# Intracluster light in the core of z$\boldsymbol{\sim}$2 galaxy proto-
clusters

S. V. Werner1, N. A. Hatch1, J. Matharu2,3,4, A. H. Gonzalez5, Y. M. Bahé6, S.
Mei7,8, G. Noirot9 & D. Wylezalek10

1School of Physics and Astronomy, University of Nottingham, Nottingham, NG7
2RD, UK
2Department of Physics and Astronomy, Texas A&M University; College Station,
TX, 77843-4242, USA
3George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and
Astronomy, Texas A&M University; College Station, TX, 77845-4242, USA
4Cosmic Dawn Center, Niels Bohr Institute, University of Copenhagen,
Rådmandsgade 62, 2200 Copenhagen, Denmark
5Department of Astronomy, University of Florida; 211 Bryant Space Science
Center, Gainesville, FL 32611, USA
6Leiden Observatory, Leiden University; Niels Bohrweg 2, NL-2333 CA, Leiden,
The Netherlands
7Université de Paris, CNRS, Astroparticule et Cosmologie; F-75013 Paris,
France
8Jet Propulsion Laboratory and Cahill Center for Astronomy & Astrophysics,
California Institute of Technology; 4800 Oak Grove Drive, Pasadena,
California 91011, USA
9Department of Astronomy & Physics, Saint Mary’s University; 923 Robie Street,
Halifax, NS B3H3C3, Canada
10Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-
Institut, Mönchhofstr 12-14, D-69120 Heidelberg, Germany
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Intracluster light is thought to originate from stars that were ripped away
from their parent galaxies by gravitational tides and galaxy interactions
during the build up of the cluster. The stars from such interactions will
accumulate over time, so semi-analytic models suggest that the abundance of
intracluster stars is negligible in young proto-clusters at $z\sim 2$ and
grows to around a quarter of the stellar mass in the oldest, most mature
clusters. In contrast to these theoretical expectations, we report on the
detection of intracluster light within two proto-clusters at $z=2$ using deep
HST images. We use the colour of the intracluster light to estimate its mass-
to-light ratio in annuli around the brightest cluster galaxies (BCG), up to a
radius of 100 kpc. We find that $54\pm 5$% and $71\pm 3$% of the stellar mass
in these regions is located more than 10 kpc away from the BCGs in the two
proto-clusters. This low concentration is similar to BCGs in lower redshift
clusters, and distinct from other massive proto-cluster galaxies. This
suggests that intracluster stars are already present within the core 100 kpc
of proto-clusters. We compare these observations to the Hydrangea
hydrodynamical galaxy cluster simulations and find that intracluster stars are
predicted to be a generic feature of group-sized halos at $z=2$. These
intracluster stars will gradually move further away from the BCG as the proto-
cluster assembles into a cluster.

###### keywords:

Galaxies: clusters: general – Galaxies: evolution – Galaxies: photometry

††pubyear: 2023††pagerange: Intracluster light in the core of
z$\boldsymbol{\sim}$2 galaxy proto-clusters–Intracluster light in the core of
z$\boldsymbol{\sim}$2 galaxy proto-clusters

##  1 Introduction

In the standard cosmological paradigm small density fluctuations of dark
matter in the early Universe rapidly collapsed into triaxial structures called
halos, which provided a gravitational well deep enough to trap gas and produce
the first stars. Over the following 13 billion years, these halos merge to
produce progressively larger halos. What happens to the stars in these merging
halos is a matter of debate that is pivotal to our understanding of the
evolution of galaxies.

Clusters of galaxies are the most massive halos in the Universe and are
therefore the most extreme examples of hierarchical merging. As such, their
central galaxies, known as brightest cluster galaxies (BCGs), are uniquely
suited to study the process of hierarchical galaxy formation. Early galaxy
formation models (De Lucia & Blaizot, 2007) predicted that BCGs would undergo
protracted growth, in step with the growth of their dark matter halos. But
observations of distant BCGs conflicted with these predictions and demanded
only modest growth in both size and mass since z$\sim$1 (Collins et al., 2009;
Whiley et al., 2008; Chu et al., 2021). To account for this lack of growth,
some models were updated to remove a fraction of the stars from the central
galaxies of the merging halos and deposit them as free-floating stars in the
merged halo which is visible as diffuse, intracluster light (Contini et al.,
2013). These new models produce modest BCG growth since z$\sim$1 and a
corresponding rapid increase in intracluster light over the same period. As a
result, these models predict negligible amounts of intracluster light in
z$\sim$2 proto-clusters (Contini & Gu, 2021). On the other hand, intracluster
stars have been observed in massive clusters up to $z=1.75$ (DeMaio et al.,
2020) and $z=1.85$ (Joo & Jee, 2023), and diffuse UV light has been observed
in a proto-cluster at $z=2.2$ (Hatch et al., 2008). Therefore, intracluster
light appears to be a generic feature of halo assembly, even early on, and not
just a low-redshift phenomenon. Recent reviews of intracluster light
observations and theory can be found in Montes (2022) and Contini (2021).

To test these models we investigate the amount of intracluster light present
within the core of two galaxy proto-clusters at z$\sim$2\. CARLA J$1018+053$
(hereafter CARLA J1018) was discovered to be an over-density of galaxies
around a radio-loud quasar at z$\sim$1.95 (Noirot et al., 2018; Wylezalek et
al., 2013), with potential intracluster light associated with the over-density
(Noirot et al., 2018). XLSSC-122 was first identified as a faint X-ray source
by the XMM Large Scale Structure survey (Willis et al., 2013), which was
subsequently discovered to belong to a $M_{500}=6.3\pm 1.5\times 10^{13}$ M⊙
halo (Mantz et al., 2018) and spectroscopically confirmed to be a large galaxy
over-density at $z=1.98$ using HST grism spectra (Willis et al., 2020; Noordeh
et al., 2021). Both proto-clusters contain similar amounts of stars ($\sim
10^{12}$ M⊙), indicating that the two regions may contain a similar amount of
dark matter. However, XLSSC-122 has a large mass gap between its first and
second most massive galaxies, unlike CARLA J1018, whose three most massive
galaxies have comparable masses. This suggests that XLSSC-122 has already
assembled much of its dark matter into a common halo, while CARLA J1018 is
still a sprawling proto-cluster consisting of several lower-mass halos
(Golden-Marx et al., 2022).

The separation between BCG and intracluster light is difficult to define
observationally. Some authors use a surface brightness limit to separate
between the two (e.g. Burke et al., 2015), whereas others fit multiple Sérsic
profiles to the light and define the intracluster light to be the outermost,
flat component (e.g. Zhang et al., 2019; Joo & Jee, 2023). In this work we do
not try to separate the two structures due to the technical challenge of
observing the faint intracluster light at high redshifts. Instead, we infer
the presence of intracluster light in systems which have low concentrations of
stars within the central 100 kpc of the proto-cluster. Measuring the light
concentration within this radial distance is justified by the recent
measurements of Joo & Jee (2023) who showed that the BCG typically dominates
only the central 10 kpc region (or $\sim$30 kpc if the BCG is fit with two
Sérsic components) for clusters above $z=1.3$. Therefore, we will infer the
presence of intracluster light in proto-clusters which exhibit low stellar
mass and light concentrations within the central 10 kpc compared to the area
encompassed by a radius of 100 kpc around the BCGs, and if they contain
significant light at a radial distance beyond 50 kpc from the BCG core.

Throughout this paper, we assume a flat, $\Lambda-$cold dark matter
cosmological model, parameterized by $\mathrm{\Omega_{M}}$=0.315,
$\mathrm{\Omega_{\Lambda}}$=0.685,$\mathrm{H_{0}}$=67.4 km
$\mathrm{s^{-1}Mpc^{-1}}$ (Aghanim et al., 2020), and all magnitudes are based
on the AB system.

##  2 Data

###  2.1 Protocluster sample

The protoclusters for this study were selected from a sample of four z$\sim$2
spectroscopically confirmed proto-clusters: XLSSC-122 at $z=1.98$ (Willis et
al., 2020), CARLA J$1018+053$ at $z=1.96$, CARLA J$0800+4029$ and CARLA
J$2039-2514$ both at $z=2.00$ (Wylezalek et al., 2014; Noirot et al., 2018).
CARLA J$0800+4029$ and CARLA J$2039-2514$ were deemed unsuitable for this
study due to contamination of the BCG and the surrounding intracluster light:
a large foreground galaxy and bright star lies along the line of sight to the
BCG of CARLA J$2039-2514$, and the most massive galaxy in CARLA J$0800+4029$
is likely to be the luminous $[F140W]=19.7$ radio-loud quasar, SDSS
J$0800+4029$.

###  2.2 Hubble Space Telescope Data

High resolution images for XLSSC 122 were harvested from the HST archive
(programme ID 15267). The WFC3 images were taken through the $F140W$ filter at
four different orientations (across 12 orbits), with a total exposure time of
5,171 seconds, and one orbit of data was taken through the $F105W$ filter,
observed at a single orientation, that resulted in a total exposure time of
2,611 seconds. High resolution images and grism spectra were harvested for
CARLA J1018 from programme ID 13740. The $F140W$ images were taken in two
orbits, each at a different orientation, for a total of 973 seconds. The
remaining time of each orbit was used to observe through the G141 grism,
details of which are provided in Noirot et al. (2016, 2018).

We performed full end-to-end processing of the HST images and grism data using
the grism redshift & line analysis software for space-based slitless
spectroscopy (Brammer, 2019). The images were flat-fielded using both pixel to
pixel flat fields and a delta correction. The sky background is fit during the
cosmic ray correction step CRCORR by computing a linear fit to the accumulated
signal from each readout. The astrometric registration uses GAIA eDR3 data to
perform a fine alignment and a final combined mosaic of all orientations for
each filter was achieved using Astrodrizzle and the default distortion
correction tables. The output images have a pixel scale of 0.06 arcsec. The
HST images were masked to remove bad pixels and pixels with less than 66% of
the median image weight (measured from the drizzled weight images).
Furthermore, the $F105W$ image of XLSSC 122 exhibited a defect which was
masked using a rectangular aperture of 10.8 by 40 arcsec, centred on
[$34.4286$, $-3.7694$] and angled by $20^{\circ}$.

We then extracted the grism spectra from the CARLA J1018 data. A source model
was constructed from the science image, which was then used to produce a
contamination model for the G141 grism spectra. The contamination model was
subtracted and finally the clean G141 grism spectra were extracted.

###  2.3 Ground-Based Images

Images of CARLA J1018 at broad wavebands of $z$, J, H, Ks and two narrow-bands
at 1.06 and 1.19µm were obtained using FORS and HAWK-I instruments on the Very
Large Telescope, ESO via programmes 094.A-0343 and 096.A-0317. The 1.06 and
1.19µm narrow-band images were obtained because they tightly bracket the 4000Å
and Balmer breaks of galaxies at z$\sim$2, so greatly improve the photometric
redshift, age and mass measurements of the proto-cluster galaxies. The near-
infrared HAWK-I data were reduced using standard near-infrared reduction
techniques with the ESO MVM software (Vandame, 2004). The FORS $z-$band data
were reduced using the theli data reduction pipeline (Schirmer, 2013). We
added an archival $i-$band image of this field taken on the William Herschel
Telescope (Cooke et al., 2015).

Since the $z-$band image is used to measure the colour of the intracluster
light, we ensured the sky background is as flat as possible through the
following processes. Each exposure was first flat-fielded using dome flats.
Then a single static background model was created from all the exposures taken
in each night. The sources were first masked, then exposures were median
combined without any astrometric correction (to correct for the dithering) to
produce a sky background model. The structure in the model included low-level
fringing and gradients. Each exposure was then corrected for this background
model. Finally, we eye-balled each exposure for satellite trails, anomalous
reflected light, and poor chip regions and masked these regions on the
individual exposures before they were coadded together to produce the final
science-grade image.

Flux and astrometric calibration for J, H and Ks images was achieved using
2MASS catalogues (Skrutskie et al., 2006). For the other ground-based images,
relative flux calibration is done based on the universal properties of the
stellar locus using stellar libraries (Pickles, 1998; Ivanov et al., 2004) and
applying offsets to the instrumental magnitudes so that colours of stars in
the images match the reference locus. Finally, we applied Galactic extinction
corrections (Schlegel et al., 1998). Properties of these ground-based data are
presented in Table 1.

Table 1: Properties of the ground-based images of CARLA J1018 used to construct the proto-cluster galaxy catalogue in Table 3. Image depths were measured in 2 arcsec diameter apertures. Filter | 3$\sigma$ image depth | PSF FWHM (arcsec)
---|---|---
$i$ | 25.59 | 0.80
$z$ | 25.14 | 0.64
NB 1.06 | 23.69 | 0.75
NB 1.19 | 23.68 | 0.60
J | 24.58 | 0.64
H | 23.47 | 0.44
K | 23.48 | 0.64

The J, H and Ks images were combined to create a deep image from which we
detected sources using SExtractor (Bertin & Arnouts, 1996). Since the
resolution of the images varied, we Gaussian-smoothed each to match the image
with the poorest resolution (the $i-$band image) before fluxes were measured
within 2-arcsec-diameter circular apertures. Total fluxes were obtained by
applying an aperture correction determined from the growth curves of
unsaturated stars. Uncertainties on the fluxes were taken to be the square
root of the photon counts in the apertures plus the standard deviation of the
total photon counts within 2-arcsec-diameter apertures placed in empty regions
of the images. The final object catalogue was cleaned by removing any source
that was located within the regions with less than 30% of the total observing
time in each of the seven ground-based images.

Table 2: Surface brightness limits. Limiting surface brightness limits for CARLA J1018 and XLSSC-122 images defined as the 3$\sigma$ limit derived over a 100 $\mathrm{arcsec^{2}}$ area. Cluster | Filter | $\mathrm{\mu_{lim}(mag/arcsec^{2})}$
---|---|---
CARLA J1018 | $F140W$ | 29.2
CARLA J1018 | z | 27.1
XLSSC-122 | $F140W$ | 30.3
XLSSC-122 | $F105W$ | 30.3

###  2.4 Sky subtraction and surface brightness limits

Intracluster light has a low surface brightness and therefore is particularly
sensitive to errors in the measurement and subtraction of the background
light. It is therefore important to robustly measure the sky background and
estimate the uncertainty in the four images we use to calculate the luminosity
and colour of the intracluster light. The HST images will not be affected by
atmospheric emission, and neither target is in a region contaminated by
significant amounts of Galactic cirrus, so we expect the background light of
these images to be dominated by Zodiacal light and exhibit a smooth
distribution over the whole image. However, the $z-$band image comes from a
ground-based instrument and is therefore subject to a variable atmospheric sky
background, whilst the $F105W$ can be affected by a time varying background
due to 1.083 $\mu$m He I emission line from the Earth’s atmosphere.

We first measure and subtract a global background from the images. To do this,
we detected all sources using SExtractor. We used the default sextractor
parameters but change the following: detect_minarea=5, detec_thresh=1.9,
analysis_threshold=1.9, deblend_mincont=0.005 for CARLA J1018, and further
updated detect_thresh=1.7, and analysis_threshold = 1.7 to detect the fainter
sources in the deeper XLSSC image. We then masked all sources to 8 times their
semi-major and minor axes to ensure no source light was visible. Finally, we
masked the entire 150 kpc region around the BCG to ensure our background
measurement was not affected by any potential intracluster light.

We fit a Gaussian to the pixel flux distribution from these masked images. The
centre of the peak of the Gaussian fit is taken as the global background and
subtracted from the original images. By subtracting this background pedestal
we also remove any diffuse light from unresolved faint galaxies not associated
with the proto-clusters. The standard deviation of the pixel flux
distribution, $\sigma$, is used to derive the limiting magnitudes through
$\mathrm{\mu_{lim}=Z_{p}-2.5\times\log\frac{3\sigma}{pix\sqrt{\Omega}}}$,
where $\mathrm{Z_{p}}$ is the zero point of the image, pix is the pixel scale
and $\Omega$ is the solid angle in $\mathrm{arcsec^{2}}$ over which the
limiting magnitude is defined. This equation only remains valid over small
solid angles where the noise is dominated by pixel-to-pixel variations and
Poisson noise. In order to readily compare with the depths of current and
future surveys, e.g., Borlaff et al. (2022), we list the limiting $3\sigma$
surface brightness of these images in Table 2 calculated over 100
$\mathrm{arcsec^{2}}$.

We quantify whether any large-scale variations in the background are present
in the four images we use to measure the intracluster light flux and colour.
To do this we placed 5.8 arcsec-radius apertures (corresponding to 50 kpc at
the redshift of the proto-clusters) in random locations over the masked
images. The distribution of this background measurement conforms to a Gaussian
for the HST images, which implies that the background noise is uncorrelated
and does not contain large variations on this scale. The background in the
ground-based z-band image is well matched to a Gaussian but has a tail to low
fluxes. Only 6% of the apertures had anomalously low fluxes. An investigation
into the $z-$band image showed that these low fluxes were caused by a
clustering of individual low-value pixels in a certain region of the image
(far from the BCG of the proto-cluster). Thus, there is no evidence that there
are large-scale variations in the background of the $z-$band image. Clustered
low-valued pixels were not observed near the BCG and so this should not affect
the measured colour of the intracluster light.

##  3 Methodology

Table 3: Properties of 15 members of CARLA J1018 identified through template fits to the combined grism spectroscopy and photometry. A map of their locations in the proto-cluster is shown in Figure 1. Label | Position | Log($\mathrm{M_{*}/M_{\odot}}$) | $\mathrm{I_{mem}}$ | mag | Observed
---|---|---|---|---|---
| (J2000) |  |  |  | M/L
Quasar |  | 10h18m27.8s
---
+05d30m29.9s
- | 1.0 | 19.47 | -
a |  | 10h18m30.5s
---
+05d31m00.6s
11.59 | 0.83 | 21.50 | 1.73
b |  | 10h18m29.9s
---
+05d31m04.6s
11.41 | 0.98 | 21.27 | 0.93
c |  | 10h18m30.0s
---
+05d31m06.6s
11.24 | 0.53 | 21.48 | 0.76
d |  | 10h18m30.7s
---
+05d30m55.0s
11.08 | 0.95 | 21.49 | 0.53
e |  | 10h18m30.0s
---
+05d31m04.1s
11.03 | 0.37 | 21.50 | 0.48
f |  | 10h18m28.6s
---
+05d29m43.9s
11.00 | 0.79 | 22.09 | 0.77
g |  | 10h18m30.1s
---
+05d31m00.6s
10.77 | 0.40 | 23.27 | 1.34
h |  | 10h18m30.6s
---
+05d30m56.6s
10.71 | 0.16 | 23.14 | 1.04
i |  | 10h18m30.7s
---
+05d30m57.2s
10.57 | 0.10 | 22.55 | 0.44
j |  | 10h18m28.3s
---
+05d29m29.8s
9.76 | 0.95 | 23.19 | 0.12
#162 |  | 10h18m28.1
---
+05d29m30.68s
- | 1.0 | 24.20 | –
#446 |  | 10h18m28.2
---
+05d30m19.71s
- | 0.55 | 24.23 | –
#354 |  | 10h18m27.4
---
+05d30m34.47s
- | 0.99 | 24.63 | –
#336 |  | 10h18m31.2s
---
+05d31m13.2s
– | 1.0 | 24.11 | –
Figure 1: The HST $F140W$ image of CARLA J1018 with marked proto-cluster
galaxies. Red circles mark proto-cluster galaxies with strong continuum
emission; blue circles mark emission-line galaxies that do not have enough
continuum to allow us to measure their mass. The radio-loud quasar is marked
by a black diamond. The insert details the region with the highest galaxy
density that we take to be the proto-cluster core, with galaxy a chosen as the
BCG.

###  3.1 Identifying the BCG of CARLA J1018

Figure 2: Spectral energy distributions of the six most massive galaxies in
CARLA J1018. The black circles show the grism spectral data while the blue
squares show the photometry from the ground-based images. The galaxy template
that best fits the spectral energy distribution is shown in red.

To identify the BCG of CARLA J1018 we first construct a galaxy member
catalogue using both photometric and grism data. We used a two-step process to
identify the members of the CARLA J1018 proto-cluster within the HST field-of-
view. We first fitted the ground-based photometry with a suite of galaxy
templates using eazy version 0.5.2 (Brammer et al., 2008) using no redshift
prior. The templates were stepped in redshift from 0.01 to 6 over a grid of
$\Delta z/(1+z)=0.01$. During this fitting we iteratively adjusted the
zeropoints of the photometry to minimize the template fit residuals. We then
combined the zeropoint-adjusted photometric data and grism spectroscopy for
the 169 sources that were detected in both data sets.

We then fitted these data with a suite of galaxy templates known as Flexible
Stellar Population Synthesis models (Conroy et al., 2009; Conroy & Gunn, 2010)
using the software grizli version 1.3.2 (Brammer, 2019). The templates were
stepped in redshift over a coarse grid of $\Delta z=0.004$ between the 68%
confidence redshift intervals determined by the eazy fitting procedure.
Finally, the templates were stepped in redshift over a fine grid of $\Delta
z=0.001$ around the peaks in the redshift probability distribution.

There are 275 sources which are detected in the HST image that are too faint
to have counterparts in the ground-based images. These sources have low levels
of continua but can be strong line emitters, so we fit their grism spectra
with galaxy templates stepped in redshift from 0.01 to 6 over the same coarse
and fine grids as before. We visually inspected each of the fits and removed
any spectral extractions that were unreliable due to poor modelling of the
contamination by nearby sources.

The best-fit redshifts from the template fitting had uncertainties of
typically $\Delta z=0.006$ for emission line galaxies with strong continuum
(e.g. galaxy j in Figure 1) or with extremely strong continuum and strong
Balmer/4000Å breaks (e.g. galaxy a). However, for galaxies without strong
emission lines the typical uncertainty was much larger at $\Delta z=0.05$.
Therefore, selecting protocluster members by their best-fit redshifts could
introduce a bias against locating passive proto-cluster galaxies. We therefore
identified proto-cluster members using two criteria.

We first selected galaxies with a best-fit redshift within a broad window of
$z\mathrm{{}_{cl}\pm 0.05}$, then removed those galaxies that did not have a
highly peaked redshift probability distribution function over the redshift
interval $z\mathrm{{}_{cl}\pm 0.02}$. This interval corresponds to $\pm$2000
km/s, which is three times the typical velocity dispersion of massive clusters
at this redshift (Willis et al., 2020). We defined $\mathrm{I_{mem}}$ as the
integral of the redshift probability distribution function over the redshift
interval $z\mathrm{{}_{cl}\pm 0.02}$, and calculated this for each galaxy. We
start with an initial guess of the cluster’s redshift at
$z\mathrm{{}_{cl}}=1.95$, determined by previous work (Noirot et al., 2018),
then iteratively redefine the cluster’s redshift as the mean redshift of
galaxies with $\mathrm{I_{mem}}>0.5$ resulting in $z\mathrm{{}_{cl}}=1.96$.
$\mathrm{I_{mem}}$ is strongly dependent on the signal-to-noise of the data so
galaxies with strong line emission or continuum have larger $\mathrm{I_{mem}}$
than lower luminosity members. We therefore eye-balled the redshift
probability distribution functions and settled on the choice of
$\mathrm{I_{mem}}>0.1$ as defining the redshift probability distribution
function as being ‘highly peaked.’ This value is low enough that it did not
rule out low luminosity galaxies with Balmer/4000Å breaks that were
distinguishable by eye (such as galaxy i), but high enough that it removed
galaxies without any clear features in the observed spectral energy
distribution or the redshift probability distribution function. Using the
criteria of $\mathrm{I_{mem}}>0.1$ and having a best-fit redshift within
$z\mathrm{{}_{cl}\pm 0.05}$ resulting in 15 proto-cluster members, which we
show in Figure 1 and list in Table 3. The photometry and best-fit stellar
population templates for the six most massive proto-cluster members are
provided in Figure 2.

To obtain stellar masses we fit the ground-based photometry with stellar
population templates using FAST (Kriek et al., 2009). The stellar population
templates are based on Bruzual & Charlot models (Bruzual & Charlot, 2003) with
exponentially declining star formation histories, dust attenuation and a
Chabrier initial mass function (Chabrier, 2003). The redshift of the cluster
members is fixed at $z\mathrm{{}_{cl}}=1.96$, but the masses do not change
significantly if the redshift is fixed to the most probable grism redshift.
Table 3 lists the properties of the 15 proto-cluster members, including the
radio-loud quasar SDSSJ101827+0530 that was first used to identify this
cluster. We estimate the observed $F140W$ mass-to-light for each galaxy using
their stellar masses and observed-frame $F140W$ luminosities.

We identify 6 common members with the original membership catalogue from
Noirot et al. (2018): the quasar, galaxy j (labelled #138 in Noirot et al.
2018), and all numbered galaxies in Table 3. All numbered galaxies copy the
labels given in Noirot et al. (2018). The addition of the ground-based
photometry allowed us to reclassify two possible members selected by Noirot et
al. (2018), their #127 and #647, as being H$\alpha$ emitters at a lower
redshift. Galaxies labelled a – i are new detections enabled by the additional
photometry and the grizli software used to reanalyse the grism data. These new
detections have weaker emission lines but stronger Balmer and 4000Å breaks
than the galaxies in the original catalogue.

The selection of a BCG for the proto-cluster from Table 3 is not straight-
forward as the galaxies labelled a to d, as well as the quasar, could all be
contenders for the most massive galaxy in the proto-cluster. To differentiate
between these galaxies, we consider each galaxy’s local density because the
barycentre of the proto-cluster is likely to be the region with the highest
galaxy density. We rule out the quasar based on its relative isolation
compared to the high-density region around galaxies a – d shown within the
insert of Figure 1. Out of galaxies a – d, we select galaxy a as the BCG
because it is the most massive and has the highest galaxy density on the scale
of 100 kpc out of all galaxies in the proto-cluster.

###  3.2 Identifying the BCG of XLSSC-122

We use the XLSSC-122 proto-cluster membership catalogue presented in Noordeh
et al. (2021) and stellar masses of the XLSSC-122 galaxies that were derived
from 2-band photometry in Willis et al. (2020). However, to compare them with
the stellar masses we derive for the CARLA J1018 galaxies, we convert the
stellar masses from a Salpeter IMF to Chabrier IMF by multiply the masses by
0.61. From this galaxy catalogue, we select the most massive galaxy as the
BCG, which is galaxy #529 at $\mathrm{RA}=34.4342$, $\mathrm{Dec}=-3.7588$,
with $[F140W]=20.64$ and a stellar mass of $5\times 10^{11}$ M⊙. This galaxy
lies near the centre of the X-ray contours (Willis et al., 2020), and
therefore is likely to lie close to the centre of the gravitational well of
the most massive dark matter halo in the proto-cluster. Due to the longer
wavelength coverage of the data on the CARLA J1018 field, the masses of the
CARLA J1018 galaxies are likely to be more accurate compared to those of the
XLSSC 122 catalogue, which were derived from only 2-band photometry ($F105W$
and $F140W$).

##  4 Results

Figure 3: HST images of the core of the CARLA J1018+0530 (upper panels) and XLSSC 122 (lower panels) proto-clusters (F140W band). The left images show the BCG, intracluster light and surrounding galaxies at the native resolution of the HST images. On the right, we highlight the light from the intracluster stars by masking all galaxies, except for the BCG, then smoothing the remaining pixels with a Gaussian 2D kernel of $\sigma=0.12$ arcsec. The dashed circles mark a radial distance from the BCG centre of 10, 50 and 100 kpc. The white lines on the colour bar marks the 3$\sigma$ (7$\sigma$), 5$\sigma$ (12$\sigma$), and 10$\sigma$ (24$\sigma$) depths in the CARLA J1018+0530 (XLSSC 122) images within an area of 1 sq arcsec, as shown by the white circle in the top right. Table 4: The $F140W$ surface brightness, $F140W$ luminosity and stellar mass of the BCG & intracluster light within the z$\sim$2 proto-clusters. The luminosity was measured inside circular apertures and annuli centered on the BCG. The uncertainties account for any residual variations in the background as they are measured from the standard deviation of flux measured in $\sim$1000 randomly distributed apertures across each image. Note that the stellar mass uncertainties are purely statistical and do not account for systematic uncertainties due to the uncertain mass-to-light ratio (see Section 5.4 for details). The average surface brightness within each aperture is greater than the $3\sigma$ surface brightness limit of the images that is listed in Table 2.  | Surface brightness (mag/arcsec2) | Luminosity ($\mathrm{10^{11}L_{\odot}}$) | Stellar mass ($\mathrm{10^{11}M_{\odot}}$)
---|---|---|---
Aperture (kpc) | ¡10 | 10 – 50 | 50 – 100 | ¡10 | 10 – 50 | 50 – 100 | ¡10 | 10 – 50 | 50 – 100
CARLA J1018 | 23.37$\pm$0.02 | 26.4$\pm$0.1 | 27.2$\pm$0.1 | 1.8$\pm$0.1 | 2.4$\pm$0.2 | 3.2$\pm 0.4$ | 1.5$\pm$0.1 | 0.8$\pm$0.1 | 1.0$\pm$0.1
XLSSC 122 | 22.77$\pm$0.01 | 26.1$\pm$0.1 | 27.5$\pm$0.1 | 2.2$\pm$0.1 | 2.6$\pm$0.1 | 2.8$\pm$0.4 | 1.2$\pm$0.1 | 1.4$\pm$0.1 | 1.6$\pm$0.2

###  4.1 Quantifying the intracluster light in z$\sim$2 proto-clusters

To isolate the diffuse light in these proto-clusters we mask all the high
surface brightness sources except for the BCG. We use the sextractor-derived
source catalogue described in section 2.4 and mask all objects, except the
BCG, to four times the semimajor and semi-minor axes of objects using the
sextractor parameters (a_image and b_image). We checked the resulting masked
images by eye and increased the mask size, by up to 10 times the semi-major
and semi-minor axis, for large galaxies and very bright stars for which the
smaller mask was insufficient. The masked galaxies in the 100 kpc surrounding
the BCGs can be seen in Figure 3. In this figure we also see diffuse low
surface brightness emission extending up to 100 kpc from the BCG which
resembles intracluster light.

We quantify the amount of light in the proto-cluster cores by measuring the
luminosity of the BCG and intracluster light within three projected annuli of
¡10 kpc, 10 to 50 kpc and 50 to 100 kpc around each BCG (marked on Figure 3)
and list them in Table 4. The inner-most aperture is likely to be dominated by
light from the BCG whilst the outer annulus is likely to be dominated by
intracluster light (Joo & Jee, 2023). The uncertainty in the background within
each of these apertures was estimated by placing apertures, of the same size
and shape, at random locations over the fully masked image described in the
section above on sky subtraction and image depth. The standard deviation of
the fluxes (within the $\sim$1000 apertures which have a comparable unmasked
area as the regions of interest) is taken as the uncertainty in the sky
background.

We find that both proto-clusters contain at least two times more light in the
region beyond 10 kpc than within 10 kpc of their central galaxies,
demonstrating that these proto-clusters host significant amounts of
intracluster light. We also measure the total light within a 100 kpc-radius
circular aperture, and defined the concentration of light as the luminosity
within 10 kpc compared to the luminosity within a 100 kpc radius, with
uncertainties resulting from the fractional errors in the 10 and 100kpc
apertures added in quadrature. We find the light concentration in the centre
of the XLSSC 122 proto-cluster is 0.29$\pm$0.03, and 0.23$\pm$0.02 in the
CARLA J1018 proto-cluster.

Figure 4: Radial surface brightness profiles for the BCG within the CARLA
J1018 (purple) and XLSSC 122 (blue) proto-clusters. All other galaxies were
masked from the $F140W$ HST images. The horizontal dotted lines at the bottom
of the figures show the $3\sigma$ image depths for CARLA J1018 (top) and XLSSC
122(bottom). In the left panel, we compare the surface brightness profiles of
the BCGs to the three most massive galaxies within the proto-clusters that lie
far outside the cores (# 300 and # 305 from XLSSC 122, Noordeh et al. 2021,
and galaxy f within CARLA J1018). The BCGs have a uniquely extended morphology
that is not shared by other proto-cluster galaxies. In the right panel, the
surface brightness profiles are compared to BCGs at lower redshifts (DeMaio et
al., 2020); redshift-corrected to $z=2$ to enable a direct comparison with the
two proto-clusters at z$\sim$2\.

We check whether the presence of diffuse light is unique to the BCGs or is a
generic feature of massive proto-cluster galaxies by comparing the projected
circular radial profiles of the BCGs to other proto-cluster galaxies with
similar stellar masses of more than $\mathrm{10^{11}}$ M⊙. We only find three
galaxies with such high masses outside the central 100 kpc of the proto-
clusters (galaxies labelled #300 and #305 in XLSSC 122 by Noordeh et al. 2021
and galaxy f from CARLA J1018). The surface brightness profiles of these three
galaxies, shown in the left panel of Figure 4, are much steeper than the BCGs,
and the light concentration of these galaxies are all greater than 0.89 which
is three times higher than either of the BCGs. The BCGs, therefore, have a
distinct light profile that is more extended than other massive proto-cluster
galaxies.

In the right panel of Figure 4, we compare the light profile of the $z\sim 2$
BCGs to BCGs at $z\sim 1.5$ that are known to be surrounded by intracluster
light (DeMaio et al., 2019). Joo & Jee (2023) performed multi-Sérsic fitting
to many of these profiles and found that light in the inner 10 kpc was
dominated by the BCG, whereas light beyond 10 kpc was either dominated by the
intracluster light component, or dominated by an extended, flat bulge
component of the BCG up to at most 30 kpc, and then intracluster light
dominated beyond. The surface brightness profiles of the proto-cluster BCGs
have remarkably similar profiles to the $z\sim 1.5$ cluster BCGs beyond 10
kpc, which we interpret as evidence that intracluster light is already present
in these proto-clusters.

Figure 5: The colour of the BCG and intracluster light (red) compared to the
proto-cluster galaxies (black dots) in XLSSC 122 (left) and CARLA J1018
(right). The intracluster light in XLSSC 122 has a similar colour to the red
proto-cluster galaxies and we assume that the intracluster stars have the
mass-weighted mass-to-light ratio of protocluster galaxies with colours of
$[F105W-F140W]>1.1$. The colour of the intracluster light in CARLA J1018 is
significantly bluer in the outskirts than in the core region. We therefore
calculate the mass of the stars within 10 kpc using the mass-weighted mass-to-
light ratio of protocluster galaxies with colours of $[z-F140W]>1.5$, whilst
the mass of the stars beyond 10 kpc are calculated using the mass-weighted
mass-to-light ratio of protocluster galaxies with colours of $[z-F140W]<1.3$.

Figure 6: The concentration of stellar mass within the z$\sim$2 proto-clusters
(purple symbols), defined as the ratio of stellar mass within 10 kpc to the
stellar mass within 100 kpc, versus the total halo mass ($\mathrm{M_{500,c}}$.
Grey and blue symbols show lower redshift clusters gathered from the
literature (DeMaio et al., 2020), which suggests an inverse relationship
between the stellar mass concentration of the core and the total cluster mass
($\mathrm{M_{500,c}}$). In the left panel, the dashed lines display the
predicted concentrations from the semi-analytic models of Contini & Gu (2021),
whilst in the right panel the solid lines display the predicted concentrations
from the Hydrangea hydrodynamical simulations (Bahé et al., 2017).

###  4.2 Stellar mass and concentration of the BCG and intracluster stars

To compare our discovery of intracluster light within proto-clusters to the
predictions of simulations, such as Contini & Gu (2021), we need to convert
the luminosity to an estimate of the stellar mass. We use the colour of the
light to estimate the mass-to-light ratio in each annulus. We combine the HST
$F140W$ images with images of light from below the Balmer break in the rest-
frame of the proto-cluster galaxies. For XLSSC 122 we use an HST image taken
through the $F105W$ filter, whilst for CARLAJ1018 we use a $z$-band image
taken from the ground (from VLT). We estimate the colour of the light in three
radial bins for XLSSC 122 and two wider bins for the shallower CARLA J1018
images and compare them to the colours of the proto-cluster galaxies in Figure
5.

The light within 100 kpc of the BCG of XLSSC 122 has a similar
$[F105W]-[F140W]$ colour as the proto-cluster members that reside on the red
sequence ($[F105W]-[F140W]>1.1$). We assume that the intracluster light is
produced by the stripping and destruction of proto-cluster galaxies, and that
all galaxies are stripped equally. Under these assumptions, it is appropriate
to use the mass-weighted mass-to-light ratio of all the XLSSC-122 proto-
cluster galaxies with $[F105W]-[F140W]>1.1$. Using the stellar masses
(renormalised to a Chabrier IMF) listed by Noordeh et al. (2021), we find that
such red galaxies contain a total mass of $\mathrm{10^{12}}$ M⊙. We transform
the observed fluxes into absolute magnitudes to derive a total $F140W$
luminosity of 1.8$\times\mathrm{10^{12}L_{\odot}}$. Thus, the observed mass-
to-light ratio through the $F140W$ filter is 0.56 for the light in XLSSC 122.

The colour of the light within the core of CARLA J1018 varies with radius. To
compare the colour of the diffuse light with the colour of the galaxies, we
perform aperture photometry on the $F140W$ and $z-$band images using four
times the semi-major and semi-minor axis of the catalogues detected by
SExtractor for the masking. These large apertures are chosen to ensure we have
all the galaxies’ light, even in the ground-based $z-$band image, which has a
larger PSF than the space-based $F140W$ image.

In the inner 10 kpc, the light matches the colour of the red sequence galaxies
with $[z-F140W]>1.7$. The mass-weighted mass-to-light ratio for these galaxies
is 0.89, which we adopt for the light within this aperture. This ratio is
larger than that found for XLSSC 122 because XLSSC 122 contains several
bright, low mass galaxies which bring down the mass-averaged mass-to-light
ratio of the red galaxies. The CARLA J1018 $F140W$ and grism data is shallower
than the XLSSC 122 data which results in fewer detections of low-mass red
galaxies. However, any undetected low-mass galaxies are unlikely to greatly
influence the mass-averaged mass-to-light ratios: the core region of CARLA
J1018 contains several $\mathrm{10^{11}}$ M⊙ galaxies which negates the impact
of any (undetected) low-mass galaxies on the mass-averaged mass-to-light
ratios.

Beyond 10 kpc, the diffuse light of CARLA J1018 is significantly bluer and is
similar to galaxies $i$ and $j$. The other five blue galaxies do not have
measurable masses as they are not detected in the images taken by the VLT, and
therefore they cannot be included in this calculation. The mass-weighted mass-
to-light ratio of galaxies $i$ and $j$ is 0.32.

We convert the light measured in each aperture to stellar mass using these
mass-to-light ratios and list them in Table 4. The main limitation of these
results is the strong dependence of the stellar concentration on the assumed
mass-to-light ratios for each radial bin. Simulations suggest that the
intracluster light comes from stripping of the massive galaxies in the forming
cluster (Merritt, 1984; Rudick et al., 2006), which justifies our using the
mass-weighted mass-to-light ratios of the galaxies to estimate the mass-to-
light ratio of the intracluster stars. However, to be cautious we explore how
alternative mass-to-light ratios affect our conclusions in section 5.4.

We define the concentration of stellar mass as the fraction of stellar mass
within 100 kpc that lies within the central 10 kpc,
$\mathrm{\frac{M_{*}(<10kpc)}{M_{*}(<100kpc)}}$, and find that the stellar
mass is more centrally concentrated in CARLA J1018, with
$\mathrm{\frac{M_{*}(<10kpc)}{M_{*}(<100kpc)}}=0.46\pm 0.05$, compared to
XLSSC 122, with $\mathrm{\frac{M_{*}(<10kpc)}{M_{*}(<100kpc)}}=0.29\pm 0.03$.
The quoted uncertainties are only from uncertainties in the light measurement
within each aperture and do not include any systematic uncertainty from the
assumed mass-to-light ratio. In Figure 6, we compare these stellar mass
concentrations of the proto-cluster cores with lower redshift clusters from
the sample of DeMaio et al. (2020).

The stellar mass concentration of the lower redshift clusters exhibits a mild
trend with halo mass and no dependency on redshift. XLSSC 122 lies on the same
relation of concentration-halo mass as the lower redshift clusters, and we use
this relation to estimate a halo mass of CARLA J1018 based on its stellar mass
concentration. To find a relation between
$\mathrm{\frac{M_{*}(<10kpc)}{M_{*}(<100kpc)}}$ and $\mathrm{M_{500,c}}$,
where $\mathrm{M_{500,c}}$ is the mass within the radius at which the density
is 500 times the critical density of the Universe, we applied a least-squares
algorithm to all clusters in the sample of DeMaio et al. (2020), regardless of
their redshift. We derive the following relation:
$\mathrm{\frac{M_{*}(<10kpc)}{M_{*}(<100kpc)}=2.57-0.16\times logM_{500,c}}$.
The stellar concentration of 0.46 within CARLA J1018 implies an approximate
total cluster mass of $\mathrm{M_{500,c}\sim 10^{13.4}M_{\odot}}$. We note
this is within a factor of five of the halo mass estimate of Mei et al. (2022)
based on the galaxy overdensity, but both estimates should be considered
unreliable as they have been derived through methods that have not been well
tested.

###  4.3 Comparing the proto-cluster stellar mass concentration to simulations

The concentration of stellar mass in the central 100 kpc of these proto-
clusters provide us with a well-defined quantity that we compare to two state-
of-the-art simulations of intracluster light formation. In Figure 6a we
compare our data to the predictions of intracluster light from the semi-
analytic model of Contini & Gu (2021). The intracluster stars in this model
are produced from an analytic model that takes a fraction of the stars from
satellite galaxies as they orbit the BCG, as well as harvesting a fraction of
the stars from galaxies merging with the BCG. Full details of the model are
provided in Contini et al. (2013).

Once stripped, the intracluster stars are assumed to follow an NFW profile
(Navarro et al., 1997) adapted such that the concentration parameter of the
intracluster light, $\rm C_{ICL}$, is modulated by a constant, ${\gamma(z)}$.
By varying the stellar concentration parameter, these simulations can
reproduce the observed stellar mass within 100 kpc of the centre of clusters
at $0<z<1.5$ (Contini & Gu, 2020). We use the optimal concentrations derived
by Contini & Gu (2020): ${\gamma(0)=3}$, and ${\gamma(>0)=5}$, for the lines
shown in Figure 6a.

These models are designed to match the observed slow growth rate of the BCG,
so in this simulation the BCG has mostly assembled by $z\sim 1$ and the
surrounding intracluster light builds up around it over the following 7 Gyr.
The stellar concentrations therefore decrease with decreasing redshift as
stars from mergers and stripping preferentially accumulate beyond the
outskirts of the BCG. The highest redshift model predictions are at z$\sim
1.5$, since above this redshift the intracluster light is predicted to be
negligible and the stellar concentrations tend towards unity.

The Contini & Gu (2021) predictions agree reasonably well with the observed
concentrations at $z=0$ and $0.5$, although the predictions are higher than
most of the observations. The main discrepancy occurs at $z=1.5$ where the
models have significantly higher concentrations than both $z\sim 2$ proto-
clusters as well as other clusters at $z\sim$1.5. This remains true regardless
of the assumed halo mass of CARLA J1018. As shown fig. 1 of Contini & Gu
(2021), and reproduced in Fig. 7, these models underpredict the mass of
intracluster stars at $z=1.5$ within the $10<R<100$ kpc annulus surrounding
the BCGs, which explains why the predicted concentrations are much higher than
observed. Our discovery of BCGs at $z\sim 2$ with low stellar concentrations
and significant stellar mass at $>10$ kpc implies that the formation of the
intracluster light began earlier than predicted by this model.

We next compare the observed stellar mass concentrations to the Hydrangea
hydrodynamical simulations (Bahé et al., 2017). These are a suite of 24 zoom-
in simulations of massive galaxy clusters within which the equations of
gravity are solved for collisionless dark matter and stellar particles, with
additional hydrodynamical equations solved for gas particles. Numerical
subgrid algorithms are used to solve for the other ingredients of galaxy
formation, such as cooling, star formation, stellar feedback and black hole
growth (see see Schaye et al. 2015 and Bahé et al. 2017 for details).

The positions of star particles are traced throughout the simulation so the
stellar distribution can be used to test the fidelity of the model. Using
these simulations, Alonso Asensio et al. (2020) showed that the distribution
of the intracluster stars closely follows that of the total mass distribution
at $z\sim 0$. This agrees with recent observations that showed the
intracluster light followed the mass distribution within the central 140 kpc
(Montes & Trujillo, 2018). However, we caution that these simulations produce
too many stars in the centres of clusters and the BCGs end up three times too
massive by the present day (Bahé et al., 2017). This means that the galaxy
model has not yet solved the issue of restraining the BCG stellar growth.

To create the data shown in Figure 6b we extracted the stellar mass
concentration within four snapshots of the simulations: $z=0.0$, $z=0.47$,
$z=1.49$ and $z=1.99$. Within each snapshot, we identified the central galaxy
(the BCG) of each dark matter halo with a mass greater than $10^{12}$ M⊙. The
stellar mass concentration is calculated as the ratio of stellar mass within a
projected radius of 10 kpc to the stellar mass within a projected radius of
100 kpc, excluding any stars within these 2D apertures that are
gravitationally bound to satellite galaxies. We separated the data from each
snapshot into halo mass bins, then calculated the median stellar mass
concentration and the standard deviation of the concentration for the halos in
each halo mass bin, which are displayed in Figure 6b.

In these hydrodynamical simulations the redistribution of stars during mergers
and stripping depends only on gravity and the position of stars within
galaxies. Hence the distribution of BCG and intracluster stars in this
simulation is a direct prediction of hierarchical merging, modulated only by
the galaxy evolution model.

We find that the concentrations from these simulations are in reasonable
agreement with the observations at $z=0$ and 0.5, although the simulations
tend have higher concentrations than the observations, similar to the semi-
analytic models mentioned above.

In contrast to the semi-analytic models of Contini & Gu (2021), the
concentrations of the hydrodynamical simulations at $z>0.5$ have little
further evolution with redshift in the $M>10^{13}$ M⊙ mass regime, and only
minor evolution at lower masses. In general, the hydrodynamical simulations
predict that the stellar concentration depends on the halo’s total mass, but
has relatively little dependency on redshift, especially at $z>0.5$. Thus,
there is no redshift at which the model does significantly worse at
reproducing the observations; the stellar light is slightly more concentrated
in the simulated haloes than in the observations at all redshifts probed.

Bahé et al. (2017) has, however, shown that the simulations produce BCGs that
are too massive which can impact the stellar concentrations. Therefore we also
compare the predicted and observed stellar mass in the annulus $10<R<100$ kpc
surrounding the BCGs in Fig. 7. The Hydrangea simulations predict a similar
amount of intracluster stars to the observations at
$\mathrm{M_{500,c}}<10^{14}$ M⊙, but unfortunately do not probe haloes of
masses $\mathrm{M_{500,c}}>10^{14}$ M⊙ where most of the $z\sim 1.5$
observations exist. The stellar mass within this region of the two proto-
clusters lies on the upper bound of the predictions, but within the scatter.

The Hydrangea simulations, therefore, predict a level of intracluster light
that is consistent with the observations at $z=2$, but the concentrations are
higher than observed because the simulations produce too much mass in the
central 10 kpc of the BCG. We therefore still lack a simulation model that can
predict realistic amounts of intracluster light at $z=2$ while also
restraining excessive BCG growth.

Figure 7:  The amount of stellar mass in the annulus $10<R<100$ kpc around the
BCGs in the $z=2$ proto-clusters (purple symbols), and $z\sim 1.5$ clusters
from (DeMaio et al., 2020, blue diamonds), versus the total halo mass,
$\mathrm{M_{500,c}}$. The dashed blue line displays the predicted
concentrations from the semi-analytic models of Contini & Gu (2021) at
$z=1.5$, and the solid lines display the predicted concentrations from the
Hydrangea hydrodynamical simulations (Bahé et al., 2017) at three different
redshifts. The Hydrangea simulations are in reasonable agreement with the
observations in the overlapping mass range ($\mathrm{M_{500,c}}<10^{14}$ M⊙),
whereas the semi-analytic models underpredict the amount of intracluster stars
at these high redshifts.

##  5 Discussion

Figure 8:  The location where the stellar mass of the Hydrangea proto-
clusters’ BCG and intracluster light ends up by $z=0$. The coloured lines show
the $z=0$ location of stars that were located at $z=2$: within 10 kpc of the
BCG centre (dark blue); between 10 and 50 kpc (light blue); and between 50 and
100 kpc (green).

###  5.1 The implications of finding intracluster light in proto-clusters

Our work extends the baseline over which intracluster light has been
investigated to $z\sim 2$. At this epoch, typically less than 20% of the
matter that will end up in the cluster has assembled into the main halo
(Muldrew et al., 2015), and the halos that we have observed are below the
general limit of a cluster-sized halo and more akin to galaxy groups. But our
images show that the central 100 kpc of these proto-clusters already contain
intracluster stars.

The Hydrangea simulations agree that intracluster light can exist at such a
high redshift, and go further to suggest that intra-halo stars, i.e. stars
that are in halos but gravitationally unbound from any galaxy, are present in
massive haloes up to at least $z\sim 2$. As these massive haloes merge to form
larger groups and accrete onto clusters their intra-halo stars will combine.
Stars that were already unbound from galaxies when they accrete onto the
cluster are defined as having been ‘pre-processed’. Since the Hydrangea
simulations suggest that all massive halos contain intra-halo stars, it is
likely that pre-processed stars are a significant source of intracluster
stars. Therefore semi-analytic simulations should take care to include intra-
halo stars at $z>1$, even in halos of masses as low as $10^{12}$ M⊙.

Our findings also argue against a significant contribution of intracluster
stars within the central 100 kpc coming from the stripping of satellite
galaxies as they orbit in the cluster. Such a stripping mechanism would build
up intracluster light over time, regardless of whether the halo grows
significantly in mass. Thus, if stripping of orbiting satellites were a
dominant contributor to intracluster stars we would expect the stellar mass
concentration to strongly depend on redshift, and only weakly depend on halo
mass. Such evolution in the stellar mass concentration can be seen in the
models of Contini & Gu (2021) displayed in Figure 6a, but these do not match
the trends seen when combining our data with the larger sample from DeMaio et
al. (2020).

Our observational data find the opposite trends: a dependence on halo mass and
little (or no) dependence on redshift. The stellar mass concentration in the
$z\sim 2$ proto-clusters is comparable to group-sized halos at $0.1<z<0.9$
which have similar masses. The groups at $z<0.9$ have had much more time to
strip stars from satellites than the $z\sim 2$ proto-clusters, thus such stars
cannot be a major source of intracluster stars within the central 100 kpc. It
is plausible, however, that such stars contribute much more to the
intracluster light at larger radii.

These results support the recent finding of Ko & Jee (2018) and Joo & Jee
(2023) which revealed massive clusters at $z\sim 1$ that contained $\sim 17$%
of the total stellar light of the clusters within the diffuse intracluster
component, which is similar to the fraction of intracluster light in local
clusters. These authors suggested that the dominant form of ICL production
could be through the accretion of pre-processed stray stars, and our
observations provide evidence of an abundance of such stars in proto-clusters.

###  5.2 The fate of the BCG and intracluster stars found in proto-clusters

The amount of intracluster stars in the proto-clusters is likely to increase
over time because the proto-clusters are likely to evolve into clusters that
are an order of magnitude more massive (Muldrew et al., 2015). As we can see
from Fig. 7, such massive clusters are predicted to have significantly more
stellar mass in the $10<R<100$ kpc region than their low mass progenitors.
Furthermore, local clusters are known to have significant intracluster light
at more than 100 kpc distant from the BCG.

In Figure 8 we explore the fate of the stars within 100 kpc of the $z=2$ BCGs
that were identified in the $M>10^{13}$ M⊙ Hydrangea haloes. We first divide
the stellar population at $z=2$ into three radial bins: $<10$ kpc, between 10
and 50 kpc, and between 50 and 100 kpc. We then plot the fraction of stellar
mass within each of these bins that ends up at various radii within the
cluster at $z=0$. Since we want to know where the $z=2$ stars end up, the
stellar mass of each stellar particle is always taken as the one measured at
$z=2$. By $z=0$, however, stellar mass loss will reduce the mass of the
stellar particles, but this does not change the profiles significantly.

Over time the $z=2$ stars diffuse from their initial position with most stars
moving to larger radii. Only half of the stars that lay within the central 10
kpc of the BCG remain within the same region. The other half move further out
and a few percent reach distances of more than 100 kpc. Similarly,
approximately half of the stars in the $10<R<50$ kpc bin remain in the same
location and the other half move to larger distances; almost a quarter of the
stars travel to distances larger than 100 kpc. The largest amount of movement
occurs in the $50<R<100$ kpc bin, where only $\sim 30$% of the stars remain in
the same bin by $z=0$ and over 55% move further out beyond 100 kpc and several
percent reaching distances of over 400 kpc. Overall, by $z=0$ the stars end up
further away from the BCG than at $z=2$.

Spread over such a large area, the resulting surface brightness from the stars
at $R>100$ kpc would likely be below current measurements of nearby clusters.
Therefore, further production of intracluster stars or accumulation of
previously stripped stars from infalling groups (e.g. Bahé et al. 2019) must
occur to result in the prominent intracluster light seen at several 100 kpc
from the BCGs in present day massive clusters. Such growth in the intracluster
light is expected given the results of Burke et al. (e.g. 2012) and DeMaio et
al. (2020) who showed that the stellar mass in clusters grows from the inside-
out. Burke et al. (2012) showed that the low-surface brightness light
($\mu_{J}>22$ mag arcsec-2) in the ${R<R}_{500}$ region of $z=1$ clusters
grows by $2-4$ times by the present day, whereas DeMaio et al. (2020) showed
that the amount of stellar mass within the central 100 kpc of clusters
continued growing until $z\sim 0.4$. These works suggest the intracluster
light beyond 100 kpc will likely continue growing to the present day, and the
mass growth rate of intracluster stars exceeds that of the halo. Therefore,
the diffuse light we see in the proto-clusters is likely to grow both in size
and mass over the following 10 Gyr.

###  5.3 Prospects for detecting proto-cluster intracluster light with ESA’s
Euclid Mission

Our discovery of intracluster light at $z\sim 2$ means that it is possible to
use the signature of diffuse low surface brightness light and low stellar mass
concentrations to identify clusters and proto-clusters from high-resolution
images, such as will be provided by ESA’s Euclid mission. This is particularly
useful at $z>1.5$, where the photometric redshifts that Euclid’s cluster
finders use are not precise enough to identify galaxy clusters. The presence,
or lack, of intracluster light can be used to remove contaminants from the
cluster catalogues based on photometric redshifts. Furthermore, since the
presence of diffuse light is unique to the central galaxies in proto-clusters,
this is an excellent way to identify the dominant halo within a proto-cluster.

The Euclid Wide Survey is predicted to reach a surface brightness of 29.1
mag/$\mathrm{arcsec^{2}}$ in VIS (3$\sigma$ over 100 $\mathrm{arcsec^{2}}$)
and 27.7 mag/$\mathrm{arcsec^{2}}$ for Y, J, and H$-$band NISP images
(Scaramella et al., 2022; Borlaff et al., 2022), whilst the Deep Survey will
reach 2 magnitudes fainter. This means that the Deep Survey will reach similar
depths to the HST $F140W$ images we use in this work ($29.2$ and $30.3$
mag/$\mathrm{arcsec^{2}}$ in CARLA J1018 and XLSSC-122, respectively) but over
a much larger area.

It is also likely that intracluster light will be detected in the Wide Survey
of Euclid. The surface brightness of the intracluster light in the region
between 10 and 50 kpc ($\sim$100 $\mathrm{arcsec^{2}}$) in both proto-clusters
presented in this work is $[F140W]\sim 26.5$ mag/$\mathrm{arcsec^{2}}$, and
$[F140W]\sim 27.1$ mag/$\mathrm{arcsec^{2}}$ averaged over the larger region
between 10 and 100 kpc ($\sim 430\,\mathrm{arcsec^{2}}$). Thus, we predict
that the intracluster light in both proto-clusters should be detected in the
near-infrared images of Euclid’s Wide Survey.

Whether the intracluster light is also detected in the VIS images depends on
the colour of the light. The reddest colour of the intracluster light that we
measure is $[z]-[F140W]\sim 2$, which means the surface brightness could be as
low as $z=29.1$ mag/$\mathrm{arcsec^{2}}$. The VIS instrument covers the
wavelength range $550$ to $900$ nm, so it covers light blueward of the
$z-$band image we use in this work. Hence, intracluster light at $z\sim 2$ is
likely to be detected in VIS images of the Deep Survey, but we are unlikely to
detect intracluster light in the Wide Survey unless the intracluster stars are
young and blue. We conclude that the NISP images are better suited to search
for intracluster light in distance clusters and proto-clusters.

Additionally, the intracluster light maps in Figure 3 show that the light is
not uniform and brighter regions of diffuse emission will appear well above
Euclid’s detection limits. This will allow detailed measurements of the
morphology and colours of the intracluster light.

The Vera C. Rubin Observatory (LSST) will provide complementary data in the
optical bands to even greater depth than the Euclid survey. However, the
prospects of detecting intracluster light in proto-clusters with LSST are
limited for two reasons. First, the survey is optimised for depth in the
optical bands and the $z$ and $y$ band images will be the shallowest.
Therefore, the LSST survey will probe the rest-frame ultraviolet light from
proto-cluster intracluster stars which will only be prominent when the
intracluster stars are young. Second, the relatively poor spatial resolution
of LSST data compared to Euclid means that it will be harder to separate
galactic light from diffuse intracluster light in the dense core of proto-
clusters.

###  5.4 The impact of the mass-to-light ratio on the stellar mass
concentration

The uncertainties on the colour, and hence mass-to-light ratio, of the
intracluster light beyond 10 kpc within CARLA J1018, and beyond 50 kpc in
XLSSC 122 can significantly affect our conclusions of a low stellar mass
concentration, so it is worth investigating how different mass-to-light ratios
will affect our conclusions. First, we consider an extreme case in which the
mass-to-light ratio beyond 50 kpc of XLSSC 122 is extremely low such that the
mass in this region is negligible. Even in this extreme case, the mass
concentration would increase to only 0.46$\pm$0.04, which is still compatible
with the trend for other clusters seen in Figure 6 and lies far below the
model predictions of Contini & Gu (2021).

Next, we consider the lowest plausible value of the mass-to-light ratio for
the ICL beyond 10 kpc in CARLA J1018. We start by examining colour variations
in the ICL. We place four rectangular apertures across the brightest region of
the ICL in the $F140W$ image, but not covering the central 10 kpc from the
BCG. The centres of the apertures were at [$154.6255$, 5.5183], [154.6264,
5.5175], [154.6279, 5.5161], [154.6288, 5.5152], each of $39\times 93$ kpc and
at an $45^{\circ}$ angle. All apertures had measurable $F140W$ and $z-$band
fluxes at more than a 1.5$\sigma$ level. The colours of the four regions were
$[z]-[F140W]=0.9$, $1.1$, $1.0$ and $1.6$ from South-east to North-west, which
means there is colour variation in the intracluster light and a single mass-
to-light ratio does not capture the complexity of this system. Nonetheless, we
can use a single mass-to-light ratio to estimate a minimum mass in this outer
region and take that as a lower limit to the true mass. The colour of the
intracluster light in the annulus of 10 to 100 kpc is $[z]-[F140W]=1.2\pm
0.4$. Thus, the minimum colour of the intracluster light, assuming maximal
measurement uncertainties is $[z]-[F140W]=0.8$. The intracluster light in all
smaller regions have a redder colour that this, reassuring us that this is the
bluest possible colour of the intracluster light.

We compare this colour to a set of stellar population models in Figure 9. Such
a blue colour can only be achieved with a stellar population model that is
actively forming new stars, such as a constant star formation history or a
very young (0.5 Gyr), exponentially declining model with a long timescale for
the decay of the star formation rate. The mass-to-light ratio also depends on
the assumed IMF, with a Salpeter IMF producing a higher mass-to-light ratio
than the Chabrier IMF. Throughout this work we assume a Chabrier IMF, however,
evidence points to a peculiar stellar IMF in clusters (Friedmann & Maoz,
2018). By assuming a Chabrier IMF, we therefore take the minimum plausible
mass-to-light ratio for the intracluster light. For a Chabrier IMF, a colour
of $[z]-[F140W]=0.8$ corresponds to a minimum mass-to-light ratio of 0.14.
Applying this minimum mass-to-light ratio to the intracluster light beyond 10
kpc, the luminosity concentration of 0.23 implies a mass concentration of
0.66. This value is still compatible with the observed trend for lower-
redshift cluster BCGs, and below the measurements for other massive galaxies
in the proto-cluster.

Figure 9: The relationship between the [$z-F140$] colour and mass-to-light
ratio for galaxies at $z=1.96$. The colour of the intracluster light in CARLA
J1018 between 10 and 100 kpc is shown as the black point with $1\sigma$
uncertainties. The grey diamonds display the variety of intracluster light
colour in the four rectangular regions described in the text. The coloured
lines show the mass-to-light ratio from galaxies simulated with different star
formation histories and Chabrier (solid) or Salpeter (dashed) initial mass
functions. The crosses from the bottom left to top right of each line mark the
colour of galaxies formed at $z=2.5$, 3, 4, 5 and 6 and observed at $z=1.96$.
The lowest possible colour of the intracluster corresponds to a minimum mass-
to-light ratio of 0.14. We take this to be the minimum possible mass-to-light
ratio for the intracluster light in CARLA J1018.

###  5.5 Defining the BCGs in the proto-clusters

The selection of the BCG can also affect our conclusions of a low stellar mass
concentration. There is no other plausible candidate for the BCG in XLSSC 122
since the galaxy we have labelled as the BCG is 1 mag brighter, and 7.6 times
more massive than the second ranked galaxy in this proto-cluster (Noordeh et
al., 2021). On the other hand, the selection of galaxy a as the BCG of CARLA
J1018 is not certain as galaxies b, c, d, as well as the quasar, could all be
the most massive galaxy in the proto-cluster. Galaxy b is also brighter than
galaxy a in F140W, although both galaxies have consistent fluxes within
uncertainties in the $K-$band, and as can be seen from Fig. 2, the SED fits
predict that redward of 2-microns, galaxy a is likely to be brighter than
galaxy b. We therefore used the local surface density of galaxies to determine
which of these galaxies is most likely to be at the barycentre of the proto-
cluster. We selected galaxy a because it is the most massive and has the
highest galaxy density on the scale of 100 kpc out of all galaxies in the
proto-cluster.

Whilst these reasons justify our choice of galaxy a as the BCG, we also find
that our results do not qualitatively change if we chose galaxies b, c or d to
be the BCG: we still find significant diffuse light beyond 10 kpc of the BCG
core regardless of which galaxy is chosen to be the BCG. Quantitatively, the
amount of light within the 100 kpc radius would be reduced if the BCG was
chosen to lie at the edge of the high-density region shown in the insert of
Figure 1, and the amount of diffuse light that would be classified as residing
beyond 100 kpc would increase. For example, if we selected galaxy b as the
BCG, then we obtain a BCG+ICL observed F140W magnitude of $21.70\pm 0.02$ mag
within 10 kpc and $20.9\pm 0.2$ mag in the 10 to 100 kpc annulus. This results
in a light concentration of $0.32\pm 0.03$. This is slightly more concentrated
than if we selected galaxy a as the BCG, but it is still far lower than the
light concentration found for the other massive proto-cluster galaxies located
outside the core. Therefore the exact values of the mass and light
concentrations will increase, although they are still low compared to other
massive galaxies, both within and beyond the proto-cluster. Thus, our
conclusion remains valid as long as the dense region in the insert of Figure 1
is the barycentre of the proto-cluster.

The argument given above only holds if we can use the surface density of
galaxies as a proxy for the true 3D density; if the dense core region in the
insert of Figure 1 is only due to the projection of unrelated galaxies, then
this region may not be the barycentre of the proto-cluster. We therefore
compare the probability that the galaxy overdensity is due to a chance line-
of-sight distribution to the probability that these galaxies are in close
proximity and are interacting with each other.

The area of the region depicted in the insert of Figure 1 is $0.31\times 0.32$
co-moving $\mathrm{Mpc^{2}}$ ( $16.8\times 17.1\mathrm{arcsec^{2}}$) and the
line-of-sight co-moving radial distance spanned by the interval $\Delta
z=0.04$ is 60.4 Mpc, so the volume is $6.1\ \mathrm{Mpc^{3}}$. The number
density of $>\mathrm{10^{11}}$ M⊙ galaxies at $z\sim 2$ is $10^{-4}$ Mpc-3
(Muzzin et al., 2013) so the probability of observing any galaxy more massive
than $10^{11}$ M⊙ in this volume is 0.06%. The probability of detecting five
unrelated galaxies, of more than $\mathrm{10^{11}}$ M⊙, within this volume is
vanishingly small at less than one in a trillion.

On the other hand, the chance of observing two massive galaxies that are in
the process of merging is much higher. Simulations predict that a
$\mathrm{10^{11}}$ M⊙ galaxy at $z=2$ will merge with another galaxy, of at
least a quarter of its mass, at a rate of 0.15 Gyr-1 (Rodriguez-Gomez et al.,
2015). Galaxy mergers can be identified as close pairs of galaxies, and the
length of time a merger is visible depends on the projected separation and
mass ratio of the pair. For galaxies within a $1:4$ mass ratio this timescale
varies from a few hundred Myr to 1.5 Gyr depending on the projected separation
(Lotz et al., 2011). The projected separations of the galaxies in the core
region range between 12 and 36 kpc (proper) so these mergers will be visible
for an average of 0.6 – 1 Gyr. Thus, the probability of observing a massive
galaxy undergoing a merger with another nearby galaxy is 10 to 15%. Since
there are five galaxies more massive than $\mathrm{10^{11}}$ M⊙ in the core,
and hence 10 unique pairs, there is a 60 to 80% chance that we would observe
these galaxies undergoing a merger. Assuming each merger is mutually exclusive
and treating the closer merger pair as a single entity, the probability of
observing five massive galaxies merging at the same time is 0.01 – 0.05%. This
is much higher than the chance of observing 5 unrelated massive galaxies
distributed across the 60.4 cMpc line-of-sight, hence it is more likely that
the dense galaxy group we have observed in CARLA J1018 is the barycentre of
the proto-cluster than a chance line of sight alignment.

The space density of $>10^{11}$ M⊙ galaxies is $10^{-4}$ Mpc-3 (Muzzin et al.,
2013), and we have calculated that between one in a hundred to one in twenty
of these will be undergoing extreme merging events such as that seen in the
core of the CARLA J1018 proto-cluster. This means the space density of such
extreme merging events is $10^{-8}$ Mpc-3. This is the same space density as
galaxy clusters with masses greater than ${10^{15}}$ M⊙ in the nearby Universe
(Vikhlinin et al., 2009). It is therefore plausible that such extreme merging
events signpost the formation of the core within the most massive galaxy
clusters.

##  6 Conclusions

We report on the detection of intracluster light within two proto-clusters at
$z\sim 2$ using deep HST near-infrared images. This extends our understanding
of intracluster light to the numerous group-sized halos that exist at this
redshift; previous measurements focused on the most extreme (and rare)
cluster-sized halos at $z\sim 1.5$ which may not be typical cluster
progenitors.

We identified the BCGs of the proto-clusters as the most massive galaxies
within the densest regions of the proto-clusters, and measure the amount of
diffuse light surrounding these galaxies. We found that the flux of diffuse
light between 10–100 kpc is more than double the flux from within 10 kpc. We
showed that this extended morphology is similar to the profiles of BCGs within
massive clusters at $1.24<z<1.75$ which are known to host intracluster light.
Furthermore, this profile differs from the other massive galaxies in the
proto-cluster, whose light profiles are at least a factor of 3 more
concentrated than the BCGs. Based on these observations, we conclude that the
proto-clusters contain significant intracluster light.

We used the colour of the intracluster light to estimate its mass-to-light
ratio and calculate the concentration of stellar mass in the core of the
proto-clusters. We found that only a quarter to a half of the stellar mass
within 100 kpc is located within the central 10 kpc. We combine our data with
that of DeMaio et al. (2020) to show that this low concentration is comparable
to that found in similar-sized halos at lower redshifts, and such low
concentrations at $z\sim 2$ are in disagreement with the semi-analytic models
of intracluster light by Contini & Gu (2021). Our discovery implies that the
formation of the intracluster light began earlier than the $z\sim 1-1.5$
period predicted by these models.

To investigate how this intracluster light could form so early, we compared
the stellar mass concentrations in clusters and proto-clusters to that of
central galaxies of massive halos in the Hydrangea hydrodynamical simulations
(Bahé et al., 2017). We found that these simulations agree with the trend in
the observations: the stellar mass concentration depends on the halo mass, but
does not depend on redshift. Hydrangea also predicts that intra-halo stars are
ubiquitous in massive halos at all redshifts, and even found in halos with
masses as low as $10^{12}$ M⊙. We interpret these findings as evidence that
pre-processed free-floating stars from accreted halos is a major contributor
to the intracluster light within 100 kpc of clusters and protoclusters, whilst
few of the stars in this region were stripped from orbiting satellite
galaxies.

## Data Availability

All data used in the analysis of this paper can be downloaded from the
Mikulski Archive for Space Telescopes, https://archive.stsci.edu, or the ESO
Science Archive Facility, http://archive.eso.org.

## Acknowledgements

For the purpose of open access, the author has applied a creative commons
attribution (CC BY) to any author accepted manuscript version arising.

We thank the reviewer, Chris Collins, for useful feedback and Leonardo
Ferreira for helping with the technical details of HST data reduction. SW
thanks the University of Nottingham, UK, Vice Chancellor International
Scholarship. NAH thanks the Science and Technology Facilities Council, UK,
consolidated grant ST/T000171/1. GN thanks the Natural Sciences and
Engineering Research Council Canada, Discovery Grant and Discovery Accelerator
Supplement and the Canadian Space Agency, grant 18JWST-GTO1. YMB thanks the
Dutch Science Organisation (NWO), Veni grant 639.041.751. JM thanks the George
P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy
at Texas A&M University. DW thanks the German Research Foundation, Emmy
Noether Grant WY 179/1-1, the Daimler and Benz Foundation and the German Space
Agency, Verbundforschung grant 50 OR 2213. Based on observations collected at
the European Organisation for Astronomical Research in the Southern Hemisphere
under ESO programmes 094.A-0343(C), 094.A-0343(D), 094.A-0343(E),
096.A-0317(A), 096.A-0317(B), 096.A-0317(C).

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