\begin{cases}\frac{|\Delta v|\ -\ 400\ km\ s^{-1}}{H(z)}&\Delta v\ >\
400\ km\ s^{-1}\\\ 0&\Delta v\leq\ 400\ km\ s^{-1}\end{cases}$

where $H(z)=100h~{}km~{}s^{-1}~{}Mpc^{-1}$. For low velocity separation, small
line-of-sight distances are collapsed to zero. This is a correction for small-
scale redshift space distortions along the line-of-sight caused by
gravitational motions within systems of galaxies. The impact parameter of the
galaxy with respect to the AGN sight line and $D_{z}$ are added in quadrature
to obtain the three dimensional distance $d\textsubscript{g}$.

Figures 12 and 13 show distance to nearest galaxy, dg, versus column density,
NHI, for void (red) and wall absorbers (black), comparing respectively with
volume-limited and apparent-magnitude limited samples of SDSS DR7. As
expected, the denser apparent-magnitude limited sample yields closer matches.
Previous studies (e.g. Penton et al. 2002a; Stocke et al. 2006; Keeney et al.
2018) have generally found that Ly $\alpha$ absorbers at higher dg have lower
equivalent width or column density. Our results are similar, in that higher-
NHI absorbers tend to be more closely associated with galaxies. The large-
scale environment of Ly$\alpha$ absorbers in walls or voids does not
noticeably affect the distribution of dg, apart from the fact that void
absorbers are considerably more prevalent at higher dg, because they occupy
regions of lower galaxy density. In Figure 13 we see a population of void
absorbers that are close to galaxies (dg $<$ 1 h-1 Mpc); these matches tend to
occur close to the void edges. A relatively small number of wall absorbers are
also relatively isolated from bright galaxies; these occupy voids that are
below the cutoff radius of the VoidFinder algorithm, 10 h-1 Mpc (in other
words, a less stringent definition of voids would have caused those to be
labeled "void absorbers").

Figure 12: Scatterplot of atomic hydrogen column density $\log{N_{HI}}$ vs.
distance to nearest galaxy dg in the volume-limited sample (0.003 $\leq$ z
$\leq$ 0.107, Mr $<$ -20.09) of SDSS DR7 for the 605 HST/COS absorbers in SDSS
DR7. Wall absorbers are black, void absorbers red. Figure 13: Scatterplot of
atomic hydrogen column density $\log{N_{HI}}$ vs. distance to nearest galaxy,
dg, in the apparent-magnitude limited ($<17.77$) galaxy sample in SDSS DR7
($0.003\leq z\leq 0.107$) for the 605 HST/COS absorbers in SDSS DR7. Wall
absorbers are black, void absorbers red.

##  5 Discussion

The spatial distribution of HST/COS Ly$\alpha$ absorbers inside voids shares
characteristics with both a uniform random distribution and the strongly
clustered galaxy distribution. The void density profile of Ly$\alpha$
absorbers as a function of scaled voidcentric distance, shown in Figure 8,
appears consistent with a uniform distribution; the prominent density spike in
the lowest bin is not statistically significant, as indicated by the size of
the errorbar. On the other hand, there is a significant density enhancement of
Ly$\alpha$ absorbers close to the void-wall boundary, as shown in Figure 6,
which plots the void density profile of Ly$\alpha$ absorbers as a function of
distance to cosmic walls. This density enhancement near void boundaries shows
that Ly$\alpha$ absorbers are not randomly distributed inside voids. A
similar, possibly related rise in density appears near void boundaries in the
density profile of galaxies shown in Figure 6.

We conclude that there are two populations of Ly$\alpha$ absorbers inside
voids: one with a spatial distribution that appears nearly random, and another
associated with galaxies near the edges of voids. This interpretation is
supported by our analysis of the cumulative distribution function of
Ly$\alpha$ absorbers inside voids. Their cumulative distribution is close to
random, but slightly skewed toward the void edges. As seen in Figure 13, only
lower column density absorbers ($\log{N_{HI}}<15$) are far from any galaxies.
This isolated population of Ly$\alpha$ absorbers is mainly found in voids.
There are also some wall absorbers that are far from any galaxies, but such
absorbers reside in underdense regions that are too small to be classified as
voids by the VoidFinder algorithm (the maximal sphere radius cannot be less
than 10 h-1 Mpc). By contrast, the absorbers associated with galaxies include
both low and high column density systems.

Previous research has also suggested there may be two populations of IGM
clouds detected in Ly$\alpha$ absorption. Wilde et al. (2021) found that high
column density absorbers (NHI $>$ 1014 cm-2) are usually close enough to be
physically associated with a galaxy (within two virial radii of a galaxy).
Weaker Ly $\alpha$ absorbers were more widely distributed, probably because
they tend to be associated with extended large-scale structure but not
particular galaxies or galaxy groups. Tejos et al. (2012), a study of HST/STIS
absorbers in SDSS DR7, proposed that there are three populations of Ly$\alpha$
absorbers associated with galaxies, overdense large-scale structure, and
underdense large-scale structure. They noted that absorbers in underdense
large-scale structure, or the interior volume of voids, may not be randomly
distributed.

Ly $\alpha$ absorption primarily traces a diffuse phase of the IGM, defined by
(Kitayama & Suto, 1996) as being below a threshold temperature (T$<$105) and
threshold density,

$\delta_{th}=6\pi^{2}(1+0.4093(\frac{1}{f_{\Omega}}-1)^{0.9052})$ (2)

where

$f_{\Omega}=\frac{\Omega_{m}(1+z)^{3}}{\Omega_{m}(1+z)^{3}+(1-\Omega_{m}-\Omega_{\Lambda})(1+z)^{2}+\Omega_{\Lambda}}$
(3)

Cosmological simulations (Davé et al., 2010; Rodríguez Medrano et al., 2021)
suggest that this diffuse phase constitutes about 40 per cent of the IGM.
Hotter, more ionized phases are weak in Ly $\alpha$, but may be traced by the
O VI absorption line. Thus the spatial distribution of Ly $\alpha$ absorbers
depends not only on the baryon distribution, but also the ionisation fraction
of intergalactic hydrogen. Environmental conditions in the interiors of voids,
namely isolation from the effects of shock-heating from structure formation
and adiabatic super-Hubble expansion, cool and lower the ionisation fraction
of intergalactic hydrogen. Hydrodynamic simulations by Cen (2011) show that
shock heating of halo gas in dense wall regions prevents most of it from
cooling within the current age of the universe. This likely explains why voids
have more Ly $\alpha$ absorbers than walls, despite the fact that they contain
less gas by mass.

We find a significant over-representation of HST/COS absorbers in the lowest
quartile of column density inside the interior eighth of void volume (compared
to a random distribution), which suggests that there could be a special
population of low column density absorbers created by cold and diffuse
hydrogen near the centers of voids. This population could contribute to the
peak in the density profile of Ly$\alpha$ absorbers near the void center, in
the lowest bin of Figure 8, although as noted previously, the peak is not
statistically significant. Results from cosmological hydrodynamic simulations
also suggest that cold, neutral hydrogen gas is preferentially found near void
centres, where there is no shock-heating from structure formation. Kreckel et
al. (2011), a study of galaxies in the Enzo simulation (Bryan, 1999), found
that low-luminosity dwarf galaxies are over-represented near the centre of the
void region. A more recent cosmological simulation using over a thousand voids
by Rodríguez Medrano et al. (2021) found that most intergalactic hydrogen in
the interiors of voids exists in a diffuse, low temperature phase (T$<$1015
K), which is strong in Ly $\alpha$ absorption.

We have focused our examination on Ly $\alpha$ absorption systems, but note
that metal absorption components present in HST/COS AGN spectra can provide a
fuller picture of the gas conditions in voids. Since intergalactic hydrogen is
highly ionised, it is mostly undetectable in FUV absorption. Stocke et al.
(2019), a spectroscopic study of gas associated with galaxy groups in the FUV,
failed to detect a diffuse intergroup medium that would complete the baryon
census. Nicastro et al. (2018) claimed detection of these missing baryons
through x-ray spectroscopy. The missing baryons are a hot phase of the WHIM
($T=10^{5.7}-10^{6.3}\ K$) located in large galaxy overdensities. Complex
feedback between the IGM, CGM, and galaxies shape their evolution. Matter
circulated from the IGM into galaxies fuels star formation (Erb, 2008;
Prochaska & Wolfe, 2009; Genzel et al., 2010). Supernovae and AGN feedback
cause gas outflow from galaxies into the CGM and ultimately IGM, altering
their primordial composition by introducing metals (e.g. Madau et al. 2001;
Pallottini et al. 2014; Bower et al. 2006). We note that three O VI
components, which trace WHIM, fall within the footprint and redshift limit of
our SDSS DR7 void catalog. Two of these are inside voids, and one is well
within the void interior, at a scaled voidcentric distance of less than a
half.

##  6 Conclusions

We characterize the spatial distribution and intrinsic properties of HST/COS
Ly $\alpha$ absorbers within voids detected in the nearby volume mapped by
SDSS DR7. These voids fill 68 per cent of the survey volume, and contain a
comparable fraction of absorbers, but only a fifth of the galaxies. The void
density profile of all Ly $\alpha$ absorbers as a function of scaled
voidcentric distance appears consistent with a uniform distribution in the
interiors of voids. Similarly, the cumulative distribution function of Ly
$\alpha$ absorbers inside voids shows they are similar to a random
distribution, but have a slight tendency to reside close to the edges of
voids. In detail, the spatial distribution of absorbers inside voids depends
on HI column density. Absorbers in the lowest quartile of HI column density
are more centrally concentrated in the deep interiors of voids, whereas
absorbers in the highest quartile of column density are skewed toward the void
wall boundaries. Near the void-wall boundary, we find a slight but
statistically significant enhancement in Ly $\alpha$ absorber density, in the
same region where galaxy density prominently rises to form the walls that
bound voids. We interpret these findings in terms of two populations of Ly
$\alpha$ absorbers in the low-redshift universe. One is associated with
galaxies and covers the full range of column density. This population is
likely to include gas that is in the diffuse IGM phase as well as some WHIM as
defined by Davé et al. (2010). The other population of absorbers is more
uniformly distributed, consists only of lower column density systems
($\log$NHI $<$ 14.5), and is likely to be purely in the diffuse IGM phase.

## Data Availability

The data underlying this article are available at
https://archive.stsci.edu/prepds/igm/.

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