11institutetext: Insituto de Física y Astronomía, Universidad de Valparaíso,
Avda. Gran Bretaña 1111, 2340000 Valparaíso, Chile
11email<EMAIL_ADDRESS>22institutetext: Dipartimento di Fisica e
Astronomia Galileo Galilei, Università degli Studi di Padova Vicolo del
$L^{\prime}$Osservatorio 3, 35122 Padova Italy 33institutetext: INAF
Osservatorio Astronomico di Padova, vicolo dell’Osservatorio 5, I-35122
Padova,Italy 44institutetext: Instituto de Investigación Multidisciplinar en
Ciencia y Tecnología, Universidad de La Serena, Raúl Bitrán, 1305 La Serena,
Chile 55institutetext: Departamento de Astronomía, Universidad de La Serena,
Av. Juan Cisternas 1200 Norte, La Serena, Chile 66institutetext: Núcleo de
Astronomía, Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av.
Ejército 441, Santiago, Chile 77institutetext: INAF-Osservatorio di
Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93/3, 40129 Bologna
Italy 88institutetext: INAF-IASF, via Bassini 15, I-20133, Milano, Italy
99institutetext: Department of Astronomy, University of Massachusetts Amherst,
710 N. Pleasant St, Amherst, MA 01003, USA 1010institutetext: Departamento de
Ciencias Fisicas, Facultad de Ciencias Exactas, Universidad Andres Bello,
Fernandez Concha 700, Las Condes, Santiago, Chile 1111institutetext: Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
1212institutetext: Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
1313institutetext: Gemini Observatory, NSF’s NOIRLab, 670 N. A’ohoku Place,
Hilo, Hawai’i, 96720, USA 1414institutetext: Department of Physics and
Astronomy, University of California, Davis, One Shields Ave., Davis, CA 95616,
USA 1515institutetext: Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA 1616institutetext: Instituto de Física,
Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile
1717institutetext: European Southern Observatory, Av. Alonso de Córdova 3107,
Vitacura, Santiago, Chile

# Metal content of the circumgalactic medium around star-forming galaxies at z
$\sim$ 2.6 as revealed by the VIMOS Ultra-Deep Survey

Méndez-Hernández  H  Cassata 11 P 2233 Ibar  E 11 Amorín  R 4455 Aravena  M 66
Bardelli  S 77 Cucciati  O 77 Garilli  B 88 Giavalisco  M 99 Guaita  L 1010
Hathi  N 1111 Koekemoer  A 1111 Le Brun  V 1212 Lemaux  B.C 13131414 Maccagni
D 88 Ribeiro  B 1212 Tasca  L 1212 Tejos  N 1616 Thomas  R 1717 Tresse  L 1212
Vergani  D 77 Zamorani  G 77 Zucca  E 77

(Received XXXX XX, 2021; accepted XXXX XX, 2022)

###### Abstract

Context. The circumgalactic medium (CGM) is the location where the interplay
between large-scale outflows and accretion onto galaxies occurs. Metals in
different ionization states flowing between the circumgalactic and
intergalactic mediums are affected by large galactic outflows and low-
ionization state inflowing gas. Observational studies on their spatial
distribution and their relation with galaxy properties may provide important
constraints on models of galaxy formation and evolution.

Aims. The main goal of this paper is to provide new insights into the spatial
distribution of the circumgalactic of star-forming galaxies at $1.5<z<4.5$
($\langle z\rangle\sim$2.6) in the peak epoch of cosmic star formation
activity in the Universe. We also look for possible correlations between the
strength of the low- and high-ionization absorption features (LIS and HIS) and
stellar mass, star formation rate, effective radius, and azimuthal angle
$\phi$ that defines the location of the absorbing gas relative to the galaxy
disc plane.

Methods. The CGM has been primarily detected via the absorption features that
it produces on the continuum spectrum of bright background sources. We
selected a sample of 238 close pairs from the VIMOS Ultra Deep Survey to
examine the spatial distribution of the gas located around star-forming
galaxies and generate composite spectra by co-adding spectra of background
galaxies that provide different sight-lines across the CGM of star-forming
galaxies.

Results. We detect LIS (C ii and Si ii) and HIS (Si iv, C iv) up to
separations $\langle b\rangle=$ 172 kpc and 146 kpc. Beyond this separation,
we do not detect any significant signal of CGM absorption in the background
composite spectra. Our Ly$\upalpha$, LIS, and HIS rest-frame equivalent width
($W_{0}$) radial profiles are at the upper envelope of the $W_{0}$
measurements at lower redshifts, suggesting a potential redshift evolution for
the CGM gas content producing these absorptions. We find a correlation between
C ii and C iv with star formation rate and stellar mass, as well as trends
with galaxy size estimated by the effective radius and azimuthal angle.
Galaxies with high star formation rate (log[SFR/(M⊙yr${}^{-1})]>1.5$) and
stellar mass (log[M★/M⊙]¿10.2) show stronger C iv absorptions compared with
those low SFR (log[SFR/(M⊙yr${}^{-1})]<0.9$) and low stellar mass
(log[M★/M⊙]¡9.26). The latter population instead shows stronger C ii
absorption than their more massive or more star-forming counterparts. We
compute the C ii / C iv $W_{0}$ line ratio that confirms the C ii and C iv
correlations with impact parameter, stellar mass, and star formation rate. We
do not find any correlation with $\phi$ in agreement with other high-redshift
studies and in contradiction to what is observed at low redshift where large-
scale outflows along the minor axis forming bipolar outflows are detected.

Conclusions. We find that the stronger C iv line absorptions in the outer
regions of these star-forming galaxies could be explained by stronger outflows
in galaxies with higher star formation rates and stellar masses that are
capable of projecting the ionized gas up to large distances and/or by stronger
UV ionizing radiation in these galaxies that is able to ionize the gas even at
large distances. On the other hand, low-mass galaxies show stronger C ii
absorptions, suggesting larger reservoirs of cold gas that could be explained
by a softer radiation field unable to ionize high-ionization state lines or by
the galactic fountain scenario where metal-rich gas ejected from previous star
formation episodes falls back to the galaxy. These large reservoirs of cold
neutral gas around low-mass galaxies could be funnelled into the galaxies and
eventually provide the necessary fuel to sustain star formation activity.

###### Key Words.:

galaxies: evolution – galaxies: high-redshift – galaxies:ISM – galaxies: CGM

##  1 Introduction

The circumgalactic medium (CGM, 10kpc-$\sim$300 kpc) is the gas reservoir
between the interstellar medium (ISM, $\lesssim 10$kpc) and the intergalactic
medium (IGM, $\gtrsim 300$kpc). It is characterized as an active interface
where galaxies reprocess their baryonic material. Up to $\sim$50% of the total
baryonic mass is found in the CGM at low redshift ($z\sim 0.2$) (Wolfe et al.,
2005; Werk et al., 2014; Zheng et al., 2015) and at high redshift (Hafen et
al., 2019), thus representing a significant gas reservoir that can, for
example, feed the ISM with gas to form new stars (Zhu & Ménard, 2013; Thom et
al., 2012; Richter et al., 2016). Supernovae explosions or strong stellar
winds can deposit metals in the surrounding medium, gas that is mixed with
pristine gas accreted from the IGM (Prochaska & Wolfe 2009; Bauermeister et
al. 2010; Tumlinson et al. 2011, 2017; Kacprzak 2017).

Since the first discoveries of circumgalactic gas around star-forming galaxies
(Boksenberg & Sargent, 1978; Kunth & Bergeron, 1984; Bergeron, 1986), its
study by direct detection of emission has been a challenge (van de Voort &
Schaye, 2013; Burchett et al., 2021). The CGM has been primarily detected via
the absorption features that it produces on light from background sources. In
a pioneering study at high redshift ($z\gtrsim 1.5$), Adelberger et al. (2003,
2005) studied the dependence of the absorption strength on the projected
angular separation between foreground and background galaxies (i.e. impact
parameter $b$); they reported absorption detection at impact parameters up to
40 kpc and found that absorption strength weakens significantly at larger
separations. Thanks to their brightness, quasars are typically used as
background sources to probe the CGM around foreground galaxies (Bergeron &
Boissé, 1991; Steidel et al., 1994; Kacprzak et al., 2010), which allows the
signal produced by extremely low column densities (N${}_{\rm{HI}}\simeq
10^{12}$ cm-2) to be identified independently of the properties of the
targeted galaxy (e.g. luminosity and/or redshift) (Tumlinson et al., 2017;
Péroux & Howk, 2020). This technique has been used successfully to probe the
CGM of galaxies up to redshifts $z\sim$5 (Matejek & Simcoe, 2012) and has led
to the discovery that the CGM is gas rich and has a multi-phase nature
(Adelberger et al., 2003; Steidel et al., 1994; Steidel, 1995; Songaila, 2001;
Tripp et al., 1998; Kacprzak et al., 2010; Werk et al., 2016).

The CGM has been also characterized using the ‘down-the-barrel technique’,
which uses the targeted galaxy itself as a background source. Absorption lines
redshifted with respect to the galaxy rest-frame give evidence of the presence
of gas flowing towards the galaxy. This result has been interpreted as a
strong indication of inflowing material onto the host galaxy (Sato et al.,
2009; Rubin et al., 2012; Martin et al., 2012), while outflows have been
identified as blueshifted absorptions in galaxy spectra (Martin, 2005; Chen et
al., 2010). Although the location of the gas producing the detected absorption
is unconstrained, this technique has been successful in studying galactic
inflows and outflows from the spectroscopy of star-forming galaxies up to
$z\sim 2-3$ (Kornei et al., 2012; Rudie et al., 2012; Heckman et al., 2015;
Heckman & Borthakur, 2016).

Recently, three more techniques have been used to explore the CGM. The first,
gravitational-arc tomography, takes advantage of strong gravitational lensing
and uses giant bright lensed arcs as background sources to map the CGM of
foreground galaxies providing a tomographic view of the absorbing gas (Lopez
et al., 2018; Claeyssens et al., 2019; Lopez et al., 2020; Tejos et al., 2021;
Mortensen et al., 2021). The second technique takes advantage of deep three-
dimensional datacubes observations to study the cold CGM of high-redshift
($z>2$) star-forming galaxies, and has reported the ubiquitous presence of
Ly$\upalpha$ haloes in these galaxies (Steidel et al., 2011; Matsuda et al.,
2012; Momose et al., 2014; Wisotzki et al., 2016; Leclercq et al., 2017; Chen
et al., 2020), whose line properties are correlated to their spatial location
(Leclercq et al., 2020) and that can extend up to 4Mpc beyond the CGM (Chen et
al., 2020; Bacon et al., 2021). The third technique uses the spectra of bright
afterglows of long gamma-ray bursts (GRBs) to derive the kinematic properties
of the CGM gas around their host galaxies and constrain the physical
properties (Gatkine et al., 2019, 2022).

Alongside these diverse techniques used to study the CGM, the large
spectroscopic extragalactic surveys have allowed the statistical extraction
and analysis of the weak signals from different metal absorption using the
stacking of hundreds of spectra (Steidel et al., 2010). These large datasets
have been helpful to overcome the limitations of finding galaxy–QSOs pairs at
concordant redshifts (Steidel et al., 1994; Bouché et al., 2007), increasing
statistics, and facilitating vast parameter space exploration (York et al.,
2006; Bordoloi et al., 2011; Zhu & Ménard, 2013). At low redshift
($z_{\rm{med}}\sim$0.5) CGM analyses have been focused on the study of
absorption lines of Ly$\upalpha$ (Chen et al., 2001b), C iv (Chen et al.,
2001a), O vi (Tumlinson et al., 2011), and Mg ii (Bowen et al., 1995; Bouché
et al., 2007; Steidel et al., 1994), and their dependence on stellar mass
(Bordoloi et al., 2011), inclination (Kacprzak et al., 2010), and azimuthal
angle (Shen et al., 2012; Bordoloi et al., 2014b). At higher redshifts, the
observed metal absorption lines are mostly limited to Si ii, C ii, C iv, and
Si iv; the first two are called low-ionization state (LIS, T=$10^{4-4.5}$K)
lines, and the last two high-ionization state (HIS, T=$10^{4.5-5.5}$K) lines
(Steidel et al., 2010). At high redshift (z¿2) several authors have reported
the presence of high-velocity outflows. Lehner et al. (2014) demonstrated that
O vi successfully probes outflows in star-forming galaxies, and reported
velocity widths in the range 200-400kms-1. Next, Du et al. (2016) analysed
several ionization lines (e.g. Si ii, Fe ii, Al ii, Ni ii, Al iii, C iv) to
probe the multi-phase nature of the CGM and detected C iv blueshifted offsets
concordant with 76kms-1 velocity outflows. Their results show a direct link
between C iv absorption and star formation rate. Later on, Jones et al. (2018)
reported velocity outflows of $\sim$150km-1, as shown by several LIS and HIS
absorptions in nine gravitationally lensed star-forming galaxies($z\simeq
2-3$), suggesting that galaxy outflows regulate the galaxy chemical evolution.
Similar outflow detections inferred from different ionization absorption lines
have been reported, and stellar mass and star formation rate have been invoked
as their main drivers (Zhu & Ménard, 2013; Turner et al., 2014; Trainor et
al., 2015; Gatkine et al., 2019; Price et al., 2020). However, as suggested by
Dutta et al. (2021), LIS and HIS absorption detections (from which velocity
outflows can be inferred), could be affected by large-scale environmental
processes (Dutta et al., 2021; Wang et al., 2022) or their available neutral
gas content (Berry et al., 2012; Oyarzún et al., 2016; Du et al., 2018), and
their correlation with stellar mass and star formation rate might in fact be a
consequence of a main-sequence offset rather than simply correlated with the
star formation rate or stellar mass (Cicone et al., 2016; Gatkine et al.,
2022).

Numerical simulations consider that the CGM comes from gas accreted from the
IGM, followed by stellar winds from the central galaxy and the gas ejected or
stripped from satellites (Hafen et al., 2019; Christensen et al., 2018).
Simulations reveal that the accretion efficiency depends on the galaxy stellar
mass, decreasing from $\sim$80% for M${}_{\bigstar}\sim 10^{6}$M⊙ galaxies to
$\sim$60% for M${}_{\bigstar}\sim 10^{10}$M⊙ galaxies (Dekel et al., 2005;
Kereš et al., 2005; Hafen et al., 2020). Once accreted, this material can
remain in the CGM for billions of years leading to a well-mixed halo gas
before it interacts with the ejected large-scale stellar winds produced by
starbursts (Martin, 2005; Weiner et al., 2009). At $z=2$ most metals are found
to be located in the ISM or stars of the central galaxy, and by $z=0.25$ most
of it will end up in the CGM and IGM (e.g. Peeples et al. 2014; Anglés-Alcázar
et al. 2017; Hafen et al. 2020; Oppenheimer et al. 2016; Nelson et al. 2021).

The way in which this pristine material is accreted into galaxies may depend
on its location relative to the galaxy disc plane defined by the azimuthal
angle ($\phi$). Various observational studies highlight a correlation between
the strength of the Mg ii LIS absorption line and the azimuthal angle
(Bordoloi et al., 2011, 2014b; Kacprzak et al., 2011; Bouché et al., 2012,
2013). Although weak Mg ii detections along the minor axis have been reported
(e.g. Lan et al. 2014), it has been found that strong Mg ii absorptions are
preferably detected along the major-axis of galaxies, suggesting the presence
of inflowing material potentially feeding future star formation. On the other
hand, C iv and O vi (HIS lines) absorptions seem stronger along the minor
axis, probably evidence of strong stellar winds enriching the CGM (Tumlinson
et al., 2011; Kacprzak et al., 2015). Recently, Péroux et al. (2020) used
cosmological hydrodynamical simulations to examine the physical properties of
the gas located in the CGM of star-forming galaxies ($z<1$) as a function of
angular orientation. They found that the CGM properties vary strongly with the
impact parameter, stellar mass, and redshift. They reported a higher average
CGM metallicity at large impact parameters ($b>$100kpc) along the minor versus
major axes. Moreover, they tentatively found that the average metallicity of
the CGM depends on the azimuthal angle, showing that the low-metallicity gas
preferably inflows along the galaxy major axis, while outflows are commonly
located along the minor axis, in agreement with previous observations
(Bordoloi et al., 2011; Bouché et al., 2012; Kacprzak et al., 2012, 2015).
These results present a picture where star-forming galaxies accrete co-planar
gas within narrow stream-flows providing fresh fuel for the new generation of
stars; later, this population will produce metal-enriched galactic-scale
outflows along the minor axis (Kacprzak, 2017). However, even though the
presence of bipolar outflows collimated along the minor axis is expected to
evolve with redshift (expected to be ubiquitous at z = 1), it has been
difficult to demonstrate its presence at z = 2, mostly as the result of the
absence of gaseous galactic discs sculpting the outflows (Nelson et al.,
2019).

In order to better understand the mechanisms of galaxy growth in earlier
phases of the history of the Universe, and to investigate a possible cosmic
evolution of such mechanisms, similar studies at higher redshifts are needed.
Observations along different lines of sight (l.o.s.) can probe different parts
of the CGM, and the identification of low- and high-ionization metal
absorption lines can give information on the possible multi-phase nature of
the CGM. However, using QSO–galaxy pairs to study the CGM is not
straightforward as the identification of the galaxies responsible for the
metal absorptions detected on the spectra of background quasars is not an easy
task. Stacking analyses of background galaxy spectra that are located in the
vicinity of foreground galaxies provides an alternative tool to overcome
sensitivity limitations, exploiting large extra-galactic surveys containing a
large number of individual spectra. In this work we seek to characterize the
presence of low- (LIS: O i+Si ii, C ii, Si ii, Fe ii), intermediate- (IIS: Al
iii), and high-ionization (HIS: Si iv, C iv) state metal absorption (see Table
2) in the CGM of a star-forming galaxy population at $\langle z\rangle$ $\sim$
2.6 using UV spectra obtained from the large VIMOS Ultra Deep Survey (VUDS; Le
Fèvre et al. 2015). We use thousands of galaxies with the most reliable
redshift measurements and the highest S/N spectra (with reliability flags 3
and 4; see Le Fèvre et al. 2015; Tasca et al. 2017), a sample broadly
representative of the bulk of the star-forming galaxy population at these
redshifts (Lemaux et al., 2022). To detect the dim signal coming from low- and
high-ionization line absorptions produced in the CGM of these star-forming
galaxies, we stack the spectra of close (in projection) background galaxies to
establish the metal distribution in the CGM and explore their dependence on
the physical and morphological properties of star-forming galaxies (e.g.
impact parameter $b$, star formation rate, stellar mass, galaxy effective
radius, and azimuthal angle) at the peak epoch of cosmic star formation
activity in the Universe.

The manuscript is organized as follows. Section 2 summarizes the VUDS survey
properties relevant to our analyses. Section 3 presents our stacking analysis
method for measuring the metal equivalent widths ($W_{0}$), while Section 4
presents our $W_{0}$ results for Ly$\upalpha$, and multiple LIS, IIS, and HIS
metal lines observed our star-forming galaxy sample across different physical
and morphological properties. We discuss our results in Section 5, and finally
we present our conclusions in Section 6. Throughout the text we use
$\Lambda$CDM cosmology with H0 = 70 km s-1 Mpc-1, $\Omega_{\rm M}$=0.3, and
$\Omega_{\Lambda}$=0.7, and distances are given in physical units (kpc).

##  2 The VUDS parent sample

The VUDS has obtained spectra of 5590 galaxies in the redshift range
$1.5<z<4.5$. A detailed description of the survey observations, the methods
applied to process the data, and the derived parameters including the
spectroscopic redshifts $z_{\rm{spec}}$ is given in Le Fèvre et al. (2015). A
description of the VUDS-DR1 first data release can be found in Tasca et al.
(2017). The VUDS spectroscopic targets are selected based on their photometric
redshifts and observed optical flux; the targets have $z_{phot}$ \+
1$\sigma_{\rm z}\geq$ 2.4 and i${}_{AB}\leq$ 25\. The wavelength range of each
spectrum is between 3600 $<\uplambda/\AA<$ 9350, accumulating 14 hrs of
integration time in each of the LRBLUE and LRRED grisms of the VIMOS
spectrograph on the ESO Very Large Telescope (Le Fèvre et al., 2003), with a
spectral resolution R $\sim$ 230($\sim 7\,\AA$) and reaching a S/N=5 on the
continuum at 8500 $\AA$. We note that the VUDS observations were taken using
the VIMOS low-resolution multi-slit mode with a minimum slit length optimized
to 6 arcsec, maximizing the number of observed slits per mask (see Bottini et
al. 2005).

Standard data processing was performed using the VIPGI environment (Scodeggio
et al., 2005), followed by redshift measurements using the EZ package (Garilli
et al., 2010). The final UV rest-frame flux-limited sample is broadly
representative of the bulk of the star-forming galaxy population at these
redshifts ($2<z<5$) (Lemaux et al., 2022). A critical aspect of VUDS is the
large comoving volume covered, totalling 1 deg2 in three fields: COSMOS
(Scoville et al., 2007), ECDFS (Giacconi et al., 2002), and VVDS02h (Le Fèvre
et al., 2005, 2013).

For the purposes of this study the instrumental set-up translates into the
ability to follow lines redder than Ly$\upalpha$ ($\geq 1215.6\AA$) at
redshifts higher than 1.5. We decided to restrict the VUDS sample to 2100
galaxies, selected in the redshift range $1.5<z<4.5$ ($z_{\rm{flag}}=3,4$,
i.e. $95-100\%$ probability of being correct). We note that the velocity
accuracy of redshift measurements is expected to be in the range d$z$ / (1 +
$z$) = 0.0005-0.0007, or an absolute velocity ($\sigma^{-1}_{v}$) accuracy
150-200 km (Le Fèvre et al., 2013, 2015; Tasca et al., 2017). The rich broad-
band imaging available for galaxies in VUDS is used for spectral energy
distribution (SED) fitting (Tasca et al., 2015; Thomas et al., 2017) using the
Galaxy Observed-Simulated SED Interactive Program (GOSSIP; Franzetti et al.
2008) to derive various global galaxy properties, for example stellar mass,
star formation rate (SFR), dust extinction E(B-V), age, and metallicity.

GOSSIP is a tool that performs SED fitting by using a combination of spectro-
photometric measurements from different bands to match a set of synthetic
galaxy spectra based on emission from stellar populations. GOSSIP uses model
spectra from galaxy population synthesis models (Bruzual & Charlot, 2003;
Maraston, 2005) and uses the probability distribution function (PDF) of each
galaxy parameter to determine the best SED fit. Figure 1 shows SFR versus
stellar mass for 5590 star-forming galaxies at $z>1.5$ and $2<z<3.5$ selected
from the VUDS survey, and the 238 star-forming galaxies that we finally
selected and scrutinized in this work (see Section 3). These 238 galaxies have
stellar masses and star formation rates of log[M★/M⊙])=$9.73\pm 0.4$ and
log[SFR/(M⊙yr-1)]=$1.38\pm 0.39$.

Figure 1: Star formation rate versus stellar mass for 5590 star-forming
galaxies selected from the VUDS survey at $z>1.5$ (grey open squares) and at
$2<z<3.5$ (yellow crosses), and the 238 star-forming galaxies (blue stars)
considered in this work. The black dot-dashed line shows the main sequence of
star-forming galaxies for $1.5<z<2.5$ including its $\pm.3$dex scatter
represented by the green shaded region, as defined by Hathi et al. 2016. The
top and right panels report the distributions in stellar mass and SFR for the
238 star-forming galaxies evaluated in this work.

Exploiting the Hubble Space Telescope (HST) $F814W$ images (Koekemoer et al.,
2007) that are available as part of the COSMOS Survey (Scoville et al., 2007),
morphological parameters have been estimated for 1242 star-forming galaxies
($z_{\rm{flag}}=4,3,2,9$, i.e. $75\%$ probability of being correct) with
9.5¡log[M★/M⊙]¡11.5. In particular, Ribeiro et al. (2016) run Galfit (Peng et
al., 2002, 2010), a standard parametric profile-fitting tool, estimating
Sersic indices ($n$), azimuthal angles, major-to-minor axis ratios ($q$), and
effective radii ($r_{\rm eff}$). Figure 2 shows the distribution of the 97
selected galaxy pairs (see Section 3) with available morphological parameters.
Table 1 shows the detailed number of subsets of galaxies.

Figure 2: Projected angular separation ($\theta$) amongst galaxy foreground-
background galaxy pairs, axial ratio (q), effective radius (reff), and
azimuthal angle ($\phi$) distributions of the star-forming (foreground)
galaxies used in our analyses. The morphological parameters were obtained from
the parametric measures of Ribeiro et al. (2016), see section 2 for details.
Table 1:  VUDS fg-bg galaxy pair sample.

Sample | N
---|---
Galaxies $z>1.5$, $z_{\rm{flag}}$=3, 4, 2, 9 aa$a$VUDS parent sample. | 5590
Galaxies $z>1.5$, $z_{\rm{flag}}$=3, 4 bb$b$Star-forming galaxies at $z>1.5$. | 2100
fg-bg galaxy pairs, $z_{\rm{flag}}$=3, 4 cc$c$Star-forming galaxies with morphological parameters available. | 238
Galaxies fitted with Galfit, $z_{\rm{flag}}$=3, 4, 2, 9 dd$d$Close fg-bg galaxy pairs. | 1242
fg-bg galaxy pairs, $z_{\rm{flag}}$=3, 4 + Galfit ee$e$Close fg-bg galaxy pairs with morphological parameters. | 97
111 Number of objects of our fg-bg galaxy pair sample sample (see Sect. 2 for
details).

##  3 Analysis

In this work we describe our probe of the CGM around galaxies at $z\sim$ 2.6,
near the epoch at which the cosmic SFR density of the Universe reaches its
peak, by using the spectra of background (bg) galaxies as ‘spotlights’
illuminating the CGM. At these redshifts individual bg galaxies are not bright
enough to individually detect low- and high-ionization state metal absorption
lines. Thus, we stack spectra of bg galaxies to look for absorption lines
produced by the CGM around foreground (fg) star-forming galaxies. To select a
sample of close galaxy pairs(fg-bg) out of the VUDS survey, we imposed similar
criteria to those described by Steidel et al. (2010): (i) galaxy spectra for
the fg and bg galaxies must possess an accurately determined redshift
($95-100\%$; see Le Fèvre et al. 2015; Tasca et al. 2017 for details), (ii) a
redshift separation 0.1 $<z_{\rm{bg}}$ \- $z_{\rm{fg}}\leqslant$ 1.0 between
fg-bg galaxy pairs to ensure that each spectrum contains a significant common
spectral coverage after shifting to the rest-frame of the fg galaxy and to
avoid an overlap between the $fg$ CGM and the $bg$ galaxy absorptions, and
iii) a maximum projected angular separation of 23$\arcsec$.

Figure 3: Redshift distribution of the star-forming galaxy pairs (foreground
and background) selected in this work. The $\Delta$z = $z_{bg}$-$z_{fg}$
distribution is also included in the top right corner.

Stacking the fg spectra provides the absorptions at the foreground galaxy’s
rest-frame. Figure 3 shows the redshift distributions of the foreground and
background galaxy pairs and the fg-bg pairs redshift difference ($\Delta
z=z_{bg}-z_{fg}$) distribution in the top right corner. The spectroscopic
sample includes 238 spectra within the redshift range 1.5 ¡ z $\lesssim$ 4.43
($\langle z\rangle$ = $2.6\pm 0.41$) and is limited to a 23$\arcsec$ maximum
projected angular separation distance amongst galaxy pairs that correspond to
187.2 kpc at z=2.6. This sample is then split into four different bins
according to the angular projected separation, $\theta\leqslant
11\aas@@fstack{\prime\prime}8$, $11\aas@@fstack{\prime\prime}8<\theta\leqslant
16\aas@@fstack{\prime\prime}5$, $16\aas@@fstack{\prime\prime}5<\theta\leqslant
20\arcsec$, and $20\arcsec<\theta\leqslant 23\arcsec$, identified as samples
S1, S2, S3, and S4, and were defined in such a way that each bin contains
approximately the same number of galaxies (see Table 3) providing a comparable
S/N for each composite spectra. These angular projected separation bins
correspond to projected physical distances (hereafter impact parameters) $b$:
$\leqslant$ 68.6 kpc, 68.6 kpc $<b\leqslant$113.5 kpc, 113.5 kpc $<b\leqslant$
146.2 kpc, and 146.2 kpc $<b\leqslant$ 172.8 kpc for samples S1, S2, S3, and
S4. We note that the conversion from angular separation to physical impact
parameter varies $\pm 3\%$ over the full redshift range $(1.5<z<4.5)$ of the
foreground galaxy sample, thus in the following impact parameter $b$ and
projected angular separation $\theta$ will be used interchangeably. Table 3
contains a summary of the statistical properties of the galaxy pair samples.

To generate our fg and bg composite spectra we co-added individual spectra as
follows. For each pair of galaxies, the spectrum of the fg was i) shifted to
its own rest-frame; ii) continuum-normalized using the full wavelength
range222Full observed wavelength coverage of $3650<\uplambda<9350\,[\AA],$
which at $z\sim$2.6 translates into a rest-frame wavelength coverage of
$1013<\uplambda<2597\,[\AA]$.; iii) resampled333We made use of pysynphot
(Blagorodnova et al., 2014) to resample our spectra. to a common wavelength
resolution $\Delta\uplambda$, defined by the maximum of the shifted wavelength
resolution ($\Delta\uplambda_{shf\textunderscore fg}$) distribution of the
galaxy sample used to generate the composite spectra (e.g.
$\Delta\uplambda\sim 2\AA$ for $fg$ composite spectra as shown in Figure 4);
and iv) smoothed with a Gaussian kernel whose width size $\Delta\uplambda$ was
defined before.

A similar approach was used to produce stacked spectra of the bg galaxies.
Each individual bg galaxy spectrum was i) shifted into the fg galaxy’s rest-
frame using the same systemic redshift applied to their corresponding fg
galaxy spectrum; ii) continuum normalized using the full wavelength range1;
iii) resampled to a common wavelength resolution $\Delta\uplambda$, defined by
the maximum of the shifted wavelength
resolution($\Delta\uplambda_{shf\textunderscore bg}$) distribution of the
galaxy sample used to generate the composite spectra; iv) smoothed with
$\Delta\uplambda$ Gaussian kernel as defined before. The strong interstellar
absorption features (see Fig 4 and Table 2) located at the redshift of each bg
rest-frame were masked because they can potentially contaminate the composite
signal at the fg rest-frame.

Finally, the foreground and background spectra were co-added independently to
produce composite stacked spectra. In all cases, for each spectral bin, we
calculated both the average and the median value, eventually producing both an
average and median co-added spectrum.

##  4 Results

Rest-frame UV spectra of star-forming galaxies at redshift $z\sim 3$ are
commonly dominated by the emission of O and B stars; the CGM and/or IGM media
imprint absorption features on this UV continuum (Sargent et al., 1980;
Bergeron, 1986; Bergeron & Boissé, 1991; Lanzetta et al., 1995). Composite
spectra can provide different l.o.s. of the average absorption strength
produced by the gas located in these media (Adelberger et al., 2005; Shapley
et al., 2003). Figure 4 shows the median and average composite spectra by
stacking the 238 foreground galaxies. The lower panel shows a histogram of the
fraction of galaxies contributing to each spectral bin of the co-added
spectrum. In our analysis the separation zero ($b=0$) l.o.s. defines the
interstellar medium properties of the foreground galaxies, while larger
separations ($b>0$) l.o.s. define the properties of the CGM around the
foreground galaxies at different separations.

While the l.o.s that we use to study the CGM cross through the whole CGM at a
given separation, the information about the ISM comes only from the
absorptions produced by the gas located in the half-galaxy that is the closest
to the observer. For this reason, to compare the strength of the absorptions
at separation 0 (the ISM) and at separation $>0$ (the CGM), the former need to
be corrected for this incompleteness. Following Steidel et al. (2010), we
apply the following factors: 1.45 for low-ionization species (Si ii, C ii),
1.70 for Si iv, and $\sim 2$ for C iv. The different l.o.s. probed by the
background galaxy’s light passing through the foreground CGM help us to trace
neutral and ionized gas in Hii star-forming regions and the large-scale
stellar winds produced by star formation activity (Shapley et al., 2003). The
main spectral features identified in our fg composite spectra (Figure 4) in
the 1100-2000$\AA$ range are summarized in Table 2.

Table 2:  Main spectral features observed in our VUDS stacked spectra in the
1100-2000 $\AA$ rest-frame range.

Spectral line |  $\lambdaup$ [$\AA$] | Type
---|---|---
C iii | 1176 | Photospheric
Si ii | 1192 | LIS absorption
Si iii | 1206 | IIS absorption
Ly$\upalpha$ | 1215.7 | H i
N v | 1238, 1242 | Photospheric
Si ii | 1260 | LIS absorption
Si ii* | 1264.0 | Interstellar
O i+Si ii | 1303.2 | LIS absorption
Si ii* | 1309.0 | Interstellar
C ii | 1334.5 | LIS absorption
O iv | 1343.0 | Photospheric
Si iv | 1393.8, 1402.8 | HIS absorption
Si iii | 1417 | Photospheric
S v | 1501.8 | Photospheric
Si ii | 1526.7 | LIS absorption
C iv | 1548.2, 1550.8 | HIS absorption
Fe ii | 1608, | LIS absorption
Fe ii | 1610, | LIS absorption
He ii | 1640 | Stellar wind
O iii] | 1660, 1666 | Nebular
Al ii | 1670.7 | LIS absorption
Ni ii | 1709.6 | LIS absorption
N iv | 1718.5 | Stellar wind
Ni ii | 1741.5, 1751.9 | LIS absorption
Si ii | 1808 | LIS absorption
Al iii | 1854.7, 1862.7 | IIS absorption
Si iii] | 1889 | Nebular
C iii] | 1908.7 | Nebular

Le Fèvre et al. (2015); Halliday et al. (2008); Shapley et al. (2003); OTELO
(OSIRIS Tunable Emission Line Object survey
http://research.iac.es/proyecto/otelo/pages/data-tools/spectral-line-
summary.php).

Figure 4: Composite UV spectra of 238 VUDS star-forming galaxies. Top: Median
(black) and average (red) composite spectra shifted to rest-frame of 238
foreground galaxies with projected angular separations $<$ 23$\arcsec$
($b<187.2$ kpc at z=2.6). Bottom: Fraction of contributing individual spectra
to the composite spectra per unit wavelength. Several spectral lines of
interest are indicated: H i (Ly$\upalpha$) emission–absorption (blue), low-
ionization state metal absorption lines (cyan), intermediate-ionization state
metal absorption lines (peach), high-ionization state metal absorption lines
(magenta), interstellar fine-structure emission line (green), absorption
stellar photospheric lines (gold), emission nebular lines (lime), and
emission–absorption lines associated with stellar winds (indigo). Table 3:
Foreground–background (fg-bg) galaxy pair statistics according to the
projected angular separation ($\theta$).

ID | N | $\theta$ | $\langle\theta\rangle$ |  $b$ (kpc) |  $\langle b\rangle$ (kpc) | $z_{\rm{fg}}$ | $\langle\rm{z}_{\rm{fg}}\rangle$ | $z_{\rm{bg}}$ | $\langle\rm{z}_{\rm{bg}}\rangle$
---|---|---|---|---|---|---|---|---|---
c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | c10
ALL | 238 | ¡23$\arcsec$ | 15$\aas@@fstack{\prime\prime}$7 $\pm$ 4$\aas@@fstack{\prime\prime}$9 | 13.8 - 187.2 | 125.0 $\pm$ 39.5 | 1.5-4.4 | 2.60 | 2.1-5.3 | 3.04
S1 | 59 | ¡11$\aas@@fstack{\prime\prime}$8 | 8$\aas@@fstack{\prime\prime}$7 $\pm$ 2$\aas@@fstack{\prime\prime}$0 | 13.8 - 97.8 | 68.6 $\pm$ 16.3 | 1.5-4.3 | 2.55 | 2.1-4.9 | 2.98
S2 | 62 | 11$\aas@@fstack{\prime\prime}$8-16$\aas@@fstack{\prime\prime}$5 | 14$\aas@@fstack{\prime\prime}$4 $\pm$ 1$\aas@@fstack{\prime\prime}$4 | 92.6 - 135.9 | 113.5 $\pm$ 12.8 | 1.7-4.3 | 2.62 | 2.1-4.9 | 3.08
S3 | 60 | 16$\aas@@fstack{\prime\prime}$5-20$\arcsec$ | 18$\aas@@fstack{\prime\prime}$4 $\pm$ 0$\aas@@fstack{\prime\prime}$9 | 127.1 - 164.6 | 146.2 $\pm$ 8.8 | 1.9-3.6 | 2.66 | 2.3-4.5 | 3.11
S4 | 57 | 20$\arcsec$-23$\arcsec$ | 21$\aas@@fstack{\prime\prime}$5 $\pm$ 0$\aas@@fstack{\prime\prime}$8 | 146.7 - 187.2 | 172.8 $\pm$ 8.4 | 1.8-4.4 | 2.59 | 2.1-5.3 | 3.02

444 Column 1: Sample ID; Column 2: number of galaxies per sample; Column 3:
range of angular separation of the fg-bg pairs; Column 4: mean angular
separation of the fg-bg pairs within the $\theta$ range; Column 5: range of
the impact parameter in kpc assuming $z_{med}$ within the projected separation
bin for conversion; Column 6: mean impact parameter within the $\theta$ range
in kpc; Columns 7 and 8: redshift ranges and mean redshift of the foreground
galaxies sample within their corresponding $\theta$ range, and Columns 9 and
10: redshift ranges and mean redshift of the background galaxies sample within
their corresponding $\theta$ range.

In the 900–1900 $\AA$ range we explored the following absorption lines:
Ly$\upalpha$ ($\uplambda$ 1215.7 $\AA$), O i+Si ii ($\uplambda\uplambda$
1303.2 $\AA$), C ii ($\uplambda$ 1334.5 $\AA$), Si iv ($\uplambda\uplambda$
1393, 1402 $\AA$), Si ii ($\uplambda$ 1526.7 $\AA$), C iv
($\uplambda\uplambda$ 1548.2, 1550.8 $\AA$), Fe ii ($\uplambda$ 1608.5 $\AA$),
Al ii ($\uplambda$ 1670.8 $\AA$), and Al iii ($\uplambda$ 1862.8 $\AA$).
First, we present their equivalent widths as a function of the angular
separation between galaxy pairs ($\theta$) (see Sect. 4.1). We then examine
the correlations between the strength of the Ly$\upalpha$, LIS (C ii, Si ii),
and HIS (C iv, Si iv) lines as a function of different galaxy properties,
including stellar mass, star formation rate (see Sect. 4.2), effective radius
($r_{\rm{eff}}$), and the azimuthal angle ($\phi$) (see Sect. 4.3). We also
explore the C ii/C iv line ratio (see Sect. 4.4) as a function of the
projected angular separation, stellar mass, and star formation rate.

###  4.1 Radial dependence

Here we present absorption lines produced by gas located in the CGM of star-
forming galaxies at $z\sim 2.6$. Figure 5 shows the average absorption spectra
obtained after stacking the background galaxy spectra at the redshift of the
foreground galaxy as a function of their projected angular separation:
$<11\aas@@fstack{\prime\prime}8$,
$11\aas@@fstack{\prime\prime}8$–$16\aas@@fstack{\prime\prime}5$,
$16\aas@@fstack{\prime\prime}5$–$20\arcsec$, and $20\arcsec$–$23\arcsec$. We
note that as a consequence of the VUDS design and selection criteria, the
number of galaxies with small projected angular separations ($<6\arcsec$) is
scarce. The strengths of the line absorptions were measured by fitting a
single Gaussian profile to the stacked spectra. Equivalent widths ($W_{0}$) of
each line profile are obtained by integrating the Gaussian fit of each stacked
spectrum around the central wavelength of the Gaussian fit to the line using
an integration window within the $\pm 5\sigma$ range.

All equivalent width measurements are given in the rest-frame and we use
positive (negative) equivalent widths to indicate absorption (emission). The
errors on the equivalent width measurements are determined using a bootstrap
approach. For each set of galaxy background spectra, a thousand co-added
spectra are generated from random selections, with replacements from that same
sample in order to preserve the number of evaluated sources. For each of these
co-adds, the line absorption equivalent widths are estimated. The 16th and
84th percentiles of the distribution of equivalent widths are taken as error
intervals for the original measurement. We note that owing to the nature of
star-forming galaxies, which show a diversity of spectral features(e.g. ISM
absorption lines, photospheric stellar and nebular lines, and Ly$\upalpha$
emission), the absorption lines in our composite spectra show both an emission
and absorption component. The emission components can be produced by the same
transition responsible for producing the absorption line (e.g. Ly$\upalpha$),
produced by nearby fine-structure transitions, or in some cases they can be
completely absent.

Figure 5: Median absorption lines (thin lines) detected from our 238
foreground–background galaxy pairs, including all foreground galaxies (red)
and background galaxies split by their projected angular separations:
¡11$\aas@@fstack{\prime\prime}$8 (blue),
11$\aas@@fstack{\prime\prime}$8-16$\aas@@fstack{\prime\prime}$5 (green),
16$\aas@@fstack{\prime\prime}$5-20$\arcsec$ (cyan), and
20$\arcsec$-23$\arcsec$ (magenta). The bold lines indicate the Gaussian
profile fit to measure the strength of the line absorptions (see Sect. 4.1).

Figure 6 shows the radial profiles of the absorption rest-frame equivalent
width obtained from the average (red) and median (blue) stacked absorption
specrta presented in Figure 5. Median composite spectra are expected to be
free of artefacts and contamination such as sky residuals, unexpected
absorption or emission features in the background galaxy spectra. On the other
hand, the average composite spectra could be affected by strong absorption
lines coming from individual l.o.s. Median and average composite spectra are
in general concordant, and trace similar trends. We also tested other
combination techniques, including straight average, average sigma-clipping,
and average continuum-weighting, which produce very similar composite spectra.
Table 4 contains a summary of the measured equivalent widths as a function of
the projected angular separation, including the significance (in terms of S/N)
of the detections. Noise estimations were computed with the
DER$\\_$SNR555http://www.stecf.org/software/ASTROsoft/DER_SNR/ algorithm
(Stoehr et al., 2008) on a continuum band-pass adjacent to each central
absorption line. We limit our analyses to detections with S/N $\geq$ 3;
however, upper limits with $S/N\,<\,3$ are also included (highlighted using
solid black symbols and arrows in Figure 6) as these detections are useful to
outline the possible correlations and/or trends of the profiles. We note that
some precautions should be taken when interpreting the absorption strengths of
these spectral features as they might not reflect the true conditions of the
cold and hot gas CGM components. For instance, the balances amongst singly
ionized species of some elements (e.g. Al, Cl) can be altered by dielectronic
recombination (Black & Dalgarno, 1973; Watson, 1973; Jura, 1974) or ion-
molecule reactions (charge exchange reactions of ionized species with neutral
hydrogen and helium Steigman 1975). While the abundances relative to neutral
hydrogen of some elements (e.g. O, N, P, Cl, Si, Cr, Mn, Fe, Ni) can be
affected by factors of 2-10, Al is depleted by a factor of $\sim$ 100 (York &
Kinahan, 1979), making Al ii a biased tracer of the neutral gas phase. In
addition, Fe ii is contaminated by Fe iv ($\uplambda$ 1610 $\AA$) and Fe ii
($\uplambda$ 1611.5 $\AA$) lines (Judge et al., 1992; Shull et al., 1983;
Pickering et al., 2002), making it difficult to determine accurately its
absorption strength. Subsequently, doubly ionized species (e.g. Si iii, Al
iii) are intermediate-ionization state (IIS) tracers of moderately
photoionized warm gas sensitive to both diffuse ionized gas (traced by HIS)
and to denser partly neutral gas. Depending on the species, they can be
correlated with cold gas components (e.g. Si iii Richter et al. 2016) or hot
gas components (e.g. Al iii Vladilo et al. 2001), and they can be used to
infer the relative mix of neutral and ionized material (Howk et al., 1999).

Figure 6:  Rest equivalent width ($W_{0}$) as a function of the impact
parameter ($b$) obtained from the line profiles in Fig. 5, corresponding to
the foreground composite spectra (0 kpc) and the background composite spectra
at $\langle b\rangle$ 68.6 kpc (8$\aas@@fstack{\prime\prime}$7), 113.5 kpc
(14$\aas@@fstack{\prime\prime}$4), 146.2 kpc
(18$\aas@@fstack{\prime\prime}$4), and 172.8 kpc
(21$\aas@@fstack{\prime\prime}$5). Average and median $W_{0}$ are respectively
shown in filled red and open blue symbols; solid black symbols correspond to
upper limits with S/N ¡3. Reported values from the literature including low-
redshift values (open grey symbols): Bordoloi et al. 2018 (stars), Borthakur
et al. 2015 (pentagons), Liang & Chen 2014 (crosses), Prochaska et al. 2011
(diamonds), Werk et al. 2013 (pluses), and high-redshift values Steidel et al.
2010 (black triangles). The error bars correspond to 1$\sigma$ confidence
intervals for average (red filled circles) or median (blue open circles)
values based on a bootstrap analysis. Also included are the results from the
Kendall-Tau correlation test: the correlation coefficients $r_{\tau}$ and the
corresponding $p$-value (probability of no correlation).

We note that the composite spectra considering foreground (down-the-barrel)
galaxies (from our $fg-bg$ galaxy pairs split by separation) do not show any
significant dependency on the $W_{0}$ of absorption lines with impact
parameter $b$; these absorption lines show an average variance of $\leq 15\%$
amongst the absorption lines included in 6. This is in agreement with the
$<10\%$ variance that Steidel et al. (2010) reported for their brightest
absorption lines. Considering the background galaxies from our $fg-bg$ galaxy
pairs split by separation, our radial profiles show a general negative
gradient, as reported by previous works. As the impact parameter increases,
the strength of the detected absorption feature decreases. This is the case
for all the spectral lines considered in our analysis. Recently, Kacprzak et
al. (2021) compiled measurements of low-ionization state absorption lines (O
i, C ii, N ii, Si ii), and high-ionization state absorption lines(C iii, N
iii, Si iii, C iv, Si iv, Nv, and Ovi) in the CGM of low-redshift ($z\lesssim
0.3$) galaxies with $9\leq\rm{log[M}_{\bigstar}/\rm{M}_{\odot}]\leq 11$, using
quasars as background spotlights. Measurements of low-redshift galaxies
(Bordoloi et al., 2018; Borthakur et al., 2015; Johnson et al., 2017; Liang &
Chen, 2014; Prochaska et al., 2011; Werk et al., 2013) and high-redshift
galaxies ($z\sim 2.3$) (Steidel et al., 2010) are also overplotted in Figure
6.

Although at low redshift these lines can be detected at distances of up to 300
kpc, at high redshift using galaxy–galaxy pairs, Steidel et al. (2010)
reported detections that are limited to 100 kpc; they included 42 additional
bright quasars–galaxy pairs that provide access to the low-density gas in the
CGM, and extended their Ly$\upalpha$ detections up to 280 kpc. More recently,
using galaxy images at $\langle z\rangle\sim$ 2.4, Chen et al. (2020) measured
the Ly$\upalpha$ excess relative to the background intergalactic medium,
probing the CGM gas up to impact parameters of 2000 kpc. Here, for star-
forming galaxies at a mean redshift $\langle z\rangle$ = 2.6, we report
detections at distances up to 146 kpc and 172 kpc for HIS and
LIS–Ly$\upalpha$. These results include Al iii, which is detected for the
first time in the CGM of high-redshift star-forming galaxies up to distances
of $\sim$150 kpc. Low-ionization state lines (C ii, Si ii, Al ii) show less
steep radial profiles compared with high-ionization lines. The LIS radial
profile shows an abrupt decay at smaller radii. From separation zero to
$\langle b\rangle\sim 68$ kpc, the strengths of C ii, Si ii, and Al ii are
reduced by a factor of 1.7, 2.5, and 3.2, while Si iv and C iv are reduced by
a factor of 6.8 and 4.5.

Steidel et al. (2010) reported that at a separation of $\langle b\rangle$ =
103 kpc, lines can be hardly detected in their stacked spectra, low-ionization
state metal absorption lines cannot be detected, and C iv is detected with
marginal significance. Here we are able to detect LIS (C ii and Si ii) and HIS
(Si iv, C iv) both with S/N$\geq 3$ up to $\langle b\rangle=$ 172 kpc and 146
kpc separations. We note that beyond this separation ($\theta>23\arcsec$=172
kpc) we are unable to detect any significant signal from the background
composite spectra. This might be caused by differences in the S/N and
resolution of the individual spectra used in the two analyses. The spectral
line features considered here are more difficult to detect in our low-
resolution spectra compared to high-resolution spectra at the same S/N level.
Higher-resolution spectra could resolve spectral lines that are blended(e.g. O
i–Si ii: $\uplambda\uplambda$ 1303, 1307 $\AA$, Si iv: $\uplambda\uplambda$
1393, 1402 $\AA$) or that are affected by close photospheric, interstellar, or
nebular spectral lines(e.g. Fe ii, Fe iv: $\uplambda\uplambda 1608,1610\AA$,
Si ii, Si ii*: $\uplambda\uplambda 1260,1264\AA$), disentangling the spectral
features and thus providing more accurate $W_{0}$ measurements. Another
possibility to explain these discrepancies is that they might be the result of
differences in the S/N of both parent dataset samples. We know that the two
parent samples adopted opposite observational strategies. On the one hand,
Steidel et al. (2004) deliberately kept the total exposure times short on
their observations to maximize the number of galaxies for which redshifts
could be measured. This led to a dataset with spectral quality (S/N) that
varies considerably amongst their spectra (Steidel et al., 2004, 2010), and
that could be affecting their redshift determinations. On the other hand, VUDS
provides a homogeneous dataset with integration times of $\simeq$14h per
target, reaching a S/N on the continuum at 8500 $\AA$ of S/N=5 (Le Fèvre et
al., 2015). Moreover, in this work we consider galaxies with reliability flags
($z_{f}$ = 3, 4) with 95-100% probability of being correct. However, it is not
clear if similar constraints on their redshift determinations were adopted by
Steidel et al. (2010) to define their galaxy–galaxy pair sample. This is
crucial, as composite spectra can be affected by spectral offsets in the
individual spectra. LIS and HIS spectral absorptions could be washed out or
artificially boosted by considering individual spectra with low S/N and low-
reliability redshift determinations to generate composite spectra. The spectra
considered to generate our stacked spectra may show an average S/N higher than
the average S/N of the spectra considered by Steidel et al. (2010). If similar
separations $\langle b\rangle$ are considered, for example Steidel’s P3 sample
at $\langle b\rangle=103$ kpc ($\langle\theta\rangle$ =
12$\aas@@fstack{\prime\prime}$5) and this work’s S2 sample $b=113.5$ kpc
($\langle\theta\rangle$ = 14$\aas@@fstack{\prime\prime}$4), Steidel’s P3
sample considers approximately five times the number of objects (N=306)
considered in our S2 sample (N=62). This would imply that our spectra have an
average individual S/N that is higher than the average S/N of the dataset used
by Steidel et al. (2010), allowing us to detect similar or weaker spectral
absorptions at larger separations.

To assess the correlation between $W_{0}$ and $b$, we implemented a Kendall-
Tau correlation test. The correlation coefficients $r_{\tau}$ and the
corresponding $p$-value (the probability of no correlation) are provided in
the same figure. In all cases we find a robust anticorrelation of the strength
of the absorption line as a function of the impact parameter; in particular,
Ly$\upalpha$, C ii, C iv, and Fe ii all show a strong correlation ($p<0.05$),
while we find that O i, Si iv, Si ii, Al ii, and Al iii present a flatter
radial profile, which results in a lower significance of the anticorrelation
($p\sim 0.1$). To assess the scale of the relationship between $W_{0}$ and
$b$, we computed the slopes of the radial profiles shown in Fig 6. We find
that Ly$\alphaup$ shows a slope of -1.20. $\pm$ 0.01; LIS (O i+Si ii, C ii, Si
ii, Fe ii, and Al ii) absorption lines show slopes of -1.34 $\pm$ 0.01, -1.31
$\pm$ 0.01, -1.53 $\pm$ 0.02, -1.50 $\pm$ 0.07, and -1.44 $\pm$ 0.05,
respectively; Al iii shows a slope of -1.38 $\pm$ 0.06; and HIS (Si iv and C
iv) absorption lines show slopes of -1.10 $\pm$ 0.04 and -1.24 $\pm$ 0.01. If
we focus on low- and high-ionization lines of the same species, and consider
Si ii–Si iv and C ii–C iv absorption line pairs, we find that the slopes of
these absorption lines are different at $\geq 5\sigma$ level. Compared with
the Steidel et al. (2010) radial profiles, our results show slopes that are
different at a 5$\sigma$ level for Si ii and at a 3$\sigma$ level for C ii and
Al ii absorption lines. These differences suggest that within the CGM, cold
and dense gas is more spatially extended in galaxies at $z\sim 2.6$ compared
with galaxies at $z\sim 2.3$ and lower redshifts, as probed by Si ii C ii, in
agreement with the expected higher covering factors of neutral gas at higher
redshifts (Reddy et al., 2016; Du et al., 2018; Sanders et al., 2021).
Compared with low-redshift CGM studies (see Figure 6), our Ly$\upalpha$, LIS,
and HIS rest-frame equivalent width radial profiles are at the upper envelope
of the equivalent width measurements at lower redshifts, suggesting a
potential redshift evolution for the CGM gas content that produces these
absorptions.

Table 4:  Median absorption line strengths measured ($W_{0}\,\AA$) in stacked
spectra as a function of the average impact parameter ($\langle b\rangle$).

$\langle b\rangle$ (kpc) |  $W_{0}$ [$\AA$] | S/N |  $W_{0}$ [$\AA$] | S/N |  $W_{0}$ [$\AA$] | S/N |  $W_{0}$ [$\AA$] | S/N |  $W_{0}$ [$\AA$] | S/N
---|---|---|---|---|---|---|---|---|---|---
c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | c10 | c11
| Ly$\upalpha$ 1215.7 | O i–Si iii 1303.2 | C ii 1334.5 | Si iv 1393.8 | Si iv 1402.8
0.0 | 3.54 $\pm$ 0.02 | 58 | 2.61 $\pm$ 0.15 | 17 | 2.31 $\pm$ 0.08 | 20 | 1.91 $\pm$ 0.01 | 18 | 1.40 $\pm$ 0.05 | 67
68.6 | 1.71 $\pm$ 0.13 | 14 | 0.97 $\pm$ 0.10 | 9 | 1.37 $\pm$ 0.02 | 4 | 0.28 $\pm$ 0.06 | 4 | 0.32 $\pm$ 0.06 | 15
113.5 | 0.75 $\pm$ 0.05 | 9 | 0.59 $\pm$ 0.07 | 8 | 0.54 $\pm$ 0.01 | 3 | 0.09 $\pm$ 0.04 | 2 | ¡0.10 | ¡2
146.2 | 1.08 $\pm$ 0.13 | 13 | ¡0.26 | ¡2 | 0.30 $\pm$ 0.09 | 2 | 0.13 $\pm$ 0.19 | 3 | 0.27 $\pm$ 0.31 | 5
172.8 | 0.46 $\pm$ 0.14 | 5 | ¡0.39 | ¡2 | 0.38 $\pm$ 0.10 | 3 | ¡0.09 | ¡2 | ¡0.06 | ¡2
| Si ii 1526.7 | C iv 1548.2 | Fe ii 1608.5 | Al ii 1670.8 | Al iii 1862.8
0.0 | 0.94 $\pm$ 0.02 | 18 | 2.87 $\pm$ 0.11 | 20 | 0.99 $\pm$ 0.01 | 6 | 1.13 $\pm$ 0.03 | 10 | 1.25 $\pm$ 0.01 | 8
68.6 | 0.35 $\pm$ 0.03 | 3 | 0.70 $\pm$ 0.04 | 13 | 0.18 $\pm$ 0.03 | 3 | 0.35 $\pm$ 0.03 | 4 | 0.31 $\pm$ 0.11 | 7
113.5 | 0.24 $\pm$ 0.09 | 2 | 0.27 $\pm$ 0.04 | 2 | ¡0.03 | ¡2 | 0.18 $\pm$ 0.03 | 3 | ¡0.06 | ¡2
146.2 | 0.36 $\pm$ 0.05 | 4 | 0.24 $\pm$ 0.02 | 3 | —- | — | —- | — | 0.40 $\pm$ 0.02 | 3
172.8 | 0.39 $\pm$ 0.04 | 4 | ¡0.05 | ¡2 | —- | — | —- | — | ¡0.34 | ¡2

666 Foreground–background (fg-bg) galaxy pairs split by their average impact
parameters ($\langle b\rangle$): 68.6 kpc (N=60), 113.5 kpc (N=62), 146.2 kpc
(N=60), and 172.8 kpc (N=57). The errors on the equivalent width ($W_{0}$)
measurements correspond to 1$\sigma$ confidence intervals based on a bootstrap
analysis (see Sect. 4.1).

###  4.2 Star formation and stellar mass dependence

|
---|---
|
Figure 7: Rest equivalent width ($W_{0}$) of the absorption lines as a
function of the foreground galaxy’s stellar mass (log[M★/M⊙]), SFR
(log[M⊙yr-1]), effective radius ($r_{\rm{eff}}$), and azimuthal angle($\phi$).
The $W_{0}$ measurements come from composite spectra considering galaxy pairs
at all projected distances ($b<23\arcsec$) and split by the corresponding
galaxy property. Stellar mass and SFR $W_{0}$ were obtained from composite
spectra considering 238 bg galaxies, while $r_{\rm{eff}}$ and $\phi$ come from
composite spectra considering 97 bg galaxies (see Sect. 2 and Table 1).
Average and median $W_{0}$ are shown in solid red and open blue symbols; solid
black symbols correspond to upper limits with S/N ¡3. The error bars
correspond to 1$\sigma$ confidence intervals for average or median values
based on a bootstrap analysis. The panels include the results from the
Kendall-Tau correlation test: the correlation coefficients $r_{\tau}$ and
their corresponding $p$-value (the probability of no correlation). The panels
of absorption lines with detections in only two subsamples also show the
results from a Student’s t-test: the difference between a pair of mean values
given by the $t$ coefficient and their corresponding $p$-value (the
probability of significant difference amongst means).

To explore the dependence of low- and high-ionization state absorptions with
physical and morphological properties (i.e. star formation rate, stellar mass,
galaxy effective radius, and azimuthal angle) produced in the CGM of our high-
redshift star-forming galaxy sample, we considered galaxy pairs at all
projected distances ($b<23\arcsec$) split by the corresponding galaxy
property. A summary of the statistical properties of the galaxy pair
subsamples divided by these properties can be found in Appendix A. We note
that the Fe ii, Al iii, and Al ii lines were excluded from our following
analyses (see Sect. 4.1). Figure 7 (upper panels) shows the equivalent width
of the absorption features as a function of stellar mass and SFR for LIS (C
ii, Si ii), HIS (Si iv, C iv), and Ly$\upalpha$. We find that galaxies with
high stellar masses (log[M★/M⊙]¿10.30) and high star formation rates
(log[SFR/(M⊙yr-1)]¿1.93) show C iv (HIS) metal absorption with larger
equivalent widths. On the other hand, galaxies with low stellar masses (log
[M★/M⊙]¡9.26) and low SFRs (log[SFR/(M⊙yr${}^{-1})]<0.9$) show C ii (LIS)
metal absorptions with stronger equivalent widths. Nevertheless, Si ii and Si
iv do not show a similar trend. This might be caused by the fact that we do
not have Si ii and Si iv detections with S/N¿3 in all of our SFR and stellar
mass bins.

To quantify the robustness of the trends highlighted in Figure 7, we ran a
Kendall-Tau rank test for the absorption lines that are detected in at least
three bins. We find that SFR and stellar mass are anticorrelated with C ii,
but they correlate positively with C iv. This would imply that C ii is located
mostly in galaxies with low stellar mass(log[M★/M⊙]¡9.26) and low SFR (log
[SFR/(M⊙yr${}^{-1})]<0.9$), while C iv is detected in galaxies with high
stellar mass (log[M⋆/M⊙]¿10.2) and high SFR (log [SFR/(M⊙yr${}^{-1})]>1.5$).
The slopes of the $W_{0}$ relationships with stellar mass and SFR for C ii and
C iv are 0.79 $\pm$ 0.13, 0.61 $\pm$ 0.05 and 0.73 $\pm$ 0.08, 0.55 $\pm$
0.04, which are significantly different at $\geq 5\sigma$ level. We do not
find any robust correlation between SFR and stellar mass with Si ii, Si iv,
Fei ii, Al ii, Al iii, or Lyα, yielding a probability of no correlation above
60% in all cases. We also explored the combined effect of impact parameter
with stellar mass and SFR; however, no clear conclusion was reached due to the
low number statistics, which resulted in composite spectra with low S/N line
detection.

###  4.3 Morphological dependence

The strength of the observed metal absorption signatures in the CGM can be
explored as a function of the azimuthal angle $\phi$ between the l.o.s. and
the projected major and minor axes of the foreground galaxy. Here we define
the azimuthal angle ($\phi$) as the projected angle between the background
galaxy l.o.s. and the projected minor axis of the foreground galaxy. Small
azimuthal angles ($\phi\sim 0^{\circ}$) refer to l.o.s. passing along the
projected minor axis of the foreground galaxy, while large azimuthal angles
($\phi=90^{\circ}$) refer to l.o.s. passing along the projected major axis of
the foreground galaxy. The effective radius
($r_{\rm{eff,circ}}=r_{\rm{eff}}\sqrt{q}$ 777$q$ is the axis ratio (b/a) of
the elliptical isophotes that best fit the galaxy.) was obtained by fitting a
single Sérsic profile with no constraints on the parameters, and then was
circularized using the galaxy ellipticity (Ribeiro et al., 2016). Alongside
the effective radius, Galfit provides other structural parameters: Sérsic
index (n), the axis ratio of the ellipse (b/a), and the position angle,
$\theta_{\rm{PA}}$. Out of the 238 galaxies evaluated in this paper, only 97
are in the COSMOS field and covered by HST imaging, and therefore have
morphological parameters. To inspect the dependency of the LIS-HIS absorption
strengths with the azimuthal angle($\phi$), we split our sample into three
$\phi$ bins:[0-30]∘,[30-60]∘, and [60-90]∘. Figure 7(lower panels) reports the
equivalent widths of different spectral features in bins of $r_{\rm{eff}}$ and
$\phi$.

To check and assess the robustness of possible correlations between the
morphological parameters and the equivalent widths measured in the composite
spectra for LIS, HIS, and Lyα, we ran a Kendall-Tau rank test between $W_{0}$
and $\phi$ and $r_{\rm{eff}}$. For lines detected in only two bins the
correlation cannot be assessed; therefore, we estimated the significance of
the difference between their absorption strength ($W_{0}$). To do this we
applied a Student’s t-test to determine the probability that the $W_{0}$
variations between the low and high $r_{\rm{eff}}$ and $\phi$ populations are
not statistically significant. According to the Student’s statistics ($t$) a
large $p$-value indicates to a high probability that the null hypothesis is
correct (the two samples are not statistically significant); a small $p$-value
suggests that the difference is significant. The Kendall-Tau and Student’s
t-test results are both given in Figure 7 in the corresponding panels.

For the effective radius ($r_{\rm{eff}}$) of the galaxy, the Kendall-Tau test
shows a mild anticorrelation with C ii ($p<0.117$), while it does not show any
significant correlation with Si ii and Si iv ($p>$0.602). We find a
significant difference ($p<0.01$) in the $W_{0}$ variations between small and
large $r_{\rm{eff}}$ as shown by the Student’s t-test. However, no correlation
is found for Ly$\upalpha$. This suggests that C iv gas is usually located in
the CGM of larger galaxies, while C ii gas is located in the CGM of smaller
galaxies. Concerning the azimuthal angle, we do not find any significant
correlation with $\phi$ in any of the spectral lines inspected in agreement
with what has been reported by (Chen et al., 2021), who inspected the
azimuthal dependence of Ly${\upalpha}$ emission of 59 star-forming galaxies
($z_{med}\sim 2.3$). This is opposed to the low-redshift scenario where
galaxies show high-velocity biconical outflows oriented along the minor-axis
and accreting material along the major-axis. This result could be linked to
the metal distribution along the disc of star-forming galaxies as metal
absorption systems are often compact and poorly mixed, where cool low-
ionization metal absorbers have typical sizes of $\sim 1$ kpc (Faucher-
Giguère, 2017a), while high-ionization gas seen in absorption arises in
multiple extended structures spread over $\sim$100 kpc (Churchill et al.,
2015; Peeples et al., 2019).

###  4.4 C ii/C iv line ratio

A further inspection of the differences between LIS and HIS on the different
galaxy parameters come from the C ii/C iv equivalent width line ratio. We
focus on carbon ions as they provide stronger absorptions with higher S/N
compared to aluminium or silicate ions. Figure 8 shows the C ii/C iv line
ratio as a function of impact parameter, stellar mass, and star formation
rate. The C ii/C iv line ratio appears to anticorrelate with impact
parameter($b$), stellar mass, and star formation rate. Similarly to the
analyses for individual line absorptions, we ran a Kendall-Tau to assess
possible correlations for C ii/C iv line ratio and included it in all panels
of Figure 8. We confirm that the anticorrelations between C ii/C iv ratio and
impact parameter, stellar mass, and star formation rate are statistically
robust. This suggests that C ii is more important than C iv in the inner
regions of these star-forming galaxies, while the opposite occurs in the
outskirts at large separations.

On the other hand, star-forming galaxies and low stellar mass with low star
formation rates show a higher Cii/Civ line ratio compared with galaxies that
have high stellar mass and high star formation rates. Our results suggest that
galaxies with higher star formation rates and large stellar masses are capable
of sweeping out the highly ionized gas (traced by C iv) farther away from the
galaxy compared with less actively star-forming and less massive galaxies.
Another possible explanation is that more active and massive galaxies have
stronger ionizing fluxes, able to ionize gas at larger distances compared with
less massive and less active galaxies. Recent studies have shown that fast and
energetic outflows can push material away from the central regions in star-
forming galaxies, more effectively in galaxies with high SFR (with a weaker
dependence on stellar mass; Heckman et al. 2015; Cicone et al. 2016; Trainor
et al. 2015; Feltre et al. 2020.) The presence of an AGN can make this effect
even more dramatic, as shown by an enhanced gas budget in H i and low-
ionization gas in high-redshift ($z>2$) galaxies (Prochaska et al., 2014),
suggesting higher accretion rates or a net gain of cold gas in the CGM in
these star-forming galaxies (Faucher-Giguère et al., 2016). However, the
physical mechanism through which the AGN removes and/or heats the gas and
suppresses accretion is not clear (Tumlinson et al., 2017). Determining the
nature of the source responsible for ionizing the gas in the CGM is crucial to
improving our understanding of the multi-phase CGM, but is beyond the scope of
this paper.

Figure 8: Cii/Civ $W_{0}$ line ratio as a function of the impact parameter
$b$, and the foreground galaxy’s stellar mass and SFR. Cii/Civ $W_{0}$ values
were obtained considering the same set of fg-bg galaxy pairs. Average and
median $W_{0}$ are shown in solid red and open blue symbols; the solid black
symbols correspond to upper limits with S/N ¡3. The error bars correspond to
1$\sigma$ confidence intervals for average or median values based on a
bootstrap analysis.

###  4.5 Ly$\upalpha$ emission

As we already noted in section 4.1 (Figure 5), the Ly$\upalpha$ emission
component is clearly detected in our composite spectra. Figure 9 shows the
Ly$\upalpha_{\rm{em}}$ rest equivalent width as a function of the impact
parameter. We find that Ly$\upalpha_{\rm{em}}$ decreases as a function of the
impact parameter $b$ similarly to what Chen et al. (2021) reported from 2D
Ly$\upalpha_{\rm{em}}$ maps. We also explore the Ly$\upalpha_{\rm{em}}$
equivalent width strength as a function of the galaxy stellar mass, star
formation rate, and azimuthal angle. However, we do not find any significant
correlation in these cases. This might be caused by the fact that at $z\sim$2
the Ly$\upalpha_{\rm{em}}$–stellar mass relation is weaker compared with
galaxies at higher redshifts (Du et al., 2018). Another possibility is that
our Ly$\upalpha_{\rm{em}}$ measurements come from composite spectra, hence
from star-forming galaxies with and without direct Ly$\upalpha_{\rm{em}}$
detections (EW$\leq 0\AA$, EW$>0\AA$ and EW$\geq 20\AA$ Le Fèvre et al. 2015;
Hathi et al. 2016), covering a wide range of stellar masses and star formation
rates that may have diluted a real Ly$\upalpha_{\rm{em}}$ signal (Steidel et
al., 2011).

Figure 9: Equivalent width ($W_{0}$) for the Ly${\upalpha}$ emission as a
function of the impact parameter ($b$) obtained from the average (solid red
line) and median (dot-dashed blue line) composite spectra. The error bars
correspond to 1$\sigma$ confidence intervals for average or median values
based on a bootstrap analysis.

##  5 Discussion

Analyses of low- and high-ionization state absorption features and their
dependence on stellar mass, star formation rate, and galaxy inclination have
been widely explored at $\lesssim 0.5$ (see Tumlinson et al. 2017; Kacprzak
2017). At high redshift, however, the studies of the CGM are limited. Steidel
et al. (2010) used 512 close ($<15\arcsec=124$kpc) angular pairs of $z\sim$2–3
($z_{bg}\sim$2.3) galaxies to map the cool and diffuse gas around galaxies.
They found strong evidence suggesting the presence of superwind outflows, and
proposed a simple model of the gas in the CGM, where cool gas is distributed
symmetrically around every galaxy, accelerating radially outwards with the
outflow velocity increasing with radius. Later, Turner et al. (2014) and Lau
et al. (2016) reported detections that suggest that in galaxies at $\langle
z\rangle$ = 2.4 the CGM extends at least up to 180 kpc. Moreover, the mass of
metals found within the halo is substantial and equivalent to $\sim$25% of the
metal mass within the interstellar medium (Rudie et al., 2019). This is,
however, a lower percentage than what has been reported from studies in low-
redshift galaxies (Werk et al., 2014), which suggests a considerable
redistribution of the metal content of galaxies in an inside-out fashion over
the last $\sim$8.5 Gyr. We note that eight of the nine resonance Si ii
transitions fall within the [900-1900]$\AA$ wavelength range considered here:
$\uplambda 989\AA$, $\uplambda 1020\AA$, $\uplambda\uplambda 1190,1193\AA$,
$\uplambda 1260\AA$, $\uplambda 1304\AA$ $\uplambda 1526\AA$, and $\uplambda
1808\AA$ (Shull et al., 1981). Lines located bluewards of Lyα are not included
in our analyses as the result of the low coverage of our composite spectra at
this wavelength range and because UV continuum level bluewards of Lyα is
particularly sensitive to the dust content, metallicity, and the age of the
stellar population (Trainor et al., 2015) and their strength could be affected
by IGM absorptions (Shapley et al., 2003). The Si ii ($\uplambda 1304\AA$)
component is blended with the O i ($\uplambda 1302\AA$) absorption line and is
close to excited fine-structure emission transitions that could lower the
$W_{0}$ measurements (Trainor et al., 2015). Finally, Si ii ($\uplambda
1526\AA$) is the least resonance component affected by blends (Shapley et al.,
2003) and is the strongest Si ii line amongst their counterparts. For this
work we chose $\uplambda 1526\AA$ for our Si ii $W_{0}$ computations as this
component is free of blending effects caused by the low spectral resolution of
our dataset. However, as noted by Jones et al. (2018) Si ii transitions probe
diverse optical depths, and hence the most accurate way to compute Si ii
absorption strength is to consider the contributions of all the Si ii
resonance components ($\uplambda\uplambda\uplambda 1260,1304,1526\AA$) within
the analysed range, by averaging their strengths and deblending them from
nearby spectral features that could affect their individual $W_{0}$
measurements. Nevertheless, different studies have adopted diverse strategies
to compute the LIS (including Si ii resonance components) $W_{0}$ strength.
For example, Jones et al. (2018) averaged Si ii ($\uplambda\uplambda\uplambda
1260,1304,1526\AA$), O i ($\uplambda 1302$), C ii ($\uplambda 1334\AA$), Al ii
($\uplambda 1670\AA$), Fe ii ($\uplambda 2382\AA$), and Mg ii
($\uplambda\uplambda 2796,2803\AA$) components; Ranjan et al. (2022)
considered the average of the eight Si ii resonance components to estimate the
$W_{0}$ Si ii absorption in high-z damped Lyman-$\upalpha$ (DLA) systems; Du
et al. (2016) averaged Si ii ($\uplambda 1526\AA$), Al ii ($\uplambda
1670\AA$), Ni ii ($\uplambda\uplambda 1741,1751\AA$), Si ii ($\uplambda
1808\AA$), and Fe ii ($\uplambda 2382\AA$) absorption lines to compute an
overall LIS average absorption estimation, while later Du et al. (2018)
considered Si ii ($\uplambda 1260\AA$), O i–Si ii ($\uplambda\uplambda
1302,1304\AA$), C ii ($\uplambda 1334\AA$), and Si ii ($\uplambda 1526\AA$)
for similar computations. The differences in the number of Si ii resonance
components considered for $W_{0}$ computations could be the reason why similar
Si ii trends to those of C ii with SFR and stellar mass shown in Fig. 7 are
not appreciated. As shown by Jones et al. (2018) different low ion transitions
(Si ii , Fe ii, and Ni ii) show non-uniform covering fractions in the CGM of
star-forming galaxies at high redshift ($z\simeq 2-3$).

In this work we used a sample of 238 galaxy close pairs to probe the CGM
around star-forming galaxies at $z\sim 2.6$. Our results show an
anticorrelation between the equivalent width of the absorption lines and the
impact parameter ($b$) for this high-redshift star-forming galaxy sample and
are consistent with previous results at lower redshift. Here we detect
Ly$\upalpha$–LIS and HIS absorption at distances up to 172 kpc and 146 kpc.
Our low-ionization state (C ii, Si ii), and high-ionization state (C iv Si iv)
absorption line detections shape an upper envelope of the equivalent width
distribution coming from studies at low redshift (see Figure 6). This is
further illustrated by the differences in the slopes of the $W_{0}$ radial
profiles between low- and high-ionization state absorptions of the same ion
species, where Si ii–Si iv and C ii–C iv absorption line pairs are different
at a $\geq 5\sigma$ level. Moreover, when compared with galaxies at $z\sim
2.3$ (Steidel et al., 2010) our results show a significant difference in their
slopes at a 5$\sigma$ level for Si ii and a 3$\sigma$ level for C ii and Al ii
absorption lines. These discrepancies between LIS and HIS suggest that, within
the CGM, cold (T$<10^{4.5}$K) and dense gas is more extended in galaxies at
$z\sim 2.6$ compared with galaxies at $z\sim 2.3$ and lower redshifts, as
probed by Si ii, C ii, Si iv, and C iv. These results suggests a potential
redshift evolution for the CGM gas content that produces these absorptions. As
higher covering factors of neutral gas lead to stronger absorption lines (Du
et al., 2018), this suggests a higher content of neutral gas in high-redshift
galaxies compared with low-redshift galaxies. This concentration of neutral
gas could represent a reservoir of gas that can be later accreted onto the
galaxies to fuel future star formation (Hafen et al., 2019, 2020).

We note that it is possible to increase the maximum angular projected
separation ($\geq 23\arcsec$) allowing us to probe larger distances closer to
the CGM and IGM boundary, following Chen et al. (2020). However, we limited
our analyses to 23$\arcsec\sim$170kpc and galaxy spectra with highly reliable
redshifts to guarantee detection with good S/N. Spectra with unreliable
redshift measurements could wash out the expected metal absorptions and/or
produce spurious features in the final composite spectra. This is further
supported by the observed metallicity dependence with impact parameter, where
LIS are preferably located in the inner CGM (close to the galaxy; Lau et al.
2016), while HIS (e.g. O vi are expected to dominate the CGM at larger
separations Shen et al. 2013) making it difficult to detect weak LIS
absorptions at larger separations given their expected $W_{0}$.

###  5.1 LIS and HIS absorption dependencies.

At $z\lesssim 1$, Churchill et al. (2000) explored a sample of 45 Mg ii
absorption systems in high-resolution QSO spectra, and studied their spectra,
together with the C iv and Fe ii absorption profiles, suggesting that the gas
responsible for Mg ii and C iv absorptions arises from gas in different phases
(i.e. gas producing HIS absorption features have typical temperatures T¿105K
Tumlinson et al. 2017). Moreover, they observed an evolution of the absorbing
gas that is consistent with scenarios of galaxy evolution in which mergers and
accretion of ‘protogalactic clumps’ provide gas reservoirs responsible for the
elevated star formation activity at high redshift, while at intermediate and
lower redshifts ($z\leq$1), the balance of high- and low-ionization state CGM
gas may be related to the presence of star-forming regions in the host galaxy
(Churchill et al., 2000). Later on, Zibetti et al. (2007) found that early-
type (quiescent, red) galaxies ($0.37<z<1$) are associated with weaker Mg ii
absorptions, while stronger systems are located in late-type (star-forming,
blue) galaxies. These results provided evidence that the SFR correlates with
Mg ii absorption strength caused by the presence of outflows from star-forming
or bursting galaxies. This scenario is also supported by subsequent studies
that demonstrated that SFR correlates with outflow velocity deduced from the
Mg ii absorption strength (Weiner et al., 2009; Martin et al., 2012; Tremonti
et al., 2007; Rubin et al., 2010), and by the correlation between the stellar
mass and Ly$\upalpha$ absorption strength (Bordoloi et al., 2018; Wilde et
al., 2021).

Our detection of LIS and HIS absorption lines suggests that at $\langle
z\rangle\sim 2.6$ the C ii and C iv features are correlated with star
formation rate and stellar mass. C ii is stronger in galaxies with low star
formation rates and low stellar masses, while C iv is stronger in galaxies
with high SFR and high stellar masses. These results are consistent with what
has been reported for low-redshift galaxies in scenarios where LIS and HIS
absorbers have different spatial distributions. Low-ionization state metal
absorbers probe the gas that is less ionized than high-ionization state metal
absorbers (Nagao et al., 2006), and thus they are expected to be located in
gas regions with different density conditions (Burchett et al., 2016).
Moreover, studies of low-redshift galaxies ($z\leq 0.5$) have shown that as a
consequence of the interaction between a starburst-driven wind and the
preexisting CGM at radii as large as 200 kpc, the CGM around star-forming
galaxies with high star formation rates differs systematically compared to
galaxies with lower SFRs, as probed by the Ly$\upalpha$, Mg ii, Si ii, C iv,
and O vi absorption lines (Tumlinson et al., 2011; Borthakur et al., 2013; Lan
et al., 2014; Heckman et al., 2017). However, as suggested by Cicone et al.
(2016) and Gatkine et al. (2022), their correlation with stellar mass and star
formation rate might in fact be a consequence of a main-sequence offset,
rather than simply a correlation with star formation rate or stellar mass, and
because LIS–HIS covering factors can be affecetd by environmental processes
(Dutta et al., 2021). Hence, caution should be taken when interpreting LIS–HIS
correlations with SFR and/or stellar mass.

The origin of the reservoir of cold neutral gas around low stellar mass
galaxies and low SFRs at these distances($\langle b\rangle\approx 120$kpc; see
Appendix A) is uncertain. One explanation comes from a soft radiation field
unable to ionize HIS (i.e. C iv, Si iv) as the production of C iv and Si iv
absorption features in the CGM requires photons with energies ¿45 eV
associated with hard ionizing radiation fields from massive stars, AGN, and
radiative shocks (Feltre et al., 2020; Trainor et al., 2015). As shown by
Gatkine et al. (2022), HIS are more affected by high-velocity outflows; they
show a strong correlation with SFR and are ubiquitous in high-SFR systems.
Another possible explanation comes from the galactic fountain scenario,
predicted by cosmological galaxy formation simulations (Oppenheimer et al.,
2010; Vogelsberger et al., 2013), where the presence of cold low-ionization
gas results from metal-rich gas ejected in previous star formation episodes
that fall back to the disc (Fraternali & Binney, 2006; Hobbs et al., 2015).
Moreover, we know that stellar winds are dominant in the inner region of the
CGM ¡60kpc (Chen et al., 2020), and depending on their velocity, stellar winds
in low-mass galaxies might be able to expel material or be reaccreted as
recycled material (Sánchez Almeida, 2017). However, if the velocity outflow is
insufficient to eject material out into the IGM, the recycle timescales in
low-mass galaxies where gas returns to the galaxy can be as small as those in
high-mass systems (van de Voort, 2017). Martin et al. (2012) detected Fe ii
Doppler shifts and $V_{max}$–Mg ii values that suggest that outflows reach the
circumgalactic medium with Mg ii absorption at blueshifts as high as 700 km
s-1, reaching 70 kpc in 100 Myr, a short enough time for the host galaxy to
sustain SFR, even if the SFR declines due to an outflow. Nevertheless, our
measurements do not allow us to break down the multiple components of the
absorption features in our foreground galaxy (down-the-barrel) composite
spectra and to detect blueshifted offsets that could be related to high-
velocity outflows. We note that it is possible to combine down-the-barrel and
QSO–galaxy and/or galaxy–galaxy pairs to unambiguously detect blueshifted
absorptions relative to the galaxy systemic velocity, and quantify
independently the main properties of the detected outflow (Kacprzak et al.,
2014; Bouché et al., 2016; Lehner, 2017).

Figure 7 (lower panels) shows the dependence of line absorption strength on
the galaxy’s effective radius ($r_{\rm{eff}}$) and azimuthal angle ($\phi$).
For the dependence of the absorption strength ($W_{0}$) on the size of the
galaxy given by the effective radius($r_{\rm{eff}}$), we find that LIS
absorptions are stronger in smaller galaxies compared to HIS absorptions,
which are shown to be stronger in larger galaxies, in agreement with Rudie et
al. (2019), who reported that LIS absorption occurs spatially closer to the
galaxy, and gas producing HIS absorptions can be located well beyond the
virial radius. Regarding the dependence on azimuthal angle, we do not find any
significant correlation with $\phi$ for either LIS or HIS. However, these
results are based on the fraction of galaxies for which we have morphological
measurements ($\sim 40\%$ of the parent sample). Thus, these results have to
be confirmed by a similar morphological analysis using larger samples at these
high redshifts, as galaxy orientation plays a major role in the measured
strength of LIS and HIS. This has been shown at low redshift from studies
using analyses of down-the-barrel (Rubin et al., 2014; Bordoloi et al., 2014a)
and QSO–galaxy pairs (Kacprzak et al., 2011; Bordoloi et al., 2011). Moreover,
at z $\gtrsim 2$ star-forming galaxies have clumpy morphologies (Förster
Schreiber et al., 2011), with galactic winds that are mainly driven by
outflows from prominent star-forming clumps (Genzel et al., 2011), and have
not yet formed a stable disc (or any disc at all) capable of collimating
galactic winds into bipolar outflows (Faucher-Giguère, 2017b), indicating that
the minor–major axis dichotomy associated with rotation present at low
redshift (z¡1) is not broadly applicable at z$\sim$2-3 (Law et al., 2012;
Nelson et al., 2019; Price et al., 2020). Therefore, it is not obvious that at
high redshift ($z\gtrsim 2$) the azimuthal angle can be determined and, if it
can, whether it has any physical meaning.

The dependence of LIS and HIS absorption strength on the azimuthal angle has
been explored in the literature to prove or disprove theories on how galaxies
accrete gas from the intergalactic medium. Inflowing material along filaments
in the IGM is expected to be the largest source of accretion (Kereš et al.,
2005). Simulations have shown that accretion of metal-poor gas inflows occurs
along the major axis of galaxies, where outflows that are preferably located
along the semi-minor axis form bipolar outflows (Putman, 2017), and gas being
accreted onto galaxies that can later trigger star formation has been
supported by evidence collected from multiple CGM studies at low redshift
(Kacprzak et al., 2010, 2012, 2015, 2019; Lan & Mo, 2018; Martin et al., 2019;
Nielsen et al., 2015; Rubin et al., 2018; Zhu & Ménard, 2013; Tumlinson et
al., 2011; Bordoloi et al., 2014b; Lan et al., 2014). Recent cosmological
hydrodynamical simulations examine the physical properties of the gas located
in the CGM of star-forming galaxies as a function of angular orientation by
Péroux et al. (2020). They found that the CGM varies strongly with impact
parameter, stellar mass, and redshift. Moreover, they suggest that the inflow
rate of gas is more substantial along the galaxy major axis, while the outflow
is strongest along the minor axis.

The correlations between C ii and C iv with impact parameter, star formation
rate, and stellar mass scenario of a multi-phase CGM(where LIS absorptions are
produced by denser gas located closer to the galaxy, whether this dense
neutral gas component is part of an outflow or material falling back to the
galaxy taking part in a galactic fountain that could eventually be funnelled
to the galaxy to sustain star formation activity; Kereš et al. 2005) is not
clear and cannot be assessed by our datasets. On the other hand, HIS
absorption features associated with strong stellar winds produced by high star
formation activity capable of ionizing radiation in high stellar mass galaxies
with high star formation activity sweeping material to the outer regions of
these galaxies (Putman, 2017; Bower et al., 2016; Oppenheimer et al., 2016;
Voit et al., 2015).

Similar analyses including observations at different redshifts coming from
different complementary surveys, for example VANDELS (McLure et al., 2018;
Pentericci et al., 2018), zCOSMOS (Lilly et al., 2007, 2009), VVDS (Le Fèvre
et al., 2013), and DEIMOS10K (Hasinger et al., 2018), can help to increase the
number of galaxy pairs with close angular separations ($b<6\arcsec$), deblend
close spectral line features(e.g. C ii–O iv $\uplambda\uplambda$ 1334.5,
1343.0 $\AA$; Si iv $\uplambda\uplambda$ 1393.8, 1402.8 $\AA$), and cover
different low- and high-ionization state lines(e.g. O vi $\uplambda\uplambda$
1032, 1038 $\AA$, Mg ii $\uplambda$ 2798 $\AA$). Additionally, it has been
shown that AGN activity is dependent on stellar mass and SFR (e.g. Lemaux et
al. 2014; Bongiorno et al. 2016; Magliocchetti et al. 2020), and thus studies
considering bg–AGN and/or QSO–AGN galaxy pairs (Hennawi et al., 2006;
Prochaska et al., 2014) are needed to study the effect that the presence of an
AGN has on feedback and quenching in star-forming galaxies at low and high
redshifts.

###  5.2 C ii / C iv line ratio.

A further inspection of the differences between LIS and HIS on the different
galaxy parameters explored comes from the C ii/C iv line ratio. We find that C
ii/C iv line ratio anticorrelates with impact parameter, stellar mass, and
star formation rate. This implies that C iv is mostly located at larger
distances in more massive galaxies with higher star formation rates, while C
ii dominates at smaller impact parameters and is found mostly in low stellar
mass galaxies with low star formation rates. These results further support the
picture of a multi-phase CGM where LIS line absorptions are produced by denser
gas with lower temperatures (T$<10^{4.5}$K) that is located close to the
central galaxy, while HIS line absorptions are produced by warm gas located at
larger distances from the central galaxy. Simulations have shown that much of
the ongoing gas accretion occurs towards the edges of the galaxies to avoid
the dominant feedback (outflows) from the central regions (Stewart et al.,
2011; Fernández et al., 2012; Putman, 2017); however, we do not find
supporting evidence of the low-redshift scenario where low-ionization state
gas infalls along the major axis of star-forming galaxies, accompanied by
large-scale outflows along the minor axis forming bipolar outflows. On the
contrary, our results suggest that this scenario is not broadly applicable at
z$\sim$2\. We note that we have also explored Si ii / Si iv and Al ii / Al iii
equivalent width line ratios; however, we did not detect any significant
correlations. On the one hand, Si iv predominantly arises in denser gas closer
to galaxies more similar to other LIS state lines such as Mg ii than to those
of higher ions (Ford et al., 2013, 2014), and hence Si ii and Si iv line
absorption might be probing gas with similar physical conditions. On the other
hand, Al iii is an intermediate-ionization state (IIS) tracer of moderately
photoionized warm gas generally associated with neutral phase gas (Savage et
al., 2001; Knauth et al., 2003; Vladilo et al., 2001). In fact, Al iii
absorption is associated with low ions, as shown by the significant
correlation between the velocity widths of Al iii and low-ionization species
(e.g. Si ii, Fe ii, Zn ii, Howk et al. 1999), suggesting that a substantial
fraction of the low-ionization ions may be associated with moderately ionized
gas traced by Al iii and Fe iii (Wolfe et al., 2005) and that doubly ionized
species (e.g. Al iii, Fe iii, C iii, Si iii) often have comparable column
densities to the singly ionized species (e.g. Al ii, Fe ii, C ii, Si ii) (Mas-
Ribas et al., 2017).

###  5.3 Ly$\upalpha$ emission

Regarding Ly$\upalpha_{\rm{em}}$, several studies have been carried out to
explore the relation with galaxy properties. At low redshift Runnholm et al.
(2020) used the Lyman Alpha Reference Sample (LARS) to obtain correlations
between Ly$\alpha$ and different galaxy properties (i.e. star formation rate,
dust extinction, compactness, and the gas covering fraction). At high redshift
it has been found that bluer galaxies show stronger Ly$\upalpha_{\rm{em}}$
(Shapley et al., 2003; Pentericci et al., 2010; Berry et al., 2012; Erb et
al., 2016), and that low stellar mass galaxies with lower SFRs show stronger
Ly$\upalpha_{\rm{em}}$ than high-stellar mass galaxies with higher SFRs
(Vanzella et al., 2009; Stark et al., 2010; Erb et al., 2006; Jones et al.,
2012; Shapley et al., 2003; Kornei et al., 2010; Hathi et al., 2016).
Additionally Ly$\upalpha_{\rm{em}}$ is correlated with LIS absorption;
stronger LIS absorptions correspond to weaker Ly$\upalpha_{\rm{em}}$, as high
concentrations of neutral gas responsible for strong LIS absorption are also
responsible for scattering out of the l.o.s. Ly$\upalpha$ photons (Shapley et
al., 2003; Vanzella et al., 2009; Jones et al., 2012). More recently, Du et
al. (2018), Trainor et al. (2019), and Pahl et al. (2020) studied the
spectroscopic properties of star-forming galaxies at $z\sim$2–5 through
composite spectra grouped through different galaxy properties. They detected
stronger Ly$\upalpha_{\rm{em}}$ at higher redshift at fixed stellar mass, SFR,
and UV luminosity, and found that the LIS–Ly$\upalpha_{\rm{em}}$ relation is
redshift independent, suggesting that this is caused by the variations of the
neutral gas covering fraction favouring Ly$\alphaup$ escape and production
and/or dust content in the ISM and CGM. Moreover Oyarzún et al. (2016, 2017)
show that at high redshift ($3<z<4.6$) the Ly$\upalpha_{\rm{em}}$
anticorrelations with stellar mass, star formation rate, and UV luminosity are
stronger in low stellar mass populations, which is explained by the rapidly
increasing neutral gas fraction of the universe at higher redshifts (Du et
al., 2021).

##  6 Conclusions

In this paper we presented stacks of 238 background galaxy spectra used to
probe the CGM content and extent around star-forming galaxies at $\langle
z\rangle\sim 2.6$. We only used spectra with highly reliable spectroscopic
redshifts ($95-100\%$ probability of being correct) to identify the low-
ionization state (LIS: Si ii, C ii) and high-ionization state (HIS: C iv, Si
iv) metal absorption lines, and constrain their spatial distribution and their
dependence on stellar mass, star formation rate, azimuthal angle, and
effective radius.

We summarize our main results below:

  1. 1.

We detect LIS and HIS metal absorption lines in the CGM around star-forming
galaxies at distances up to 172 kpc and 146 kpc, respectively. The limitations
owing to the size of our sample did not allow us to follow metal lines beyond
these distances. The strength of these absorptions decreases at increasing
distances from the galaxy, consistently with results published in the
literature. At any fixed distance from the galaxy, the strength of all
absorption lines that we identify in our sample at $z\sim 2.6$ is greater than
any other measurement at lower redshift, providing evidence of a redshift
evolution of the CGM gas content responsible for producing these absorptions.

  2. 2.

We do not find any significant correlation between the LIS–HIS absorptions and
the azimuthal angle ($\phi$). This is opposed to the scenario at low redshift
where cold gas (traced by LIS line) is infalling onto galaxies along the plane
containing the disc, while the gas heated and processed by star formation
(traced by HIS lines) is outflowing perpendicularly to the plane. This can be
explained by the fact that high-redshift galaxies have not formed a stable
disc capable of collimating galactic winds into bipolar outflows. However, due
to the small sample of close pairs with available morphological features,
these trends need to be confirmed by applying a similar analysis to larger
samples at these high redshifts.

  3. 3.

We find an anticorrelation between Ly$\upalpha_{\rm{em}}$ and the impact
parameter $b$, in agreement with previous results at high redshift.

  4. 4.

To assess the relative importance of LIS and HIS absorptions, we computed the
Cii/Civ equivalent width line ratio and find that it correlates with impact
parameter $b$, stellar mass, and star formation rate. The Cii/Civ $W_{0}$ line
ratio is higher at small separations, mainly detected in star-forming galaxies
($\langle z\rangle\sim 2.6$) with low stellar masses and low star formation
rates. Conversely, low Cii/Civ line ratios are defined by stronger Civ line
absorption compared to Cii and are observed at large separations in star-
forming galaxies with higher stellar masses and star formation rates.

The results presented here provide observational evidence consistent with a
scenario where star-forming galaxies at $\langle z\rangle\sim 2.6$ possess a
multi-phase CGM where LIS metal absorptions are produced by denser gas, which
is more extended in these star-forming galaxies. Our results suggest that
galaxies with higher star formation rates and high stellar masses have
stronger ionizing fluxes that are able to ionize gas at larger distances
and/or are capable to sweep out the highly ionized gas (traced by C iv)
farther away from the galaxy compared with less massive and less star-forming
galaxies. Subsequently, star-forming galaxies with low SFR and low stellar
mass show larger reservoirs of cold gas as probed by their C ii and C iv lines
and their C ii/C iv equivalent width line ratio. These large reservoirs of
cold gas could be funnelled into the galaxies and eventually provide the
necessary fuel to sustain star formation activity. Recently, Wang et al.
(2022) has demonstrated that large-scale environment modulates star formation
by regulating the way in which galaxies breathe material in and out (accrete
and expell) by exchanging material within the CGM. This process is
synchronized with star formation rate events occurring within a galaxy, and is
related to maxima (minima) of SFR associated with a previous
decrease(increase) in the cold circumgalactic gas phase, that halts a further
rise(decline), and leads to a fall(rise) in the star formation rate at later
stages. Our results from C ii peaks and Civ troughs detected in low-mass
galaxies (low SFRs) and high-mass galaxies (high SFRs) could be interpreted as
the snapshots of these two different stages of the complex interplay between
the ISM, CGM, and IGM in which galaxies exchange material. However, we note
that high-resolution observations are required to detect outflows expelling
material or inflows accreting cold material back to the galaxy as recycled
material. We highlight that although stacking increases the S/N of the
background __spotlights, allowing us to detect the faint signal produced by
gas in the CGM, it also smears out the information about the spatial,
kinematic, and ionization properties of the CGM. Thus, we reiterate the
necessity to perform deeper observations with higher resolutions at this and
higher redshift of multiple LIS and HIS metal lines to provide better
constraints on the properties of the multi-phase CGM. It is very likely that
future and ongoing observations from large and deep spectroscopic surveys such
as VANDELS(McLure et al., 2018; Pentericci et al., 2018), zCOSMOS (Lilly et
al., 2007, 2009), VVDS(Le Fèvre et al., 2013) or DEIMOS10K (Hasinger et al.,
2018) and Integral Field Unit observations from MUSE/KMOS/JWST will help us
understand more about the multi-phase nature of the CGM. Future work should
point towards a resolved view of the velocity field of the in-falling and out-
flowing gas of galaxies at redshift $z>2$.

###### Acknowledgements.

We thank an anonymous referee for constructive comments and suggestions that
improved the manuscript. Based on data obtained with the European Southern
Observatory Very Large Telescope, Paranal, Chile, under Large Programs
175.A-0839, 177.A-0837, and 185.A-0791. This work is based on data products
made available at the CESAM data center, Laboratoire d’Astrophysique de
Marseille. This work partly uses observations obtained with MegaPrime/MegaCam,
a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope
(CFHT) which is operated by the National Research Council (NRC) of Canada, the
Institut National des Sciences de l’Univers of the Centre National de la
Recherche Scientifique (CNRS) of France, and the University of Hawaii. This
work is based in part on data products produced at TERAPIX and the Canadian
Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy
Survey, a collaborative project of NRC and CNRS. HMH acknowledge partial
support from National Fund for Scientific and Technological Research of Chile
(_Fondecyt_) through grants no. 1171710 & 1150216\. E.I. acknowledges partial
support from FONDECYT through grants N∘ 1221846 and 1171710. MA acknowledges
support from FONDECYT grant 1211951, ”ANID+PCI+INSTITUTO MAX PLANCK DE
ASTRONOMIA MPG 190030” and ”ANID+PCI+REDES 190194”. RA acknowledges support
from ANID FONDECYT Regular Grant 1202007. We thank ESO staff for their support
for the VUDS survey, particularly the Paranal staff conducting the
observations and Marina Rejkuba and the ESO user support group in Garching.
This research used Astropy,888http://www.astropy.org a community-developed
core Python package for Astronomy (Astropy Collaboration et al., 2013, 2018),
Numpy (Harris et al., 2020), Scipy (Virtanen et al., 2020) and Matplotlib
(Hunter, 2007)

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##  Appendix A Supplementary tables.

Table 5:  Foreground–background (fg-bg) galaxy pair statistics according to
the stellar mass (log[M★/M⊙]).

ID | N |  $\langle$ log[M★/M⊙] $\rangle$ |  $\langle b\rangle$ (kpc) | $\langle\rm{z}_{\rm{fg}}\rangle$ | $\langle\rm{z}_{\rm{bg}}\rangle$
---|---|---|---|---|---
c1 | c2 | c3 | c4 | c5 | c6
ALL | 238 |  9.73 $\pm$ 0.40 | 125.05 | 2.60 | 3.04
S1 | 61 |  9.26 $\pm$ 0.18 | 125.12 | 2.48 | 2.87
S2 | 63 |  9.60 $\pm$ 0.07 | 119.63 | 2.65 | 3.10
S3 | 65 |  9.87 $\pm$ 0.09 | 130.42 | 2.58 | 3.04
S4 | 49 |  10.31 $\pm$ 0.24 | 124.83 | 2.71 | 3.19
999 Column 1: Sample ID; Column 2: number of galaxies per sample; Column 3:
mean stellar mass; Column 4: mean impact parameter in kpc; Column 5: mean
redshift of the foreground galaxies sample; and Column 6: mean redshift of the
background galaxies sample.

Table 6:  Foreground–background (fg-bg) galaxy pair statistics according to
the star formation rate (log[(M⊙yr${}^{-1})]$).

ID | N |  $\langle$ log[SFR/(M⊙yr${}^{-1})]$ $\rangle$ |  $\langle b\rangle$ (kpc) | $\langle\rm{z}_{\rm{fg}}\rangle$ | $\langle\rm{z}_{\rm{bg}}\rangle$
---|---|---|---|---|---
c1 | c2 | c3 | c4 | c5 | c6
ALL | 238 |  1.37 $\pm$ 0.39 | 125.10 | 2.60 | 3.04
S1 | 60 |  0.91 $\pm$ 0.39 | 117.92 | 2.56 | 2.98
S2 | 62 |  1.21 $\pm$ 0.06 | 128.63 | 2.64 | 3.08
S3 | 59 |  1.49 $\pm$ 0.09 | 124.50 | 2.54 | 3.02
S4 | 59 |  1.92 $\pm$ 0.20 | 129.21 | 2.67 | 3.08
101010 Column 1: Sample ID; Column 2: number of galaxies per sample; Column 3:
mean star formation rate (log[SFR/(M⊙yr${}^{-1})]$); Column 4: mean impact
parameter in kpc; Column 5: mean redshift of the foreground galaxies sample;
and Column 6: mean redshift of the background galaxies sample.

Table 7:  Foreground–background (fg-bg) galaxy pair statistics according to
the azimuthal angle ($\phi$).

ID | N |  $\langle$ $\phi\rangle$ (∘) |  $\langle b\rangle$ (kpc) | $\langle\rm{z}_{\rm{fg}}\rangle$ | $\langle\rm{z}_{\rm{bg}}\rangle$
---|---|---|---|---|---
c1 | c2 | c3 | c4 | c5 | c6
ALL | 97 |  31.34 $\pm$ 18.12 | 121.54 | 2.65 | 3.08
S1 | 60 |  16.90 $\pm$ 6.20 | 107.74 | 2.69 | 3.15
S2 | 62 |  44.92 $\pm$ 6.74 | 132.53 | 2.55 | 2.92
S3 | 59 |  75.13 $\pm$ 9.10 | 118.75 | 2.70 | 3.16
111111 Column 1: Sample ID; Column 2: number of galaxies per sample; Column 3:
mean azimuthal angle ($\phi\,^{\circ}$); Column 4: mean impact parameter in
kpc; Column 5: mean redshift of the foreground galaxies sample; and Column 6:
mean redshift of the background galaxies sample.

Table 8:  Foreground–background (fg-bg) galaxy pair statistics according to
the effective radius (reff kpc).

ID | N |  $\langle$ reff $\rangle$ (kpc) |  $\langle b\rangle$ (kpc) | $\langle\rm{z}_{\rm{fg}}\rangle$ | $\langle\rm{z}_{\rm{bg}}\rangle$
---|---|---|---|---|---
c1 | c2 | c3 | c4 | c5 | c6
ALL | 97 |  8.94 $\pm$ 0.49 | 121.54 | 2.65 | 3.08
S1 | 31 |  2.70 $\pm$ 0.98 | 125.92 | 2.67 | 3.16
S2 | 33 |  6.87 $\pm$ 1.40 | 120.75 | 2.63 | 3.02
S3 | 33 |  16.88 $\pm$ 7.39 | 118.19 | 2.66 | 3.07
121212 Column 1: Sample ID; Column 2: number of galaxies per sample; Column 3:
mean effective radius (reff kpc); Column 4: mean impact parameter in kpc;
Column 5: mean redshift of the foreground galaxies sample; and Column 6: mean
redshift of the background galaxies sample.