Brightest Cluster Galaxies and Intra-Cluster Light: Their Mass Distribution in the Innermost Regions of Groups and Clusters

We assume a BCG to be a two-component system: bulge and disk. The bulge is assumed to follow a Jaffe profile (Jaffe 1983):

where $M_{J}$ is the total mass of the bulge and $r_{J}$ the scale length. By integrating, the mass contained within a sphere of radius $r$ is given by

For the disk, we assume an exponential profile and its mass within a given radius $r$ is given by:

where $M_{D,tot}$ is the total stellar mass in the disk, and $R_{D}$ the scale radius of the disk. By splitting the BCG in the two components, we are able to drop the assumption made in CG20, that is the stellar mass of the BCG is entirely contained in the innermost 100 kpc. With this approach, we can probe distances much below 100 kpc.

We model the mass profile of the ICL exactly as in CG20, by assuming a modified version of the NFW profile. The reason behind our choice is fully discussed in CG20 and in Section 1 of this paper. The NFW profile reads as follows:

where $\rho_{0}$ is the characteristic density of the halo at the time of its collapse and $R_{s}$ is its scale radius. The concentration of a dark matter halo is defined as

where $R_{200}$ is the virial radius of the halo. The modification we made in CG20 to the classic NFW profile described in Equation 4 is by introducing a free parameter in Equation 5. We define the ICL concentration as

In CG20 we argued that the parameter $\gamma$ could be a function of halo properties such as the halo mass, and redshift. We set $\gamma$ by matching the observed $M^{*}_{100}-M_{500}$ at different redshifts (not considering any halo dependence) and we found that $\gamma=3$ at $z=0$ and higher values at higher redshifts, which means that the ICL is more concentrated than the dark matter halo in which it is contained. As mentioned in CG20, this is in good agreement with recent theoretical works (e.g. Contini et al. 2018; Pillepich et al. 2018) and observational studies (e.g. Montes & Trujillo 2019).

In Figure 1 we show the predicted $M_{10-100}-M_{500}$ relation, i.e. the BCG-ICL stellar mass between 10-100 kpc and the halo mass at different redshifts (different panels), compared with the observed relation by DeMaio et al. (2020) at similar redshift. As explained above, the values of $\gamma$ used are $\gamma=3$ at $z=0$ and $\gamma=5$ at higher redshifts. This figure is similar to Figure 2 in CG20, with the exception that the first 10 kpc are not considered. As in CG20, we find a reasonable agreement with the observed relations, in particular at the present time. Nevertheless, it appears clear that our model tends to underpredict, although for $\sim 0.3$ dex, the observed relation at $z\geq 0.5$. The degree of the agreement at $z=0$, instead, is definitely excellent as it is in Figure 2 of CG20 where we account for also the first 10 kpc.

In order to investigate whether our model overpredicts the amount of stellar mass in the first 10 kpc, in Figure 2 we plot the ratio between the stellar mass within 10 kpc and that within 100 kpc, as a function of the halo mass and at different redshifts (different panels). Once again, our predictions (color lines) are compared with the observed data by De Maio et al. (black symbols). The agreement looks better than that found in Figure 1, at least at $z\leq 0.5$, although it is clear that our predictions are somewhat higher than the observed data. Considering the fact that the predicted mass within 100 kpc is either similar or lower than observed, it suggests that our model predicts a slightly higher amount of stellar mass in the first 10 kpc. Moreover, regardless of the redshift, less massive haloes have higher $M_{10}$ than more massive ones. This results from the fact that the parameter $\gamma$ is fixed with halo mass, but less massive haloes are intrinsecally more concentrated than more massive ones. Hence, on average, the percentage of ICL within the first 10 kpc is higher for less massive haloes.

To give more credit to our model, we now investigate on the BCG-ICL mass within different apertures, and on their ratio over the total, as a function of halo and BCG mass. Since observations are so far better reproduced by our model at $z=0$, we will focus only at the present time. In Figure 3 we plot the BCG-ICL mass within 30, 50 and 70 kpc as a function of halo mass, as predicted by the model (black lines), and as observed (red symbols) by Kravtsov et al. (2018). Our model can predict the right amount of BCG-ICL mass within different apertures for a wide range of halo mass. Similarly, Figure 4 shows the same information, but as a function the BCG-ICL mass. In order to be consistent with the set of observed data, we derived the amount of BCG-ICL mass within a given radius $R_{out}$ that is a function of halo mass (see Kravtsov et al. 2018 for further details). Once again, our model is in very good agreement with the observed data.

In Figure 5 we plot the ratio between the BCG-ICL within the same apertures and the total BCG-ICL mass within $R_{out}$ as a function of halo mass (a similar plot can be obtained as a function of the BCG-ICL mass with similar information). Our model predictions (black lines) compare well with the observed data (red symbols) for a wider range of halo mass with respect to the similar plots in Figure 2. Overall, the model is able to capture the trend shown by the observed data, and as already seen in Figure 2, with less massive haloes having a larger concentration of mass in the innermost regions than more massive haloes. In this case, being the normalization higher, the trend is even more visible. However, contrary to Figure 2, here the model seems to be somewhat biased low rather than high. We will come back on this in Section 4.

As shown in the previous subsection, our model is able to predict several observed scaling relations between the BCG-ICL mass within different apertures and halo/BCG-ICL total mass, in particular at $z=0$. We now make use of our model to probe the mass distributions as a function of distance from the cluster centre of the three main components (bulge, disk and ICL) separately, that is the main purpose of this study.

The first four panels of Figure 6 show the diffferential stellar mass of bulge (black line), disk (red line), ICL (green line) and their sum (purple line) as a function of clustercentric distance for four BCG-ICL systems with different mass, ranging from $\log(BCG+ICL)\sim 11.0$ (panel a1), to $\log(BCG+ICL)\sim 13.3$. These case studies have been chosen almost randomly from our sample, with the only condition of being in the lowest quartile of the mass range (a1), some percentiles before and after the median (b1 and c1), and in the highest quartile (d1). No other condition regarding the mass in the bulge or disk has been chosen, neither about the morpholgy of the BCGs, or halo mass. For these “random” case studies, it is quite evident that the total BCG+ICL stellar mass does not give a real indication of which component (and from where) starts to dominate the total distribution. This is more clear in the last four panels (a2, b2, c2 and d2) of the same figure, which are a zoom-in of the previous four of the innermost regions. In all cases the bulge, as expected, drops very fast, while disk and ICL dominate the total distributions at different clustercentric distances, with the only exception given by d2 for which the mass in the disk is small compared to that in the bulge. Very interestingly, the ICL starts to dominate the total distribution at very small radii, even at 15-20 kpc.

We now move the attention to other four case studies: two pairs of BCG-ICL systems with similar mass and disk/ICL mass ratio. Their differential mass for each component as a function of distance is shown in Figure 8, four a pair with $\log(BCG+ICL)\sim 12.1$ and disk/ICL mass $\sim 0.25$ (panels a1 and b1), and a pair with $\log(BCG+ICL)\sim 11.9$ and disk/ICL mass $\sim 0.5$ (panels c1 and d1). Again, the four BCGs have been chosen in a random manner among those in our sample, with the only conditions of having same total mass and disk/ICL mass ratio for members of each pair, and similar total mass but different disk/ICL mass ratio for pair-pair members. For these case studies, the picture looks quite different with respect to the previous ones. Indeed, all case studies have a discreet disk/ICL mass ratio, that translates in a more relevant importance of the disk compared to the ICL. From panel a1 to d1 (similar mass but increasing disk/ICL mass ratio) we can see that the disk is increasingly important, and this makes the ICL dominate the total distribution at larger radii than seen before. This trend is more visible in the zoom-in shown in the last four panels of the same figure. As expected, the bulge drops even faster because these are BCGs with a prominent disk, and the importance of the disk with respect to the ICL makes all the difference. In the two cases where the disk is a quarter of the ICL (a2 and b2), the latter starts to dominate at radii $\sim 50-60$ kpc, but when the disk is half of the ICL, the distribution of the latter meets the total one at farther distances, $>70$ kpc in the case c2 and $>100$ kpc in case d2.

It appears clear that in disk-like BCGs the ICL is less likely to dominate from the innermost regions, while for bulge-like BCGs, given the fact that the bulge drops faster than the disk, it is more likely. We address this point in Figure 10, where we show other two pairs of case studies with similar mass and bulge/BCG mass ratio and plot again the differential mass of each component as a function of distance. The first two cases (a1 and b1) are two disk-like BCGs with B/T$<0.4$ and $\log(BCG+ICL)\sim 12.0$, and the second two cases (c1 and d1) are two bulge-like BCGs with B/T$>0.7$ and $\log(BCG+ICL)\sim 13.0$. For these four cases the conditions were medium size disky BCGs and two bulge-like BCGs on the last quartile of the mass range. The reasons behind our choices is that we want to see the difference bewteen BCGs of different morphology and, at the same time, whether or not in a bulge-like BCG the ICL can dominate the total distribution in a similar way as in a smaller disky BCG. In the first two cases the disk is the component that ”competes” with the ICL and the bulge does not contribute much, while in the last two cases the bulge makes the difference and an almost absent disk does not contribute. The main features of these plots can be seen in the zoom-in provided in the last four panels of the same figure. Similar to previous cases where the disk is important with respect to the ICL, the latter component starts to dominate the total distribution at large distances (over 100 kpc), but the interesting aspect is that in massive bulge-like BCGs the ICL can be important only at distances beyond 60-70 kpc.

With all the previous case studies of different BCG-ICL systems we have shown that the ICL can be the most important component, and so not neglected, even at very small clustercentric distances such as 10-20 kpc. Moreover, the morpholgy of the BCGs, the importance of the mass in the disk with respect to that of the ICL as well as the relative importance of the total BCG mass with respect to that of the bulge, are parameters that weigh on the distance at which the ICL begins to be the only component at play, and the range of distances can be as wide as $\sim 100$ kpc. In the next section we will further discuss all our results, but mainly those of the second part of our analysis in light of the common assumptions that are generally made when distinguishing between BCG and ICL.

In Section 3.1 we presented the analysis done in order to set our model, by comparing our predictions with observational data by DeMaio et al. (2020) up to redshift $z\sim 1.5$, and by Kravtsov et al. (2018) at the present time. Overall we find a compelling agreement with observations, but a key point it is worth discussing deeper. When we plot the $M_{10-100}-M_{500}$ relation at different redshifts, we find a gap of about $\sim 0.3$ dex between our predictions and the observed ones at redshift $z\gtrsim 0.5$. A similar gap has been found in CG20 when we included the innermost 10 kpc. The question that rises naturally is: Is this gap real or explainable by invoking intrisic differences between the model and the observation? For real we mean that, as a matter of fact, it implies an evolution in mass since redshift $z\sim 0.5$ of a factor $\sim 2$ that it is not seen in the observed data. In CG20 we have addressed this point. As a possible cause for the gap we have argued that, while our predictions are exactly at that particular redshifts, $z\sim 0.5$ and present time, the observational data by DeMaio et al. span a wider range of redshift with median at $z\sim 0.5$. Another possible reason is that our BCG+ICL mass are actually lower than observed at that redshift, which could be due to the difficulty in dectecting the stellar mass at higher redshift given by all the masking done for separating the source from the sky. It might also be that our model, at least in part, underestimates the BCG+ICL mass at $z\gtrsim 0.5$.

According to DeMaio et al., it is possible to reconcile the theoretical prediction of our model (since it predicts a rapid evolution of the ICL at late times, Contini et al. 2014) with their data if most of the ICL growth actually occurs at $r>100$ kpc, which is a very reasonable explanation. However, here we try to investigate the innermost tens kpc by assuming a mass profile for every component of a BCG+ICL system, and a direct comparison with their data shows that, although minor, our model does show some evolution within 100 kpc from $z\sim 0.5$ to the present time. The current state of affairs does not allow us to answer to the question above, because the gap is small for making final statements. Nevertheless, while we suggest the need to have more data at $z\sim 0.5$ in order to get a more complete picture and a fairer comparison, we surely stress that the profiles we assumed might not completely describe the internal BCG+ICL mass distribution at any redshift, even though they do at the present time.

DeMaio et al. correctly explain that the BCG+ICL gains stellar mass in the range 10-100 kpc more rapidly than within 10 kpc by invoking the “inside-out” scenario (van Dokkum et al. 2010; Patel et al. 2013; Bai et al. 2014; van der Burg et al. 2015; Zhang et al. 2016, 2019 and others) for the growth of the stellar mass distribution. Despite the issue discussed above, our model agrees well with this scenario. Indeed, albeit our predictions are slightly biased low with respect to the observed data, the trend is reproduced, i.e., as a cluster grows in halo mass, it gains more stellar mass from the outer regions (see Figure 2).

We then conclude that our model is reliable at least at the present time, while it needs more testing at higher redshift when more data are available. Hence, a model with a Jaffe profile for the bulge, an exponential one for the disk, and an NFW distribution of the ICL mass can be a good description of the whole BCG+ICL system. In the light of this, we now discuss the main point of this paper, that is, at what distance from the centre the ICL starts to dominate the mass distribution.

In Section 3.2 we have investigated the mass distribution of several case studies of BCG+ICL systems by looking at the distribution of each component. We have shown that the distance from which the ICL starts to dominate the total distribution strongly depends on the BCG properties, such as its morphology and whether or not it has an extended disk. The radius at which the ICL dominates the total distribution (for the sake of simplicity let’s call it $R_{transition}$ hereafter) can be very short, around 10-20 kpc, but it might reach even over 100 kpc, depending on the particular case. The total BCG+ICL stellar mass does not seem to play an important role (Figure 6), while the relative contribution of the disk with respect to the ICL (Figure 8) and that of the bulge with respect to the total BCG mass (Figure 10) do.

The morphology, bulge/disk-like BCG, has a major role in determining from where the ICL becomes the dominant component. It is plausible and somewhat expected that BCG+ICL systems where the BCG has an extended disk had larger $R_{transition}$, and bulge-like BCGs, depending on the mass of their bulge, more or less shorter $R_{transition}$. Having or not an extendend disk depends mostly on the merger history of the particular BCG, mainly whether or not it has experienced a recent major merger, which totally destroys the disk. However, the disk can further form again if there is enough cold gas and time. Mergers, on the other hand, contribute also on the production of the ICL, i.e., the more the number of mergers experienced, the more the mass that will end up in the ICL component. We can distinguish among three different case scenarios that might explain the BCG+ICL distribution for BCGs (a) bulge dominated (the most common), (b) spheroidals with similar bulge and disk components, and (c) disk-like BCGs (rare objects).

In the case (a), such BCGs either have had a troubled merger history ceasing the star formation before a new disk could grow again (a1), or they had a very recent major merger and no time available to grow a new disk (a2). In the case (a1) the amount of ICL is expected to be large, given the fact that mergers do contribute to the ICL and it is very likely that stellar stripping would play an important role when satellite galaxies are merging. In the case (a2), most depends whether the ICL formed through stellar stripping at late times. Case (b) represents a sort of middle ground between (a) and (c). These BCGs might have had mergers in the past (and so formed ICL), but no recent major merger so that the disk could grow again. For disk-like BCGs, i.e. case (c), it is very likely that they did not have any major merger in the recent past (or at all), and they evolved mainly through smooth accretion/minor mergers and via star formation until gas has been available. However, such BCGs are very rare and constitute a class of BCGs for which their ICL should not be expected to be the relevant component.

Given these three possible scenarios for the formation and evolution of BCG+ICL systems, $R_{transition}$ spans a wide range. It is the shortest for systems where the BCG is a bulge-like galaxy in the low end of the mass rank, and the highest where the BCG has a prominent disk. Overall, considering our case studies, we find that 15 kpc $\lesssim R_{transition}\lesssim 100$ kpc, but can be even larger than 100 kpc in very particular cases. Let’s discuss our results in the context of the most recent observational evidence.

Recently, Montes et al. (2021) focused on a deep study of the ICL of the Abell 85 galaxy cluster by using archival data taken with Hyper Suprime-Cam on the Subaru Telescope. They measured the BCG+ICL surface brightness profile out to around 215 kpc in the g and i bands, and noticed that, at $\sim 75$ kpc, both the surface brightness and color profiles become shallower. The interpretation of this result is that the ICL starts to dominate at that radius. Not only, in agreement with the prediction of our model (Contini et al. 2014, 2019) the color profile at radius beyond 100 kpc is consistent with that of massive satellite galaxies, suggesting that the stripping of these objects is responsible for the build-up of the ICL. Their $R_{transition}\sim 70$ kpc is also in good agreement with $R_{transition}\sim 80$ kpc by Zibetti et al. (2005), who found a similar flattening of the profile at that radius. It must be noted that the value of $R_{transition}$ by Zibetti et al. is the result of a stacking of about 700 galaxy clusters taken by the SDSS. This value of the transition radius at which the ICL becomes the dominant component agrees fairly well with works (e.g., Gonzalez et al. 2005; Seigar et al. 2007; Iodice et al. 2016; Gonzalez et al. 2021) that showed that BCG+ICL systems have such a break in the profile in the range 60-80 kpc.

Similar numbers have been found by Zhang et al. (2019) from the analysis of about 300 galaxy clusters at redshift $0.2<z<0.3$. These authors described the BCG+ICL radial profile by using a triple Sersic model and found a dominant core in the innermost 10 kpc, a bulge between 30 and 100 kpc and the ICL that dominates the distribution beyond 200 kpc, but already outside 100 kpc the profile transitions from the BCG to the ICL. They suggested that this transition is a potential cut between the two components, in good agreement with Pillepich et al. 2018 who noticed that simulated haloes more massive than $5\cdot 10^{14}\,M_{\odot}$ have more ICL mass outside 100 kpc than within.

All the values of the transition radius, i.e. the radius at which the ICL starts to become the dominant component, reported above are comparable with the range predicted by our model. We stress again that, a wide range of possible values of $R_{transition}$ is preferable to a narrow one for the reasons discussed above. It strongly depends on the morphology of the BCG, of the amount of ICL with respect to the other components and, not as last, to the dymanical state of clusters, which reflects the merging history of the BCG+ICL system and so its evolution with time.