# Observational predictions for the survival of atomic hydrogen in simulated
Fornax-like galaxy clusters

Avinash Chaturvedi<EMAIL_ADDRESS>Leibniz-Institut für Astrophysik
Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany  European
Southern Observatory, Karl-Schwarzschild-Straße 2, ,85748 Garching, Germany
Stephanie Tonnesen Center for Computational Astrophysics, Flatiron Institute,
162 5th Ave, New York, NY 10010, USA  Greg L. Bryan Department of Astronomy,
Columbia University, 550 W 120th Street, New York, NY 10027, USA  Center for
Computational Astrophysics, Flatiron Institute, 162 5th Ave, New York, NY
10010, USA  Gergö Popping European Southern Observatory, Karl-Schwarzschild-
Straße 2, 85748 Garching, Germany  Michael Hilker European Southern
Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany  Paolo Serra
INAF – Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047
Selargius (CA), Italy  Shy Genel Center for Computational Astrophysics,
Flatiron Institute, 162 5th Ave, New York, NY 10010, USA

###### Abstract

The presence of dense, neutral hydrogen clouds in the hot, diffuse intra-group
and intra-cluster medium is an important clue to the physical processes
controlling the survival of cold gas and sheds light on cosmological baryon
flows in massive halos. Advances in numerical modeling and observational
surveys means that theory and observational comparisons are now possible. In
this paper, we use the high-resolution TNG50 cosmological simulation to study
the HI distribution in seven halos with masses similar to the Fornax galaxy
cluster. Adopting observational sensitivities similar to the MeerKAT Fornax
Survey (MFS), an ongoing HI survey that will probe to column densities of
$10^{18}$ cm-2, we find that Fornax-like TNG50 halos have an extended
distribution of neutral hydrogen clouds. Within one virial radius, we predict
the MFS will observe a total HI covering fraction around $\sim$ 12% (mean
value) for 10 kpc pixels and 6% for 2 kpc pixels. If we restrict this to gas
more than 10 half-mass radii from galaxies, the mean values only decrease
mildly, to 10% (4%) for 10 (2) kpc pixels (albeit with significant halo-to-
halo spread). Although there are large amounts of HI outside of galaxies, the
gas seems to be associated with satellites, judging both by the visual
inspection of projections and by comparison of the line of sight velocities of
galaxies and intracluster HI.

Atomic hydrogen – TNG50 – MeerKat Fornax survey – Intra-cluster– Covering
fraction

##  1 Introduction

The formation and evolution of galaxies is now understood to be strongly
linked with the diffuse gas filling their dark matter halos. Depending on
galaxy mass, this gas is called the circumgalactic medium (CGM) when the gas
resides in the halos of galaxies of the Milky Way mass or lower, or the
intracluster medium (ICM) for gas living in more massive cluster-sized halos
($\rm M_{tot}$ $\gtrsim$ 1014 M⊙). Various physical processes, such as gas
accretion from the intergalactic medium, and feedback driven by stars and AGN,
occur in this gaseous halo. These processes drive flows which regulate the
rate at which gas cools on to the galaxy itself, controlling the amount of
mass in the interstellar medium and hence the rate of star formation itself,
including possibly quenching (see Tumlinson et al., 2017, for a review).
Therefore, understanding the physical processes in the CGM or ICM is crucial
to building a comprehensive picture of galaxy evolution. We highlight here the
important question of the origin and survival of cold gas in the hot ICM, by
studying the phase-space distribution of cold gas in massive halos at low
redshift, with a particular focus on the observability of this gas in ongoing
and future HI surveys.

For low-mass, star-forming galaxies, it is expected that their halo can host
an abundant amount of cold gas that may be the fuel for future star formation.
The halos of massive galaxies, on the other hand, may lack cold gas, resulting
in the lack of any recent star formation activity (Gauthier & Chen, 2011). In
addition, current observational (Chen et al., 2018; Berg et al., 2019; Zahedy
et al., 2019) and simulation studies (Davé et al., 2020; Rahmati et al., 2015;
Nelson et al., 2020) suggest that at intermediate redshift (0.3 $\leq$ z
$\leq$ 0.8), massive halos have a significant amount of cold gas. For example,
Chen et al. (2018); Zahedy et al. (2019) studied luminous red galaxies (LRG)
at redshift z $\sim$ 0.21-0.55 and found that these galaxies host a high
column density of the cold gas tracers HI and MgII. Other similar studies
point toward the same conclusion that LRGs host an abundant amount of cold gas
(Zhu et al., 2014; Lan & Mo, 2018; Anand et al., 2021, 2022). At low-redshift,
simulation studies of Milky Way-like galaxies show that their CGM also host
substantial amounts of cold gas (van de Voort et al., 2019).

Recently, simulations have made improved predictions for the cold gas
distribution in halos that reproduce many of the observed galactic properties.
For example, Nelson et al. (2020) have shown that cold gas in the halos of
LRGs can be attributed to the thermal instability triggered by local density
perturbations. They suggest that these perturbations are related to gas
stripped from infalling galaxies via tidal interactions, or ram pressure
stripping. Performing a comparative study between cosmological and idealized
simulations (individual galaxy halo simulations), Fielding et al. (2020) have
also shown that cold gas extends to the virial radius for Milky Way-mass
halos. They also suggest that non-spherical accretion and satellite galaxies
contribute to the cold gas content in the outer halos. Previously,
Villaescusa-Navarro et al. (2018) performed a detailed study using the
Illustris TNG100 simulation, investigating the HI abundance and clustering
properties in halos for z $\leq$ 5\. They showed that HI density profiles are
sensitive to various processes such as AGN feedback and tidal stripping. For
massive halos, they found that HI is mostly concentrated in their satellite
galaxies, whereas for small halos it is concentrated in the central galaxy.

In contrast to intermediate redshifts, the study of cold gas in the ICM of
massive halos ($\rm M_{*}$ $\geq 10^{11}$ $\rm M_{\odot}$) in the local
Universe (z $\sim$ 0) is limited to a few studies. Nonetheless, using the HI
21 cm emission line, radio observations have demonstrated the abundant
existence of cold neutral atomic gas around early-type galaxies (E/S0)
galaxies (Serra et al., 2012, 2013b; Young et al., 2014; Serra et al., 2013a).
However, these observations are limited to tens of kpc around the targeted
galaxies and are typically not sensitive to HI column densities below $\leq$
$10^{19}$ $\rm cm^{-2}$, and therefore do not provide a comprehensive picture
of the cold gas in the ICM.

The ongoing observations from the MeerKAT Fornax survey (hereafter MFS, Serra
et al., 2019, 2023), a radio continuum and line survey of the Fornax cluster,
provides an excellent opportunity to study the HI gas in great detail in the
nearby Fornax ICM (d $\sim$ 20 Mpc). Photometric and spectroscopic studies
(Cantiello et al., 2020; Chaturvedi et al., 2022) have shown that the Fornax
cluster mass assembly is still ongoing, making it an interesting target to
study. MFS is dedicated to studying the HI distribution and kinematics within
the Fornax environment. The HI column density sensitivity of the MFS ranges
from $\sim$5$\times 10^{19}$ cm-2 at a spatial resolution of $\sim$10 arcsec
($\sim$1 kpc at Fornax distance) down to $10^{18}$ cm-2 at $\sim$100 arcsec
($\sim$10 kpc at Fornax distance). With a mosaic area of the 12 square
degrees, MFS will detect HI in the Fornax intracluster (hereafter IC) region -
which in this paper refers to the region within the massive dark matter halo
and outside satellite galaxies.

The high-resolution TNG50 cosmological simulations (Nelson et al., 2019;
Pillepich et al., 2019) provide a median spatial resolution of $\sim$100
parsec and its validation of cold gas (neutral and molecular hydrogen) against
observational work (Popping et al., 2019; Diemer et al., 2019) makes TNG50 an
ideal framework to explore the cold gas distribution in Fornax-like halos.
This also provides a chance to forecast the upcoming MFS survey results and
test the simulations against the MFS observations. In this work, we use the
TNG50 simulations (Nelson et al., 2019; Pillepich et al., 2019) and adopt the
observing criteria of the MFS to study the HI content in the TNG50 halos
similar to the Fornax galaxy cluster. We also study the HI distribution in
these halos and their IC region. We calculate the HI covering fraction for
these halos and predict the expected observed MFS HI covering fraction.

In addition, both the spatial and velocity distribution of HI gas in the ICM
of clusters and groups can be used to gain insight into the origin and
survival of this cold gas. If the gas is correlated in both position and
velocity with satellites, we can argue that the HI is likely either stripped
from satellites or cooling is induced by satellites. However, if cold gas is
not correlated with satellite galaxy positions or velocities, we might argue
that either cold gas formation is related to the central galaxy or that cold
gas survives in the ICM long enough to become virialized (e.g., Voit et al.,
2017; Rohr et al., 2023). In this paper we take the first step of making these
spatial and velocity maps, leaving gas particle tracking to future work.

The paper is organized as follows: In section 2, we briefly introduce the
TNG50 simulation and present the methodology for calculating the HI covering
fraction. Section 3 presents our results about the HI distribution and its
covering fraction. In section 4, we compare our results to current simulation
(Section 4.1) and observational (Section 4.2) studies, and discuss the likely
origin of the cold gas in the intracluster medium of Fornax-like halos
(Section 4.3). Section 5 presents the summary of the work.

##  2 Simulation and Methodology

This section briefly introduces the TNG50 simulation that we use for our
analysis as well as our criteria for selecting Fornax-like halos. In addition,
we present our methodology for calculating the HI column density and HI
covering fraction of the selected halos in TNG50 in order to compare to
observational surveys.

###  2.1 The TNG simulations

For our study, we use the TNG50 simulation (Nelson et al., 2019; Pillepich et
al., 2019), the highest resolution simulation of the IllustrisTNG cosmological
magneto-hydrodynamical (MHD) simulation suite (Nelson et al., 2018; Springel
et al., 2018; Pillepich et al., 2018; Marinacci et al., 2018; Naiman et al.,
2018). The IllustrisTNG project is a set of large cosmological simulations
that include a variety of galaxy formation physics including AGN feedback. The
model has been designed to match a wide range of observational constraints
(Pillepich et al., 2018; Springel et al., 2018) and was carried out with the
moving mesh code AREPO (Springel, 2010). The AREPO code solves the coupled
evolution of dark matter, gas, stars, and black holes under the influence of
self-gravity and ideal MHD. Developed with the key motivation to study galaxy
formation physics and understand the growth of cosmic structure physics, the
IllustrisTNG project uses three distinct simulation box sizes.

TNG50 was carried out with a box size of 51.7 Mpc per side with $2160^{3}$ gas
and dark matter cells, resulting in a baryon mass resolution of $8.4\times
10^{4}$ $\rm M_{\odot}$. In particular, we used TNG50-1 (hereafter TNG50), the
highest resolution of the three variants run, which provides a median spatial
resolution of $\sim$100 pc. We analyze this run, although the other larger
boxes (TNG100 and TNG300) contain a larger number of Fornax cluster-sized
objects, because we need high spatial resolution to study the interaction of
cold high density columns and the hot group medium. TNG50 adopts initial
conditions and cosmological parameters consistent with the Planck
Collaboration et al. (2016) cosmology with $h=0.68$, $\Omega_{b}$ = 0.05,
$\Omega_{m}$ = 0.31, $\Omega_{\lambda}$ = 0.69, and $\sigma_{8}$ = 0.82 and
assuming a flat universe governed by a $\Lambda$ cold dark matter
($\Lambda$CDM) cosmology.

Table 1: TNG50 halos similar to the Fornax galaxy cluster

TNG50 Halo ID | Virial Mass ($M_{200}$) | Virial radius ($R_{200}$) | Total HI mass | Central galaxy vel. dispersion | Halo members vel. dispersion
---|---|---|---|---|---
| Log M⊙ | ($\times$ 100 kpc) | Log M⊙ | km/s | km/s
1 | 13.97 | 9.59 | 10.80 | 384.24 | 446.20
2 | 13.81 | 8.46 | 10.37 | 373.80 | 402.12
3 | 13.54 | 6.92 | 11.24 | 306.22 | 321.83
4 | 13.50 | 6.71 | 11.07 | 204.56 | 345.08
6 | 13.54 | 6.88 | 10.67 | 279.20 | 320.58
7 | 13.52 | 6.80 | 10.38 | 348.00 | 331.76
9 | 13.51 | 6.75 | 10.49 | 254.10 | 325.88

###  2.2 Fornax-like Halo selection

In TNG50 a galaxy cluster and groups of galaxies are referred to as halo or
FOF (hereafter referred as halo), identified through the friends-of-friends
algorithm (Davis et al., 1985). Within each halo, the SUBFIND algorithm
(Springel et al., 2001) identifies the subhalos including the primary
(central) galaxy and other satellite galaxies (hereafter referred as
satellite). To find halos similar to the Fornax cluster in TNG50 at snapshot
99 (redshift z = 0), we applied a virial mass selection criterion analogous to
the Fornax cluster mass ($\rm M_{200}$ $\sim$ $5\times 10^{13}$ $\rm
M_{\odot}$, adopted from Drinkwater et al., 2001), namely the mass range of
$10^{13.5}$ $\leq$ $\rm M_{200}$ $\leq$ $10^{14}$ $M_{\odot}$, where $\rm
M_{200}$ is defined as the mass enclosed within a virial radius $\rm R_{200}$
equal to 200 times the critical density of the Universe. With this condition,
we find a total of seven halos.

For these halos, we measured the stellar velocity dispersion of their central
galaxy and found that this value is quite close to that of NGC1399, the
central galaxy of the Fornax cluster. Except for halo IDs 4 and 9, all other
halo central galaxy stellar velocity dispersions fall within $\pm$ 20 % to the
stellar velocity dispersion value of 315 kms of NGC1399 (Vaughan 2019). In
addition to this, the velocity dispersion of all the subhalos within these
halos agrees to within 15% of the observed Fornax cluster members (giants and
dwarf galaxies) mean velocity dispersion value of 374 $\pm$25 $\rm km/s$
(Drinkwater et al., 2001). A previous study of the hot X-ray emitting medium
of galaxy groups in the TNG50 cosmological simulations (Truong et al., 2020)
showed a good match to observations. More recently, a new set of zoom-in
cosmological simulations using the same model ‘TNG-cluster’ (Truong et al.,
2023) have demonstrated good agreement on a larger sample. These successes in
reproducing observable properties of galaxy clusters indicates that our seven
halos are reasonable matches to the Fornax cluster. From here onward, we refer
to these halos as Fornax-like halos. In Table 2.1, we list the physical
properties of these halos.

###  2.3 Atomic HI content

To determine the HI mass of gas cells in TNG50 Fornax-like halos, we use the
Popping et al. (2019) molecular hydrogen fraction ($\rm H_{2}$) catalogue,
previously calculated for the TNG simulations. In this work we use their
fiducial recipe, which is based on the work by Gnedin & Kravtsov (2011).

Gnedin & Kravtsov (2011) performed detailed simulations including non-
equilibrium chemistry and simplified 3D on-the-fly radiative transfer
calculations. Based on these simulations, the authors presented fitting
formulae for the $\rm H_{2}$ fraction of neutral gas as a function of the
dust-to-gas ratio of the gas, the impinging UV radiation field, and surface
density of the neutral gas. Popping et al. (2019) assume that the dust-to-gas
ratio scales with the metallicity of the neutral gas, that the local UV
radiation field scales with the SFR of the gas cell with an additional
contribution from the ionising UV background field and they calculate the gas
surface density of a gas cell by multiplying its density by the Jeans length
of the cell. A detailed description of the implementation of the Gnedin &
Kravtsov (2011) fitting formulae within the TNG simulation suite is presented
in Popping et al., 2019, (see their Section 2).

Figure 1: HI distribution in the TNG50 halo 6 at redshift z=0, colour-coded
with the HI column density. The maps are made using a pixel scale of 2 kpc and
are shown projected along the (arbitrarily chosen) z-axis. The three pink
circles indicate the viral radius of the halos marked at 0.5, 1.0 and 1.5
times $\rm R_{\rm vir}$. Dark blue color in the maps indicate the HI column
density lower than NHI= $10^{16}$ $\rm cm^{-2}$. Left: Full halo HI
distribution, right: HI distribution in the intracluster (IC) region (i.e.
after removing HI within 10 stellar half-mass radii of all galaxies).

###  2.4 Halo HI covering fraction

To understand and quantify the HI distribution in the halos, we measure their
HI covering fraction in different column densities bins (hereafter denoted as
NHI), adopting a range of NHI$>$ $10^{18}$, $10^{19}$, and $10^{20}$ $\rm
cm^{-2}$. We first measured the HI column density, by performing a two-
dimensional binning of all HI gas cells along the three projected axis X, Y
and Z (spatial position), regardless of the velocity space and adopted a pixel
size of 2 kpc, similar to the MFS spatial resolution limit. This assumes that
gas particle sizes are smaller than 2 kpc, which is generally true for the
TNG50 halos gas cells. We checked that larger gas cells have negligible
contribution to the HI mass and hence to HI column density. In Section 3.2, we
present the HI covering fraction results as a function of velocity.

We measure the HI covering fraction in two ways, similar to Rahmati et al.
(2015), as follows:

Cumulative HI covering fraction, hereafter denoted as $f_{HI}(R)$, is defined
as the fraction of surface area covered by the binned pixels having column
density higher than a given NHI value within a radius R divided by the total
area of pixels within radius $R$. $f_{HI}(R)$ is expressed as:

$f_{HI}(R)=\frac{\sum_{i=1}^{N}A_{N_{HI}}|_{R}}{\sum_{i=1}^{N}A|_{R}}$ (1)

Here $A_{N_{HI}}$ is the single pixel area with a column density equal or
higher than the given NHI value and is summed over $N$ such pixels in a given
area of radius $R$ divided by the total area of pixels in radius $R$.

Differential HI covering fraction, hereafter denoted as $f_{HI}(\Delta R)$, is
defined similarly to be cumulative HI covering fraction, except here we
consider only the covering fraction within the radial bin defined between
radius $R_{j}$ and $R_{j+1}$ and $f_{HI}(\Delta R)$ is expressed as:

$f_{HI}(\Delta R)=\frac{\sum_{i=1}^{N}A_{N_{HI}}|_{\Delta
R}}{\sum_{i=1}^{N}A|_{\Delta R}}$ (2)

We also separately measure the total HI covering fraction and the HI covering
fraction in the intracluster (IC) regions of the halos, that is, the regions
well away from identified galaxies. For the IC measurement, we first select
the satellite galaxies within a halo with a stellar mass $\geq$ $10^{8.5}$
$\rm M_{\odot}$ and having at least 10 gas cells (varying this to 1 gas
particle has no effect on our results). Then, we remove the HI gas cells
associated with these satellite (including the central galaxy) using the
SUBFIND algorithm of TNG50. This removal of HI gas is done out to ten times
the stellar half mass radius (denoted as $\rm R_{1/2*}$) of a satellite. In
TNG50, the SUBFIND algorithm identifies all the gas cells that are
gravitationally bound to a specific satellite. After removing the gas cells of
a satellite identified with the SUBFIND procedure out to 10$\times\rm
R_{1/2*}$, we measure the HI covering fraction in the same way as defined
earlier. The $\rm R_{1/2*}$ radii of satellite vary from a few kpc to tens of
kpc, and with our adopted radial limit (10$\times\rm R_{1/2*}$), we make sure
that we exclude all gas cells that are within the domain of an individual
galaxy. However, the IC measurement may contain the very extended
tidal/stripped gas tails originating from the individual galaxies.

##  3 Results

Figure 2: HI maps in the Fornax-like halos (first two rows) and in their IC
regions (bottom two rows) made with a pixel size of 2 kpc (projected along the
arbitrarily chosen z-axis). The three pink circles indicate the viral radius
of the halos marked at 0.5, 1.0 and 1.5 times $\rm R_{vir}$. Figure 3: HI
cumulative (left panel) and differential (right panel) covering fraction
profiles of Fornax-like halos HI maps (Figure 2, first two rows) measured
along the arbitrarily chosen z-axis for a pixel size of 2 kpc. The first,
middle, and bottom rows show the covering fraction for HI column densities log
NHI $\geq$ 18, 19 and 20 $\rm cm^{-2}$ respectively. The thin lines indicate
the individual halos, and the thick lines mark the average value. The vertical
dashed lines indicate the average virial radii of the halos. Figure 4: The
same as Figure 3, but for the HI distribution in the intracluster (IC) region
of Fornax-like halos HI maps (Figure 2, bottom two rows) measured along the
arbitrarily chosen z-axis for a pixel size of 2 kpc. We obtain the IC HI by
removing the gas cells gravitationally bound to all galaxies within 10$\times$
their stellar half mass radii. Note the y-axis ranges differ from Figure 3.

This section presents our results showing the HI distribution and covering
fraction in the TNG50 halos and their IC regions. For our study, we considered
gas cells gravitationally bound to a halo, including gas cells extending to an
average 1.5 $\rm R_{\rm vir}$ radii of halos. Figure 1 shows the HI
distribution in TNG50 halo 6 (left panel) and in its IC region (right panel).
Three pink circles indicate the virial radius drawn at 0.5, 1.0 and 1.5 $\rm
R_{\rm vir}$. These images demonstrates both the patchy nature of HI in the
simulated clusters, as well as it’s distributed nature. The IC image (right)
emphasizes that much of the HI (at least by area) is not immediately connected
to galaxies – that is, it is at least 10 stellar half-mass radii from any
galaxy in the simulation.

Figure 2 shows the HI distributions for all other Fornax-like halos (top two
rows) and in their IC regions (bottom two rows). The first visual impression
we get from these plots is that the large-scale distribution of HI extends
beyond 0.5 virial radii ($\sim$350 kpc) for all the halos. Otherwise, these
halos demonstrate diverse HI distributions with significant variations in the
amount of HI mass (Table 2.1). The diverse and extended HI distribution in
these halos could potentially be related to the merger/accretion history of
these halos or the activity of supermassive black holes (Zinger et al., 2020).
We can also see the streams or filamentary structures connecting the central
and satellite galaxies. We notice, in addition, a large number of small HI
regions with relatively high column densities, which are possibly not related
to any satellite. We refer to these as clouds. We caution that, unlike Nelson
et al. (2019), we have not performed Voronoi tessellation over the gas cells
to identify these clouds-like structures and it merely represents HI clumps
around the satellite galaxies and in the intra-cluster regions of these halos.
For the halos HI map, we see that the centers of the satellite are dominated
by HI column densities NHI between $10^{20}$ to $10^{21}$ $\rm cm^{-2}$.
Looking at these maps, it is quite clear that HI clouds extend out to the
virial radius (corresponding to $\sim$ 700 kpc) covering the IC regions.
Within the inner region of each halo, around $\sim$ 0.25 $\rm R_{\rm vir}$, a
large fraction of the HI gas cells are associated with the central galaxy of
the halo. In the IC region, the observed HI structures primarily have column
densities NHI$<$ $10^{20}$ $\rm cm^{-2}$, whereas the structures beyond 0.5
virial radii lie mainly at $10^{18}$ $<$ NHI/$\rm cm^{-2}$$<$ $10^{19}$. We
present the results of the HI covering fraction of halos and in the IC regions
in subsections 3.1 and 3.2, respectively.

###  3.1 HI covering fraction profiles

We used the HI projected maps as shown in Figure 1 to measure the HI covering
fraction as discussed in section 2. We measured the HI covering fractions of
halos for three projections, along the X, Y, and Z directions, using a pixel
scale of 2 kpc.

In this section, we present the HI covering fraction for the full halo maps
(top two rows in Figure 2) and in the next section, we discuss the covering
fraction of IC regions. In Figure 3 we show the cumulative and differential
covering fraction profiles measured along the (arbitrarily chosen) z-axis in
the left and right panel, respectively. For these panels, we include all of
the HI gas in the covering fraction calculation, whether or not it is within
the central or a satellite galaxy. We do this because, in a blind HI survey,
the satellite galaxies may not be identified, so the HI would be measured
globally. By definition, the innermost point of the cumulative and
differential covering fractions are the same, then the differential covering
fraction begins decreasing more steeply than the cumulative covering fraction.
The first, middle, and bottom rows in both panels show the covering fraction
for HI column density for NHI $\geq$ $10^{18}$, $10^{19}$ and $10^{20}$ $\rm
cm^{-2}$ respectively. The thin lines indicate the individual halos, and the
thick lines mark the average value.

We focus mainly on the NHI bins of $10^{18}$ and $10^{19}$ $\rm cm^{-2}$,
which are the optimal range for studying the HI distribution at $\sim$kpc
scales for the MFS. We find that regardless of the projection axis, the
average covering fraction for the NHI $\geq$ $10^{18}$ $\rm cm^{-2}$ bin
remains between 10-15% at 0.5 $\rm R_{\rm vir}$ and drops to 6-10% at 1 $\rm
R_{\rm vir}$. With increasing column density, the covering fraction decreases,
such that for the NHI $\geq$ $10^{19}$ $\rm cm^{-2}$ bin the covering fraction
drops to 5-10% at 0.5 $\rm R_{\rm vir}$ and to less then 5% at 1 $\rm R_{\rm
vir}$. The differential covering fraction at 0.5 virial radius is between
5-10% and drops to less than 5% at 1 $\rm R_{\rm vir}$.

These covering fractions quantify our visual impressions. Although all the
halos have some HI gas within 0.5 $\rm R_{\rm vir}$, it is distributed non-
uniformly in small structures that look like filaments or clouds. In Figure 3
we verify that the covering fraction of these structures is low, even when
including column densities down to $10^{18}$ cm-2. These structures and clouds
could potentially be associated with the central galaxy and satellite
galaxies, but from Figure 2 we see that the HI is clearly extended well beyond
the satellite stellar radii. However, this gas might have been stripped from
satellites to form part of the IC region, which we discuss in the next section
and in Section 4.3.

Figure 5: Halo and intra-cluster cumulative HI covering fractions at 0.5 $\rm
R_{vir}$ (upper panel) and 1 $\rm R_{vir}$ (lower panel) for three projected
axes. Open star, circle and square indicate the X, Y and Z projections,
respectively. The open black (red) star, circle and square indicate the
average values. Figure 6: Average halo and intra-cluster cumulative HI
covering fractions of seven halos at 1 $\rm R_{vir}$ for three projected axes
corresponding to different pixel scale size of HI maps. Numbers in the plot
mark the pixel size in kpc used in creating the HI maps. Figure 7: HI
distribution in the TNG50 halo 6 at redshift z=0, colour-coded with the HI
mean velocity (projected along the arbitrarily chosen Z axis) for a pixel size
of 2 kpc. Left: Full halo HI distribution, right: HI distribution in the IC
region. Figure 8: HI distribution in the TNG50 halos (top two rows) and in
their IC (bottom two rows) at redshift z=0, colour-coded with the HI velocity
(projected along the arbitrarily chosen Z axis) for a pixel size of 2 kpc.
Figure 9: HI cumulative covering fraction profiles of Fornax-like halos in the
velocity space. The top, middle, and bottom panels show the covering fraction
for HI column densities log NHI $\geq$ 18, 19 and 20 $\rm cm^{-2}$,
respectively. The thin lines indicate the individual halos, and the thick
lines mark the average value. The thick dashed lines mark the average IC HI
cumulative covering fraction in velocity space. Figure 10: HI covering
fraction profiles of Fornax-like halos in velocity space for log NHI $\geq$ 18
$\rm cm^{-2}$ gas over-plotted on the number counts of all satellite galaxies
(orange histogram) and the stellar mass velocity distribution (grey
histogram). The profiles and histograms are measured in 100 km/s bins. The
leftmost y-axis (orange) of each subplot represents the number count of
satellite galaxies, while the second axis (black) represents the log stellar
mass of satellite galaxies. Solid and dashed blue lines indicate the velocity
covering fraction of the halo and IC regions, respectively (right y-axis of
each panel).

###  3.2 Intra-cluster HI covering fraction

The bottom two rows of Figure 2 show the HI distribution in the IC regions of
the halos. The majority of pixels with column density NHI$\geq$ $10^{18}$ $\rm
cm^{-2}$ extend into the IC regions (the cumulative HI covering fraction drops
by about 30% at 1 Rvir). It is primarily pixels with high column density HI,
NHI $>$ $10^{20}$ $\rm cm^{-2}$, which are removed when only including the IC
gas cells in our column density measurement (the cumulative HI covering
fraction drops by about 70% at 1 Rvir).

Similar to Figure 3, we show the HI covering profiles for the IC regions in
Figure 4. For the NHI bins $10^{18}$ and $10^{19}$ $\rm cm^{-2}$, the
cumulative covering fraction at 0.5 $\rm R_{\rm vir}$ is between 5-10 % and
drops to less than 5% at 1 $\rm R_{\rm vir}$.

We checked the differences in the HI covering fraction along the different
projected directions and find that, on average, the HI covering fraction
remains the same and varies only by a few percent when changing the projected
axis. Figure 5 shows the cumulative HI covering fraction at 0.5 $\rm R_{vir}$
(upper panel) and 1 $\rm R_{\rm vir}$ (lower panel) between the Fornax-like
halo and their IC region in three different projected axes for a column
density NHI $\geq$ $10^{18}$ $\rm cm^{-2}$. The open blue (green) star, circle
and square indicate the covering fractions at 0.5 $\rm R_{\rm vir}$ (1 $\rm
R_{\rm vir}$) along the X, Y and Z axis projections, respectively. The open
black (red) star, circle and square indicate the average values measured at
0.5 $\rm R_{\rm vir}$ (1 $\rm R_{\rm vir}$). On average, the IC HI covering
fraction is between 70-80% of the total HI covering fraction. This suggests
that a large fraction, around $\sim$ 75% (by covering fraction) of the low-
column density HI gas that is distributed throughout these massive halos is
well outside the satellite galaxies. We also note that some pixels that had a
high column density when including the satellite gas have lower column
densities when only including IC gas. This can be seen as some red pixels in
the top panels of Figure 2 turning into green pixels in the bottom panels.

Depending on the HI column sensitivity, MFS will map the HI distribution in
Fornax at different spatial resolutions, varying from 1 to 10 kpc. We created
similar HI maps, as shown in Figure 2, with different pixel sizes ranging from
2 to 10 kpc. Examples of HI maps made with 10 kpc pixel scale are shown in
Appendix A. In Figure 6, we show the average halo and IC cumulative HI
covering fraction of the 7 halos at 1 $\rm R_{vir}$ radius for different pixel
scales. As anticipated, when degrading the pixel size of HI maps, the HI
covering fraction increases and, for NHI$\geq$ $10^{18}$ $\rm cm^{-2}$,
reaches 12% at 10 kpc pixel scale for the full halo and is around 10% for the
IC halo map. These are then our resolution-matched predicted values for the
NHI$\geq$ $10^{18}$ $\rm cm^{-2}$covering fraction that will be observed by
MFS.

Finally, in order to investigate whether we can see any signature of diffuse
HI gas in the inter-galactic medium or cosmic filamentary structures around
these mock Fornax-like halos, we made HI maps extending out to 3 $\rm R_{\rm
vir}$, which we show in Appendix B. Visually inspecting these maps, we do not
find diffuse HI in the inter-galactic medium of halos. We notice that outside
1.5 $\rm R_{\rm vir}$, there are several infalling smaller satellite galaxies,
particularly for Halos 1, 2 and 4, but they contribute a negligible amount in
the HI covering fraction profile. In particular, we computed HI covering
fractions for these maps and found similar results as for the maps shown in
Figure 2.

###  3.3 HI covering fraction in velocity space

We also measured the cumulative HI covering fraction in the line-of-sight
velocity space, adopting a velocity bin size of $\sim$100 $\rm kms^{-1}$
within a range of -700 to 700 $\rm kms^{-1}$. This allows us to connect the HI
gas at different column densities in velocity space. A correlation of HI gas
in velocity space with the satellite velocity distribution can give us hints
about its possible stripping origin from satellite galaxies. Figure 7 shows
the HI distribution in velocity space for Halo 6 (left panel) and in its IC
region (right panel). Similar to Figure 1, we created these velocity space
maps (Sec. 2.4) by performing two-dimensional binning in the phase space and
taking the mean velocities in bins corresponding to the X, Y and Z axis, with
a pixel scale of 2 kpc. In the velocity maps, we consider the halo velocity as
the zero velocity point. Remaining HI velocity maps of other halos and their
IC regions are shown in Figure 8. In these maps, we can see the distribution
of larger satellite galaxies having different velocities then the surrounding
lower density HI (first two rows in Figure 8). We used these maps to measure
the HI covering fraction in velocity space for these halos which is shown in
Figure 9. The top, middle, and bottom panels show cumulative HI covering
fraction for NHI column densities of $10^{18}$, $10^{19}$ and $10^{20}$ $\rm
cm^{-2}$ with a velocity bin size of 100 $\rm kms^{-1}$. The thin lines
indicate the individual halos, and the thick continuous and dashed lines mark
the average value of halo and IC region respectively. Vertical dashed gray
line marks the halo velocity which is taken as the zero velocity point.

We find that, for a velocity bin size of 100 $\rm kms^{-1}$, on average the
cumulative HI covering fraction is less than 4 % (2 %) for the column density
NHI $\geq$ $10^{18}$ ($10^{19}$) $\rm cm^{-2}$ and significantly drops to less
than 1% for NHI $\geq$ $10^{20}$ $\rm cm^{-2}$. The halo and IC HI velocity
covering fraction looks bimodal for most of the halos (except halo 4 and 9),
as also shown by the average HI covering fraction (continuous and dashed blue
lines in Figure 10). On a halo-by-halo comparison, we have verified that the
IC HI does not show a more Gaussian velocity distribution than the total HI,
as would be expected by virialized, ballistic gas clouds.

We can also use our HI velocity covering fraction analysis to learn about the
origin of the HI gas in the IC region. To do this, we looked for a possible
correlation between the HI velocity covering fraction and the satellite
velocity distribution. In Figure 10, we show the velocity distribution of all
satellite galaxies (all identified satellites with at least 100 cells and
stellar mass $\geq$ $10^{8.5}$ $M_{\odot}$), as a function of the number of
galaxies (orange leftmost y-axis of each panel) and their stellar mass (black
left y-axis of each panel). The grey bars in Figure 10 indicate the summed
stellar mass of galaxies binned within velocity ranges of 100 $\rm kms^{-1}$.
The orange histogram represents the number counts of all satellite galaxies in
each velocity bin. Additionally, we overlay the velocity covering fraction
(right y-axis of each panel) for log $\rm N_{HI}$ $\geq$ 18 $\rm cm^{-2}$ in
blue (total and IC HI in solid and dashed lines, respectively). For most of
the halos, we find that the velocity covering fraction for both the halo and
IC regions follows the velocity distribution of satellite galaxies. This
points towards a scenario where the IC HI gas originated from satellite
galaxies. We performed a similar analysis considering only the HI-rich
galaxies (satellite having HI gas cells outside 10 $\rm R_{1/2*}$) and found
similar correlation between the stellar mass distribution and HI velocity
covering fraction, except that the stellar mass distribution is less centrally
peaked (as we would expect for gas rich galaxies that have likely recently
entered the cluster).

We show both the number distribution and the stellar mass distribution of
satellites because both could effect the total HI mass brought into the
cluster. The stellar mass distribution of satellite galaxies may even be more
likely to predict where HI will be found as, for example, a single 1010 M⊙
galaxy is likely to fall into the cluster with more HI than two 109 M⊙
galaxies. In Figure 10, we note that besides the agreement with the number
distribution of satellites, the HI velocity covering fraction also correlates
with peaks in the velocity distribution of the stellar masses of all satellite
galaxies (grey histogram). Indeed, in Halos 3 and 7, where the satellite
stellar mass distribution shows multiple peaks, the HI velocity distribution
seems to follow the stellar mass more closely than the number of satellites.
This general agreement between the satellite and IC HI velocity distributions
suggests that IC HI originates from satellite galaxies, and the possibly
stronger relation between the satellite stellar mass and HI velocity gives a
hint that the IC HI may even originate from more massive galaxies (although we
stress that this does not necessarily imply the gas is stripped from massive
disks but may fall in as part of the galaxy’s circumgalactic gas).

Although a detailed investigation is outside the scope of this paper, we note
that it is expected that some processes occurring in clusters affect the gas
dynamics, and therefore some offset between the HI and satellite velocity
distributions is unsurprising. For example, a past merger can cause long-lived
motions in the ICM (Vaezzadeh et al., 2022), or black hole activity could
affect gas dynamics (Weinberger et al., 2017).

##  4 Discussion

In this section, we discuss our results and compare the HI covering fraction
to available observations and other cosmological simulation studies.

###  4.1 Comparison to other cosmological simulations

We begin by comparing our measured cumulative HI covering fraction with the
available HI covering fraction from the studies of Nelson et al. (2020). They
measured the abundance of cold gas in TNG50 halos for massive halos with mass
$>$ $10^{11}$ $\rm M_{\odot}$ at intermediate redshift z $\sim$ 0.5. Although
we have only 7 TNG50 halos, and apart from the evolution of the halos from
redshift z$\sim$0.5 to 0, the simulations and HI model we used are the same as
Nelson et al. (2020); therefore, the HI covering fraction should be of the
same order. Our measured HI covering fraction for NHI agrees well with the
Nelson et al. (2020) measured values. For a column density of NHI$>$ $10^{17}$
$\rm cm^{-2}$, we find a covering fraction around 70 $\pm$ 15 % at 10 kpc,
dropping to 30 $\pm$ 15% at 100 kpc, and for NHI$>$ $10^{20}$ $\rm cm^{-2}$,
at 100 kpc, the covering fraction is roughly 10%, similar to the findings of
Nelson et al. (2020). Rahmati et al. (2015) used the EAGLE simulation to study
the HI distribution around high-redshift massive galaxies. They found a strong
evolutionary trend in the HI covering fraction within the virial radius with
redshift. For an averaged HI column density in between $10^{17.3}$ $<$
NHI/$\rm cm^{-2}$$<$ $10^{21}$, the HI covering fraction drops from 70 % at z
= 4 to 10 % at z =1. The HI content of galaxies in the EAGLE cosmological
simulations was also investigated (Marasco et al., 2016; Crain et al., 2017),
finding that the highest resolution simulations reproduced the HI masses of
galaxies as well as their clustering. In addition, in dense group and cluster
environments, they found that ram pressure stripping was the primary HI mass
removal process but that galaxy interactions also played a role.

Studying the spatial distribution and ionisation state of cold gas in the CGM,
Faerman & Werk (2023) performed semi-analytical modelling of cold gas in the
CGM of low-redshift star-forming galaxies. Assuming that cold clouds in the
CGM are in local pressure equilibrium with the warm/hot phase, they reported
that cold gas can be found out to 0.6 $\rm R_{\rm vir}$ or beyond. Although we
examine more massive halos ($10^{13.5}$ $\leq$ $\rm M_{200}$ $\leq$ $10^{14}$
$M_{\odot}$) compared to Faerman & Werk (2023), we also find that the CGM of
Fornax-like halos normally shows a spatially extended distribution of cold gas
clouds out to more than 0.5 $\rm R_{\rm vir}$.

Previously, van de Voort et al. (2019) have shown that standard mass
refinement and a high spatial resolution of a few kpc scale can significantly
change the inferred HI column density. Studying zoom-in simulations of a
Milky-way mass galaxy within the virial radius, they found that the HI
covering fraction of NHI$\leq$ $10^{19}$ $\rm cm^{-2}$ at 150 kpc is almost
doubled from 18% to 30% when increasing the spatial resolution of the CGM.
Although the simulation setup of van de Voort et al. (2019) and TNG50 is
different, we compare our findings to theirs based on the similar resolutions
($\sim$1 kpc). We find that the cumulative HI covering fraction within 150 kpc
is around 25%, quite close to the van de Voort et al. (2019) result.

In addition to the van de Voort et al. (2019) work, several papers have
focused on studying CGM properties using higher spatial and mass resolution
simulations. For example, the FOGGIE group (Peeples et al., 2019) has used the
cosmological code Enzo Bryan et al. (2014) to carry out a set of simulations
with high resolution in the CGM, finding that a great deal of small-scale
structure emerged in the multiphase gas, producing many more small clouds.
However, they found that the HI covering fractions did not change
significantly. Similarly, Hummels et al. (2019) studied the simulated CGM with
an enhanced halo resolution technique in the TEMPEST simulation, again based
on ENZO cosmological zoom simulations. They found that increasing the spatial
resolution resulted in increasing cool gas content in the CGM. With an
enhanced spatial resolution in the CGM, they found that observed HI content
and column density increases in the CGM. In a similar vein Suresh et al.
(2019) explored the CGM of a $10^{12}$ $M_{\odot}$ mass halo with a super-
Lagrangian zoom in method, reaching up to $\sim$ 95 pc resolution in CGM. They
reported that enhanced resolution results in an increased amount of cold gas
in the CGM and this increase in the cold gas also results in a small increase
in the HI covering fraction. For a column density of NHI$\geq$ $10^{19}$ $\rm
cm^{-2}$, they found a HI covering fraction value of around 10 $\%$ at one
virial radius, which agrees well with our measured covering fraction of 12
$\%$ at one virial radius. More recently, Ramesh & Nelson (2024) re-simulated
a sample of Milky Way galaxies at z $\sim$ 0 from TNG50 simulation with the
super Lagrangian refinement method. Going down to a scale of 75 pc, they also
reported that the abundance of cold gas clouds increases with enhanced
resolution but did not find a large change in the covering fraction.

###  4.2 Detection of HI clouds in the Intracluster (IC) region through
observational work

For all the TNG50 Fornax-like halos, we found that the HI clouds can be found
beyond 0.5 $\rm R_{vir}$, which corresponds to an average physical scale of
around 350 kpc. Although only a few, there are observational studies showing
the existence of remote HI clouds associated with galaxies. An important
example is the detection of HI clouds in the inter-galactic medium of the
galaxy group HCG44, where the HI clouds extend to more than $\sim$ 300 kpc
(Serra et al., 2013b). Another example is the case of NGC 4532, in the Virgo
cluster, where the HI tail of the galaxy with some discrete clouds extends to
500 kpc and constitutes around 10$\%$ of the total HI mass (Koopmann, 2007).

A number of observational properties of the multiphase nature of the CGM in
groups and clusters have been explored through absorption lines of background
quasars with the HST-Cosmic Origins Spectrograph (COS). Studying a sample of
low redshift luminous red galaxies (LRG) with metal absorption lines such
MgII, CIII, and SiIII, Werk et al. (2013) measured the occurrence of cool
metal enriched CGM and reported a MgII ion covering fraction (down to very low
column densities) of 0.5 within 160 kpc radius. Using a sample of 16 LRG at z
$\sim$ 0.4 observed with the HST/COS, (Chen et al., 2018; Zahedy et al., 2019)
found a high HI covering fraction for column density NHI$>$ $10^{17.2}$ $\rm
cm^{-2}$of about 0.44 within 160 kpc impact parameter. In comparison to this,
we measured an HI covering fraction of around 0.75 for column density NHI$>$
$10^{17.2}$ $\rm cm^{-2}$at 160 kpc. Studying the CGM of a sample of 21
massive galaxies at z $\sim$ 0.5, Berg et al. (2019) measured an HI covering
fraction of column density for NHI$>$ $10^{17.2}$ $\rm cm^{-2}$within the
virial radius of 15 $\%$, which closely agrees with our average measured HI
covering fraction of 12 %. Finally, Emerick et al. (2015) compared HI covering
fractions within the virial radius in Virgo-like clusters between simulations
and observations, finding values consistent with those found here.

Most recently, using the MeerKAT observations of the Fornax A subgroup,
Kleiner et al. (2021) reported the detection of HI clouds at $\sim$220 kpc
from NGC 1316, the central galaxy of Fornax A. Another study done with the
MeerkAT telescope have detected a large extended HI cloud, extending $\sim$
400 kpc in proximity to a large galaxy group at a redshift of z $\sim$ 0.03
(Józsa et al., 2022). Although observational detections of HI clouds in the IC
regions around massive galaxies are few and rare, our and other simulation
work like Rahmati et al. (2015); van de Voort et al. (2019); Nelson et al.
(2020) strongly suggest the existence of dense small HI clumps within the ICM.
For our work we find that within the IC region, HI tends to have a column
density log $\rm N_{HI}$ $\sim$ 19 $\rm cm^{-2}$ or less, and current
observations are mostly not that sensitive yet. A strong test of cosmological
simulations will be to compare our predicted HI covering fractions with MFS
observations. If simulations overpredict the covering fraction of cold gas,
some combination of i) excess cold gas removal from satellites, ii) excess
cold gas added to the ICM from feedback or filamentary accretion, and iii)
suppressed heating of cold gas in the ICM are likely at play. On the other
hand, if simulations underpredict the HI covering fraction, some combinations
of these effects are leading to too little cold gas.

Figure 11: HI intra-cluster (IC) mass as a function of number of satellites
for our seven Fornax-like halos.

###  4.3 Possible Origin Scenario

A detailed study of the origin or production of the large amount of HI gas in
TNG50 Fornax-like halos is beyond the scope of this work. However, we
speculate here on the possible source of the HI gas we do find. Nelson et al.
(2020) studied the cold gas distribution in TNG50 massive halos at
intermediate redshift z $\sim$ 0.5. Using Lagrangian tracer analysis, they
argued that cold gas in TNG50 halos is related to gas that is removed from the
halos in infalling satellites. These gas clouds can later stimulate the
cooling process leading to a significant amount of cold gas.

Most recently, using the TNG50 simulation Ramesh & Nelson (2024) studied the
cold gas clouds in the CGM of Milky-Way like galaxies. They reported that
these high density gas clouds show clustering behaviour and this over-density
increases around satellite galaxies, suggesting that a fraction of these
clouds originate from ram-pressure stripping. This suggests that, not only for
massive halos (like our Fornax-like halos), but even for smaller galaxies, the
satellite gas stripping scenario can be important in producing HI clouds in
the CGM. We however do not discount the possibility that a fraction of these
clouds, whether around the satellite galaxies or isolated, may originate from
the in-situ condensation of hot halo CGM gas in the cluster environment, or
may be associated with outflows from the central galaxy (Fraternali & Binney,
2006). Studying the formation mechanism of high velocity clouds around the
Milky-Way like disk galaxies, Binney et al. (2009); Fraternali et al. (2015)
have suggested that condensation of hot CGM gas can produce the HI clouds. It
will be interesting to learn which is the effective mechanism for producing
these HI clouds in the CGM. Possibly all the mechanisms: a) satellite
stripping, b) thermal instability in CGM, or c) the feedback from the galaxy
play roles in the formation of these clouds and could be explored by
characterising these cloud properties in phase space (spatial and velocity)
such as was done in Ramesh & Nelson (2024).

In addition to the analysis in Section 3.3, which indicates that the IC
velocity covering fraction is associated with the satellite galaxies’ velocity
distribution, we checked if we could see any correlation between the satellite
galaxies’ number with the total IC HI mass. Figure 11 shows the halo
intracluster HI mass as function of satellite galaxy number. In Figure 11, red
stars denote all of the satellite galaxies and open squares mark the
satellites having HI gas cells outside their 10 $\times$ $\rm R_{1/2*}$. With
only 7 halos, its hard to quantify any relation, but we find that the halo IC
HI mass increases with increasing number of satellite galaxies. The IC HI mass
correlates more steeply with satellites having HI and shows less scatter. This
further suggests that the HI mass in the IC regions of Fornax-like clusters
could be associated with the stripped HI gas from satellite galaxies, similar
to the findings of Nelson et al. (2020). We find a similar level of
correlation between the total stellar mass in satellites and the halo IC HI
mass.

##  5 Summary and Conclusion

In this paper, using the publicly available TNG50 simulation data, we have
studied the distribution of HI gas in halos similar to the Fornax galaxy
cluster. Adopting the MeerKAT Fornax survey (MFS) observational conditions, we
have measured the HI covering fraction of the halos with a mass of $10^{13.5}$
$<=$ $\rm M_{200}$ $<=$ $10^{14}$ M⊙. The following points summarise our
findings and conclusions:

  1. 1.

Atomic hydrogen in TNG50 Fornax-like halos shows a wide spatial distribution,
appearing as clouds and filamentary structures (Figures 1 and 2). HI is non-
uniformly distributed and extends in patches well beyond 0.5 virial radii of
the central galaxy. On a physical scale, this corresponds to $\sim$ 350 kpc.

  2. 2.

Using our HI covering fraction measurements, we find that individual Fornax-
like halos in TNG50 show a wide scatter in the measured HI covering fraction
ranging from 3% to 15% at 1 $\rm R_{vir}$ (Figure 5). We predict the upcoming
MFS should observe a total HI covering fraction of $\sim$ 25% at 0.5 virial
radii and $\sim$ 12% at 1 $\rm R_{vir}$ (Figure 6) at NHI$\geq$ $10^{18}$ $\rm
cm^{-2}$(spatial resolution $\sim$ 10 kpc). For intracluster regions, this
values drops to $\sim$ 20% at 0.5 virial radii and $\sim$ 9% at 1 $\rm
R_{vir}$.

  3. 3.

Intracluster (IC) regions (i.e. more than 10 stellar half-mass radii from
identified galaxies) in Fornax-like halos hold a substantial fraction of the
HI. When using the NHI $\geq$ $10^{18}$ $\rm cm^{-2}$ contour, the IC HI
covering fraction at 1 $\rm R_{vir}$ (spatial resolution $\sim$ 10 kpc)
corresponds to around 75% of the total HI covering fraction (Figure 5).

  4. 4.

The HI velocity covering fraction for the Fornax-like halos (both in total and
in the IC regions only) shows a broad velocity distribution that is not
generally Gaussian, indicating that HI is not virialized in the halos (Figure
9). The HI velocity covering fraction for both halo and IC largely follows the
velocity distribution of satellite galaxies, suggesting that IC HI is
associated with satellite galaxies (Figure 10).

  5. 5.

We find that halo HI intracluster mass increases with increasing number of
satellite galaxies and shows an even stronger correlation with the satellites
having HI presence in their outskirts (Figure 11). This also suggests that HI
in the IC regions is associated with the stripped gas of satellite galaxies,
similar to the results of Nelson et al. (2020).

With this work, we have demonstrated, based on TNG50 simulation data, that HI
cold gas is predicted to co-exist and survive in the hot intracluster medium
for Fornax-like clusters. Based on HI maps of Fornax-likes halos in TNG50, we
expect MFS to find extended HI well beyond the satellites in the halo, but
should generally follow the large-scale satellite distribution, both on the
sky and in velocity space. This is also reflected in the asymmetry of the HI
in velocity space - while the average distribution of the seven halos studied
is symmetric, any individual halo can show strong asymmetries. We plan to
perform a future follow-up study to pinpoint the origin of these HI clouds,
whether they are possibly stripped or formed in situ in the cluster
environment. It will be illuminating to see what MFS will observe within the
Fornax cluster. With its higher sensitivity, there remains a good chance that
the MeerKAT telescope can provide observational support and constraints for
current and future simulation work on the multiphase nature of halo gas.

##  6 ACKNOWLEDGEMENTS

A.C. would like to thank Abhijeet Anand and Roland Sazacks for helpful
suggestions and discussions regarding this work. A.C. acknowledges the
financial and computing support from Simons Foundation and thanks the Flatiron
Institute pre-doctoral fellowship program through which this research work was
carried out. GLB acknowledges support from the NSF (AST-2108470, ACCESS), a
NASA TCAN award, and the Simons Foundation through the Learning the Universe
Collaboration.

##  Appendix A TNG50 halos maps at 10 kpc pixel size

In our paper we use pixels that are 2 kpc on a side in order to match the MFS
resolution at HI column densities of about 1019 cm-2. However, the resolution
at HI column densities of 1018 cm-2 is about 10 kpc. In Figure 6 we show how
the covering fraction at this column density increases with pixel size, and in
this Appendix Figure 12, we show HI maps made with 10 kpc pixels so the reader
can directly compare with the higher resolution maps shown in Figures 2 and 1.

Figure 12: Example of HI maps made with 10 kpc pixel scale, showing HI
distribution in the TNG50 halo 3, 6 and 7 at redshift z=0, colour-coded with
the HI column density. These maps are shown projected along the (arbitrarily
chosen) z-axis. The three pink circles indicate the viral radius of the halos
marked at 0.5, 1.0 and 1.5 times $\rm R_{\rm vir}$. Dark blue color in the
maps indicate the HI column density lower than NHI= $10^{16}$ $\rm cm^{-2}$.
Left: Full halo HI distribution, right: HI distribution in the intracluster
(IC) region.

##  Appendix B TNG50 halos maps at out to 3 $\rm R_{\rm vir}$

For our study we considered only the gas cells gravitationally bound to a halo
(Sec. 2), which generally includes cells out to an average of 1 to 1.5 $\rm
R_{\rm vir}$. Here in this Appendix Figure 13, we show TNG50 Fornax-like halos
maps out to 3 $\rm R_{\rm vir}$, demonstrating that there are several
infalling satellite galaxies, particularly for Halos 1, 2 and 4. Their
contribution to the HI covering profile are minimal. These maps also confirm
that we do not detect any signature of diffuse HI (not closely associated with
satellite galaxies) in the outer IGM of halos).

Figure 13: HI maps made with 2 kpc pixel scale, showing HI distribution in for
all the TNG50 Fornax-like halos at redshift z=0, colour-coded with the HI
column density out to 3 $\rm R_{\rm vir}$. These maps are shown projected
along the (arbitrarily chosen) z-axis. The six pink circles indicate the viral
radius of the halos marked at 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 times $\rm R_{\rm
vir}$. Dark blue color in the maps indicate the HI column density lower than
NHI= $10^{16}$ $\rm cm^{-2}$.

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