# Probing the impact of radio-mode feedback on the properties of the cool
circumgalactic medium

Yu-Ling Chang Graduate Institute of Astrophysics, National Taiwan University,
No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan  Ting-Wen Lan Graduate
Institute of Astrophysics, National Taiwan University, No. 1, Sec. 4,
Roosevelt Road, Taipei 10617, Taiwan  Department of Physics, National Taiwan
University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan  J. Xavier
Prochaska University of California, Santa Cruz, 1156 High Street, Santa Cruz,
CA 95064, USA  Kavli Institute for the Physics and Mathematics of the
Universe, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan  Lucas Napolitano
Department of Physics & Astronomy, University of Wyoming, 1000 E. University,
Dept. 3905, Laramie, WY 82071, USA  Abhijeet Anand Lawrence Berkeley National
Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA  J. Aguilar  Lawrence
Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA  S.
Ahlen Physics Dept., Boston University, 590 Commonwealth Avenue, Boston, MA
02215, USA  D. Brooks  Department of Physics & Astronomy, University College
London, Gower Street, London, WC1E 6BT, UK  T. Claybaugh  Lawrence Berkeley
National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA  A. de la
Macorra Instituto de Física, Universidad Nacional Autónoma de México, Cd. de
México C.P. 04510, México  Arjun Dey NSF NOIRLab, 950 N. Cherry Ave., Tucson,
AZ 85719, USA  P. Doel  Department of Physics & Astronomy, University College
London, Gower Street, London, WC1E 6BT, UK  S. Gontcho A Gontcho Lawrence
Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA  J.
Guy Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA
94720, USA  S. Juneau NSF NOIRLab, 950 N. Cherry Ave., Tucson, AZ 85719, USA
T. Kisner Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley,
CA 94720, USA  A. Lambert  Lawrence Berkeley National Laboratory, 1 Cyclotron
Road, Berkeley, CA 94720, USA  M. Landriau Lawrence Berkeley National
Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA  L. Le Guillou Sorbonne
Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes
Energies (LPNHE), FR-75005 Paris, France  M. Manera Departament de Física,
Serra Húnter, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona),
Spain  Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of
Science and Technology, Campus UAB, 08193 Bellaterra Barcelona, Spain  P.
Martini Center for Cosmology and AstroParticle Physics, The Ohio State
University, 191 West Woodruff Avenue, Columbus, OH 43210, USA  Department of
Astronomy, The Ohio State University, 4055 McPherson Laboratory, 140 W 18th
Avenue, Columbus, OH 43210, USA  The Ohio State University, Columbus, 43210
OH, USA  A. Meisner NSF NOIRLab, 950 N. Cherry Ave., Tucson, AZ 85719, USA  R.
Miquel  Institució Catalana de Recerca i Estudis Avançats, Passeig de Lluís
Companys, 23, 08010 Barcelona, Spain  Institut de Física d’Altes Energies
(IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193
Bellaterra Barcelona, Spain  J. Moustakas Department of Physics and Astronomy,
Siena College, 515 Loudon Road, Loudonville, NY 12211, USA  A. D. Myers
Department of Physics & Astronomy, University of Wyoming, 1000 E. University,
Dept. 3905, Laramie, WY 82071, USA  J. Nie National Astronomical
Observatories, Chinese Academy of Sciences, A20 Datun Rd., Chaoyang District,
Beijing, 100012, P.R. China  C. Poppett  Lawrence Berkeley National
Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA  Space Sciences
Laboratory, University of California, Berkeley, 7 Gauss Way, Berkeley, CA
94720, USA  University of California, Berkeley, 110 Sproul Hall #5800
Berkeley, CA 94720, USA  M. Rezaie Department of Physics, Kansas State
University, 116 Cardwell Hall, Manhattan, KS 66506, USA  G. Rossi  Department
of Physics and Astronomy, Sejong University, Seoul, 143-747, Korea  E. Sanchez
CIEMAT, Avenida Complutense 40, E-28040 Madrid, Spain  M. Schubnell
Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
University of Michigan, Ann Arbor, MI 48109, USA  H. Seo Department of Physics
& Astronomy, Ohio University, Athens, OH 45701, USA  D. Sprayberry  NSF
NOIRLab, 950 N. Cherry Ave., Tucson, AZ 85719, USA  G. Tarlé University of
Michigan, Ann Arbor, MI 48109, USA  B. A. Weaver  NSF NOIRLab, 950 N. Cherry
Ave., Tucson, AZ 85719, USA  H. Zou National Astronomical Observatories,
Chinese Academy of Sciences, A20 Datun Rd., Chaoyang District, Beijing,
100012, P.R. China

###### Abstract

We explore the influence of radio-mode feedback on the properties of the cool
circumgalactic medium (CGM). To this end, we assemble a statistical sample of
approximately 30,000 radio galaxies with background quasars by combining
optical spectroscopic measurements of luminous red galaxies (LRGs) and quasars
from the year 1 dataset of Dark Energy Spectroscopic Instrument (DESI) and
radio sources from the LOw-Frequency ARray Two-metre Sky Survey (LoTSS) DR2
catalog and the Very Large Array Sky Survey (VLASS) quick look catalog.
Galaxies with similar optical properties but with no radio counterparts in
LoTSS and VLASS are selected as the control group. We measure the cool CGM
properties of radio galaxies and their control samples traced by MgII
absorption lines, including covering fraction, rest equivalent width, and gas
kinematics. Our results show no significant difference in the properties of
gas around radio galaxies and their control sample, indicating that the
operating radio-mode feedback of massive galaxies does not produce detectable
effects on the properties of the cool CGM. Finally, we show that the CGM of
radio galaxies contain a non-negligible amount of cool gas with approximately
$10^{10}\rm\,M_{\odot}$. This abundance can place a stringent constraint on
the radio-mode feedback models.

Spectroscopy(1558) — Extragalactic astronomy(506) — Radio active galactic
nuclei(2134) — Jets(870) — Circumgalactic medium(1879)

##  1 Introduction

Feedback from supermassive black holes has been considered as a crucial
mechanism driving galaxy evolution (e.g., Fabian, 2012; Crain & van de Voort,
2023, for a review). It is required to be included in simulations in order to
explain salient observed properties of galaxies, especially the massive end of
galaxy stellar mass function (e.g., Benson et al., 2003; Bower et al., 2006;
Croton et al., 2006; Hirschmann et al., 2014; Beckmann et al., 2017;
Kondapally et al., 2023). It is also a key component to reconcile the so-
called cooling flow problem (e.g., Cowie & Binney, 1977; Fabian & Nulsen,
1977), indicating that the gas in massive halos is expected to cool in a short
period based on the X-ray emission of hot gas and to condense into new stars —
a trend which is not observed. The energy output from the feedback mechanisms
has been treated as the main source to balance this gas cooling (Rafferty et
al., 2006; Nulsen et al., 2007; Hlavacek-Larrondo et al., 2012; Fabian, 2012;
McNamara & Nulsen, 2012). In other words, in the current galaxy formation
theory, feedback from supermassive black holes regulates the amount of gas in
and out of galaxies as well as maintains the thermal content of the
circumgalactic medium (CGM) (e.g., Tumlinson et al., 2017, for a review).

One line of evidence showing the impact of feedback on the CGM properties is
from observations of galaxy clusters, such as Perseus and Cygnus A, in X-ray
and radio wavelengths (e.g., Boehringer et al., 1993; Carilli et al., 1994;
Fabian et al., 2003; McNamara et al., 2005; Bîrzan et al., 2008; Gitti et al.,
2012; Pandge et al., 2019; Eckert et al., 2021). These observations
demonstrate that hot gas ($T\sim 10^{6}-10^{7}$ K) distribution in these
galaxy clusters is clearly affected by the radio jets from supermassive black
holes, the so-called radio-mode feedback (e.g., McNamara & Nulsen, 2012;
Heckman & Best, 2014; Hardcastle & Croston, 2020, for a review). Based on the
observations, the estimated required energy to create the cavity of hot gas
and the energy output from the radio-mode feedback are consistent with each
other. This indicates that radio-mode feedback from supermassive black holes
can prevent the cooling of the hot atmosphere, regulate the gas supply, and
indeed account for the quenching of massive galaxies. Recent galaxy
simulations and subgrid models incorporating radio-mode feedback have
successfully reproduced the observed luminosity function of massive galaxies
(e.g., Bower et al., 2006; Croton et al., 2006; Gabor et al., 2011; Davé et
al., 2012; Zinger et al., 2020).

While the influence of radio-mode feedback on the properties of the CGM has
been studied, the observations have mostly focused on (1) massive systems,
such as galaxy clusters ($M_{halo}>10^{14}M_{\odot}$), and (2) the hot gas
($T\geq 10^{6}$ K) properties via X-ray observations (e.g., McNamara & Nulsen,
2007). There are limited observational efforts probing relatively less massive
halos and the properties of the cool CGM ($T\sim 10^{4}$ K), which can also be
sensitive to radio-mode feedback and be a strong constraint on the
corresponding models (Huang et al., 2016; Smailagić et al., 2023).

To probe the cool CGM properties of galaxies with radio-mode feedback in
operation, one can utilize absorption line spectroscopy (e.g., Tumlinson et
al., 2017). That is, by constructing a sample of galaxies with radio emission
having bright sources, such as quasars, in the background with lines of sight
intercepting the CGM of the galaxies. However, the number of galaxies with
radio emission and with background quasars detectable by wide-field radio
surveys is rare. This limits the observational ability to probe the impact of
radio-mode feedback on the properties of the cool CGM, and only a limited
number of relevant studies (e.g., Kauffmann et al., 2017) to date.

In this work, we overcome this observational limitation by utilizing the large
optical spectroscopic dataset obtained by the Dark Energy Spectroscopic
Instrument (DESI) survey (DESI Collaboration et al., 2016a, 2022) and the
large source catalogs provided by two radio sky surveys, the LOFAR Two-metre
Sky Survey (LoTSS, Shimwell et al., 2017) and the Very Large Array Sky Survey
(VLASS, Lacy et al., 2020). Through this approach, we study the properties of
the cool CGM around massive galaxies, such as luminous red galaxies (LRGs),
with radio-mode feedback in action and compare the gas properties with that of
a control sample without radio emission. This adds a new parameter which has
not been extensively explored in previous studies of the properties of gas
around LRGs (e.g., Zhu et al., 2014; Huang et al., 2016; Lan & Mo, 2018; Anand
et al., 2021).

Combining radio emission signals with optical galaxy properties, we construct
a sample of radio galaxies with $z>0.4$ with background quasars as well as a
control sample without radio emission and measure the properties of the cool
CGM traced by MgII absorption lines $\rm\lambda\lambda~{}2796,2803\AA$, an
absorption line species which has been widely used to probe the CGM content
across cosmic time (e.g., Lanzetta et al., 1987; Nestor et al., 2005; Nielsen
et al., 2013; Zhu & Ménard, 2013a; Lan et al., 2014; Raghunathan et al., 2016;
Huang et al., 2016; Chen et al., 2017; Lan & Mo, 2018; Lan, 2020; Anand et
al., 2021; Zou et al., 2021; Anand et al., 2021, 2022; Zou et al., 2024), and
explore the correlation between the gas properties and the presence of radio
emission, a proxy of radio-mode feedback in action.

This paper is organized in the following way: Section 2 describes our sample
and data, and Section 3 presents how we obtain the properties of MgII
absorption lines. We show our results in Section 4 and discuss the implication
in Section 5. Section 6 summarizes the paper. Throughout the paper, we adopt a
Flat-$\Lambda$CDM cosmology with the following parameters: $\Omega_{\rm
m}=0.3~{}{\rm and}~{}H_{0}=70~{}{\rm km}~{}{\rm s}^{-1}~{}{\rm Mpc}^{-1}$.

Figure 1: Examples of LRG-QSO pairs with radio counterparts in LoTSS survey
(left) and VLASS (right).The upper panels are the optical images from the DESI
Legacy Imaging Surveys (Dey et al., 2019) and the lower panels are the radio
images from the two radio surveys. Figure 2: Examples of LRG-QSO pairs without
radio counterparts in LoTSS survey (left) and VLASS (right), i.e. the control
samples. The upper panels are the optical images from the DESI Legacy Imaging
Surveys (Dey et al., 2019) and the lower panels are the radio images from the
two radio surveys. Figure 3: Distributions of redshift, color, z band
magnitude, and w1 band magnitude (from left to right) for the experimental
group and the control group from the LoTSS catalog and the VLASS catalog. The
upper panel shows the properties of the LRGs from the LoTSS samples, while the
lower panel shows those of the LRGs from the VLASS. The red and blue lines
represent the radio groups and the control groups, respectively.

##  2 Data

###  2.1 DESI

The Dark Energy Spectroscopic Instrument (DESI) is mounted on the Mayall
4-meter telescope at Kitt Peak National Observatory (DESI Collaboration et
al., 2016a, b). It consists of 5000 fibers (Silber et al., 2023) with spectral
wavelength coverage ranging from $3600-9800{\rm\AA}$ and a resolution of
2000-5000 (DESI Collaboration et al., 2022; Guy et al., 2023). The
spectroscopic classifications and redshifts for each DESI source are
determined using the Redrock pipeline111https://github.com/desihub/redrock
(Bailey et al, in preparation, Brodzeller et al., 2023). The survey includes
dark-time and bright-time observations for different type of sources (Schlafly
et al., 2023). The bright time observations cover stars in our Milky Way
(Cooper et al., 2023) and bright galaxies (BGS, Hahn et al., 2023; Juneau et
al., 2024), while the dark time observations cover relative faint
extragalactic sources, including luminous red galaxies (LRGs, Zhou et al.,
2023), emission line galaxies (ELGs, Raichoor et al., 2023), and quasars
(Chaussidon et al., 2023).

The target selection scheme for the DESI sources (Myers et al., 2023) and the
corresponding redshift performance with the DESI observations have been tested
and validated during the survey validation (SV) phase, including observations
with long exposure times (Survey Validation 1, SV1) and observations covering
about one percent of the whole DESI survey (One-percent survey) (DESI
Collaboration et al., 2023a; Lan et al., 2023; Alexander et al., 2023). In
this work, we use the LRG and quasar data from SV (Early Data release, DESI
Collaboration et al., 2023b) and the first year of the main survey. The
cosmological constraints from the baryon acoustic oscillations measurements
with the DESI first year main survey data have been published (DESI
Collaboration et al., 2024a, b, c).

The DESI LRG survey: LRGs are massive passive galaxies selected based on their
colors and brightness with redshift range $0.3<z\leq 1.1$ (Zhou et al., 2023).
For our analysis, we select LRGs without any warning flag from the DESI
pipeline, ZWARN =
0222https://github.com/desihub/redrock/blob/main/py/redrock/zwarning.py and
with DELTACHI2 $\Delta\chi^{2}>15$, a difference of $\chi^{2}$ values the
between the second and first best-fit models, to ensure a robust redshift
estimation (Zhou et al., 2023; Lan et al., 2023). We further select LRGs with
$0.4<z<1.2$ to ensure that MgII absorption lines are within the DESI
wavelength coverage. The above selection leads to a sample of $\sim 2.2\times
10^{6}$ LRGs.

The DESI QSO survey: The DESI survey observes quasars selected with the random
forest algorithm across a wide redshift range from redshift 0.5 to beyond
redshift 2 (Chaussidon et al., 2023). Redshift $>2.1$ quasars are primarily
used as background light for probing the baryonic acoustic oscillation signals
via detecting Lyman alpha forest (e.g., Ramírez-Pérez et al., 2023). Low
redshift quasars can be used as direct tracers of matter distribution.
Similarly to the LRG selection, we apply the criteria ZWARN = 0 and DELTACHI2
$>15$ to select DESI QSOs, ensuring that we include only quasars with reliable
redshift measurements from the pipeline (Chaussidon et al., 2023; Alexander et
al., 2023). We also exclude quasars with spectral signal-to-noise lower than
1, a spectral quality too low to detect absorption lines. Our quasar sample
includes $\sim 1.2\times 10^{6}$ sources in total.

###  2.2 Radio catalogs

The LOFAR Two-meter Sky Survey: The LOFAR Two-meter Sky Survey (LoTSS,
Shimwell et al., 2017) is an ongoing radio wavelength (120-168 MHz) sky
survey, aiming to cover the entire northern sky. The angular resolution is
about $6\arcsec$ with sensitivity down to $\sim 70-100$ mJy. In this work, we
make use of the second data release of LoTSS, LoTSS-DR2 (Shimwell et al.,
2022), which covers approximately 27% of the northern sky with $\sim 4\times
10^{6}$ radio sources. LoTSS-DR2 sky coverage overlaps with the sky coverage
of the DESI survey in the northern sky, making the DR2 catalog a suitable
resource for identifying radio counterparts of the DESI galaxies.

VLASS Quick Look: The Karl G. Jansky Very Large Array Sky Survey (VLASS, Lacy
et al., 2020) aims to observe the entire northern sky of $\delta>-40^{\circ}$
with three epochs at $2~{}{\rm GHz}<\nu<4~{}{\rm GHz}$ frequency band with
$2.5\arcsec$ angular resolution. We use the VLASS data based on the quick look
(QL) imaging (Gordon et al., 2021) from the first two epochs at 3
GHz333https://cirada.ca/vlasscatalogueql0, including $\sim 3.5\times 10^{6}$
sources. The first two epochs of VLASS QL data exhibit a sensitivity
comparable to that of FIRST, $\sim 1$ mJy, and cover the entire VLASS
footprint.

##  3 Analysis

###  3.1 LRG-QSO Pairs

To study the CGM of radio galaxies, we construct a sample of radio-detected
DESI LRGs with background quasars. To this end, we utilize the radio-optical
crossmatch catalog for the LoTSS DR2 (Hardcastle et al., 2023) and match those
optical identifications and DESI LRGs with a $0.75\arcsec$ search radius
(Rosario et al., 2020). Additionally, we cross-match the LRGs with radio
sources in the VLASS quick-look catalogs using a 2.5″matching radius. Around
$14\%$ and $1.6\%$ of the DESI LRGs have detected radio counterparts in LoTSS
and VLASS, respectively. We note that the different detection fractions of
LoTSS and VLASS counterparts are due to the sensitivities of the two
surveys444LoTSS is $\sim 5$ times deeper than the VLASS when converting flux
at 3 GHz, assuming $\alpha=0.5$. We have used the radio flux-limited samples
(1 mJy for LoTSS and 3 mJy for VLASS) to perform the analyses, which yield
consistent results with the whole samples.. The impact parameter (projected
distance, $r_{p}$) of the galaxies and background quasar sightlines are within
1000 kpc. To avoid potential contamination of radio emissions from background
quasars, we only include systems with the distances between quasars and the
centers of radio emission being two times larger than the distances between
LRGs and the centers of radio emission.That is, $d_{qso}\geq 2\times d_{lrg}$,
where $d_{lrg}$ is the angular separation between the LRG and the radio source
associated with it and $d_{qso}$ is the separation between the QSO and the
associated radio source for the foreground LRG.

In order to isolate the effects of radio-mode feedback on the CGM properties
of radio galaxies, we create a set of control galaxies for LoTSS pairs and
VLASS pairs. For each DESI radio LRG in the LoTSS and VLASS catalogs, two and
four control LRGs are respectively selected based on the combined nearest
Euclidean distances of four optical properties: $z$-band flux, WISE W1 flux,
$g-r$ color, and redshift555Because of the limited number of sources in the
LoTSS footprint available for selection as the control group, which is only
one-sixth the size of the VLASS control group, adding more control galaxies
for each LoTSS LRG would lead to a mismatch in the distribution of optical
properties compared to the radio sample.. All the control galaxies are
required to have no radio detection from LoTSS or VLASS within $10\arcsec$.
For the LoTSS control sample, we select DESI LRGs located in the sky coverage
of the LoTSS DR2 footprint without detected radio emission, while for the
VLASS control sample, we select DESI LRGs without detected radio emission in
the DESI dataset given that the VLASS survey covers most of the DESI
footprint. For the final control samples, we remove duplicate control systems
selected more than one time from different radio-detected LRGs.

Figure 1 and 2 show examples of LRG-QSO pairs and their corresponding radio
counterparts for both the experimental groups and the control groups. Figure 3
shows the observed properties of the radio LRGs and the control samples,
demonstrating the two groups have similar optical properties. The main
difference is that the control galaxies do not have radio emission detected in
the corresponding surveys. We check the radio morphology for the radio-
detected LRGs. For the LoTSS-detected sources, we utilize Equation 2 from
Shimwell et al. (2022) to identify extended sources. For VLASS-detected
sources with peak flux$>$ 3mJy/beam, we find the extended source using the
deconvoluted-size criteria outlined in Gordon et al. (2021). Our final samples
include $\sim 8\%$ and $\sim 21\%$ of extended LRGs for LoTSS and VLASS,
consistent with the fraction for all the sources in both radio catalogs.

We also estimate the stellar masses of the LRGs by performing spectral energy
distribution fitting with $g$, $r$, $z$, and W1 fluxes using the CIGALE
(Boquien et al., 2019). To model the spectra and obtain the stellar properties
with the CIGALE, we use Bruzual & Charlot (2003) model and assume a Chabrier
(2003) initial mass function. The stellar mass distributions are shown in
Figure 4. The results show that stellar mass distributions between the radio
LRGs and their control galaxies are consistent with each other. We note that
the VLASS sample has a higher median stellar mass ($\sim 0.2$ dex) than the
LoTSS sample, which is due to the difference of the sensitivity between the
two surveys. The VLASS, with its shallower depth, primarily detects brighter
radio galaxies which tend to be more massive(Jarvis & McLure, 2002; Best et
al., 2005).

We further include the following selections to obtain clean spectral regions
for detecting MgII absorption lines associated with the LRGs:

  * •

To avoid the possible contamination of QSO-associated absorbers, the velocity
difference between LRGs and quasars is required to be $\delta v\geq
6,000~{}{\rm km/s}$ (Napolitano et al., 2023).

  * •

We exclude the spectral regions close to the CIV emission lines of quasars
with $\delta v\lesssim 10000{\rm km/s}$ to avoid broad CIV absorption
features.

  * •

We also exclude pairs with high redshift quasars with the wavelength region of
MgII absorption lines at the galaxy redshifts overlapping with the Lyman alpha
forests with $\delta v\lesssim 12000{\rm km/s}$.

Figure 4: Stellar mass distribution of our samples from CIGALE SED fitting.
The red lines show the distribution of the LRGs from the LoTSS samples, while
the blue lines show that of the LRGs form the VLASS samples. The dashed and
solid lines represent the control groups and radio groups, respectively.

[b]  QSO-LRG pairs within $r_{p}=1000$ kpc: 1279006 LoTSS VLASS Select radio-
detected and the control group radio LRGs 35720 21014 control group 48923a
77325b After excluding QSO-associated absorbers radio LRGs 35197 20629 control
group 48165 76025 After excluding region close to CIV emission lines radio
LRGs 31585 18601 control group 43301 68343 After excluding region within
Ly$\alpha$ forest radio LRGs 26949 16013 control group 37379 59017

Table 1: Number of pairs with all the selection cuts.

  * a

Two control galaxies with the closest optical properties to each LoTSS-
detected LRG are selected. LoTSS covers a much smaller area of the sky
compared to VLASS, leading to a limited number of unique control galaxies
selected.

  * b

Four control galaxies with the closest optical properties to each VLASS-
detected LRG are selected.

Table 1 summarizes the number of pairs after each selection criterion. The
final sample consists of 26949 and 16013 radio LRG-quasar pairs from LoTSS and
VLASS respectively and 37379 and 59017 LRG-quasar pairs as the control sample.
We note that 9802 pairs overlap between the LoTSS-selected and VLASS-selected
samples.

###  3.2 MgII absorbers

To detect absorption lines in quasar spectra, the first step is to estimate
the continuum intrinsic to the source. We follow the procedure applied in Zhu
& Ménard (2013a), utilizing the Non-negative Matrix Factorization (NMF) (Lee &
Seung, 1999; Zhu, 2016) method to estimate the quasar spectral energy
distribution with twelve NMF eigenspectra bases obtained in Zhu & Ménard
(2013a). We further apply a median filter with 85 pixels (Napolitano et al.,
2023) to remove the small-scale fluctuation on the normalized spectra.

With the normalized quasar spectra, we develop an automatic algorithm to
detect MgII absorption lines around LRGs with the following procedure:

  1. 1.

We use a matched filter method with a MgII doublet profile based on SDSS
composite spectra (Lan & Fukugita, 2017) and convolve the absorption line
profile with the pixel values of each normalized spectrum across velocity
window between -1000 km/s and 1000 km/s around the LRG rest-frame. We also
apply this calculation to the error arrays to estimate the uncertainty of the
convolved spectra.

  2. 2.

From the convolved spectra and the corresponding uncertainty, we identify
spectra with pixels having maximum S/N greater than 2 and consider the
velocity of the pixel with maximum S/N as the central velocity of the MgII
absorber candidate.

  3. 3.

We use a double Gaussian profile to fit the original normalized spectra at the
central velocities of MgII absorber candidates and measure the absorption line
properties, including MgII rest equivalent widths $W_{0,\lambda 2796,2803}$,
line widths, and the final best-fit central velocities of the MgII absorber
candidates as well as their corresponding uncertainties.

  4. 4.

Finally, we consider MgII absorber candidates with S/N of $W_{0,\lambda
2796}\geq 3$ and S/N of $W_{0,\lambda 2803}\geq 2$ as detected MgII absorption
lines.

Other absorption line species, such as FeII and CIV, can accidentally fall
within the search window and mimic the MgII absorption line signals. To remove
such possible contamination, we use the MgII line ratio ($R=W_{0,\lambda
2796}/W_{0,\lambda 2803}$) as the criterion. More specifically, we calculate
the line ratio distribution as a function of $W_{0,\lambda 2796}$, using the
DESI EDR MgII absorber catalog (Napolitano et al., 2023) as a reference. For a
given $W_{0,\lambda 2796}$, we remove MgII absorbers with the line ratio
values being outside of 0.135-99.865 percentile of the $R$ distribution from
DESI EDR MgII catalog. This removes approximately $3\%$ of the systems.

Our final LRG MgII absorber samples include 957 and 1318 absorbers selected
from LoTSS and VLASS catalogs, respectively. Approximately 400 and 300 of
these absorbers are associated with radio emissions from the LoTSS and VLASS.
The numbers are summarized in Table 2.

Figure 5: Covering fraction ($f_{c}$) as a function of impact parameter ($r_{p}$). The upper panels show the $f_{c}$ for LRGs from the LoTSS samples, while the lower panels show that for LRGs from the VLASS samples. The $f_{c}$ of weak and strong absorbers are depicted correspondingly in the left and right panels. The red and blue points represent the radio groups and control groups, respectively. The solid lines and dashed lines illustrate the best-fit results for $r_{p}\leq 400~{}{\rm kpc}$ and $r_{p}\leq 1000~{}{\rm kpc}$. Green lines show the $f_{c}$ of passive galaxies in Lan (2020). The upper limits are determined at a 3-sigma confidence level, and the errors are estimated based on binomial statistics (Gehrels, 1986). Table 2: The number of pairs used to detect MgII absorption lines and the identified absorbers in both experimental and control groups from each radio catalog. | Absorbers | LRG-QSO pairs
---|---|---
| LoTSS | VLASS | LoTSS | VLASS
Radio LRGs | 415 | 305 | 26949 | 16013
| $1.5\%$ | $1.9\%$ | $\cdots$ | $\cdots$
Control Group | 542 | 1013 | 37379 | 59017
| $1.5\%$ | $1.7\%$ | $\cdots$ | $\cdots$
Table 3: Number of detected MgII absorption lines with different spectral S/N cuts. The S/N cuts for absorbers with $0.4\leq W_{0,\lambda 2796}<1~{}{\rm\AA}$ and absorbers with $W_{0,\lambda 2796}\geq 1~{}{\rm\AA}$ are 6 and 2.5, respectively. Here we also show the number of all detected absorbers with a uniform S/N cut of 6. | S/N cuts by $W_{0,\lambda 2796}$ | All S/N $\geq 6$
---|---|---
| LoTSS | VLASS | LoTSS | VLASS
Radio Pairs | 264 | 215 | 234 | 177
Control Sample | 364 | 785 | 322 | 591
Table 4: Best-fit parameters for covering fraction $f_{c}$. | $r_{p}\leq 400~{}{\rm kpc}$
---|---
| LoTSS | VLASS
| $0.4\leq W_{0,\lambda 2796}<1~{}{\rm\AA}$
| $\gamma$ | ${\rm A}$ | $\gamma$ | ${\rm A}$
Radio LRGs | $-0.88\pm 0.74$ | $0.11\pm 0.11$ | -$0.57\pm 0.43$ | $0.12\pm 0.07$
Control Group | $-0.80\pm 0.39$ | $0.11\pm 0.05$ | $-0.81\pm 0.24$ | $0.12\pm 0.03$
| $W_{0,\lambda 2796}\geq 1~{}{\rm\AA}$
| $\gamma$ | ${\rm A}$ | $\gamma$ | ${\rm A}$
Radio LRGs | $-1.62\pm 0.27$ | $0.09\pm 0.02$ | $-0.85\pm 0.34$ | $0.09\pm 0.03$
Control Group | $-1.02\pm 0.24$ | $0.07\pm 0.02$ | $-1.03\pm 0.16$ | $0.08\pm 0.01$
| $r_{p}\leq 1000~{}{\rm kpc}$
| LoTSS | VLASS
| $0.4\leq W_{0,\lambda 2796}<1~{}{\rm\AA}$
| $\gamma$ | ${\rm A}$ | $\gamma$ | ${\rm A}$
Radio LRGs | $-0.63\pm 0.24$ | $0.08\pm 0.04$ | -$0.85\pm 0.19$ | $0.16\pm 0.07$
Control Group | $-0.99\pm 0.15$ | $0.14\pm 0.04$ | $-0.86\pm 0.10$ | $0.13\pm 0.03$
| $W_{0,\lambda 2796}\geq 1~{}{\rm\AA}$
| $\gamma$ | ${\rm A}$ | $\gamma$ | ${\rm A}$
Radio LRGs | $-1.09\pm 0.12$ | $0.09\pm 0.02$ | $-1.04\pm 0.16$ | $0.11\pm 0.03$
Control Group | $-0.87\pm 0.11$ | $0.06\pm 0.01$ | $-0.97\pm 0.07$ | $0.08\pm 0.01$
Table 5: Best-fit parameters for the number density distribution of $W_{0,\lambda 2796}$ for absorbers within $r_{p}\leq 400~{}{\rm kpc}$. | LoTSS | VLASS
---|---|---
| $W^{*}$ | $N^{*}$ | $W^{*}$ | $N^{*}$
Radio LRGs | $0.60\pm 0.19$ | $3.06\pm 1.61$ | $0.48\pm 0.14$ | $4.78\pm 2.64$
Control Group | $0.56\pm 0.10$ | $3.56\pm 1.19$ | $0.69\pm 0.09$ | $2.49\pm 0.53$

###  3.3 Completeness of the sample

The detectibility of absorption lines depends on the S/N of the quasar spectra
and the strengths of the absorption lines (Zhu & Ménard, 2013b; Anand et al.,
2021). The incompleteness due to undetected absorption lines affects the
estimation of intrinsic properties of MgII absorbers, including the incidence
rate around galaxies. To assess the effect of incompleteness and correct for
it, we perform Monte Carlo simulation by creating mock MgII absorption lines
as a function of $W_{0,\lambda 2796}$ and S/N of the spectra. The mock MgII
absorption profiles are based on a set of composite spectra built by stacking
MgII absorption lines detected in DESI year 1 quasar sample (Napolitano et al.
in prep.) with the pipeline developed by Napolitano et al. (2023). In the
simulations, we have also taken the DESI spectral resolution at different
redshifts into account. Finally, we estimate the detection rate ($\rm
N_{recovered}/N_{input}$) of MgII absorbers as a function of absorber
redshift, $W_{0,\lambda 2796}$, and S/N of the spectra. The details of the
detection rate are shown in the Appendix. The inverse of the detection rate is
used as a weight, $w$, to correct for the undetected absorbers due to the
noise of the spectra.

However, using the weights to recover the none-detection will reach its
limitation due to the fact that for spectra with too low S/N, one can not
detect any absorbers with $W_{0,\lambda 2796}$ below the noise level. To avoid
reaching such a limitation, we adopt a conservative selection. For $0.4\leq
W_{0,\lambda 2796}<1\rm\,\AA$, we only consider the detection from the
normalized spectra with $S/N\geq 6$ and for $W_{0,\lambda 2796}\geq
1\rm\,\AA$, we only consider the detection from the normalized spectra with
$S/N\geq 2.5$. These two threshold values are determined based on our
simulations showing that with such cuts, using weights to correct for the
undetected absorbers is effective. Finally, we summarize our samples with the
spectral S/N selections in Table 3. In the following, we define “weak”
absorbers as having $0.4\leq W_{0,\lambda 2796}<1\rm\,\AA$ and “strong”
absorbers as those with $W_{0,\lambda 2796}\geq 1\rm\,\AA$.

##  4 Results

###  4.1 MgII covering fraction

We first explore the radial distribution of gas traced by MgII absorption
lines around DESI radio LRGs and the control sample. To this end, we measure
the MgII covering fraction, $f_{c}$, indicating the probability of detecting
absorbers around galaxies with

$f_{c}=\frac{\sum_{i}^{N_{abs}}w_{i}}{N_{\rm quasars}},$ (1)

where $w_{i}$ is the weight for each detected absorber, $N_{abs}$ is the total
number of detected absorbers, and $N_{\rm quasar}$ is the total number of LRG-
QSO pairs for detecting MgII absorbers.

Figure 6: Best-fit slopes for covering fraction $f_{c}$. The left and right
panels illustrate outcomes specific to weak and strong absorbers. The circles
represent LRGs from the LoTSS samples, and the triangles represent those from
the VLASS samples. The blue, red, and green data show the results for the
control groups, radio groups, and galaxies from Lan (2020), respectively.

Figure 5 shows the $f_{c}$ as a function of ${\rm r}_{p}$ with two $W_{\lambda
2796}$ bins for strong ($W_{0,\lambda 2796}\geq 1\rm\,\AA$) and weak absorbers
($0.4\leq W_{0,\lambda 2796}<1\rm\,\AA$) with the upper and lower panels
indicating the results for DESI LRGs with LoTSS and VLASS respectively. The
red and blue data points show the $f_{c}$ measurements of radio galaxies and
the corresponding control sample respectively. As shown in Figure 5, the
covering fraction of strong and weak absorbers decreases with $r_{p}$ which is
consistent with the overall gas distribution traced by MgII absorbers around
galaxies (Zhu et al., 2014; Huang et al., 2016; Lan et al., 2014; Lan & Mo,
2018; Lan, 2020; Huang et al., 2021; Anand et al., 2021). Moreover, we
quantify the possible difference in cumulative distributions of the covering
fraction between the radio and the control samples with the Kolmogorov-Smirnov
test (KS test) in 2 dimensions (Peacock, 1983; Fasano & Franceschini,
1987)666https://github.com/Gabinou/2DKS, $W_{\lambda 2796}$ and $r_{p}$. The
p-values for the weak and strong absorbers for the LoTSS are 0.420 and 0.275,
respectively. For the VLASS, the p-value is 0.668 for the weak absorbers and
0.985 for the strong absorbers. These results indicate no detectable
difference in the $f_{c}$ between radio LRGs and the control galaxies for both
strong and weak absorbers around radio LRGs and the control sample.

To summarize the gas distribution, we use a power-law function,

$f_{c}=A\times\bigg{(}\frac{r_{p}}{100~{}{\rm kpc}}\bigg{)}^{\gamma},$ (2)

to describe the $f_{c}$ measurements for both $r_{p}\leq 400~{}{\rm kpc}$
(solid lines) and the extended range up to $r_{p}\leq 1000~{}{\rm kpc}$
(dashed lines), as illustrated in Figure 6. The best-fit parameters are
summarized in Table 4. Figure 6 shows the best-fit $\gamma$ values of the
covering fraction and the $\gamma$ values obtained in Lan (2020) within 600
kpc, demonstrating that the measurements within virial radius of dark matter
halos are consistent. The fitting result indicates that the $f_{c}$
distribution becomes flatter when considering gas distribution at larger
scales $r_{p}\leq 1000~{}{\rm kpc}$ for both weak and strong absorbers. This
behavior can be explained by the transition between one-halo and two-halo
terms of the matter distribution (e.g., Zhu et al., 2014).

Figure 7: Number density distribution of the rest equivalent widths
$W_{0,\lambda 2796}$ for absorbers with $r_{p}\leq 400$ kpc. The left and
right panels show the distributions, respectively corresponding to the
absorbers of LRGs from the LoTSS samples and the VLASS samples. The red and
blue colors represent the radio groups and the control groups, respectively.
The dashed lines are the best-fit exponential functions. Errors are the
confidence levels derived from Poison statistics (Gehrels, 1986).

###  4.2 Rest equivalent width distributions

Besides the covering fraction, we measure the number density distribution of
the rest equivalent width, $W_{0,\lambda 2796}$ (${\rm dN}/{\rm d}W_{0,\lambda
2796}$), around LRGs as shown in Figure 7. Here we only use systems with
quasar spectra $S/N>6$ to avoid incompleteness. To focus on absorbers
predominantly linked with halos, we display only those within $r_{p}\leq 400$
kpc. Following Zhu & Ménard (2013a), we adopt an exponential function, ${\rm
dN}/{\rm d}W_{0,\lambda 2796}~{}=~{}N^{*}~{}\times~{}e^{{-W_{0,\lambda
2796}/W^{*}}}$, to fit the $W_{0,\lambda 2796}$ number density distribution,
and our best-fit parameters are shown in Table 5. No significant difference is
found between the radio LRGs and the control samples for both LoTSS and VLASS,
with the KS test p-values 0.901 and 0.204777Here we used a nearly completed
sample of sources with S/N $\geq 8$ for the KS test., respectively. We note
that the shape of ${\rm dN}/{\rm d}W_{0,\lambda 2796}$ around LRGs with
$W^{*}\sim 0.55\pm 0.05$ is consistent with the shape of overall MgII
population from Zhu & Ménard (2013a) with $W^{*}\simeq 0.6$ at redshift $\sim
0.65$.

###  4.3 Gas kinematics

We now explore the gas kinematics of radio galaxies by investigating the line
of sight (LoS) velocity difference, $dv$, between the gas traced by MgII
absorption lines and the galaxies. The $dv$ distributions are shown in Figure
8, where we consider absorbers mostly bounded with the halos within $r_{p}\leq
400$ kpc. To quantify the possible difference between the $dv$ distributions,
we perform the KS test between the $dv$ distribution of radio LRGs and their
control sample. The calculation yields p-values of 0.507 for the LoTSS sample
and 0.061 for the VLASS sample respectively. This indicates that there is no
detectable difference in $dv$ distributions between the radio galaxies and
control groups from both LoTSS and VLASS. In addition, in Figure 8, we show
the $dv$ distribution from SDSS LRGs (Anand et al., 2021). The $dv$
distributions of the LoTSS samples are consitent with the SDSS LRGs while
distributions of the VLASS samples are broader than the distribution of SDSS
LRGs. We discuss the difference in Section 5.

We further measure the LoS velocity dispersion as a function of $r_{p}$. For
each $r_{p}$ bin, we use the median absolute deviation (MAD) scaled to the
standard deviation as an estimator for the LoS velocity dispersion and
estimate the corresponding errors by bootstrapping. We have subtracted the
instrumental resolution ($\sim 40~{}{\rm km/s}$) and redshift uncertainty of
LRGs ($\sim 50~{}{\rm km/s}$) in quadrature to measure the intrinsic velocity
dispersion of the gas. The results are illustrated in Figure 9, and Table 6
further shows the dispersion values for sources within $r_{p}\leq 400$ kpc and
$r_{p}>400$ kpc. We find that the measurements around radio LRGs and the
control samples are consistent with each other. For the gas in the inner
region ($r_{p}\leq 400~{}{\rm kpc}$), the radio LRGs and the control samples
from both LoTSS and VLASS have a lower velocity dispersion ($\sigma\sim
200-300$ km/s), similarly to the results in previous studies (Zhu et al.,
2014; Lan & Mo, 2018), while at larger scales, gas exhibits a higher velocity
dispersion, reaching $\sim 500{\rm km/s}$. This behavior is consistent with
the contribution from Hubble flow at larger scales.

Figure 8: Distribution of the light-of-sight gas-galaxy velocity difference ($dv$) of the LRG within $r_{p}\leq 400$ kpc. The left panel displays the $dv$ distribution of LRGs from the LoTSS samples, and the right panel shows that of LRGs from the VLASS samples. The red and blue lines correspondingly represent the radio groups and control groups. We also show the distribution of passive galaxies in Anand et al. (2021). Figure 9: Gas velocity dispersion as a function of impact parameter. The left and right panels show the results of LoTSS and VLASS LRGs respectively. The red, blue, and green points represent the radio LRGs, control groups, and the passive galaxies from Zhu et al. (2014); Lan & Mo (2018), respectively. The velocity dispersion obtained in this work is estimated using MAD scaled to the standard deviation. Table 6: Gas velocity dispersion of our samples separated with two impact parameter bins. |  $r_{p}\leq 400$ kpc |  $r_{p}>400$ kpc
---|---|---
| LoTSS | VLASS | LoTSS | VLASS
| [km/s] | [km/s] | [km/s] | [km/s]
Radio LRGs | $289\pm 58$ | $313\pm 72$ | $480\pm 38$ | $445\pm 45$
Control Group | $231\pm 42$ | $279\pm 27$ | $494\pm 47$ | $426\pm 30$
Figure 10: Comparison of the covering fraction ($W_{0,\lambda
2796}>0.4\rm\,\AA$) with previous studies. The blue points, orange points,
purple band, and green band are the $f_{c}$ for the LRGs from our LoTSS
samples, our VLASS samples, Anand et al. (2021), and Lan & Mo (2018),
respectively. The data from Anand et al. (2021) and Lan & Mo (2018) are scaled
to an equivalent redshift of 0.7 using evolution trend from Lan (2020).

##  5 Discussion

###  5.1 Comparison with previous studies

We compare our measurement of $f_{c}$ ($W_{0,\lambda 2796}>0.4\,\rm\AA$) of
radio-detected LRGs with the measurements of SDSS LRGs from Lan & Mo (2018)
and Anand et al. (2021) in Figure 10. Overall, the decreasing trends of
$f_{c}$ are consistent with each other with similar slopes. As DESI and SDSS
adopt different criteria for selecting LRG samples, which yield different
stellar mass and redshift distributions, we scale the SDSS measurement using
the evolution trend based on Lan (2020). If we consider the median redshifts
of SDSS LRGs ($z\sim 0.5$) and radio-detected LRGs ($z\sim 0.7$) in this work,
the redshift evolution of $f_{c}$ of strong absorbers will yield
$\bigg{(}\frac{1+0.7}{1+0.5}\bigg{)}^{2.5}\sim 1.4$ As illustrated in Figure
10, after adjusting for evolution, the $f_{c}$ of the SDSS LRGs from Lan & Mo
(2018) and Anand et al. (2021) is consistent with that of the radio-detected
LRGs from DESI at a given impact parameter.

In addition to the covering fraction, we observe a larger gas velocity
dispersion at larger scales, as compared to the measurement from Zhu et al.
(2014) (Figure 9). This difference is possibly due to the approaches used to
calculate the velocity dispersion. Zhu et al. (2014) measure the velocity
dispersion from the composite spectra via stacking analysis, Together with a
median filtering for spectral processing, this method might mediate the signal
far from the line center. We note that using a similar approach as adopted in
this work, Anand et al. (2021) also find a larger velocity dispersion for gas
of LRGs in the outer region.

Figure 11: Velocity dispersion as a function of stellar masses. The blue data
represents both the radio LRGs and the corresponding control galaxies from the
LoTSS catalog, while the orange data represents that from the VLASS catalog.
The blue and orange bands show the dispersion for all sources selected with
LoTSS and VLASS. The filled points are the results from high-mass sources,
while the open points are those from low-mass sources. The term ‘low-mass
sources’ and ‘high-mass sources’ refer to those with stellar mass above and
below the median of the samples, which is $10^{11.2}~{}M_{\odot}$ for LoTSS
and $10^{11.4}~{}M_{\odot}$ for VLASS.

Finally, among our own measurements, we quantify the potential differences
between all the radio and the control LRGs selected with the LoTSS and the
VLASS, regardless of whether it has radio emission or not. The gas velocity
dispersion888Similar to Figure 9, the dispersion shown in this section is
estimated using MAD scaled to the standard deviation. of LRGs in the inner CGM
($<200$ kpc) for LoTSS samples is $211\pm 32~{}{\rm\,km/s}$, while that for
the VLASS samples is $303\pm 38~{}{\rm\,km/s}$, as illustrated by the blue and
red band in Figure 11. The inner gas around radio-detected LRGs and control
LRGs from VLASS exhibits higher velocity dispersion compared to those from
LoTSS. This difference in gas properties can be explained by the stellar mass
difference of the two samples. In Figure 11, we divide the sample based on
their median stellar mass, $\sim 10^{11.2}~{}M_{\odot}$ and $\sim
10^{11.4}~{}M_{\odot}$ for LoTSS and VLASS, into high-mass and low-mass
sources. The figure indicates that the gas dispersion for the absorbers around
high-mass LRGs (stellar mass above the median value) from VLASS-selected
samples is apparently higher than the others. Additionally, LRGs with
comparable stellar masses ($\sim 10^{11}-10^{11.4}$), for LoTSS-selected
sources and low-mass VLASS-selected sources, display similar gas dispersion in
their CGM. We note that the absorbers beyond $r_{p}=400$ are affected by the
haloes of other nearby galaxies, and their velocity dispersion is not strongly
correlated with the stellar mass.

As shown in Figure 4, the median stellar mass of the VLASS samples is $\sim
0.2$ dex higher than that of the LoTSS samples. This 0.2 dex difference in the
median stellar mass yields a larger difference in halo mass at the high mass
end. Based on the stellar-to-halo mass relation (SHMR) from Girelli et al.
(2020), the estimated halo mass difference between the two samples can reach
$\sim 0.5$ dex. If we assume the typical halo mass of the LoTSS sample is
similar to the overall DESI LRG population $10^{13.4}\,M_{\odot}$ (e.g., Yuan
et al., 2023), the typical halo mass of the VLASS sample will be about
$10^{13.9}\,M_{\odot}$. Their corresponding dark matter velocity dispersion
values are $\sim 270$ and $\sim 400$ km/s based on Elahi et al. (2018). This
yields a similar sub-virial gas motion $\frac{\sigma_{gas}}{\sigma_{DM}}\sim
0.75$ within 200 kpc around VLASS and LoTSS samples. We note that this value
is higher than previous measurements around SDSS LRGs
($\frac{\sigma_{gas}}{\sigma_{DM}}\sim 0.5$). We will explore such a
difference in the future with the entire DESI LRG sample. The differences in
gas kinematics illustrated in Figure 8 between LoTSS-selected and VLASS-
selected sources could also be influenced by the disparities in stellar masses
of the two samples. Additionally, the properties of the VLASS samples are
consistent with the measurements of galaxy clusters, showing that the CGM in
clusters traced by MgII has a higher covering fraction and velocity dispersion
(e.g., Cherrey et al., 2023; Anand et al., 2022).

###  5.2 CGM mass around radio galaxies

With the covering fraction obtained in Section 4.1, we can quantify the
typical amount of cool HI gas around the radio-detected LRGs. We estimate the
mass of neutral hydrogen traced by MgII absorbers residing in the CGM with

$M_{\rm HI}(<400\,\rm kpc)\sim 2\pi\,m_{\rm
H}\int_{10\rm\,kpc}^{400\rm\,kpc}\hat{N}_{\rm HI}\,f_{c}(r_{p})r_{p}dr_{p},$
(3)

where $\hat{N}_{\rm HI}$ is the empirical relation between $W_{0,\lambda
2796}$ and $N_{HI}$ from Lan & Fukugita (2017),

$\hat{N}_{\rm HI}=10^{18.96}\left(\frac{W_{0,\lambda
2796}}{1\,\rm\AA}\right)^{1.69}(1+z)^{1.88}\,\rm cm^{-2}.$ (4)

The median value of samples $z\sim 0.67$ is adopted. For weak absorbers, we
take the median value of our MgII absorbers $W_{0,\lambda 2796}\sim
0.65\rm\,\AA$ and for strong absorbers, we take the median value $W_{0,\lambda
2796}\sim 1.5\,\rm\AA$. The final estimated $M_{HI}$ for LRGs with LoTSS is
$9.9\times 10^{9}~{}{\rm M_{\odot}}$ and for LRGs with VLASS is $1.3\times
10^{10}~{}{\rm M_{\odot}}$. Given that the covering fractions around control
samples are consistent with the radio LRGs, the control samples have similar
mass of neutral hydrogen within 400 kpc. The excess of gas may originate from
thermal instabilities in the halos of LRGs (Huang et al., 2016; Nelson et al.,
2020), star-forming satellite galaxies within the LRG halos and their
neighboring halos (Hafen et al., 2019; Lan, 2020), as well as gas accreting
through filaments (Kereš et al., 2009; Huang et al., 2016).

This result indicates that there is a non-negligible amount of cool neutral
gas around massive galaxies with possible radio-mode feedback in action. This
mass measurement can place constraints on the models of feedback in
simulations. For example, Khrykin et al. (2023) use the SIMBA simulations
(Davé et al., 2019) to explore the impact of various feedback models on the
CGM properties and find that including radio-mode feedback reduces the amount
of baryons in the CGM by a factor of 5 in halo mass $\sim 10^{13}\,M_{\odot}$,
while only reducing by a factor of 2 as the halo mass increasing to $\sim
10^{13.5}\,M_{\odot}$. For another example, Zinger et al. (2020) show that
radio-mode feedback changes the thermal properties of the CGM by enhancing the
entropy and thereby increasing the gas cooling time. The properties of the
cool gas are expected to be affected as well. As summarized in Crain & van de
Voort (2023), adopting different assumptions and subgrid recipes of AGN
feedback, the state-of-the-art simulations predict different amount of baryons
in the halos. From these simulations, one can estimate the amount of cool
neutral gas around radio galaxies, compare with the measurements reported in
this work, and test those feedback models. Furthermore, our gas dispersion
measurements could also constrain the gas outflow and their initial velocity
for the feedback models (Nelson et al., 2019; Lan & Mo, 2019; Mitchell et al.,
2020).

###  5.3 Impact of the radio jets

From the X-ray and radio observations showing the interaction between radio
jets and hot gas, one would expect that as they propagate, radio jets impact
the surrounding medium. However, our results show no discernible differences
between the properties of the cool CGM of galaxies with and without radio
emission. Unlike the hot CGM, radio-mode feedback might not produce detectable
effects on the properties of the cool CGM with our current sample. In the
following, we discuss two possible scenarios for such a result.

Time and Distance Scales: The majority of our radio sources do not have an
extended radio emission structure. It is possible that the radio-mode feedback
just starts its operation. Therefore, the radio jets do not have sufficient
time to propagate into larger scale ($\sim 100\,\rm kpc$) (e.g, Hardcastle et
al., 2019). To comprehensively analyze gas properties for galaxies with
various radio morphologies, more extensive radio surveys are required. These
surveys should feature resolution and sensitivity sufficient to distinguish
small extended structures and detect low surface brightness sources.

Another possibility is that the power of feedback and/or the duration of
feedback is not strong and long enough to propagate into larger scales. For
radio galaxies with stellar masses around or above $10^{11}~{}{\rm
M_{\odot}}$, their typical active period spans 10-100 Myr (e.g., McNamara &
Nulsen, 2012; Turner & Shabala, 2015) and their jets can on average span tens
of kpc, with the rare bright ones possibly extending to $\sim 200-300$ kpc or
even larger (e.g., Turner & Shabala, 2015; Hardcastle et al., 2019; Lan &
Prochaska, 2021). Given that we only have a handful of sightlines probing the
inner CGM, the effect of radio-mode feedback might be below the noise level of
the current measurements.

Opening angle: While powerful radio jets can extend to several hundred kpc,
the typical observed jet structures are asymmetric with certain direction
(e.g., Hardcastle & Croston, 2020), being consistent with the unified model of
AGNs (Urry & Padovani, 1995; Netzer, 2015; Padovani et al., 2017). For
example, based on the observations from the Monitoring Of Jets in Active
galactic nuclei with VLBA Experiments (MOJAVE)
program999https://www.cv.nrao.edu/MOJAVE/index.html, the radio jets typically
have relatively small opening angles with a median value of around
$20^{\circ}$ (Pushkarev et al., 2017). Given the small opening angles, the
background lines of sight may not intercept with the most affected regions by
the radio jets. This will dilute the signals and prevent us from detecting the
impact of radio jets with a limited number of sightlines in the inner CGM.

DESI is going to observe $\sim 8$ million LRGs (Zhou et al., 2023) and $\sim
3$ million QSOs (Chaussidon et al., 2023) during its five-year mission. In its
first year of the main survey, DESI has already observed $\sim 3.5$ million
LRGs and $\sim 1.5$ million QSOs. It is anticipated that the number of known
LRG-QSO pairs will triple after DESI completes its operation, with the number
of their radio counterparts also expected to increase by approximately
threefold. With such a large number of LRG-QSO pairs, we will be able to
conduct a more comprehensive study of the relationship between radio jets and
the CGM of LRGs.

##  6 Conclusions

We investigate how radio-mode feedback impacts the properties of the cool CGM
traced by MgII absorbers. To this end, we constructed two large samples of
$\sim 30,000$ radio LRGs and background QSO pairs using the latest DESI
spectroscopic measurements and two large radio source catalogs from LoTSS and
VLASS. We also built two corresponding control galaxy samples that match the
host galaxy properties of the radio LRGs but without detected radio emission.
With these datasets, we measured and compared the CGM properties around radio
LRGs and their control samples and explored possible signals correlating with
the presence of radio emission.

Our results show no significant differences between the properties of the cool
CGM of radio LRGs and their control samples, including the gas radial
distribution, MgII rest equivalent width distributions and the gas kinematics.
This result indicates that there is no detectable correlation between the
presence of radio emission and the cool CGM properties. Among the LRG samples,
we find that the gas velocity dispersion around radio LRGs in VLASS is higher
than that around radio LRGs in LoTSS. This can be explained by the fact that
radio LRGs in VLASS on average have higher stellar masses and therefore prefer
to live in more massive halos. Finally, we estimate the amount of cool gas
mass in the CGM of radio LRGs being approximately $10^{10}M_{\odot}$ — a none-
negligible amount of cool gas reservoir. These novel measurements can be used
as strong observational constraints on the models of AGN feedback adopted in
simulations, providing valuable insights into the impact of radio-mode
feedback on baryon distribution around galaxies and the growth of massive
galaxies.

In the near future, combining the updated versions of the LoTSS and VLASS
catalogs, as well as upcoming deeper and wider sky surveys from the Square
Kilometre Array (SKA, Braun et al., 2015) and the next generation VLA (ngVLA,
Di Francesco et al., 2019) with optical large spectroscopic datasets,
including the complete 5-year DESI dataset, we will be able to increase the
sample size by at least a factor of 2 and obtain more precise measurements of
the CGM properties of radio galaxies. With such measurements, one will
possibly reveal the signatures of radio-model feedback on the cool CGM for the
first time and thereby test the current models of AGN feedback and galaxy
evolution.

## Data Availability

All data points shown in the figures are available in a machine-readable form
on Zenodo https://doi.org/10.5281/zenodo.11143902.

## Ackowledgments

We thank Vicky Fawcett and Siwei Zou for their constructive comments that
greatly helped improve the paper. YLC and TWL were supported by the National
Science and Technology Council (MOST 111-2112-M-002-015-MY3), the Ministry of
Education, Taiwan (MOE Yushan Young Scholar grant NTU-110VV007,
NTU-110VV007-2, NTU-110VV007-3), National Taiwan University research grant
(NTU-CC-111L894806, NTU-CC-112L894806, NTU-CC-113L894806). YLC is supported by
NSTC 112-2811-M-002-059.

This material is based upon work supported by the U.S. Department of Energy
(DOE), Office of Science, Office of High-Energy Physics, under Contract No.
DE–AC02–05CH11231, and by the National Energy Research Scientific Computing
Center, a DOE Office of Science User Facility under the same contract.
Additional support for DESI was provided by the U.S. National Science
Foundation (NSF), Division of Astronomical Sciences under Contract No.
AST-0950945 to the NSF’s National Optical-Infrared Astronomy Research
Laboratory; the Science and Technology Facilities Council of the United
Kingdom; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation;
the French Alternative Energies and Atomic Energy Commission (CEA); the
National Council of Science and Technology of Mexico (CONACYT); the Ministry
of Science and Innovation of Spain (MICINN), and by the DESI Member
Institutions: https://www.desi.lbl.gov/collaborating-institutions. Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views
of the U. S. National Science Foundation, the U. S. Department of Energy, or
any of the listed funding agencies.

The authors are honored to be permitted to conduct scientific research on
Iolkam Du’ag (Kitt Peak), a mountain with particular significance to the
Tohono O’odham Nation.

LOFAR data products were provided by the LOFAR Surveys Key Science project
(LSKSP; https://lofar-surveys.org/) and were derived from observations with
the International LOFAR Telescope (ILT). LOFAR (van Haarlem et al. 2013) is
the Low Frequency Array designed and constructed by ASTRON. It has observing,
data processing, and data storage facilities in several countries, which are
owned by various parties (each with their own funding sources), and which are
collectively operated by the ILT foundation under a joint scientific policy.
The efforts of the LSKSP have benefited from funding from the European
Research Council, NOVA, NWO, CNRS-INSU, the SURF Co-operative, the UK Science
and Technology Funding Council and the Jülich Supercomputing Centre.

The National Radio Astronomy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. CIRADA is funded by a grant from the Canada Foundation for Innovation
2017 Innovation Fund (Project 35999), as well as by the Provinces of Ontario,
British Columbia, Alberta, Manitoba and Quebec.

##  Appendix A Detection Rate Simulation

We simulated the detection rate using mock absorption lines to calibrate the
number of detected weak absorbers found in realistic QSO spectra with low S/N.
Figure 12 illustrates the detection rate of MgII absorbers as a function of
absorber redshift, $W_{0,\lambda 2796}$, and S/N of the spectra. More details
about the completeness of our absorption samples are shown in section 3.3.

Figure 12: Detection rate of MgII absorbers as a function of absorber
redshift, $W_{0,\lambda 2796}$, and S/N of the spectra. The left to right
panels show the results for redshift bins 0.4, 0.6, and 0.8, respectively. The
different colors represent various rest equivalent widths for the mock
spectra. The vertical dashed lines represent the spectral S/N cut for weak
absorbers ($0.4<W_{0,\lambda 2796}<1\rm\,\AA$).

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