Specific Frequencies and Luminosity Profiles of Cluster Galaxies and Intracluster Light in Abell 1689

The current work uses the same deep imaging data, obtained in Program GO-11710 with the Hubble Space Telescope (HST) Advanced Camera for Surveys Wide Field Channel (ACS/WFC), as was analyzed by AM13. To summarize, we observed the central region of A1689 for 28 orbits in the F814W bandpass, the ACS/WFC bandpass with the highest total throughput. The individual exposures were calibrated with the standard HST pipeline, corrected for charge transfer inefficiency (Anderson & Bedin 2010), and then geometrically corrected and combined with the Apsis pipeline (Blakeslee et al. 2003) into a single stacked image of total exposure time 75,172 s and a resampled pixel scale of 0033 pixel⁻¹. The point-spread function (PSF) in the final image has an FWHM of 0086, or 2.6 pixels, and thus is adequately sampled. As in AM13, we use the AB photometric system, on which the F814W zero-point is 25.947 mag; the Galactic extinction toward A1689 in this bandpass is 0.04 mag (Schlafly & Finkbeiner 2011). We refer the reader to AM13 for a more detailed description of the observations and image reductions.

At the distance of A1689, the GCs appear as point sources. Thus, in AM13 we optimized the source detection and magnitude measurements for point sources. The source detection was done with SExtractor  (Bertin & Arnouts 1996) on a residual image with all large galaxies subtracted, bright stars and areas of poor subtraction masked, and a ring median filter applied; magnitudes were derived from PSF photometry using DAOPhot (Stetson 1987) on an unfiltered version of the residual image at the coordinates of the SExtractor detections. We performed detailed, realistic completeness tests, where the input magnitudes of the artificial stars followed a Gaussian distribution modeled on the expected GC luminosity function (GCLF). The fraction of recovered stars as a function of magnitude was described by a four-parameter modified-Fermi function that included the effect of Eddington bias on the magnitudes near the detection limit (see AM13 for details). Furthermore, we corrected for contamination from background galaxies and foreground stars and included the effect of gravitational lensing on the spatial and magnitude distributions of the background galaxies.

In AM13, we detected a total of 8283 unresolved sources (classified as point sources by DAOPhot sharpness and goodness-of-fit criteria) within the ACS/WFC field of view (FOV) over the magnitude range $27.0\lt {I}_{814}\lt 29.32$ mag, where the faint limit corresponds to the magnitude where we recovered 50% of the sources in the completeness tests, and the bright limit corresponds to $\sim 3\sigma$ brighter than the turnover of the GCLF. (Note that the value of 8212 point-source detections quoted by AM13 over this magnitude range referred only to objects within the FOV and inside a projected radius of 400 kpc of the cD galaxy; see Figure 3 of that work.) Using the coordinates of the objects in this sample, we constructed a surface number density map of GC candidates, corrected for incompleteness and background contamination as detailed in AM13, by smoothing with a Gaussian filter of FWHM = 10'' ($\sigma =4\buildrel{\prime\prime}\over{.} 25$). Masked regions were interpolated; following these corrections, the integral of the GC density map over the FOV gives 7940 objects to the detection limit. This represents just over 5% of the GCLF; the correction for integrating over the GCLF is a factor of ∼19.3. AM13 mainly used the GC map for illustrative purposes in comparing to the galaxy light, lensing mass, and X-ray surface brightness distributions. In the present work, we use this number density map to model the GC populations of the individual galaxies and ICL component in A1689.

A simple way to characterize quantitatively the structure of any galaxy is through parametric fitting of its luminosity profile, and a Sérsic  function (Sérsic 1968) is one of the most widely used models for describing diverse types of galaxies. It has the form

$$\begin{eqnarray}&&I(r)={I}_{e}\exp \left\{-{b}_{n}\left[{\left(\displaystyle \frac{r}{{R}_{e}}\right)}^{1/n}-1\right]\right\},\end{eqnarray} \tag{ 1 }$$

where R_e is the effective radius that encloses half of the light; I_e is the intensity at R_e; n is the Sérsic  index, which governs the shape of the radial profile; and ${b}_{n}\approx 1.9992n-0.3271$ (Graham & Driver 2005). To decompose the contributions of individual galaxies to the total luminosity profile in A1689, we use GALFIT  (Peng et al. 2010) to fit 2D Sérsic  functions, convolved with the PSF, to 180 of the brightest galaxies in the ACS/WFC FOV. For selecting the sample of galaxies to be modeled by GALFIT, we used SExtractor  with a background grid size BACK_SIZE = 64 pix and FILTERSIZE = 3, which we found gave enough leverage to model the background variation without removing much light from the galaxies we wished to detect (the GALFIT  modeling was done on the image without this background modeling). The central cD in A1689 is the brightest and most extended galaxy in the cluster, contributing to the local background of many of the other galaxies in the FOV. As a first step in modeling its light distribution, we masked all point and extended sources (except the cD itself) and modeled the galaxy as a single Sérsic  profile; this model was then subtracted from the original image. A second iteration of the central galaxy model is done later, after all the other galaxies have been subtracted (see Section 3.2).

The sample of 180 galaxies (including the cD) to be fitted was selected based on size and apparent magnitude, without considering cluster membership. By matching these objects against NED and the sample of A1689 galaxies studied by Halkola et al. (2006, hereafter H06), we found that 94 of the 180 are confirmed (or very likely) cluster members based on spectroscopic or photometric redshifts. For each galaxy in the full sample, a region 20 times larger than the equivalent R_e from SExtractor  was extracted, and we used GALFIT  to fit simultaneously all the galaxies that fall in the subimage down to 1 mag fainter than the object itself; fainter galaxies and point sources were masked. Due to the very high galactic density in A1689, it is common to have contamination from neighbor galaxies that are close to but not within the subimage; thus, we included the sky as a free parameter with an initial guess obtained from a smooth large-scale background map (from a second SExtractor  pass with a coarser background grid, BACK_SIZE = 1024). We used a weight image that included instrumental and photometric contributions, performed the fits with PSF convolution, and constrained the possible range of fitted parameters. We inspected the results of all fits; in some cases, we were able to improve the fit by increasing the subimage size or changing the parameter constraints.

We performed two sets of fits: we modeled each galaxy as both a single- and a double-component Sérsic  profile. At the very deep surface brightness levels reached by our data, complex structure (cores, disks, arms, rings, and tidal features) is discernible in many of the galaxies. Because of the greater flexibility when fitting two Sérsic  components instead of one, the results were generally better with the double Sérsic model. Even for apparently smooth and regular ellipticals, the single Sérsic  model left notable residuals; some examples are shown in Figure 1. Thus, we opted to use the results from our two-component Sérsic  models for all the galaxies. In order to have a single set of parameters characterizing each galaxy, we take the total luminosity to be the sum of the two components and ${R}_{e}^{\mathrm{GAL}}$ to be the luminosity-weighted average R_e. Using the robust biweight indicator (Beers et al. 1990), the scatter in the differences of the total magnitudes given by the single and double Sérsic fits for all galaxies is 0.20 mag; the scatter estimated from the median absolute deviation (1.48 $\,\times \,$ MAD) is 0.16 mag. Dividing these number by $\sqrt{2}$ provides an estimate of the systematic error from the assumed model (probably the dominant uncertainty). We inspected the residuals after subtracting the double Sérsic GALFIT model for each galaxy and classified the results as reliable (161 galaxies) or unreliable (18 galaxies). In Figure 2, we present histograms of the recovered R_e and n values for our fits; the distributions are fairly typical of those found from Sérsic  modeling of other cluster galaxy samples (e.g., Blakeslee et al. 2006; Ferrarese et al. 2006). The fitted photometric parameters are tabulated in the Appendix.

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A1689 has been extensively studied because of its extreme mass, high galactic density, numerous arcs, and relatively modest redshift. One particular study relevant to the present work is that of H06, who analyzed earlier ACS/WFC data and used a combination of strong lensing and masses estimated for individual galaxies to derive the total and stellar mass distributions in the cluster. To estimate the galaxy masses, they derived structural parameters by fitting Sérsic profiles and assumed that the galaxies followed the fundamental plane. The H06 imaging data had only 16% of the exposure time of our deep F814W images and were taken in the F775W bandpass, which is 34% narrower. The signal-to-noise ratio of our photometric data is therefore a factor of 3 greater.

Figure 3 compares our total ${I}_{814}$ magnitudes to the F775W (${i}_{775}$, similar to SDSS $i^{\prime}$) magnitudes reported by H06. We have applied a 0.044 mag correction for Galactic extinction (Schlafly & Finkbeiner 2011) to the uncorrected H06 magnitudes, as well as an offset for the expected color $({i}_{775}-{I}_{814})=0.10\pm 0.02$ mag, calculated for an early-type galaxy spectrum at $z=0.18$. Of the 80 galaxies they measured, 77 unambiguously match objects in our sample. Of the H06 objects that were not matched, one is outside our field because the observations had slightly different orientations; another is a highly elongated, tangentially aligned object that we masked as a possible background arc; and the third may have a positional error because it is several arcseconds away from an unmatched galaxy that we modeled. In addition, we have used a different approach to fitting the cD (see the following section), so we use a different symbol to represent it (a star). For the matched objects, our magnitude measurements agree very well with H06, except for one very deviant point, which H06 find to be 2.5 mag brighter than we do. The discrepant object is a small galaxy located within a dense region near the cluster center; examining our residuals, we are confident that our measurement is accurate. It is likely that the H06 model for this one galaxy was contaminated by light from its brighter neighbors, especially the cD, but again we emphasize the overall agreement. The median offset (after the above extinction and color corrections) is 0.02 mag, and the biweight scatter in the differences is 0.24 mag, or 0.22 mag if estimated from the MAD. Assuming that the two data sets contribute equally to the scatter and dividing by $\sqrt{2}$ implies a measurement error of ∼0.15 mag. Given the higher signal-to-noise ratio of our images, this seems a conservative estimate of the errors.

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BCGs occupy the nexus between large-scale structures of $\gtrsim 1$ Mpc and the roughly kiloparsec scales of individual galaxies. Their structures are intricately intertwined with that of the surrounding cluster, including the ICL, making it a challenge to disentangle properties such as total stellar luminosity or the size of the GC population. The cD galaxies were first identified on photographic plates and defined by Matthews et al. (1964) as elliptical BCGs located in the centers of galaxy clusters and surrounded by extended low surface brightness envelopes (many were also associated with radio sources). In A1689, the BCG has an extended, low surface brightness profile and thus is classified as a cD; we refer to it interchangeably by either term. However, the definition of cD has actually become less clear with the advance of astronomical instrumentation. The supposed unique characteristic of cD galaxies is the extended envelope, originally characterized as an excess at large radii with respect to a de Vaucouleurs profile (Sérsic  with $n=4$), but such a profile might also be represented by a Sérsic of higher n. In the literature, cD profiles have been modeled as a double de Vaucouleurs profile, de Vaucouleurs + exponential, Sérsic  + exponential, and a single Sérsic  with $n\gt 6$ (Gonzalez et al. 2005; Seigar et al. 2007; Donzelli et al. 2011; Bender et al. 2015). Despite the diverse representations, there is a general consensus that a significant portion of the extended envelope results from stripping of cluster galaxies (Gallagher & Ostriker 1972; Vílchez-Gómez 1999; Gonzalez et al. 2005). Stellar material stripped from cluster galaxies is also one definition of the ICL; thus, in some cases, the difference between a cD envelope and ICL may be a matter of semantics.

Kinematic information can provide insight into the transition from BCG to extended halo or ICL, especially if there is an offset between the velocities of the BCG and cluster. Based on mean velocity and dispersion, Bender et al. (2015) showed that the envelope of the cD NGC 6166 does not belong dynamically to the central galaxy but to the surrounding A2199 cluster potential. Interestingly, although they were able to measure distinct kinematics for the galaxy and the envelope (or ICL), they did not find any photometric discontinuity between these components, and the overall surface brightness profile was well fitted with a single Sérsic  model. More generally, Veale et al. (2017b) analyzed the wide-field kinematics of a complete mass-selected sample of luminous early-type galaxies and found that those in cluster-sized halos preferentially show rising dispersion profiles at large radius, while equally massive galaxies with similar profiles, but in more isolated regions, generally show radially declining dispersions. Thus, disentangling a BCG halo from ICL may require both photometric and kinematical profiles. However, this becomes difficult at large distances and in very dense regions with numerous overlapping galaxies, such as in A1689.

In order to model accurately the extended profile of the central galaxy and extended light, we subtracted the models for the other 179 galaxies that we had fitted, masked other bright objects and areas of poor residuals, and used the task ellipse within IRAF to measure the isophotes of the remaining light. Because the galaxy is not circular but elliptical, we calculate the equivalent circularized radius as ${R}^{\mathrm{circ}}=a\sqrt{1-\epsilon }$, where a is the semimajor axis and is the ellipticity of the isophote. In Figure 4, the black points show the radial surface brightness profile of the central component, which includes the light from the BCG and an obvious extra component at large radii that we attribute to ICL.

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The radial surface brightness profiles of the most massive elliptical galaxies generally flatten at small radii, so that their central surface brightness is lower than the inward extrapolation of the best-fit outer Sérsic  model. Such profiles can be well described by a "core-Sérsic" model (Graham et al. 2003; Trujillo et al. 2004), a Sérsic profile that flattens to an inner power law; it has the following form:

$$\begin{eqnarray}I(r)\, & = & \ {I}_{b}\,{2}^{-(\gamma /\alpha )}\exp \left[{b}_{n}{\left({2}^{1/\alpha }\displaystyle \frac{{R}_{b}}{{R}_{e}}\right)}^{1/n}\,\right]\\ & & \times {\left[1+{\left(\displaystyle \frac{{R}_{b}}{r}\right)}^{\alpha }\right]}^{\gamma /\alpha }\exp \left\{-{b}_{n}{\left[\displaystyle \frac{{R}^{\alpha }+{{R}_{b}}^{\alpha }}{{{R}_{e}}^{\alpha }}\right]}^{1/(\alpha n)}\right\},\end{eqnarray} \tag{ 2 }$$

where R_b is the break radius (transition point between a standard Sérsic  profile and the inner power law), I_b is the intensity at R_b, α indicates how sharp the transition is, and γ is the slope of the inner component.

We tried multiple approaches for simultaneously fitting the central galaxy and ICL with a combination of core-Sérsic and Sérsic functions, using a maximum likelihood method. First, we performed the analysis with all the parameters free; the resulting fit is shown in the top panel of Figure 4. The fit appears excellent and gives a combined integrated magnitude of ${m}_{814}=14.7$ mag; the central core-Sérsic model, representing the BCG, contributes only ∼18% of the light in this model, and the remaining ∼82% is ICL. However, the best-fit n = 1.4 for the BCG is lower than expected for such a bright galaxy, while the ICL component has n = 2.

Donzelli et al. (2011) analyzed the surface brightness profiles of 430 BCGs, finding that half of the sample required two Sérsic  components: an inner one with $1\lesssim n\lesssim 7$, plus an outer exponential ($n\approx 1$) component. Thus, it is somewhat unusual for the ICL component to have a larger Sérsic index than the BCG. Moreover, core-Sérsic galaxies generally have $n\gt 4$, even when they are not BCGs. For instance, the galaxy sample analyzed by Kormendy et al. (2009) included 10 classed as "core galaxies," which had best-fit Sérsic indices ranging from 5.2 to 11.8. The largest n was for M87, which might be "biased" by an ICL component. However, with M87 excluded, the remaining nine core galaxies had a median n of 7.1, with no significant correlation with luminosity (all the cored galaxies were luminous). This is consistent with the results of Ferrarese et al. (2006), who fitted multiband profiles to 100 galaxies in the Virgo Cluster, including core-Sérsic models for the brightest ones. Thus, $n\approx 7$ appears to be a good average for galaxies that are well described by core-Sérsic models.

We therefore performed another fit to the combined BCG+ICL profile in A1689, constraining n = 7 for the core-Sérsic component; the rest of the parameters were left free. The result is shown in the middle panel of Figure 4. The combined magnitude is again ${m}_{814}=14.7$ mag (the total luminosity is well constrained), but in this case the contribution from the BCG is 41%, more than double the amount when all parameters were free. For the ICL component, we find n = 1.6, which is very similar to the results of Cooper et al. (2015), who fitted double Sérsic profiles to high-resolution N-body simulations of galaxy clusters and found a median best-fit value of n = 1.66 for the diffuse outer component.

In order to explore the maximum amount of light that could be assigned to the BCG, we tried a third case in which we only fitted a single core-Sérsic model to the light within ${R}^{\mathrm{circ}}\lt 25\,\mathrm{kpc}$ and then took the integral of this fit as the total BCG luminosity. The result is shown in the bottom panel of Figure 4. In this case, the BCG has n = 8.7, which is still within the observed range, with magnitude ${m}_{814}=15.0$ mag; since the total magnitude of the combined distribution is 14.7 mag, the BCG represents ∼77% of the light in this case, and the ICL (representing the excess of light with respect to the single model) would have an integrated ${m}_{814}=16.3$ mag. This is a lower limit on the ICL, which must contribute at least some luminosity even at projected radii $\lt 25\,\mathrm{kpc}$. Overall, we prefer the second model, with n constrained for the core-Sérsic component based on literature considerations, the BCG contributing ∼40% of the light, and the ICL accounting for the remaining ∼60%. We use this model in the following sections to estimate separately the specific frequencies of the BCG and ICL. However, it should be remembered that the plausible range for the ICL component is anywhere from ∼23% to ∼82%.

Figure 5 (middle panel) shows our final 2D galaxy light model, constructed from the GALFIT models of the 179 noncentral galaxies and our ellipse model for the combined cD and ICL. The left panel of Figure 5 shows the ACS/WFC image, and the right panel shows the residuals after subtracting the full luminosity model. Although only 94 of the modeled galaxies are confirmed members of A1689, the models for the other galaxies are needed to characterize the full light distribution and derive accurate magnitudes for the known members. Note that areas of imperfect galaxy subtraction were masked before deriving the isophotal model described above; thus, the excess of light associated with the clump of galaxies to the upper right of the cD did not contribute to the ICL component seen in the 1D profiles of Figure 4.

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The situation for the GC spatial distribution is similar to the case of the starlight in the sense that the GC populations of many galaxies in the FOV overlap. We therefore follow a similar approach: we use the 2D GC number density map (described in Section 2.2) and simultaneously fit multiple Sérsic components to it with GALFIT. However, we were not able to identify a significant GC system (an excess of point sources on the map) for many of the galaxies modeled previously from the starlight. The main reason for this is that, as shown by AM13, the GCs only represent ∼0.8% of the stellar mass in the field and thus have a much lower signal-to-noise ratio than the starlight. In addition, the Gaussian filtering, which was necessary to have a continuous number density map, smooths out the overdensities for many of the smaller galaxies. The filtering was done on a physical scale of $\sigma =13\,\mathrm{kpc}$, so only galaxies that have significant excesses on this scale can be modeled.

To select the GC systems to be fitted, we visually inspected the subimage region of the GC number density map corresponding to each of the 180 galaxies (including the cD) for which we had modeled the stellar light with GALFIT. We selected the cases where a significant excess was identifiable (see Figure 6 for some examples), resulting in a sample of 66 GC systems to be fitted. Because of the extensive overlapping of GC systems on the smoothed map, rather than analyzing small subimages around each galaxy, we divided the GC map into quadrants (see Figure 7). Within each quadrant, we performed simultaneous fitting of all the selected GC systems within it, as well as an extended background component for the central GC system. Each GC system was modeled by a single Sérsic function convolved with the smoothing kernel used in constructing the map. The initial guesses for the Sérsic parameters were taken to be the best-fit values from the galaxy models in Section 3.1. The effective radius of each GC system ${R}_{e}^{\mathrm{GC}}$ was constrained to be between 0.5 and 4.0 times ${R}_{e}^{\mathrm{GAL}}$ (e.g., Peng et al. 2008), the central coordinates were constrained to be no more than 3 kpc in X and Y from the galaxy center (giving a maximum offset of 4.2 kpc, which is large but only $\sim 1/3$ of the smoothing kernel), and a minimum normalization of 50 GCs was imposed. Because the GC system of the cD galaxy overlaps all of the quadrants, it was modeled again, independently, using the full map after subtracting all other models, as detailed below.

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We inspected all 66 GC models and their residuals after subtraction from the density map and visually classified 50 of them as reliable fits. Some examples of the 16 rejected fits are shown in Figure 8. Of the 50 reliable fits, 36 are associated with confirmed cluster members, but in three of these cases, the luminosity model was classified as poor, leaving a sample of 33 confirmed members with good fits for both the GCs and galaxy light. The ratio of the normalizations of these fits yields the GC specific frequencies presented in Section 4.2 and tabulated in Appendix.

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For the sake of consistency, we wish to follow a similar treatment for the GCs to that for the stellar light. Therefore, we again use the ellipse task to construct the radial profile of the surface number density of GCs for the central components (black squares in Figure 9), after subtracting Sérsic models for all other GC systems. We note that Durrell et al. (2014) and Cho et al. (2016) followed a similar approach in modeling the smoothed GC number density maps around the cD galaxies in Virgo and Coma, respectively.

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Although an excess in the outer region is not as obvious for the GCs as for the galaxy light, we again perform three types of fits, illustrated in Figure 9: a single core-Sérsic (top panel), a core-Sérsic plus Sérsic  (middle panel), and a double Sérsic  (i.e., testing the significance of a flat core in the GC distribution; bottom panel). We find that the fit with two standard Sérsic models is significantly worse than the core-Sérsic + Sérsic case; a core of ${R}_{b}\approx 20\,\mathrm{kpc}$ is required. Somewhat surprisingly, the model prefers exponential profiles (we constrained $n\geqslant 1$ for both components), whether or not there is a core. For consistency with the light, we take the two-component Sérsic/core-Sérsic model, in which ∼42% of the GCs are associated with the cD and the other ∼58% are ICGCs. This is remarkably consistent with the decomposition found in Section 3.2 for the central galaxy and surrounding ICL, suggesting that the cD and ICL have very similar specific frequencies. However, given the similarity of the fits in the top and middle panels of Figure 9, the uncertainty in the decomposition is large, and a single-component model with $n\approx 4$ provides a reasonable fit. It is simply easier to separate the cD from the ICL using the starlight than the GCs, because the surface density of the GCs is so much lower. Figure 10 shows our final GC number density model (middle panel) compared to the observed distribution (left panel). The residuals (right panel) are clearly not perfect, but the model gives a reasonable representation of the gross structure.

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Although the ICL constitutes a significant amount of the total optical light, it is difficult to detect because of its very diffuse and extended nature. Also, the ICL is centrally concentrated in the cluster, and therefore it is difficult to distinguish from the stellar light of the central galaxy (see Section 3.2). There is also evidence that the ICL evolves with time in amount and morphology. This was noted by Schombert (1988), who found that the luminosity of the cD envelope correlates with parameters indicative of the dynamical stage of the cluster, such as richness, morphological type, and X-ray luminosity. Rudick et al. (2006) studied the formation and evolution of ICL in three simulated galaxy clusters, finding that as the galaxy cluster evolves, high-luminosity features dilute into fainter and more extended structures. These authors defined the ICL as all the light at V-band surface brightness ${\mu }_{V}\lt 26.5$ mag arcsec⁻², but a later study (Rudick et al. 2011) found that the amount of ICL increased with time regardless of definition, although the inferred total could vary at any given time by a factor of two, depending on one's definition.

In Section 3.2, we found that the ICL represented ${59}_{-37}^{+22}$% of the combined light of the BCG+ICL in A1689, where the substantial error bars represent the range of values from the different types of compositions we explored. This amounts to ${11}_{-7}^{+4}$% of the total light in the ACS FOV. This is very similar to the 7%–15% range found by Mihos et al. (2017) for the Virgo Cluster and consistent with the 10%–40% range found in simulations by Contini et al. (2014), who also noted that there was a large halo-to-halo scatter in the ICL fraction and no clear dependence on halo mass.

We note again that the excess in the surface brightness profile that we modeled as the ICL (Figure 4) was not caused by the group of galaxies to the upper right of the BCG, since we masked that region when we determined the isophotes. However, as discussed by Mihos et al. (2005, 2017), modeling the ICL with a simple radial profile can be misleading, since it often shows streams and other structures that may be associated with (but not bound to) individual cluster galaxies. Thus, although we believe we have made the best possible decomposition of A1689's central light profile into BCG and ICL components, the amount of ICL may be underestimated (by ∼10%–20%), as excess light is visible in the residual image near the locations of some bright galaxies, and this would not be represented within the two-component Sérsic  model.

Similarly, although ICGCs appear to be a common feature of galaxy clusters, it is not easy to identify them. The ICGCs blend in with the GC population of the BCG at small clustercentric radii and have low surface densities blending in with the background at larger radii. As noted above, the only clear detections of ICGCs have been in relatively nearby clusters. However, numerical simulations predict that at least 30% of the total GC populations in evolved clusters may be ICGCs (Yahagi & Bekki 2005), and this is also the fraction of ICGCs found by Peng et al. (2011) for the Coma Cluster.

For A1689, we have found in Section 3.4 that ICGCs account for ∼58% of the combined BCG + intracluster GC population. This is similar to the breakdown found for the stellar light (and even more uncertain). However, because the S_N of the central component is several times larger than average, the ICGCs represent roughly 35% of the total GC population in the ACS FOV. AM13 did not perform any decompositions and thus could not estimate a reliable ICGC fraction, but concluded that it was no more than half; our result here is consistent with this upper limit. In this model, the BCG contributes 26% of the GCs to the total, and all the other galaxies in the field contribute the remaining 39%.

The specific frequency is defined as the number of GCs normalized to a galaxy luminosity of ${M}_{V}=-15$ (Harris & van den Bergh 1981):

$$\begin{eqnarray}&&{S}_{N}={N}_{\mathrm{GC}}\,{10}^{0.4({M}_{V}+15)}.\end{eqnarray} \tag{ 3 }$$

Early studies showed that S_N is dependent on morphological type (Harris 1991). Since then, S_N has been extensively studied in galaxies with different luminosities, morphologies, and environments, in order to understand why ${N}_{\mathrm{GC}}$ does not scale in a simple linear way with the field stars, i.e., why the formation efficiency of GCs per unit stellar mass varies among galaxies. This is an important key for unlocking the early stages of galaxy formation and assembly. It is still not entirely clear what drives the large scatter in S_N for galaxies of the same mass. An important motivation of the current work is to examine the behavior of S_N within the extremely dense environment of the A1689 core and to compare with galaxies that have evolved under different conditions. The total mass of A1689 within 2 Mpc is $1.3\times {10}^{15}$ M_⊙ (Sereno et al. 2013). A particularly good comparison sample comes from the 100 early-type galaxies studied in the ACS Virgo Cluster Survey (ACSVCS; Côté et al. 2004), the largest sample of GC populations analyzed in a homogeneous way. Virgo has a total mass of $5.5\times {10}^{14}$ M_⊙(Durrell et al. 2014). As part of the ACSVCS, Peng et al. (2008) confirmed the U-shape trend of S_N with luminosity and found that most dwarf galaxies with high S_N are located within 1 Mpc of M87, the central galaxy in Virgo, suggesting an environmental dependence of GC formation efficiency with density. However, the innermost few dwarfs have lower S_N values, probably as a consequence of their GCs being stripped by the strong gravitational tides of M87 or by the cluster itself (and becoming ICGCs).

As in AM13, to estimate the S_N of our A1689 sample, we convert the I-band total magnitudes (corrected for extinction) from GALFIT  to V band using

$$\begin{eqnarray}&&{M}_{V}={M}_{814}-{K}_{814}+(V-{I}_{814}),\end{eqnarray} \tag{ 4 }$$

where K₈₁₄ is the F814W K-correction of 0.11 mag for a giant elliptical at the redshift of A1689 and $(V-{I}_{814})=0.83$ mag is the rest-frame color on the AB system. Figure 11 shows S_N as a function of M_V for the ACSVCS sample (gray dots) and our A1689 sample. The color code of the A1689 points indicates the clustercentric distance. The star and triangle indicate the values for the cD galaxy (${{S}_{N}}^{\mathrm{cD}}\approx 18$) and the ICL (${{S}_{N}}^{\mathrm{ICL}}\approx 17$), respectively. The error bars cover the range in magnitudes from the different cases considered in Section 3.2.

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The orange dashed line indicates S_N as a function of galaxy magnitude for a population of 50 GCs, the lower limit imposed in the GALFIT  fitting; only a few systems had results actually constrained by this limit. The cyan dashed curves are theoretical predictions from Georgiev et al. (2010), which assume a constant GC formation efficiency $\eta ={M}_{\mathrm{GC}}/{M}_{h}$ per total halo mass M_h, where ${M}_{\mathrm{GC}}$ is the total mass in GCs. The galaxy luminosity for these models is calculated from $L\propto {M}_{h}^{5/3}$ for galaxies of stellar mass ${M}_{\star }\lt 3\times {10}^{10}$ M_⊙ (star formation presumed regulated by stellar feedback), and $L\propto {M}_{h}^{1/2}$ for galaxies with ${M}_{\star }\gt 3\times {10}^{10}$ M_⊙ (star formation presumed regulated by virial shocks, including AGN induced). These simple scalings give a reasonable approximation to the variation in ${M}_{h}/L$ with stellar mass. For A1689, we find that most of the galaxies, including the BCG, fall within the range of values observed for systems in the local universe, indicating $1\times {10}^{-5}\lt \eta \lt 3.5\times {10}^{-4}$, although the scatter is large and we do not probe a large range in luminosity. As evident from the point colorings, there is a weak tendency for galaxies with higher S_N to be within ∼150 kpc of the cluster center.

The most outlying point in Figure 11 is located at ${M}_{V}\approx -20.5$ and ${S}_{N}\approx 14$ and has ID #156 in the data tables. This galaxy is discordant with previous results indicating that galaxies of intermediate luminosity have universally low ${S}_{N}\lesssim 2$ (Peng et al. 2008). To examine this object in more detail, the top set of six panels in Figure 12 shows a zoomed-in region around this galaxy, its corresponding location in the GC density map, the galaxy and GC models, and residuals. Interestingly, the galaxy is ∼250 kpc from the cluster center, outside the heavily crowded region. There is no indication that the fits are poor or misleading in this case, although the GC surface density is fairly low. The galaxy appears quite normal except for its relatively high S_N. Figure 12 also shows the corresponding sets of images for the other two outliers in Figure 11: galaxy #63 (middle set of panels), which has ${M}_{V}\approx -21.5$ and ${S}_{N}\approx 13;$ and galaxy #134 (bottom panels), which has ${M}_{V}\approx -21.0$ and ${S}_{N}\approx 10$. Only for the third object does it appear that there could be significant contamination from a neighbor galaxy.

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Despite some broad morphological themes, the early-type galaxy class is composed of galaxies with a wide range of properties (kinematics, stellar and dust content, mass-to-light ratio, among others). Emsellem et al. (2007, 2011) introduced a kinematical classification for early-type galaxies (accounting for projection effects) by defining two kinematical classes: slow rotators (complex velocity fields with little net angular momentum, often showing decoupled cores) and fast rotators (ordered velocity fields dominated by rotation). In this classification scheme, only ∼30% of morphologically identified early-type galaxies are slow rotators, once considered a common characteristic of spheroidal systems (Cappellari et al. 2011). However, the fraction of slow rotators increases with mass, reaching ≳80% for stellar masses ${M}_{\star }\gt 5\times {10}^{11}$ M_⊙ (Veale et al. 2017a).

The kinematical classification is based on the projected stellar angular momentum ${\lambda }_{R}$ (measured within R_e) and projected ellipticity . The boundary between slow and fast rotators is ${\lambda }_{R}=0.31\sqrt{\epsilon }$ (dashed line in bottom panel of Figure 13), with the former being below the line and the latter above. This "dichotomy" is reminiscent of the one pointed out by Bender et al. (1989), who classified elliptical galaxies as boxy or disky based on the deviations of their isophotes from perfect ellipses and reported correlations of these characteristics with radio and X-ray emission. Numerical simulations (Naab et al. 2009; Lagos et al. 2011; Rodriguez-Gomez et al. 2016) imply that dry major mergers (mass ratios of order 3:1) form boxier, slow-rotating spheroidal systems, while wet or dry minor mergers with high angular momentum results in disky systems. However, there is not a sharp demarcation between either the isophotal or kinematical classes, and there appears to be a range of formation scenarios for each case.

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Cappellari et al. (2011) studied the kinematical version of the morphology–density relation and found that as the galactic density increases, the fraction of early-type fast rotators decreases in a manner similar to the decrease of spiral galaxies in the classic morphological version of the relation (Dressler 1980). More specifically, the fraction of slow rotators in their sample was only a few percent, except in the Virgo Cluster core, where it increased to ∼20%. These authors suggested that the dynamical processes operating in high-density environments make them more efficient in producing slow rotators. More recently, Veale et al. (2017a) explored a wider range of environments and concluded that the apparent trend was actually driven by the underlying correlation of slow rotator fraction with stellar mass, coupled with the tendency for more massive galaxies to occur in higher-density regions. Motivated by these considerations, D'Eugenio et al. (2013) determined the fraction of slow rotators in the core of A1689, a much denser environment than the Virgo Cluster or any other nearby region. These authors used FLAMES/GIRAFFE on the Very Large Telescope to obtain integral field spectroscopy of 29 bright galaxies in A1689 and measure ${\lambda }_{R}$, finding a similar fraction of slow rotators to that in Virgo, despite the much higher density.

Using these kinematical data, we have made a first attempt to explore the behavior of S_N as a function of ${\lambda }_{R}$. In the top panel of Figure 13 we reproduce Figure 4 of D'Eugenio et al. (2013), but only for galaxies for which we were able to estimate S_N, with the S_N values indicated by the color code. Given the sample size, it is difficult to make general conclusions, but it is clear that the slow rotators do not all have high S_N values. On the other hand, the galaxies with high S_N are all fairly round ($\epsilon \lt 0.15$), independently of whether they are fast or slow rotators. Moreover, the galaxies with higher values of ${\lambda }_{R}$ tend to have lower specific frequencies. To highlight the latter point, the bottom panel of Figure 13 plots S_N as a function of ${\lambda }_{R}$. The apparent anticorrelation between these quantities is significant at the 94% confidence level; if galaxy #156 (the biggest outlier in Figure 11) were excluded, the significance would increase to 97%, although there is no a priori reason to exclude this galaxy. Such an anticorrelation between S_N and ${\lambda }_{R}$ could occur if galaxies with low angular momentum experienced a larger number of dissipative mergers earlier in their history and formed greater numbers of GCs in the process, or it could indicate a lower ${M}_{\star }/{M}_{h}$ ratio in slow rotators, if ${N}_{\mathrm{GC}}$ scales reliably with halo mass.

Numerical simulations show that when galaxies interact, their dark matter halos are more affected than the stars (Mistani et al. 2016), which are much more centrally concentrated. However, because the GC system is spatially more extended than the field stars, the GCs are among the first stars to "notice" the interaction and undergo stripping if enough of the dark matter halo has been disrupted (Smith et al. 2013). This could be reflected as an asymmetrical shape and/or offset in the centroid of the GCs system with respect to the starlight. Such a displacement of the GC system has been found for a high-velocity early-type dwarf in the dense core of the Coma Cluster (Cho et al. 2016), as well as for the cD NGC 4874 itself.

To investigate whether the galaxies in A1689 show any evidence for offsets between the GCs and starlight, we calculate the clustercentric radial position of each galaxy (${r}_{\mathrm{Gal}}$) and its associated GC system (${r}_{\mathrm{GC}}$), based on the centroids given by the best-fit Sérsic models for each. We define r = 0 at the luminosity center of the cD galaxy, which coincides well with the geometrical center of the X-ray emission. We expect ${r}_{\mathrm{Gal}}$ = ${r}_{\mathrm{GC}}$ for undisturbed galaxies. However, if the high-S_N central GC system is augmented by stripping GCs from cluster galaxies as they pass through the cluster core, we might expect ${r}_{\mathrm{Gal}}\gt {r}_{\mathrm{GC}}$ or ${r}_{\mathrm{Gal}}\lt {r}_{\mathrm{GC}}$, depending on the point in the orbit at which the galaxy is observed. Of course, local interactions with neighboring galaxies might also disrupt the extended GC distributions.

Figure 14 shows the histogram of offsets, where ${r}_{\mathrm{Gal}}\mbox{--}{r}_{\mathrm{GC}}\gt 0$ for galaxies with the fitted GC centroid closer to the cluster center and ${r}_{\mathrm{Gal}}\mbox{--}{r}_{\mathrm{GC}}\lt 0$ for galaxies with the GC system offset in the direction away from cluster center. While there are more galaxies with GC systems offset away from the cluster center, the difference is not significant. The distribution is quite uniform, without a strong peak at zero, likely indicating the limitations of our GC system centroiding as a consequence of the smoothing. However, we believe that this is an interesting area for future studies with large samples of GC systems in rich nearby clusters such as Coma, where it is possible to reach farther along the GCLF and the centroiding is not as limited by the resolution.

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In AM13, we found that A1689 harbored $162,{850}_{-51,300}^{+75,450}$ GCs, integrated over the GCLF, within a projected radius of 400 kpc of the cluster center. As shown in Figure 3 of AM13, the ACS/WFC areal coverage is incomplete to 400 kpc; the GCLF-integrated number within the ACS FOV is ${{\rm{153,600}}}_{-{\rm{48,400}}}^{+{\rm{71,200}}}$. By analogy with other clusters, AM13 speculated that the total GC number within the virial radius of 3 Mpc may be several times larger, or $\sim 5\times {10}^{5}$. Based on these results, the A1689 GC population was the largest and most distant that had ever been studied. The error bars on the above values are dominated by the uncertainty on the GCLF extrapolation, which was based on M87 (Peng et al. 2009) translated to do the distances of A1689, with K-corrections and 2.25 Gyr of passive evolution, and a GCLF width $\sigma =1.4\,\pm 0.1$ mag. Harris et al. (2017) advocated using $\sigma =1.3\pm 0.1$ mag for A1689 and similar cluster fields with a mix of early-type galaxies; adopting this value increases the extrapolated numbers by 29% to ${{\rm{198,000}}}_{-62,400}^{+91,800}$ GCs within the ACS FOV.

The cluster A2744, which has a total mass of ∼2 × 10¹⁵ M_⊙ (Boschin et al. 2006) and $z=0.308$, is the nearest of the Hubble Frontier Fields (Lotz et al. 2017), and the brightest members of its GC system are clearly visible (Blakeslee et al. 2015). Lee & Jang (2016, hereafter LJ16) reported an extrapolated total of 385,000 GCs, with a quoted error of only 6%. These authors assumed the Milky Way GCLF with $\sigma =1.2$ mag and that the observed F814W bandpass matched identically the rest-frame r band. They did not report the actual number of detected GC candidates, but Harris et al. (2017), referencing a private communication, states that 664 GC candidates were detected (after completeness and contamination corrections) to ${I}_{814}=29.0$ mag; this is on the Vega system and corresponds to ${I}_{814}=29.4$ AB mag, or 4 mag brighter than the GCLF turnover adopted by LJ16. The extrapolated total based on these numbers exceeds 10⁶ GCs, in contrast to what was reported by LJ16. Recognizing this, Harris et al. used a slightly revised set of GCLF parameters for A2744 with $\sigma =1.3$ mag and derived a total of ${3.9}_{-2.1}^{+7.2}\times {10}^{5}$ GCs, where the error bars now include realistic uncertainties on the GCLF and were calculated following the same prescription as in AM13. However, the assumed GCLF turnover magnitude was still not fully consistent with the value adopted for the A1689 extrapolation; using the same approach as in AM13, we estimate that the turnover should occur at an observed AB magnitude ${I}_{814}=32.9\pm 0.2$ mag. For $\sigma =1.3\,\pm 0.1$ mag, the extrapolation now gives ${1.9}_{-0.9}^{+2.1}\times {10}^{5}$ GCs. With the brighter assumed turnover, the detections go $0.4\,\sigma$ farther along the GCLF, lessening the extrapolation; likewise, the error bars are smaller, in a fractional sense, than those reported by Harris et al. (2017).

Given the above estimates, one can only conclude that the number of GCs in A2744 appears similar to that found in A1689, but the value is much more poorly constrained for A2744, with an uncertainty range at least a factor of two larger. The fundamental reason is that AM13 detected more than 10 times as many GC candidates in A1689, and the required extrapolation was a factor $\lt 20$, rather than $\gt 200$ as in A2744. However, there are additional reasons for caution in interpreting the result for A2744. In the case of A1689, the AM13 analysis accounted for the effects of Eddington bias (which causes an overestimate of the true population), gravitational magnification of the background counts, and passive luminosity evolution; numbers were stated explicitly for the sizes of all these corrections. None of these issues were even mentioned by LJ16. Despite their quoted 6% uncertainty, LJ16 stated that their result was "a rough estimate of the total number of GCs in the Abell 2744 field." We concur on this point and conclude that the population of GCs in A1689 remains the largest that has been reliably measured to date. Future observations with the James Webb Space Telescope (JWST) should reveal even larger GC systems in other high-density regions.

The favored explanation for the depletion of the light in the centers of massive "core" galaxies is the coalescence of binary supermassive black holes (SMBHs) in the final stages of galaxy merging, and the resultant "scouring" of stars on orbits that pass near the galaxy center. As the binary SMBHs orbit their common center of mass, stars interact and are ejected from the system, removing angular momentum and causing the binary orbit to shrink (Begelman et al. 1980; Merritt & Milosavljević 2005). Numerical simulations of binary SMBHs predict that the amount of depleted mass correlates with the number of mergers and the total SMBH mass ${M}_{\mathrm{BH}}$ (Ebisuzaki et al. 1991; Merritt 2006).

There is an extensive body of work on empirical relations between ${M}_{\mathrm{BH}}$ and properties of the host galaxy (or its spheroidal component), such as luminosity, velocity dispersion (${\sigma }_{v}$), Sérsic index, and ${N}_{\mathrm{GC}}$ (for reviews, see Ferrarese & Ford 2005; Kormendy & Ho 2013; McConnell & Ma 2013). Some simulations predict that the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{v}$ relation gets steeper at high masses (Boylan-Kolchin et al. 2006), and this was found observationally by McConnell et al. (2011), who reported the discovery of two SMBHs that where significantly more massive than predicted by the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{v}$ relation, suggesting a possibly different growth process at these high masses. Rusli et al. (2013) explored the relations between depleted stellar mass, core size, total luminosity, ${\sigma }_{v}$, and ${M}_{\mathrm{BH}}$. They found that the strongest correlation for core galaxies was between R_b (as determined from core-Sérsic fitting) and ${M}_{\mathrm{BH}}$, having the form

$$\begin{eqnarray}\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{3\times {10}^{9}\,{M}_{\odot }}\right) & = & (0.59\pm 0.16)\\ & & +(0.92\pm 0.20)\mathrm{log}\left(\displaystyle \frac{{R}_{b}}{\mathrm{kpc}}\right),\end{eqnarray} \tag{ 5 }$$

with a quoted intrinsic scatter of 0.28 dex in mass. From our best core-Sérsic fit, we obtain a core radius ${R}_{b}\,=3.8\pm 0.2\,\mathrm{kpc}$ for the A1689 cD, which would imply an extraordinary SMBH mass ${M}_{\mathrm{BH}}\approx (4\pm 2)\times {10}^{10}$ M_⊙. However, the above empirical scaling is not constrained for ${R}_{b}\,\gt \,1\,\mathrm{kpc}$ or ${M}_{\mathrm{BH}}\gt 2\times {10}^{10}$ M_⊙. In fact, applying the somewhat steeper R_b–${M}_{\mathrm{BH}}$ relation from Thomas et al. (2016) would imply an even more enormous ${M}_{\mathrm{BH}}$, greater by a factor of two, even though the relations were fitted to essentially the same data and agree closely at ${R}_{b}\lt 1\,\mathrm{kpc}$. Thus, the safest conclusion is simply that ${M}_{\mathrm{BH}}$ likely exceeds $2\,\times \,{10}^{10}$ M_⊙ in the A1689 BCG if its core has become depleted by the same physical process as in more nearby core galaxies for which ${M}_{\mathrm{BH}}$ has been measured.

Postman et al. (2012) used HST imaging to study the very large depleted core in the A2261 BCG, which they described as the largest known in any galaxy. Bonfini & Graham (2016) fitted the same data with a core-Sérsic model and determined ${R}_{b}=3.6\,\mathrm{kpc}$, which they likewise characterized as the largest known. The latter authors suggested that depleted cores of such large sizes are formed by mechanisms other than scouring by binary black holes, including scouring by a gravitationally bound group of three or more SMBHs (Kulkarni & Loeb 2012), a scenario that might reasonably occur in a region as dense as the center of A1689. In the case of the A2261 BCG, there are multiple galactic nuclei visible within the break radius, and Bonfini & Graham suggest that the very large core more likely results from the dynamical effects of these massive luminous perturbers. We note that McNamara et al. (2009) reported a core radius of 3.8 kpc in the BCG of MS 0735.6+7421, although this galaxy has significant dust in its center. After this paper was submitted, Dullo et al. (2017) reported an even larger core radius of 4.2 kpc for the BCG of A2029. For A1689, there are no other luminous nuclei or obvious dust features within the cD's large break radius.

Another ${M}_{\mathrm{BH}}$ correlation that has been studied in the literature is with the total number of GCs in the host galaxy (Burkert & Tremaine 2010; Rhode 2012; Harris et al. 2014). The most recent version has the form

$$\begin{eqnarray}&&\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}\right)=(8.27\pm 0.06)\,+\,(0.98\pm 0.09)\mathrm{log}\left(\displaystyle \frac{{N}_{\mathrm{GC}}}{500}\right),\end{eqnarray} \tag{ 6 }$$

with an intrinsic scatter of 0.30 dex in mass, after excluding galaxies classified as S0. For comparison, we calculate the ${M}_{\mathrm{BH}}$ predicted by the above relation using the GC population of the central galaxy obtained from our preferred two-component fit (${N}_{\mathrm{GC}}\approx {\rm{39,600}}$; see Figure 9), obtaining ${M}_{\mathrm{BH}}\approx {1.4}_{-0.7}^{+1.4}\,\times {10}^{10}$ M_⊙. However, if we consider the combined number of GCs from the BCG and intracluster components (${N}_{\mathrm{GC}}\approx {\rm{99,300}}$), the result is ${M}_{\mathrm{BH}}\approx {3.3}_{-1.7}^{+3.3}\times {10}^{10}$ M_⊙. Interestingly, the latter value agrees better with the estimate from R_b, but as in that case, we are again exploring an unprecedented regime requiring a large extrapolation. It would be extremely interesting to probe the limits of these empirical ${M}_{\mathrm{BH}}$ correlations by obtaining a dynamical mass for the SMBH in A1689. However, given the large distance and low central surface brightness, this is unlikely to be possible in the near future, even with the upcoming launch of JWST.