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# Modelling gas around galaxy pairs and groups using the Q0107 quasar triplet

Alexander Beckett1,2, Simon L. Morris1, Michele Fumagalli3,4, Nicolas Tejos5,
Buell Jannuzi6, Sebastiano Cantalupo3
1Centre for Extragalactic Astronomy, Durham University, South Road, Durham DH1
3LE, UK
2Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA
3Dipartimento di Fisica G. Occhialini, Università degli Studi di Milano
Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
4INAF - Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, 34143
Trieste, Italy
5Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla
4059, Valparaíso, Chile
6Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson,
AZ 85721, USA Contact e-mail<EMAIL_ADDRESS>
(Last updated 2023 Feb 21; in original form 2023 Feb 21)

###### Abstract

We examine to what extent disk and outflow models can reproduce observations
of H i gas within a few virial radii of galaxies in pairs and groups. Using
highly-sensitive HST/COS and FOS spectra of the Q0107 quasar triplet covering
Ly$\alpha$ for z$\lesssim$1, as well as a deep galaxy redshift survey
including VIMOS, DEIMOS, GMOS and MUSE data, we test simple disk and outflow
models against the H i absorption along three lines-of-sight (separated by
200-500 kpc) through nine galaxy groups in this field. These can be compared
with our previous results in which these models can often be fit to the
absorption around isolated galaxies. Our models can reproduce $\approx$ 75% of
the 28 identified absorption components within 500 km s-1 of a group galaxy,
so most of the H i around groups is consistent with a superposition of the CGM
of the individual galaxies. Gas stripped in interactions between galaxies may
be a plausible explanation for some of the remaining absorption, but neither
the galaxy images nor the galaxy and absorber kinematics provide clear
evidence of such stripped material, and these unexplained absorbers do not
preferentially occur around close pairs of galaxies. We find H i column
densities typically higher than at similar impact parameters around isolated
galaxies ($\approx$ 2.5$\sigma$), as well as more frequent detections of O vi
than around isolated galaxies (30% of sightlines to 7%).

###### keywords:

intergalactic medium – quasars: absorption lines – galaxies: evolution

††pubyear: 2023††pagerange: Modelling gas around galaxy pairs and groups using
the Q0107 quasar triplet–A.6

##  1 Introduction

The exchange of gas between galaxies and their surroundings plays a vital role
in their evolution. Cool gas that provides fuel for star formation needs to be
accreted from outside the galaxy in order to explain the observed star-
formation rates and gas content of galaxies (e.g. Freundlich et al., 2013;
Scoville et al., 2017). Cool gas is also ejected from galaxies by stellar-
feedback- or AGN-driven winds, and models suggest that these processes are
important in regulating its star formation (e.g. Lehnert et al., 2013;
Somerville & Davé, 2015; Salcido et al., 2020). This reservoir of gas
surrounding galaxies is known as the circumgalactic medium (CGM, e.g.
Tumlinson et al. 2017), and is usually defined as extending to the virial
radius.

This material is difficult to observe in emission due in part to its low
density (although emission-line maps of gas on CGM scales have become more
common in recent years, e.g. Chen et al. 2019; Fossati et al. 2019a; Zabl et
al. 2021; Leclercq et al. 2022), so is most commonly detected using absorption
features along the lines-of-sight to background sources, often quasars (e.g.
Bahcall & Spitzer, 1969; Bergeron, 1986; Bergeron et al., 1994; Weymann et
al., 1998; Adelberger et al., 2005; Chen et al., 2010; Prochaska et al., 2011;
Rubin et al., 2018; Pointon et al., 2019; Wilde et al., 2021; Lehner et al.,
2021). These absorption-based studies often discuss large numbers of galaxy-
sightline pairs, whether as targeted surveys (e.g. Tumlinson et al., 2013;
Bielby et al., 2019) or by utilizing other surveys and/or archival data (e.g.
Wild et al., 2008), but are usually limited to a single line-of-sight through
the gas around any galaxy or group. Some studies are able to utlilize quasar
pairs or triplets (lensed or projected, e.g. Fossati et al., 2019b; Maitra et
al., 2019), bright background galaxies (e.g. Zahedy et al., 2016; Péroux et
al., 2018; Chen et al., 2020; Okoshi et al., 2021) or gravitationally-lensed
arcs (e.g. Lopez et al., 2018, 2020; Tejos et al., 2021; Mortensen et al.,
2021), but these are not common enough to produce statistically meaningful
samples of galaxy-absorber pairs.

Many observations find evidence for disk-like accreting and rotating
structures along the major axis of galaxies (e.g. Charlton & Churchill, 1998;
Steidel et al., 2002; Bouché et al., 2016; Ho et al., 2017; Zabl et al., 2019;
French & Wakker, 2020), and this is generally reproduced by simulations, with
simulated CGM structures aligned with the galaxy major axis (e.g Ho & Martin,
2019; Mitchell et al., 2020a; DeFelippis et al., 2020; Hafen et al., 2022).
Similarly, evidence for outflowing material is often found along the minor
axis of galaxies (e.g. Bland & Tully, 1988; Heckman et al., 1990; Finley et
al., 2017; Lan & Mo, 2018; Schroetter et al., 2019; Burchett et al., 2021;
Zabl et al., 2021), which are also reproduced by simulations (e.g Nelson et
al., 2019; Mitchell et al., 2020b; Pandya et al., 2021). This leads to some
observations finding a bimodality in the azimuthal angles of detected
absorption (absorption is found primarily along the major and minor axes, e.g.
Kacprzak et al., 2012; Bouché et al., 2012; Kacprzak et al., 2015), as well as
differences in flow rates and metallicities along galaxy major and minor axes
in simulations (e.g. Péroux & Howk, 2020).

However, gas flows around galaxy groups are likely far more complex. For
example, in the nearby M81/M82 group, H i observations reveal a conical
outflow structure on small scales, but clear distortion on larger scales due
to the other group galaxies (e.g. Sorgho et al., 2019). Tidal interactions are
expected to produce a significant fraction of Ly$\alpha$ absorbers in groups
(e.g. Morris & van den Bergh, 1994), and likely contribute to other observed
ions (e.g. Chen & Mulchaey, 2009). Some studies have identified possible tidal
material in absorption, but this is usually difficult to distinguish from
other origins (e.g. Chen et al., 2014; Guber et al., 2018). Ram-pressure
stripping is also likely to affect the state of the CGM and any intra-group
gas during interactions (e.g. Fumagalli et al., 2014; Fossati et al., 2019a).
This removal of gas from galaxies and their CGM affects not only the gas
itself, but also leads to ‘quenching’ of star formation in group galaxies
(e.g. Peng et al., 2010; Wetzel et al., 2013; Jian et al., 2017; Kuschel et
al., 2022)

There have been numerous case studies focusing on the gas in individual galaxy
groups, using a variety of absorption features, but also emission lines in
more recent cases. Some of these find material that can be associated with a
particular galaxy, including some likely outflows and accretion (e.g. Péroux
et al., 2017; Johnson et al., 2018), but also material that cannot be
associated with a galaxy, and therefore forms an intra-group medium (e.g
Bielby et al., 2017; Epinat et al., 2018), as well as suggestions of tidal
material (e.g. Kacprzak et al., 2010; Chen et al., 2019). Where multiple
absorption/emission components can be identified, material consistent with
both disk/outflow structures and tidal/intra-group material can sometimes be
seen in the same galaxy group (e.g. Nateghi et al., 2021; Leclercq et al.,
2022).

Statistical studies utilizing large samples of galaxy groups are also used to
determine the dominant processes in these systems. Bordoloi et al. (2011)
found that Mg ii absorption near galaxy groups could be due to a superposition
of the halos around individual galaxies. In contrast, Nielsen et al. (2018)
found that a superposition model could not match the absorber kinematics, and
preferred a model in which most cool gas was associated with the group itself
rather than any member galaxy. More recently, Dutta et al. (2020) found Mg ii
absorption more extended around galaxy groups than isolated galaxies, but also
a clear dependence on galaxy properties, suggesting that both the galaxy halos
themselves and the interactions between galaxies contribute to the absorption.

If material stripped from galaxies contributes substantially to the gas
content in groups, then we may expect gas in these groups to have a higher
metal content (having passed through the galaxy and been enriched by cycles of
star formation, e.g. Oppenheimer et al. 2016). However, this is not found by
Pointon et al. (2019).

The distribution of gas in groups therefore remains unclear. Emission from the
CGM remains difficult to detect due to a low density, which usually limits
such studies to scales of $\lesssim$100 kpc (e.g. Burchett et al., 2021;
Leclercq et al., 2022). There remains inconsistency in defining galaxy groups,
which are subject to different algorithms, linking lengths, and detection
limits in different studies. This makes direct comparisons between
observations, or with simulations, difficult (e.g. Oppenheimer et al., 2021).
The power of absorption studies is limited by the presence of sufficiently
bright background sources, so in most cases the gas around any galaxy group is
probed by only a single line-of-sight and we cannot measure gas properties
elsewhere in the group.

It is this final difficulty which we seek to address in this paper. We study
the Q0107 field, a quasar triplet at z $\sim$ 1 with separations of $\sim$ 1
arcminute ($\approx$ 400 kpc at z = 0.5), with basic quasar properties given
by Table 1. The use of multiple lines-of-sight through a densely-surveyed
field helps to constrain the gas structures and properties on CGM scales.

This field has been utilized in several previous studies, including early
studies of the size scales of Ly$\alpha$ absorbers (e.g. Dinshaw et al., 1997;
D’Odorico et al., 1998; Young et al., 2001), analysis of the coincidences
between absorption in the different lines-of-sight (e.g. Petry et al., 2006;
Crighton et al., 2010), construction of the 2D 2-point correlation functions
of absorption in both H i and O vi (Tejos et al. 2014, hereafter T14, Finn et
al. 2016), and detailed radiative transfer modelling of a small number of
absorbers (e.g. Muzahid, 2014; Anshul et al., 2021). Improvements to the
available data, such as higher-resolution spectra of the three quasars, high-
resolution imaging from the Hubble Space Telescope, and IFU observations of
the field, have enabled our recent works extending these results.

In Beckett et al. (2021), hereafter denoted as Paper 1, we examined some
statistical properties of the relationship between gas and galaxies in this
field. We found a bimodality in the azimuthal angle distribution of detected
galaxy-absorber pairs, likely evidence for the existence of disk and outflow
structures along the projected major and minor axes of galaxies, extending to
$\approx$ 300 kpc. A higher incidence of O vi absorption along the minor axis,
and a preference for the velocity of H i absorption near the major axis to be
aligned with the galaxy kinematics, support this hypothesis. We investigated
this further in Paper 2 (Beckett et al., 2022), in which we attempted to fit
simple disk and outflow models to isolated galaxies in our sample, finding
that many absorbers (13 of 26 within 500 km s-1, or 12 of 20 within 300 km
s-1, and impact parameters up to 600 kpc) could be fit using such models,
whilst remaining consistent with the observations of the other sightlines.

This work continues to use the disk and outflow models from Paper 2, but
extends coverage to galaxy pairs and groups in our sample. By combining
disk/outflow models, we can examine the hypothesis in which most absorption in
groups results from the CGM of the individual galaxies. We also search for
signs of tidal material based on the kinematics of the gas relative to nearby
galaxies.

In Section 2 we summarize the galaxy and quasar data used in this study,
discussed more extensively in Paper 1 and references therein, as well as
selection of the sub-sample of galaxy groups considered in this work. Section
3 summarizes the toy models used in our attempts to reproduce the observed
absorption (covered in more detail in Paper 2), whilst Section 4 describes in
detail the absorption around each galaxy group, and the process of attempting
to fit our models to that absorption. We then discuss the overall results in
Section 5, and finally summarize in Section 6.

Throughout this work we quote physical sizes and distances unless otherwise
stated, and use the Planck 2018 flat $\Lambda$CDM cosmology (Planck
Collaboration, 2020), with $\Omega_{m}$ = 0.315 and $H_{0}$ = 67.4 km s-1
Mpc-1.

Object | RA (J2000) | Dec (J2000) | Redshift | R-mag
---|---|---|---|---
Q0107-025 A | 01:10:13.14 | -2:19:52.9 | 0.960 | 18.1
Q0107-025 B | 01:10:16.25 | -2:18:51.0 | 0.956 | 17.4
Q0107-0232 (C) | 01:10:14.43 | -2:16:57.6 | 0.726 | 18.4
Table 1: Co-ordinates, redshifts and R-band magnitudes of the three quasars,
taken from Crighton et al. (2010)

##  2 Data

This paper uses the same absorber and galaxy catalogues as our previous two
papers covering this field, which utilise the galaxy catalogues compiled by
T14. We therefore only briefly describe the observations here; these are
described in more detail in Paper 1 and T14.

###  2.1 IGM data

Spectra of the three quasars were taken to cover the Ly$\alpha$ transition of
H i along each line-of-sight from $z=0$ to the redshift of the quasar. These
use the spectrographs on the Hubble Space Telescope, with the G130M and G160M
gratings on the Cosmic Origins Spectrograph (COS, Green et al., 2012, program
GO-11585, PI: Neil Crighton) and the G190H and G270H gratings on the Faint
Object Spectrograph (FOS, observations detailed in Young et al. 2001),
covering a wavelength range of 1135-3277 Å. This includes a range of metal
ions in addition to Ly$\alpha$. QSO-C was not observed using the G130M and
G270H gratings, with these made unnecessary by a sub-damped Lyman-$\alpha$
system at z $\approx$ 0.56 obscuring any flux below 1420 Å, and a lower QSO
redshift respectively. Details of the observations and properties of the
observed spectra are listed in Table 2 of Paper 1.

Our absorption line catalogue was produced by T14, and also used by Finn et
al. (2016) and our earlier papers. It contains 430 absorption systems, of
which 272 are H i. The process of producing this catalogue is detailed in T14.

The signal-to-noise ratio of the COS spectra (using results from Keeney et al.
2012), as well as the H i column density distribution of our sample, imply a
3$\sigma$ detection limit of $\sim 10^{13}\textrm{cm}^{-2}$. The FOS detection
limit is slightly higher, at $\sim 10^{13.5}\textrm{cm}^{-2}$.

We note that Ly$\alpha$ absorbers in the IGM are usually found with Doppler
widths $>$ 20 km s-1(e.g Davé et al., 2010), so most are resolved in the COS
spectra (Ly$\alpha$ below z $\approx$ 0.45). Absorption in the FOS spectra is
often unresolved and more likely to be blended with other features, but for
Ly$\alpha$ these issues can often be mitigated using Ly$\beta$ or higher-order
Lyman transitions that remain in the COS wavelength range. Where these
mitigations are not possible, absorbers may have a large Doppler parameter
that appears as a broad-Ly$\alpha$ absorber (BLA). Whether such a BLA
appearing around our galaxies may indicate high temperatures or is unresolved
narrower absorption is discussed in each case (Section 4 and Appendix A).

###  2.2 Galaxies

Our sample of galaxy groups is drawn from the spectroscopic galaxy catalogue
described in Paper 1, which builds on that used in T14. This forms a highly
heterogeneous galaxy survey, with VIMOS, DEIMOS, GMOS and CFHT-MOS
observations of differing area, depth and completeness (referred to as MOS
observations throughout), supplemented by MUSE fields centered on the A and B
lines-of-sight. Additionally, high-resolution imaging from the Hubble Space
Telescope is used to provide position angle and inclination estimates for some
galaxies. These observations, the methods used to combine them and ensure
consistency, and the resulting survey properties, are discussed in detail in
Paper 1 (their Section 2). In this work we only provide a brief summary of
this information.

####  2.2.1 MOS

The multi-object spectrograph on the Canada-France-Hawaii Telescope (CFHT-MOS)
(Le Fevre et al., 1994) was used to obtain spectra for 29 galaxies in the
Q0107 field, described in Morris & Jannuzi (2006), whilst VIMOS (LeFevre et
al., 2003) took 935 spectra (ESO programs 086.A-0970, PI:Crighton; and
087.A-0857, PI: Tejos). 642 galaxies in this field were observed using DEIMOS
(Faber et al. 2003, program A290D, PIs: Bechtold and Jannuzi), with 210
spectra added by GMOS (Davies et al. 1997, program GS-2008B-Q-50, PI:
Crighton).

Galaxies appearing in more than one of these surveys were used to ensure
consistent wavelength calibration across all MOS surveys (and therefore
consistent redshifts in the resulting catalogue). As DEIMOS has the best
resolution, the redshifts of VIMOS and GMOS objects were adjusted to match the
DEIMOS frame, requiring a systematic shift of $\Delta z\sim$ 0.0008 for the
VIMOS data, and 0.0004 for the GMOS data see Section 3 of T14).

####  2.2.2 MUSE

GTO observations (ESO program ID 094.A-0131, PI Schaye) cover
$1^{\prime}\times 1^{\prime}$ fields of view around QSOs A and B. These
provide galaxy kinematics for galaxies near to the lines-of-sight, and are
also slightly deeper than the MOS surveys. The MUSE data cover the wavelength
range from 4750 to 9350 Å with FWHM of $\approx$2.7 Å, and offer seeing of
$0.96^{\prime\prime}$ for QSO-A, and $0.82^{\prime\prime}$ for QSO-B.

We reduced the data using a pipeline similar to many recent papers (e.g
Fumagalli et al., 2016, 2017; Fossati et al., 2019b; Lofthouse et al., 2020;
Bielby et al., 2020), primarily using ESO routines, but also utilizing the
CUBEX package (Cantalupo et al., 2019) to apply a renormalization between the
different IFUs, stacks and slices, and an improved, flux-conserving sky
subtraction.

Objects were detected using the SExtractor software (Bertin & Arnouts, 1996),
applied to the white-light image. Summing the total flux within the SExtractor
aperture produced the 1D spectra, for which redshifts were estimated using
MARZ (Hinton et al., 2016).

####  2.2.3 Combined Galaxy Catalogue

Combining the spectra from multiple instruments into a single galaxy catalogue
for this field requires matching the astrometry of galaxies observed by
multiple instruments, so that duplicates can be removed. We then checked other
galaxy properties to ensure these were consistent across the different
observations.

We confirmed accurate astrometry for each instrument by comparing the
brightest objects in the MOS and MUSE catalogues with the SDSS source
catalogue (Albareti et al., 2017). Coordinates from the MOS catalogues matched
the SDSS results within 0.5$"$, whilst the MUSE results required a shift of
$\approx$1$"$. After this shift, we matched objects appearing within 1$"$ in
both catalogues, finding no additional matches within 2$"$. Magnitudes
obtained by integrating the MUSE spectra were compared with the results from
the MOS surveys, and found to be consistent within the estimated
uncertainties.

We also compared redshifts to ensure that all of our galaxy samples are in the
same frame as the absorption features. Across a large sample of
galaxy–absorber pairs, any velocity offsets should average to zero, with no
systematic offset. We found that the corrections applied when producing the
T14 catalogue (described in Section 2.2.1) had already removed any systematic
shift, with precision better than 10 km s-1, whilst the MUSE data required a
shift of $\approx$ 30 km s-1to match the MOS redshifts.

We utilize the duplicate observations, where a single galaxy was observed by
the same instrument on multiple occasions, to estimate the uncertainties in
our redshift measurements. We calculated the velocity differences between each
pair of duplicate spectra, and used the standard deviation of the velocity
differences to estimate the uncertainty in the redshifts estimated from each
instrument. These are given in Table 5 of Paper 1, and vary between 30 km s-1
(for well-determined redshifts in DEIMOS) and 190 km s-1 (for single-feature
detections in VIMOS).

Our MUSE observations contain no duplicates. As MUSE has a higher resolution
than GMOS, but lower than DEIMOS, we take the GMOS values as conservative
estimates of the velocity uncertainties for MUSE galaxies with the same
confidence flags.

####  2.2.4 HST imaging

High-resolution imaging obtained using the ACS instrument on the Hubble Space
Telescope (Ryon, 2019) is available for this field in the F814W band (Program
GO-14660, PI Straka). This imaging enables a much clearer view of any
distortions of the galaxies due to interactions, as well as much improved
measurements of position angles and inclinations than are possible with the
lower-resolution ground-based imaging available previously. This image does
not cover the full field of our MOS surveys, so these improved position angle
and inclination estimates are only available for a subset of galaxies in our
catalogue, as shown in Figure 1.

We modelled galaxies in both our redshift catalogue and the HST image using
GALFIT (Peng et al., 2002). This uses chi-squared minimization to produce a
best-fitting model of a galaxy’s morphology. We used the SExtractor results as
initial guesses in attempting to fit a Sersic disk to each galaxy. Where
necessary, additional model components were introduced until a reasonable fit
was found. This more advanced modelling, taking account of the point-spread
function of the image, reduced the average uncertainty on both inclination and
position angle measurements by a factor of $\approx$ 3 relative to the
SExtractor results.

We excluded galaxies for which the fit clearly failed to converge to a
reasonable result, but included galaxies that have large uncertainties on
position angle due to being near to face-on. This produced a list of 109
galaxies for which position angle, inclination and redshift measurements were
found.

###  2.3 Sample of galaxy groups

Paper 2 considered only isolated galaxies, defined as those with no detected
companion within 500 kpc and 500 km s-1, making it unlikely that the region
within a galaxy’s virial radius overlaps with that of another detected galaxy.
We also additionally imposed the constraint that no other galaxy must lie
within 1 Mpc of any of the lines-of-sight within the 500 km s-1 window. In
this work we consider galaxies that are not isolated, and therefore for the
purposes of this work a group is any set of galaxies with pairwise separations
smaller than 500 kpc and 500 km s-1, or any set of multiple galaxies within 1
Mpc of at least one of the three lines-of-sight in a 500 km s-1 window.

This definition of ‘group’ requires only two galaxies, and also has a larger
‘linking length’ (maximum distance between galaxies for them to be considered
in the same group) than many similar studies that define group galaxies (e.g.
Bordoloi et al., 2011; Nielsen et al., 2018; Fossati et al., 2019b). However,
we do use a smaller window than some other studies considering isolated
galaxies (e.g. COS-halos, Tumlinson et al., 2013). Therefore all galaxies in
our sample are considered as ’group’ or ’isolated’, but we include groups with
larger galaxy separations than other works.

These ‘group’ galaxies make up the majority of our full sample, so it is
impractical to model the absorption around all of these (more than 50 groups).
As our models rely on position angle and inclination measurements obtained
from the HST imaging, we selected our sample from groups that have at least
two galaxies lying in the HST field (of which there are 18). Because of the
time-consuming nature of modelling group absorption, we manually select a
sample of nine groups that meet this restriction, and intentionally span a
large range in group properties including redshift as well as number and mass
of group galaxies. With the difficulty in determining our uncertainties
described in Section 3, the expected gains from modelling the remaining groups
would not substantially improve the strength of our conclusions.

Our range of redshifts and stellar masses is intended to be comparable to that
seen in our isolated sample from Paper 2, and therefore includes some groups
beyond z $\approx$ 0.73, where only the A and B sightlines are available. The
selection was made ‘blindly’ with respect to the nearby absorption, in order
to avoid biasing our results. Similarly, we do not preferentially select
groups containing galaxies in the MUSE fields, as these are biased towards
low-mass, star-forming galaxies and only a small subset of these have useful
kinematics.

We also check for any additional bias introduced through this selection, by
comparing our nine selected groups with the nine groups not selected for this
work. If the largest group in the field (G-202) is removed, the selected and
not-selected samples have similar average properties in terms of galaxy number
(selected and non-selected samples with a median of 4 galaxies within 1 Mpc
and 500 km s-1), total galaxy mass ($10^{11.1}$ and $10^{11.2}$ $M_{\odot}$
respectively), and closest impact parameter (120 and 135 kpc). However, our
selected sample is slightly biased towards lower redshifts (0.52 vs 0.65). Any
alternative sample of groups selected to cover the redshift range seen in
Paper 2 would therefore tend to have similar galaxy properties.

We note that the definition of ‘group’ does vary substantially across our
large redshift range, such that a group at low redshift would be seen as an
isolated galaxy is it were at a higher redshift, with any satellite galaxies
going undetected. However, this does not strongly affect our sample, as most
of our groups have at least two members that could be detected up to z
$\approx$ 1\. G-517 is the only group likely to be classified as isolated if
it lay at a different redshift, whilst G-383 (consisting of two faint
galaxies) could appear isolated in a small redshift range but would more
likely go undetected entirely.

Table 2: Summary of group properties for our selected sample of galaxy groups. Columns are as follows: (1) Group reference used throughout the paper; (2) group central redshift; (3) number of detected galaxies within 500 km s-1of the central redshift and 1 Mpc of at least one QSO line-of-sight; (4) total stellar mass of detected galaxies ; (5) closest impact parameter of any galaxy to any line-of-sight; (6) minimum separation between two detected galaxies; (7) r-band luminosity ratio between brightest two galaxies; (8)-(10) estimated galaxy detection limits in the MOS and MUSE surveys, showing continuum estimates in terms of $L_{\star}$ and SFR limits on emission-line-only detections. Group Ref | z | N gals | total $\textrm{M}_{\star}$ | $\textrm{b}_{min}$ | Min Pair | Lum Ratio | Det Lim (MOS) | Det Lim (MUSE) | Det Lim (Line-only)
---|---|---|---|---|---|---|---|---|---
|  |  | $\textrm{log}_{10}(\textrm{M}_{\odot})$ | (kpc) | (kpc) |  | ($L_{\star}$) | ($L_{\star}$) | ($\textrm{M}_{\odot}$/yr)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
G-202 | 0.202 | 25 | 11.9 $\pm$ 0.2 | 103 | 17 | 2.6 | 0.004 | 0.003 | 0.004
G-238 | 0.238 | 4 | 11.5 $\pm$ 0.2 | 236 | 42 | 1.5 | 0.006 | 0.004 | 0.005
G-383 | 0.383 | 2 | 9.7 $\pm$ 0.2 | 38 | 5 | 1.5 | 0.018 | 0.011 | 0.016
G-399 | 0.399 | 5 | 11.1 $\pm$ 0.2 | 122 | 71 | 3.3 | 0.020 | 0.013 | 0.018
G-517 | 0.517 | 2 | 10.3 $\pm$ 0.2 | 95 | 320 | 29.5 | 0.04 | 0.02 | 0.03
G-536 | 0.536 | 6 | 11.5 $\pm$ 0.4 | 120 | 4 | 1.4 | 0.04 | 0.03 | 0.04
G-558 | 0.558 | 7 | 11.1 $\pm$ 0.5 | 148 | 53 | 1.2 | 0.04 | 0.03 | 0.04
G-876 | 0.876 | 4 | 11.1 $\pm$ 0.4 | 75 | 26 | 2.1 | 0.13 | 0.08 | 0.12
G-907 | 0.907 | 2 | 10.7 $\pm$ 0.5 | 170 | 594 | 1.7 | 0.15 | 0.09 | 0.13
Table 3: Summary of galaxy properties for our selected sample of group galaxies. For each group only galaxies with position angle and inclination measurements are shown. Derivation of these properties is described in more detail in Paper 1. Column descriptions: (1) Group ID used in this work; (2) Galaxy ID (MUSE and MOS IDs were collated separately; MUSE ID is used for galaxies featuring in both MOS and MUSE catalogues); (3, 4) On-sky coordinates of galaxy; (5) Observed magnitude in the SDSS r-band; (6) Galaxy luminosity in SDSS r-band as a multiple of $L_{\star}$ ($L_{\star}$ estimate from Montero-Dorta & Prada (2009), uncertainties smaller than 0.005 $L_{\star}$ are omitted); (7) Stellar mass estimated as in Johnson et al. (2015) (for most galaxies the largest uncertainty is a scatter of 0.15 dex in their relation); (8) Halo mass estimated using the abundance matching technique from Behroozi et al. (2010); (9) Star-formation flag denoting a star-forming or non-star-forming galaxy; (10) Star-formation rate estimated from galaxy emission lines, using the Kennicutt (1998) and Kewley et al. (2004) calibrations for H$\alpha$ and [O ii] respectively (uncertainties are a combination of scatter in these relationships and uncertainty in the line fit); (11) Line used to estimate SFR (SFRs estimated from H$\beta$ using the correlation between SFR estimated from H$\alpha$ and H$\beta$ line luminosity, generating a substantially larger uncertainty); (12) Note of whether emission-line kinematics from the MUSE data are available for this galaxy.  Group | Galaxy | RA | Dec | r-band | Luminosity | $\textrm{M}_{\star}$ | $\textrm{M}_{h}$ | SF Flag | SFR | Line | Kinematics
---|---|---|---|---|---|---|---|---|---|---|---
|  | ∘ | ∘ |  | ($L_{\star}$) | $\textrm{log}_{10}(\textrm{M}_{\odot})$ | $\textrm{log}_{10}(\textrm{M}_{\odot})$ |  | ($\textrm{M}_{\odot}$/yr) |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
G-202 | B-22 | 17.5600 | -2.3173 | 22.86 $\pm$ 0.03 | 0.02 $\pm$ 0.01 | 8.4 $\pm$ 0.2 | 10.9 $\pm$ 0.3 | non-SF | 0.06 $\pm$ 0.04 | H$\alpha$ | Poor
| 25962 | 17.5589 | -2.3548 | 21.46 $\pm$ 0.01 | 0.07 $\pm$ 0.01 | 8.7 $\pm$ 0.1 | 11.0 $\pm$ 0.3 | SF | 0.5 $\pm$ 0.3 | H$\alpha$ | No
| 31704 | 17.5453 | -2.2958 | 22.58 $\pm$ 0.02 | 0.03 $\pm$ 0.01 | 8.2 $\pm$ 0.1 | 10.8 $\pm$ 0.3 | SF | 0.08 $\pm$ 0.05 | H$\alpha$ | No
| 31787 | 17.5556 | -2.3002 | 21.35 $\pm$ 0.01 | 0.08 $\pm$ 0.01 | 9.7 $\pm$ 0.1 | 11.5 $\pm$ 0.2 | SF | 0.5 $\pm$ 0.2 | H$\alpha$ | No
| 32497 | 17.5567 | -2.3000 | 18.46 $\pm$ 0.01 | 1.10 $\pm$ 0.01 | 11.0 $\pm$ 0.1 | 13.1 $\pm$ 0.5 | non-SF | 2.3 $\pm$ 1.9 | H$\alpha$ | No
| 32778 | 17.5458 | -2.2893 | 19.59 $\pm$ 0.01 | 0.39 $\pm$ 0.01 | 10.2 $\pm$ 0.1 | 11.8 $\pm$ 0.3 | SF | 1.5 $\pm$ 0.5 | H$\alpha$ | No
G-238 | 26677 | 17.5604 | -2.3491 | 20.59 $\pm$ 0.01 | 0.22 $\pm$ 0.01 | 9.7 $\pm$ 0.2 | 11.4 $\pm$ 0.3 | SF | 1.3 $\pm$ 0.4 | H$\alpha$ | No
| 29214 | 17.5395 | -2.3244 | 21.38 $\pm$ 0.01 | 0.11 $\pm$ 0.01 | 8.9 $\pm$ 0.1 | 11.1 $\pm$ 0.3 | SF | 0.4 $\pm$0.1 | H$\alpha$ | No
G-383 | A-48 | 17.5535 | -2.3299 | 23.96 $\pm$ 0.09 | 0.03 $\pm$ 0.01 | 9.6 $\pm$ 0.2 | 11.5 $\pm$ 0.3 | non-SF | <0.04 | H$\alpha$ | No
| A-49 | 17.5534 | -2.3296 | 25.90 $\pm$ 0.51 | 0.02 $\pm$ 0.01 | 8.7 $\pm$ 0.6 | 11.1 $\pm$ 0.4 | non-SF | <0.02 | H$\alpha$ | No
G-399 | A-56 | 17.5605 | -2.3287 | 25.17 $\pm$ 0.27 | 0.01 $\pm$ 0.01 | 8.5 $\pm$ 0.5 | 11.0 $\pm$ 0.3 | SF | 0.05 $\pm$ 0.01 | H$\alpha$ | No
| A-69 | 17.5620 | -2.3255 | 22.06 $\pm$ 0.01 | 0.19 $\pm$ 0.01 | 9.8 $\pm$ 0.2 | 11.6 $\pm$ 0.3 | SF | 0.4 $\pm$ 0.2 | H$\alpha$ | Poor
| B-7 | 17.5672 | -2.3244 | 21.37 $\pm$ 0.01 | 0.36 $\pm$ 0.01 | 10.6 $\pm$ 0.2 | 12.3 $\pm$ 0.5 | non-SF | <0.1 | H$\alpha$ | No
G-517 | B-34 | 17.5780 | -2.3143 | 25.39 $\pm$ 0.26 | 0.02 $\pm$ 0.01 | 7.6 $\pm$ 0.6 | 10.7 $\pm$ 0.4 | SF | <0.04 | [O ii] | No
| B-43 | 17.5643 | -2.3119 | 21.50 $\pm$ 0.01 | 0.59 $\pm$ 0.01 | 10.3 $\pm$ 0.2 | 12.0 $\pm$ 0.4 | SF | 3.8 $\pm$ 1.5 | [O ii] | Yes
G-536 | A-36 | 17.5598 | -2.3322 | 21.30 $\pm$ 0.01 | 0.77 $\pm$ 0.01 | 10.9 $\pm$ 0.2 | 12.9 $\pm$ 0.7 | SF | 6 $\pm$ 3 | [O ii] | Yes
| A-37 | 17.5599 | -2.3320 | 22.30 $\pm$ 0.06 | 0.31 $\pm$ 0.02 | 10.6 $\pm$ 0.2 | 12.4 $\pm$ 0.6 | SF | 1.3 $\pm$ 0.4 | [O ii] | Poor
| A-40 | 17.5649 | -2.3308 | 25.61 $\pm$ 0.27 | 0.02 $\pm$ 0.01 | 9.4 $\pm$ 0.4 | 11.4 $\pm$ 0.3 | SF | 0.03 $\pm$ 0.02 | [O ii] | No
G-558 | A-72 | 17.5538 | -2.3253 | 23.66 $\pm$ 0.13 | 0.10 $\pm$ 0.01 | 9.7 $\pm$ 0.5 | 11.6 $\pm$ 0.4 | SF | 0.7 $\pm$ 0.2 | [O ii] | Yes
| A-75 | 17.5555 | -2.3238 | 25.02 $\pm$ 0.29 | 0.03 $\pm$ 0.01 | 8.3 $\pm$ 0.4 | 10.9 $\pm$ 0.4 | SF | 0.5 $\pm$ 0.1 | [O ii] | Yes
G-876 | A-32 | 17.5580 | -2.3325 | 23.61 $\pm$ 0.05 | 0.30 $\pm$ 0.01 | 10.6 $\pm$ 0.2 | 12.4 $\pm$ 0.6 | SF | 7 $\pm$ 2 | [O ii] | Yes
| A-38 | 17.5573 | -2.3318 | 23.88 $\pm$ 0.13 | 0.24 $\pm$ 0.03 | 10.8 $\pm$ 0.3 | 12.6 $\pm$ 0.8 | SF | 4.7 $\pm$ 1.1 | [O ii] | Yes
G-907 | A-16 | 17.5600 | -2.3347 | 24.34 $\pm$ 0.18 | 0.17 $\pm$ 0.03 | 10.4 $\pm$ 0.5 | 12.2 $\pm$ 0.9 | SF | 2.3 $\pm$ 0.6 | [O ii] | Poor
| B-19 | 17.5721 | -2.3181 | 24.88 $\pm$ 0.25 | 0.10 $\pm$ 0.03 | 10.4 $\pm$ 0.5 | 12.2 $\pm$ 0.8 | SF | 1.1 $\pm$ 0.3 | [O ii] | Poor

The properties of the resulting group sample are listed in Table 2, with
individual galaxy properties shown in Table 3, and their locations on the sky
illustrated in Figure 1. Only galaxies within the HST field are shown
(although we discuss the presence of more distant galaxies when modelling the
absorption within these groups).

Figure 1: The layout of the surveys used in this study. The background image
was taken with the Kitt Peak 4-metre Telescope. The solid green square shows
the region covered by HST imaging, whilst the smaller magenta squares show the
MUSE fields centered on QSOs A and B. The quasars are shown by red circles,
with A the southernmost and C the northernmost. The galaxies within the HST
field that are analysed in this work are spread across the two panels, with z
$<$ 0.5 galaxies in the left panel, and higher-redshift galaxies in the right
panel. These are coloured by group and labelled by the group identifier listed
in Table 2.

We note that star-formation rates of galaxies in groups and clusters tend to
be lower than field galaxies for similar stellar masses (e.g. Larson et al.,
1980; Wetzel et al., 2013). This is found for our full sample and group
definitions used in Paper 1, with a K-S test on specific star-formation rates
yielding a difference of $\approx$ 2.5$\sigma$. The sample of group galaxies
used in this work and the sample of isolated galaxies from Paper 2 are not
large enough for a statistical comparison to produce meaningful results, but
we do find our group sample to have slightly lower average sSFRs and lower
proportion of SF galaxies (using our template classification detailed in Paper
1).

The stellar masses and SFRs of galaxies in our sample are shown in Figure 2,
which can be directly compared to the similar figure in Paper 2. These two
subsamples span a similar range in mass and SFR. Both our Paper 2 and Paper 3
subsamples are biased towards low-mass and star-forming galaxies, as we focus
on galaxies near to the sightlines, where the increased depth and easier
detection of emission-line galaxies using MUSE has a larger impact on the
sample.

Figure 2: Stellar mass vs star-formation rate for galaxies in our sample.
Faded points show the overall galaxy sample (identical to Figure 5 from Paper
1), whilst galaxies detailed in this work are bold and labelled with the
galaxy MOS or MUSE ID as given in Table 7. Galaxies identified as star-forming
are shown in blue, with non-star-forming galaxies in red. The grey dashed line
indicates an sSFR of 0.02 $\textrm{Gyr}^{-1}$, an approximate match to the
SF/non-SF designations that were made using template fitting. Masses are
estimated using Equations 1 and 2 from Johnson et al. (2015) and star-
formation rates estimated using the H$\alpha$ or [OII] (3727 Å) luminosities.
These measurements are detailed in Paper 1. The objects marked with triangles
are upper limits where no clear emission line is detected. Note that the small
number of non-star-forming galaxies with apparent extremely high SFRs are due
to fringing effects in the VIMOS data (see T14 Section 3.1) being fit as
emission lines. These erroneous measurements do not affect our results.

##  3 Models

We use the same three basic models as in Paper 2, namely a power-law halo, bi-
conical outflow, and rotating disk. In that work we include a full description
of the model parameters, the process of using the galaxy observations and
model parameters to generate synthetic spectra, and the process of optimizing
for the best-fit models (Section 3 and Appendix A therein).

To briefly summarize, the strength of absorption caused by a spherical halo
with power-law density profile is determined by its index $\alpha$ and the
distance between the galaxy and sightline, whilst its velocity is constant and
may be offset from the galaxy by $v_{\delta}$. An outflow has a constant
radial velocity $v_{out}$ and has non-zero density only within a polar angle
$\theta_{out}$. We assume a constant outflowing flux, leading to a density
profile of $r^{-2}$ within the cone of the outflow. A hollow cone, such that
density is zero close to the galaxy minor axis (within $\theta_{in}$), is
allowed for, but in most cases is not required. Disks have an exponential
profile with scale heights $h_{r}$ and $h_{z}$, alongside radial and azimuthal
velocity components $v_{r}$ and $v_{\phi}$ respectively. All three model types
also have an allowed thermal or turbulent velocity $v_{t}$ that broadens the
absorption profile (we do not attempt to distinguish between thermal and
turbulent velocities).

In addition to these free parameters, the measurements of galaxy position
angle and inclination (from the GALFIT models applied to the HST image) are
required as inputs to these models, alongside the chosen galaxy orientation
($S_{Nr}$ and $S_{Wr}$, described in Paper 2). Both the direction of galaxy
rotation and the direction along the minor axis that points away from the
observer may be unconstrained, although the MUSE kinematics and the direction
of any spiral arms can be used, if visible, to constrain these before
modelling the absorption. We note that none of the models in this paper are
constrained by the direction of galaxy spiral arms, and that only in the case
of G-536 do we rule out any models based only on the galaxy kinematics.

Model spectra are generated by combining 10pc segments along each line-of-
sight. Each segment has a density determined by the distance and orientation
between the sightline segment and the galaxy as well as the density profile of
the model, and a line-of-sight velocity determined by the model
outflow/infall/rotation velocities projected into the direction of the line-
of-sight. Combining these yields a column density, and therefore optical
thickness, as a function of velocity or wavelength. The model absorption
profile is calculated by combining the optical thickness of all model
components included (i.e. the total result from all disk and outflow models
around galaxies in the group), converting this to a transmission spectrum, and
then convolving with the instrumental line-spread function.

As we discuss in Paper 2, creating an automated routine to find the best-fit
parameters of these models is complex and time-consuming, so is not considered
for a small sample within a single field. Instead we consider each possible
model (halo, disk or outflow for each galaxy with inclination and position
angle measurements), and determine which absorption components could be fit by
such a model without producing excess absorption in the synthetic spectrum
over that seen in the observations, for any of the three lines-of-sight. This
primarily concerns eliminating model combinations that do not produce velocity
offsets in the correct direction, or match the relative column densities that
would be produced in the different sightlines. We then iteratively adjust the
model parameters to produce a reasonable fit, and finally find the combination
of models that reproduces the maximum number of observed absorption
components.

This method identifies the various models capable of reproducing each observed
absorption feature, although it does not provide a quantitative measure of the
best fit (which would likely depend substantially on the priors chosen on the
parameter space). Throughout this work we therefore list the different model
combinations found to produce a reasonable approximation of the observed
spectra.

##  4 Absorption in Galaxy Groups

We now apply these models to the absorption in galaxy groups, and attempt to
reproduce the H i absorption components visible in the QSO spectra at the
group redshift. Although Ly$\alpha$ is usually preferred, in some cases it is
saturated, blended, or lies in the lower-resolution FOS spectra, so Ly$\beta$
provides better constraints on the models. Below we discuss our preferred
combination of models for three of these groups, including the model
parameters and the reasons for rejecting alternative combinations. The
remaining six groups are discussed in Appendix A.

###  4.1 G-238

Group G-238 consists of two star-forming galaxies (29214 and 26677) appearing
in the HST field at z $\approx$ 0.24. These are the two nearest galaxies to
the lines-of-sight at this redshift, although there are several others at
larger impact parameters. The observations are detailed in Table 4 and Figure
3.

QSO-A features two absorption components at this redshift, with the redder
absorber featuring O vi detected at a significant level. No significant
absorption is detected in B or C, but some weak absorption in C could be
hidden by molecular lines from the sub-DLA. Both of the absorbers are at very
similar velocities to the two galaxies, but a simple halo model requires a
steep density profile (much steeper than $r^{-2}$), otherwise it would produce
absorption in B that is inconsistent with observations. QSO-A also lies close
to the minor axis of 26677 and the major axis of 29214. A model consisting of
an outflow and disk around the two galaxies respectively can approximately
produce the results seen in the observations.

These galaxies are reasonably well-separated, lying outside of each others’
virial radii, so it is not surprising that we see no clear sign of interaction
in the absorption. The absorption at impact parameters $\approx$ 250 kpc from
both galaxies lies outside the virial radius, but within the impact parameter
range that exhibits a bimodal position angle distribution. We suggest in Paper
1 that this is likely due to disk and outflow structures similar to the models
used here. This combination of models is also supported by the detection of O
vi at a redshift matching the redder Ly$\alpha$ component that we identify as
a likely outflow. The other absorber has O vi to H i ratio less than 1/5 of
this, better fitting accretion from the IGM. We also note that neither a disk
around galaxy 26677 nor an outflow around 29214 would intersect any of the
lines of sight at small distances, so both of these structures may also exist
around these galaxies.

Table 4: Summary of galaxy and absorber properties for group G-238. Any additional galaxies and metal absorbers have velocities shown relative to the first galaxy (26677). with columns as follows: (1) Group redshift; (2) Galaxy ID; (3) Galaxy luminosity (as a multiple of $L_{\star}$; (4) Galaxy inclination; (5) Line-of-sight identifier; (6) Impact parameter between galaxy and line-of-sight at the group redshift; (7) Azimuthal angle between galaxy major axis and the line-of-sight; (8) Absorber column density; (9) Absorber Doppler parameter; (10) Velocity offset between galaxy and absorber (Any additional galaxies and metal absorbers have velocities shown relative to galaxy 26677); (11) Any detected metal ions at the same redshift as this H i absorber. z | Galaxy | Lum ($L_{\star}$) | Inc | LOS | Imp (kpc) | Azimuth | log(N H i) | b ( km s-1) |  $\Delta$v ( km s-1) | Other ions
---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
0.238 | 26677 | 0.22 |  $67^{\circ}$ $\pm$ $1^{\circ}$ | A | 262 |  $81^{\circ}$ $\pm$ $1^{\circ}$ | 13.99 $\pm$ 0.20 | 43 $\pm$ 7 | -10 $\pm$ 100 |
|  |  |  | A | 262 |  $81^{\circ}$ $\pm$ $1^{\circ}$ | 13.75 $\pm$ 0.35 | 54 $\pm$ 21 | +60 $\pm$ 100 | O vi
|  |  |  | B | 502 |  $69^{\circ}$ $\pm$ $1^{\circ}$ | (None, limit $\sim$12.8) |  |  |
|  |  |  | C | 934 |  $81^{\circ}$ $\pm$ $1^{\circ}$ | (None, limit $\sim$12.9) |  |  |
| 29214 | 0.11 |  $43^{\circ}$ $\pm$ $3^{\circ}$ | A | 236 |  $8^{\circ}$ $\pm$ $5^{\circ}$ |  |  | (+70) |
|  |  |  | B | 422 |  $52^{\circ}$ $\pm$ $5^{\circ}$ |  |  |  |
|  |  |  | C | 654 |  $84^{\circ}$ $\pm$ $5^{\circ}$ |  |  |  |
| (22676) | 0.32 |  | A | 859 |  |  |  | (-180) |
|  |  |  | B | 1069 |  |  |  |  |
|  |  |  | C | 1519 |  |  |  |  |
| (33195) | 0.04 |  | A | 919 |  |  |  | (+440) |
|  |  |  | B | 616 |  |  |  |  |
|  |  |  | C | 495 |  |  |  |  |
Figure 3: Details of the absorption and galaxy environment around group G-238.
The upper two rows of panels illustrate the galaxies and the models used, as
follows. Upper-Left: HST image of the galaxy, with projected major axis shown
in red. Upper-Middle: Velocity map based on emission lines detected in MUSE,
scaled and rotated to match the HST image. Only spaxels with a 3$\sigma$ line
detection are shown. (Note that both galaxies in this group lie outside the
MUSE fields.) Upper-Right: Wide view showing the location of the three QSOs
(cyan, grey and orange connected dots representing QSOs A, B and C). The
locations of other galaxies at this redshift are indicated by grey crosses;
the estimated galaxy virial radius by a dashed black circle; and schematics of
models proposed to fit the absorption by red and blue ellipses for outflows
and disks respectively. Central Panel: The galaxies at this redshift, with the
galaxies shown in the upper panels bolded, and others faded. Each galaxy is
shown three times, showing the impact parameter between that galaxy and each
of the three QSOs. The horizontal bar denotes the velocity uncertainty derived
from the galaxy redshift measurement. Bottom panel: The transmission of the
quasar spectra at the wavelength of Ly$\alpha$ at the group redshift. The
observed QSO spectra are shown as solid lines, with dashed lines giving the
synthetic spectra produced by our models. Vertical lines passing through both
panels show detected H i absorption components. The model shown in the lower
panel is a disk with rotation velocity $\sim$ 100 km s-1 around galaxy 29214,
and an outflow with opening angle $20^{\circ}$ and velocity 120 km s-1.
Additional absorbers identified by red ticks are mostly molecular lines at the
redshift of the sub-DLA at z $\approx$ 0.56, except for the weak absorption in
LOS-B (5), which is Ly$\beta$ from z $\approx$ 0.47.

###  4.2 G-399

A-56, A-69 and B-7 are the three galaxies within the HST image at z $\approx$
0.399. The state of the gas causing absorption in the sightlines at this
redshift is modelled in Anshul et al. (2021); both sightlines feature
transitions from multiple metal ions. The details are given in Table 5 and
illustrated in Figure 4. Note that the absorption features in QSO-C are
identified with transitions from different redshifts.

B-7 is the largest galaxy in this group, and the closest to QSO-B, but is non-
star-forming. The other two galaxies within the HST field are star-forming
galaxies but also less massive. A-69 lies on the edge of the MUSE field, with
the edge of the field running approximately along the major axis. There may be
a velocity gradient across the galaxy, but this is not clear. A-56 lacks a
well-determined orientation, as it is indistinguishable from a point source in
the HST image.

An outflow around A-69 is capable of producing two absorption components in A,
but not the factor of $\approx$10 difference in column density between the two
components and the much stronger absorption in B. However, combining this
outflow with a disk can reproduce the observed absorption in A whilst
remaining consistent with B and C. An outflow with $30^{\circ}$ half-opening
angle and 160 km s-1 velocity, alongside an extended H i disk with 160 km s-1
rotation returns an approximate match. An outflow around B-7 is ruled out, as
the large velocity offset required to match the absorption in A alongside the
opening angle required to cover LOS-A would produce a substantially broader
absorption feature.

No disk or outflow around any of the galaxies could produce the absorption in
B without substantially exceeding the observed levels of absorption in A or C.
The high column density in B is metal-enriched, exhibiting absorption from a
range of metal ions, and has a line-of-sight velocity between the two larger
galaxies in this group. This may suggest that this material has been stripped
from one of the galaxies, or that an outflow from one of the galaxies has been
distorted by interaction with the CGM of the other such that it can no longer
be fit by our toy models.

Anshul et al. (2021) find that the absorption in QSO-A is consistent with
solar metallicity in both components, and use a two-phase model with a low-
ionization phase traced by H i and C iii (among other ions) and a higher-
ionization phase traced primarily by O vi. The low-ionization phase is
consistent with photoionization in the stronger component, and the O vi in
both components is consistent with collisionally ionized, T $\gtrsim 10^{5}$ K
gas. This would appear to be consistent with the O vi resulting primarily from
outflowing material in both components. They note that the material observed
would likely have been ejected from the central galaxy $>$ 600 Myr ago. It
therefore seems possible that the material we have modelled as a rotating disk
has been recycled from this outflow, but only gas that has cooled efficiently
is seen in this disk. In this scenario, the stronger absorption component
consists of both the proposed cool disk and a warm outflow; the cool disk
dominates this absorption component for the low-ionization phase, but less so
for the O vi. This would explain the similar metallicity of both phases and
components. Stripped material near the minor axis could also reproduce the
observations in place of this possible outflow.

Anshul et al. (2021) also find multiple phases in the absorption in B, with a
broad Ly$\alpha$ component alongside the O vi and a narrower component
matching the C iii in a lower-ionization phase. They find that the low-
ionization phase is consistent with photoionized gas at $\sim$1/10th solar
metallicity, and that the O vi could be produced either by diffuse hot gas at
similar metallicity, or by cooler collisionally-ionized gas with near-solar
metallicity. They suggest that these could respectively trace either the
diffuse, hot CGM or intra-group medium, or the interface between a low-
ionization cloud and the hot-CGM (that cloud possibly originating from an
outflow).

If this absorption in B is due to a hot and diffuse CGM or intra-group medium,
it must either be distorted or patchy, as a spherical distribution cannot
match the ratio of absorption strengths in the two sightlines. Similarly, our
biconical outflow models cannot reproduce this ratio, suggesting (if an
outflow exists) either a substantial change in outflow rate with time, a very
patchy medium, or distortion due to the interaction between the two galaxies.

Figure 4: Details of the absorption and galaxy environment around group G-399. The layout is identical to that shown in Figure 3, with kinematics measured from the H$\alpha$ emission line seen in the MUSE data, and the model shown in the lower panel combines an outflow with $25^{\circ}$ half-opening angle and 160 km s-1 velocity with a disk with 150 km s-1 rotation and 50 km s-1 infall, both around galaxy A-69. All five absorption components labelled with red ticks are molecular lines associated with the sub-DLA at z$\approx$0.56. Note that galaxy A-69 lies at the edge of the MUSE field, so the velocity map is truncated approximately along the dashed grey line. Table 5: Summary of galaxy–absorber group at z $\sim$ 0.399. Any additional galaxies and metal absorbers have velocities shown relative to the first galaxy (A-56). Columns are identical to those in Table 4. z | Galaxy | Lum ($L_{\star}$) | Inc | LOS | Imp (kpc) | Azimuth | log(N H i) | b ( km s-1) |  $\Delta$v ( km s-1) | Other ions
---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
0.399 | A-56 | 0.01 |  $35^{\circ}$ $\pm$ $35^{\circ}$ | A | 122 |  $76^{\circ}$ $\pm$ $45^{\circ}$ | 13.15 $\pm$ 0.09 | 15 $\pm$ 6 | -100 $\pm$ 40 |  C iii, O vi
|  |  |  | A | 122 |  $76^{\circ}$ $\pm$ $45^{\circ}$ | 14.14 $\pm$ 0.03 | 35 $\pm$ 2 | -10 $\pm$ 40 |  C iii, O vi
|  |  |  | B | 325 |  $38^{\circ}$ $\pm$ $45^{\circ}$ | 16.77 $\pm$ 0.02 | 24.9 $\pm$ 0.5 | -90 $\pm$ 40 |  C i, N iii, Si iii, O iii, O vi
|  |  |  | C | 921 |  $11^{\circ}$ $\pm$ $45^{\circ}$ | (None, limit $\approx$13.0) |  |  |
| A-69 | 0.19 |  $77^{\circ}$ $\pm$ $2^{\circ}$ | A | 186 |  $82^{\circ}$ $\pm$ $2^{\circ}$ |  |  | (-40) |
|  |  |  | B | 254 |  $74^{\circ}$ $\pm$ $2^{\circ}$ |  |  |  |
|  |  |  | C | 857 |  $44^{\circ}$ $\pm$ $2^{\circ}$ |  |  |  |
| B-7 | 0.36 |  $82^{\circ}$ $\pm$ $1^{\circ}$ | A | 285 |  $70^{\circ}$ $\pm$ $1^{\circ}$ |  |  | (-150) |
|  |  |  | B | 205 |  $12^{\circ}$ $\pm$ $1^{\circ}$ |  |  |  |
|  |  |  | C | 846 |  $1^{\circ}$ $\pm$ $1^{\circ}$ |  |  |  |
| (26721) | 0.2 |  | A | 937 |  |  |  | (+80) |
|  |  |  | B | 1318 |  |  |  |  |
|  |  |  | C | 1626 |  |  |  |  |
| (34572) | 1.2 |  | A | 1251 |  |  |  | (+210) |
|  |  |  | B | 889 |  |  |  |  |
|  |  |  | C | 280 |  |  |  |  |

###  4.3 G-876

A-32 is an $\approx 0.3L_{*}$ galaxy at z $\sim 0.88$, inclined at $\sim
30^{\circ}$. It is paired with A-38, a galaxy of similar magnitude that is
less than 30 kpc away. Neither galaxy shows any signs of morphological
distortion in the HST image or any kinematic signatures of interaction between
the two galaxies; both galaxies show a velocity gradient along their major
axis that is likely due to rotation (with velocity $\approx$ 100 km s-1). This
system is detailed in Table 6 and Figure 5.

A-38 is redshifted by $\sim$50 km s-1 relative to A-32, and is therefore at
the same redshift as the absorption in sightline A, whilst sightline B is
blueshifted by 100 km s-1 relative to this galaxy. This also exhibits a $\sim$
100 km s-1 velocity gradient.

Sightline A lies at a distance of $\sim$100 kpc along the major axis of A-32
and 75 kpc at $\sim 20^{\circ}$ to the major axis of A-38, with sightline B at
$\sim$600 kpc along the minor axis. Both show absorption, with H i column
densities $\sim 10^{15.8}$ and $10^{15.4}$ $\textrm{cm}^{-2}$ and Doppler
parameters 30 and 20 km s-1 respectively. Sightline A features O iii and O iv
absorption at this redshift, whilst sightline B does not show any metal
absorption. However, the detection limit for these ions allows for the gas
seen in LOS-B to have similar O iii and O iv column densities to that in A.
Note that as both Ly$\alpha$ and Ly$\beta$ lie in the FOS gratings at this
redshift, the Doppler parameters are not resolved; higher-order lines
appearing in COS constrain the Doppler widths but reveal no additional
structure. These galaxies lie beyond the redshift of QSO-C, so no absorption
can be detected in the third sightline.

The relatively similar column densities alongside a large difference in impact
parameter prevents any of our models from simultaneously matching both
absorbers. That the absorption in A is close to the major axis of both
galaxies, whilst B is near the minor axis of both galaxies, would suggest that
these could be a disk and outflow respectively.

If the absorption in sightline A is associated with A-32, it is co-rotating
and could be part of an extended disk with rotation velocity $\approx$100 km
s-1 (depending on any infall component). If associated with A-38, the
absorption in A must have comparable rotation and infall velocities, in order
to produce absorption with no clear line-of-sight velocity offset.
Alternatively, a power-law halo around A-38 could reproduce this lack of
velocity offset.

An outflow from either galaxy can also reproduce the absorption in B. In order
to reproduce the velocity offset, these putative outflows would require
velocities of $\approx$140 km s-1 (from A-32) or $\approx$210 km s-1 (from
A-38). We note that A-38 cannot produce both a disk matching A and an outflow
matching B, as the need for the disk velocity offsets to ‘cancel’ fixes the
galaxy orientation, whilst an outflow matching B requires the opposite
orientation.

This still leaves several possible combinations of models that can reproduce
the observations. A reasonable fit is shown in Figure 5, and combines an
outflow with velocity 140 km s-1and opening angle $40^{\circ}$ and a disk with
rotation velocity 100 km s-1, both originating from A-32.

We also note that galaxy 26501 is substantially brighter than either A-32 or
A-38, so may be contributing to the absorption in LOS-B. Furthermore, the
velocity difference between the two galaxies and the location of each galaxy
near the major axis of the other suggest orbital angular momentum with similar
alignment to the rotation of both galaxies. Therefore the absorption that
could be identified as a disk around one galaxy may also be tidal material
resulting from their interaction, or larger-scale accretion into the group,
rather than associated with one of the galaxies.

Figure 5: Details of the absorption and galaxy environment around group G-876. The layout is identical to that shown in Figure 3, with kinematics measured from the [O ii] emission line seen in the MUSE data, and the model shown in the lower panel combines an outflow with velocity 160 km s-1and opening angle $40^{\circ}$ and a disk with rotation velocity 100 km s-1.  Table 6: Summary of galaxy–absorber group G-876. Any additional galaxies and metal absorbers have velocities shown relative to the first galaxy (A-32). Note that this group is beyond the redshift of QSO-C, so no absorption could be detected. Columns are identical to those in Table 4. z | Galaxy | Lum ($L_{\star}$) | Inc | LOS | Imp (kpc) | Azimuth | log(N H i) | b ( km s-1) |  $\Delta$v ( km s-1) | Other ions
---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
0.876 | A-32 | 0.30 |  $55^{\circ}$ $\pm$ $3^{\circ}$ | A | 97 |  $19^{\circ}$ $\pm$ $4^{\circ}$ | 15.78 $\pm$ 0.30 | 30 $\pm$ 5 | 40 $\pm$ 20 |  O iv (0), O iii (-10)
|  |  |  | B | 597 |  $79^{\circ}$ $\pm$ $4^{\circ}$ | 15.45 $\pm$ 0.47 | 22 $\pm$ 3 | -50 $\pm$ 20 |
| A-38 | 0.24 |  $54^{\circ}$ $\pm$ $5^{\circ}$ | A | 75 |  $16^{\circ}$ $\pm$ $5^{\circ}$ |  |  | (+50) |
|  |  |  | B | 588 |  $86^{\circ}$ $\pm$ $5^{\circ}$ |  |  |  |
| (26501) | 0.80 |  | A | 879 |  |  |  | (+30) |
|  |  |  | B | 1062 |  |  |  |  |
| (29799) | 0.38 |  | A | 1197 |  |  |  | (+180) |
|  |  |  | B | 755 |  |  |  |  |

##  5 Discussion

Table 7: Summary of galaxies in groups and the best-fitting toy models (ordered by redshift). Only galaxies with estimated position angles are shown in this table. Columns are as follows: (1) Group identifier; (2)-(5) Galaxy IDs, luminosities, star-formation class derived from template fitting and presence of kinematics, as given in Table 3; (6) Brief description of model combinations found to produce a reasonable fit.  Group | Galaxy | Lum ($L_{\star}$) | SF-Class | Kinematics | Model(s)
---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6)
G-202 | B-22 | 0.02 | SF | Poor | (4/5 absorbers) B-22 outflow, $\theta$=$15^{\circ}$, v=250 km s-1, extent > 100 kpc
| 25962 | 0.07 | non-SF | No | AND 31787 outflow, $\theta$=$20^{\circ}$, v=50 km s-1, extent > 400 kpc
| 31704 | 0.03 | SF | No | AND 32778 disk, height ratio $\approx$10, $v_{\phi}$= 120 km s-1, $v_{r}$= 0 km s-1, extent > 400 kpc
| 31787 | 0.08 | SF | No | (other options possible, e.g. 25962 disk, but less likely)
| 32497 | 1.1 | non-SF | No |
| 32778 | 0.4 | SF | No |
G-238 | 26677 | 0.2 | SF | No | (2/2 absorbers) 26677 outflow, $\theta$=$20^{\circ}$, v=120 km s-1, extent > 260 kpc
| 29214 | 0.1 | SF | No | AND 29214 disk, height ratio $\approx$40, $v_{\phi}$= 100 km s-1, $v_{r}$= 30 km s-1, extent > 240 kpc
|  |  |  |  | (29214 disk and halo possible instead, with similar disk parameters)
G-383 | A-48 | 0.03 | non-SF | Poor | (3/3 absorbers) A-48 outflow, $\theta$=$10^{\circ}$, v=600 km s-1, extent > 40 kpc
| A-49 | 0.01 | SF | Poor | AND A-49 disk, height ratio $\approx$100, $v_{\phi}$= 150 km s-1, $v_{r}$= 40 km s-1, extent > 400 kpc
|  |  |  |  | (A-48 disk with $v_{\phi}$= 320 km s-1, $v_{r}$= 0 km s-1also possible)
|  |  |  |  | (some parameters very uncertain due to edge-on galaxy pair)
G-399 | A-56 | 0.01 | SF | No | (2/3 absorbers) A-69 outflow, $\theta$=$25^{\circ}$, v=160 km s-1, extent > 180 kpc
| A-69 | 0.19 | SF | Poor | AND A-69 disk, height ratio $\approx$100, $v_{\phi}$= 150 km s-1, $v_{r}$= 50 km s-1, extent > 200 kpc
| B-7 | 0.36 | non-SF | No | (strongest absorber not fit by any toy model)
G-517 | B-34 | 0.12 | SF | No | (No detected absorption)
| B-43 | 0.6 | SF | Yes | (Upper limit logN $\approx$13.3)
G-536 | A-36 | 0.8 | SF | Yes | (4/7 absorbers) A-36 outflow, $\theta$=$55^{\circ}$, v=140 km s-1, extent > 120 kpc
| A-37 | 0.3 | SF | Poor | AND A-40 disk, height ratio $\approx$100, $v_{\phi}$= 110 km s-1, $v_{r}$= 60 km s-1, extent > 400 kpc
| A-40 | 0.02 | SF | No | (other absorption may be due to stripping in galaxy interactions, A-37 disk also possible)
G-558 | A-72 | 0.10 | SF | Yes | (2/3 absorbers) A-72 outflow, $\theta$=$40^{\circ}$, v=150 km s-1, extent > 500 kpc
| A-75 | 0.03 | SF | Yes | OR A-75 outflow, $\theta$=$50^{\circ}$, v=70 km s-1, extent > 350 kpc
| A-77 | 0.04 | SF | No | AND
|  |  |  |  | A-75 disk, height ratio $\approx$70, $v_{\phi}$= 90 km s-1, $v_{r}$= 50 km s-1, extent > 200 kpc
|  |  |  |  | OR A-75 halo, $v_{\delta}\approx$ 0, $\alpha\gtrsim 2$
|  |  |  |  | (sub-DLA not fit, absorber is likely due to a galaxy that is not detected)
G-876 | A-32 | 0.30 | SF | Yes | (2/2 absorbers) A-32 disk, height ratio $\approx$20, $v_{\phi}$= 100 km s-1, $v_{r}$= 0 km s-1, extent > 100 kpc
| A-38 | 0.24 | SF | Yes | OR A-38 disk, height ratio $\approx$10, $v_{\phi}$= 100 km s-1, $v_{r}$= 100 km s-1, extent > 80 kpc
|  |  |  |  | AND
|  |  |  |  | A-32 outflow, $\theta$=$40^{\circ}$, v=160 km s-1, extent > 600 kpc
|  |  |  |  | OR A-38 outflow, $\theta$=$35^{\circ}$, v=210 km s-1, extent > 600 kpc
G-907 | A-16 | 0.17 | SF | Yes | (2/2 absorbers) A-16 disk, height ratio $\approx$20, $v_{\phi}$= 100 km s-1, $v_{r}$= 50 km s-1, extent > 200 kpc
| B-19 | 0.10 | SF | Poor | AND B-19 outflow, $\theta$=$60^{\circ}$, v=80 km s-1, extent > 200 kpc
|  |  |  |  | OR
|  |  |  |  | A-16 outflow, $\theta$=$60^{\circ}$, v=150 km s-1, extent > 180 kpc
|  |  |  |  | AND B-19 disk, height ratio $\approx$20, $v_{\phi}$= 130 km s-1, $v_{r}$= 40 km s-1, extent > 180 kpc

The model fits shown above can now be discussed in the context of our previous
works, especially the sample of isolated galaxies considered in Paper 2, as
well as results from the literature. We summarize the best-fitting results for
each galaxy group in Table 7.

###  5.1 Model success

Firstly, our disk and outflow models provide a plausible fit for 21 of the 28
detected H i components within 500 km s-1 and 500 kpc of our sample galaxies.
This 75% success rate is somewhat higher than the $\approx$50-60% found for
the isolated galaxy sample in Paper 2 (13 of 26 within 500 km s-1 and 12 of 20
within 300 km s-1), a $\approx$2$\sigma$ difference under binomial statistics.
We note that our ‘success rate’ represents an upper limit on the fraction of
detected H i absorbers that originate in the disk, halo and outflow structures
described by our models. A successful fit to our models only tentatively
identifies an absorber as a possible disk/halo/outflow. Several alternative
origins for apparently successful fits are discussed below.

It may be expected that for group galaxies with gravitational interactions,
such forces would distort any structure in the CGM and reduce the rate at
which these models can reproduce the absorption at large scales. This is seen
in, for example, the M81 group, where 21 cm emission is seen tracing both a
disk-like and biconical outflow structure around M82 on small scales, but
distorted in the direction of M81 on larger scales (e.g. Sorgho et al., 2019).
Such distortions would be expected to reduce the success rate of our models in
galaxy groups, although in some circumstances our disk and outflow models
could appear successful even with these distortions present.

Our higher success rate for group galaxies over isolated galaxies could
suggest that galaxy interactions are not having a significant impact on our
sample. However, there are several effects that could counter any impact of
group interactions.

Firstly, the larger number of galaxies near to each absorber increases the
number of free parameters available for our models, and therefore the
likelihood of obtaining a reasonable fit even if the models do not reflect the
true physical state of the gas (or reflect the state of the gas poorly due to
effects such as intermittent outflows and changes in ionization state, as well
as distortions due to group interactions). However, the groups for which some
H i absorption cannot be fit by our models appear to be those with the largest
number of galaxies, whereas for those with 2-4 galaxies we have been able to
find a plausible fit to all identified absorbers (a difference of $\approx
2\sigma$ in mean Ngals). This suggests that the increased number of free
parameters, largest for groups with many galaxies, is not the primary reason
for our high success rate.

We also search for other differences between the properties of the groups for
which all absorbers were fit, and those with some absorption that could not be
fit. No significant differences were found in their redshifts, total stellar
masses, impact parameters to the nearest or most massive galaxy, ratios of
stellar masses or luminosities of the brightest two galaxies, or the projected
separations of the tightest pair of galaxies in each group. These tests
therefore provide little indication of the likely origins of unexplained
absorbers. We do find that individual absorbers that were not consistent with
any of our models have higher H i column densities than those we could
successfully fit, and discuss these in more detail in Sections 5.4 and 5.5.

Second, the larger number of galaxies, and resulting smaller impact parameters
between the lines-of-sight and the nearest galaxy, may also contribute to the
success of our models. With the known correlation between impact parameter and
column density (e.g. Werk et al., 2014; Wilde et al., 2021), this contributes
to generally higher H i column densities in our groups (median H i column
densities of $10^{14.5}$ and $10^{13.8}\textrm{cm}^{-2}$ in absorbers
associated with this work and our Paper 2 sample respectively). These higher
column densities also make successful fits more likely, as weak absorption
produced by the toy models can more easily be ‘hidden’ under other absorbers,
and column densities are less constrained once absorption begins to saturate.
The smaller impact parameters also increase the likelihood of probing any
inflowing or outflowing structures closer to the galaxy than any distortions
caused by interactions within the group.

Third, it is possible that some absorption resulting from group interactions
could be fit by our models regardless. This could include material along the
plane of a galaxy interaction masquerading as an accreting disk, and stripped
material near the galaxy minor axis appearing consistent with an outflow.
These false fits are unlikely to occur where multiple absorbers are reproduced
by a single model, due to the extra constraints, but may contribute to some of
our model fits based on a single absorber.

Studies of cool CGM gas using Mg ii absorption have come to differing
conclusions on the origin of the more extended absorption in galaxy groups.
Bordoloi et al. (2011) suggest that a superposition of CGM absorption from the
constituent galaxies can reproduce the observed results, whereas Nielsen et
al. (2018) prefer a model in which absorbers are generally associated with the
intra-group medium rather than any individual galaxy. Using samples extending
to slightly higher redshifts, Fossati et al. (2019b) suggest that this is
material originating primarily from tidal interactions between group galaxies,
whilst Dutta et al. (2020) support a model with contributions from individual
halos and tidal interactions.

Our models cannot directly test for tidal material (although we do discuss
this briefly in Section 5.4), but do produce a superposition of possible
structures sometimes found in the CGM of isolated galaxies. However, this
differs from the superposition model tested in Bordoloi et al. (2011), Nielsen
et al. (2018) and Dutta et al. (2020) in that the covering fraction of these
CGM structures in groups is not constrained to be the same as that around
isolated galaxies.

Our high model success rate provides some support for a superposition model
for groups using our definition and sample selection, but does not rule out a
contribution from intra-group and tidal material. The apparent difference
between this conclusion and that of Nielsen et al. (2018) may in part result
from our larger linking lengths, so our group sample contains some galaxy
pairs with larger separations, which are less likely to be affected by group
interactions. Our sample also features galaxies at large impact parameters
that may explain weak absorbers seen in group environments, which are not
satisfactorily explained under their superposition model. Dutta et al. (2020)
found a similar result, ruling out superposition as the origin for their
strongest and weakest absorbers. Nielsen et al. (2018) found that combining
the expected galaxy-absorber velocity offsets (as observed around isolated
galaxies) with the galaxy-galaxy offsets seen in groups produced a model
absorber-absorber velocity distribution significantly wider than observed.
However, possibly due to including faint MUSE galaxies near the lines-of-
sight, our groups exhibit smaller galaxy-galaxy velocity differences than
their sample, reducing this inconsistency.

We also note that our sample includes galaxies fainter than those included in
the Bordoloi et al. (2011) sample. Their lack of faint galaxies likely leads
to some interacting galaxies being classified as isolated, therefore making
the absorption profiles of group and isolated galaxies more similar.

Our high success rate at reproducing absorption in our sample of galaxy groups
suggests that this superposition of disk and outflow structures, similar to
those sometimes found around isolated galaxies, may explain a substantial
fraction of absorption found around these groups. However, the increase in
parameter space due to the larger number of galaxies, effects due to the
higher column densities and smaller impact parameters, and absorption from
other sources (e.g. intra-group and tidal material) mis-identified as
disk/outflow material, are all likely to contribute to the higher success rate
found fitting these models to gas around groups than around isolated galaxies.

###  5.2 Model parameters

We briefly discuss the model parameters that produce the best fit for the
absorption near these galaxy groups. In most cases these are similar to those
found near isolated galaxies in Paper 2, where we discuss the parameters in
more detail, but some differences are highlighted here.

Table 8: Model outflow properties around galaxies for which outflows can reproduce some of the observed absorption components. Column descriptions: (1)-(5) are from Table 3; (6) specific star-formation rate; (7) maximum impact parameter at which outflow is detected; (8) maximum extent at which absorption is detected (at the point of highest H I density along the sightline with the largest impact parameter); (9) galaxy virial radius; (10) model half-opening angle; (11) model outflow velocity; (12) escape velocity from the location of the sightline at the maximum observed extent. (Note that the starred escape velocities denote $r/r_{vir}$ > 2, so escape velocity is calculated assuming the outflowing material lies beyond the galaxy halo, rather than within an isothermal halo.)  Galaxy | z | $\textrm{M}_{\star}$ | $\textrm{M}_{h}$ | SFR | sSFR | $\textrm{b}_{max}$ | Extent | $\textrm{r}_{vir}$ | $\theta_{out}$ | $\textrm{v}_{out}$ | $\textrm{v}_{esc}$
---|---|---|---|---|---|---|---|---|---|---|---
|  | $\textrm{log}_{10}(\textrm{M}_{\odot})$ | $\textrm{log}_{10}(\textrm{M}_{\odot})$ | ($\textrm{M}_{\odot}$/yr) | $\textrm{Gyr}^{-1}$ | (kpc) | (kpc) | (kpc) | (∘) | ( km s-1) | ( km s-1)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
B-22 | 0.202 | 8.4 $\pm$ 0.2 | 10.9 $\pm$ 0.3 | $0.06\pm 0.04$ | $0.22^{+0.19}_{-0.10}$ | 100 | 110 $\pm$ 10 | 90 $\pm$ 20 | 15 | 250 | 110 $\pm$ 30
31787 | 0.202 | 9.7 $\pm$ 0.1 | 11.5 $\pm$ 0.2 | 0.5 $\pm$ 0.2 | 0.08 $\pm$ 0.04 | 390 | 460 $\pm$ 10 | 130 $\pm$ 30 | 20 | 50 | 60* $\pm$ 30
A-48 | 0.383 | 9.6 $\pm$ 0.2 | 11.5 $\pm$ 0.3 | < 0.04 | < 0.01 | 40 | 40 $\pm$ 10 | 120 $\pm$ 30 | 10 | 600 | 210 $\pm$ 50
A-69 | 0.399 | 9.8 $\pm$ 0.2 | 11.6 $\pm$ 0.3 | 0.4 $\pm$ 0.2 | 0.06 $\pm$ 0.03 | 190 | 200 $\pm$ 10 | 130 $\pm$ 30 | 25 | 160 | 130 $\pm$ 40
A-36 | 0.536 | 10.9 $\pm$ 0.2 | 12.9 $\pm$ 0.7 | 6 $\pm$ 3 | 0.08 $\pm$ 0.05 | 120 | 140 $\pm$ 10 | 360 $\pm$ 190 | 55 | 140 | 650 $\pm$ 200
A-72 | 0.558 | 9.7 $\pm$ 0.5 | 11.6 $\pm$ 0.4 | 0.7 $\pm$ 0.2 | $0.13^{+0.20}_{-0.08}$ | 430 | 530 $\pm$ 20 | 120 $\pm$ 60 | 40 | 150 | 60* $\pm$ 30
A-75 | 0.558 | 8.3 $\pm$ 0.4 | 10.9 $\pm$ 0.4 | 0.5 $\pm$ 0.1 | 2.3 $\pm$ 1.3 | 370 | 410 $\pm$ 20 | 80 $\pm$ 30 | 50 | 70 | 30* $\pm$ 10
A-32 | 0.876 | 10.6 $\pm$ 0.2 | 12.4 $\pm$ 0.6 | 7 $\pm$ 2 | 0.16 $\pm$ 0.11 | 600 | 740 $\pm$ 30 | 210 $\pm$ 100 | 40 | 160 | 50 $\pm$ 30
A-38 | 0.876 | 10.8 $\pm$ 0.3 | 12.6 $\pm$ 0.8 | 4.7 $\pm$ 1.1 | 0.08 $\pm$ 0.05 | 590 | 730 $\pm$ 40 | 250 $\pm$ 160 | 35 | 210 | 160 $\pm$ 100
B-19 | 0.907 | 10.4 $\pm$ 0.5 | 12.2 $\pm$ 0.8 | 1.1 $\pm$ 0.3 | $0.05^{+0.10}_{-0.02}$ | 170 | 240 $\pm$ 20 | 170 $\pm$ 110 | 60 | 80 | 250 $\pm$ 160
A-16 | 0.907 | 10.4 $\pm$ 0.5 | 12.2 $\pm$ 0.9 | 2.3 $\pm$ 0.6 | $0.09^{+0.18}_{-0.05}$ | 180 | 230 $\pm$ 30 | 170 $\pm$ 120 | 60 | 150 | 250 $\pm$ 170

####  5.2.1 Outflows

Table 8 lists the possible outflows that can reproduce some of the Ly$\alpha$
absorption seen near these groups of galaxies.

The possible outflows have model parameters that are generally consistent with
our results from Paper 2, with a range of half-opening angles extending to
$\approx 60^{\circ}$ and velocities mostly between 50 and 250 km s-1
(excepting the proposed A-48 outflow, for which our best estimate is 600 km
s-1 but much lower velocities of $\sim$200 km s-1 lie within the 1$\sigma$
range, as the galaxy is very close to edge-on). The larger number of possible
outflows over our Paper 2 result is due to a larger number of galaxies in the
vicinity of each absorber, so each absorber is more likely to be consistent
with at least one possible outflow model.

There is also very little difference in the extents of these outflows (median
200 kpc in groups, 180 kpc isolated; mean 280 and 270 kpc), whether or not
these are normalized to the virial radius (mean extent $\approx$1.9 $r_{vir}$
and median $\approx$1.5 $r_{vir}$ for both samples). The median impact
parameter to our putative outflows is similar to the median impact parameter
between detected H i and the nearest galaxy (190 kpc). This supports the
existence of outflows extending to at least the virial radius from isolated
and group galaxies, more similar to those in the FIRE simulations with cosmic
rays included (e.g. Hopkins et al., 2021), than other models suggesting
outflows rarely extend past the virial radius.

Using our best-fit results, seven of the eleven possible outflows would exceed
escape velocity were the galaxy isolated, comparable to the two of four
outflows exceeding escape velocity in Paper 2. Although the very small sample
in Paper 2 provided some suggestion of a correlation between sSFR and
$v/v_{esc}$, we do not find a significant correlation using the larger sample
here ($\approx 1\sigma$). Schroetter et al. (2019) note that the outflows they
find using Mg ii absorption tend to only exceed escape velocity from low-mass
galaxies ($\textrm{M}_{\star}/\textrm{M}_{\odot}\lesssim 10^{9.6}$). Whilst
our two model outflows from galaxies with smaller masses than this do indeed
appear to exceed escape velocity, several of our higher-mass galaxies also
exhibit outflows exceeding their escape velocities. These outflows are probed
at scales larger than the virial radius, whereas our two outflows around large
galaxies probed on scales $<r_{vir}$ do not achieve escape velocity. This
appears to support the continued acceleration at large radii seen in the
simulations by Hopkins et al. (2021) with cosmic rays included, although, as
they discuss, only the material near or above the escape velocity would be
capable of reaching these scales in the absence of additional acceleration.

In Paper 2, we noted that the model outflows in Schroetter et al. (2019) did
not feature opening angles as wide as the 45-$60^{\circ}$ found in our
isolated sample, possibly due to their stellar masses tending to be larger and
resulting in an increased collimation effect. Our group sample includes a
larger number of high-mass galaxies, especially at high redshifts, and our
model half-opening angles remain large for these galaxies. However, our models
suggest narrower outflows provide a better fit to the galaxies at lower
redshift, which also tend towards lower masses, opposite to the trend expected
due to collimation. This trend may be weaker than it appears, as some of the
higher-redshift objects (in the A-16 and A-32 groups) are unresolved and the
absorber width does not help to constrain the outflow opening angle.

If those relying on unresolved absorption are removed, our total (group and
isolated) sample of outflows has opening angles much more similar to those
seen in Schroetter et al. (2019), but still shows a trend of wider outflows at
higher masses and redshifts. It is unclear whether the redshift or mass
difference is contributing to the difference in opening angle, but there are
observations suggesting that outflows at higher redshifts are closer to
isotropic with respect to the galaxy (e.g. Chen et al., 2021).

Table 9: Model disk properties around galaxies for which disks can reproduce some of the observed absorption components. Column descriptions: (1)-(4) are from Table 3; (5) model scale height ratio (i.e. relative disk thickness); (6) maximum impact parameter at which this structure is detected (7) maximum observed disk extent (the 3-d distance from galaxy to the point on the line-of-sight where it intersects the disk plane, for the sightline with largest impact parameter with detected absorption); (8) virial radius; (9) virial velocity; (10) model circular velocity; (11) model radial/infall velocity. Galaxy | z | $\textrm{M}_{\star}$ | $\textrm{M}_{h}$ | $\textrm{h}_{r}/\textrm{h}_{z}$ | $\textrm{b}_{max}$ | Extent | $\textrm{r}_{vir}$ | $\textrm{v}_{vir}$ | $\textrm{v}_{\phi}$ | $\textrm{v}_{r}$
---|---|---|---|---|---|---|---|---|---|---
|  | $\textrm{log}_{10}(\textrm{M}_{\odot})$ | $\textrm{log}_{10}(\textrm{M}_{\odot})$ |  | (kpc) | (kpc) | (kpc) | ( km s-1) | ( km s-1) | ( km s-1)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
32778 | 0.202 | 10.2 $\pm$ 0.1 | 11.8 $\pm$ 0.3 | 20 | 410 | 420 $\pm$ 10 | 170 $\pm$ 60 | 130 $\pm$ 50 | 150 | < 20
29214 | 0.238 | 8.9 $\pm$ 0.1 | 11.1 $\pm$ 0.3 | 40 | 240 | 240 $\pm$ 10 | 100 $\pm$ 20 | 70 $\pm$ 20 | 100 | 30
A-49 | 0.383 | 8.7 $\pm$ 0.6 | 11.1 $\pm$ 0.4 | 200 | 410 | 410 $\pm$ 10 | 90 $\pm$ 50 | 80 $\pm$ 40 | 170 | < 20
A-69 | 0.399 | 9.8 $\pm$ 0.2 | 11.6 $\pm$ 0.3 | 100 | 190 | 730 $\pm$ 300 | 130 $\pm$ 30 | 110 $\pm$ 30 | 150 | 40
A-40 | 0.536 | 9.4 $\pm$ 0.4 | 11.4 $\pm$ 0.3 | 100 | 400 | 460 $\pm$ 60 | 110 $\pm$ 40 | 100 $\pm$ 30 | 110 | 70
A-75 | 0.558 | 8.3 $\pm$ 0.4 | 10.9 $\pm$ 0.4 | 70 | 180 | 290 $\pm$ 60 | 80 $\pm$ 30 | 70 $\pm$ 20 | 90 | 50
A-32 | 0.876 | 10.6 $\pm$ 0.2 | 12.4 $\pm$ 0.6 | 20 | 100 | 110 $\pm$ 10 | 210 $\pm$ 100 | 230 $\pm$ 130 | 100 | < 20
A-38 | 0.876 | 10.8 $\pm$ 0.3 | 12.6 $\pm$ 0.8 | 10 | 80 | 90 $\pm$ 10 | 250 $\pm$ 160 | 250 $\pm$ 160 | 80 | 90
B-19 | 0.907 | 10.4 $\pm$ 0.5 | 12.2 $\pm$ 0.8 | 20 | 170 | 250 $\pm$ 50 | 170 $\pm$ 110 | 190 $\pm$ 120 | 130 | 40
A-16 | 0.907 | 10.4 $\pm$ 0.5 | 12.2 $\pm$ 0.9 | 20 | 180 | 290 $\pm$ 70 | 170 $\pm$ 120 | 200 $\pm$ 130 | 100 | 50

####  5.2.2 Disks

We show the best-fitting parameters for absorption fit by our disk model in
Table 9.

The successful disk-like structures also appear similar to our results from
Paper 2, with scale height ratios from 10 to $\sim$ 300, and extents ranging
from less than 100 kpc to more than 1 Mpc. The average extents ($\approx$ 300
kpc) are also similar. However, we find substantially smaller circular
velocities than around isolated galaxies (by $\approx$ 270 to 120 km
s-1median, or 3 $v_{vir}$ to 1), and also produce a better fit using smaller
infall velocities for our group models. These infall velocities are often
better constrained than for isolated galaxies (for which we generally assumed
an infall velocity of 0.6$v_{vir}$), as with more high-column density
absorption in groups it is more likely that multiple absorbers can be fit by a
single model.

Given the small sample size, especially around isolated galaxies, this
$\approx 1.5\sigma$ difference in circular velocity may simply be due to the
galaxy properties and sightline configurations that feature in the sample
(although the extents and impact parameters are similar). The assumed infall
velocity for isolated galaxies, and its effect on the rotational velocities
required to fit the observed absorption, may also contribute, but changing
this assumption will increase the rotation velocity for some models and
decrease it for others.

A real difference between circular velocities of accreting material onto
isolated and group galaxies may be detected here, but it is difficult to
demonstrate when using absorption at only one or two locations around each
galaxy. For example it is possible that, rather than seeing absorption due to
gas falling onto one of the individual galaxies within our groups, we are
seeing material falling into the group halo, which would likely extend further
than the halo of an isolated galaxy of the same stellar mass as one of the
group galaxies. Interaction between infalling material and group gas could
slow its apparent velocity and contribute to the observed difference (as a
similar interaction between the CGM and galaxy ISM appears to cause velocity
lag in the ISM, Bizyaev et al. 2022). Alignment between the group galaxies and
large-scale structure (e.g. Tempel & Libeskind, 2013; Zhang et al., 2015; Hirv
et al., 2017) could lead to accretion at larger scales looking similar to
accretion onto an individual galaxy (possibly supported by several of our
groups featuring multiple galaxies with similar position angles, most
noticeably G-383 and G-876). Accretion from large-scale structure into a
galaxy group may also have been observed by Bielby et al. (2017).

####  5.2.3 Azimuthal angle dependency

We also briefly note that attempting to identify disks and outflows purely by
cutting in position angle and inclination (as in e.g. Bordoloi et al., 2011;
Zabl et al., 2019; Schroetter et al., 2019) produced results inconsistent with
our models when applied to our Paper 2 sample of isolated galaxies, although
our models were more likely to support disks and outflows near the major and
minor axes respectively. We apply this same cut here, and show the results in
Figure 6.

All of our model outflows lie in the region that would be identified as such
using these geometric cuts, whilst our model disks spread over both regions.
These results reinforce our conclusions from Paper 2, showing that these
geometric cuts are useful but are unlikely to produce pure disk or outflow
samples.

Figure 6: Azimuthal angle against inclination for galaxy-absorber pairs in our
sample. Absorbers identified as probing a possible outflow are shown in red,
with disks in blue. We also shade the regions used to identify the ‘primary’
disk and outflow subsamples in MEGAFLOW in blue and red respectively (Zabl et
al., 2019; Schroetter et al., 2019).

###  5.3 Correlations between group size and absorption

Figure 7: Column density against total galaxy stellar mass found within 500 km
s-1and 1 Mpc of H i absorbers. Faded points show our full sample of detected H
i absorption, whilst bold points show absorbers within 500 km s-1of the galaxy
groups considered in this work. The bold points are also coloured by the best-
fitting model type, with bold grey points showing absorption that could not
reasonably be fit by our models. Faded lines show the median for each model
type in both measurements.

Whether the gas around galaxy groups results primarily from a superposition of
the CGM of the individual galaxies, or from stripped material, increasing the
number of galaxies in a group is expected to increase the column densities of
gas seen around the group. It is therefore unsurprising that we find a
correlation between the number of galaxies in a group, and the number of H i
absorption features identified within a 500 km s-1 window. We also find a
strong correlation between the column density of an absorber, and the number
or total mass of nearby galaxies (using any combination of a 500 or 300 km s-1
window in redshift and 300, 500 or 1000 kpc in impact parameter), with
Spearman co-efficients suggesting > 95% confidence in all of these cases.

These correlations persist if the sample is split to only absorbers in the COS
spectra (z $\lesssim$ 0.45) and those in the FOS spectra. This relationship
between group size and absorption is therefore present across our 0 $<$ z $<$
1 redshift range and is robust to the changing galaxy and absorber detection
limits across this range.

The total stellar mass of nearby galaxies to each H i absorber (using a 500 km
s-1velocity window and 1000 kpc impact parameter cut) is shown in Figure 7.
There is no significant difference between the number or total mass of nearby
galaxies surrounding absorbers identified as disks and those identified as
outflows using our toy models (using any of the above cuts). As in Paper 2, we
find no significant difference between the column densities of disk and
outflow absorption. We do find a small difference in Doppler widths (outflows
with median $\approx$50 km s-1, disks $\approx$40 km s-1), but large
uncertainties due to unresolved absorption mean that this is also not
significant.

The absorbers within these groups that could not be fit using either model
have higher H i column densities and exist in more massive groups, although
the significance is again limited by a small sample size. If these consist of
material that has been ejected from galaxies and forms an intra-group medium,
this would likely be more prevalent in denser, more massive groups with more
interactions between galaxies, as is found here.

###  5.4 Galaxy interactions

Tidal interactions between galaxies in groups are expected to strip gas out of
the galaxies, which should be detectable (e.g. Morris & van den Bergh, 1994).
Streams of stars and gas attributed to tidal effects are seen around nearby
galaxies (e.g. Majewski et al., 1996; Ibata et al., 2001; Foster et al., 2014;
Sorgho et al., 2019), and there are suggestions of observed tidal material
around more distant galaxies using emission lines (e.g. Epinat et al., 2018;
Johnson et al., 2018). However, identifying this material in absorption is
challenging. By considering absorption that could not be reproduced using our
toy models, and by looking at close pairs of galaxies most likely to be
interacting, we attempt to identify tidal material in our observations.

Although not included in the main sample due to the difficulty of fitting
position angle and inclination measurements, the Q0107 field features a clear
ongoing galaxy merger, denoted B-39 and illustrated in Figure 8. We do not
attempt to fit our disk/outflow models to this merger. Additionally, the
absorption at this redshift is blended with Ly$\beta$ from z$\approx$0.72,
making it difficult to identify associated Ly$\alpha$ components.

The VPFIT results suggest two weak components in sightline A, one close to the
merger systemic redshift and another $\approx$120 km s-1 redward, and one
stronger component in sightline C, with a small blueshift relative to the
systemic redshift. Based on the directions and velocities of the stellar
arms/streams seen in the Figure, absorption from an extension of these streams
would have the opposite velocity offset to that observed in both of these
lines-of-sight.

However, given the lack of other nearby galaxies, it seems likely that at
least some of the absorption observed can be attributed to the interaction
between these galaxies, possibly on a previous pass between these galaxies
such that their orbits have changed the line-of-sight velocity relative to the
large-scale absorption. Simulations suggest stripped gas may be found opposing
the direction of motion, depending on the orbital configuration (Rodríguez et
al., 2022), so tidal material cannot be ruled out.

Several absorbers around the galaxy groups we consider in this work can not be
reasonably approximated by our disk/outflow/halo toy models. If a large
proportion of these absorbers are due to tidal material, these would likely be
found more frequently near to close galaxy pairs. However, we do not find any
significant difference between the closest pair separations of groups with
unexplained absorption, and those for which all absorbers can be fit by our
models.

Despite the lack of evidence for absorption due to interactions between
galaxies across the sample as a whole, we can still look individually at these
unexplained absorbers and consider whether tidally-stripped material can
provide a reasonable explanation.

The unexplained absorption in G-202 has a velocity offset close to our cut-off
of 500 km s-1, and is therefore likely associated with other galaxies (its
high column density making a physical association with at least one galaxy
likely, see e.g. T14 and Paper 1). However, B-22 does appear distorted, with a
tail of extended emission visible in the direction of LOS-B. Tidal material is
therefore a possible explanation for some of the absorption in this sightline,
but this absorption is reasonably approximated by our toy models.

The sub-DLA near G-558 could not be fit using our models, and likely has an
undetected host galaxy much closer to the line-of-sight than the detected
group of galaxies.

Strong, metal-enriched absorption in G-399 lies at a velocity between the two
large galaxies in this group. As discussed in Anshul et al. (2021), this
contains a warm component as well as a cooler gas phase. This is consistent
with intra-group material, lying within $r_{vir}$ of the largest group galaxy,
and could be tidal in origin.

The galaxies A-36 and A-37 are close together (< 10 kpc, with A-40 a more
distant companion), and appear distorted in the HST image, suggesting that
they are interacting. The unexplained absorption components all lie blueward
of all three galaxies, but have a much larger velocity offset than the
velocity difference between the galaxies. This would suggest that this
absorption does not identify material ejected by the interactions between
these two galaxies. This absorption may be associated with the more massive,
but distant, galaxies with a smaller velocity offset.

Therefore, in the four galaxy groups with unexplained absorption, stripped
material appears a reasonable hypothesis for two, only one of which contains a
nearby pair of galaxies that is likely interacting.

Stronger evidence for tidal material could come from absorption in the
direction of visible stellar streams, or material that lies between the
interacting galaxies in velocity and in projection on the sky. This is not the
case for the groups in this study, so whilst tidally-stripped gas may be the
most likely explanation for a small fraction of absorbers, we do not have good
evidence of its detection in this work.

Figure 8: Details of the absorption and galaxy environment around the galaxy
merger B-39 at z $\sim 0.45$. The layout is identical to that shown in Figure
3, but no model is shown as the position angle and inclination of these
galaxies could not be measured. The galaxy kinematics are measured from the [O
iii] emission line seen in the MUSE data. Tick marks (1) and (2) show the
Lyman n=6 transition from z$\approx$0.88; whilst (3)-(6) show Ly$\beta$ from
z$\approx$0.72.

###  5.5 Metal absorption

Around the twelve isolated galaxies in Paper 2, only two of the H i absorbers
also featured metal absorption around the same galaxy. However, many of the
absorbers detected here in galaxy groups do feature metal lines, most commonly
C iii and O vi, despite similar coverage and signal-to-noise ratio. (No other
ions are detected more than three times near our group redshifts, so we
primarily discuss C iii and O vi here.) This is consistent with our results
from Paper 1, in which O vi detections only appear at impact parameters < 350
kpc from non-group galaxies111Note that this uses the friends-of-friends
algorithm to discriminate between group and non-group galaxies as described in
Paper 1. This differs from the definitions of ‘isolated’ and ‘group’ galaxies
used in Paper 2 and this work in that the linking lengths used in Paper 1 vary
with redshift in order to correct for the changing detection limit with
redshift, and exclude MUSE galaxies in order to achieve consistent detection
limits across the field. The average linking lengths are comparable to the 500
km s-1 and 500 kpc used here., but are often more extended in group
environments (e.g. Johnson et al., 2015; Tchernyshyov et al., 2022).

Figure 9: Column densities of H i, C iii and O vi absorption found within 500
km s-1of our group galaxies. Only metals within 30 km s-1of detected H i are
included. Upper limits where metals are not detected are shown by downward-
pointing triangles. Points are coloured by best-fitting model type (disk,
outflow or none). The median column densities of absorbers with detected
metals are shown along each axis.

Figure 9 shows the column densities of C iii and O vi associated with H i
absorbers around our galaxy groups, coloured by the type of model that
provides the best fit to that absorber. In both cases there is no significant
difference in either the H i or metal column densities between the two models.
This could suggest that, if our simplified models are indeed indicative of
outflow cones and accreting disks around these galaxies, the accreting
material does not have significantly different metal content than the
outflowing material. However, it is possible that both the metal content and
ionization state differ substantially between disks and outflows, such that
the C iii and O vi column densities appear similar. The similar H i Doppler
parameters of the disk and outflow absorbers suggest similar gas temperatures,
but the metal ions likely trace different phases. We would therefore need a
more detailed analysis of more metal species in order to confidently determine
the metal content of these structures.

With its lower ionization stage, it is unsurprising that C iii correlates more
strongly with H i than O vi. We find with > 99% confidence (using a Spearman
rank with non-detections included or excluded) that the column densities of H
i and C iii are correlated, although we note that this correlation is not
significant if absorbers that could not be fit by our toy models are excluded.
There is not a significant correlation with O vi column density. The CGM/IGM
is known to be multi-phase (e.g. Tripp et al., 2008; Werk et al., 2014; Concas
et al., 2019; Anshul et al., 2021; Nateghi et al., 2021), and hence O vi
likely probes a warmer phase of material than H i and C iii, with warm
outflows and halos often proposed (e.g Werk et al., 2016; Oppenheimer et al.,
2016; Ng et al., 2019).

In isolated systems, accreting material would be expected to have a lower
metallicity than that in outflows, due to enrichment of outflows through
stellar evolution within the galaxy (e.g. Péroux & Howk, 2020). However,
observations have often failed to detect a relationship between azimuthal
angle and metallicity (e.g. Péroux et al., 2016; Kacprzak et al., 2019),
possibly in part due to the mixing by azimuthal angle discussed in Paper 2
(and briefly in Section 5.2.3 of this work). Our sample from Paper 2 has too
few metal detections to test this effect, but the numbers of O vi absorbers
found along the major and minor axes using our full galaxy sample (Section 4.2
of Paper 1) do suggest higher metal content for minor-axis absorbers. It seems
possible that, due to interactions between galaxies, metal enriched gas is
more common around group galaxies, and therefore accreting material in group
environments has metal content more similar to outflowing material than gas
accreting onto isolated galaxies. However, other studies have found
suggestions that low-metallicity gas can be masked by the presence of higher-
metallicity gas in the line-of-sight (e.g. Pointon et al., 2019), which would
allow our H i to be dominated by low-metallicity accretion despite strong
metal detections with a different origin (e.g. warm halo, stripped material,
intra-group gas).

We also note several high-column-density, metal-enriched absorbers that are
not identified as disks or outflows. However, one of these is the sub-DLA in
LOS-C, which likely has an undetected host galaxy and may not be strongly
affected by the larger-scale environment. Another is close to 500 km s-1
offset from the galaxy group considered, and is therefore more likely to be
associated with other galaxies at smaller velocity offsets. The third lies
within the velocity ranged spanned by the nearby group, and could plausibly
form part of an intra-group medium.

##  6 Summary & Conclusions

In this study we use multiple lines-of-sight to constrain the origins of H i
absorption seen around 9 pairs and groups of galaxies at z$<$1\. By fitting
simple disk, halo and outflow models around these galaxies we attempt to
determine to what extent the absorption features seen in galaxy groups could
be attributed to a superposition of the CGM around the individual galaxies, an
extended intra-group medium, or material stripped from the CGM of the galaxies
by interactions within the group. We model the absorption around nine galaxy
groups in the Q0107 field, probed by three lines-of-sight, and find that:

  1. 1.

Our disk and outflow models reproduce a slightly larger fraction of the
identified H i absorbers where multiple galaxies are present ($\approx$75%)
than around the isolated galaxies we consider in Paper 2 ($\approx$60%). This
supports a model for which a superposition of absorption from the group
galaxies results in the observed spectra. Sample variance and a larger
parameter space (due to multiple nearby galaxies) appear to be plausible
contributors to this higher success rate.

  2. 2.

Our ‘group’ sample includes systems with larger separations and lower masses
than many previous works considering absorption around group and isolated
galaxies. The larger number of galaxies also leads to a smaller impact
parameter between absorption and the closest galaxy. Both effects may also
contribute to our high success rate and resulting preference towards the
superposition model.

  3. 3.

The best-fitting parameters for our model outflows are generally similar to
those seen for isolated galaxies in our previous work (Paper 2, submitted),
including several that appear to extend beyond the virial radius. However, a
larger number of putative outflows have smaller opening angles; these galaxies
preferentially have lower masses and redshifts than those with apparent wider
outflows. This means our overall sample has parameters more similar to
Schroetter et al. (2019), who use similar models for Mg ii absorption.

  4. 4.

Our model disks have smaller rotation velocities than those around isolated
galaxies (120 to 270 km s-1, $\approx 1.5\sigma$), despite similar impact
parameters. This may be due to interactions between infalling material and the
extended group halo, but could also be due to the galaxy/sightline
configurations sampled in this field. In order to constrain the rotation
velocities, we have also had to assume an infall velocity in some cases, which
may be distorting the results.

  5. 5.

We do not detect any difference in the column densities of absorbers
identified as likely disks and outflows, and their Doppler widths do not
differ significantly. This matches our results from isolated galaxies in Paper
2. There does not appear to be a difference in the number or total stellar
mass of galaxies in groups hosting these possible disks and outflows, although
high-column-density absorbers do tend to be seen in denser galaxy environments
(both in galaxy number and mass).

  6. 6.

Absorption that cannot be fit by our models does not occur more frequently in
groups with a close pair of galaxies, and therefore does not provide evidence
of material stripped by galaxy interactions. Tidally-stripped material is a
plausible explanation for two of the four groups hosting these unexplained
absorbers, but is not supported by additional evidence such as the absorption
matching the velocity offsets between galaxy pairs or lying in the directions
of possible tidal stellar features seen in the HST images.

  7. 7.

There is no significant difference between the C iii or O vi contents of
absorbers identified as disks and outflows. Whilst outflowing material is
generally expected to be warmer and more metal-enriched, material accreting
onto a group galaxy may have been recently stripped or ejected from another
nearby galaxy, and thus be more enriched than accretion from the IGM onto an
isolated galaxy. We do not find a significant correlation between H i and O vi
column densities, which fits expectations of these ions tracing different gas
phases.

This paper, alongside our previous works using the galaxy and QSO data
covering the Q0107 field, demonstrates some advantages of using multiple
lines-of-sight probing the gas around galaxies. In addition to being a highly-
efficient way to build large samples of galaxy-absorber pairs, which we
utilized to detect both a bimodality in the azimuthal angle of these pairs and
a preference for aligned angular momentum between gas and galaxies in Paper 1,
these sightlines also provide some constraints on the possible CGM structures
seen in absorption, and therefore the origins of absorbing material.

Through kinematic and column density considerations, we are able to rule out
simple disk and outflow models for some absorption seen in the three
sightlines, and tentatively identify some absorption as likely originating
from disk or outflow structures. However, the large number of model parameters
available when considering possible models in galaxy groups makes this
identification yet more uncertain.

Searching for significant correlations between model parameters and
galaxy/group properties will require a larger sample of such observations,
probing a wider space of sightline configurations and group properties.
Constraining more complex models encompassing a wider range of physical
processes (entrainment of gas, changing ionization states, etc.) and therefore
with a larger range of free parameters, will require a larger number of
sightlines for each galaxy or group.

Whilst relatively few configurations of sightlines can be used to probe the
CGM/IGM in this way using current instruments, and such sensitive Ly$\alpha$
measurements at low redshift are only possible using the HST/COS instrument,
future instruments will enable these techniques to be used across a much
larger number of systems, especially at higher redshifts. CGM tomography at
higher redshifts is included in the science cases for several instruments on
the ELT (e.g. Maiolino et al., 2013; Evans et al., 2015; Marconi et al.,
2021), which will be able to use much fainter objects as background sources at
these higher redshifts, and BlueMUSE (Richard, 2019) will provide efficient
observations of galaxies surrounding such sightlines whilst extending
Ly$\alpha$ coverage to lower redshifts than most other ground-based
observations.

Our work studying the Q0107 system therefore serves as a useful test case for
techniques that can be applied to much larger samples (especially at higher
redshifts) in the near future.

## Acknowledgements

Firstly, we thank the anonymous referee for their insightful comments that
have improved the quality of this paper.

This work is based on observations made with the NASA/ESA Hubble Space
Telescope, obtained from the data archive at the Space Telescope Science
Institute. STScI is operated by the Association of Universities for Research
in Astronomy, Inc. under NASA contract NAS 5-26555. We also make use of
observations collected at the European Southern Observatory under ESO
programmes 086.A-0970, 087.A-0857 and 094.A-0131; at the W.M. Keck Observatory
under programme A290D; and at the Gemini Observatory under programme
GS-2008B-Q-50.

We thank Matteo Fossati for providing the MARZ templates used for estimating
redshifts and their uncertainties. We also thank Jill Bechtold for leading the
effort to obtain the Keck/DEIMOS data.

We thank the contributors to SCIPY222http://www.scipy.org/,
MATPLOTLIB333https://matplotlib.org/, ASTROPY444https://www.astropy.org/, and
the PYTHON programming language, the free and open-source community and the
NASA Astrophysics Data system555https://ui.adsabs.harvard.edu/ for software
and services.

This work also made use of the DiRAC system at Durham University, operated by
the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC
Facility666http://www.dirac.ac.uk/.

AB acknowledges the support of a UK Science and Technology Facilities Council
(STFC) PhD studentship through grant ST/S505365/1. SLM acknowledges the
support of STFC grant ST/T000244/1.

SC gratefully acknowledges support from Swiss National Science Foundation
grants PP00P2_163824 and PP00P2_190092, and from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation
programme grant agreement No 864361. MF also acknowledges funding from the ERC
under the Horizon 2020 programme (grant agreement No 757535). This work has
been supported by Fondazione Cariplo, grant No 2018-2329.

## Data Availability

The raw data from the Hubble Space Telescope may be accessed from the MAST
archive777http://archive.stsci.edu/, and that from the WM Keck Observatory
from the Keck Observatory Archive888https://koa.ipac.caltech.edu/cgi-
bin/KOA/nph-KOAlogin. That from the European Southern Observatory may be
accessed from the ESO
Archive999http://archive.eso.org/eso/eso_archive_main.html, and that from the
Gemini Observatory may be accessed from the Gemini Science
Archive101010http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/gsa/. The relevant
program IDs are given in Section 2 of this paper. The derived data generated
in this research will be shared on reasonable request to the corresponding
author.

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##  Appendix A Description of additional groups

###  A.1 G-202

G-202 is the largest group of galaxies in this field (both in number of
galaxies and total stellar mass), at z $\approx$ 0.2. B-22, the only galaxy in
the group that lies in the MUSE field, is a small galaxy with a distorted
shape, possibly due to tidal interactions within this group. Our estimate of
the galaxy’s position angle may be slightly affected, but we have taken the
orientation of the bright central component (having a larger uncertainty but
less likely to be distorted). An additional 5 galaxies at this redshift have
estimated position angles, and an further 19 lie within 1 Mpc of at least one
of the lines-of-sight.

Absorption is visible in all three lines-of-sight, although several of the
absorption components visible in Figure 10 are due to features other than
Ly$\alpha$, including Lyman lines and molecular hydrogen lines from the sub-
DLA at z=0.558. The five absorption components we have attempted to fit are
listed in Table 10, alongside another strong absorber in LOS-B which is close
to 500 km s-1 blueward of the galaxy. This large velocity offset makes it
unlikely to be associated with any of the galaxies in the HST field, and more
likely associated with one of the galaxies with slightly lower redshift.

Despite the relatively dense galaxy environment, a combination of disks and
outflows provides a good approximation to four of the five components, and
there may be a contribution to the fifth from a molecular line. The model
shown in the Figure is an outflow with half-opening angle $\approx 15^{\circ}$
and velocity $\approx$250 km s-1 from galaxy B-22 (matching the bluer
component in B), an outflow with half-opening angle $\approx 20^{\circ}$ and
velocity $\approx$50 km s-1 from galaxy 31787 (matching the absorption in A),
and a disk with rotation of 150 km s-1 and negligible infall around galaxy
32778 (matching the strong absorption in C and redder component of absorption
in B).

Stripped material is expected in groups of interacting galaxies (e.g Morris &
van den Bergh, 1994), and the distortion in B-22 may be due to this. However,
a ‘tail’ of gas extending out along the path of this apparent stream would not
intersect any of the three lines-of-sight. All absorbers identified have
widths $\lesssim$ 50 km s-1, so we also do not clearly identify any hot intra-
group gas.

Two components of absorption in LOS-B are also seen in C iii and O vi, with
redshifts matching the two Ly$\alpha$ components. No metals are detected in
the A or C sightlines, imposing 1$\sigma$ upper limits of $10^{12.9}$ and
$10^{13.6}$ $\textrm{cm}^{-2}$ on C iii and O vi respectively in sightline A,
whilst these lines could not be detected in LOS-C due to the sub-DLA. With the
metals in C unconstrained, the absorbers in B and C could have similar C
iii/Ly$\alpha$ and O vi/Ly$\alpha$ ratios, consistent with both probing
rotating/accreting material associated with the same galaxy. The C
iii/Ly$\alpha$ and O vi/Ly$\alpha$ ratios of the bluer absorption component in
B (identified as an outflow in our best model result) are lower than that of
the redder component (identified as accretion), but these ions likely trace
different ionization phases, so their ratios may not reflect a difference in
the metal content of the gas.

If the accreting material does indeed have a higher metal content, it could
have been stripped or ejected from other group galaxies, rather than accreted
from the IGM, but we cannot distinguish this from a scenario in which the
carbon and oxygen in the accreting material are ionized such that C iii and O
vi represent a larger fraction.

We also note that B-22, with a proposed strong outflow, has a lower SFR (and
sSFR) than most galaxies in this group. Therefore this putative outflow is
either sustained by a very low star-formation rate, or the galaxy has quenched
in the past $\approx$ 300 Myr. The disk model also requires angular momentum
aligned on scales of $\approx$ 400 kpc, larger than seen in most models.
Despite these difficulties, we cannot rule out a superposition of disk/outflow
models for this group.

Figure 10: Details of the absorption and galaxy environment around group G-202. Features shown are identical to those in Figure 3, with kinematics measured from the H$\alpha$ emission line seen in the MUSE data. Three components make up the model shown in the lower panel: an outflow with half-opening angle $\approx 15^{\circ}$ and velocity $\approx$ 250 km s-1from galaxy B-22; an outflow with half-opening angle $\approx 20^{\circ}$ and velocity $\approx$ 50 km s-1from galaxy 31787; and a disk with rotation velocity $\approx$ 150 km s-1and infall of $\lesssim$ 20 km s-1around galaxy 32778. Additional absorbers other than Ly$\alpha$ are marked with red ticks and identified as follows: (1) and (2) as the Lyman n=5-0 transition from z=0.536 in LOS-B and LOS-A respectively; (3) as Ly$\delta$ from z=0.500 in LOS-B; (4) and (5) as the Lyman n=6 transition from z=0.558 in LOS-C (where it is associated with the sub-DLA at z=0.558) and LOS-A; (6) as Ly$\beta$ from z=0.425; and (7)-(10) as molecular lines from the sub-DLA.  Table 10: Summary of galaxy and absorber properties for G-202. Columns are labelled as in Table 4, although details of galaxies outside the HST field are shown more briefly. z | Galaxy | Lum ($L_{\star}$) | Inc | LOS | Imp (kpc) | Azimuth | log(N H i) | b ( km s-1) |  $\Delta$v ( km s-1) | Other ions