In this chapter we delve into the formation and primary characteristics of two significant components within galaxy clusters the brightest cluster galaxies BCGs and the intracluster light ICL. Drawing upon recent and pertinent studies in the field we explore the mechanisms driving their growth from high redshift to the present day i.e. mergers and stellar stripping. Mergers between satellite galaxies and the BCGs account for a significant amount of ICL as well as stellar stripping which is responsible for the formation of the bulk of it. We also examine how these formation mechanisms are intertwined with the dynamical state of their host clusters suggesting their potential utility as luminous tracers of dark matter.
['Astrophysics - Astrophysics of Galaxies']
Brightest Cluster Galaxies and the Intracluster Light
{'Brightest Cluster Galaxies and the Intracluster Light': 'Emanuele Contini ,a , Sukyoung K. Yi a and Seyoung Jeon a  \na Yonsei University, Department of Astronomy and Yonsei University Observatory, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea  \n© 20xx Elsevier Ltd. All rights reserved.  \nEmanuele Contini: emanuele.contini82@gmail.com', 'Glossary': 'Brightest cluster galaxy  \nIntracluster Light Di ff  \nStellar stripping  \nthe main galaxy in the center of a galaxy cluster. use light from stars not bound to any galaxy in within the cluster. Process acting on satellite galaxies due to tidal interactions with the host halo.', 'Nomenclature': 'BCG Brightest Cluster Galaxy  \nBGG  \nBrightest Group Galaxy  \nICL Intra-Cluster Light  \nFOF Friend-of-Friend', 'Abstract': 'In this chapter, we delve into the formation and primary characteristics of two significant components within galaxy clusters: the brightest cluster galaxies (BCGs) and the intracluster light (ICL). Drawing upon recent and pertinent studies in the field, we explore the mechanisms driving their growth from high redshift to the present day, i.e., mergers and stellar stripping. Mergers between satellite galaxies and the BCGs account for a significant amount of ICL, as well as stellar stripping which is responsible for the formation of the bulk of it. We also examine how these formation mechanisms are intertwined with the dynamical state of their host clusters, suggesting their potential utility as luminous tracers of dark matter.', 'Key Points': '- · BCGs: these galaxies undergo multiple phases of growth. In the early Universe, abundant cold gas facilitates their growth in mass through intense star formation. In a second step, due to hierarchical clustering, satellite galaxies of varying types, masses and morphology merge with BCGs. In later stages, this rapid growth via mergers transitions to what is termed as smooth accretion, involving the gradual incorporation of dwarf galaxies or significantly smaller objects.\n- · Main formation channels of the ICL: mergers between satellites and the BCG, stellar stripping of stars from satellites due to tidal forces during their orbits, and the accretion or pre-processing of material from external sources (formed through mergers and / or stellar stripping).\n- · BCG + ICL can serve as luminous tracers of the dark matter distribution, particularly the ICL, and are linked to the dynamical state of their host.', '1 Introduction': 'Galaxy clusters are the largest virialized structures in the Universe, extraordinary laboratories for studying galaxy formation and evolution. Although the amount of baryonic matter in the Universe is very low, around 5%, clusters host galaxies of di ff erent mass, size, and morphology. Among these galaxies, the brightest cluster galaxies (BCGs) stand out as particularly peculiar. Situated at the centers of the potential wells of dark matter halos, BCGs possess properties that significantly di ff er from those of other member galaxies, typically referred to as satellites. Since the galactic cannibalism theory (Ostriker and Tremaine 1975) has been proposed, according to which central galaxies accrete satellites through mergers, it became evident that BCGs constitute the final stage of the evolution of galaxies that reside in the center of dark matter halos, where they grow in mass by acquiring the stellar and gaseous material coming from satellites that inevitably merge with them.  \nStars in galaxies are bound to the potential well of the galaxy itself and, under some circumstances, they can be stripped and become part of what we call intracluster light (ICL). The ICL is an important component of galaxy clusters that is made of stars not bound to any member galaxy and that feel only the potential well of the dark matter halo (e.g., Contini 2021; Montes 2022). It was first discovered by Zwicky (1937), but only during the past two decades the scientific community has spent a remarkable e ff ort in studying the properties, and their implications (see, e.g., the reviews by Montes 2022; Arnaboldi and Gerhard 2022). The physical mechanisms responsible for the ICL formation are strictly linked to the evolution of the BCGs, i.e., from the satellite galaxies that orbit in the clusters and merge with the BCG.  \nMeantime, tidal forces acting on orbiting satellites can be very e ff ective, such that some of their mass can be lost in the process or they can even be totally disrupted. This stellar material is what the ICL is made of, unbound stars that leave the galaxy where they were born.  \nBCGs and ICL have a very common formation history, in the sense that their formation and assembly are strictly connected through physical processes such as the stellar material coming from satellite galaxies orbiting around the potential well of the cluster and that eventually merge with the BCG. Among this processes, which will be discussed in Section 3.1, three of them are fundamental for both the growth of the BCG and the ICL, namely: mergers (see Def.1, Monaco et al. 2006; Murante et al. 2007; Contini et al. 2014, 2024b), stellar stripping due to tidal interactions between satellites and the BCG (Rudick et al. 2009, 2011; Contini et al. 2018; DeMaio et al. 2018; Montes and Trujillo 2018; Contini et al. 2024a), and accretion of stellar material from outside the virialized region, also called preprocessing (Mihos et al. 2005; Sommer-Larsen 2006; Ragusa et al. 2023; Joo and Jee 2023; Contini et al. 2024a). Given their intimate connection and the unclear separation between them (we will come back to this point in the following), these two components are often treated as a single system, and the only distinction is purely based either on the distance from the cluster center (e.g., Pillepich et al. 2018; Contreras-Santos et al. 2024), or an isophote with a given surface brightness limit (e.g., Zibetti et al. 2005; Montes et al. 2021).  \nOne approach to discerning the transition between BCG-bound stars and ICL is by fitting the combined BCG + ICL profile distribution with a multiple Sersic (Sersic 1968) profile (e.g., Kravtsov et al. 2018; Zhang et al. 2019). The innermost distribution represents the BCG, the outermost the ICL, and the transition region between the two can be viewed as the stellar halo typically surrounding the BCG, particularly evident in nearby clusters (Longobardi et al. 2015). However, although BCG and ICL have common formation histories, they are quite di ff erent in terms of properties. Therefore, another approach to delineating these components involves examining their characteristics, such as colors, ages, and metallicity (Morishita et al. 2017; Montes and Trujillo 2018; DeMaio et al. 2018; Contini et al. 2019). For instance, if the ICL primarily comprises stars from stripped satellite galaxies, its color, age, and metallicity would di ff er from those of the BCG. In such cases, the ICL would likely appear bluer, younger, and more metal-poor compared to the BCG. Conversely, in scenarios where mergers are the primary mechanism, gradients in colors (or age and metallicity) would not be expected (e.g., Contini et al. 2019).  \nThis chapter serves as an introduction to the primary mechanisms governing the formation and evolution of BCGs and ICL, along with their key properties. Our approach integrates observational evidence with theoretical predictions from simulations and analytic models, which have now achieved remarkable accuracy in matching the observed properties of galaxies in general. In Section 2, we provide a brief overview of the BCGs formation, delving into the main theoretical aspects underlying their assembly. Section 3 is dedicated to the formation of the ICL, where we analyze various mechanisms potentially responsible for its formation alongside observed properties such as colors, age, and metallicity. Given that many studies treat BCGs and ICL as a unified system, as will be elucidated in subsequent sections, Section 4 focuses on the combined BCG + ICL, considering their properties and proposed procedures for reliably separating the two components. We conclude the chapter in Sections 5 and 6, exploring the utility of BCG / ICL distributions in shedding light on dark matter and the evolution of these components in the latter stages of the evolution of the Universe. Finally, Section 7 provides a summary of the main points covered in the chapter.', '2 Brightest cluster galaxies': "BCGs are among the most massive objects in galaxy clusters, and among the most massive and luminous galaxies in the Universe. As mentioned in the introduction, these galaxies have formation and assembly histories that di ff er quite significantly from the rest of the galaxies that we know (Contini et al. 2014 and reference therein). The pioneering work by De Lucia and Blaizot (2007) elucidated that BCGs at the cores of their dark matter halos form hierarchically, meaning they result from the merging of smaller building blocks provided by satellite galaxies orbiting within the potential well of the cluster. These galaxies undergo multiple phases of growth. In the early Universe, abundant cold gas facilitates their mass increase through intense star formation. Subsequently, due to hierarchical clustering, galaxies merge to form larger entities, with BCGs benefiting most by assimilating mass from merging satellite galaxies of varying types, masses, and morphologies. In later stages, this rapid growth via mergers transitions to what is termed as smooth accretion , involving the gradual incorporation of dwarf galaxies or significantly smaller objects.  \nThe duration of each growth phase and its dependence on external factors, such as the typical environment in which BCGs reside, remain unclear. It is plausible to assume that BCGs in smaller dark matter halos have had fewer opportunities to grow through mergers compared to those in larger halos, simply due to di ff erences in the availability of building blocks between the two scenarios. Particularly in observational studies (Lidman et al. 2012; Lin et al. 2013; Oliva-Altamirano et al. 2014), the growth rate during the latter half of the Universe's lifespan is debated. While numerical simulations and semi-analytic models (Murante et al. 2007; Contini et al. 2018; Ragone-Figueroa et al. 2018) suggest similar growth rates, observations report varying figures, ranging from 100% (Lidman et al. 2012) to 50% (Lin et al. 2013), with instances of no growth observed as well (e.g., Oliva-Altamirano et al. 2014).  \nBCGs are also found in galaxy groups, where they are referred to as brightest group galaxies (BGGs). However, it is common to use the general term 'BCGs' without clear di ff erentiation between galaxy groups and clusters. Nevertheless, BGGs and BCGs exhibit di ff erences in their properties. Both simulations and observations have revealed that, on average, BGGs are less luminous, less massive, and have lower stellar velocity dispersions compared to BCGs (Sohn et al. 2020; Marini et al. 2021; Einasto et al. 2022). The properties of BCGs are crucial in understanding their host clusters. Several studies (Shaaban et al. 2023 and references therein) have investigated the connection between BCG properties and those of their host clusters, examining surface brightness profiles, position angles, alignments, X-ray emissions, size, and others. Despite their names, it must be noted that BCGs are not always the central galaxies of their hosts (Kluge et al. 2020) and, on the other way around, central galaxies are not always the brightest ones. It has been estimated that between 20% and 40% of central galaxies are not the brightest (Skibba et al. 2011; Hoshino et al. 2015), and M87 in Virgo is a prominent example.  \nFig. 1 An example of a BCG merger tree is illustrated in the figure. Circles represent galaxies that currently reside within the FOF group of the main progenitor of the BCG, while triangles represent galaxies that have not yet joined this group. The symbols are color-coded based on the B-V color, and their size scales with the stellar mass of the galaxies. The main progenitor branch, referred to in the text, is depicted as the left-most branch in the figure. Credit: De Lucia and Blaizot (2007).  \n<!-- image -->  \nAn essential aspect of galaxy formation and evolution, applicable to all galaxies but particularly significant for BCGs, is the di ff erentiation between the concepts of formation and assembly. De Lucia and Blaizot (2007) provided clear insights into these concepts, demonstrating that the disparity between formation and assembly times is more pronounced for BCGs compared to other galaxies. The assembly time is defined as the time when the main progenitor (i.e., the main branch of the merger tree) has half of the final mass of the BCG at z = 0, while the formation time includes in the definition all the progenitors of the BCG. De Lucia and Blaizot (2007) showed that, while BCGs can form pretty early ( z ∼ 5), half of the stellar mass is actually assembled much later ( z ∼ 0 . 5).  \nA nice example of a BCG merger tree is illustrated in Figure 1, where circles refer to galaxies residing in the FOF group of the main branch, and triangles those that have not yet joined it. Symbols are also color coded based on the B-V color, an indicator of age and metallicity, and their size scales with the stellar mass. The main progenitor branch is the left-most one. This visualization e ff ectively demonstrates the discrepancy between the two defined times, especially noticeable for BCGs, depending on whether all branches or only the main one are considered. It showcases that a significant portion of stars forms early, within separate objects, before eventually being assembled into the final BCG. This study remains a milestone in the field of hierarchical clustering, as it underscores the necessity of a hierarchical framework to fully comprehend the history of BCGs.  \nThe concepts of formation and assembly are crucial in understanding the formation and evolution of the ICL as well. Just as the assembly of BCGs is intimately linked to that of their host halos, so too is the assembly of the ICL. As we will explore further in subsequent sections of this chapter, the assembly history of BCGs is closely intertwined with that of the ICL. This interconnectedness underscores the complex and dynamic nature of galaxy cluster environments, where the formation and evolution of both BCGs and the ICL are intricately linked.", '3 Intracluster light': "The ICL, also known as di ff use light (DL), is a distinctive component of galaxy clusters and groups. Initially discovered by Zwicky (1937), it has garnered significant attention in recent years from numerous authors (Zibetti et al. 2005; Sommer-Larsen 2006; Rudick et al. 2009; Krick and Bernstein 2007; Puchwein et al. 2010; Burke et al. 2012; Martel et al. 2012; Contini et al. 2014; DeMaio et al. 2015; Iodice et al. 2017; Groenewald et al. 2017; Morishita et al. 2017; Mihos et al. 2017; Ko and Jee 2018; Spavone et al. 2018; Tang et al. 2018; Montes and Trujillo 2018; Jim'enez-Teja et al. 2019; Zhang et al. 2019; DeMaio et al. 2020; Yoo et al. 2022; Ragusa et al. 2023; Joo and Jee 2023; Contini et al. 2023; Contreras-Santos et al. 2024, among others. For a more comprehensive list of references, please consult the reviews by Contini 2021, Arnaboldi and Gerhard 2022 and Montes 2022). It quickly became evident that the ICL is a crucial factor to consider when modeling the formation and evolution of galaxies using numerical simulations and / or semi-analytic models (e.g., Puchwein et al. 2010; Contini et al. 2014). This is particularly significant as the ICL can constitute up to 40% or more of the total light within the virial radius of clusters. Beyond its role in contributing to the overall stellar budget, studying its properties can provide insights into the mechanisms driving the assembly of galaxy groups and clusters.  \nAs mentioned previously, the ICL consists of stars that are not gravitationally bound to any specific galaxy within the cluster and are influenced solely by the potential well of the dark matter halo. These stars were originally part of satellite galaxies that either merged with  \n<!-- image -->  \nFig. 2 The innermost 200 kpc of the masked and unmasked F160W images are depicted for 12 groups and clusters within the redshift range 0 . 29 < z < 0 . 89 . In the unmasked images, pixels brighter than 22 mag arcsec -2 are represented in white, while black regions in the masked images indicate masked sources. Credit: DeMaio et al. (2018).  \nthe BCG, were stripped away while orbiting around it, or were accreted from other objects during the formation of the cluster (Ragusa et al. 2023; Contini et al. 2024b). Experts in this field suggest that the primary mechanisms responsible for the formation of the ICL are threefold: mergers between satellites and the BCG, the stripping of stars from satellites due to tidal forces during their orbits, and the accretion or pre-processing of material from external sources. Although in situ star formation was initially proposed (Puchwein et al. 2010), observational evidence later refuted this idea (Melnick et al. 2012), indicating minimal ongoing star formation in the regions occupied by the ICL. Further elaboration on these processes will be provided in Section 3.1.  \nThe ICL can constitute a substantial fraction of mass or light within the virialized region of galaxy clusters, typically ranging from 5% to 40%, with no discernible trend in relation to cluster mass (Montes 2022; Ragusa et al. 2023) or redshift (Joo and Jee 2023; Contini et al. 2024b). Investigating the role of the ICL in determining the total stellar mass within clusters, particularly the scatter in this relationship,  \ncan provide insights into the dynamical state of the clusters under study (Ragusa et al. 2023; Contini et al. 2023; Jim'enez-Teja et al. 2024). Our research has focused on studying various properties such as metallicity, colors, and age to gain a deeper understanding of the formation mechanisms of the ICL. For instance, if the properties of the ICL closely resemble those of the BCG, it suggests shared formation mechanisms. An illustrative example of this, which we will revisit in Section 4.3, is the presence or absence of gradients in colors and / or metallicity across both the BCG and the ICL. The absence of such gradients may imply that mergers are the primary formation mechanism, while the presence of gradients could suggest a more gradual mechanism such as stellar stripping (Contini et al. 2019).  \nAn important challenge in studying the ICL arises from its di ff use nature, as it permeates regions that may also be occupied by stars still bound to other galaxies. Consequently, separating the ICL from other components presents a significant challenge. In numerical simulations or semi-analytic models, the distinction between ICL stars and others is clear, thanks to available dynamical and kinematic information. However, in observations, this task becomes daunting due to the lack of such detailed information. Separating the ICL from the rest, including the BCG, is particularly challenging, to the extent that many authors opt to study the entire BCG + ICL system without attempting separation (Contini 2021; Montes 2022 and references therein). Despite these definitional challenges, the ICL serves as a valuable tool for understanding the formation and assembly of clusters by linking its properties with their dynamical stages. Below, we explore how recent studies utilize the ICL to investigate the dark matter content in clusters.  \nBefore delving into the mechanisms responsible for the formation of the ICL, it is worthwhile to examine the typical distribution of the ICL in clusters. This is illustrated in Figure 2, adapted from DeMaio et al. 2018, which depicts the innermost 200 kpc of 12 groups and clusters at the lowest redshifts in their sample. The authors di ff erentiated the contribution of the ICL by masking satellite galaxies and provided both unmasked and masked images. A comparison between the two images for the same clusters reveals a significant remaining light, which includes the contribution from the BCG. In Section 4.1, we will explore potential techniques for separating the ICL from the BCG.", '3.1 Formation mechanisms': "The growth of the ICL can be attributed to several channels, with stellar stripping and mergers being the primary processes investigated (Monaco et al. 2006; Murante et al. 2007; Somerville et al. 2008; Guo et al. 2011; Martel et al. 2012; Contini et al. 2014, 2018). Stellar stripping occurs when stars belonging to a satellite galaxy are stripped away by tidal forces acting on the satellite itself, while mergers involve the unbinding of a fraction of the satellite's mass during the merger process with the BCG. However, stellar stripping and mergers are not the only mechanisms proposed. Additionally, other processes must be considered, including the disruption of dwarf galaxies (Conroy et al. 2007; Purcell et al. 2007; Giallongo et al. 2014; Contini et al. 2014; Annunziatella et al. 2016; Raj et al. 2020), in situ star formation (Puchwein et al. 2010), and the accretion of ICL already formed elsewhere (Contini et al. 2014, 2023; Joo and Jee 2023; Ragusa et al. 2023), also known as pre-processing.  \nThe disruption of dwarf galaxies is a common process occurring within groups and clusters. Physically, it is akin to stellar stripping, but in this scenario, the tidal forces are so intense that the galaxy is completely destroyed. This phenomenon primarily occurs near the cluster center where tidal forces are strongest, and at low redshifts when halos are generally more concentrated compared to their higher redshift counterparts (Gao et al. 2011; Contini et al. 2012). Despite the frequency of dwarf galaxy disruption, studies (Contini et al. 2014) have demonstrated that it contributes minimally to the stellar mass gained by the ICL. Indeed, research by various authors (e.g., Montes and Trujillo 2018; Contini et al. 2018, 2024b) has shown that stripping of intermediate / massive galaxies (log M ∗ > 10 . 5) accounts for approximately 70% of the material originating from stellar stripping. Consequently, the disruption of dwarf galaxies has been discounted as a primary channel in the formation of the ICL.  \nIn situ star formation was initially observed in simulations by Puchwein et al. (2010), where it was found to contribute significantly (about 30%). However, subsequent observational evidence (Melnick et al. 2012) contradicted these findings, indicating that in situ star formation contributes no more than approximately 1%. It is worth noting that, at the time of writing this chapter, a study by Ahvazi et al. (2024) claims that in situ star formation in three massive clusters from the TNG50 simulations can account for approximately 8% to 28% of the total ICL. Furthermore, this study suggests that the majority of these stars are formed directly within the ICL, hundreds of kiloparsecs away from the center of the host halo. It should also be noted that there are some claims that stars can be formed in the intracluster medium, either through stripped gas, or directly in gas (e.g., Gullieuszik et al. 2020).  \nPre-processing or the accretion of already processed ICL is considered to be a significant channel for the formation of the ICL. Preprocessed ICL refers to the ICL formed within some groups that later merge during the assembly of a given cluster. During these mergers, the groups also bring along their own ICL contents, which merge with the cluster's ICL once the merger is complete. Several studies (e.g., Contini et al. 2024b and references therein) have demonstrated that pre-processed ICL can contribute up to 30%-40% of the total ICL in clusters at the present time. However, it is important to note that pre-processing is not a direct means of forming ICL (Contini et al. 2024b). The ICL primarily forms through the processes described earlier, and part of it can be accreted during the assembly history of clusters. Therefore, this channel is essentially a sub-channel (see, e.g., the discussion in Contini et al. 2024b).  \nStellar stripping and mergers are now recognized as the two most significant channels in the formation of the ICL, with pre-processing considered a sub-channel. However, quantifying the contributions of stellar stripping and mergers separately is challenging, particularly due to the dependency on the definition of a merger. Authors often have varying definitions of what constitutes a merger, especially concerning the timing of when a merger begins. For instance, Murante et al. (2007) asserted that approximately 75% of the ICL forms through mergers, while Contini et al. (2014) found that around ∼ 80% originates from stellar stripping. This discrepancy arises from the authors' adoption of di ff erent definitions of a merger . If the timing of when a merger begins is not uniformly defined, the contribution from mergers can result in varying percentages. In Contini et al. (2014), and generally in semi-analytic models, a merger is defined as the moment when  \nthe satellite can no longer be distinguished from the central galaxy, e ff ectively becoming the same object. However, while orbiting very close to the central galaxy, the satellite may undergo significant tidal stripping. In this scenario, the stripped stars can also be considered as originating from the merger channel if the satellite is on the verge of merging. In a subsequent study, Contini et al. (2018) demonstrated that by relaxing their definition of a merger to align more closely with that of Murante et al., which was based on information in the merger trees, the percentage of ICL attributed to the merger channel converged with that claimed by Murante et al..  \nIt is important to note, however, that since the work of Murante et al., numerical simulations have made significant advancements in terms of accuracy and mass resolution. It is pertinent to revisit this point with more resolved simulations available today. For instance, leveraging the TNG300 simulation of the IllustrisTNG project (see Pillepich et al. 2018 and references therein), Montenegro-Taborda et al. (2023) demonstrated that a fraction ranging from 50% to 60%, depending on the mass of the host halo, of the ICL originates from the merger channel, encompassing very minor, minor, and major mergers.  \nHow can we quantify the respective contributions of mergers and stellar stripping to the formation of the ICL? One approach, commonly employed in observations, involves studying the main properties of the ICL itself, without the need for separation from the BCG. Mergers and stellar stripping are expected to imprint distinct characteristics on the ICL, thus examining its properties (or considering the entire BCG + ICL system) allows us to discern which process plays the most significant role. In the subsequent section, we will explore how certain properties of the ICL can provide insights into this matter.", '4 BCGs and ICL properties': 'The only viable approach, observationally, to gain insight into the mechanisms underlying the formation of BCGs and ICLs is by examining their properties. However, this poses significant challenges in observations, as isolating the BCG + ICL from the contributions of satellites is inherently di ffi cult. Additionally, the ICL is a faint component that may even fall below the sky level, further complicating its isolation. Before delving into the most important (and studied) properties of BCGs and ICL, we will address in the next sub-section the primary techniques for separating the ICL from the BCG. This step is crucial for understanding the distribution of the two components and, more importantly, recognizing the absence of a specific observable quantity capable of delineating a clear boundary between them without some compromise.', '4.1 Separation of the two components': "The separation of the ICL from the BCG presents significant challenges in observational studies, whereas it is comparatively easier in theoretical approaches. Simulations and semi-analytic models have the advantage of utilizing dynamical and kinematic information, which greatly facilitates the task when coupled with a reliable definition of the ICL. For instance, in simulations, we possess detailed information regarding the positions and velocities of every individual star particle, allowing for the straightforward separation of the ICL from the BCG via the velocity distribution of the BCG + ICL stars (see, e.g., Dolag et al. 2010). Using this method, it becomes evident that the total velocity distribution is not simply governed by a single Maxwellian distribution, but rather a combination of two Maxwellian distributions-one describing the distribution of stars belonging to the BCG and the other characterizing the stars belonging to the ICL.  \nHowever, the velocity distribution method is generally not applicable in observational studies due to the lack of information on individual stars. A similar approach, albeit limited to nearby objects, involves examining the bimodality of the velocity distribution of Planetary Nebulae (Longobardi et al. 2015). Their velocity distribution can be segregated into a narrow component associated with the BCG and a broader one linked to the ICL, thereby allowing for an estimation of the transition region between the two components. Unfortunately, this method is often impractical due to the distances of most observed targets from us.  \nAmong the observational methods commonly used, two noteworthy techniques are the isophotal limit cut-o ff (e.g., Zibetti et al. 2005) and profile fitting methods (e.g., Zhang et al. 2019). These methods di ff er fundamentally, often resulting in di ff erent separations when applied to the same target. Both techniques rely on thorough masking of external sources. The isophotal limit cut-o ff method involves a subjective cuto ff in surface brightness, below which all remaining light is considered ICL. This simplistic approach does not account for the ICL in the transition region between the two components and is susceptible to contamination from massive galaxies within the clusters.  \nAnother widely used method in observations is profile fitting, which employs functional forms to fit the BCG + ICL light. This method typically assumes at least two components to describe both the BCG and ICL, but a minimum of three is necessary to characterize the transition region between them. The triple Sersic profile fitting is commonly used for this purpose. While profile fitting o ff ers the advantage of describing the transition between the BCG and the ICL, it is heavily reliant on the specific functional forms chosen.  \nIt is worth noting that recent studies, both observational and theoretical, have adopted a trend of not attempting to separate the two components (e.g., Montes and Trujillo 2018; Pillepich et al. 2018; Contreras-Santos et al. 2024). In these cases, a simple assumption is made to consider a certain distance from the BCG where the light is assumed to originate from the BCG, and beyond this distance, from the ICL. While this approach completely overlooks the transition region between the two components, it can be considered reasonable if the assumed distance lies within this region. Another reliable criterion for determining this distance is the transition radius between the two components, as suggested by Contini et al. (2022) (but see also Proctor et al. 2024; Brough et al. 2024). This radius can be quantified in observations via profile fitting and easily derived in theoretical models.  \nFig. 3 A collection of ICL fractions at different redshifts, ranging from the present day to redshift z ∼ 2 , is presented. The plot clearly illustrates that the ICL fraction is already significant at high redshifts and comparable to that observed in the local Universe. References: (1) Rudick et al. (2011); (3) Burke et al. (2012); (5) Montes and Trujillo (2018); (8) Presotto et al. (2014); (10) Burke et al. (2015); (11) Morishita et al. (2017); (12) Alamo-Mart'ınez and Blakeslee (2017); (13) Ellien et al. (2019); (14) Feldmeier et al. (2004); (15) Griffiths et al. (2018); (16) Jee (2010); (17) Jim'enez-Teja et al. (2018); (18) Jim'enez-Teja et al. (2019); (19) Krick and Bernstein (2007); (21) Yoo et al. (2021), and they point labelled as This study are from Joo and Jee (2023). Credit: Joo and Jee (2023).  \n<!-- image -->  \nz", '4.2 Fraction of ICL in galaxy clusters': "The quantification of ICL mass is perhaps one of the most straightforward properties to assess. Assuming a reasonably trustworthy separation of the ICL from the BCG, the significance of the ICL in galaxy groups and clusters can be evaluated by plotting the ICL mass over the total stellar mass within a specified radius from the cluster center, as a function of cluster mass within a given overdensity. Alternatively, to avoid the separation from the BCG, several studies have considered the stellar mass in BCG + ICL over the total (e.g., Gonzalez et al. 2013). By compiling the observed fraction of ICL mass, it becomes apparent that the ICL cannot be disregarded. Indeed, it can account for as much as 40%-50% of the total stellar mass within the virial radius of a group or cluster (see the review by Montes 2022).  \nThere is no general consensus on whether the ICL fraction depends on the halo mass, but most studies to date suggest that it is independent of halo mass, at least for log M halo ≥ 13 (see Contini et al. 2024a for results in a lower halo mass range). However, the relation is characterized by a significant scatter (e.g., Contini 2021). If this is indeed the case, it implies that the physical processes discussed above, responsible for ICL formation, are similarly e ffi cient regardless of the mass of the host. Furthermore, given the observed scatter in the relation, which is also predicted by several theoretical models (e.g., Murante et al. 2007; Guo et al. 2011; Contini et al. 2014; Pillepich et al. 2018; Contini et al. 2023), it is essential to understand which halo properties can account for it. We will revisit this point shortly. An important caveat to consider when comparing the ICL fraction derived from di ff erent studies, whether observational or theoretical, is the radius within which the ICL fraction is computed. While most ICL fractions are computed within the virial radius of the halo, and attention must be paid to the definition of the virial radius, others are computed within a specified distance from the center, especially in observational studies constrained by the limits of the observation (e.g., Montes and Trujillo 2018).  \nA crucial aspect related to the formation of the ICL pertains to its evolution over time in terms of the ICL fraction. Theoretical studies generally concur (e.g., Murante et al. 2007; Contini et al. 2014, 2024b) that the ICL forms relatively late. However, there is mounting observational evidence indicating that the ICL fraction is already substantial at high redshift (Ko and Jee 2018; Joo and Jee 2023). These two points are not necessarily contradictory, given that (a) the term 'formation time' typically refers to when the bulk of the ICL is established  \nFig. 4 The fraction of ICL as a function of halo mass is depicted, with color-coding based on the concentration of the halo. At a given halo mass, more concentrated halos tend to host a higher fraction of ICL. The red and blue lines represent the average fraction of the halos in the highest and lowest concentration ranges, respectively. Credit: Contini et al. (2023).  \n<!-- image -->  \nand (b) at high redshifts, while the amount of ICL may be lower, the total stellar mass within a halo is also lower compared to more evolved objects in the present universe. Figure 3, extracted from Joo and Jee (2023), presents various observed ICL fractions at di ff erent redshifts. The figure illustrates that high-redshift objects harbor comparable amounts of ICL relative to lower-redshift counterparts, implying that the ICL is already prominent at high redshifts (relative to the total stellar mass). Recent theoretical studies, such as Contini et al. (2024b), have demonstrated that models can reproduce the observed fractions and their redshift dependence, aligning with the principal findings of Joo and Jee (2023). Indeed, while previous theoretical studies were focused on the assembly history of the ICL, which means selecting a given object at the present time and read its history through the merger tree in order to derive the ICL formation time, more recent theoretical studies such that quoted above selected massive groups and clusters directly at high redshifts. The two selections are very di ff erent in their essence.  \nThe scatter in the ICL fraction-halo mass relation is crucial for explaining the primary driver of ICL formation, yet it remains a topic of debate. At a given halo mass, the ICL fraction can vary from a few percent to roughly 50%, indicating significant variability within halos of similar mass. How can we account for this variability? It likely depends on factors related to either the physical mechanisms driving ICL formation or certain halo properties, possibly linked to their assembly history. As discussed earlier, mergers and stellar stripping are the primary channels for ICL formation. Regardless of which process dominates, they are expected to operate di ff erently in halos of similar mass but with di ff erent ICL content. One possible explanation is that halos in a more evolved dynamical stage tend to have a higher fraction of ICL (Ragusa et al., 2023; Contini et al., 2023). This is because more evolved halos formed earlier, providing more time for ICL formation. In Figure 4, adapted from Contini et al. (2023), the ICL fraction is plotted against halo mass, color-coded based on halo concentration. Halo concentration is defined as the ratio of the virial radius to the scale radius assuming an NFW profile (Navarro et al., 1997). Notably, the plot reveals significant scatter, particularly on group scales (larger scales are limited by statistics). The scatter predicted by their model aligns with observed trends across a wide range of halo masses. Importantly, the color-coding indicates that, on average, more concentrated (redder) halos exhibit a higher ICL fraction. This suggests that more dynamically evolved halos tend to have a higher proportion of ICL than less concentrated counterparts.  \nHow can we explain the connection between the dynamical state of the halo and its ICL fraction within the context of ICL formation? The answer lies in the role of stellar stripping and mergers in ICL formation. If stellar stripping, as predicted by the model of Contini et al. (2023) and supported by many observations, is the primary mechanism, then the stronger tidal forces in more concentrated halos would lead to a higher ICL fraction. Additionally, massive satellites experience faster dynamical friction, allowing them to reach the most concentrated regions earlier than less massive satellites. Consequently, they are more susceptible to stellar stripping and contribute more to the ICL content. In the following subsection, we will explore how observational results on the main properties of ICL and BCGs shed light on the dominant mechanisms and the types of satellites involved.", '4.3 Colors, metallicity and age': "The formation and evolution of BCGs and ICL are interconnected, as the ICL is often regarded as an envelope surrounding the BCG with which it is associated. However, since the ICL consists of stars not bound to the BCG itself, their formation histories may di ff er, potentially  \nexperiencing growth in stellar mass at di ff erent times, driven by distinct mechanisms. We will delve into this point shortly, but it is crucial to clarify that observationally, the only way to understand the role of these mechanisms in the growth of both components is by examining their properties, particularly their colors, metallicities, and ages. Despite the complexities arising from the age-metallicity degeneracy, these parameters are essential for deciphering which mechanisms predominantly contribute to the growth of the ICL.  \nHaving outlined the two primary mechanisms for ICL formation, alongside the significant mode of mass growth through pre-processing, we can now explore how mergers and stellar stripping fit into various scenarios where colors, age, and metallicity may be similar or di ff erent in BCGs and ICL. Let's focus on three possible scenarios that emerge when measuring one of these properties in regions dominated by the BCGcompared to those where the ICL dominates. Notably, we can analyze these scenarios without needing to separate the two components, thus avoiding several complications associated with such separation. For simplicity, we assume that the BCG dominates the central regions, while the ICL becomes prominent at greater distances from the center. Let's consider the distribution of colors (although the same logic applies to the other properties) in the BCG + ICL as a whole, as a function of distance from the central regions. We can envision three possible scenarios:  \n- (1) colors become bluer with increasing distance;\n- (2) colors become redder with increasing distance;\n- (3) colors remain constant regardless of the distance from the central regions.  \nIn the first scenario, we observe a net negative gradient from the center to larger distances, while in the second scenario, the gradient is positive. In the last case, there is no change in colors, resulting in no gradient at all. Each of these possibilities o ff ers insights into how mergers or stripping might influence the observed color distribution.  \nViolent relaxation processes during mergers are quite strong (Murante et al. 2007), su ffi ciently robust to mix up the stellar populations. When a satellite merges with the BCG, some stars originally belonging to the satellite become unbound and join the ICL component. Depending on the magnitude of the merger (minor or major), the BCG's disk may be completely destroyed. In any case, mergers have the power to mix up stellar populations, making the last scenario the expected color distribution following a recent merger. Several observations support this idea (Raj et al. 2020; Ragusa et al. 2021; Joo and Jee 2023). Conversely, several other studies (DeMaio et al. 2015; Iodice et al. 2017; Morishita et al. 2017; Montes and Trujillo 2018) support a gradient in the color distribution.  \nIn the case we observe a gradient in the color distribution, stellar stripping is the first candidate at play. Indeed, contrary to mergers, this mechanism is more gentle, as it occurs when the satellite and BCG are not physically connected, and only part of the satellite's stars are e ff ectively stripped, mostly the outermost ones. The gradient, whether positive or negative, depends on the type of satellites undergoing stripping. Bluer colors indicate relatively younger stars, suggesting that, overall, the ICL stellar population is younger than that of the BCG, with these stars mainly originating from the outskirts of intermediate or massive satellites.  \nIn present-day groups and clusters, the typical observation reveals a negative gradient in colors or metallicity (as indicated in the references above), i.e., a bluer and more metal-poor ICL. However, there are instances of flat distributions, which may result from recent major mergers or multiple minor mergers (e.g., Contini et al. 2019; Joo and Jee 2023). Nonetheless, while stellar stripping may explain most observations for nearby objects, the scenario can di ff er at higher redshifts. With mergers being more frequent, the likelihood of a mix-up of the stellar population increases. This was demonstrated in a recent study of the ICL in objects at high redshift by Joo and Jee (2023), who investigated ten galaxy clusters in the redshift range 1 < z < 2 using deep IR imaging data. They found that, consistent with present-day observations, the ICL fraction in these clusters is comparable to that found in the present Universe. Moreover, they observed no clear correlation between colors and cluster-centric distance, leading them to conclude that stellar stripping is not the main mechanism at play in these high-redshift environments.  \nIt is worth noting that, although most cases with flat color / metallicity distributions can be explained as results of mergers, in particular situations, stellar stripping can also be invoked. If the typical colors of the largest contributors to the ICL in a given cluster are similar to those of the BCG, stellar stripping of these satellites would inevitably result in a flat color distribution. This implies that flat color / metallicity distributions are not always evidence of recent mergers.", '5 ICL distribution in groups and clusters': "The measurable properties of the ICL serve as valuable tools for understanding not only how it was formed and assembled over time through the processes described above, but also as indicators of its distribution within dark matter halos. This characteristic is pivotal in ICL studies because, comprising stars not gravitationally bound to any galaxy and influenced solely by the potential well of the dark matter halo, it provides insights into the properties of dark matter. Specifically, the ICL can serve as a luminous tracer of the dark matter distribution (Yoo et al. 2024 and references therein).  \nThe concept of linking the distribution of the ICL with that of dark matter is relatively recent (Montes and Trujillo 2019), although initial attempts were made several years ago. For instance, Zibetti et al. (2005) were among the first to propose that the ICL distribution could be approximated by an NFW profile, while Jee (2010) utilized the ICL along with weak lensing to trace dark matter structures in clusters. Over time, various authors have explored connections between the ICL and dark matter halos (Contini 2021), but only in recent years has this approach been developed with a high level of precision and examined from di ff erent perspectives.  \nFundamentally, these studies operate under the implicit assumption that since dark matter particles are collisionless and the ICL is bound only to the halo's gravitational potential, the distribution of ICL stars may resemble that of dark matter. This assumption suggests that the two components could be described by similar profiles, as assumed in recent theoretical investigations (Contini et al. 2020; Contini 2021). Initially, Harris et al. (2017) concluded that the ICL was more centrally concentrated than dark matter. This finding was subsequently  \ncorroborated by studies such as those by Contini et al. (2020) and Contini (2021), which assumed an NFW profile for the ICL with a higher concentration compared to the dark matter halo. These studies demonstrated that by assuming a more concentrated ICL distribution, their models could reproduce the observed BCG + ICL mass within various apertures and across di ff erent redshifts. Moreover, their model was used to predict the typical radius of transition between the BCG and ICL (Contini et al. 2022), providing a method for separating these two components  \nThe most significant findings, however, arise from observational studies (though supported by theoretical evidence). For instance, Montes and Trujillo (2019) quantified the average separation between the ICL and dark matter distributions in six clusters from the Hubble Frontiers Field. Utilizing the Modified Hausdor ff distance, which gauges the average distance between two distributions, they determined that the mean separation between the total mass distribution and the ICL is approximately ∼ 25 kpc. Furthermore, the ICL proved to be more adept at describing the dark matter distribution than previous proxies, such as X-ray measurements. Subsequently, Alonso Asensio et al. (2020) and Yoo et al. (2022) theoretically corroborated these results using similar techniques.  \nNumerous recent studies have endeavored to establish a link between the ICL and dark matter (Pillepich et al. 2018; Zhang et al. 2019; Deason et al. 2021; Sampaio-Santos et al. 2021; Kluge et al. 2021; Chun et al. 2023; Contini et al. 2023, 2024b; Jim'enez-Teja et al. 2024). To summarize a few, Zhang et al. (2019) investigated a cluster sample from the Dark Energy Survey and identified a universal radial dependence of the BCG + ICL surface brightness. However, they concluded that there was insu ffi cient evidence to support the ICL as a reliable tracer of the cluster matter distribution, but rather as an excellent indicator of the total cluster mass. Meanwhile, Kluge et al. (2021) focused on the alignments of the BCG and ICL with their host dark matter halo, finding that the ICL aligns more closely than the BCG, thus proposing the ICL as a dependable tracer of the dark matter distribution (see also Ragone-Figueroa et al. 2020).  \nRecent observational and theoretical works have also explored the relationship between the ICL and the dynamical state of the host halo (Ragusa et al. 2023; Contini et al. 2023, 2024b; Jim'enez-Teja et al. 2024; Yoo et al. 2024). The underlying concept is that if the ICL forms through mechanisms associated with the overall assembly of the halo, its properties should be linked to the particular growth stage and / or dynamical state of the halo. For instance, Jim'enez-Teja et al. (2024) observed a higher ICL fraction in clusters that experienced a major merger relatively recently compared to those in a more advanced dynamical stage. This finding contrasts with the results of another observational study by Ragusa et al. (2023), where a higher ICL fraction was observed in groups and clusters with a greater proportion of early-type galaxies, typically found in more evolved objects. These last results align with the theoretical predictions of Contini et al. (2023, 2024b), who found a higher average ICL fraction in halos that are more concentrated and formed earlier than others, a trend later extended to Milky Way-like halos (Contini et al. 2024a).", '6 Evolution with time of BCGs and ICL': 'BCGs and ICL, despite being distinct entities, share common pathways of formation. It has been demonstrated (e.g., Contini et al. 2018) that at least part of their formation is attributed to physical mechanisms contributing to both their growth, namely stellar stripping and mergers. The extent to which each mechanism contributes to the two components remains a topic of debate, not only between observers and theorists but also among authors within the same field. It is reasonably certain that BCGs undergo at least two growth phases: a rapid one at high redshifts due to mergers, and a smoother accretion at lower redshifts. Here we are excluding the initial stage of intense star formation (which is distinct from ICL formation) happening at high redshifts (before z ∼ 2 -3), depending on the mass of the galaxy (see, e.g., De Lucia and Blaizot 2007). Most theories predict a late formation of the ICL, implying that mechanisms driving early BCG growth may not fully account for the initiation of ICL formation. However, it is evident that regardless of the primary mechanism driving ICL formation, it must also play some role in BCG growth. For instance, if mergers or smooth accretion primarily drive ICL growth, they also contribute to BCG growth at later times. Conversely, if stellar stripping is predominant, galaxies subject to stripping are destined to merge with the BCG. In essence, while BCGs and ICL are distinct components, they share common features in their formation, as discussed below.  \nBeginning with the evidence that the ICL is dynamically bound to its host (Montes and Trujillo 2018; Yoo et al. 2022) and the understanding that more massive halos host the most massive BCGs (e.g., Moster et al. 2018), we can infer that the growth of both BCGs and ICL are somehow linked to the dynamical evolution of the host halo. Under this premise, BCGs and ICL should evolve similarly from a certain point in time, which is pivotal for the ensuing discussion. The hierarchical manner in which BCGs accumulate mass entails that they acquire most of their stellar mass at high redshifts, with their growth diminishing rapidly after redshift z ∼ 1 (e.g., Burke et al. 2015). Coinciding with this, numerical simulations and semi-analytic models (e.g., Murante et al. 2007; Contini et al. 2014) suggest that around redshift z ∼ 1, the ICL undergoes an acceleration in its growth. To quantify the growth of BCGs and ICL after this redshift, which roughly corresponds to the last 7-8 billion years, numerical methods indicate that the ICL accumulates approximately 80% of its stellar mass by the present time. In contrast, observations yield varying estimates for BCG growth during this period, with some claiming no growth (Oliva-Altamirano et al. 2014), approximately 50% growth (Lin et al. 2013; Burke et al. 2015), and others suggesting a doubling in mass (Lidman et al. 2012). However, it must be noted that the selection of the progenitors in observations is not trivial, and might be a ff ected by progenitor bias, i.e., the assumption that high redshift galaxies are drawn from the same distribution as the low redshift galaxies.  \nThe evolution of BCGs and ICL over the last 7-8 billion years has been extensively examined by Contini et al. (2018) using their semianalytic model, which enables the tracking of the growth of both components and elucidates whether they co-evolve. Co-evolution in this context does not necessarily imply that BCGs and ICL assemble the same amount of stellar mass during this period, but rather that they do so at similar rates, irrespective of the total mass accumulated, and through the same underlying mechanisms. Figure 5 from Contini et al. (2018) illustrates the residual mass of the ICL (red lines) and BCGs (black lines) normalized by their masses at redshift z = 1. Solid lines represent the median, while dashed lines indicate the 16th and 84th percentiles of the distributions. Normalizing at z = 1 ensures that  \nFig. 5 The residual mass of the ICL (red lines) and BCGs (black lines) normalized by the mass at redshift z = 1 . Solid lines represent the median, while the dashed lines represent the 16th and 84th percentiles of the distributions. Credit: Contini et al. (2018).  \n<!-- image -->  \nthe earlier growth of the two components is cancelled out, allowing for a focus on their di ff erential growth rates. Essentially, the figure quantifies the rate at which BCGs and ICL grow, with the slope of the lines at each redshift indicating the acceleration of this growth rate. The authors demonstrated that the slopes of the black (BCGs) and red (ICL) lines become equivalent after z ∼ 0 . 7, indicating that BCGs and ICL co-evolve beyond this redshift.  \nThe co-evolution of BCGs and ICL over the last few billion years has significant implications, aligning well with most of the observational findings mentioned previously. This co-evolution suggests that despite being physically distinct components, they share common formation pathways. The prevailing scenario posits that BCGs predominantly form stars through early star formation, followed by rapid growth via mergers. Concurrently, as halos become increasingly centrally concentrated over time, stellar stripping becomes more potent, initiating the formation of the ICL. As time progresses, BCGs acquire less mass compared to earlier epochs, while the ICL undergoes rapid growth. Nevertheless, mergers and stripping continue to contribute to both components, with the growth of the ICL accelerating in the last few billion years as dark matter halos become more concentrated or dynamically evolved. Consequently, a portion of the stellar mass in satellites destined to merge is subjected to stripping and eventually incorporated into the ICL.', '7 Concluding remarks': "The most relevant takeaway is that, despite being separate entities, BCGs and ICL share many commonalities, particularly in their growth over the last few billion years and, in some cases, similar properties such as colors, metallicity, and age. As discussed earlier, understanding their properties is crucial for unraveling their formation and evolution. Violent processes like mergers would homogenize the stellar populations of both components, resulting in similar colors or metallicities, whereas gentler mechanisms like stellar stripping of satellite galaxies would lead to gradients in these observables depending on the typical satellites that have been stripped. Despite some exceptional cases, the ICL is usually bluer, less metal-rich, and younger than the associated BCG.  \nRegarding BCGs, they represent the most massive galaxies in the Universe, and due to their unique location in galaxy groups and clusters, their growth di ff ers significantly from the rest of the galaxy population. A rapid growth at high redshift due to intense star formation activity is followed by growth through mergers at lower redshifts. The studies mentioned above have highlighted that BCG growth can also be almost negligible in some cases after z ∼ 1, but overall they grow by a factor of approximately 1.5-2 in the latter half of the Universe's lifespan. In contrast, the ICL has a di ff erent early history. While BCGs grow via mergers, the ICL begins to form through both mergers and stellar stripping. However, the bulk of the ICL forms after z ∼ 1 on average because stellar stripping becomes more powerful over time, particularly as the concentration of the host halo increases. Haloes of the same mass at lower redshifts are more concentrated and dynamically evolved, leading to di ff erences in the production of stray stars from high redshift to more recent times.  \nAs mentioned earlier in the chapter, given the rapid advancement of numerical simulations in terms of accuracy and resolution, it is crucial to reassess the primary contributors to the ICL. While its significance depends on the definition of mergers, conducting a comprehensive study considering various definitions is feasible. We aim to conduct such a study ourselves, utilizing suitable simulations such as YZiCS (Choi and Yi 2017) or the upcoming simulation New Cluster (Han et al., in preparation). These simulations o ff er high resolutions, particularly New Cluster, making them suitable for investigating this topic.  \nAnother crucial point of this chapter is the link between the ICL, or BCG + ICL content, and the dynamical state of their host. These components can serve as luminous tracers of the dark matter distribution, particularly the ICL, considering it is a collisionless component like  \ndark matter. This approach holds promise for studying dark matter, understanding the intrinsic di ff erences between relaxed and unrelaxed halos, as well as their assembly history. Recently, Yoo et al. (2024) focused on the spatial distribution between dark matter and baryonic components such as gas, satellites, BCG + ICL, and stellar particles alone in a theoretical manner. Their study echoes previous works such as Montes and Trujillo (2019), Alonso Asensio et al. (2020), Yoo et al. (2022), and others. By investigating the potential similarities in the distribution of dark matter and the mentioned components, they conclude that the spatial distribution of BCG + ICL and gas exhibits high similarity with that of dark matter, particularly for relaxed clusters (i.e., more evolved). This result implies once again that the ICL, together with the BCG, can be used to trace dark matter, serving as a probe of the dynamical state of the host halo.  \nDefinition 1. Mergers between dark matter halos are typically defined as the moment when the smaller halo enters the virial radius of the larger one, e ff ectively becoming a subhalo (Springel 2005). The definition of a merger between galaxies, however, is somewhat controversial and lacks a universal standard due to the di ffi culty in determining the exact start and end times of the process. 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