Intracluster Light at the Frontier II: The Frontier Fields Clusters
aa r X i v : . [ a s t r o - ph . C O ] O c t MNRAS , 1–17 (2017) Preprint 11 October 2017 Compiled using MNRAS L A TEX style file v3.0
Intracluster Light at the Frontier II: The Frontier FieldsClusters
Mireia Montes ⋆ and Ignacio Trujillo , Department of Astronomy, Yale University, 06511 New Haven, CT, USA Instituto de Astrof´ısica de Canarias,c/ V´ıa L´actea s/n, E38205 - La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna, E38205 La Laguna, Tenerife, Spain
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Multiwavelength deep observations are a key tool to understand the origin of thediffuse light in clusters of galaxies: the intra-cluster light (ICL). For this reason, wetake advantage of the Hubble Frontier Fields survey to investigate the properties ofthe stellar populations of the ICL of its massive intermediate redshift (0.3 < z < ∼ kpc from thebrightest cluster galaxy. We found that the average metallicity of the ICL is [Fe/H] ICL ∼− . , compatible with the value of the outskirts of the Milky Way. The mean stellarages of the ICL are between to Gyr younger than the most massive galaxies ofthe clusters. Those results suggest that the ICL of these massive ( > M ⊙ ) clustersis formed by the stripping of MW-like objects that have been accreted at z < , inagreement with current simulations. We do not find any significant increase in thefraction of light of the ICL with cosmic time, although the redshift range explored isnarrow to derive any strong conclusion. When exploring the slope of the stellar massdensity profile, we found that the ICL of the HFF clusters follows the shape of theirunderlying dark matter haloes, in agreement with the idea that the ICL is the resultof the stripping of galaxies at recent times. Key words: galaxies: clusters — galaxies: evolution — galaxies: photometry —galaxies: haloes
The most revealing signature of galaxy cluster assembly iscontained within a diffuse component occupying the spacebetween the galaxies in the clusters. This component is com-posed of a substantial fraction of stars ( − of the totallight of the cluster, Krick & Bernstein 2007) . These starsconstitute the so-called intra-cluster light (ICL, see Mihos2016 for a review). This diffuse light is thought to form pri-marily by galaxies that interact and merge during the hier-archical accretion history of the cluster (e.g. Gregg & West1998; Mihos et al. 2005; Conroy et al. 2007; Presotto et al.2014; Contini et al. 2014).Despite its enormous importance for understandingclusters, the ICL is still mostly unexplored. This compo-nent is extremely challenging to probe due to its very lowsurface brightness ( µ V & mag/arcsec , e.g. Mihos et al.2005; Zibetti et al. 2005; Rudick et al. 2010). In addition,the ICL is normally contaminated by foreground and ⋆ E-mail: [email protected] (MM) background (in projection) galaxies. Moreover, the sep-aration between the ICL and the outer regions of thebrightest central galaxies is an ill-defined problem (e.g.Gonzalez et al. 2005; Krick & Bernstein 2007; Rudick et al.2011; Jim´enez-Teja & Dupke 2016).In order to comprehend the process of galaxy clusterevolution, it is important to determine how and when theICL formed. In this sense, a useful tool to determine theproperties of the ICL is the study of its stellar populations.In fact, the ages and metallicities of the ICL population re-flect the properties of the progenitor galaxies from which itsstars got stripped. For example, Contini et al. (2014) pre-dicted that the bulk of the ICL light is produced by themost massive (M ∗ ∼ − M ⊙ ) galaxies as they fall into thecluster core (see also Rudick et al. 2011; Cooper et al. 2013).If this is the case, the ICL should exhibit a mean metallic-ity similar to the outer regions of these massive satellites.Additionally, the age of the ICL stellar populations shouldgive us an upper limit on when the formation of the ICLtook place. This is because we do not expect any star for-mation in the ICL component after their stars have been © M. Montes & I. Trujillo stripped from their progenitor objects. In this sense, know-ing the age and metallicity of the ICL of the clusters allowus to infer how (and when) the assembly history of theseclusters was, ranging from the shredding of dwarf galaxies(Purcell et al. 2007; Contini et al. 2014), to violent mergerswith the central galaxies of the cluster (Murante et al. 2007;Conroy et al. 2007), or in situ formation (Puchwein et al.2010).In addition to the age and metallicity of the ICL,probing how the amount of stellar mass of this componenthas changed with redshift indicates the growth speed of theclusters. Particularly interesting is the z ∼ . epoch, a periodof time crucial to understand galaxy cluster evolution as it isexpected that they may have accreted as much as half theirmass by then (e.g. De Lucia & Blaizot 2007). Simulations(e.g. Rudick et al. 2011; Contini et al. 2014) show thatthere is a strong evolution in the fraction of light containedin the ICL with respect to the total light of the clustersince z ∼ . . However, given both the ambiguity in definingthe ICL and the observational difficulties in characterizingit, studies have found inconsistent results in the correlationbetween the fraction of light in this component and redshiftor mass of the cluster (e.g. Lin & Mohr 2004; Zibetti et al.2005; Krick & Bernstein 2007; Guennou et al. 2012;Giallongo et al. 2014; Presotto et al. 2014; Burke et al.2015). Finally, the spatial distribution of the stars belong-ing to the ICL might also encode information about theentire assembly history of the halo it belongs to. Recently,Pillepich et al. (2017b) showed that the slope of the stellardensity profile of the ICL can help us understand theunderlying dark matter halos (see also Pillepich et al.2014).The Hubble Frontier Fields (HFF) survey representsthe largest investment of HST time for deep observations ofgalaxy clusters. This survey consists in observations of verymassive galaxy clusters in the redshift range . < z < . .With its incomparable depth, those images represent an ex-cellent opportunity to study the properties of the ICL. Agesand metallicities of the ICL can be studied in detail tak-ing advantage of the inclusion of very deep near-infrared(NIR) data to break the age-metallicity degeneracy (e.g.Anders et al. 2004). The goal of this paper is to explorethis question in detail and characterize the age and metal-licity of the ICL of massive clusters at large radial distancesfrom the centre (R > kpc) with unprecedented accuracy.Different scenarios for the origin of the ICL result in dif-ferent stellar population properties and provide insightfulevidence for the formation of both ICL and cluster. In ourpilot project (Montes & Trujillo 2014, hereafter Paper I),we demonstrated that we can derive the age and metal-licity properties as well as the stellar mass fraction of theICL for the HFF cluster Abell 2744. We found that the ICLis ( ∼ Gyr) younger and more metal-poor than the centerof the most massive galaxies of the cluster ( Z ∼ Z ⊙ , while Z gal ∼ Z ⊙ ). The methodology applied in this paper differsfrom the one conducted in Paper I, where we relied in rest-frame colours to infer the age and metallicity radial profiles.In this paper, we are using the complete information givenby all the broadband filters, from F435W to F160W. Throughout this work, we adopt a standard cosmolog-ical model with the following parameters: H =70 km s − Mpc − , Ω m = . and Ω Λ = . . All magnitudes are in the ABmagnitude system. Our work is based in the complete HST data of the sixHFF clusters (ID13495, PI: J. Lotz and ID13386). The ACSimages were taken in the following filters: F435W, F606Wand F814W. NIR observations include imaging in four filtersF105W, F125W, F140W, F160W. The data were directly re-trieved from the archive . The HFF team reduced the datafor each cluster using a two-step process. First, the expo-sures were reduced following standard HST procedures bothfor the ACS and WFC3 data, quality inspected, geometri-cally corrected and combined. Those two latter steps wereperformed using Astrodrizzle , while the alignment of theimages has been done with Tweakreg. Once this step is com-plete, the images are reprocessed using all the informationfrom all the exposures. Specifically this step includes: recali-bration and bad pixel/cosmic-ray rejection, ”self-calibration”of the ACS data, improve WFC3 flagging of pixels affectedfor persistence due to bright sources and reprocess those im-ages affected by time variable sky, and combine the images ofboth cameras to produce the deepest images of the clusters.The ACS WFC ”self-calibration” step identifies and removesthe pixels affected by charge transfer efficiency (CTE) result-ing in a smoother image and a narrower pixel noise distribu-tion. Also, a few of the HFF observations in the IR exhibit atime-variable sky background signal due to time variable at-mospheric emission. The exposures were corrected from thisvariable emission and included into the final mosaics. Moreinformation about the processing of the HFF data can befound here . For both cameras, flat fields are claimed to beaccurate to better than across the detector. The mosaicswe used consist on drizzled science images with pixel size . ′′ . In the case of the WFC3, this pixel size is closer toone half of the original pixel.To conduct our goals a detailed process to avoid bi-ases and contaminations is required. First, we correctedby the effect of the PSF across the different bands. Ithas been shown in the literature that the main effect ofthe PSF is to bring light from the center to the out-skirts of the galaxies and, therefore, change their proper-ties (e.g. Capaccioli & de Vaucouleurs 1983; Trujillo & Fliri2016). That produces a redder ICL, a change in the shapeof the spectral energy distribution (SED) and, therefore, achange in the derived ages and metallicities. To compensatefor this effect, we PSF-matched all the images to the worstresolution one: F160W. As we need to characterize the PSFaccurately up to a large distance (Sandin 2014), we builtthe PSFs of each band in two steps. The inner region is cre-ated using the software Tiny Tim . Based in the shapes of theinner profiles, the outer parts are assumed to follow an ex-ponential behaviour. Once the PSFs of each band are built,we created a kernel for each image such as the convolution of http://drizzlepac.stsci.edu/ https://archive.stsci.edu/pub/hlsp/frontier/abell2744/images/hst/v1.0-epoch2/hlsp_frontier_hst_abell2744_v1.0-epoch2_readme.pdf MNRAS000
The most revealing signature of galaxy cluster assembly iscontained within a diffuse component occupying the spacebetween the galaxies in the clusters. This component is com-posed of a substantial fraction of stars ( − of the totallight of the cluster, Krick & Bernstein 2007) . These starsconstitute the so-called intra-cluster light (ICL, see Mihos2016 for a review). This diffuse light is thought to form pri-marily by galaxies that interact and merge during the hier-archical accretion history of the cluster (e.g. Gregg & West1998; Mihos et al. 2005; Conroy et al. 2007; Presotto et al.2014; Contini et al. 2014).Despite its enormous importance for understandingclusters, the ICL is still mostly unexplored. This compo-nent is extremely challenging to probe due to its very lowsurface brightness ( µ V & mag/arcsec , e.g. Mihos et al.2005; Zibetti et al. 2005; Rudick et al. 2010). In addition,the ICL is normally contaminated by foreground and ⋆ E-mail: [email protected] (MM) background (in projection) galaxies. Moreover, the sep-aration between the ICL and the outer regions of thebrightest central galaxies is an ill-defined problem (e.g.Gonzalez et al. 2005; Krick & Bernstein 2007; Rudick et al.2011; Jim´enez-Teja & Dupke 2016).In order to comprehend the process of galaxy clusterevolution, it is important to determine how and when theICL formed. In this sense, a useful tool to determine theproperties of the ICL is the study of its stellar populations.In fact, the ages and metallicities of the ICL population re-flect the properties of the progenitor galaxies from which itsstars got stripped. For example, Contini et al. (2014) pre-dicted that the bulk of the ICL light is produced by themost massive (M ∗ ∼ − M ⊙ ) galaxies as they fall into thecluster core (see also Rudick et al. 2011; Cooper et al. 2013).If this is the case, the ICL should exhibit a mean metallic-ity similar to the outer regions of these massive satellites.Additionally, the age of the ICL stellar populations shouldgive us an upper limit on when the formation of the ICLtook place. This is because we do not expect any star for-mation in the ICL component after their stars have been © M. Montes & I. Trujillo stripped from their progenitor objects. In this sense, know-ing the age and metallicity of the ICL of the clusters allowus to infer how (and when) the assembly history of theseclusters was, ranging from the shredding of dwarf galaxies(Purcell et al. 2007; Contini et al. 2014), to violent mergerswith the central galaxies of the cluster (Murante et al. 2007;Conroy et al. 2007), or in situ formation (Puchwein et al.2010).In addition to the age and metallicity of the ICL,probing how the amount of stellar mass of this componenthas changed with redshift indicates the growth speed of theclusters. Particularly interesting is the z ∼ . epoch, a periodof time crucial to understand galaxy cluster evolution as it isexpected that they may have accreted as much as half theirmass by then (e.g. De Lucia & Blaizot 2007). Simulations(e.g. Rudick et al. 2011; Contini et al. 2014) show thatthere is a strong evolution in the fraction of light containedin the ICL with respect to the total light of the clustersince z ∼ . . However, given both the ambiguity in definingthe ICL and the observational difficulties in characterizingit, studies have found inconsistent results in the correlationbetween the fraction of light in this component and redshiftor mass of the cluster (e.g. Lin & Mohr 2004; Zibetti et al.2005; Krick & Bernstein 2007; Guennou et al. 2012;Giallongo et al. 2014; Presotto et al. 2014; Burke et al.2015). Finally, the spatial distribution of the stars belong-ing to the ICL might also encode information about theentire assembly history of the halo it belongs to. Recently,Pillepich et al. (2017b) showed that the slope of the stellardensity profile of the ICL can help us understand theunderlying dark matter halos (see also Pillepich et al.2014).The Hubble Frontier Fields (HFF) survey representsthe largest investment of HST time for deep observations ofgalaxy clusters. This survey consists in observations of verymassive galaxy clusters in the redshift range . < z < . .With its incomparable depth, those images represent an ex-cellent opportunity to study the properties of the ICL. Agesand metallicities of the ICL can be studied in detail tak-ing advantage of the inclusion of very deep near-infrared(NIR) data to break the age-metallicity degeneracy (e.g.Anders et al. 2004). The goal of this paper is to explorethis question in detail and characterize the age and metal-licity of the ICL of massive clusters at large radial distancesfrom the centre (R > kpc) with unprecedented accuracy.Different scenarios for the origin of the ICL result in dif-ferent stellar population properties and provide insightfulevidence for the formation of both ICL and cluster. In ourpilot project (Montes & Trujillo 2014, hereafter Paper I),we demonstrated that we can derive the age and metal-licity properties as well as the stellar mass fraction of theICL for the HFF cluster Abell 2744. We found that the ICLis ( ∼ Gyr) younger and more metal-poor than the centerof the most massive galaxies of the cluster ( Z ∼ Z ⊙ , while Z gal ∼ Z ⊙ ). The methodology applied in this paper differsfrom the one conducted in Paper I, where we relied in rest-frame colours to infer the age and metallicity radial profiles.In this paper, we are using the complete information givenby all the broadband filters, from F435W to F160W. Throughout this work, we adopt a standard cosmolog-ical model with the following parameters: H =70 km s − Mpc − , Ω m = . and Ω Λ = . . All magnitudes are in the ABmagnitude system. Our work is based in the complete HST data of the sixHFF clusters (ID13495, PI: J. Lotz and ID13386). The ACSimages were taken in the following filters: F435W, F606Wand F814W. NIR observations include imaging in four filtersF105W, F125W, F140W, F160W. The data were directly re-trieved from the archive . The HFF team reduced the datafor each cluster using a two-step process. First, the expo-sures were reduced following standard HST procedures bothfor the ACS and WFC3 data, quality inspected, geometri-cally corrected and combined. Those two latter steps wereperformed using Astrodrizzle , while the alignment of theimages has been done with Tweakreg. Once this step is com-plete, the images are reprocessed using all the informationfrom all the exposures. Specifically this step includes: recali-bration and bad pixel/cosmic-ray rejection, ”self-calibration”of the ACS data, improve WFC3 flagging of pixels affectedfor persistence due to bright sources and reprocess those im-ages affected by time variable sky, and combine the images ofboth cameras to produce the deepest images of the clusters.The ACS WFC ”self-calibration” step identifies and removesthe pixels affected by charge transfer efficiency (CTE) result-ing in a smoother image and a narrower pixel noise distribu-tion. Also, a few of the HFF observations in the IR exhibit atime-variable sky background signal due to time variable at-mospheric emission. The exposures were corrected from thisvariable emission and included into the final mosaics. Moreinformation about the processing of the HFF data can befound here . For both cameras, flat fields are claimed to beaccurate to better than across the detector. The mosaicswe used consist on drizzled science images with pixel size . ′′ . In the case of the WFC3, this pixel size is closer toone half of the original pixel.To conduct our goals a detailed process to avoid bi-ases and contaminations is required. First, we correctedby the effect of the PSF across the different bands. Ithas been shown in the literature that the main effect ofthe PSF is to bring light from the center to the out-skirts of the galaxies and, therefore, change their proper-ties (e.g. Capaccioli & de Vaucouleurs 1983; Trujillo & Fliri2016). That produces a redder ICL, a change in the shapeof the spectral energy distribution (SED) and, therefore, achange in the derived ages and metallicities. To compensatefor this effect, we PSF-matched all the images to the worstresolution one: F160W. As we need to characterize the PSFaccurately up to a large distance (Sandin 2014), we builtthe PSFs of each band in two steps. The inner region is cre-ated using the software Tiny Tim . Based in the shapes of theinner profiles, the outer parts are assumed to follow an ex-ponential behaviour. Once the PSFs of each band are built,we created a kernel for each image such as the convolution of http://drizzlepac.stsci.edu/ https://archive.stsci.edu/pub/hlsp/frontier/abell2744/images/hst/v1.0-epoch2/hlsp_frontier_hst_abell2744_v1.0-epoch2_readme.pdf MNRAS000 , 1–17 (2017)
CL at the Frontier that kernel with our images results in a new image matchingthe resolution of F160W. Details on the full process can befound in Section A1. An accurate background determination of the HFF data isvery difficult, particularly in the IR bands, as the ICL al-most fills the entire image. Furthermore, a preliminary ex-ploration of the images showed that most of them had theirbackground over subtracted during the data reduction pro-cess. To correct for such artificial sky, we add a constantbackground to the images. To do that, we measured the skyin each band of each cluster in ∼ apertures of r = pix ( . ′′ ), located farther away from the cluster centre (i.e. > kpc for the clusters with two brightest cluster galaxies(BCGs) and > kpc for clusters with one BCG; see belowfor the BCG definition). In addition, we avoid any source ordiffuse light so we can estimate a sky value for our imageswithout contamination. To test the gaussianity of our skydistributions, we performed Kolmogorov-Smirnov tests thatindicate that a Gaussian distribution is compatible with thedata, with p-values > . .To measure the ICL accurately, it is crucial to masksall sources that might contaminate the diffuse light. Themajority of the HFF clusters are merging or have under-gone a recent merger (Lotz et al. 2017), hence in some casesthe choice of which galaxy is the BCG is unclear. Conse-quently, when the difference in the magnitudes of the twomost massive galaxies is small, we chose both as BCGs. Theclusters where we have two BCGs are: A2744, M0416 andA370. Once identified our BCGs, we proceeded to mask allthe galaxies of the cluster as well as foreground and back-ground sources. The masking process is detailed in SectionA2. The masked images are presented in Fig. A3.The purpose is to study the properties of the stellarpopulations of the ICL down to the faintest surface bright-ness possible. Therefore, to estimate the surface brightnesslimits down to where we can explore the ICL, we calculatedthe r.m.s of the images on boxes of × arcsec located onthe sky for each of the clusters. The surface brightness lim-its we provide correspond to σ detections above the sky inthe PSF-matched images. The surface brightness limits arelisted, in each band and for each of the clusters in Table 1. The goal of this work is to study the stellar populations ofthe HFF clusters from the center of their BCG(s) to theouter parts of the clusters. To that end, we derived the ra-dial SEDs of the clusters in logarithmic spaced bins from to kpc from the BCG(s). The distance of each pixelon the images is computed as the elliptical distance to itsnearest BCG, where the morphological parameters of thesegalaxies are given by SExtractor (see Montes & Trujillo 2014for further details). For each radial bin, the surface bright-ness was obtained averaging the pixel values. The errors ofthe SED values are a combination from the photometric er-rors and the zeropoint uncertainties. The photometric errors Restframe λ (Å)182022242628 µ A B ( m a g / a r c s e c ) AS1063 R = 2 kpcR = 12 kpcR = 54 kpcR = 115 kpc
Figure 1.
Example of SEDs at four radial distance for one of theHFF clusters, AS1063. The filled circles represent the SED derivedfrom the images and redshifted to their restframe wavelength,while the solid lines represent the best fitting Vazdekis et al.(2016) models at each radius. The errors of the photometry aresmaller than the size of the circles. The surface brightness, verti-cal axis, is corrected by cosmological dimming. The bluest band,F435W, in the SEDs at R = and R = kpc shows a level ofbackground contamination above , therefore we are not usingit for the fits. are drawn from jackknife resampling, i.e. repeating the pho-tometry in a subsample of the data for each bin. The num-ber of subsamples taken was . We corrected our data forGalactic extinction (Schlafly & Finkbeiner 2011) using theCardelli et al. (1989) extinction law. We also corrected forcosmological dimming. As each image has a different depth,we decided to use a simple method to determine up to whichradius our photometry is reliable. For that, we determine thecontamination of sky background pixels in each spatial bin.To do that, we compared the observed distribution of countsin each spatial bin with the sky background distribution (seeSection 2.1 for the determination of the background). Thephotometry in each band is estimated until the level of back-ground contamination is more than . As we expect old orintermediate ages for the ICL (Paper I), it should be fainterin the bluer filters. This implies that our completeness is ul-timately limited by the noise in the observed optical filters.Eliminating the optical filters from our analysis increasesthe degeneracy between age and metallicity, i.e. the errorson the determination of those quantities. Fig. 1 shows anexample of different SEDs at different radial distances. Weare not plotting the bluest band, F435W, for the SEDs at R = and R = kpc as their level of sky backgroundcontamination is more than . Taking advantage on the large wavelength range of our dataset, we fitted single stellar population (SSP) models to ex-plore whether it is possible to detect stellar population gra-
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M. Montes & I. Trujillo
Cluster Redshift R.A. (2000) Dec (2000) SB limits (mag/arcsec )(z) (hh:mm:ss) (dd:mm:ss) F435W F606W F814W F105W F125W F140W F160WAbell 2744 . . ± .
09 31 . ± .
12 31 . ± .
10 31 . ± .
12 31 . ± .
09 31 . ± .
11 30 . ± . MACSJ0416.1-2403 . . ± .
11 31 . ± .
14 31 . ± .
14 31 . ± .
11 31 . ± .
12 31 . ± .
11 30 . ± . MACSJ0717.5+3745 . . ± .
13 31 . ± .
09 31 . ± .
10 31 . ± .
11 31 . ± .
16 31 . ± .
11 30 . ± . MACSJ1149.5+2223 . . ± .
11 31 . ± .
09 31 . ± .
11 31 . ± .
12 31 . ± .
12 31 . ± .
14 30 . ± . Abell S1063 . . ± .
15 31 . ± .
10 31 . ± .
10 31 . ± .
12 31 . ± .
11 31 . ± .
11 30 . ± . Abell 370 . . ± .
16 31 . ± .
15 31 . ± .
11 31 . ± .
10 31 . ± .
11 31 . ± .
11 30 . ± . Table 1.
Summary of the main properties of the six HFF clusters. The surface brightness limits (3 σ above the sky) are calculated inboxes of × arcsec . These limits have been obtained for the images at the same spatial resolution as the F160W image. dients from the center of the BCG(s) to the outer parts ofthe cluster. Note that considering an SSP at each radius is arough assumption since we expect the ICL to be formed bythe accretion of a variety of galaxies, especially at large dis-tances from the center of the cluster (see Paper I). Nonethe-less, and for simplicity, we follow the approach as describedin Section 3.2.1 in Montes et al. (2014), and briefly describedhere.In this work, we use the UV-extended E-MILES SSPmodels from Vazdekis et al. (2016) for the Padova 2000isochrones. The E-MILES models cover the spectral range − ˚A, and consist of metallicities in the range − . ≤ [Fe/H] ≤ . and ages from . to . Gyr, fora suite of initial mass function (IMF) types with varyingslopes. To diminish the uncertainties due to width of thesteps in age and metallicity, we expanded the grid of modelswith metallicities and ages linearly interpolating theoriginal SSPs. Our choice of IMF is a Salpeter (1955) IMF,i.e. a unimodal IMF with a slope of . . For each cluster, themaximum age allowed in our fits is the age of the universeat the given redshift.The observed SEDs are compared with the model SSPsto obtain information of the stellar populations at each ra-dius (see Fig. 1). For this, we first redshifted the model tothe redshift of the cluster. Then, we convolved the redshiftedmodel with the filter response of our photometric filters toretrieve synthetic photometry for comparison. We used a χ -minimization approach to obtain the best fit model to ourdata (Eq. 2 in Montes et al. 2014), as well as the 1- σ confi-dence levels. As the parameters to fit are three: age, metal-licity and luminosity, the number of spectral bands requiredfor fitting are at least four.We run the fitting procedure for each of the jackkniferealizations of the SEDs. The final ages and metallicities arethe median of the ages and metallicities of the realizations.The errors are the median errors of each of the fits dividedby the square root of the number of realizations. In Fig. 2, we present the age and metallicity profiles foreach of the HFF clusters. In the left panels, we overplotthe colour coded distance bins to the masked image of thecluster. Middle and right panels are, respectively, the ageand metallicity profiles up to kpc, depending on thecluster. As we mentioned in Paper I, the definition of ICL iscontroversial as it is unclear how to disentangle, if possible,between the BCG(s), especially the outskirts, and the ICL.Several studies attempt this by defining a surface bright-ness threshold (e.g. Feldmeier et al. 2004; Mihos et al. 2005;Krick et al. 2006; Krick & Bernstein 2007; Burke et al.2015). In our case, we define ICL as the light beyond > kpc (see Gonzalez et al. 2005; Toledo et al. 2011). Althoughthis choice of radius is not perfect, as it could include afraction of light from the outskirts of the BCG(s), it al-lows us to compare with previous spectroscopic studies thatderive ages and metallicities for the ICL at those distances(e.g. Coccato et al. 2010; Melnick et al. 2012; Edwards et al.2016). Furthermore, Presotto et al. (2014) fit a de Vau-couleurs profile to the BCG of MACSJ1206.2-0847 ( z ∼ . ).They found that at R > kpc there is an excess of light withrespect to the r fit. They identify this deviation from a deVaucouleurs profile as the signature of the ICL. The regionwe consider ICL is highlighted as an orange shaded area inFig. 2. According to the middle panels in Fig. 2, there is acontinuos negative age gradient from the centre of the clus-ter to their outskirts. That implies that the outskirts of theclusters are younger than the centre of the BCG(s). That istrue also for the metallicity gradients (right panels in Fig. 2)where we can see that the stellar populations become moremetal-poor as the distance from the BCG(s) increases. Thedistances, ages and metallicities values are listed in TableB1. Abell 2744
Abell 2744 is the nearest cluster of the HFFsurvey (z = . ) also known as ”Pandora’s Cluster”.It comprises different mass substructures (Merten et al.2011) and a complex velocity structure suggestive of a merg-ing system (Braglia et al. 2007; Merten et al. 2011). TheHFF survey imaged the most massive southern structure,the core (Merten et al. 2011). Its velocity dispersion is σ = ± km/s − (Owers et al. 2011). In Fig. 2, it is shownthat this cluster presents a negative gradient in age, rang-ing from ∼ Gyr in the centre of the BCGs to ∼ . Gyr inthe ICL, the orange shaded region. Despite the differences inmethodology and stellar population models, this agrees withour previous results for this cluster (see Paper I), where wefound that the ICL was between ± Gyr younger than thecenter of the most massive galaxies of the cluster. For the
MNRAS , 1–17 (2017)
CL at the Frontier
10" = 45.4 kpc
A2744 A g e s ( G r ) [ F e / H ]]
10" = 53.4 kpc
M0416 A g e s ( G r ) [ F e / H ]]
10" = 63.8 kpc
M0717 A g e s ( G y r ) [ F e / H ]] Figure 2.
Gradients of age and metallicity as a function of radial distance to the BGC(s) of the clusters. Left panels show the image ofthe cluster in the F160W filter and overplotted are the different spatial regions in which the SEDs are measured. The central and rightpanels are the age and metallicity radial gradients derived from the fitting to the SEDs as described in Section 3.2. We also marked inorange the region of the ICL ( R > kpc). The colours of the spatial regions in the left panels correspond to the colours of the circles inthe age and metallicity gradients. metallicity, we find a value of [Fe/H] ∼ − . for the ICL, Z ∼ . , while for the BCGs is [Fe/H] ∼ . (Z ∼ . ). Thismetallicity value is slightly lower than what we found inPaper I but in agreement within errors. MACSJ0416.1-2403
This object is an elongated mergingcluster (Mann & Ebeling 2012), also part from the CLASHsurvey (Postman et al. 2012). It has a velocity dispersionof ± km/s − (Ebeling et al. 2014). One of the most prominent features in the image of the cluster is the presenceof a bright star within arcminute from the cluster core.Although the FF images avoid the center of the star, thehalo and spikes can be clearly seen. Therefore, we decidedto aggressively mask that region (see Fig. A3). The agesrange from ∼ Gyr in the core of the BCGs to . ± . Gyrin the region of the ICL ( > kpc) giving a difference of ∼ Gyr. The metallicities range from [Fe/H] ∼ . to ∼ − . . MNRAS , 1–17 (2017)
M. Montes & I. Trujillo
10" = 63.7 kpc
M1149 A g e s ( G y r ) [ F e / H ]]
10" = 49.2 kpc
AS1063 A g e s ( G y r ) [ F e / H ]]
10" = 51.6 kpc
A370 A g e s ( G y r ) [ F e / H ]] Figure 2.
Continued
MACSJ0717.5+3745
This cluster is the farthest (z = . , Edge et al. 2003), one of the most massive and thestrongest lenser of all the clusters in the HFF sample(Lotz et al. 2017). The velocity dispersion is ± km/s − (Ebeling et al. 2007). It has some stars and a fore-ground galaxy in the field of view (FOV). The extendedoutskirts of this foreground galaxy is a source of contamina-tion of the ICL, therefore we decided to mask most of theleft side of the image (see Fig. A3). The ages range from ∼ Gyr in the centre of the cluster to ∼ Gyr in the outerparts, a difference of Gyr. The metallicities range from[Fe/H] ∼ . to [Fe/H] ∼ − . . MACSJ1149.5+2223
A cluster at z= . ,MACSJ1149.5+2223 is an X-ray elongated clusterwith a complex merger history (Kartaltepe et al. 2008;Zitrin & Broadhurst 2009; Lotz et al. 2017). Its velocitydispersion is ± km/s − (Ebeling et al. 2007). Thiscluster also presents two bright stars and a foregroundgalaxy near the core of the cluster, therefore the lower rightpart of the image is masked to prevent contamination (seeFig. A3). The ages range from ∼ Gyr to ∼ Gyr in theICL region, a difference of Gyr. The metallicities go from[Fe/H] = . to ∼ − . for the ICL. MNRAS000
A cluster at z= . ,MACSJ1149.5+2223 is an X-ray elongated clusterwith a complex merger history (Kartaltepe et al. 2008;Zitrin & Broadhurst 2009; Lotz et al. 2017). Its velocitydispersion is ± km/s − (Ebeling et al. 2007). Thiscluster also presents two bright stars and a foregroundgalaxy near the core of the cluster, therefore the lower rightpart of the image is masked to prevent contamination (seeFig. A3). The ages range from ∼ Gyr to ∼ Gyr in theICL region, a difference of Gyr. The metallicities go from[Fe/H] = . to ∼ − . for the ICL. MNRAS000 , 1–17 (2017)
CL at the Frontier AS1063
This is massive cluster with significant substruc-ture and a velocity dispersion of ± km/s − (G´omez et al. 2012; Gruen et al. 2013) at z= . (G´omez et al. 2012). It is the most relaxed of the se-lected HFF clusters (Lotz et al. 2017). The ages range from ∼ Gyr in the centre of the cluster to ∼ . Gyr in the ICLregion, a difference of ∼ Gyr. The metallicities go from[Fe/H] = . to ∼ − . for the ICL. Abell 370
Abell 370 is a very well studied lensing clus-ter (see references in Lotz et al. 2017) at z = . (e.g.Struble & Rood 1999). Its total velocity dispersion is ± km/s − (Dressler et al. 1999). The ages range from ∼ Gyr in the centre of the BCGs to ∼ . Gyr in the ICL re-gion. The metallicities go from [Fe/H] = . to ∼ − . forthe ICL. Recently, both observations (Burke et al. 2015) and simu-lations (Rudick et al. 2011; Contini et al. 2014) have sug-gested that there is a strong evolution in the fraction of lightcontained in the ICL at later times, z < . Burke et al. (2015)showed that the most dramatic evolution in the fraction ofthis component starts at z ∼ . (see also Krick & Bernstein2007). Therefore, the redshift range spanned by the HFFclusters, . < z < . , appears as an interesting epoch toexplore whether it is the onset of the ICL in galaxy clus-ters. In order to investigate this, we derived the fractionof light contained in the ICL in the following fashion. Wemeasured the ICL flux from the clusters images applying anICL threshold of µ V = mag/arcsec to be able to com-pare with previous studies and simulations. To measure thetotal cluster light, we derived again the masks for each clus-ter but this time not including all the galaxies belongingto the cluster. The mask was constructed using the avail-able spectroscopic and photometric redshifts provided bythe HFF team (Lotz et al. 2017) when available. We alsoused grism redshifts for AS1063 and A370 provided by theGLASS team and NED photometric redshifts for A2744and A370. We identify a galaxy as a member of the clusterif its redshift does not depart from the redshift of the clus-ter by more than ∆ z = . , to account for the photometricredshift errors. As the brighter cluster members have spec-troscopic or grism redshift available, the choice of ∆ z onlyaffects low mass galaxies. We tried with different values of ∆ z and the changes were insignificant (if any). It is worthstressing that our estimation of the total stellar light of thecluster depends on its redshift. In other words, the higherthe redshift the larger the number of low mass galaxies weare missing. We discuss how this incompleteness can affectour results in Appendix D.To construct the mask, we assigned a redshift value tothe pixels of the images using the segmentation map givenby the SExtractor runs (see Section A2). Then, we maskedthe area subtended by those objects whose redshifts do not https://archive.stsci.edu/prepds/glass/ http://ned.ipac.caltech.edu/ correspond to the cluster and also those without redshift.Finally, the image in the rest-frame V-band for each clus-ter, necessary for applying the ICL criteria, is computed byinterpolating among the observed HST images.We present the fraction of total cluster light containedin the ICL of the HFF clusters in the V-band as the blue andred filled circles in Fig. 3. Red filled circles in Fig. 3 indicatethe fraction of the ICL contained in a slice in µ V from 26 to27 mag/arcsec ( ∼ σ above the background). To account forthe possible bias introduced by imposing a faint-end limit onthe ICL (see also Rudick et al. 2011; Burke et al. 2015) wealso measure the fraction of ICL by including all the pixelsfainter than our ICL threshold mag/arcsec (blue filledcircles in Fig. 3). When doing that, we find an average in-crease in the ICL fraction is ∼ . In Fig. 3, we comparedwith the observational data in Burke et al. (2015). They de-rived ICL fractions for CLASH clusters below a surfacebrightness threshold in the B-band of 25 mag/arcsec andabove 26 mag/arcsec . The threshold in the B-band is equiv-alent to a threshold of . mag/arcsec in the V-band, as-suming a colour of B-V = . (Vazdekis et al. 2016), for anage of Gyr and [Fe/H] = − . , similar to our derived agesand metallicities for the ICL. As their threshold is brighter,the ICL fractions in Burke et al. (2015) include more lightfrom the inner parts of the cluster than in our case, i.e.we reach further out from the inner parts of the cluster. Themeasured fractions for the HFF clusters for both < µ V < mag/arcsec and µ V > mag/arcsec are listed in Table 2.The slope of the Burke et al. (2015) points shows a steepincrease in the fraction of ICL with redshift indicating thatthe build-up of this component is fairly rapid with decreas-ing redshift. In our data, we see a slight increase on the ICLfraction with decreasing redshift, as predicted by simula-tions (Rudick et al. 2011; Contini et al. 2014) although notas steep as in Burke et al. (2015). However, we are exploringa narrow redshift range with respect to Burke et al. (2015),therefore any conclusions must be taken with caution.We also plotted in Fig. 3 the redshift evolution of theICL fraction from Rudick et al. (2011) simulations for a clus-ter of mass M = . × M ⊙ , lower than the mass of theHFF clusters. Their data points are measured using the samesurface brightness threshold than in this work: i.e. µ V > mag/arcsec . However, they include all the light brighterthan µ V = mag/arcsec (Rudick et al. 2006), magni-tudes fainter than our fainter lower limit ( mag/arcsec ).Consequently, the difference between the fraction of ICLfrom their simulations and our observations could be mainlycaused by the light we are missing in our observations. Wefound an average increase of in the ICL fraction whenwe lower our faint limit to include all the light below mag/arcsec . In the same way, Burke et al. (2015) observedan increase of when they lowered their faint limit from . to mag/arcsec in the B-band. Unfortunately, thereis no estimate of the amount of light we could be missing.The transition between BCG and ICL happenssmoothly, making it difficult to disentangle between bothcomponents. To overcome this issue we have used a sur-face brightness threshold approach, which is unable to ac-count for the amount of ICL that (in projection) is abovethe BCG. Therefore, to account for it, we decided to per-form a linear fit to the surface brightness of each cluster inthe restframe V-band for the ICL region, i.e. R > kpc, as MNRAS , 1–17 (2017)
M. Montes & I. Trujillo F r a c t i o n o f I C L li g h t i n c l u s t e r Burke et al. 2015Rudick et al. 201126<µ V <27 mag/arcsec µ V >26 mag/arcsec R Figure 3. Fraction of light in the V-band in the ICL componentas a function of redshift. Red filled circles correspond to a slicein surface brightness in the V-band from 26 to 27 mag/arcsec .Blue filled circles correspond to all the light fainter than µ V = mag/arcsec while the orange squares correspond to the fractionof ICL light for R < R kpc. The green polygon are the frac-tions derived in Burke et al. (2015), for clusters from CLASHbetween µ B = and mag/arcsec . The black line is the pre-diction of Rudick et al. (2011) for the fraction of ICL measuredwith µ V > mag/arcsec . a way to describe this component. The functional form forthe fit is suggested by the relatively flatness of the ICL pro-files (see Krick & Bernstein 2007; Cooper et al. 2015). Usingthe fit as the ICL profile, we have evaluated the fraction ofICL for three different apertures: kpc < R < R limit , R < R limit and R < R (the latter are the orange filled squares in Fig.3). R limit is defined as the radius in which the number ofbands for the SSP fits are at least four. They can be foundin Table B1 as the last bin with age and metallicity foreach cluster. R is the radius where the mean mass den-sity exceeds the critical density by a factor of . Theyare taken from Mantz et al. (2010); Maughan et al. (2012);Ehlert et al. (2013) and Sayers et al. (2013), and are on av-erage ∼ . Mpc. There are two clusters, M0717 and M1149,whose fractions change radically when we change the outerradius. Those two clusters are significantly less concentratedthan the rest of the FF clusters. Therefore, as we go fartherfrom the centre of the cluster, the quantity of light in theICL diminishes, but we are including more galaxies, morestellar mass, of the cluster resulting in an overall decrease ofthe fraction of light in the ICL.The ICL fractions derived for the different apertures arealso listed in Table 2. The average fraction of ICL is ∼ from the centre of the BCG(s) to the outer parts of thecluster, R < R . None of these definitions of ICL support aredshift evolution of the fraction of ICL, although the red-shift range we are exploring is not large enough to draw anystrong conclusion. N o r m a li z e d l o g ( ρ ) ( / c ) A2744MACS0416MACS0717MACS1149AS1063A370 Figure 4. Mass normalized density profiles for the HFF clusters. The possibility that the stellar halo or ICL properties mightprovide information about the assembly history of the parentdark matter halo has motivated substantial effort to studythe outskirts of galaxies and clusters. These diffuse com-ponents are thought to be direct evidence of hierarchicalgrowth in the cold dark matter scenario in the sense thatmore massive dark matter haloes will accrete more, andmore luminous, satellites (e.g. Gao et al. 2004). Recently,Pillepich et al. (2017b) analysed a sample of galax-ies in the IllustrisTNG simulation (Vogelsberger et al. 2014;Pillepich et al. 2017a; Weinberger et al. 2017). They foundthat there is a strong correlation between the slope of thedensity profile of the stellar halo and the total mass of thesystem spanning a wide range of halo masses (M = ∼ to M ⊙ ).To explore this, we have derived the stellar mass den-sity profiles for the HFF clusters. To this end, we have fol-lowed the procedure we used in Paper I (see also Bakos et al.2008). Applying Equation 1 and 2 from Paper I, we linkedthe observed surface brightness in the restframe z-band toa mass to light (M/L) ratio. The M/L ratio was derivedfrom the prescriptions given by Bell et al. (2003), using ani-z colour for a Salpeter 1955 IMF. Then, the radial profileswere derived using the same distance bins as in the caseof the SEDs. Fig. 4 shows the density profiles of the HFFcluster normalized by their total stellar mass ( R < R limit ) forcomparison. The differences between the normalized profilesof the clusters are small. As galaxies merge into the BCG,one will expect to find a less steep profile as cosmic timeprogresses. However, we do not see any redshift dependenceof the slope of the density profile with redshift, pointingthat redshift might not be the driver of this change (at leastfor these massive clusters). Additionally, relaxed clusters aredynamically older clusters that have already been throughsignificant mergers. Consequently, one could expect to seea shallower density profile in relaxed clusters. However, wedo not see any evidence of a difference in the most relaxedcluster in the sample, AS1063. MNRAS , 1–17 (2017) CL at the Frontier Cluster % of light in ICL < µ V < µ v > 26 50 < R < R limit R < R limit R < R Abell 2744 . ± . 07 3 . ± . 13 7 . ± . . ± . . ± . MACSJ0416.1-2403 . ± . 03 1 . ± . 04 5 . ± . . ± . . ± . MACSJ0717.5+3745 . ± . 01 0 . ± . 02 18 . ± . . ± . . ± . MACSJ1149.5+2223 . ± . 03 1 . ± . 05 19 . ± . . ± . . ± . Abell S1063 . ± . 04 3 . ± . 06 15 . ± . . ± . . ± . Abell 370 . ± . 02 1 . ± . 03 6 . ± . . ± . . ± . Table 2. Fractions of ICL light measured in the V-band for the HFF clusters. The first two columns are the fractions assuming a surfacebrightness threshold to define the ICL region, while in the other columns the ICL component is thought to follow a linear profile, derivedfrom a fit to the surface brightness profile in the V-band (R > kpc). µ V is in mag/arcsec . The slopes of the stellar mass density profiles are com-puted fitting a linear relationship in logarithmic space tothe ICL component ( R > kpc, see Fig C1). Pillepich et al.(2017b) measured the 3D spherically averaged density pro-files for the stars. To translate between our observed 2Dslope to their 3D slope we used Equation 5 in Stark (1977).The total masses of our clusters ( M ) were computed usingthe relationship between M and velocity dispersion givenby Munari et al. (2013). The velocity dispersions for each ofthe clusters are given in Sec. 3.3.1.We warn the reader that the comparison withPillepich et al. (2017b) has to be taken with caution assome approximations were made that might not be accu-rate enough. For instance, we are comparing slopes derivedat different radii. To measure the slope, we took the profileat R > kpc ending in most cases around ∼ kpc, whilePillepich et al. (2017b) fits the slope in a wider range ( kpc < R < R hm , with R hm being the 3D half mass radius). Inother words, we assumed that the slope of the stellar massdensity profile is not changing at larger radius (a reason-able assumption given the profiles in Fig. 1 in Pillepich et al.2014). The HFF clusters are more massive than the objectsexplored in Pillepich et al. (2017b). Nevertheless, we canexplore whether the reported relationship holds at highermasses. In Fig. C1, the individual stellar mass density pro-files for the HFF are presented (blue circles) along with thefits to the ICL component (red dashed line) and Fig. 5 showsthe slope of the stellar mass density profiles of the ICL com-ponent as a function of M . The squares represent the Il-lustrisTNG data from Pillepich et al. (2017b), for a volumeof ∼ Mpc (TNG100, black squares) and ∼ Mpc (TNG300, grey squares).Note that the PSF in the z-band might have an effect inthe slope of the stellar mass density, as the PSF sends lightfrom the inner parts of sources to their outer parts modifyingtheir intrinsic profile. However, the PSF effect should notplay a major role due to the smooth profile shape of theICL (see a detailed discussion about this on the Appendixin Paper I). The results presented in this work show the extraordinarypower of the HFF survey to address the origin and evolutionof the ICL. This impressive data makes possible to explore M (M ⊙ )−6.5−6.0−5.5−5.0−4.5−4.0−3.5−3.0−2.5−2.0 α D HFF Clusters TNG100 TNG300 Figure 5. Slope of the stellar mass density profile for R > kpcvs. the mass of the halo (M ). Blue filled circles are our measuredslopes for the HFF clusters. Black and grey squares correspond tothe IllustrisTNG simulations taken from Pillepich et al. (2017b),for a volume of ∼ Mpc and ∼ Mpc . They measured thestellar mass density profiles between kpc to R hm . the properties of the ICL in 6 very massive clusters in theinteresting redshift range . − . ; a period of time crucialto understand the formation of this elusive component ingalaxy clusters. Recently, numerical simulations have suggested that the ori-gin of the ICL is the result of the disruption and tidalstripping of massive ( − M ⊙ ; stellar mass) satellitegalaxies infaling in the cluster (see also Purcell et al. 2007;Martel et al. 2012; Contini et al. 2014; Cooper et al. 2015).Since most of the ICL is produced by tidal stripping of mas-sive satellites, this component is expected to have a metal-licity that is similar to that of these galaxies (Contini et al.2014). That also naturally predicts a gradient in the ICLas the more massive galaxies, more metal-rich, are closerto the centre of the cluster (by mass segregation, e.g.,Presotto et al. 2012; Roberts et al. 2015). The results pre- MNRAS , 1–17 (2017) M. Montes & I. Trujillo sented in this paper are in good agreement with these pre-dictions. Let’s expand on this.In Section 3.3, we present the age and metallicity pro-files for the HFF clusters. We find negative age and metal-licity gradients with radius for all the HFF clusters. On av-erage, we are probing the ICL down to radial distances of ∼ kpc in all the clusters ( < R < kpc, orange area inFig. 2). The metallicity of the ICL ranges between [Fe/H] ICL = − . to − . (Z ∼ . − . Z ⊙ ). These metallicities aresimilar to those found in the outskirts of the Milky Way(e.g., Cheng et al. 2012), suggesting that the tidal strippingof MW-like galaxies is the main responsible for the formationof the ICL of these clusters. As the galaxies fall into the clus-ter potential, their less bounded material, their outskirts,will be stripped more easily. We have also found a gradientin metallicity from the center to the ICL region. This is anatural consequence of dynamical friction: the most massivegalaxies approach the inner cluster regions faster than theirless massive counterparts.The mass-metallicity relationship of Gallazzi et al.(2005) can be used as a proxy to derive the metallicity ofthe progenitors of the ICL. A galaxy with the metallicity ofthe ICL would have a typical stellar mass of . − . × M ⊙ . This range of masses are slightly smaller but compatiblewith that of the Milky Way (e.g., . × M ⊙ ; McMillan2011). If we take into account that it is the outer regions ofthe galaxies the places that are more easily stripped then,taking into account the metallicity gradient of the galaxies,objects even more massive than ∼ M ⊙ are good candi-dates to be the primordial source of metallicity for the ICL.The observed ages of the stellar population of the ICLare between to Gyr younger than the BCG(s). This couldbe understood if active star forming galaxies orbiting thecluster ceased forming stars due to ram pressure strippingof their gas content (e.g. Boselli et al. 2009; Chung et al.2009). Then, those stars are stripped from the galaxies andbecome ICL. If we assume that the stellar populations ofthe BCG(s) were formed at z ∼ − , then the observed agedifference is compatible with the ICL being assembled at z < . The measured ages for the ICL are consistent with theages ( ∼ . Gyr) derived spectroscopically by Toledo et al.(2011) for a cluster at z ∼ . and Adami et al. (2016) for acluster at z ∼ . ( . Gyr).The metallicities derived for the ICL of the HFF arein agreement with previous observational studies for bothnearby and similar redshift clusters (e.g., Williams et al.2007; Coccato et al. 2011; Paper I; DeMaio et al. 2015). Re-cently, Morishita et al. (2017) explored the colours of theICL of the HFF clusters. They also found that onlymetallicity gradients are not able to reproduce the observedcolours, but negative age gradients are also required. Theirresults suggest that the ICL is dominated by stars of ages ∼ − Gyr, similar to the ages we found here for the ICL.Their inferred metallicities also agree with a subsolar metal-licity.The above numbers for age and metallicity are, ofcourse, average values and do not describe entirely the largediversity of ages and metallicities expected in the ICL. Infact, both spectroscopic and red giant branch estimates of ahandful of clusters have shown that the ICL correspondsto a mixture of young, intermediate and old, metal-poorand metal-rich stars, in varying fractions (Melnick et al. 2012; Edwards et al. 2016). Because of the methodologywe are using here, our estimates are luminosity-weighted(while in Melnick et al. 2012; Edwards et al. 2016 are mass-weighted). In this sense, our results should be understood asa description of the average properties of the ICL. In Section 3.4, we derived the fraction of ICL to the totallight of the cluster using several definitions. The most widelyused definition from the observational point of view is to ap-ply a cut in surface brightness and assume as ICL the lightfainter than that threshold. Using this definition, we foundthat there is a slight increase in the fraction of ICL with cos-mic time, i.e. decreasing redshift. Note, however, that we areexploring a narrow redshift range . < z < . and we haveonly very massive clusters, therefore any conclusion mustbe taken with caution. This observed increase is in qualita-tive agreement with the results by Krick & Bernstein (2007)and Burke et al. (2015), who found that the ICL grows afactor of ∼ − between . < z < . .There is a discrepancy between the values of the frac-tion of ICL for M0416 and AS1063 reported by Burke et al.(2015) ( . ± . and . ± . ) and the values we found here( . ± . and . ± . ). This disagreement is caused bythe difference in magnitude threshold at defining the ICL,i.e. their threshold is brighter (they are including more lightfrom the inner parts of the cluster). In addition, our maskingcriteria might have some effect. For example, because HFFimages are deeper than the ones in the CLASH survey, weneeded to mask part of M0416 cluster to avoid contamina-tion of a bright star in the FOV (see Section 3.3.1).In the case of our lowest redshift cluster, A2744, theHFF survey only observed one of the substructures. Using alarger FOV, including most of the cluster, Krick & Bernstein(2007) found a fraction of in the r-band and in theB-band for this cluster. This is in tension with our mea-surement ( < . mag/arcsec in the B-band, which translates in ∼ 25 mag/arcsec in theV-band, assuming B-V = . ( Gyr and [Fe/H] = − . ,Vazdekis et al. 2016). This is one magnitude brighter thanin our case. Therefore, they are including more light fromthe central parts of the cluster than us. On the other hand,Jim´enez-Teja & Dupke (2016) explored the ICL fraction ofA2744 using the images from the HFF survey. They usedChebyshev-Fourier functions to disentangle between BCGand ICL without prior assumptions on the properties of thesystem. They found an ICL fraction of . ± . . In thiscase, the main difference with our result comes from the in-clusion of ICL light that is embedded (in projection) into theBCG and a simple surface brightness threshold is unable toaccount for.The methodology used in Jim´enez-Teja & Dupke (2016)is conceptually similar to the two-component profiles used inprevious ICL studies (e.g. Gonzalez et al. 2005; Zibetti et al.2005; Giallongo et al. 2014). To explore how this measure-ment of the ICL could affect our results, we fitted a linearprofile to the surface brightness distribution in the V-bandof each of the clusters at R > kpc, see Section 3.4. On do-ing this, we are able to account for the light of the ICL which MNRAS000 25 mag/arcsec in theV-band, assuming B-V = . ( Gyr and [Fe/H] = − . ,Vazdekis et al. 2016). This is one magnitude brighter thanin our case. Therefore, they are including more light fromthe central parts of the cluster than us. On the other hand,Jim´enez-Teja & Dupke (2016) explored the ICL fraction ofA2744 using the images from the HFF survey. They usedChebyshev-Fourier functions to disentangle between BCGand ICL without prior assumptions on the properties of thesystem. They found an ICL fraction of . ± . . In thiscase, the main difference with our result comes from the in-clusion of ICL light that is embedded (in projection) into theBCG and a simple surface brightness threshold is unable toaccount for.The methodology used in Jim´enez-Teja & Dupke (2016)is conceptually similar to the two-component profiles used inprevious ICL studies (e.g. Gonzalez et al. 2005; Zibetti et al.2005; Giallongo et al. 2014). To explore how this measure-ment of the ICL could affect our results, we fitted a linearprofile to the surface brightness distribution in the V-bandof each of the clusters at R > kpc, see Section 3.4. On do-ing this, we are able to account for the light of the ICL which MNRAS000 , 1–17 (2017) CL at the Frontier is (in projection) in the central regions of the cluster but isoutshined by the brightness of the brightest galaxies. Oncethis missing ICL light is included, we found that on average,the fraction of ICL is ∼ (for R < R ). Morishita et al.(2017) also explored the fraction of ICL of the HFF clusters.Their methodology also accounts for the light embedded inthe BCG. Their ICL fractions for R < kpc compared toour R < R estimations are in agreement with the exceptionof two clusters: M0717 and A370. For A370, one possible ex-planation for the discrepancy could be the different choiceof BCGs (two in our case) that might be responsible forthe lower fraction of ICL in our measurements. For M0717,our more conservative masking criteria could be causing thedisagreement.Observations and simulations (e.g. Seigar et al. 2007;Donzelli et al. 2011; Pillepich et al. 2014; Cooper et al.2015; Pillepich et al. 2017b) suggest a two-component de-scription of the BCG+ICL light profile, with the outer com-ponent exhibiting an exponential form in most cases. Note,however, that to assume an exponential profile for the ICLin the inner regions is something that observations alonecan not prove. Consequently, simulations are needed to seewhether assuming an exponential form for the entire lightprofile of the ICL is justified or not.Using an exponential fit to describe the ICL, we findonly a mild evolution of the fraction of light in the ICL withcosmic time. That is in agreement with the lack of evolu-tion in the fraction observed by Guennou et al. (2012) be-tween z = and z = . . However, a redshift dependence, suchas the one observed here when using the interval < µ V < mag/arcsec for the defining the ICL and in Burke et al.(2015), might be caused (at least partially) by a bias con-nected with the way the ICL is measured using a surfacebrightness cut. At higher redshift, stellar populations areyounger (both in the ICL and in the BCGs) and thereforebrighter in the optical bands while at lower redshift, agesget older (particularly for the BCGs) and the stars fainterat optical wavelengths. If a fixed surface brightness limit isused for defining the ICL then, the location (in radial po-sition) of the isophote of a given surface brightness will becloser to the centre as comic time progresses. This is due tothe brightness of the BCGs gets dimmer with cosmic timemuch faster than the ICL (which is continuously formingby the accretion of new, younger, satellites). This effectivelyincludes more light as ICL at lower redshifts. This effect ismore pronounced in the optical bands than in the IR, espe-cially in the B-band. That could explain the steep increasein the ICL fraction observed in Burke et al. (2015) (B-band)compared to the increase observed in this work (V-band).Although, an increase in the fraction of ICL withtime is expected from simulations (e.g. Rudick et al. 2011;Contini et al. 2014), we should be careful when comparingour results with the simulations. Ideally, one would like tomeasure the ICL light fractions in the rest-frame IR bands,to reduce the effect of the evolution of age that affects drasti-cally the brightness of the stellar populations in the optical.Alternatively, one could try estimating the ICL stellar massfraction. Finally, accounting for the missing ICL light pro-jected in the BCG might also diminish this effect.Relaxation may also play a role in the fraction of ICLin a cluster. Relaxed clusters are dynamically older clustersthat have already been through significant mergers. There- fore, one could expect that they would have on averagehigher ICL fractions (Rudick et al. 2011; Cui et al. 2014).There is a slight evidence that the most relaxed cluster inour sample, AS1063, has a higher fraction of ICL comparedto the other clusters. Nonetheless, with a sample of only clusters is still premature to conclude whether relaxationplays a role or not. In the future, larger samples of clus-ters, with different dynamical states, will clarify this issue.Finally, we want to remind the reader that our conclusionsare based on ages and metallicities that are derived usingan SSP, i.e. they work as average values of the population.Naturally, this is an oversimplification. A full understandingof the stellar population properties of the ICL requires theuse of spectroscopy. In Section 3.5 and inspired by the results of Pillepich et al.(2014, 2017b), we explored the relationship between theslope of the stellar mass density profile of the ICL, α D ,and the total mass of the system. In Fig 5, we see that theHFF clusters follow the extrapolation of the theoretical ex-pectation between the α D and M . The range of slopeswe measured in the HFF clusters is − . < α D < − . . Thatmeans that the stellar halo of the clusters could be as shal-low as the underlying dark matter halo, i.e. they could havesimilar slopes (the dark matter slopes range between − . to − , Pillepich et al. 2014). That both components have simi-lar shapes can be explained because more massive halos tendto accrete more and more luminous satellites (e.g. Gao et al.2004) at recent times. Those satellites tend to deposit theirstars at large radii ( ∼ kpc, Cooper et al. 2015) forminga less centrally concentrated stellar profile. The ages andmetallicities reported for the ICL also agree with this sce-nario.In this paper, we have studied the ICL of the HubbleFrontier Fields clusters. Taking advantage of their exquisitedepth and multiwavelength coverage we have explored theproperties of the stellar populations of this diffuse compo-nent with an unprecedented accuracy. We find that: • The average metallicity of the ICL is [Fe/H] ICL ∼ -0.5.This value is similar to that measured in the outskirts ofthe MW, suggesting that material stripped from MW-likesatellites can be the dominant component of the ICL. • The average age of the stellar populations of the ICL isbetween 2 to 6 Gyr younger that the age of the central partof the BCG(s). Assuming that the ICL is not forming newstars, that suggests that the ICL is assembled at z < . • Our results are compatible with no substantial increasein the fraction of light in the ICL with decreasing redshift.However, the redshift range explored is narrow ( < • To measure the evolution of the ICL light fraction withcosmic time, we discourage the use of blue bands. The bluefilters are very sensitive to the evolution of the stellar pop-ulations, and so, imposing a surface brightness threshold todefine the location of the ICL might introduce an artificialredshift dependence. • As predicted by simulations, the slope of the stellarmass density profile at high halo masses ( ∼ ) resembles MNRAS , 1–17 (2017) M. Montes & I. Trujillo the underlying dark matter profile, an indication of the ori-gin of the ICL as debris of accreted satellites at recent times.The results presented in this work show the extraordi-nary power of deep and multiwavelength surveys to addressthe origin and evolution of the ICL and the clusters them-selves. In the future, larger samples will provide a more com-plete picture on the evolution of the ICL at different clusterhalo masses and different redshifts. ACKNOWLEDGEMENTS We thank the referee for constructive comments that helpedto improve the original manuscript. We would like to thankSTScI directors M. Mountain, K. Sembach and J. Lotz,and all the HFF team for making these extraordinary dataavailable. We also thank Chris Mihos for sharing their sim-ulation predictions and Javier Rom´an for useful commentsthat helped us polish this manuscript. Support for this workwas provided by NASA through grant HST-AR-14304 fromthe Space Telescope Science Institute, operated by AURA,Inc. under NASA contract NAS 5-26555 and by the SpanishMinisterio de Econom´ıa y Competitividad (MINECO; grantAYA2013-48226-C3-1-P). REFERENCES Adami C., et al., 2016, A&A, 592, A7Anders P., Bissantz N., Fritze-v. Alvensleben U., de Grijs R.,2004, MNRAS, 347, 196Bakos J., Trujillo I., Pohlen M., 2008, ApJ, 683, L103Bell E. F., McIntosh D. H., Katz N., Weinberg M. D., 2003, ApJS,149, 289Boselli A., Boissier S., Cortese L., Gavazzi G., 2009,Astronomische Nachrichten, 330, 904Braglia F., Pierini D., B¨ohringer H., 2007, A&A, 470, 425Burke C., Hilton M., Collins C., 2015, MNRAS, 449, 2353Capaccioli M., de Vaucouleurs G., 1983, ApJS, 52, 465Cardelli J. A., Clayton G. C., Mathis J. S., 1989, ApJ, 345, 245Cheng J. Y., et al., 2012, ApJ, 746, 149Chung A., van Gorkom J. H., Kenney J. D. 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M., 2015, MNRAS, 451, 2703Cui W., et al., 2014, MNRAS, 437, 816De Lucia G., Blaizot J., 2007, MNRAS, 375, 2DeMaio T., Gonzalez A. H., Zabludoff A., Zaritsky D., BradaˇcM., 2015, MNRAS, 448, 1162Donzelli C. J., Muriel H., Madrid J. P., 2011, ApJS, 195, 15Dressler A., Smail I., Poggianti B. M., Butcher H., Couch W. J.,Ellis R. S., Oemler Jr. A., 1999, ApJS, 122, 51Ebeling H., Barrett E., Donovan D., Ma C.-J., Edge A. C., vanSpeybroeck L., 2007, ApJ, 661, L33Ebeling H., Ma C.-J., Barrett E., 2014, ApJS, 211, 21 Edge A. C., Ebeling H., Bremer M., R¨ottgering H., van Haar-lem M. P., Rengelink R., Courtney N. J. D., 2003, MNRAS,339, 913Edwards L. O. V., Alpert H. S., Trierweiler I. L., Abraham T.,Beizer V. G., 2016, MNRAS, 461, 230Ehlert S., Allen S. W., Brandt W. N., Xue Y. Q., Luo B., von derLinden A., Mantz A., Morris R. G., 2013, MNRAS, 428, 3509Feldmeier J. J., Mihos J. C., Morrison H. L., Harding P., KaibN., Dubinski J., 2004, ApJ, 609, 617Gallazzi A., Charlot S., Brinchmann J., White S. D. M., TremontiC. A., 2005, MNRAS, 362, 41Gao L., White S. D. M., Jenkins A., Stoehr F., Springel V., 2004,MNRAS, 355, 819Giallongo E., et al., 2014, ApJ, 781, 24G´omez P. L., et al., 2012, AJ, 144, 79Gonzalez A. H., Zabludoff A. I., Zaritsky D., 2005, ApJ, 618, 195Gregg M. D., West M. J., 1998, Nature, 396, 549Gruen D., et al., 2013, MNRAS, 432, 1455Guennou L., et al., 2012, A&A, 537, A64Jim´enez-Teja Y., Dupke R., 2016, ApJ, 820, 49Kartaltepe J. S., Ebeling H., Ma C. J., Donovan D., 2008,MNRAS, 389, 1240Krick J. E., Bernstein R. A., 2007, AJ, 134, 466Krick J. E., Bernstein R. A., Pimbblet K. A., 2006, AJ, 131, 168Lan T.-W., M´enard B., Mo H., 2016, MNRAS, 459, 3998Lin Y.-T., Mohr J. J., 2004, ApJ, 617, 879Lotz J. M., et al., 2017, ApJ, 837, 97Mann A. W., Ebeling H., 2012, MNRAS, 420, 2120Mantz A., Allen S. W., Ebeling H., Rapetti D., Drlica-WagnerA., 2010, MNRAS, 406, 1773Martel H., Barai P., Brito W., 2012, ApJ, 757, 48Maughan B. J., Giles P. A., Randall S. W., Jones C., FormanW. R., 2012, MNRAS, 421, 1583McMillan P. J., 2011, MNRAS, 414, 2446Melnick J., Giraud E., Toledo I., Selman F., Quintana H., 2012,MNRAS, 427, 850Merten J., et al., 2011, MNRAS, 417, 333Mihos J. C., 2016, in Bragaglia A., Arnaboldi M., Rejkuba M.,Romano D., eds, IAU Symposium Vol. 317, The General As-sembly of Galaxy Halos: Structure, Origin and Evolution. pp27–34 ( arXiv:1510.01929 ), doi:10.1017/S1743921315006857Mihos J. C., Harding P., Feldmeier J., Morrison H., 2005, ApJ,631, L41Montes M., Trujillo I., 2014, ApJ, 794, 137Montes M., Trujillo I., Prieto M. A., Acosta-Pulido J. A., 2014,MNRAS, 439, 990Morishita T., Abramson L. E., Treu T., Schmidt K. 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L., 2010, ApJ, 720, 569MNRAS000 , 1–17 (2017) CL at the Frontier Rudick C. S., Mihos J. C., McBride C. K., 2011, ApJ, 732, 48Salpeter E. E., 1955, ApJ, 121, 161Sandin C., 2014, A&A, 567, A97Sayers J., et al., 2013, ApJ, 768, 177Schlafly E. F., Finkbeiner D. P., 2011, ApJ, 737, 103Seigar M. S., Graham A. W., Jerjen H., 2007, MNRAS, 378, 1575Slater C. T., Harding P., Mihos J. C., 2009, PASP, 121, 1267Sofue Y., 1993, PASP, 105, 308Stark A. A., 1977, ApJ, 213, 368Struble M. F., Rood H. J., 1999, ApJS, 125, 35Toledo I., Melnick J., Selman F., Quintana H., Giraud E., ZelayaP., 2011, MNRAS, 414, 602Trujillo I., Fliri J., 2016, ApJ, 823, 123Vazdekis A., Koleva M., Ricciardelli E., R¨ock B., Falc´on-BarrosoJ., 2016, MNRAS, 463, 3409Vogelsberger M., et al., 2014, MNRAS, 444, 1518Weinberger R., et al., 2017, MNRAS, 465, 3291Williams B. F., et al., 2007, ApJ, 656, 756Zibetti S., White S. D. M., Schneider D. P., Brinkmann J., 2005,MNRAS, 358, 949Zitrin A., Broadhurst T., 2009, ApJ, 703, L132de Jong R. S., 2008, MNRAS, 388, 1521 APPENDIX A: DETAILS ON DATAREDUCTIONA1 PSF matching The scatter light from nearby bright source affects dramat-ically low surface brightness features on the images, suchas the ICL, as the contamination of the wings of the PSFsdominate at fainter magnitudes (de Jong 2008; Slater et al.2009; Sandin 2014). It has also been shown that the wingsof the PSF change with wavelength being more prominentat redder bands. To consistently derive age and metallicityprofiles for the six HFF clusters, we followed this approach:we PSF-matched the images to the F160W image, which hasthe worst spatial resolution. By doing this, we ensure thatour results are not artificially biased to redder colours dueto the increasing prominence of the wings at longer wave-lengths.Obtaining a good PSF from the HFF fields is difficult due tothe small field of view of the images (i.e. we have few brightstars to select) and the contamination of the wings of thePSF by the same ICL. Consequently, we used, for model-ing the internal region of the PSF, a model PSF generatedby the software TinyTim . The size of the model PSFs was ∼ × arcsec . The PSF derived from TinyTim was thenrebinned to the current pixel size of our images ( . ′′ ) androtated according to the orientation of the camera. To deriverealistic light profiles from the center of the galaxies down tothe ICL in each band, it is important to accurately charac-terize the PSF of each image to large radial distances, largerthan the size of the object to measure (Sandin 2014). As theeffect of the wings is crucial for the goals of this work, wedecided to extend the TinyTim PSFs using an exponentialprofile for both the ACS and the WFC3 PSFs. The choice ofthe exponential profiles was based on how well it reproducesthe outer parts of the Tiny Tim PSF. An example of theradial profiles for the final PSFs can be seen in Figure A1.The size of the final PSFs is × arcsec .Once the extended PSF models were generated, we de-rived the kernels for each of the images using the IRAF task Figure A1. Extended PSFs for three different bands: F435W,F814W and F160W. The left panels show the images of the PSFswhile on the right panels, we plotted the radial profiles for thePSFs. The red solid line is the original Tiny Tim PSF that onlyextends ∼ × arcsec . The blue line is the exponential profileused as an extension for the PSF reaching the × arcsec .As seen, the extension reproduces the shape of the wings of the TinyTim PSF between to arcsec. Finally, the black dashedline is the radial profile of the combination of the TinyTim PSFuntil arcsec and the exponential profile down to arcsec inradius. lucy . Finally, once convolved with these kernels, the finalimages match the resolution of the F160W image. To checkthat the procedure was working correctly, we applied theprevious kernels to our PSFs in each band. As expected,the convolution of the kernels with the PSFs produces theF160W PSF (see Fig. A2). A2 Masking In the case of deep surveys such as the HFF which aim todiscover high redshift galaxies, the detection of sources mustbe optimized not only for those faint and small galaxies butalso for large and closer objects. For that reason, we runSExtractor in the F160W image in a ”hot+cold” mode, i.e.two separate SExtractor runs. The ”cold” mode will detectthe extended bright galaxies from the cluster while the ”hot” MNRAS , 1–17 (2017) M. Montes & I. Trujillo -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 F l u x ( c o un t s ) F160W PSFF814W PSFF814W PSF-matched Figure A2. Comparison of the radial profiles of the convolvedF814W PSF (dashed red line) with the F160W PSF (blue line).The original F814W PSF is also plotted (black solid line). mode is optimized to detect the faint and small sources. Inour case, as the images are filled by the ICL, we run the”hot” mode in an unsharp masked image (Sofue 1993), toenhance the image contrast especially at the central parts ofthe clusters. To create the unsharp masked image, a gaus-sian filter with σ = pix was convolved with the image andthen subtracted from the original image. The ”cold” maskwas further expanded (dilated) pixels while the ”hot” wasdilated pixels. We, then combined the two masks to cre-ate the final mask for our images. Stars were masked man-ually, masking beyond their observed size to ensure littlecontamination from their wings. As the spikes of very brightstars can reach very far away, we masked around ∼ arc-sec from their cores to ensure that the light of the stars areno longer dominant. The extended spikes were masked sep-arately as well. Other residual and foreground sources werealso masked manually. In M0717 and M1149, very brightsources are located close to the centre of the clusters, i.e.:we have foreground galaxies and stars. We conservativelydecided to mask part of the image, to ensure that no con-tamination will affect the measurement of the ICL in theseclusters. The final masks were visually inspected to manu-ally mask any remaining light that was missed by the processdescribed above. This was repeated several times for each ofthe clusters to ensure that we minimize the contaminationfrom galaxy outskirts and foreground and background lightsources. The masked images can be seen in Fig. A3. APPENDIX B: TABULATED AGE ANDMETALLICITY RADIAL PROFILES FOR THEHFF CLUSTERS The age and metallicity radial profiles for the HFF clustersare listed in Table B1. The ages and metallicities are themedian ages and metallicities of the fits to the jackkniferealizations of the SEDs, using the Vazdekis et al. (2016)SSP models. The errors are the median errors divided bythe square root of the number of realizations. MNRAS000 MNRAS000 , 1–17 (2017) CL at the Frontier A2744 E N10"= 45.4 kpc MACS0416 E N10"= 53.4 kpc MACS0717 E N10"= 63.8 kpc MACS1149 E N10"= 63.7 kpc AS1063 E N10"= 49.2 kpc A370 E N10"= 51.6 kpc Figure A3. F160W masked images of the HFF clusters. In all the images, north is up and east is left. Images are kpc on eachside. For M0416, M0717 and M1149, the presence of a bright foreground source close to the cluster made us mask a part of the image toavoid contamination of the ICL.MNRAS , 1–17 (2017) M . M o n t e s & I . T r u ji ll o Abell 2744 MACSJ0416.1-2403 MACSJ0717.5+3745 MACSJ1149.5+2223 Abell S1063 Abell 370Bin (kpc) Age (Gyr) [Fe/H] Age (Gyr) [Fe/H] Age (Gyr) [Fe/H] Age (Gyr) [Fe/H] Age (Gyr) [Fe/H] Age (Gyr) [Fe/H]0 - 0.5 . ± . . ± . 03 9 . ± . . ± . 09 3 . ± . . ± . 04 3 . ± . . ± . 04 7 . ± . . ± . 03 3 . ± . . ± . . ± . . ± . 04 6 . ± . . ± . 05 3 . ± . . ± . 04 3 . ± . . ± . 04 7 . ± . . ± . 02 4 . ± . . ± . . ± . . ± . 04 7 . ± . . ± . 04 3 . ± . . ± . 05 3 . ± . . ± . 04 7 . ± . . ± . 02 5 . ± . . ± . . ± . . ± . 04 6 . ± . . ± . 04 5 . ± . . ± . 07 3 . ± . . ± . 04 7 . ± . . ± . 03 4 . ± . . ± . . ± . . ± . 05 6 . ± . . ± . 05 5 . ± . − . ± . 08 3 . ± . − . ± . 04 7 . ± . . ± . 03 4 . ± . . ± . . ± . . ± . 05 5 . ± . . ± . 05 3 . ± . . ± . 08 3 . ± . − . ± . 04 7 . ± . . ± . 04 4 . ± . . ± . . ± . . ± . 06 4 . ± . . ± . 05 3 . ± . − . ± . 09 3 . ± . . ± . 04 6 . ± . . ± . 04 4 . ± . . ± . . ± . . ± . 07 3 . ± . . ± . 06 3 . ± . − . ± . 10 2 . ± . . ± . 04 5 . ± . . ± . 04 5 . ± . . ± . . ± . . ± . 05 4 . ± . . ± . 03 1 . ± . − . ± . 09 3 . ± . − . ± . 04 5 . ± . . ± . 04 5 . ± . . ± . . ± . − . ± . 07 4 . ± . . ± . 04 2 . ± . − . ± . 10 3 . ± . − . ± . 04 5 . ± . . ± . 04 5 . ± . . ± . . ± . − . ± . 08 2 . ± . − . ± . 09 2 . ± . − . ± . 12 2 . ± . . ± . 04 9 . ± . . ± . 04 3 . ± . − . ± . . ± . − . ± . 09 2 . ± . − . ± . 12 1 . ± . − . ± . 09 2 . ± . . ± . 04 3 . ± . − . ± . 08 2 . ± . . ± . 44 - 64.2 . ± . − . ± . 07 1 . ± . − . ± . 14 2 . ± . − . ± . 14 2 . ± . . ± . 04 2 . ± . − . ± . 09 2 . ± . − . ± . . ± . − . ± . 07 1 . ± . − . ± . 19 1 . ± . − . ± . 25 2 . ± . . ± . 04 1 . ± . − . ± . 07 1 . ± . − . ± . . ± . − . ± . ··· ··· . ± . − . ± . 41 1 . ± . . ± . 04 1 . ± . − . ± . 10 1 . ± . − . ± . 137 - 200 . ± . − . ± . ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· Table B1. Age and metallicity radial profiles of the HFF clusters. The age and metallicities are the median ages and metallicities coming from jackknife realizations of thephotometry of the clusters. The final radial bin explored ( R limit ) is defined as the farthest spatial bin with accurate ages and metallicities (i.e. those bins where the number of reliablefilters is > ) M N R A S , ( ) CL at the Frontier APPENDIX C: STELLAR MASS DENSITYPROFILES In Fig. C1, we present the stellar mass density profiles ofeach of the HFF clusters. The stellar mass density ( ρ in M ⊙ / pc ) was computed using the same approach as in PaperI but using the i-z colours to compute the M/L ratio (seeSec. 3.5). The blue filled circles are the observed profile ofBCG(s) + ICL while the red dashed line is the fit to theprofile in the range kpc < R < R limit . APPENDIX D: TOTAL STELLAR MASS OFTHE CLUSTER AND COMPLETENESS In this section, we provide an estimate on the bias in the to-tal stellar mass of our clusters caused by the different masscompleteness due to their different redshifts. The measureof the total stellar mass depends on the redshift as we aremissing more faint galaxies in our high redshift clusters com-pared to the closest ones. A detailed account for this effect isnot trivial in our analysis, but we provide here with a roughestimation of how this can contribute in our analysis.Our closest cluster, A2744 is at z = . , whereas thefarthest cluster, M0717 is located at z = . . This meansa difference in distance modulus between both clusters ofDM= . − . = . . In this sense, at quantifying thecontribution of light from detected galaxies in our closestcluster, we are including galaxies, on average, which are 1.46mag fainter than the faintest in the farthest cluster. In termsof stellar mass (assuming a similar M/L), this means that wedetect galaxies which are 4 times less massive in our closercluster than in our farthest one. The faintest galaxies wedetect as members of our clusters has a typical magnitudeof r ∼ (restframe), which at the redshift of our closestcluster is equivalent to M r = − . = − . and for thefarthest cluster M r = − . = − . . Assuming that thestellar mass function of the galaxies in these clusters hasnot changed dramatically in such redshift interval and thatthey look similar to the stellar mass distribution of nearbyrich clusters (e.g. Fig. 2 in Lan et al. 2016), then we canhave a rough estimation of the stellar mass we are missingin the interval − . to − mag. Using Fig. 4 from Lan et al.(2016), and assuming the Conditional Luminosity Functionsform holds for fainter magnitudes, we can see that for themost massive cluster ( log M ∼ . , bottom right panel),the total number of galaxies should double from − . to − . In this sense, the missing mass located in less massivegalaxies in our farthest clusters would be of the order of (i.e. × ) less. So, if anything, the fraction of ICL in ourhigh-z clusters could be overestimated by compared tothe value we would have got taking into account the missinggalaxies. This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS , 1–17 (2017) M. Montes & I. Trujillo l o g ( D e n s i t y ) ( M ⊙ / p c ) A2744 FitDensity of BCG+ICL l o g ( D e n s i t y ) ( M ⊙ / p c ) MACS0416 FitDensity of BCG+ICL l o g ( D e n s i t y ) ( M ⊙ / p c ) MACS0717 FitDensity of BCG+ICL l o g ( D e n s i t y ) ( M ⊙ / p c ) MACS1149 FitDensity of BCG+ICL l o g ( D e n s i t y ) ( M ⊙ / p c ) AS1063 FitDensity of BCG+ICL l o g ( D e n s i t y ) ( M ⊙ / p c ) A370 FitDensity of BCG+ICL Figure C1. Stellar mass density profiles for the BCG(s) + ICL of the HFF clusters (blue points). The red dashed lines are the linearfits in log space to the ICL component R > kpc from which we derived the slopes of the stellar mass density profiles for Fig. 5.MNRAS000