# Clumpiness of Observed and Simulated Cold Circumgalactic Gas

Ramona Augustin1, Céline Péroux2,3, Aleksandra Hamanowicz2, Varsha Kulkarni4,
Hadi Rahmani5,6, Anita Zanella7
1Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD,
21218, USA
2European Southern Observatory, Karl-Schwarzschildstrasse 2, D-85748 Garching
bei München, Germany
3Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de
Marseille) UMR 7326, 13388, Marseille, France
4Dept. of Physics and Astronomy, Univ. of South Carolina, Columbia, SC 29208,
USA
5GEPI, Observatoire de Paris, PSL Research University, CNRS, Place Jules
Janssen, 92190 Meudon, France
6School of Astronomy, Institute for Research in Fundamental Sciences (IPM), PO
Box 19395-5531 Tehran, Iran
7Istituto Nazionale di Astrofisica, Padova Astronomical Observatory, Vicolo
dell’Osservatorio 5, 35122 Padova, Italy
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Determining the clumpiness of matter around galaxies is pivotal to a full
understanding of the spatially inhomogeneous, multi-phase gas in the
circumgalactic medium (CGM). We combine high spatially resolved 3D
observations with hydrodynamical cosmological simulations to measure the cold
circumgalactic gas clumpiness. We present new adaptive-optics-assisted
VLT/MUSE observations of a quadruply lensed quasar, targeting the CGM of 2
foreground $z\sim$1 galaxies observed in absorption. We additionally use zoom-
in FOGGIE simulations with exquisite resolution ($\sim$0.1 kpc scales) in the
CGM of galaxies to compute the physical properties of cold gas traced by Mg II
absorbers. By contrasting these mock-observables with the VLT/MUSE
observations, we find a large spread of fractional variations of Mg II
equivalent widths with physical separation, both in observations and
simulations. The simulations indicate a dependence of the Mg II coherence
length on the underlying gas morphology (filaments vs clumps). The $z_{\rm
abs}$=1.168 Mg II system shows coherence over $\gtrsim$ 6 kpc and is
associated with an [O II] emitting galaxy situated 89 kpc away, with SFR
$\geq$ 4.6 $\pm$ 1.5 $\rm M_{\odot}$/yr and $M_{*}=10^{9.6\pm 0.2}M_{\odot}$.
Based on this combined analysis, we determine that the absorber is consistent
with being an inflowing filament. The $z_{\rm abs}$=1.393 Mg II system traces
dense CGM gas clumps varying in strength over $\lesssim$ 2 kpc physical
scales. Our findings suggest that this absorber is likely related to an
outflowing clump. Our joint approach combining 3D-spectroscopy observations of
lensed systems and simulations with extreme resolution in the CGM put new
constraints on the clumpiness of cold CGM gas, a key diagnostic of the baryon
cycle.

###### keywords:

quasars: absorption lines – galaxies: structure – galaxies: evolution

††pubyear: 2020††pagerange: Clumpiness of Observed and Simulated Cold
Circumgalactic Gas–Clumpiness of Observed and Simulated Cold Circumgalactic
Gas

##  1 Introduction

In recent years, it has become well established that the circumgalactic medium
(CGM) plays a major role in galaxy evolution (see review in Tumlinson, Peeples
& Werk 2017). Pristine gas from the cosmic filaments traverses the CGM as it
is accreted onto galaxies, fueling star formation. Simultaneously, on-going
star formation, supernovae and active galactic nuclei drive hot, metal-
enriched outflows from the galaxy which mix with and affect the pristine gas
inflows. Hence the gas in the CGM is directly affected by and regulates the
central galaxy’s evolution. Mapping the phase and structure in the halos of
galaxies thus provides a key diagnostic of the baryon cycle taking place in
the CGM.

However, due to its diffuse nature, directly mapping those CGM structures in
emission has remained challenging (Bertone et al., 2010; Augustin et al.,
2019; Wijers et al., 2019). Recording emission line flux maps of the CGM is
possible for the brightest observable emission lines (typically Ly$\alpha$
around quasars at high redshift, e.g. Cantalupo et al. 2014; Arrigoni Battaia
et al. 2019). Only recently, deep observations at the Very Large Telescope
(VLT) have allowed us to map the Ly$\alpha$ emission around normal galaxies
(Wisotzki et al., 2016; Leclercq et al., 2017, 2020). The metal enrichment and
clumpiness of these halos are however not constrained by these Ly$\alpha$
observations.

In a complementary approach, absorption studies using bright background
sources, such as quasars, have proven to be successful in detecting the
diffuse gas in the CGM. This technique provides insight into the average
composition and statistical distribution of gas around galaxies through
stacking (e.g. York et al., 2006; Bordoloi et al., 2011; York et al., 2012;
Khare et al., 2012; Rudie et al., 2012) or averaging ensembles of absorber
properties (e.g. Adelberger et al., 2005; Werk et al., 2014; Péroux et al.,
2014). These studies report a characteristic drop of metal line strength with
increasing impact parameter. Such statistical studies provide key information
regarding the averaged CGM cold gas distribution around different galaxy
populations, where cold gas refers to 104K gas (as opposed to molecular).
However, one of the drawbacks of absorption studies is that the information
gained is limited to a isolated pencil beam along a single line of sight.

To further constrain the CGM structure around galaxies, alternative approaches
have to be used. Studies of absorbers along close quasar pairs have provided
new information on the clumpiness of the gas in single systems probed by
adjacent lines-of-sight (Hennawi et al., 2006; Martin et al., 2010; Rubin et
al., 2015). These works infer that the high-ionization material arises
predominantly in large, quiescent structures extending beyond the scale of the
absorber host dark matter halos rather than in ongoing galactic winds. On
smaller scales, gravitationally lensed background objects provide multiple
images as background sources to study the material in absorption (e.g. Rauch
et al., 2001; Ellison et al., 2004; Lopez et al., 2007; Chen et al., 2014;
Rubin et al., 2018; Kulkarni et al., 2019). Such observations allow us to
determine the coherence scale which is the length scale over which the gas
traced by Ly$\alpha$ or metals does not vary. Rubin et al. (2018) suggest that
even weak Mg II absorbers show a high degree of coherence over large scales
($\sim$8$-$22 kpc). Taken together, these observations indicate that the
coherence length of C IV systems is larger than that of Mg II systems. This is
qualitatively consistent with the simple picture of clumpy, low ionisation,
gas embedded in larger, more homogeneous, and more highly ionised outer halos.
In the gravitational lens approach, the range of linear scales probed is
directly related to the instrument spatial resolution capabilities. More
recently, it has become possible to use extended background sources (e.g.
Lopez et al. 2018; Péroux et al. 2018; Mortensen et al. 2020) to probe cold
gas over continuous areas on sub-kpc scales. These results confirm the trend
of absorption strength decreasing with increasing impact parameter, in
agreement with the statistics towards quasars (Lopez et al., 2018; Mortensen
et al., 2020; Lopez et al., 2020). Specifically, Péroux et al. (2018) find a
good efficiency of cold gas mixing on kpc-scales in the CGM of a typical
$z\sim$1 galaxy.

From a theoretical view-point, the ability of cosmological hydrodynamical
simulations to reproduce the column density distribution of H I, the line
widths and profiles tracing the temperature of the gas, and the evolution of
the line density with redshift has been one of the great successes of the last
few decades (Rahmati et al., 2013, but see Gaikwad et al. 2017). Such
simulations have provided insight into the broad physical environments within
and between galaxies probed by various H I column density regimes, and thus
allowed us to assess the implications of their observational properties.
However, cosmological hydrodynamical simulations are still limited by their
resolution, as most of the physical processes which play a key role in galaxy
evolution (e.g. star formation and its feedback, black hole growth and its
feedback) occur at scales well below what can be simulated. There have been
numerous recent efforts to increase the resolution in the typically
underresolved CGM regions of galaxies (Hummels et al., 2018; van de Voort et
al., 2019; Peeples et al., 2019; Suresh et al., 2019). Indeed, this step is
key to simulate the cold phase ($\sim 10^{4}$ K) of the gas traced by e.g. Mg
II absorbers in observations. For these reasons, efforts in the last few years
have mostly focused on the higher-ionisation phase of the CGM (Ford et al.,
2016; Gutcke et al., 2017; Suresh et al., 2017; Muratov et al., 2017; Corlies
et al., 2020). The most recent high-resolution cosmological simulations now
allow to study the cool gas content and clumpiness of the CGM (e.g. Peeples et
al., 2019; Zheng et al., 2020; Nelson et al., 2020; van de Voort et al.,
2020).

In this work, we make use of both Adaptive Optics (AO) supported VLT/MUSE
observations with an image quality of 0.7 arcsec FWHM and zoom-in cosmological
FOGGIE Peeples et al. (2019) simulations with exquisite resolution ($\sim$ 0.1
kpc scales) in the CGM region to put new constraints on the cold gas
clumpiness in the CGM of $z\sim$1 galaxies. This work is structured as
follows: Section 2 presents the observations used for this study. Section 3
details the analysis of the observations, and in Section 4 we introduce the
simulations. The analysis and interpretation of the nature of the cold CGM gas
is discussed in Section 5, before we conclude in Section 6. Throughout this
work we assume a flat $\Lambda$CDM cosmology with $\Omega_{m}$ = 0.3 and
$H_{0}$ = 68 km/s/Mpc.

##  2 New AO-MUSE observations

The quasar WFI 2033$-$4723 ($J$ = 16.3 mag and J2000 coordinates:
203342.12–472343.9) lies at a redshift $z_{\rm QSO}$=1.66 (Morgan et al.,
2004; Eigenbrod et al., 2006). The source is known to be lensed by a
foreground galaxy at a spectroscopically determined redshift of $z_{\rm
lens}$=0.657 (Ofek et al., 2006; Eigenbrod et al., 2006; Sluse et al., 2019)
resulting in a system of four distinct images. The left panel of Figure 1
displays the Hubble Space Telescope (HST) broad-band imaging illustrating the
configuration of the system: four distinct quasar images with the lens galaxy
clearly located in the center. To achieve a spatial resolution which allows
for separation of the four images, we took advantage of the Science
Verification (SV) program of the in the wide-field (60 arcsec $\times$ 60
arcsec) mode with MUSE. The data were taken on 17 September 2017 in the
nominal mode (Program 60.A-9189, PI: R. Augustin). The MUSE field was observed
for 1h and was rotated by 90 deg between the exposures to minimize flat-
fielding imperfections.

To improve on the depth of the observations we added (in a seeing-weighted way
- see description of the reduction) archival MUSE data of the same field. The
field had been observed in natural-seeing wide-field mode with MUSE in several
visits between 2014 and 2016 for a total of 5.4h (Program 097.A-0454, PI: D.
Sluse and Science Verification 60.A-9306) with the goal to improve on
measurements of the Hubble constant $H_{0}$ (Suyu et al., 2017; Sluse et al.,
2019). In order to benefit from the deepest possible data, we have fully
reprocessed and combined both the archival and our SV data. All the data were
reduced with version 2.6 of the ESO MUSE pipeline (Weilbacher, 2015) as well
as custom-developed codes. We run the muse_scibasic and muse_scipost recipes
for each sub-cubes. These functions perform all the necessary data reduction
steps, including correction for bias, dark, bad pixels as well as air
wavelength and geometry calibration, baryocentric correction, flux
calibration, first-step telluric sky subtraction and astrometry. Further
optimised sky subtraction was carried out with the Zurich Atmosphere Purge
(ZAP) software (Soto et al., 2016). Since the MUSE spectra are calibrated at
air wavelength, we use air rest wavelengths throughout our analysis to
determine redshifts.

First, we run Sextractor (Bertin & Arnouts, 1996) on the MUSE white light
image to create a segmentation map. This is then used to mask all objects in
the field in order to select the sky regions. The ZAP software then performs a
Principle Component Analysis on the resulting sky spectra which is further
subtracted from the cube. Finally, we combined all the individual data cubes
by assigning longer exposure times and the better seeing values a larger
weight, in order to achieve the optimal depth and spatial resolution in the
final data product. The resulting cube has a spatial sampling of 0.2 arcsec
per pixel, a spectral sampling of 1.25 Å per pixel and a wavelength coverage
extending from 4750 to 9350 Å. The image quality of the final combined data
was measured from the quasar images. The resulting point spread function has a
full width at half maximum (FWHM) of 0.7 arcsec at 7000Å, as measured on the
central quasar (image B). The right panel of Figure 1 shows the MUSE narrow-
band image of the lensed system, indicating the labels for the four images
(labelled A1, A2, B and C) and showing in green contours the pixels that were
extracted for each image’s spectrum.

##  3 Analysis of Integral Field Spectroscopic Data

Figure 1: Left Panel: HST broad-band composite image from three filters in the
optical and near-infrared (Suyu et al., 2017) of $z_{\rm QSO}$=1.66
WFI2033–4723. The lensed quasar produces four distinct images. Also apparent
in this image is the $z_{\rm lens}$=0.657 lens galaxy. Given the lensing
effect, the separation between B and C is 5 kpc at $z$=1.168 and 2.3 kpc at
$z$=1.393, corresponding to the intervening Mg II systems. Right Panel: MUSE
narrow-band observations of the same system with labels for the individual
images as used throughout this work. The green contours illustrate the pixels
used to extract the spectrum of each quasar image. While the spatial
resolution offered by the HST is unmatched by the ground-based data, MUSE
Integral Field Spectroscopy aided with the AO-system uniquely allows us to
recover the spectral information.

###  3.1 Quasar Spectroscopy and Absorption Features

Table 1: Measurements for the two Mg II absorption systems (at $z_{\rm abs}$=1.168 and $z_{\rm abs}$=1.393): SNR, Equivalent Widths (EW) in units of Å and in the case of the $z_{\rm abs}$=1.168 system, the velocity offsets (in km/s) between the absorber sightlines and the [O II] emitter.  QSO images | A1 | A2 | B | C
---|---|---|---|---
$\mathbf{z_{\rm abs}}$=1.393
SNR at the absorber
SNR | 129 | 81 | 106 | 60
Rest Equivalent Widths
EW2796 [Å] | < 0.1 | < 0.1 | 0.05 $\pm$ 0.01 | 0.41 $\pm$ 0.04
EW2803 [Å] | < 0.1 | < 0.1 | 0.03 $\pm$ 0.01 | 0.32 $\pm$ 0.03
$\mathbf{z_{\rm abs}}$=1.168
SNR at the absorber
SNR | 40 | 35 | 34 | 32
Rest Equivalent Widths
EW2796 [Å] | 0.09 $\pm$ 0.01 | 0.08 $\pm$ 0.01 | 0.15 $\pm$ 0.02 | 0.05 $\pm$ 0.01
EW2803 [Å] | 0.05 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.07 $\pm$ 0.02 | 0.02 $\pm$ 0.02
Velocity Offset to [O II] emitter at z= 1.16895 $\pm$ 0.00007
$\Delta v$ [km/s] | 20 $\pm$ 50 | 70 $\pm$ 50 | 70 $\pm$ 50 | 110 $\pm$ 50
Figure 2: Mg II absorption features against the four quasar images in the
$z_{\rm abs}$=1.168 absorption system. Both lines of the Mg II doublet are
clearly detected in all four spectra. The offset orange lines show the sky
spectrum. The spike between the doublet is a noisy residual from the sky
subtraction which is masked in the subsequent analysis.  Figure 3: Mg II
absorption features against the four quasar images in the $z_{\rm abs}$=1.393
absorption system. The Mg II absorption is detected against quasar images C
and B, and remains undetected in the two remaining spectra (A1 and A2). The
offset orange lines show the sky spectrum.

We obtain the spectrum of the four individual quasar images from the MUSE data
cube. We extract the flux from carefully selected pixels (see green mask in
Figure 1), constructing an area which encompasses at least the FWHM of the
point spread function (PSF). For the two fainter images (B and C), an aperture
size of 7 px = 1.4 arcsec in diameter maximises the signal-to-noise ratio
(SNR) of the resulting spectra. For the brighter counter-images A1 and A2, a
smaller aperture of 5 px = 1 arcsec in diameter was used to avoid overlap
between the two nearby images. The apertures are centered by eye on the
brightest pixels for each quasar image. A small, yet inconsequential offset of
1 px from the brightest pixel for image A1 is applied, to minimise the overlap
with image A2. We want to note that for our absorption measurements the chosen
area is not critical. The chosen apertures as seen in
QFitsView111https://www.mpe.mpg.de/$\sim$ott/dpuser/qfitsview.html are shown
in Figure 1. While we take care in the extraction of the spectra to have
separate spectra for A1 and A2, we do note that due to their proximity, the
spectra are likely not completely independent.

Given the redshift of the lens galaxy ($z_{\rm lens}$=0.66), the MUSE spectra
cover absorption features of Mg I, and Ca H+K lines. We report no detections
for any of these absorption lines in any of the four extracted spectra. We
further undertake a blind search for additional absorbers and detect two Mg II
systems: one at $z_{\rm abs}$=1.168 and one at 1.393 (Figures 2 and 3). The
lower redshift absorber is detected in the four quasar spectra. The latter
system is detected solely against quasar images C and B and remains undetected
towards the two remaining images (A1 and A2). Figures 2 and 3 show these Mg II
absorption systems. We calculate the rest-frame equivalent width of each of
these systems by integrating the line profiles following the standard
definition:

$\rm EW(F,\delta F)=(1+z)^{-1}\,\int(1-((F\pm\delta F)/F_{cont})\,d\lambda$
(1)

where $\rm F/F_{cont}$ is the continuum normalized flux of the spectrum. For
detected absorption features, we measure the EW for each Mg II line (2796,
2803Å) in the normalised spectra. In order to remove the signatures intrinsic
to the quasar, a local power-law continuum is fitted. Dividing the observed
spectra with their associated continua results in four normalised quasar
spectra corresponding to each of the four images. The errors on the EWs are
calculated from flux uncertainties and propagating the errors in equation 1.

For the non-detections, we calculate the corresponding 5$\sigma$ ($\sigma$ in
eq. 2) limit of EW${}_{\rm Mg\,II}$ (see Table 1) using the relation between
the observed-frame equivalent width ($\rm EW_{limit}$), the resolving power
(R), and the SNR per resolution element (Ménard & Péroux, 2003) at a given
observed wavelength ($\rm\lambda_{obs}$):

$\rm EW_{limit}[\text{\AA}]<\sigma*\dfrac{\lambda_{obs}[\text{\AA}]}{R\times
SNR}$ (2)

Table 1 lists the corresponding spectral SNR, rest-frame EW of Mg II from
detections and limits from non-detections for each of the absorption systems.

###  3.2 Emission Galaxy Spectroscopy

Figure 4: MUSE narrow-band image around the [O II] emission line at $z_{\rm
abs}$=1.168. The lensed quasar images are subtracted, showing negative flux
values at the position indicated by the yellow stars. The [O II] emission line
is shown in light colour at an impact parameter of 10.8 arcsec (89 kpc) North
of the lensed system. Figure 5: MUSE spectrum of the galaxy associated with
the $z_{\rm abs}$=1.168 Mg II absorber. The blue line shows the extracted [O
II] emission line, binned with a 3-pixel kernel. At MUSE spectral resolution,
the doublet structure of [O II] lines is not well-separated, which results in
smearing of the different velocity components. The red line indicates the
Gaussian fit to the emission line. The orange line displays the sky spectrum
in the MUSE cube, also binned with a 3-pixel kernel and arbitrarily scaled in
the y-direction. Figure 6: Spectral Energy Distribution (SED) fit to the
galaxy associated with the $z_{\rm abs}$=1.168 Mg II absorption system. The
points with error bars indicate the continuum magnitudes observed with HST at
optical and near infrared wavelengths (F555W, F814W, F125W, F140W and F160W).
The red spectrum is the result from the SED fit with LePhare code (Arnouts et
al., 1999; Ilbert et al., 2006) leading to a stellar mass of the counterpart
galaxy of $M_{*}=10^{9.6\pm 0.2}M_{\odot}$. We overplot the MUSE spectrum in
grey which precisely matches the spectrum resulting from the SED fit. The
inset on the top-left corner shows the HST continuum V-band image of the
galaxy. The galaxy within the red circle is detected at the absorber redshift,
while the other objects are below the detection limit or at a different
redshift.

Integral field spectroscopy (IFS) is exceptionally well-suited for studies of
multiply lensed images as well as the associated foreground galaxies. The
high-spatial resolution achieved thanks to the adaptive optics coupled with
the spectral resolution of MUSE means that independent spectra can be
extracted for each of the images of the lensed quasar (see section above).
Furthermore, the 3D information allows us to search in emission for galaxies
associated with both the lens and the identified Mg II absorption systems. The
search for emission line counterparts is performed by eye in a narrow-band
image centered on the expected emission line.

At the redshift of the lens (zlens=0.657), [O II] and [O III] emission lines
are covered by the MUSE observations. We do not detect these emission lines in
the MUSE cube down to a SFR threshold of 0.01 $\rm M_{\odot}$/yr. At the
redshift of the $z_{\rm abs}$=1.393 Mg II system, the [O II] emission line is
also covered by the MUSE observations, but the [O II] 3729 line lies close to
a sky emission line which results in additional contamination. We do not
report counterpart galaxies to this absorbers down to a SFR detection limit of
0.02 $\rm M_{\odot}$/yr. We find a counterpart galaxy at the redshift of the
$z_{\rm abs}$=1.168 Mg II system. The [O II] emission line is detected to the
North of the quasar images at a distance of 10.8 arcsec, corresponding to 89
kpc at the redshift of the absorber (see Figure 4). At the MUSE spectral
resolution, the doublet structure of [O II] lines is not well-separated when
extracting the spectrum integrating over the whole galaxy, which results in
smearing of the different velocity components (see also Hamanowicz et al.
2020). To calculate the total flux in the emission line, we fit a gaussian
function to the spatially integrated [O II] profile (shown in Figure 5). From
the [O II] emission flux, we determine the star formation rate (SFR) of the
galaxy to be SFR = 4.6 $\pm$ 1.5 $\rm M_{\odot}$/yr following Kennicutt
(1998). This SFR is not dust corrected, as we have no accurate means of
determining the dust correction, and therefore presents a lower limit on the
true SFR of this galaxy. The SFR detection limit in the data calculated from
the sky level for that redshift is 0.01 $\rm M_{\odot}$/yr.

The galaxy is also detected in continuum in archival HST images. The MAST data
archive provides the magnitudes of the galaxy in 5 different bands at optical
and near infrared wavelengths (F555W, F814W, F125W, F140W and F160W). We use
the magnitude determination in these bands to perform a Spectral Energy
Density (SED) fit of the stellar population in this object. To this end, we
utilize the SED fitting code LePhare (Arnouts et al., 1999; Ilbert et al.,
2006). The results of the SED fit, shown in Figure 6, matches precisely the
MUSE galaxy spectrum where they overlap. The fit indicates a stellar mass of
the counterpart galaxy of $M_{*}=10^{9.6\pm 0.2}M_{\odot}$. We note that there
are other objects closeby in projection, but they are either at a different
redshift or are not detected in MUSE data cube. We further run Sextractor
(Bertin & Arnouts, 1996) on the HST V-band (F555W) image in order to determine
the position angle of the galaxy to be PA=$-$48$\pm$41 degrees. The error is
large due to the round appearance of the galaxy. We derive the "azimuthal
angle" between the image A1 quasar line-of-sight and the projected galaxy’s
major axis on the sky to be 45$\pm$41 degrees. We can therefore not constrain
the absorber alignment with respect to the galaxy orientation. We use the
redshifts resulting from the centroids of the [O II] emission line as well as
the Mg II absorption lines at $z_{\rm abs}$=1.168 to calculate the velocity
offset of the various absorption features to the systemic redshift of the host
galaxy. The centroids were determined from a first moment analysis using
astropy specutils centroid function and verified by eye. The errors on the
velocities include wavelength calibration uncertainties of $\sim$ 20 km/s. The
results are tabulated in Table 1.

###  3.3 Physical Distances at the Absorbers’ Redshift

To relate the physical properties of gas detected in absorption along the
lines-of-sight of the quasar images to the foreground objects, we calculate
the separation between the images in the absorber plane in physical units. We
perform this calculation in comoving space, denoting all following distances
as comoving distances. The approach is analogous to equation 2 in Cooke et al.
(2010) and equation 1 in Kulkarni et al. (2019), who express their derivation
in angular diameter distances.

At the quasar’s redshift (zQSO=1.66), the separation of all the four images is
naturally zero. Assuming our cosmology, we calculate the distances between two
quasar images in the absorber plane ($d_{\rm abs}$) from the distances in the
lens plane ($d_{\rm lens}$) in the following way:

$d_{\rm abs}=\frac{d_{\rm abs-QSO}}{d_{\rm lens-QSO}}*d_{\rm lens}$ (3)

where $d_{\rm abs-QSO}$ is the distance between the foreground absorber and
background quasar and $d_{\rm lens-QSO}$ is the distance between the lens
galaxy and the background quasar. The comoving distance between the lens
(zlens=0.657) and the quasar (zQSO=1.66) is 1579 $h^{-1}$ Mpc. For the low-
redshift Mg II system, the distance between the absorber ($z_{\rm abs}$=1.168)
and the quasar is 669 $h^{-1}$ Mpc; while the distance between the high-
resdshift Mg II absorber ($z_{\rm abs}$=1.393) and the quasar is 342 $h^{-1}$
Mpc. The resulting physical distances for each of the two Mg II systems range
from 0.6 to $\sim$5 kpc and are tabulated in Table 2.

##  4 CGM Zoom-in Hydrodynamical Cosmological Simulations

Figure 7: Example synthetic absorption line spectrum. This mock CGM Mg II
$\lambda$2796Å systems were created using the Trident package to pierce random
sightlines through the modelled halo from the FOGGIE hydrodynamical
cosmological simulations. We integrate over the multiple components of an
absorber to calculate the EW as those would not be resolved in our MUSE data.

Figure 8:  Mg II halo at z=1.2 from the FOGGIE simulations. The Mg II column
densities corresponding to the observed range are shown on the top, while the
density-weighted radial velocity of the gas (inflow blue, outflow red) is
displayed at the bottom. The grey structure in the center of the upper panel
depicts the density projection of the galactic disc, showing the galaxy’s
orientation to be close to edge-on. This halo has a virial radius of 84 kpc, a
dark matter halo mass of $\rm 10^{11.4}M_{\odot}$, a stellar mass of $\rm
10^{10.5}M_{\odot}$, a SFR of $\rm 10M_{\odot}/yr$, and an ISM mass of $\rm
10^{9.4}M_{\odot}$. This mock halo indicates the Mg II structures range from
small, dense clumps, to extended, large filaments. It also appears that
extended structures with log(N$\rm{}_{Mg\,II})\sim$ 12-13 are preferentially
tracing inflow filaments while most clumpy structures with
log(N$\rm{}_{Mg\,II})>$ 13 trace dense, outflowing material as illustrated by
the radial velocity map which presents both the velocity and direction of
these gas flows. We therefore conclude that there may be structural
differences in Mg II clouds depending on whether they trace inflows or
outflows.

In order to constrain the cold gas in CGM and the nature of the detected Mg II
absorbers, we make use of CGM simulations with high spatial resolution. We use
the FOGGIE simulation suite which is designed for exquisite resolution ($\sim$
0.1 kpc scales) in the CGM of galaxies which evolve into Milky-Way-like
systems at z=0 (Peeples et al., 2019). We create mock observations from these
cosmological zoom-in simulations. For the comparison, we choose the ‘Tempest’
halo with forced refinement in the CGM at redshift z=1.2, to match our
observations (see Zheng et al., 2020, for further information on this
simulation). This halo has a virial radius of 84 kpc, a Dark Matter mass of
$\rm 10^{11.4}M_{\odot}$, a stellar mass of $\rm 10^{10.5}M_{\odot}$, a SFR of
$\rm 10M_{\odot}/yr$, and an interstellar medium (ISM) mass of $\rm
10^{9.4}M_{\odot}$. The stellar mass of the simulated halo $\sim$10 times
larger than the galaxies observed with MUSE. However, the stellar-mass halo-
mass relation for isolated field galaxies (e.g. Read et al. 2017) suggests
that our galaxy has a comparable halo mass ($\rm\sim 10^{11}M_{\odot}$) to the
one in this simulation.

Next, we use the Trident package (Hummels, Smith & Silvia, 2017) to create
mock spectra from idealised background source piercing through the simulated
halo. Trident uses the information of the gas cells from the simulation
(density, temperature, metallicity, velocity) so that spatial resolution is
kept the highest possible. The Morton (2003) atomic data are used to determine
the Mg II densities in each gas cell as well as the effective redshift along a
given sightline. Trident furthermore creates Voigt profiles and returns a
synthetic normalised absorption spectrum. We shoot random sightlines through
the halo (excluding the ISM region of the central and satellite galaxy) to
create synthetic spectra. Figure 7 shows example spectra of CGM Mg II
$\lambda$2796Å absorbers. While Trident also produces noisy mock spectra, we
choose to perform the analysis on noise-less outputs to recover the simulated
Mg II properties. By performing our analysis on those outputs, we recover the
"true" underlying distribution of EW fractional differences in the simulated
galactic halo.

We measure the EW of such absorbers by integrating over the absorption signal,
in an analogous way to the analysis performed on the observed spectra (see eq.
1). The thus measured EWs are used for comparison with the observations (see
Section 5.1 and Figure 9).

A Mg II column density projected map of this halo is shown in the upper panel
of Figure 8. The range of plotted column densities is chosen such that the
lower limit of the color bar is matched to the detection limit in the
observations. The column densities measured in the $z_{\rm abs}$=1.168 Mg II
system are represented by the yellow/orange part of the colorbar, whereas the
higher redshift absorber lies into the dark red region. The simulations
indicate the prevalence of a variety of structures: while a large fraction of
the cells in the halo are below the detection limit, the structures which are
above the observations detection limit ($\rm 10^{11.5}cm^{-2}$) range from
small, dense clumps, to extended, large filaments. We note that the map shown
in this figure does not encompass the whole region within the virial radius,
but instead targets the high-resolution CGM region of the simulation. We focus
here on the highly resolved structures which are a least 20 kpc away from the
galactic center, as the lensed quasar images pierce random sightlines through
the CGM gas of a foreground galaxy. The bottom panel of Figure 8 shows the
density weighted radial velocity projection of the halo. The clump like
structures seen in the Mg II column density map are coinciding with outflowing
dense gas structures, whereas the filamentary structures are tracing inflows
onto the galaxy. Towards the lower right corner there is a fast outflow which
is too hot to host Mg II absorbers.

##  5 Nature of the Cold Circumgalactic Gas

###  5.1 Clumpiness traced by the Fractional Difference in Equivalent Width

####  5.1.1 Results from Observations

The Mg II systems observed with MUSE against four quasar images put new
constraints on the clumpiness of cold metals in the CGM of $z\sim$1 galaxies.
In order to quantify the underlying spatial structure of the Mg II absorbers,
we calculate the fractional variation in EW to determine the coherence lengths
of absorbers. While other statistics could have been used, this diagnostic is
commonly used in literature (Ellison et al., 2004; Rubin et al., 2018) and it
enables comparison with previous works. We follow the definition for the
fractional difference in EW of two sightlines (X and Y), where EW(sightlineX)
$>$ EW(sightlineY):

$\rm EWfrac=\dfrac{EW(sightlineX)-EW(sightlineY)}{EW(sightlineX)}$ (4)

The results are tabulated in Table 2 and illustrated in the right panel of
Figure 9. The Figure shows our data as stars, where filled symbols indicate
that Mg II was detected towards both sightlines. Due to possible cross-
contamination of the spectra between sightlines A1 and A2, that fractional
difference in EW is presumably biased towards lower values. We additionally
extract a spectrum between images A1 and A2 to include this component which is
of order of 0.005 Å to the error budget. We also report similar measurements
from the literature: detections and literature sample from Rubin et al.
(2018), to which we added the more recent measurements (Kulkarni et al.,
2019).

Figure 9: Mg II $\lambda$2796Å Equivalent Width (EW) fractional difference (see equation 4) as a function of physical separation between two random sightlines through a halo. Left panel: Observed fractional difference from our work (stars), detections and literature sample from Rubin et al. (2018), to which we added newer measurements (Kulkarni et al., 2019). The colour coding indicates the EW strength as indicated on the upper colour bar. Middle panel: Simulated fractional difference from random sightlines piercing the simulated Mg II halo shown in Figure 8. We report a clear trend of high EW Mg II systems (blue, mainly located in the central part of the halo) showing large variation over all scales ($\sim$1-100 kpc). Low EW Mg II systems (green) display a large scatter in fractional variation at all scales, indicating that those probe a variety of structures, from clouds to filaments with large coherence lengths over tens of kpc. This large coherence length is due to both the low EW systems being more extended around the central galaxy and forming larger coherent structures in the CGM. Right panel: Separating the halo shown in Figure 8 into structures of clumps and filaments, we show the normalized distribution of strongly (EW fractional difference > 0.5) varying systems from the middle panel for the separations up to $\sim$6 kpc. Clumps vary equally over all those scales, while filaments show a trend with separation and vary more at scales of $\gtrsim$ 3 kpc. For this reason we conclude that the $z_{\rm abs}$=1.168 system is consistent with the signatures from a filament, while the $z_{\rm abs}$=1.393 system is consistent with the signatures from a clump. Table 2: Mg II line variation as traced by EW fractional difference for the two Mg II systems in the MUSE observations. QSO Images | EW Fractional Difference | Physical Separation [kpc]
---|---|---
$\mathbf{z_{\rm abs}}$=1.168
A1 - A2 | 0.16$\pm$0.20 | 1.7 $\pm$ 0.2
A1 - C | 0.51$\pm$0.09 | 3.6 $\pm$ 0.2
A2 - C | 0.42$\pm$0.11 | 4.1 $\pm$ 0.2
B - A1 | 0.35$\pm$0.11 | 5.9 $\pm$ 0.2
B - A2 | 0.45$\pm$0.10 | 4.8 $\pm$ 0.2
B - C | 0.68$\pm$0.07 | 5.0 $\pm$ 0.2
$\mathbf{z_{\rm abs}}$=1.393
A1 - A2 | — | 0.8 $\pm$ 0.1
B - A1 | > 0.28 | 2.7 $\pm$ 0.1
B - A2 | >0.38 | 2.2 $\pm$ 0.1
C - A1 | >0.91 | 1.7 $\pm$ 0.1
C - A2 | >0.92 | 1.9 $\pm$ 0.1
C - B | 0.87$\pm$0.02 | 2.3 $\pm$ 0.1

Rubin et al. (2018) suggest that even weak Mg II absorbers show a high degree
of coherence over large scales ($\sim$8$-$22 kpc). The absorber at $z_{\rm
abs}$=1.168 reported here is in line with this conclusion. The Mg II line
strength in the absorption system at $z_{\rm abs}$=1.393, however, varies
strongly on kpc scales, indicating a highly inhomogeneous and clumpy structure
of dense Mg II clouds. This raises the question of the dependence of the
coherence scale on the strength of the absorber and the geometry of the
underlying CGM structure. While filaments will produce large coherence lengths
thanks to their elongated shape, the variation in EW can be strong in the
perpendicular direction. Small dense gas clumps, individually show small
coherence lengths of typically kpc scales. However depending on the sky
covering fraction of small gas clumps, it may be possible, but less likely, to
find two sightlines in a halo which probe individual structures of similar EWs
but at large physical separation, also resulting in apparent large coherence
lengths. The natural expectation thus would have Figure 9 indicating a typical
physical scale above which the scatter in EW fractional difference becomes
important. The latest results indicate a large scatter of the EW fractional
variations on scales $>$ 2 kpc. For scales $<$ 2 kpc, fewer data points are
available as those scales are close or below the typical spatial resolution
scales one can probe with multiple sightlines. However, they show less scatter
and typically little variation on those spatial scales.

In the quadruply lensed system reported here, the benefit of studying four
closeby ($<$ 6 kpc) sightlines is that these observations are less prone to
geometrical effects. The quasar sightlines probe absorption towards different
directions (which is not possible with only a pair of sightlines) and enable
us to determine the elongation and extent of the underlying structures,
obtaining constraints on whether the absorber probes filamentary or clumpy
structures. Indeed, the simulations introduced in the previous section
demonstrate that there is a variety of structures in the CGM of $z\sim$1
galaxies, which challenges the interpretation of the fractional difference in
EW depending on the orientation of probing sightlines.

####  5.1.2 Results from Simulations

We analyse the mock Mg II halo presented in Section 4 in an analogous way to
the observations, by calculating the EW fractional difference of randomly
choosen sightline pairs through the halo for different physical scales. The
results are shown in the middle panel of Figure 9. We plot sightlines with
0.05 Å $<$ EW $<$ 2 Å in order to match the EW range of the observations. We
find that in this EW range, the halo shows indications of both filamentary and
clumpy structures in the CGM as well as the outskirts of the galactic disk. We
exclude the low density CGM which remains under the typical Mg II detection
limits and the central part of the galaxy with EW $>$ 2Å which typically
consists of several absorbing components in velocity space and are therefore
not suitable for comparison with the observations.

Thanks to the high spatial resolution we are confident in the EW fractions at
sub-kpc scales and find that we would theoretically expect a similar scatter
at those scales as for larger separations. However, this is not seen in the
observational data and may stem from resolution effects in the observations.

In the mock halo, we report a clear trend for high EW Mg II systems (blue,
corresponding to $\rm log(N_{Mg\,II}[cm^{-2}])\gtrsim 14$) showing large
variation over all scales ($\sim$ 1-100 kpc) due to their compactness and
small covering fraction. Those high EW systems are mostly found in the inner
regions of the halo, close to the galaxy, which explains the decrease of low
fractional difference points at large separations. The outflowing clumps
identified in Figure 8 with 13 $\rm<log(N_{Mg\,II}[cm^{-2}])<$ 14 have
equivalent widths of $\sim$ 0.3 $-$ 0.5 Å, which is in the range we observe
for the $z_{\rm abs}$=1.393 Mg II system. Figure 8 shows that the gas with 12
$\rm<log(N_{Mg\,II}[cm^{-2}])<$ 13 arises in a mixture of geometries, with
filaments dominating over clumps. Those filaments have EW values of $<$ 0.2 Å
(similar to our observed system at $z_{\rm abs}$=1.168) and seem to show the
largest coherence lengths of up to $\sim$ 100 kpc. Low EW Mg II systems
(green, EW $<$ 0.5 Å) show a large scatter in fractional variation at all
scales, indicating that those probe a variety of structures, from clouds to
filaments with large coherence lengths over tens of kpc. However, the apparent
coherence length of up to 100 kpc from random pairs of sightlines is
misleading as those are most likely probing independent, separated structures.

To further investigate the coherence lengths of different CGM structures
(clumps, filaments), we compute the fractional EW difference in clumps and
filaments separately (right panel of Figure 9). We limit the data points for
this plot to strongly varying systems (EW fractional difference $>$ 0.5) and
to spatial scales of up to 6.3 kpc where the scatter in the middle panel of
Figure 9 increases. Clumps are found to vary strongly almost equally over all
those scales, whereas filaments show a trend of stronger variation with larger
separation, indicating coherence over larger scales, as illustrated by the
column density map in Figure 8. This therefore confirms that absorption
systems that vary strongly on scales of $<$2 kpc most likely trace clumps,
rather than the edges of a filament. This result allows us to interpret the
nature of the Mg II systems (see Sections 5.2.2 and 5.2.3).

Nelson et al. (2020) have recently studied the formation and distribution of
Mg II clouds in Illustris TNG50 for a similar halo in terms of halo mass.
Surprisingly, their Mg II absorbers show a homogeneous distribution of small
clouds around the halo, which is different from what we observe in the FOGGIE
halo. The two works agree that the majority of Mg II systems trace inflows,
however there are clear morphological differences in Mg II systems between the
two simulations. This may be due to different physics implemented in the
simulations (e.g. magnetic fields or different feedback models). Indeed, the
dependence of the CGM structure on the physics implemented in a simulation has
recently been demonstrated by van de Voort et al. (2020) who show that the
distribution of cool gas and mixing of metals is affected by magnetic fields
and feedback. Future investigations of cool clumps in the CGM, both in
simulations and observations are therefore needed to draw further conclusions
on the nature of CGM clouds.

###  5.2 Nature of the Observed Systems

####  5.2.1 Lens Galaxy at $z_{\rm lens}$=0.657

The quadruple quasar images are known to be produced by a foreground massive
galaxy (Eigenbrod et al., 2006). Recently, Sluse et al. (2019) have
investigated the environment of this lensed quasar and spectroscopically
determined the lens redshift to be $z_{\rm lens}$=0.657. The fiducial lens
model for this system with Einstein radius $\theta_{E}$ = 0.944 arcsec,
suggests a halo mass of $M\approx 10^{11.5}M_{\odot}$ (Rusu et al., 2019).
Recent studies, like the COS-LRG survey (Chen et al., 2018; Zahedy et al.,
2019), commonly find cold, metal enriched gas in the CGM of massive,
elliptical and typically quenched galaxies. However, in our data no tracers of
cold gas ($\rm log(N_{Mg\,I})<11.1~{}cm^{-2}$, $\rm
log(N_{Ca\,II~{}H+K})<11.7~{}cm^{-2}$) are detected against any of the four
quasar images. This result implies that there is little 104 K gas around this
massive galaxy. We note, however, that the Mg I 2852 line is weaker than Mg II
2796 which is not covered by the MUSE spectrum and that Ca II H+K usually
traces ISM gas. A detection of Ca II H+K would likely indicate a satellite
galaxy rather than CGM gas clouds. In addition, we do not detect [O II]
emission associated with the lens, indicating a low SFR, as expected from a
quenched elliptical galaxy.

####  5.2.2 Mg II Absorber at $z_{\rm abs}$=1.168

The Mg II absorber at $z_{\rm abs}$=1.168 is clearly detected against all four
quasar images. The absorption feature is particularly strong against counter-
image B, with a rest-frame equivalent width EW2796=0.15$\pm$0.02Å. The
absorption is weaker towards the other 3 images with EW2796 ranging from
0.05$\pm$0.01Å to 0.09$\pm$0.01Å. Individual values for this weak
(EW(2796)$<$0.3 Å) absorption system are reported in Table 1. The detection of
Mg II absorption towards all four quasar images implies a cloud coherence
length of at least 6 kpc for this absorber.

Additionally, we detect an [O II] emitting galaxy at the redshift of the
absorber. The emititer, situated 89 kpc from the absorber, is a low-mass
object (stellar mass of M⋆ = $10^{9.6\pm 0.2}$ M⊙) and has a star formation
rate (uncorrected for dust-depletion) of SFR $\geq$ 4.6 $\pm$ 1.5 $\rm
M_{\odot}$/yr. We find a fairly high value compared to SFRs of galaxies
associated with typical heavy-element absorption systems at these redshifts
(e.g. Kulkarni et al., 2006; Péroux et al., 2011; Augustin et al., 2018). The
physical separation indicates that the absorption feature likely probes gas in
the CGM of that foreground galaxy. In velocity space, we find the absorber to
be blueshifted with respect to the host galaxy but the measurements are not
robust enough to draw further conclusions on the nature of the absorbing
cloud.

The canonical view is that inflows preferentially occur along the major axis,
while outflows are aligned with the minor axis, corresponding to the path of
least resistance (Péroux et al., 2011; Bouché et al., 2012; Schroetter et al.,
2019; Peroux et al., 2020). The so-called "azimuthal angle" between the quasar
line-of-sight and the projected galaxy’s major axis on the sky therefore in
principle constrains this alignment. In this case, the azimuthal angle of
45$\pm$41 degrees does not indicate a high likelihood of either accretion or
outflow. Given the distance to the [O II] emitter and the strength of the Mg
II absorption, the absorber could also be associated with another closeby
dwarf galaxy. However, due to the lack of nearby [O II] emission and no clear
signs of rotation in the absorption velocities, we do not confirm this
hypothesis.

The system at $z_{\rm abs}$=1.168 which consists of weak measured Mg II EWs
shows little variation in EW fractional difference up to $\sim$ 5-6 kpc. Based
on the simulation snapshot, these properties indicate that the absorber is
probing a filamentary structure, potentially from gas infalling onto the
galaxy. Indeed, a qualitative description of the simulations (bottom panel of
Figure 8) indicates that the spatially homogeneous filamentary structures are
aligned with inflow dominated regions, while the highly clumpy structures
trace outflowing regions. The inflowing filaments in Figure 8 show Mg II
column densities of $\rm log(N_{Mg\,II}[cm^{-2}])\sim 12$ with little spatial
variation, in line with our observations of the absorber at $z_{\rm
abs}$=1.168. Given the qualitative consistency of our observed data with
simulated inflow regions, we therefore suggest that the absorber may trace an
inflowing filament onto the [O II] emitting galaxy.

####  5.2.3 Mg II Absorber at $z_{\rm abs}$=1.393

The Mg II absorber at $z_{\rm abs}$=1.393 is clearly detected against image C,
tentatively towards image B but not in the two other quasar image spectra (A1
and A2), with EW2796 ranging from 0.05$\pm$0.01Å in image B to 0.41$\pm$0.04Å
in image C. Individual measurements are reported in Table 1.

At the absorber redshift, the physical separations between counter-images B
and C is 2.3 kpc and that between A1 and C is 1.7 kpc. (Table 2). At the
redshift of the Mg II absorbers, no galaxies are detected down to SFR < 0.02
M⊙/yr, so that the location of the gas with respect to a bound system is not
known. Given than the Mg II absorption line is solely detected against quasar
images C and B, we assume that the metal cloud is centered close to image C.
This configuration puts strong constraints on the coherence length of the cold
gas cloud associated with this Mg II absorber. Given the non-detections
against counter-images A1 and A2, we conclude that the density of the Mg II
cloud varies significantly over scales smaller than 2 kpc (between C and A1).

The system at $z_{\rm abs}$=1.393 is a large equivalent width absorber against
one quasar image but marginally or no detected towards the others. The system
thus presents sizeable EW fractional differences. With the additional insights
from simulations, we infer that the absorber is likely probing one of the
numerous small, dense outflowing CGM gas clumps (Figure 8).

##  6 Conclusions

Here, we present new 3D spectroscopy VLT/MUSE observations of a
gravitationally lensed quasar displaying four bright images. The adaptive
optics system of MUSE provides the necessary spatial resolution to enable the
extraction of individual spectra of each of the quasar images. To reach deep
observations without losing the spatial resolution, we have carefully combined
our AO observations with archival observations by weighting individual
exposures on their image quality. The combination of the cubes is performed by
assigning a larger weight to longer exposure times and better seeing values.
In this work, we systematically search for foreground absorption features,
both at the known redshift of the lens and along the entire line-of-sight. We
detect [O II] emission associated with one of the Mg II absorbers. We further
present specifically designed cosmological hydrodynamical zoom-in FOGGIE
simulations of an equivalent Mg II halo with enhanced spatial resolution in
the CGM in order to capture the small-scale physics and substructure of the
bulk of the gas in the galactic ecosystem. The combination of observations and
simulations put new constraints on the spatial clumpiness of cold (T = 104K)
gas around galaxies.

Our main results can be summarised as follows:

  * •

We report the non detection of cold 104 K gas around the massive ($M\approx
10^{11.5}M_{\odot}$) $z_{\rm lens}$=0.657 lens galaxy.

  * •

We calculate the EW fractional difference of both the new observations
together with an extended literature sample and the simulated Mg II halo. We
find that fractional difference depends on the underlying structure of the
absorber, with extended inflow filaments showing coherence length on larger
scales than outflowing clumpy structures.

  * •

We show that the $z_{\rm abs}$=1.168 Mg II system possibly probes an inflowing
gas filament onto an [O II] emitting galaxy situated 89 kpc away with SFR
$\geq$ 4.6 $\pm$ 1.5 $\rm M_{\odot}$/yr and $M_{*}=10^{9.6\pm 0.2}M_{\odot}$.

  * •

Using similar lines of argument, we establish that the physical properties of
the $z_{\rm abs}$=1.393 Mg II system indicate that this absorber likely traces
dense CGM gas clumps varying in strength over $\sim$ 2 kpc physical scales.

Enlarged samples of multiply lensed bright quasars observed with IFU
instruments combined with state-of-the-art zoom-in hydrodynamical simulations
are essential to put new constraints on the clumpiness of the gas in the CGM
of galaxies, a key diagnostic of the baryon cycle.

## Acknowledgements

We thank Kate Rubin for sharing data and Molly Peeples, Jason Tumlinson and
the FOGGIE222https://foggie.science collaboration for making their simulations
available and for related discussions. This work has made use of the
yt333https://yt-project.org package (Turk et al., 2011). RA was supported by
NASA grants 80NSSC18K1105 and HST GO # 15075. VPK acknowledges partial support
from NASA grants NNX17AJ26G and 80NSSC20K0887. This research made use of
Astropy,444http://www.astropy.org a community-developed core Python package
for Astronomy (Astropy Collaboration et al., 2013, 2018).

## Data Availability

All data incorporated into the article are available on request.

## References

  * Adelberger et al. (2005) Adelberger K. L., Shapley A. E., Steidel C. C., Pettini M., Erb D. K., Reddy N. A., 2005, ApJ, 629, 636
  * Arnouts et al. (1999) Arnouts S., Cristiani S., Moscardini L., Matarrese S., Lucchin F., Fontana A., Giallongo E., 1999, MNRAS, 310, 540
  * Arrigoni Battaia et al. (2019) Arrigoni Battaia F., Hennawi J. F., Prochaska J. X., Oñorbe J., Farina E. P., Cantalupo S., Lusso E., 2019, MNRAS, 482, 3162
  * Astropy Collaboration et al. (2013) Astropy Collaboration et al., 2013, A&A, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration et al., 2018, AJ, 156, 123
  * Augustin et al. (2018) Augustin R., et al., 2018, MNRAS, 478, 3120
  * Augustin et al. (2019) Augustin R., et al., 2019, MNRAS, 489, 2417
  * Bertin & Arnouts (1996) Bertin E., Arnouts S., 1996, A&AS, 117, 393
  * Bertone et al. (2010) Bertone S., Schaye J., Dalla Vecchia C., Booth C. M., Theuns T., Wiersma R. P. C., 2010, MNRAS, 407, 544
  * Bordoloi et al. (2011) Bordoloi R., et al., 2011, ApJ, 743, 10
  * Bouché et al. (2012) Bouché N., et al., 2012, MNRAS, 419, 2
  * Cantalupo et al. (2014) Cantalupo S., Arrigoni-Battaia F., Prochaska J. X., Hennawi J. F., Madau P., 2014, Nature, 506, 63
  * Chen et al. (2014) Chen H.-W., Gauthier J.-R., Sharon K., Johnson S. D., Nair P., Liang C. J., 2014, MNRAS, 438, 1435
  * Chen et al. (2018) Chen H.-W., Zahedy F. S., Johnson S. D., Pierce R. M., Huang Y.-H., Weiner B. J., Gauthier J.-R., 2018, MNRAS, 479, 2547
  * Cooke et al. (2010) Cooke R., Pettini M., Steidel C. C., King L. J., Rudie G. C., Rakic O., 2010, MNRAS, 409, 679
  * Corlies et al. (2020) Corlies L., Peeples M. S., Tumlinson J., O’Shea B. W., Lehner N., Howk J. C., O’Meara J. M., Smith B. D., 2020, ApJ, 896, 125
  * Eigenbrod et al. (2006) Eigenbrod A., Courbin F., Meylan G., Vuissoz C., Magain P., 2006, A&A, 451, 759
  * Ellison et al. (2004) Ellison S. L., Ibata R., Pettini M., Lewis G. F., Aracil B., Petitjean P., Srianand R., 2004, A&A, 414, 79
  * Ford et al. (2016) Ford A. B., et al., 2016, MNRAS, 459, 1745
  * Gaikwad et al. (2017) Gaikwad P., Khaire V., Choudhury T. R., Srianand R., 2017, MNRAS, 466, 838
  * Gutcke et al. (2017) Gutcke T. A., Stinson G. S., Macciò A. V., Wang L., Dutton A. A., 2017, MNRAS, 464, 2796
  * Hamanowicz et al. (2020) Hamanowicz A., et al., 2020, MNRAS, 492, 2347
  * Hennawi et al. (2006) Hennawi J. F., et al., 2006, ApJ, 651, 61
  * Hummels et al. (2017) Hummels C. B., Smith B. D., Silvia D. W., 2017, ApJ, 847, 59
  * Hummels et al. (2018) Hummels C. B., et al., 2018, arXiv e-prints,
  * Ilbert et al. (2006) Ilbert O., et al., 2006, A&A, 457, 841
  * Kennicutt (1998) Kennicutt Robert C. J., 1998, ARA&A, 36, 189
  * Khare et al. (2012) Khare P., Vanden Berk D., York D. G., Lundgren B., Kulkarni V. P., 2012, MNRAS, 419, 1028
  * Kulkarni et al. (2006) Kulkarni V. P., Woodgate B. E., York D. G., Thatte D. G., Meiring J., Palunas P., Wassell E., 2006, ApJ, 636, 30
  * Kulkarni et al. (2019) Kulkarni V. P., Cashman F. H., Lopez S., Ellison S. L., Som D., José Maureira M., 2019, ApJ, 886, 83
  * Leclercq et al. (2017) Leclercq F., et al., 2017, A&A, 608, A8
  * Leclercq et al. (2020) Leclercq F., et al., 2020, A&A, 635, A82
  * Lopez et al. (2007) Lopez S., Ellison S., D’Odorico S., Kim T. S., 2007, A&A, 469, 61
  * Lopez et al. (2018) Lopez S., et al., 2018, Nature, 554, 493
  * Lopez et al. (2020) Lopez S., et al., 2020, MNRAS, 491, 4442
  * Martin et al. (2010) Martin C. L., Scannapieco E., Ellison S. L., Hennawi J. F., Djorgovski S. G., Fournier A. P., 2010, ApJ, 721, 174
  * Ménard & Péroux (2003) Ménard B., Péroux C., 2003, A&A, 410, 33
  * Morgan et al. (2004) Morgan N. D., Caldwell J. A. R., Schechter P. L., Dressler A., Egami E., Rix H.-W., 2004, AJ, 127, 2617
  * Mortensen et al. (2020) Mortensen K., Keerthi Vasan G. C., Jones T., Faucher-Giguere C.-A., Sanders R., Ellis R. S., Leethochawalit N., Stark D. P., 2020, arXiv e-prints, p. arXiv:2006.00006
  * Morton (2003) Morton D. C., 2003, ApJS, 149, 205
  * Muratov et al. (2017) Muratov A. L., et al., 2017, MNRAS, 468, 4170
  * Nelson et al. (2020) Nelson D., et al., 2020, arXiv e-prints, p. arXiv:2005.09654
  * Ofek et al. (2006) Ofek E. O., Maoz D., Rix H.-W., Kochanek C. S., Falco E. E., 2006, ApJ, 641, 70
  * Peeples et al. (2019) Peeples M. S., et al., 2019, ApJ, 873, 129
  * Péroux et al. (2011) Péroux C., Bouché N., Kulkarni V. P., York D. G., Vladilo G., 2011, MNRAS, 410, 2237
  * Péroux et al. (2014) Péroux C., Kulkarni V. P., York D. G., 2014, MNRAS, 437, 3144
  * Péroux et al. (2018) Péroux C., Rahmani H., Arrigoni Battaia F., Augustin R., 2018, MNRAS, 479, L50
  * Peroux et al. (2020) Peroux C., Nelson D., van de Voort F., Pillepich A., Marinacci F., Vogelsberger M., Hernquist L., 2020, arXiv e-prints, p. arXiv:2009.07809
  * Rahmati et al. (2013) Rahmati A., Pawlik A. H., Raičević M., Schaye J., 2013, MNRAS, 430, 2427
  * Rauch et al. (2001) Rauch M., Sargent W. L. W., Barlow T. A., 2001, ApJ, 554, 823
  * Read et al. (2017) Read J. I., Iorio G., Agertz O., Fraternali F., 2017, MNRAS, 467, 2019
  * Rubin et al. (2015) Rubin K. H. R., Hennawi J. F., Prochaska J. X., Simcoe R. A., Myers A., Lau M. W., 2015, ApJ, 808, 38
  * Rubin et al. (2018) Rubin K. H. R., et al., 2018, ApJ, 859, 146
  * Rudie et al. (2012) Rudie G. C., et al., 2012, ApJ, 750, 67
  * Rusu et al. (2019) Rusu C. E., et al., 2019, arXiv e-prints, p. arXiv:1905.09338
  * Schroetter et al. (2019) Schroetter I., et al., 2019, MNRAS, 490, 4368
  * Sluse et al. (2019) Sluse D., et al., 2019, MNRAS, 490, 613
  * Soto et al. (2016) Soto K. T., Lilly S. J., Bacon R., Richard J., Conseil S., 2016, MNRAS, 458, 3210
  * Suresh et al. (2017) Suresh J., Rubin K. H. R., Kannan R., Werk J. K., Hernquist L., Vogelsberger M., 2017, MNRAS, 465, 2966
  * Suresh et al. (2019) Suresh J., Nelson D., Genel S., Rubin K. H. R., Hernquist L., 2019, MNRAS, 483, 4040
  * Suyu et al. (2017) Suyu S. H., et al., 2017, MNRAS, 468, 2590
  * Tumlinson et al. (2017) Tumlinson J., Peeples M. S., Werk J. K., 2017, ARA&A, 55, 389
  * Turk et al. (2011) Turk M. J., Smith B. D., Oishi J. S., Skory S., Skillman S. W., Abel T., Norman M. L., 2011, ApJS, 192, 9
  * Weilbacher (2015) Weilbacher P., 2015, in Science Operations 2015: Science Data Management. p. 1, doi:10.5281/zenodo.34658
  * Werk et al. (2014) Werk J. K., et al., 2014, ApJ, 792, 8
  * Wijers et al. (2019) Wijers N. A., Schaye J., Oppenheimer B. D., Crain R. A., Nicastro F., 2019, arXiv e-prints, p. arXiv:1904.01057
  * Wisotzki et al. (2016) Wisotzki L., et al., 2016, A&A, 587, A98
  * York et al. (2006) York D. G., et al., 2006, MNRAS, 367, 945
  * York et al. (2012) York D. G., et al., 2012, MNRAS, 423, 3692
  * Zahedy et al. (2019) Zahedy F. S., Chen H.-W., Johnson S. D., Pierce R. M., Rauch M., Huang Y.-H., Weiner B. J., Gauthier J.-R., 2019, MNRAS, 484, 2257
  * Zheng et al. (2020) Zheng Y., Peeples M. S., O’Shea B. W., Simons R. C., Lochhaas C., Corlies L., Tumlinson J., 2020, arXiv e-prints, p. arXiv:2001.07736
  * van de Voort et al. (2019) van de Voort F., Springel V., Mandelker N., van den Bosch F. C., Pakmor R., 2019, MNRAS, 482, L85
  * van de Voort et al. (2020) van de Voort F., Bieri R., Pakmor R., Gómez F. A., Grand R. J. J., Marinacci F., 2020, arXiv e-prints, p. arXiv:2008.07537