††thanks: ⋆E-mail:

# Star formation beyond galaxies: widespread in-situ formation of intra-
cluster stars in TNG50

Niusha Ahvazi  1,2,⋆Laura V. Sales  0009-0002-1233-2013 1 Julio F. Navarro
0000-0002-3790-720X 3 Andrew Benson  0000-0003-3862-5076 2 Alessandro Boselli
0000-0001-5501-6008 4 and Richard D’Souza5
1Department of Physics and Astronomy  0000-0001-9269-8167 University of
California  Riverside  900 University Avenue  Riverside  CA 92521  USA
2Carnegie Observatories  813 Santa Barbara Street  Pasadena  CA 91101  USA
3Department of Physics and Astronomy  University of Victoria  Victoria BC V8W
3P6  Canada
4Aix Marseille Univ  CNRS  CNES  LAM  Marseille  France
5Vatican Observatory  Specola Vaticana  V-00120  Vatican City State
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We study the fraction of the intra-cluster light (ICL) formed in-situ in the
three most massive clusters of the TNG50 simulation, with virial masses $\sim
10^{14}$$\;\rm\mathrm{M}_{\odot}$. We find that a significant fraction of ICL
stars ($8\%$-$28\%$) are born in-situ. This amounts to a total stellar mass
comparable to the central galaxy itself. Contrary to simple expectations, only
a sub-dominant fraction of these in-situ ICL stars are born in the central
regions and later re-distributed to more energetic orbits during mergers.
Instead, many in-situ ICL stars form directly hundreds of kiloparsecs away
from the central galaxy, in clouds condensing out of the circum-cluster
medium. The simulations predict a present-date diffuse star formation rate of
$\sim$1 $\mathrm{M}_{\odot}$/yr, with higher rates at higher redshifts. The
diffuse star forming component of the ICL is filamentary in nature, extends
for hundreds of kiloparsecs and traces the distribution of neutral gas in the
cluster host halo. We discuss briefly how numerical details of the baryonic
treatment in the simulation may play a role in this result and conclude that a
sensitivity of $1.6\times 10^{-19}-2.6\times 10^{-18}$ erg s-1 cm-2 arcsec-2
in Hα flux (beyond current observational capabilities) would be necessary to
detect this diffuse star-forming component in galaxy clusters.

###### keywords:

galaxies: clusters: intracluster medium – Galaxy: formation – Galaxy:
evolution

##  1 Introduction

The simplest models of galaxy formation suggest that most stars in a cluster
should form in the high-density regions of individual galaxies. These models
imply that the majority of stars in the intra-cluster light (ICL) originate
from the tidal removal of stars from luminous galaxies with mass similar to
the Milky Way (MW) (Puchwein et al., 2010; Cui et al., 2014; Cooper et al.,
2015; Contini et al., 2013, 2018, 2019; Montenegro-Taborda et al., 2023), with
relatively small contributions from dwarf mass galaxies, particularly in group
environments with halo virial masses $<10^{13}\;\rm\mathrm{M}_{\odot}$ (Ahvazi
et al., 2023). Nevertheless, observational studies (Barfety et al., 2022;
Hlavacek-Larrondo et al., 2020) and some numerical simulations (Puchwein et
al., 2010) indicate that a non-negligible fraction of ICL stars are formed in-
situ.

In-situ ICL stars could have formed in the brightest cluster galaxy (BCG)
galaxy and been later pushed onto highly energetic orbits by mergers. An
alternative, more intriguing, possibility is that stars form directly in the
circum-cluster medium (CCM), far away from the high density regions of the
BCG. This low-density mode of star formation is potentially interesting, as it
might occur under very different physical conditions than the normal star
formation in galaxies, with consequences for the multi-phase nature of the CCM
and its metallicity, as well as for the age distribution of ICL stars,
especially if in-situ star formation continues to the present day. From an
observational perspective, if a substantial amount of stars form outside
galaxies, this would have strong implications for wide-field surveys in the UV
or Hα, which are especially sensitive to the presence of young stars.

Several mechanisms have been suggested to explain in-situ ICL star formation.
One of the most commonly cited is the compression of gas associated with the
ram-pressure trails of infalling galaxies, a phenomenon that has been detected
in both observations (Smith et al., 2010; Mihos et al., 2016; Boselli et al.,
2018a; Gullieuszik et al., 2020) and some numerical simulations (Kronberger et
al. 2008; Kapferer et al. 2009; Tonnesen & Bryan 2012; Lee et al. 2020; Calura
et al. 2020; Steyrleithner et al. 2020; Vollmer et al. 2021; Göller et al.
2023, for a detailed discussion see section 5.3.1 in review paper by Boselli
et al. 2022). Another possible mechanism is star formation within the tails of
stripped material formed during gravitational fly-by encounters of gas-rich
systems (see see NGC 4254 in Virgo, Boselli et al. 2018b; VCC 1249, Battaia et
al. 2012; IC3418, Hester et al. 2010; Fumagalli et al. 2011; Kenney et al.
2014).

In-situ star formation in the CCM is also predicted to be widespread at high-
redshift, where AGN feedback might be less powerful and unable to offset the
short timescales for cooling in the dense regions of the CCM (Webb et al.,
2015b). In such a scenario, spontaneous run-away cooling in the CCM might lead
to an increase of density high enough to trigger violent star-formation events
in locations outside galaxies (Hlavacek-Larrondo et al., 2020).

Interestingly, observations of off-center star formation at large distances
from the BCG are consistent with this scenario for a few high-$z$ clusters
(Webb et al., 2015a; Hlavacek-Larrondo et al., 2020; Barfety et al., 2022), in
some cases predicting as much as a MW-worth of stars contributed to the CCM by
such cooling events.

Some observations of isolated HII regions in nearby clusters, such as the
Virgo cluster, may also hint at a more sustained but lower-level star
formation activity taking place directly in the CCM/ICL region (Gerhard et
al., 2002; Bellazzini et al., 2018). However, it is not always trivial to
disentangle whether these isolated star-forming clouds are CCM-born material
or belong to some older ram-pressure or interaction events in the cluster
(Junais et al., 2021; Jones et al., 2022).

Figure 1: Projected density maps for different stellar components in Group 1
at $z=0$: bound satellites (left), accreted ICL (middle), and in-situ formed
ICL (right). The magenta and orange circles indicate twice the stellar half-
mass radius of the stars in the central host galaxy ($2\,\rm r_{h_{*}}$) and
the virial radius ($\rm r_{200}$), respectively. These are the bounds used to
define the ICL component in our study.

Numerical simulations therefore emerge as valuable tools to explore this mode
of star formation within the realistic framework of the $\Lambda$CDM model.
For instance, Puchwein et al. (2010) estimate that approximately $\sim 30\%$
of the ICL stars formed in their clusters (with masses between $2\times
10^{13}$ and $1.5\times 10^{15}\,\rm\mathrm{M}_{\odot}$) originated at
distances consistent with being CCM-born.

Various numerical methods have been employed to study the formation of cold
gas in the CCM, which could give rise to star formation outside galaxies.
Runaway local production of cold gas in the CCM, as well as thermal
instability, have been shown to lead to multi-phase structures in idealized
hot haloes (Maller & Bullock, 2004; Kaufmann et al., 2006, 2009; McCourt et
al., 2012; Sharma et al., 2012).

Given that the cold-phase CCM resulting from such processes is a small-scale
phenomenon, it has been studied largely in idealized numerical experiments
(Fielding et al., 2020). Previous work by Oppenheimer et al. (2018)
demonstrated a relatively significant abundance of cold, low-ionization gas in
the CCM of EAGLE galaxies, albeit with uncertainties regarding the numerical
robustness of the hydrodynamical technique in this regime (see also Ford et
al. 2013).

Semi-analytic models have also been developed to explain the unique, possibly
drag-induced sub-virial kinematics of cold gas flowing through luminous red
galaxy host haloes (Afruni et al., 2019). In the context of IllustrisTNG,
Nelson et al. (2018) showed that TNG is consistent with empirical OVI
constraints in the CCM.

The cold gas content of galaxies themselves (both neutral HI and molecular H2)
has also been favorably compared against data in several regimes. Nelson et
al. (2020) also demonstrated that group mass haloes hosting massive galaxies
are filled with a hot, virialized plasma at $\sim 10^{7}$ K, and that they
contain a large abundance of cold gas with a characteristic temperature of
$\sim 10^{4}$ K. This cold phase of the CCM takes the form of thousands of
small, $\sim$ kpc-sized clouds, which fill the inner halo out to hundreds of
kpc (similar to predictions by Maller & Bullock 2004 for MW-mass halos).

There are, however, several important caveats when studying the formation of
star-forming clouds in the CCM, mostly connected with limitations of numerical
techniques. Approaches such as SPH have been shown to be unable to track the
evolution of instabilities, such as the Kelvin-Helmholtz instability, leading
to the formation of more dense clouds that are artificially long-lived
compared to similar numerical experiments run with grid-base techniques
(Agertz et al., 2009; Torrey et al., 2012).

The lack of, or inadequate treatment of other important physics, such as heat
conduction, magnetic fields or metal diffusion might also complicate the
interpretation of results from simulations (see the discussion in Puchwein et
al. 2010). It is clear that, for any numerical technique chosen, high
resolution becomes key to study in-situ star formation in low-mass clouds
embedded in the hot CCM of clusters, especially considering the low masses of
these clouds.

In this context, we present here a study of the in-situ formation of stars and
their contribution to the ICL using the three most massive groups/clusters in
the TNG50 simulations (Pillepich et al., 2018b; Nelson et al., 2019), one of
the highest-resolution cosmological simulations of low-mass clusters with
virial mass $\sim 10^{14}\;\rm\mathrm{M}_{\odot}$ at $z=0$.

This article is organized as follows: in Section 2, we provide a comprehensive
overview of the simulation employed, including some definitions crucial for
the subsequent sections. Section 3 presents our findings, together with an in-
depth discussion. Finally, Section 4 summarizes the key conclusions drawn from
this study.

##  2 Simulation

We use the cosmological hydrodynamical simulation IllustrisTNG (Pillepich et
al., 2018b; Springel et al., 2018; Marinacci et al., 2018; Naiman et al.,
2018; Nelson et al., 2019). The IllustrisTNG project111https://www.tng-
project.org is a suite of state-of-the-art cosmological galaxy formation
simulations that come in different physical sizes and mass resolutions. In
this work we use the highest resolution baryonic run TNG50-1 (TNG50 for
short), which has a volume of approximately $50^{3}\,\rm Mpc^{3}$. It has
$2\times 2160^{3}$ resolution elements, and the baryon and dark matter
particle masses are $8.5\times 10^{4}\mathrm{M}_{\odot}$ and $4.5\times
10^{5}\mathrm{M}_{\odot}$, respectively. The IllustrisTNG cosmological
parameters are consistent with $\Lambda$CDM model determined by Planck XIII
(Planck Collaboration et al., 2016) to be
$\Omega_{m}=0.3089,\,\Omega_{b}=0.0486,\,\Omega_{\Lambda}=0.6911,\,H_{0}=100\,h\mathrm{kms}^{-1}\mathrm{Mpc}^{-1}$
with $h=0.6774,\,\sigma_{8}=0.8159,$ and $n_{\mathrm{s}}=0.9667.$

Gravity and baryons are followed using the Arepo moving mesh code (Springel,
2010). The baryonic treatment is based on the code used for its predecessor
simulation suite, Illustris (Vogelsberger et al., 2013a, 2014a, 2014b; Genel
et al., 2014; Nelson et al., 2015), with modifications implemented to better
track the formation and evolution of galaxies (as described in Pillepich et
al., 2018a).

The updated IllustrisTNG sub-grid models account for star formation, radiative
metal cooling, chemical enrichment from SNII, SNIa, and AGB stars, stellar
feedback, and super-massive black hole feedback. The star formation in the
Interstellar Medium (ISM) is treated in a sub-resolution fashion following a
variation of the Springel & Hernquist (2003) with the adoption of a Chabrier
(2003) initial mass function, and model the star-forming dense ISM gas using
an effective equation of state where stars form stochastically above a gas
density of $\rho_{\rm sfr}$ = $0.13$ $cm^{-3}$ with a star formation time-
scale of $t_{\rm sfr}$ = $2.2$ Gyr (refer to Vogelsberger et al. 2013b for
detailed explanations). These models were calibrated to reproduce a set of
observational constraints that include the observed $z=0$ galaxy stellar mass
function (Vogelsberger et al., 2014a), the cosmic star formation rate (SFR)
density (Genel et al., 2014), colors and morphologies of the present day
galaxy population (Sales et al., 2014; Snyder et al., 2015; Rodriguez-Gomez et
al., 2017).

Figure 2: Projected density profiles of distinct components within the three
most massive groups in TNG50. The solid black curves represent the total
stellar component, while the red curves depict the ex-situ (merged) stellar
component, and the blue curves illustrate the in-situ stellar component. The
orange circles denote satellite galaxies with stellar masses exceeding
$10^{8}\mathrm{M}_{\odot}$ (upon vertical re-scaling by a factor of $10^{2}$).
Dotted black lines trace the dark matter component, and purple dotted lines
represent the median stellar mass surface density profiles from Cooper et al.
(2013). The shaded area delineates the region associated with the BCG, defined
within $2\,r_{h_{*}}$ for the central of each group. Arrows in matching colors
indicate twice the half-mass radius of each component

Galaxies in the simulations are identified using `SUBFIND` (Springel et al.,
2001; Dolag et al., 2009) on Friends-of-Friends (FoF) groups (Davis et al.,
1985) identified with a linking length set to 0.2 times the mean interparticle
separation. The object at the center of the gravitational potential of each
group is called the “central” galaxy, while all other substructures are
“satellites”. The time evolution of galaxies and halos through the 99
snapshots of the simulation is followed using the SubLink merger tree
algorithm (Rodriguez-Gomez et al., 2015).

Table 1: Quantities related to the 3 most massive groups. | Group 0 | Group 1 | Group 2
---|---|---|---
M200 [$\mathrm{M}_{\odot}$] | $1.8\times 10^{14}$ | $9.4\times 10^{13}$ | $6.5\times 10^{13}$
M${}_{\mathrm{BCG}}^{*}$ [$\mathrm{M}_{\odot}$] | $3.6\times 10^{12}$ | $9.7\times 10^{11}$ | $1.1\times 10^{12}$
M${}_{\mathrm{ICL}}^{*}$ [$\mathrm{M}_{\odot}$] | $1.8\times 10^{12}$ | $5.8\times 10^{11}$ | $5.9\times 10^{11}$
M${}_{\mathrm{ICL}}^{*,\mathrm{in-situ}}$ [$\mathrm{M}_{\odot}$] | $1.4\times 10^{11}$ | $1.6\times 10^{11}$ | $1.3\times 10^{11}$
fICL | $0.48$ | $0.60$ | $0.56$
F${}_{\mathrm{ICL}}^{\mathrm{in-situ}}$ | $0.08$ | $0.28$ | $0.23$

###  2.1 Defining ICL and cleaning method

We focus the analysis on the $3$ most massive systems included in the TNG50
box, which fulfill $M_{200}/\rm M_{\odot}>5\times 10^{13}$, comparable to
nearby systems such as the Fornax and the Virgo clusters. Virial masses for
these systems are listed in table 1, where virial quantities are defined at
the virial radius $\rm r_{200}$, corresponding to the distance at which the
enclosed density is $200$ times the critical value.

To define the particles that are considered part of the ICL we proceed as
follows. For each of our groups, we remove all stars that `SUBFIND` considers
bound to surviving satellite galaxies. The left panel of Fig. 1 shows an
illustration of this component for our Group 1. Furthermore, to avoid possible
contamination by stars in the outskirts of the surviving satellites that are
wrongly assigned to the host halo by `SUBFIND`, we further apply a “cleaning”
of our ICL: we remove any stellar particle within $4\,\rm r_{h_{*}}$ of the
center of any subhalo with $M_{*}>10^{8}$$\;\rm\mathrm{M}_{\odot}$, where $\rm
r_{h_{*}}$ refers to the stellar half mass radius of the subhalo. This ensures
that any stars from satellites and their surrounding stellar halo are not
considered part of the ICL.

This leaves us with a sample consisting of all the remaining stellar particles
in the FoF group that are beyond $2\,\rm r_{h_{*}}$ of the central galaxy and
within the virial radius $r_{200}$ of the host cluster, which we call ICL.
Stars in the ICL are further divided into those born “in-situ” and those
“accreted”. Following Rodriguez-Gomez et al. (2016), our algorithm checks if
the star is bound to the main progenitor of the central galaxy at the time of
birth (or the closest snapshot to it), in which case it is labeled as in-situ,
or it is otherwise associated by `SUBFIND` to a different substructure in the
SubLink merger tree, in which case it is labeled as accreted. The catalogs for
in-situ/accreted are provided within the IllustrisTNG database. As an
illustration, the middle and right panels of Fig. 1 show the accreted and in-
situ components of the ICL in Group 1, respectively.

To quantify the mass within the ICL and, specifically, the in-situ stellar
component, we introduce the fractions $f_{\mathrm{ICL}}$ and
$F_{\mathrm{ICL}}^{\mathrm{in-situ}}$. Various definitions of these fractions
exist in the literature, and for the purpose of our study, we adopt the
following definitions:

$f_{\mathrm{ICL}}=\frac{M_{\mathrm{ICL}}^{*}}{M_{\mathrm{BCG}}^{*}},$ (1)

and

$F_{\mathrm{ICL}}^{\mathrm{in-situ}}=\frac{M_{\mathrm{ICL}}^{*,\mathrm{in-
situ}}}{M_{\mathrm{ICL}}^{*}},$ (2)

where $M_{\mathrm{ICL}}^{*}$ refers to the mass of the stellar component in
the ICL, $M_{\mathrm{ICL}}^{*,\mathrm{in-situ}}$ represents the mass of the
in-situ stellar component in the ICL, and $M_{\mathrm{BCG}}^{*}$ is the
stellar mass within $2\,\rm r_{h_{*}}$ of the central galaxy. The values for
these quantities in the three most massive systems in TNG50 are presented in
table 1.

###  2.2 Hα predictions

Figure 3: Star formation rate (SFR) plotted against stellar mass for various
components within each group. Results for the BCGs are represented by orange
stars, those for the ICL component by blue squares, and those for satellites
within the ICL region by grey circles. Violet points illustrate the SFR
distribution for BCGs in TNG50 within the mass range limit. Quenched
satellites are positioned in the lower region, characterized by a fixed SFR
value of $5\times 10^{-5}\mathrm{M}_{\odot}/$yr. For comparison the main
sequence relation for the galaxies in Virgo cluster from Boselli et al. (2023)
are shown by blue and red markers, the extrapolated relations for late-type
nearby galaxies are shown by green dashed line (Boselli et al., 2015), the
relation for a large sample of SDSS galaxies are shown by brown dashed line
(Peng et al., 2010), and work by Speagle et al. (2014) is presented in orange
dashed line.

In order to compare results with the recent observations of the ICL in nearby
clusters (i.e. Virgo), we use the calibration of Kennicutt & Evans (2012) to
convert the star formation rates to Hα luminosities. These calibrations are
based on evolutionary population synthesis models, in which the emergent
spectral energy distributions (SEDs) are derived for synthetic stellar
populations with a prescribed age mix, chemical composition, and Kroupa (2001)
initial mass function (IMF). The resulting relation is

$\log
L_{\mathrm{x}}=\log(\dot{M}_{*}/\mathrm{M}_{\odot}\,\mathrm{yr}^{-1})+\log
C_{\mathrm{x}},$ (3)

where $L_{\mathrm{x}}$ denotes the $H_{\alpha}$ luminosity in units of
$\mathrm{erg}\,\,\mathrm{s}^{-1}$, $\dot{M}_{*}$ represents the star formation
rate in units of $\mathrm{M}_{\odot}\,\mathrm{yr}^{-1}$, and $C_{\mathrm{x}}$
is the logarithmic SFR calibration constant which we set to be 41.27
(Kennicutt & Evans, 2012; Murphy et al., 2011; Hao et al., 2011).

##  3 Results

We begin by characterizing the mass distribution within our groups. Fig. 2
illustrates the projected radial distribution of stars (solid thick black
line), dark matter (black dotted line), and satellite galaxies with
$M_{*}>10^{8}\mathrm{M}_{\odot}$ (depicted as orange circles) after projecting
each group along the $x$ axis. The stellar component is predicted to fall off
more steeply than both the dark matter and the satellite galaxies in these
groups (upon vertical re-scaling by a factor of $10^{2}$, the satellite
galaxies appear to closely trace the dark matter distribution in this
simulation). For comparison, the purple dotted line represents the stellar
mass surface density profiles from Cooper et al. (2013), averaged for halos
with $10^{13.5}<M_{200}/\mathrm{M}_{\odot}<10^{14}$. These results align
closely with our stellar profiles (solid black lines) for the two less massive
clusters. However, in the case of our most massive cluster, having a halo mass
twice that of the most massive halo in their sample, differences with the
predictions in Cooper et al. (2013) are evident. Note that the tagging method
in Cooper et al. (2013) does not properly account for the in-situ star
formation in the BCG, therefore giving a flatter slope in the inner regions.
We further divide the stars according to their origin: in-situ (represented by
the thin blue dot-dashed curve) and accreted (depicted by the thin red long-
dashed curve). While the dominance of the in-situ population is expected
within the BCG (the region highlighted by gray shading), their relatively
substantial contribution to the ICL at hundreds of kpc is intriguing. In our
systems, in-situ born stars contribute between $8\%$ and $28\%$ of the stellar
mass in the ICL (refer to the top right corner of each panel for the specific
percentage of each group).

An inspection of the birth place of the in-situ labelled stars in the ICL
shows that the majority of them are formed already at large distances from the
BCG (although not associated with substructures) and are not stars from the
central galaxy kicked-off by mergers, a common formation path for in-situ
stars in the diffuse stellar halos of MW-like galaxies, and as is the case for
our most massive cluster (which experienced a recent major merger in its
formation history). However, for the remaining groups in our sample, over 60%
of the in-situ ICL is formed at $r>40$ kpc or $r>2\,\rm r_{h_{*}}$ (where
distance is in physical kpc and is measured with respect to the BCG or its
main progenitor at the time of birth of the star). This suggests that gas in
the CCM must somehow become available for star formation beyond the inner
regions dominated by the BCG. This star formation mode is thus happening in
unconventionally diffuse conditions, very different from the star formation
resulting from the dense interstellar medium of galaxies.

We calculate the total SFR of CCM gas at $z=0$ for our groups and compare this
to the level of star formation ongoing in the central BCG as well as in other
galaxies. Fig. 3 highlights that, taken as a unit, the ICL (integrated within
the virial radius) is forming stars at rates comparable to that of the BCG and
other massive galaxies. For this comparison, we assign a stellar mass to the
ICL equal to the sum of all in-situ and accreted stellar particles that lay
beyond $2\,\rm r_{h_{*}}$ and up to the virial radius and that are not
associated to any satellite or identified substructure by `SUBFIND`.
Similarly, we compute its SFR by summing the star formation rates of all gas
cells that are not gravitationally bound to any substructure within the same
region. Fig. 3 shows that while the ICL lays systematically below the “main
sequence” of star forming galaxies (magenta points show central galaxies
within the TNG50 box), its SFR is comparable to many of the massive satellite
galaxies in the group (gray circles) and slightly above the SFR of the central
BCG in the case of Group 1 (middle panel). For comparison, we present the
extrapolated “main-sequence” relation derived from the galaxies in the Virgo
cluster (see Boselli et al. 2023), for a sample with normal HI gas content
(HI-normal) and deficient HI gas content (HI-deficient); the mean values and
standard deviations for HI-normal and HI-deficient objects are shown by blue
and red markers. We are also presenting results from late-type nearby galaxies
in the Herschel Reference Survey by Boselli et al. 2015 (dashed green line), a
large statistical sample of SDSS galaxies from Peng et al. 2010 (dashed brown
line), and the extrapolated time-dependent main-sequence relation derived by
Speagle et al. 2014 (dashed orange line).

The ongoing star formation in the CCM shows a decreasing trend with distance
from the center of the cluster. Fig. 4 presents the surface density of star
formation rate ($\Sigma_{\rm SFR}$), computed by projecting our groups along
the $x$-axis and integrating star formation within square bins of $2$ kpc on
each side. Different colors represent different groups, while individual
points of the same color depict the scatter between various regions within a
given group. Bins with no star formation at all are not shown. The thick solid
curve corresponds to the median trend (considering all groups collectively) of
$\Sigma_{\rm SFR}$ as a function of clustercentric distance, highlighting that
the inner regions of the CCM exhibit more prominent star formation compared to
the outskirts.

Figure 4: Star formation rate surface density profiles for the three most
massive groups in TNG50. Different colored points represent different groups,
with individual points of the same color illustrating the scatter between
various regions at a given clustercentric distance for each group. Vertical
lines, color-matched to each group, indicate $2\,\rm r_{h_{*}}/\rm r_{200}$.
The black solid line represents the median trend, and the grey shaded region
corresponds to the 25-75 percentile dispersion of $\Sigma_{\rm SFR}$ as a
function of clustercentric distance for all groups. Figure 5: Projected maps
of star-forming gas, the dark matter component and HI gas in the three most
massive groups in TNG50, presented in columns from left to right for groups 0,
1 and 2. Rows from top to bottom show: SFR, dark matter surface density, and
HI gas surface density. The colorbar on the right side of each row indicates
the respective quantities displayed. The ICL is highlighted by bounds marked
with magenta and orange circles, representing $2\,\rm r_{h_{*}}<r<\rm
r_{200}$. These results underscore the widespread nature of star formation,
organized in filamentary structures within the ICL of our targeted groups.

To ease comparison with observations, we convert $\Sigma_{\rm SFR}$ into a
surface density of Hα luminosity (right vertical axis) as explained in detail
in Sec. 2.2 and following Kennicutt & Evans (2012). Typical values in the CCM
of our sample span $\Sigma_{\mathrm{H}_{\alpha}}\sim 10^{38}\rm-10^{36}$$\;\rm
ergs\,\rm s^{-1}\,\rm kpc^{-2}$ with considerable scatter. These values are
lower than the average measured $\Sigma_{\mathrm{H}_{\alpha}}\sim
10^{40}$$\;\rm ergs\,\rm s^{-1}\,\rm kpc^{-2}$ in central regions of disk
galaxies, but comparable to the values in the outskirts of MW- and LMC-like
objects (Tacchella et al., 2022; Bundy et al., 2015). Beyond clustercentric
distances $r>0.8\,\rm r_{200}$ diffuse star formation is rare in all our
systems.

Projected maps of our halos in Fig. 5 show in more detail where the star
formation in the intracluster space is happening. Panels on the first row show
the star-forming gas in the region $2\,\rm r_{h_{*}}<r<\rm r_{200}$ (bounds
shown with magenta and orange circles) color coded by SFR (color map on the
right). Star formation at $z=0$ is widespread in these systems and follows
filament-like patterns. We highlight that special care was taken to remove any
material gravitationally associated with surviving satellites, as described in
Sec. 2.1, and this star formation is occurring in gas seemingly associated to
the central host halo and not to bound substructures. In fact, further
inspection of each system revealed that the filamentary nature of the star-
forming gas follows the distribution of neutral gas in the main host halo
(bottom row), and looks loosely linked to the dark matter distribution (middle
row) for at least 2 of the systems (groups 1 and 2).

Figure 6: Main Panel: $x$–$y$ projection of star-forming gas in Group 1,
color-coded by the flux of Hα and smoothed to 1 arcmin, revealing the
filamentary structure of the star-forming gas. Magenta and orange circles
represent regions at $2\,\rm r_{h_{*}}$ and $\rm r_{200}$. Zoomed-in Panels:
Hα flux of star-forming gas (smoothed to 3 arcsec), with yellow points
representing stellar particles. These findings suggest that star-forming
regions are not necessarily linked to ram-pressure tails from gas-rich
galaxies. Instead, stars appear to be forming within cloudlet-like structures,
condensing along filamentary structures within the CCM.

To gain further insight, we zoom into smaller regions of group 1 in Fig. 6.
The yellow points show the distribution of the stellar particles in each box
and reveal the presence of several galaxies, some with associated stellar
streams—most prominently observable in the two innermost regions (red and
green panels). The presence of the ICL is apparent in panels as a diffuse
yellow stellar background on the end closer to the central region of cluster.
We highlight the presence of star forming gas colored in magenta by their
estimated $\mathrm{H}_{\alpha}$ flux (refer to the color bar on the side of
the main panel). For the zoomed-in panels, the color maps are calculated in
$\sim 0.24\times 0.24$ kpc bins to align with the $3$ arcsec spatial
resolution of the VESTIGE survey of the Virgo cluster (Boselli et al., 2018a),
while the main panel is smoothed to 1 arcmin.

The zoomed-in regions in Fig. 6 show that the majority of the star forming gas
is mostly unrelated to the distribution of stars or galaxies. Star forming
regions are also not obviously associated to ram-pressure tails from gas-rich
galaxies note that this is different from what has been observed in cases such
as Smith et al. (2010); Mihos et al. (2016); Boselli et al. (2018a);
Gullieuszik et al. (2020), where the association of the star-forming region to
tails of ram-pressure stripped galaxies is clear upon visual inspection.
Instead, stars seem to be forming in cloudlet-like objects with tens-of-pc
typical size, which condensate along filamentary structures in the CCM.

Figure 7: Average stellar mass formation rate for the in-situ (blue shaded
histogram) and merged (red histogram) components of the ICL. The in-situ
intra-cluster star formation is a continuous phenomenon over time, with an
average peak intensity around $z\sim 2-3$ (cosmic times $2-4$ Gyr).

This is not the first time that small-scale cold clouds in the CCM have been
reported in TNG50. In a detailed analysis of the CCM in $z=0.5$ halos, Nelson
et al. (2020) highlighted this fundamental prediction from the TNG model in
combination with the high resolution achieved by TNG50. These small-scale cold
clouds seem consistent with being seeded by local inhomogeneities in gas
density that later grow due to increased cooling. While the role of magnetic
fields in forming these clouds is not clear, the magnetic pressure in these
clouds is large and exceeds the thermal pressure, providing support and making
these features long-lived, on the scale of several Gyrs. Interestingly, the
results in this work show that some of these cold clouds manage to become
star-forming and contribute a non-negligible fraction of the stars to the
diffuse ICL component.

In agreement with the findings of Nelson et al. (2020), the metallicity of in-
situ born ICL stars (with $r_{\rm born}>2\,\rm r_{h_{*}}$) is relatively high,
registering a median value of $[Fe/H]\sim-0.77$ with a substantial scatter of
approximately $0.39$ dex, comparable to the accreted ICL, the metallicity of
dwarf galaxies with $M_{*}\sim 10^{8}$$\;\rm\mathrm{M}_{\odot}$, and the
outskirts of more luminous, MW-like galaxies. This suggests that the gas
seeding these density perturbations has galaxy-like abundances and it likely
comprises gas that has, a long time ago, been stripped from infalling
galaxies. Obvious associations to those satellites do not seem to persist
until $z=0$ in our simulations, suggesting that the timescales for the clouds
to form and become star-forming are comparable to the orbital times of the
satellites.

The physical conditions for the star-forming clouds seem comparable to those
of normal star-forming regions in the ISM of galaxies. The median density of
the star-forming cells flagged as part of the ICL is $\sim 0.2\;\rm cm^{-3}$,
which is just above the density threshold for star formation in the TNG
baryonic treatment $n\approx 0.1\;\rm cm^{-3}$. Interestingly, the fraction of
stellar mass born in-situ in the ICL seems quite independent of numerical
resolution, as clusters selected in TNG100 show similar levels of star
formation rate in the ICL (see Appendix A). The presence of these in-situ born
stars in the ICL is therefore not driven by the increase in resolution from
TNG50 to TNG100 but is instead a more fundamental consequence (or prediction)
of the model.

It is also important to note that at the current integrated star formation
rates shown in the intra-cluster region of our simulated clusters, SFR $\sim$
1 $\rm\mathrm{M}_{\odot}$/yr (see Fig. 3), it would take $\sim 100$ Gyr to
form the total mass of the in-situ ICL stars listed in Table 1. This diffuse
mode of star formation must therefore have also been present at earlier times,
and with higher intensity. We confirm this by showing the distribution of
stellar mass formed in-situ in a given time-bin in Fig. 7. This is calculated
by adding all the stellar mass of the in situ-labeled stars in the ICL with a
given age divided by the size of the time-bin to provide an average star
formation rate. The blue shaded histograms indicate that the in-situ intra-
cluster star-formation is a rather continuous phenomena over time and was, on
average, stronger around $z\sim 2$-$3$ (i.e., cosmic times $2$-$4$ Gyr). As an
illustration, we show in Fig. 8 the predicted SFR maps for our highest mass
group at three different redshifts: $z=3.7,\,2.3\,\rm and\,0.9$. In all cases,
extended star forming areas appear out to almost the virial radius of the
cluster progenitor.

Figure 8: Projected maps of star-forming gas at different redshifts for Group
0, arranged in columns from left to right: x-y, x-z, and y-z projections. The
projections are normalized by the virial radius of the cluster at each
redshift, with the specific value provided in the top left corner of the last
panel in each row. Rows from top to bottom correspond to redshifts
$z=3.7,\,2.3,\,0.9$. The colorbar on the right side indicates the star
formation rate (SFR) in each region. The ICL is highlighted by bounds
represented by magenta and orange circles, signifying $2\,r_{h_{*}}<r<\rm
r_{200}$. These results emphasize the presence of a diffuse mode of star
formation within the ICL of our targeted groups, even at earlier redshifts.

Have these star-forming regions been detected in observations? In the nearby
universe, ongoing star formation in the tails of ram-pressured stripped
galaxies has been observed in the past, for example in the Virgo cluster
(Mihos et al., 2016; Boselli et al., 2018a). However, the predictions from
TNG50 are different in nature from these observations, since the star-forming
cloudlets are currently not associated with any satellite. In that sense, they
are closer to a recently identified class of young, isolated, and star-forming
clouds in Virgo, see Jones et al. (2024); Beccari et al. (2017). We cannot
rule out that this gas originated as ram-pressure tails stripped from galaxies
in the distant past, where any possible correlation with the galaxy
distribution has been long erased. However, if that is the case, the timescale
for turning this gas into stars seems too long compared to observations of
ram-pressure tails which can still be traced back to their original galaxy.
Therefore we consider this a different process than what is observed in ram-
pressure tails.

The color coding of the gas in Fig. 6 indicates that, at $z=0$, the expected
Hα surface brightness for the intra-cluster gas is rather modest, $\Sigma_{\rm
H_{\alpha}}\sim 1.6\times 10^{-19}$–$2.6\times 10^{-18}$ $\rm erg\;\rm
s^{-1}\;cm^{-2}\;\rm arcsec^{-2}$, which could partially explain why this
phenomena has so far escaped detection. For comparison, the most extended and
deepest surveys available, such as VESTIGE, have a sensitivity $\Sigma_{\rm
H_{\alpha}}\sim 2\times 10^{-18}$ $\rm erg\;\rm s^{-1}\;cm^{-2}\;\rm
arcsec^{-2}$ at 3 arcsec angular resolution (Boselli et al., 2018a). On the
other hand, there are claims of detection of runaway cooling of the hot gas in
high-$z$ clusters leading to star formation events with SFR $\sim$ 900
$\rm\mathrm{M}_{\odot}$/yr offset from the main host galaxy (Hlavacek-Larrondo
et al., 2020) that might be comparable to some of the in-situ formed stars in
our simulations.

Finally, we must also consider the possibility that these in-situ formed ICL
stars are a numerical effect born out of specific choices made for the
baryonic treatment in the simulation. The fact that most star-forming clouds
sit near the density threshold for star formation suggests that increasing the
value of that parameter might significantly lower the occurrence of stars born
in the in-situ ICL component, but more rigorous tests must be performed to
quantify this effect.

##  4 Summary and Conclusions

We use the cosmological hydrodynamical simulation TNG50 to study the formation
of in-situ ICL in Virgo-like systems. We select the 3 most massive clusters in
the box with virial masses $M_{200}=6.5\times 10^{13}$-$1.8\times
10^{14}$$\;\rm\mathrm{M}_{\odot}$. We find that a significant fraction, $\sim
8\%$-$28\%$ of the present-day mass in the ICL, was formed in-situ. When
analyzed in detail, and contrary to what is commonly believed, the majority of
these in-situ stars are born directly into the diffuse light component at
hundreds of kiloparsecs from the main host and directly from the CCM gas,
rather than brought in and dispersed during merger events. This diffuse star-
formation proceeds in cloudlets that condense along filamentary-like
structures that are aligned with the neutral gas and dark matter distributions
and are not clearly associated with ram-pressure stripping of gas in infalling
galaxies.

At $z=0$ the expected Hα surface brightness due to this diffuse mode of star
formation reaches $\sim 6.8\times 10^{-19}$ $\rm erg\;\rm s^{-1}\;cm^{-2}\;\rm
arcsec^{-2}$, just below the detection limits of the ongoing surveys in Virgo
when smoothed on scales of $3$ arcsec. In the simulated clusters, star
formation maps at higher redshift suggest that extended star formation is
present throughout the history of the cluster, making it an interesting target
for discovery with facilities such as JWST.

One interesting application of our results is that orphan supernova events
would be expected to occur in relative isolation in the ICL. While such events
have not yet been reported, with a predicted average SFR of $\sim 1$
$\mathrm{M}_{\odot}$/yr, we expect only $\sim$ 1 SN per $\sim 200$ yr in a
Virgo-like system222We have assumed a power-law mass function following
Salpeter (1955), for the mass range of $0.1$–$20$ $\;\rm\mathrm{M}_{\odot}$
with stars more massive than $8$ $\;\rm\mathrm{M}_{\odot}$exploding as SN,
which results in $\sim 7.2\%$ of the total stellar mass formed able to
generate a SN event. Assuming a mean SN mass $12$ $\;\rm\mathrm{M}_{\odot}$,
we anticipate the occurrence of 1 SN in $167$ ($\sim 200$) years., suggesting
that a concurrent survey of hundreds of clusters might be needed for detecting
such rare events.

If ongoing star formation in the intra-cluster region of observed clusters is
really lacking, then this would signal shortcomings in the treatment of star
formation in simulations like TNG50, especially in low-density regions. The
formation of stars in these extended and diffuse structures is possible
because of the condensation of denser clouds embedded in the more diffuse CCM,
as reported by Nelson et al. (2020). Numerical techniques such as that used in
Arepo have been shown to lead to less artificial formation of clouds compared
to other techniques such as SPH (Agertz et al., 2009; Torrey et al., 2012),
but it is possible that other numerical effects are still at play. We
emphasize that further studies of the effect of the star formation threshold
in models such as those of TNG would be desirable to determine their role in
the formation of stars in such unexpected conditions.

## Acknowledgements

We gratefully acknowledge the contributions of several individuals who
supported this research. NA and LVS would like to acknowledge the financial
support received from the NASA ATP-80NSSC20K0566, NSF-CAREER-1945310 and NSF-
AST-2107993 grants. NA would like to acknowledge the support provided by the
UCR-Carnegie Graduate Fellowship.

## Data Availability

This paper is based on halo catalogs and merger trees from the IllustrisTNG
Project (Nelson et al., 2019). These data are publicly available at
https://www.tng-project.org/.

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##  Appendix A Effect of resolution

To assess the impact of resolution on the star formation rates found within
the ICL regions in our studied groups in TNG50, we turn our attention to the
results obtained from TNG100. TNG100-1, part of the same suite of cosmological
hydrodynamical simulations, represents a larger baryonic run with a volume of
$110.7\,\rm Mpc^{3}$ and $2\times 1820^{3}$ resolution elements (lower
resolution compared to TNG50, which features $2\times 2160^{3}$ resolution
elements). In this run, the baryon and dark matter particle masses are
$1.4\times 10^{6}$$\;\rm\mathrm{M}_{\odot}$and $7.5\times
10^{6}$$\;\rm\mathrm{M}_{\odot}$, respectively.

For the comparison, we exclusively consider groups with virial masses similar
to those examined in our study ($M_{\rm 200}\gtrapprox 6.5\times 10^{13}$),
resulting in a subset of 26 groups in TNG100.

In Fig. 9, we juxtapose the star formation rates in TNG50 and TNG100 for both
central and ICL regions. The results reveal no discernible difference in the
ICL star formation rates among various groups between the two simulations
(represented by navy squares for TNG50 results and light blue squares for
TNG100 results), aside from a larger scatter in the TNG100 results, primarily
due to the larger sample size in the more extensive box of TNG100).

Figure 9: Star formation rate (SFR) plotted against stellar mass for different
groups in both TNG50 and TNG100 simulations. Results for central galaxies are
represented by stars, with orange denoting centrals in TNG100 and red for
TNG50. The ICL component is illustrated by squares, with light blue indicating
ICL in TNG100 and navy blue for TNG50.