The progenitors of the intra-cluster light and intra-cluster globular clusters in galaxy groups and clusters

We use the IllustrisTNG50 cosmological hydrodynamical simulation, complemented by a catalog of tagged globular clusters, to investigate the properties and build up of two extended luminous components: the intra-cluster light (ICL) and the intra-cluster globular clusters (ICGC). We select the 39 most massive groups and clusters in the box, spanning the range of virial masses $5 \times 10^{12}<\rm M_{200}/\rm M_{\odot}<2 \times 10^{14}$. We find good agreement between predictions from the simulations and current observational estimates of the fraction of mass in the ICL and its radial extension. The stellar mass of the ICL is only $\sim10\%-20\%$ of the stellar mass in the central galaxy but encodes useful information on the assembly history of the group or cluster. About half the ICL in all our systems is brought in by galaxies in a narrow stellar mass range, $M_*=10^{10}-10^{11}$ $\rm M_{\odot}$. However, the contribution of low-mass galaxies ($M_*<10^{10}$ $\rm M_{\odot}$) to the build-up of the ICL varies broadly from system to system, $\sim 5\%-45\%$, a feature that might be recovered from the observable properties of the ICL at $z=0$. At fixed virial mass, systems where the accretion of dwarf galaxies plays an important role have shallower metallicity profiles, less metal content and a lower stellar mass in the ICL than systems where the main contributors are more massive galaxies. We show that intra-cluster GCs are also good tracers of this history, representing a valuable alternative when diffuse light is not detectable.


INTRODUCTION
One of the most striking features of high density environments is the intra-cluster light (ICL), a diffuse component of light that originates from populations of stars that are not associated with individual galaxies and are instead gravitationally bound to the host dark matter halo.The ICL is thought to be a product of the tidal stripping of stars from galaxies as they traverse the cluster or group environments and was first proposed and subsequently discovered by Zwicky (1937Zwicky ( , 1951Zwicky ( , 1952Zwicky ( , 1957) ) in the Coma cluster.The direct link between the ICL and satellite galaxies makes the formation of this diffuse light a natural prediction of the hierarchical assembly model in Cold Dark Matter (CDM, White & Rees 1978;Conroy et al. 2007;Montes & Trujillo 2018;Contini 2021).
The ICL has cosmological relevance primarily in two aspects.First, it represents a visible tracer of the unseen dark matter distribution, with several theoretical works supporting a good correlation between the shape and orientation of the ICL and those of the underlying dark matter halo (Montes & Trujillo 2019;Alonso Asensio et al. 2020;Contini & Gu 2020;Deason et al. 2020;Gonzalez et al. 2021).Second, and the main focus of this paper, the ICL is built by ★ E-mail: niusha.ahvazi@email.ucr.edu/ nahvazi@carnegiescience.edu the tidal disruption of many satellite galaxies, some of which do not survive until today.As such it can help unravel the past formation history of the host group or cluster halo (Montes 2022;Contini 2021, and references therein), in a similar way that stellar halos can help reconstruct the merger histories of smaller mass halos in the MW-like regime (e.g., Bullock & Johnston 2005).
The stellar mass content of the ICL is directly related to the stellar mass-halo mass relation and serves as a probe of the past assembly history of galaxy clusters.A number of observational constraints on the amount of ICL have been reported in the literature, with studies using deep imaging to estimate the total amount of ICL in galaxy clusters (e.g.Zibetti et al. 2005;Mihos et al. 2017;Krick & Bernstein 2007;Morishita et al. 2017;Jiménez-Teja et al. 2019a;McGee & Balogh 2010).These studies have found that the ICL typically makes up a significant fraction of the total light in galaxy clusters, ranging from <10% to 50% depending on the cluster and the methods used to estimate the ICL (see Montes 2022).
Numerical simulations predict that the bulk of the ICL mass comes from the tidal stripping of massive satellites (10 < log(M/M ⊙ ) < 11) (Puchwein et al. 2010;Cui et al. 2014;Cooper et al. 2015;Contini et al. 2013;Contini et al. 2019;Montenegro-Taborda et al. 2023).Particularly, disk-like massive satellites are thought to significantly contribute to building the ICL through a large number of small stripping events (Contini et al. 2018).However, other lessdominant mechanisms may also contribute stars to the ICL including the total disruption of low mass satellites (Purcell et al. 2007), stars ejected into the inter-cluster medium after a major merger (Murante et al. 2007) and the pre-processing of accreted groups (Rudick et al. 2006).Due to the well established relation between stellar mass and metallicity in galaxies, the nature of the progenitors that build up the ICL can be observationally constrained from stellar metallicities.Furthermore, each of these mechanisms are expected to leave distinct patterns on the metallicity and their gradients.
Constraining the contribution of each mechanism can be extremely challenging due to the faint (  ∼ 26.5 mag/arcsec2 ) and extended characteristics of the ICL, which can often only be probed by broadband photometry.Yet, over the last two decades, significant progress has been made.A number of observational studies have highlighted the presence of clear negative radial color gradients (Krick & Bernstein 2007;Rudick et al. 2009;Melnick et al. 2012;DeMaio et al. 2015) in the ICL of the majority of clusters studied at  ∼ 0.5.While such gradients could potentially arise due to changes in metallicity (Montes & Trujillo 2014;DeMaio et al. 2015) or variations in the ages of the stars (Morishita et al. 2017;Montes & Trujillo 2018), it suggests that violent relaxation after major mergers with the BCG cannot be the dominant source of ICL.Although, the observed metallicities of the ICL ([Fe/H] ICL ∼ −0.5) align with the notion that the ICL stars likely originate either from stars located in the outer regions of galaxies with stellar masses approximately 5 × 10 10 M ⊙ (DeMaio et al. 2018;Montes & Trujillo 2018;Montes et al. 2021) or from the dissolution of dwarf galaxies, the amount of ICL is often used as an argument against the latter as this would dramatically alter the faint end of the cluster galaxy luminosity function (e.g.Zibetti et al. 2005;DeMaio et al. 2018).Only a small number of clusters have been identified with flat color gradients (e.g.Abell 370) -indicating an ICL formed through the expulsion of stars into the intra-cluster medium during a major merger event (Krick & Bernstein 2007;DeMaio et al. 2015DeMaio et al. , 2018)).While the vast variety of observations point to the progenitors of the ICL being the tidal stripping of massive satellites (10 < log(M/M ⊙ ) < 11) consistent with theoretical predictions, the ICL of the two closest well-studied clusters, the Virgo and Coma, which can be studied in significant detail, suggest very different assembly mechanisms.Williams et al. (2007), studying the RGB populations of the Virgo cluster (∼15 Mpc) using a single and deep HST pointing, found that 70% of the stars have a metallicity of [M/H] ∼ −1.3) indicating that the ICL was built up primarily through the disruption of dwarf galaxies.Similarly, Gu et al. (2020) spectroscopically studied the ICL of the Coma cluster in the low S/N regime finding it to be old and metal-poor ([M/H] ∼ −1.0) -consistent with the accretion of low-mass galaxies or the tidal stripping of the outskirts of massive galaxies that have ended their star formation early on.The low metallicity of the ICL of the Virgo and the Coma cluster clearly suggests that the contribution of dwarf galaxies to the ICL can be significant.This is clearly in tension with the observations of clusters further away as well as the current theoretical paradigm, requiring further study and perhaps a revision of understanding of the contribution of dwarf galaxies to the ICL.
One way to observationally disentangle the various formation mechanism is to study how the ICL correlates with the mass of the cluster and with redshift.However, as we probe deeper into the universe and examine systems at earlier redshifts, the low surface brightness of the intra-cluster light becomes increasingly difficult to capture.In such cases, an alternative path to study the dark matter halos may be offered by globular clusters (GCs).These ancient, dense clusters of stars are commonly found in nearly all types of galaxies and are thought to be among the oldest and (often) metal-poor stellar populations in the universe (Gratton et al. 2019).They are believed to have formed before the majority of galaxies and are relatively luminous (Schauer et al. 2021), making them easily detectable at large distances and earlier redshifts and a powerful tool to study the distribution of dark matter and ICL in the early universe.
GCs can be very numerous in groups and clusters.While for MWlike galaxies they populate host halos by the hundreds, in the Virgo cluster more than 10,000 have been cataloged around M87 (Durrell et al. 2014).Studies have shown that the abundance of GCs is closely related to the amount of dark matter in the halos (Spitler & Forbes 2009;Harris et al. 2013;Hudson et al. 2014;Harris et al. 2015).Therefore, GCs can offer an alternative path to study the dark matter halos in galaxy groups and clusters, especially when the ICL is not easily captured.
A large fraction of GCs associated with a given system are members of the intra-cluster globular cluster (ICGC) component, which has been observationally confirmed in Fornax (Schuberth et al. 2008), Coma (Madrid et al. 2018), Abell 1689 (Alamo-Martínez & Blakeslee 2017), Virgo (Lee et al. 2010;Ko et al. 2017;Longobardi et al. 2018) and Centaurus A (Taylor et al. 2017) for example.This intra-cluster component is expected to arise mostly by the gravitational removal of GCs from satellite galaxies that interacted with the groups, and predominantly from satellites that did not survive until today (Ramos-Almendares et al. 2020).In this way, the origin of the ICGCs and the ICL are therefore expected to be strongly linked, and one might naively expect similar properties and building blocks for both components.However, the way stars and GCs occupy halos is different, in particular in the low mass end of dwarf galaxies, and it is as yet unclear how this may impact the way GCs and the ICL trace each other.
In this study, we take advantage of the recently published catalog of GCs1 , which are tagged post-processing into the cosmological hydrodynamical simulation IllustrisTNG50 to explore the properties of the ICL and GC components of groups and clusters.The paper is organized as follows: in section 2, we present a brief description of the simulation and definitions used in our study.In section 3, we introduce the general properties of the ICL component predicted by the simulation.In section 4, we analyze the progenitors of the ICL component, and in section 5, we investigate the use of GCs as tracers of the formation history of ICL.Finally, in section 6, we summarize the main results of our study.
The evolution of gravity and hydrodynamics are followed using the arepo moving mesh code (Springel 2010).The galaxy formation baryonic treatment is based on its predecessor simulation suite, Illustris (Vogelsberger et al. 2013(Vogelsberger et al. , 2014a,b;,b;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); Weinberger et al. (2017).
The updated Illustris-TNG sub-grid models accounts for star formation, radiative metal cooling, chemical enrichment from SNII, SNIa, and AGB stars, stellar feedback, and super-massive black hole feedback (Weinberger et al. 2017;Pillepich et al. 2018a).These models are shown to reproduce several of the  = 0 basic galaxy scaling relations, including the stellar mass -size (Genel et al. 2018), the color bimodality (Nelson et al. 2018) and galaxy clustering (Springel et al. 2018), among others.As such, they are representative of the present day population of galaxies in the universe and reproduce the main environmental trends observed in satellites.Of particular relevance to this work, the abundance of low-mass and intermediate mass galaxies seems consistent with observationally estimated stellar mass functions (e.g.Pillepich et al. 2018a;Vázquez-Mata et al. 2020;Engler et al. 2021).

Identification of groups and clusters
Groups are identified using spatial information based on a Friendsof-Friends (FoF) algorithm (Davis et al. 1985).Individual selfgravitating subhalos and galaxies are later found in these groups using SUBFIND (Springel et al. 2001;Dolag et al. 2009).The object at the center of the gravitational potential of each group is called the "central" galaxy, while all other substructures are "satellites" (or "subhalos").SUBFIND identifies substructures with a minimum of 32 particles and we additionally apply M DM ⩾ 5.4 × 10 7 M ⊙ (at the time of infall) to remove the chances of including spurious baryonic clumps that are not bonafide galaxies.The time evolution of galaxies and halos through the 99 snapshots of the simulation is followed by using the SubLink merger trees (Rodriguez-Gomez et al. 2015).
We identify groups and low mass clusters in TNG50 by selecting all host halos with virial masses  200 /M ⊙ ⩾ 5 × 10 12 , where virial quantities are measured within the virial radius, or  200 , defined as the radius of a sphere where the mean density of the group is 200 times the critical density of the Universe.This selection results in 39 groups and clusters, containing 3305 and 5020 satellite galaxies with  * > 10 7 M ⊙ within the virial radius and FoF group boundaries, respectively.

The intra-cluster light (ICL) in groups and clusters
For the purpose of this work we define the ICL as all stellar particles that are unbound to any substructure, (exclusively) bound to the group as a whole, and located within a radial range of 0.15 r 200 < r < r 200 from the host galaxy, where r 200 is the virial radius of the group.Different definitions of ICL are commonly assumed in the literature, both in simulations and observational work.We have experimented with several of these definitions and explicitly checked that none of our main conclusions depends qualitatively on the specific criteria adopted here.For a more detailed view, we collect in Appendix A some examples on how the exact definition of ICL affects some of our reported results.
Further inspection of our selection of ICL particles revealed an excess of stars located on the periphery of several satellites.These stellar particles are considered unbound by SUBFIND (and therefore included as ICL candidates) but are still clearly part of the satellite or substructure in the 6D space of positions and velocities.We therefore applied two extra requirements in order to "clean" our ICL sample.Each stellar particle needs to be at least 10 × r h * away from any massive satellite (the ones larger than M/M ⊙ > 10 10 ), where r h * is the stellar half mass radius of the satellite.In addition, we ensure that the velocity of the particles satisfy V/V C > 2.5 to be considered part of the ICL, where V C is the circular velocity at 2 × r h * of the satellite.This procedure satisfactorily removes extra stellar particles with positions and velocities strongly correlated with the local substructure.Note that similar methods are used in observations of the ICL to reduce the light contamination from the central galaxy and the satellite galaxies.

In-situ vs. ex-situ
In this paper, we frequently use the terms "in-situ" and "ex-situ" to distinguish between different types of stellar populations: those born from gas bound to the main branch progenitor in the SubLink merger tree of a galaxy ("in-situ") versus those born in external galaxies and later brought in to the descendant object during mergers or tidal stripping events ("ex-situ").
To classify stars as ex-situ or in-situ, we use the stellar assembly catalogs, offered as auxiliary data in the TNG database.The classification method was introduced in detail in Rodriguez-Gomez et al. (2016) and is based on the SUBFIND association of the newly formed stars (at the time of birth) to either the main progenitor of the central galaxy (in-situ) or to a substructure that later merges into the system (ex-situ).Main or secondary progenitors are defined using the SubLink merger trees.

Globular Clusters
We use the catalog of GCs presented in Doppel et al. (2023) for our TNG50 systems.GCs are tagged for all galaxies with M * ,max ≥ 5 × 10 6 M ⊙ that infall or interact with our groups and clusters.The tagging is done at infall time for all galaxies, after which the dynamics of the GCs is followed naturally by tracking the positions and velocities of the particles flagged as GC candidates.The simulated GCs are shown to follow known scaling relations for galaxy-GCs and, in addition, to give rise to a population of intracluster GCs (ICGCs) as a combination of tidal stripping of GCs from merging galaxies and a native GC population tagged onto the central galaxy (Ramos-Almendares et al. 2020;Doppel et al. 2023).The slope and normalization of this ICGC component is in rough agreement with current observational constraints (see Fig. 5 in Doppel et al. 2023).In Appendix B we summarize the technical details of the GC tagging technique, for additional information we refer the reader to Doppel et al. (2023).
For this work, we use from this catalog the ICGCs, identified as tagged GCs that are currently not associated to any substructure according to SUBFIND and "cleaned" with the same method described in section 2.2 for the ICL.As an example of how these GCs are distributed in our systems, we show in Fig. 1, projected maps of multiple groups from our sample.These plots show the stellar component (gray-scale in the background) with the position of the ICGCs highlighted by the cyan dots.These few examples illustrate interesting differences in size, shapes and concentration of the GC and ICL components, suggesting a link to their different formation histories.

ICL mass content
In order to quantify the amount of mass in the ICL we define the fraction of mass in the ICL as: where M * ICL is the stellar mass in the ICL and M * BCG is the stellar mass within 2 × r h * of the central galaxy.Solid circles with black outlines in Fig 2 show  ICL for our sample of groups and clusters plotted against the virial mass of each group.We note that various definitions of this fraction have been used in the literature.In particular, a lower limit to  ICL might be found by dividing the mass of the ICL by the total mass of stars within the virial radius  ICL,tot =  ICL / * , 200 .For comparison, we show  ICL,tot in Fig. 2 with downward triangles connected to the solid symbols.In general we find that the ICL fraction can change by more than a factor of two by adopting common definitions in the literature (see Appendix A).In this work,  ICL will refer to Eq. 1 unless specified otherwise.
Our systems span from 5 × 10 12 to nearly 2 × 10 14 M ⊙ in virial mass, sampling the range from isolated elliptical galaxies comparable to Centaurus A to moderate mass galaxy clusters such as Fornax, and conservative mass estimates of the Virgo cluster.The ICL mass fraction shows a subtle increase with virial mass, with typical values 5-10% in our low mass systems and ∼ 20% for our more massive clusters.The relation also exhibits a substantial degree of dispersion at a given mass.We trace back the dispersion in this relation to the assembly history of each group.The color coding in the left panel of Fig. 2 shows that, at fixed halo mass, groups with a longer time since their last major merger tend to show lower ICL mass fractions than groups where the last major merger was more recent.This trend has been quantified by categorizing the systems into "red" and "blue" groups, based on whether their last major merger occurred within 7.5 Gyr or after.Major mergers are here defined as merger events of the central galaxy with satellites of stellar mass ratios greater than 0.25 measured at the time of maximum stellar mass of the companion merging galaxy (Rodriguez-Gomez et al. 2015).
This correlation between mass in the ICL and the assembly history of the system is consistent with being an extension into the larger mass regime of the trend found for stellar halos in MW-like galaxies (e.g., Elias et al. 2018) and is also in agreement with findings in other simulations of MW-like and groups and cluster systems using the Horizon-AGN simulations Cañas et al. (2020).Similarly, several observational studies at low and intermediate redshift find a consistent pattern where higher ICL fractions are common in systems undergoing active mergers while lower fractions are characteristic in more passive or relaxed objects (Jiménez-Teja et al. 2018, 2019b, 2021;de Oliveira et al. 2022;Dupke et al. 2022).
On the right panel of Fig. 2 we explore how TNG50 predictions compare to available theoretical and observational constraints to validate our systems.On the theoretical side, our results seem to agree, within the dispersion at a given mass, with semi-analytical models from Contini et al. (2013; shaded orange) and N-body + stellar tagging simulations of Rudick et al. (2011;shaded cyan).
Our results seem to also agree well with several observational constraints available in the literature (symbols with error bars), in particular, bearing in mind that the definition of ICL, band-width and depth of the observational data varies from system to system.We discuss in more detail the compilation of individual measurements in Appendix D and also summarize the information in table D1.
Most observational constraints seem to suggest that the ICL has less than ∼ 30% of the light of the BCG, in good agreement with our results.Only NGC 5018 (red diamond), HCG 79 (highest purple triangle) and the Fornax cluster (pink triangle) have  ICL > 0.3.While in general we do not reproduce such large ICL fractions in our simulated systems, two of our groups have  ICL ≥ 0.3.A careful look into the formation history of these systems (with FoF group IDs 4 and 12 in TNG50) revealed that their large ICL fractions can be attributed to two different factors.Group 4 presents a central galaxy that is under-massive compared to what is expected of its virial halo mass, such that when computing the ICL fraction it appears larger than other systems.Closer inspection revealed that this group had a rather late major merger (time ∼ 12.3 Gyr) that significantly increased its total mass but has not yet propagated into the central galaxy yet.Reassuringly, this group has several large mass satellites that presumably will merge soon with the central bringing its mass into agreement with its halo mass, at which point we expect  ICL to align with the lower values found in the sample.The second group, FoF group 12, is currently undergoing a major merger with a large satellite companion and the stripped material of this interaction is actively increasing the ICL mass without contributing yet to the central galaxy.Both of these examples are expected to decrease their  ICL after the current interactions are settled.
Our analysis of the groups in TNG50 also revealed the presence of a substantial in-situ stellar component within the ICL, in agreement with previous studies of stellar halos in the predecessor Illustris simulation (D'Souza & Bell 2018;Elias et al. 2018) for smaller mass systems and a more recent study of cluster mass halos using TNG300 simulation by Montenegro-Taborda et al. 2023 (see Sec. 2.3 for a description of the in-situ definition).We highlight in Fig. 2 where the ICL fraction would fall if one only considers the accreted component (gray filled circles), indicating that the inclusion or not of this component does not strongly modify our results.A more detailed study of the in-situ ICL is deferred to a forthcoming paper.

ICL radial extent
The physical size at which the density profile of the ICL reaches a given surface brightness limit is an observable that may help constrain theoretical models on the formation of galaxies and their associated diffuse stellar component.In order to establish a fair comparison between observations and simulations, we randomly project our simulated groups and clusters generating their 2D surface brightness maps.Following Rich et al. (2019), we measure the radius at which the surface brightness reaches 28 mag/arcsec 2 in the r-band, using the available stellar particle magnitudes from TNG50.
We characterize the radial extension of the ICL in our simulated systems by defining two different radii,  28 and  28 , an ellipsoid-base and a circle-based definition following common practice in the field.First, we measure the average surface brightness in circular bins and find the (circular) radius  28 where the surface brightness is closest to 28 mag/arcsec 2 .Second, we measure the surface brightness map with a 3 kpc × 3 kpc resolution and fit an ellipse to the regions of this map exhibiting a surface brightness of 28 magnitudes per square arcsecond (excluding any low surface brightness features that may result from interactions of subhalos).The semi-major axis of this ellipse was then used as a proxy of radial extension ( 28 ).Note that, on average, this surface brightness limit is predicted to occur at ∼ [0.2 − 0.3]r 200 in our systems, extending significantly beyond the central galaxy.Next generation surveys using Euclid or JWST are expected to reach several magnitudes fainter, mapping further out regions at ∼ [0.3 − 0.9]r 200 (see Fig. C1 in Appendix C).
Fig. 3 shows the size of our simulated systems as a function of the stellar mass of the central (top panel) and the virial radius of the group (bottom panel).As expected, the elliptical semi-major axis tends to be slightly larger than the circularly-averaged radius  28 , but they both trace similar trends.The ICL size follows a power law relation with the mass of the central galaxy, consistent with observational constraints available at the low mass end of our sample.
The top panel of Fig. 3 shows this good agreement by including observational results for the stellar halo of galaxies in the HERON survey (Rich et al. 2019) (magenta, purple and gray symbols) and also the fit provided in Muñoz-Mateos et al. ( 2015) (gray dashed line).Our sample, while in agreement in the low mass end, seems to predict a slightly steeper increase in size with stellar mass for the highest mass objects than expected from the gray dashed line.
The bottom panel of Fig. 3 indicates that the size of the ICL also shows a good correlation with the virial radius of the system, although with significant scatter.The gray and cyan dashed lines are best-fit linear relations (y = a + b x) between the logarithmic sizes of the ICL and the halos, characterized by the parameters a and b.For the elliptical radius  28 , we find the parameter values to be  = −1.57and  = 1.41 with r.m.s scatter of ∼ 0.1 dex, while for the circular radius  28 , the values are  = −1.81 and  = 1.45 with a scatter measured to be ∼ 0.1 dex.The existence of a correlation between the radial extension of the ICL and the virial radius of the host halo demonstrates that the assembly of these two components is intertwined and reaffirms the validity of the ICL as observational tracer of the distribution of dark matter in these objects.

THE PROGENITORS OF THE ICL IN GROUPS AND CLUSTERS
A myriad of disrupted satellites are expected to contribute to the build up of the ICL as a consequence of the hierarchical formation scenario, making it a unique probe of the particular assembly history of a given object.Yet, while the individual formation histories may vary from halo to halo, common trends arise that may be used to infer details of the formation and assembly of a given object from the properties of their diffuse stellar component.For instance, in the case of MW-mass galaxies, simulations suggest that the properties of the  We explore in what follows what are the typical building blocks of the ICL in more massive objects like groups and clusters, and what observational signatures may be useful to decode details of their assembly.
Fig 4 shows the fractional contribution of stars to the ICL of two different groups (orange and blue curves) that come from progenitors of a given stellar mass  * ,max .Both groups are selected to have comparable mass,  200 ∼ 3.2 × 10 13 M ⊙ , but different accretion histories.Here we choose to characterize the mass of the progenitors using their maximum stellar mass  * ,max , and we build the cumulative histogram of stellar particles brought in by progenitors more massive than a given  * ,max .The group depicted in orange corresponds to a case where most of the mass in the ICL is contributed by relatively massive galaxies while the group shown in blue allows for significant contribution of progenitors in the regime of dwarf galaxies.
We quantify this by means of  25 ,  50 and  90 , which are defined as the mass of the progenitors in such cumulative distribution contributing 25%, 50% and 90% of the mass in the accreted ICL.For illustration, we highlight  90 in Fig. 4 with vertical dotted lines and an inverted triangle, computed as the intersection of the cumulative distribution of accreted stars in each group and the 0.9 horizontal line. 50 and  25 are also denoted by a circle and a triangle for each group along the horizontal axis.The larger contribution of dwarf galaxies to the build up of the ICL in the group shown in cyan is now clearly shown by its lower mass  90 = 5.2 × 10 8 M ⊙ compared to  90 = 5.2×10 9 M ⊙ in the case of the group in orange.Differences for  50 and  25 between these two groups are smaller, but systematic.
The typical progenitors of the ICL for the full sample of groups and clusters are shown in the left panel of Fig. 5. Our results suggest that the predominant contributors to their ICL are massive galaxies with  50 ≥ 10 10 M ⊙ , regardless of the host halo mass in this somewhat narrow  200 range.This is in agreement with previous works in the literature which identify M * ∼ 10 10 -10 11 M ⊙ as the main progenitors of the ICL in groups (e.g., Contini et al. 2013;Contini et al. 2019;Montes & Trujillo 2018;Montes et al. 2021).However, a comparison of the  90 values uncovers a larger variability of contributions of dwarf galaxies from halo to halo, with some systems having  90 ∼ 10 10 M ⊙ -and therefore having negligible mass brought in by dwarf galaxies with  * ∼ 10 9 M ⊙ and belowwhile other systems show a more significant contribution by dwarfs with typical  90 < 10 9 M ⊙ .This is further illustrated in the right panel of Fig. 5, which depicts the fraction of ICL mass contributed by galaxies with  * ,max < 10 10 M ⊙ as a function of the halo virial mass.As anticipated, these fraction can be quite different from system to system, even in the case of similar halo masses.For instance, for groups with  200 ∼ 10 13 M ⊙ , the fraction of mass brought into the ICL by low mass galaxies with  * ,max < 10 10 M ⊙ varies from 10% to 40%, these extremes being examples of systems where dwarf galaxies play little to a significant role, respectively.Symbols in the right panel of Fig. 5 are colored according to the previously introduced  90 and highlights the good correlation between both indicators: systems with a substantial contribution from low mass galaxies have a high fraction of stars brought in by progenitors with  * ,max < 10 10 M ⊙ and a low  90 value while systems built up mostly by large galaxies have a small fraction  and large  90 values.
This opens up the possibility to use different observables to attempt determine the kind of accretion history of a halo given the observed properties of their ICL.One such key observable is the metallicity profile.Fig 6 illustrates the metallicity profile for three representative groups with differing formation histories and virial masses (as indicated by the legends).The blue curve in each panel depicts the median metallicity of the stellar particles in the ICL at each radius, while the blue shaded region represents the 25th and 75th percentiles.A linear fit of the form  = log(r) + b is in general a roughly good description of our profiles (see red lines) and allow us to quantify for each object the slope of the metallicity profile () and its intercept ().Fig. 7 shows interesting correlations in the ICL observables that imprinted by the kind of progenitors that built each individual object.At a given host halo mass, systems with a larger contribution from dwarfs (blue-ish points) show less total mass in the ICL (left panel), a lower average metallicity (middle panel) and also flatter metallicity profile slopes (right-hand panel).Systems with mostly massive progenitors (red colors) tend to show strongly declining metallicity profiles.Not shown here for brevity, the metallicity profile intercepts correlates well with the median metallicity.In all panels points have been color-coded by  90 and only the accreted component of the ICL is being considered here.However, our main results would not substantially change if, instead, we would show the total ICL (in-situ plus accreted, gray triangles on the right panel).We have explicitly checked that similar trends exist with the stellar age profiles, with most systems displaying decreasing age profiles with radius, and some showing considerably flatter age distributions.However ages seemed less well correlated with the assembly history of the group and cluster than the information provided by metallicity.
The ICL mass and metallicity should then be considered a valuable tool to reconstruct details on the past merger history of systems assembled within ΛCDM.Similar correlations on amount of mass, overall metallicity and metallicity gradients with the diffuse component build-up have been found in the regime of stellar halos for  Our results extend upwards the range of halo masses over which these correlation are expected, including now the regime of groups and clusters.

TRACING THE FORMATION HISTORY OF THE ICL THROUGH GLOBULAR CLUSTERS
We investigate how well the GCs can trace the ICL in our systems using the GC catalog presented in Doppel et al. (2023).As detailed in section 2.4, we use only intra-cluster GCs (ICGCs)-GCs not gravitationally bound to any structure according to SUBFIND and that the cleaning criteria in section 2.2.As briefly discussed in Doppel et al. (2023), the GC tagging model predicts that the ICGC component forms via the tidal stripping of GCs from their host galaxies as they interact with their new host environment after infall.The buildup of ICGCs is thus, in a similar fashion to the ICL, a result of the hierarchical assembly of their host systems.The GC catalog follows the population of surviving GCs with mass  GC > 7 × 10 3 M ⊙ , and while we do not make the distinction between "red" and "blue" GCs as in Doppel et al. (2023), their Fig. 5 shows that the mass density of the simulated ICGC is in good agreement with available observational constraints.
As in the case of the ICL, we find a large spread on the distribution of progenitors that build the the intra-cluster GC component in our groups.Using a similar concept to that introduced for  25 ,  50 and   90 , we define similar quantities but considering only the stellar mass that brought in the 25%, 50% and 90% of the mass in GCs in the ICGC component.Fig. 8 compares the progenitors for the ICL and the GCs.We find that GCs can be very good tracers of the most massive contributors to the ICL, in particular  25 and  50 for the stars or GCs in the diffuse component are very similar, indicating that the progenitors that build up to half of the ICL also bring along about half of the GCs in the ICGC.However, we find a clear bias in the contributors as quantified by  90 : taking the progenitors that bring 90% of the GCs typically leads to smaller masses than the progenitors contributing 90% of the stellar mass in the ICL (left panel Fig. 8).This means that when using GCs to reconstruct the merger history of groups and clusters, one should keep in mind that the contribution from dwarf galaxies will be over-represented compared to the contribution of the same dwarfs to build the diffuse light component.This result can be intuitively understood from the different scaling of GCs and stellar mass with the halo mass.In the considered GC model, the mass of GCs scales as a power-law of halo mass (Doppel et al. 2023) while abundance matching results suggest a more steep decrease in the efficiency of low mass halos to form stars compared to more massive galaxies like the MW (abundance matching is better described by a double power-law).As a result, dwarfs contribute fractionally more GCs than stars to the diffuse components.Interestingly, as found for the case of the ICL, there is a sizable range in the typical contributor of the ICGC.For some of our GC systems,  90 is found to be galaxies with  * ∼ 10 10 M ⊙ , indicating little role played by low mass galaxies.However, there are also cases with  90 ∼ 5 × 10 7 M ⊙ , indicating dwarfs with masses typical of dSph galaxies playing a role.These differences in the accretion histories of these objects should remain imprinted in the chemical properties of their intra-cluster GC component and offer an avenue to constrain formation histories of massive hosts in cases where measurements of diffuse light becomes too challenging or implausible.

CONCLUSIONS
Using the cosmological hydrodynamical simulation TNG50, we have conducted a comprehensive study of two luminous tracers of dark matter in the outskirts of halos: the intra-cluster light (ICL) and the globular cluster (GC) population.We select all groups and clusters with  200 > 5 × 10 12 M ⊙ resulting in a sample of 39 host halos that span the virial mass range  200 = [0.5−20]×10 13 M ⊙ and sample a wide range of formation histories.We use the catalog of GCs tagged to the TNG50 groups and clusters presented in Doppel et al. (2023), allowing one of the first explorations of both luminous tracers in high density environments.We focus on the study of possible imprints of these individual accretion histories on observable properties of the ICL and GCs populations.Our findings can be summarized as follows: • TNG50 predictions for the fraction of light in the ICL,  ICL , are in reasonable agreement with current observational constraints for groups and low mass clusters.In addition,  ICL is predicted to increase with virial halo mass, albeit with significant dispersion.We find that this dispersion is well correlated with the assembly history in our systems causing variations in the dynamical state of the system and the ICL.Objects with more recent major mergers tend to show an excess of ICL compared to older or earlier assembled systems of comparable mass.
• There is a good correlation between the radial extent of the ICL (as measured by the radius where the surface brightness profile reaches 28 mag/arcsec 2 ) and the stellar mass of the central galaxy.This size-mass scaling relation for the ICL seems to agree with the one found observationally for lower mass galaxies as part of the stellar halos in the HERON survey (Rich et al. 2019).The radial extent of the ICL also shows a power-law relation to the virial radius of the halo, offering an observational means with which to constrain  200 independent of abundance matching methods.The typical r.m.s scatter in the relation between ICL-size and virial radius is ∼ 0.1 dex.
• The mass of the ICL is deposited by a wide range of progenitors.Some of our systems show sizable contributions from dwarf galaxies with  * < 10 9 M ⊙ , while others are built up almost entirely by systems as or more massive than the Milky Way.We find that the metallicity and metallicity profiles of the ICL retain information on these different assembly histories: halos with a higher contribution from dwarf galaxies generally have shallower metallicity profiles, overall lower average metallicities and also a lower amount of mass/light in the ICL.These findings are different from the common interpretation of flat metallicity profiles as evidence of large major mergers (Krick & Bernstein 2007;DeMaio et al. 2015DeMaio et al. , 2018)).In our systems, it is the incidence of low mass galaxies the main responsible for flattening up the -profiles.A larger role of dwarf galaxies in the build up of the ICL is also manifested by an overall lower metallicity content compared to systems built up by more massive satellite contributors.
• Finally, our study highlights that intra-cluster globular clusters (ICGCs) may also serve as a valuable tool to reconstruct the assembly history of the halos.We find that lower mass dwarfs tend to make more significant contributions to the ICGC population than to the stars in the ICL, a bias that must be taken into account when reconstructing assembly histories based on metallicity of GCs or ICL.This can be understood as a consequence of the single power-law relation of GCs with halo mass, which gives higher weight to the low mass halos compared to the double-power law expected for the stars in abundance matching relations.
Several of the trends studied here represent an extension of properties highlighted for the stellar halos of galaxies like the Milky Way, including trends on amount (Pillepich et al. 2014;Elias et al. 2018), metallicity (D'Souza & Bell 2018;Monachesi et al. 2019) and radial extension (Rich et al. 2019) and their link to the assembly history of each halo.Encouragingly, the ICL in groups and clusters are more massive/brighter than in systems like the Milky Way, offering an advantage from the observational point of view to study this diffuse component.The increased sensitivity of upcoming observations with JWST and Euclid VIS Deep survey promise to reach ∼ 31 mag/arcsec 2 levels in a few hours integration time.On median, for our simulated systems, this would result in detections for the ICL component all the way out to ∼ 0.7 200 , opening a new window to explore the predictions of hierarchical assembly expected for galaxies within ΛCDM.we span a range of host halo masses, we normalize the horizontal axis to the virial radius of each system.The shaded grey region illustrates the whole range of surface brightness covered by our entire sample.This variation in profile is given by two factors: object-to-object differences in assembly history and mass in the ICL and, also important, the range of host halo masses being included.For illustration, the median surface brightness including only the three most massive clusters with  200 ∼ 10 14 M ⊙ is shown by the dashed black line, which is systematically ∼ 1 magnitude brighter that considering the whole sample.The area being shaded by hatching for / 200 < 0.15 separates the inner regions attributed to the BCG and not considered part of the ICL.
The turquoise horizontal dashed line indicates the 28 mag/arcsec 2 limit at which we measure the radius of each group.2016) for applications to stellar halo studies).We predict that observational campaigns in the future targeting ∼ 31 mag/arcsec 2 are a promising avenue to map the stellar diffuse component in groups and clusters out to at least half the virial radius.

APPENDIX D: SUMMARY OBSERVATIONS
In this section, we present the observational data utilized for the ICL fraction-halo mass relation.Although efforts were made to gather data from sources employing consistent definitions and methods, some studies included in this compilation used different techniques 3 These limits correspond to a sky fluctuation of 3 in an area of 10 × 10 arcsec 2 .2008) employed wavelet techniques 5 to measure the ICL in six objects from the Hickson Compact Group (HCG) catalog, resulting in a wide range of observed ICL fractions.The ICL fractions varied from no detected ICL in HCG 88 to approximately 33% for HCG 79 (the fraction representing the ratio of ICL light to the total light of the group in the R band).Some studies have combined observational results with semi-analytical simulations to estimate the ICL fraction, such as the deep survey of the Virgo cluster conducted by Mihos et al. (2017), which estimated a range of 7-15% for the ICL fraction.
Furthermore, variations in the choice of observational bands used to infer the ICL fraction can be noticed.Different bands can yield different measurements of the ICL fraction.For example, Ragusa et al. (2021) investigated HCG 86 and found an ICL fraction of 14% in the r band and 19% in the g band, highlighting how the choice of band in observations can influence the measured amount of light attributed to the ICL.
An interesting outcome of these measurements is the dispersion observed in the ICL fraction at a given halo mass.Iodice et al. (2020) compared the ICL fractions of several different objects using the same method and demonstrated how features present in the ICL, outer envelope of the brightest cluster galaxy, and the presence of HI can indicate different evolutionary stages and mass assembly histories for different groups and clusters.
Additionally, some studies have linked the ICL fraction to the mean morphology of the group or cluster.Poliakov et al. (2021) measured the ICL fraction for multiple HCG objects and found that the mean surface brightness of the intra-group light correlates with the mean morphology of the group, with brighter intra-group light observed in groups with a larger fraction of early-type galaxies.It is important to note that the investigated groups in the TNG50 simulations exhibit various morphologies and formation histories, which may contribute to the wide variation in ICL fractions at a given mass.
Table D1 below provides a summary of the observational results compiled from multiple sources.Observation was conducted in B and V bands (Mihos et al. 2017) Using results of simulations (Rudick et al. 2009), Mihos et al. (2017) estimated 5-10% of the ICL should be the form of coherent streams (the relatively high surface brightness tidal features that represent material most recently stripped from their host galaxies), which help them estimate the whole amount of ICL luminosity.

Figure 1 .
Figure 1.Projected position of the luminous (stellar (gray-scale background) + ICGCs (cyan dots)) components in the ICL of 4 randomly selected groups from our sample (the virial mass of each group is quoted on the bottom left of each panel).Orange, magenta, and lime circles show the position of r 200 for the group, and 0.15 × r 200 , and 2 × r h * , respectively.

Figure 2 .
Figure 2. ICL fraction vs virial mass of the halos.Predictions by TNG50 are shown with filled large circles (upper limit), and empty downward triangles (lower limit).Fraction of only ex-situ stellar component in ICL are shown by grey circles.Left panel: ICL fractions are colored by the time of the last major merger occurred for the central galaxy.The light 'red' and 'blue' dotted lines show the average of ICL fraction for the corresponding red and blue points.Right panel: Results from other simulation are shown by the shaded regions, and several observational studies are shown with different colored markers for comparison.references along with the reported quantities are presented in table D1 in Appendix D.

Figure 3 .
Figure 3. Size of the extended stellar halo measured by fitting ellipses to the surface brightness maps (black stars), and by measuring radius from radial binning of surface brightness maps (turquoise stars).Upper panel: Size-stellar mass relation, compared to observations from Rich et al. (2019) (colored markers) and relation from Muñoz-Mateos et al. (2015) (gray dashed line).Lower panel: Size as a function of virial radius of the group.Grey and turquoise dashed lines correspond to measurements of semi-major axis of the best fit ellipse and radius of the circular profile, respectively.
stellar halos are dominated by one or two most massive progenitors, which naturally explains the correlation between stellar halo mass and metallicity (e.g., D'Souza & Bell 2018; Deason et al. 2016).

Figure 4 .
Figure 4. Example of two groups with different ICL progenitor mass functions.The vertical axis shows the cumulative fraction of stellar mass deposited in the ICL by galaxies with maximum stellar mass > M * ,max .Markers on the x-axis correspond to the measured M 25 (triangle), M 50 (circle), and M 90 (pointing down triangle), and horizontal and vertical lines correspond to the measurement of the M 90 for the groups highlighted here.The group in orange has an ICL contributed mostly by massive progenitors with  * ,max ∼ 10 10 M ⊙ while the one in blue has significant contributions from lower mass dwarf galaxies with  * ,max ∼ 5 × 10 8 M ⊙ , as shown by their different  90 values.

Figure 5 .
Figure5.Left panel: Stellar mass of the progenitors that brought a percentile of mass to the ICL as a function of virial mass of the groups.Pink triangles, blue circles, and purple pointing down triangles correspond to M 25 , M 50 , and M 90 , respectively.Note the large scatter in  90 indicating a varied contribution of dwarf galaxies to the build up of the ICL.Right panel: fraction of the accreted ICL that was contributed by (dwarf) galaxies with stellar masses below  * ,max = 10 10 M ⊙ .Symbols are colored by M 90 for each group (from the left panel) and highlight the good correspondence between the two metrics.At similar halo mass, some groups have about half of their ICL built by low mass galaxies with  * ,max = 10 10 M ⊙ while others show less than 10% contribution from these dwarfs.

Figure 6 .
Figure 6.Illustration of the metallicity profiles of three randomly selected groups from our sample, with the median and 25-75 percentile depicted by the blue line and shaded region, respectively.The best-fit linear relation (in log) is highlighted in red and quoted in each panel.Most systems show a negative metallicity profile with radius, but the slope changes substancially from system to system.

Figure 7 .
Figure 7. Left panel: stellar mass of the accreted component in the ICL as a function of the virial mass.Middle panel: median metallicity of the accreted stars in the ICL as a function of the virial mass.Right panel: the slope of the metallicity profile as a function of virial mass for the merged component, with black triangles representing the results for all the stellar components.All panels are color-coded by the  90 of each group.Systems where dwarf galaxies play a role in building the ICL (low  90 ) tend to have lower ICL mass, lower overall metallicity and metallicity profiles than systems with accretion dominated by more massive galaxies.

Figure 8 .
Figure 8.Typical mass of progenitors that build the ICL (x-axis) and the intracluster-GCs (y-axis) as quantified by M 25 (left), M 50 (middle), and M 90 (right) of each population.The gray dashed line corresponds to the one to one relation.Our findings indicate that GCs can serve as a good tracers of the most massive contributors to the ICL, although it is important to note that the contribution from dwarf galaxies may be over-represented when looking at GCs in comparison to the ICL (right panel).

Figure A1 .
Figure A1.Left panel: ICL fraction as a function of virial mass.Right panel: stellar mass content in the ICL as a function of virial mass.The different colors correspond to various definitions of ICL.
For comparison, we have included estimates of the surface brightness limits for the James Webb Space Telescope (based on the study of ICL in SMACS 0723 by Montes & Trujillo 2022 3 ), the Euclide VIS Deep survey(Borlaff et al. 2022) 3 , and the Dragonfly Telephoto Array's deep nearby galaxy survey (which provides g-band surface brightness profiles down to 31-32 mag/arcsec 2 , see Merritt et al. (

Figure C1 .
Figure C1.Surface brightness profiles of our sample of groups and clusters.The black line represents the median profile for the entire sample, while the dashed black line corresponds to the median profile of the three most massive groups.The shaded region illustrates the dispersion across all groups in our sample.The gray hatched region indicates the extent of the BCG.