THE HST/ACS COMA CLUSTER SURVEY. IV. INTERGALACTIC GLOBULAR CLUSTERS AND THE MASSIVE GLOBULAR CLUSTER SYSTEM AT THE CORE OF THE COMA GALAXY CLUSTER^*

Massive elliptical galaxies at the centers of galaxy clusters— often brightest cluster galaxies (BCGs) and sometimes cD galaxies—generally have little ongoing star formation with only minor evolution since z ~ 1, and only a shallow relationship between their stellar mass and their host cluster mass (e.g., Lin & Mohr 2004; Whiley et al. 2008). In the standard hierarchical paradigm, however, the most massive halos should be the last to assemble, and so these galaxies have traditionally presented problems for formation models.

Recent simulations suggest that this paradox can be resolved in a picture where the stars that end up in the most massive galaxies form early, energy feedback from supernovae and active galactic nuclei subsequently suppress star formation, and the assembly of these galaxies through dry mergers continues right up to the present day (De Lucia & Blaizot 2007; although see Bildfell et al. 2008 for evidence that feedback is not 100% efficient). Thus, even if there is little star formation at late times, these galaxies are still expected to further assemble stellar mass at z < 2. This predicted increase in the masses of BCGs over time, however, may be in conflict with observations that show little mass evolution of BCGs from z ~ 1.5 to the present (Collins et al. 2009).

It is expected that the dry merging or tidal stripping of satellites should not only contribute stars to the central galaxy itself, but also to an intracluster component that has previously been associated with the extended stellar envelopes of cD galaxies (Matthews et al. 1964), and is sometimes labeled as a "diffuse stellar component" (Monaco et al. 2006) or simply "intracluster light" (ICL). This component can make up a large fraction of the total luminosity at the center of galaxy clusters (Oemler 1976) and if added to the stellar mass of central cluster galaxies might naturally explain current contradictions between simulation and observation. Purcell et al. (2007) simulated the formation of the ICL from the shredding of satellite galaxies, finding that in massive clusters, the ICL can dominate the total stellar mass of the combined ICL+BCG system, which is consistent with observations of low redshift clusters (Gonzalez et al. 2005; Seigar et al. 2007).

In fact, there is increasing observational evidence that a significant fraction (10%–40%) of the total stellar light in a galaxy cluster is intergalactic. Starting with Zwicky (1951), many detections of low surface brightness starlight in galaxy clusters—both in cD envelopes and in the regions between galaxies—support the existence of substantial intracluster stellar populations (Welch & Sastry 1972; Uson et al. 1991; Vilchez-Gomez et al. 1994; Gregg & West 1998; Trentham & Mobasher 1998; Feldmeier et al. 2002, 2004a; Lin & Mohr 2004; Adami et al. 2005; Zibetti et al. 2005; Mihos et al. 2005; Gonzalez et al. 2005; Seigar et al. 2007; Gonzalez et al. 2007; Krick & Bernstein 2007). In nearby clusters, there have also been direct detections of intergalactic red giant branch stars (Ferguson et al. 1998), asymptotic giant branch stars (Durrell et al. 2002), planetary nebulae (Theuns & Warren 1997; Mendez et al. 1997; Feldmeier et al. 1998; Feldmeier et al. 2004b; Okamura et al. 2002; Arnaboldi et al. 2004; Gerhard et al. 2007; Arnaboldi et al. 2007; Castro-Rodriguéz et al. 2009; Doherty et al. 2009), novae (Neill et al. 2005), and supernovae (Gal-Yam et al. 2003). Detections of intergalactic light have also been made in compact groups (Da Rocha & Mendes de Oliveira 2005). These studies tend to show that the richer and more massive the group or cluster, the larger the fraction of intergalactic light.

Another important clue to the formation of massive ellipticals is that those residing at the centers of galaxy clusters often host extremely large populations of globular clusters (GCs). The star-forming events that form globular clusters will mostly form stars that end up in the field, so it is natural that the number of GCs in a galaxy should roughly scale with that galaxy's stellar luminosity or mass. However, the ratio of GCs to starlight—usually characterized as the specific frequency, S_N (Harris & van den Bergh 1981)—has long been known to vary across galaxy mass and morphology, with giant central elliptical galaxies harboring the largest GC systems and having some of the highest specific frequencies. This abundance of GCs in galaxy clusters appears explainable if the number of GCs scales with either total baryonic mass at the cluster center, including hot gas (McLaughlin 1999), or the total dynamical mass of the cluster (Blakeslee et al. 1997). Blakeslee (1997, 1999) observed that the number of GCs in galaxy clusters was directly related to cluster mass, but the relatively constant BCG luminosity thus led to high S_N. It is possible that the high specific frequencies are because measurements of the galaxy luminosity typically do not include a substantial ICL component, and that the high S_N in central cluster galaxies would be more normal if the ICL was included. Galaxy-specific frequency also varies with galaxy stellar mass (or luminosity) in a way that is consistent with the expected variation in galaxy stellar mass fraction (or mass-to-light ratio; Peng et al. 2008; Spitler & Forbes 2009).

This connection between GCs and total mass has interesting implications, particularly in massive galaxy clusters where the predicted build up of stellar mass in central galaxies should be paralleled by the build up of a large GC system. If much of the stellar mass in galaxy clusters resides in the low surface brightness ICL then there should also be a corresponding population of intracluster GCs (IGCs) that are not gravitationally bound to individual galaxies, but directly to the cluster itself. Moreover, the detection of point-source IGCs in the nearest clusters is a much easier observational endeavor than measuring the faint ICL, giving us a window onto the nature of the diffuse stellar content.

There are other reasons to expect substantial populations of IGCs. West (1993) proposed that GC formation may be biased toward the largest mass overdensities, i.e., galaxy clusters. West et al. (1995) also proposed that populations of IGCs were responsible for the high S_N seen in cD galaxies. More recently, spectroscopy of ultra-compact dwarfs (UCDs) and massive GCs (also dubbed dwarf-globular transition objects; Haşegan et al. 2005) have uncovered a population of compact stellar systems in galaxy clusters resembling the most massive GCs or dE nuclei stripped of their host galaxies (Drinkwater et al. 2003; Hilker et al. 2007; Mieske et al. 2008; Gregg et al. 2009; Madrid et al. 2010; Chiboucas et al. 2010). These objects, while generally more massive than typical GCs and consequently may have different origins, might be the so-called tip of the iceberg for a large population of free-floating, normal globular clusters.

In fact, a number of extragalactic GC studies over the past few years have strongly suggested the presence of IGCs in nearby galaxy clusters. In the Virgo and Fornax Clusters, serendipitous discoveries of GCs in intergalactic regions using Hubble Space Telescope (HST) imaging (Williams et al. 2007), ground-based imaging (Bassino et al. 2003), and spectroscopy (Bergond et al. 2007) point to the existence of IGC populations. However, it is often unclear whether these GCs are truly intergalactic or are part of the extended halos of cluster galaxies (c.f. Schuberth et al. 2008). A recent study by Lee et al. (2010), however, used data from the Sloan Digital Sky Survey (SDSS) and found statistically significant detections of GC candidates throughout the Virgo cluster. In more distant galaxy clusters, candidate IGC populations have been identified as point-source excesses in HST imaging (Jordán et al. 2003; West et al. 2011).

It is possible that some IGCs and intracluster stars formed in situ, i.e., in cold, intergalactic gas that never accreted onto or was stripped from galaxies. It is also possible that IGCs formed very early and at high efficiencies in dwarf-sized subhalos (e.g., Moore et al. 2006; Peng et al. 2008) and whose host galaxies were subsequently tidally destroyed by interactions with the cluster potential. Another possibility is that IGCs were formed in larger galaxies and were stripped through tidal interactions with the cluster potential or with other galaxies (see, e.g., simulations of Yahagi & Bekki 2005; Bekki & Yahagi 2006).

The formation of the IGC population is obviously linked to that of the ICL, although the observed properties of the two populations may be different. For example, the detectability of the ICL is highly dependent on its surface brightness, whereas IGCs are detectable even in isolation. Simulations by Rudick et al. (2009) show that the ICL is supplied by tidal streams that originally have relatively high surface brightness but then disperse to become fainter and harder to detect. ICL studies using surface photometry are thus more sensitive to recent disruptions, whereas the IGC population is a less temporally biased tracer of the full intracluster stellar population.

The study of extragalactic GC systems has been transformed by the high spatial resolution imaging of the HST, with observations of hundreds of GC systems now in the archives and published literature (e.g., Jordán et al. 2009). HST's deep sensitivity to compact or unresolved sources, and its ability to distinguish background galaxies from likely GCs, makes it an ideal tool for extragalactic GC studies. However, the relatively narrow field of view of HST's cameras and the close proximity of the galaxies being studied (D 100 Mpc) mean that most HST studies have focused on GC systems directly associated with galaxies. Observations of wider fields are usually conducted with ground-based telescopes (e.g., McLaughlin 1999; Bassino et al. 2006; Rhode et al. 2007) that gain area at the cost of spatial resolution.

The Coma cluster of galaxies (Abell 1656) is one of the nearest rich, dense clusters, and is a fundamental target for extragalactic studies. Studies of GC systems in Coma from the ground using surface brightness fluctuations (Blakeslee et al. 1997; Blakeslee 1999) and using HST (Kavelaars et al. 2000; Harris et al. 2000, 2009) all point to large GC systems around the cluster's giant elliptical galaxies, particularly around the central massive galaxy, NGC 4874 (Harris et al. 2009). Although many photometric studies support the existence of an intracluster stellar light component in Coma (e.g., Zwicky 1951; de Vaucouleurs & de Vaucouleurs 1970; Welch & Sastry 1972; Kormendy & Bahcall 1974; Mattila 1977; Melnick et al. 1977; Thuan & Kormendy 1977; Bernstein et al. 1995; Gregg & West 1998; Calcáneo-Roldán et al. 2000; Adami et al. 2005) and even velocities for intracluster planetary nebulae have been measured (Gerhard et al. 2007; Arnaboldi et al. 2007), evidence for or against the existence of IGCs is much more muddled. A search for IGCs in Coma using ground-based data by Marín-Franch & Aparicio (2002, 2003) did not find a surface brightness fluctuation signal that would have hinted at the presence of IGCs, mainly because of the shallow limiting magnitude of their photometry.

At a distance of 100 Mpc, the value we adopt for this paper (m − M = 35; Carter et al. 2008), 1' on the sky subtends 29 kpc in the cluster, and the mean of the GC luminosity function (GCLF) in giant ellipticals is I_Vega = 26.44 mag. This regime of projected areal coverage and GC apparent brightness makes it reasonable to conduct a contiguous survey of the Coma cluster core for GCs, unbiased by the locations of individual galaxies, using the HST Advanced Camera for Surveys (ACS) Wide Field Channel (WFC).

The HST/ACS Coma Cluster Survey is a Treasury Survey originally approved for 164 orbits. One of the main components of this survey was a contiguous ACS/WFC mosaic of the core of the Coma cluster, making it the ideal data set to investigate the existence of intergalactic GCs. Hints of this population have already appeared in studies of UCDs by Madrid et al. (2010) and Chiboucas et al. (2010). This paper presents the first compilation and description of IGCs in the Coma cluster.

The data used in this study are from the HST/ACS Coma Cluster Survey. The survey observations and data reduction are described in detail by Carter et al. (2008), the catalog generation for the public data release is described by Hammer et al. (2010), and an in-depth analysis of galaxy structural parameters and completeness is presented in Balcells et al. (2011). We summarize the relevant information here.

The Coma Cluster Survey, as originally designed, consisted of a large central ACS mosaic of the Coma cluster core, and 40 targeted observations in the outer regions of the cluster. The central mosaic was designed to be 42 contiguous ACS/WFC pointings in a 7 × 6 tiling configuration, and covering a 21' × 18' area. Each pointing is observed in two filters, F475W (g) and F814W (I), with exposure times of 2560s and 1400s, respectively. Unfortunately, the failure of the ACS/WFC (2007 January) meant that only 28% of the survey was completed: 19 pointings in or around the central mosaic, and 6 in the outer regions. Within the core, the central galaxy NGC 4874 was observed, but the other giant elliptical, NGC 4889, was not imaged before the ACS failure. Despite the shortfall, the current observations still provide the largest set of deep, high-resolution imaging available for this important galaxy cluster. Recent studies of compact galaxies in Coma (Price et al. 2009) and spectroscopy of Coma cluster members (Smith et al. 2008) are part of a concerted effort to study galaxy evolution in the Coma cluster built around this HST Treasury survey.

The ACS data reduction was performed using a dedicated Pyraf/STSDAS pipeline that registered and combined images while performing cosmic-ray rejection. The dithered images were combined using Multidrizzle (Koekemoer et al. 2002), which uses the Drizzle algorithm (Fruchter & Hook 2002). For this study, we used the data drizzled for the ACS Coma Survey Data Release 2 (DR2). However, except for Visits 3, 10, and 57, the F814W images on which the bulk of this paper is based are identical to those in Data Release 1 (DR1).

Our images of the Coma cluster reveal a striking amount of detail: cluster members across the mass spectrum, globular clusters, background galaxies, and a few foreground stars. Given the different spatial scales of these objects on the sky, it is important to generate catalogs with detection parameters optimized for the subject under study. For our purpose of studying the globular clusters between galaxies, we used the well-tested Source Extractor software package (Bertin & Arnouts 1996) with parameters optimized for point-source detection, and which are effectively identical to those used by Hammer et al. (2010) in the public data release.²² Photometry was put on the AB magnitude system using the zero points of Sirianni et al. (2005). All magnitudes in this paper are AB unless otherwise specified.

For most visits, the area between galaxies is much larger than that occupied by galaxies and the catalogs can be considered effectively complete to the same level except in the close vicinity of cluster galaxies. The one exception is Visit 19, which contains NGC 4874 and many other ellipticals in the cluster core (Figure 1(a)). This pointing is nearly entirely dominated by the light from one galaxy or another; it is also the one with the highest concentration of GCs. To address this, we implemented an iterative galaxy subtraction algorithm that produced a fully background subtracted image (Figure 1(b)).

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We subtracted the 10 brightest galaxies from Visit 19. We started from the brightest (NGC 4874 itself) and worked to the faintest of the ten. In each case, we first manually masked all the bright galaxies except for the one being subtracted. We then used the IRAF ellipse and bmodel tasks (Jedrzejewski 1987) to model the isophotes of the object galaxy. Because the ellipse fitting only occurs out to a finite radius, the resulting model will have finite extent and the subsequent subtraction will leave a sharp discontinuity in the image. For convenience of object detection, we extended the ellipse-generated models with a power-law fit to the last five data points in the profile at fixed ellipticity. This allowed for a smooth subtraction out to the borders of the ACS image. After subtracting one galaxy, we then repeated the process with the next brightest galaxy on the subtracted image. After the last galaxy was subtracted, we used Source Extractor to create and subtract a background map that removed large scale variations. This last step is important because it allows us to recover from any large scale over- or under-subtractions due to mismatches between the power-law extensions and the true surface brightness profiles of the galaxy. A similar technique was used with success by Jordán et al. (2004) in ACS images of Virgo cluster galaxies, although that was only for single galaxies.

After galaxy subtraction, we generated catalogs with Source Extractor, using variance maps that accounted for the extra Poisson noise expected from the subtracted galaxy light. These catalogs contain objects much closer to the centers of galaxies, and to NGC 4874 in particular. Photometry was obtained by using 3 pixel radius (015) circular apertures with aperture corrections and zero points from Sirianni et al. (2005). Unless otherwise specified, all magnitudes in this paper are on the AB system. These objects are included in the DR2 catalogs of Hammer et al. (2010).

We use artificial star tests to quantify the spatially varying detection efficiency across our images. This is particularly important for the galaxy-subtracted image containing NGC 4874, where the bright galaxy light affects the depth of our observations.

We first use routines in DAOPHOT II (Stetson 1987) to construct an empirical point-spread function (PSF) using bright point sources in Visit 19. At the distance of the Coma cluster, nearly all globular clusters are unresolved with HST and can be well approximated by point sources (the mean half-light radius of GCs, r_h ≈ 3 pc, is only ~6% the full width at half-maximum of the PSF). Because detection is done only in the F814W band, we only add artificial stars to these images.

When adding point sources into the images, we avoid objects in the image as well as artificial stars already placed so as to avoid incompleteness due to confusion. We run the exact same detection pipeline on these images as we do to create our object catalog and record whether the objects were detected as a function of magnitude and position. The number of artificial stars added and measured—7,000,000 in Visit 19 alone and approximately 4240 arcmin⁻² for the other visits—ensures that we can derive a completeness curve for any position in the survey and for any GC selection criteria.

In a typical blank area in our images observed with the full exposure time, the 90% completeness level is at I ≈ 26.8 mag, and the 50% completeness level is at I ≈ 27.3 mag. At R ≈ 2' from the center of NGC 4874, however, these limits are 1.5 mag shallower.

One of the main benefits of GC studies with HST is the ability to use morphology and resolution to separate GCs from their main contaminants, background galaxies. At Coma distances, GCs are point sources when observed with HST, but the great majority of background galaxies are resolved. We use this ability to select against background contaminants and produce a relatively clean sample of GC candidates.

We use a rough but effective concentration criterion to select GCs. Figure 2 shows the "magnitude-concentration" diagram for objects, where we measure a concentration index, C_4–10 using the difference in magnitude measured in a 4 pixel diameter aperture and a 10 pixel diameter aperture. Figure 2 shows that this index works well to distinguish point sources from extended sources. Here, we show the distribution of objects in Visit 19 (the one containing NGC 4874), which has the largest number of GC candidates. We overplot the objects from Visit 59, which is the most remote of our fields and contains mostly background galaxies. The red lines show our selection region where we exclude nearly all of the background galaxies. Although we experimented with different cuts in this diagram, including a variable width of the selection region with magnitude, the variations were not significant and we decided in the end that simplicity was best, choosing a cut of ±0.2 mag around the median concentration for point sources (〈C_4–10〉 = 0.45).

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For the purposes of this study, we wish to maximize the number of good GC candidates, while also balancing the increasing number of background contaminants with magnitude. Because of the depth and high spatial resolution of our data, we chose a fairly conservative magnitude limit, including objects with I < 26.5 mag. At this magnitude, our data is 97% complete in regions free of galaxy light, so completeness corrections are only important toward the centers of galaxies. At the Coma cluster distance (m − M = 35), assuming an extinction A_I = 0.017 mag for NGC 4874 (Schlegel et al. 1998), this limit should include a significant fraction of the GCs in a Gaussian GC luminosity function (GCLF) typical of giant ellipticals. We use the recently measured I-band GCLF measurement for the Virgo cD galaxy M87 (Peng et al. 2009), which was performed with deep HST/ACS observations in the same F814W filter used by the ACS Coma Survey. Peng et al. (2009) quote a GCLF Gaussian mean and sigma of μ_I,Vega = −8.56 mag and σ = 1.37 mag. For AB magnitudes, we add 0.436 mag to μ_I,Vega (Sirianni et al. 2005). Assuming these values for a Gaussian GCLF, our GC catalog magnitude limit should include ~39% of all GCs and ~75% of the luminosity in GCs.

This is likely an oversimplification, however, as both the mean and width of the GCLF is known to vary with galaxy mass (Jordán et al. 2006, 2007). If we assume a Gaussian GCLF typical of dwarf ellipticals in clusters (μ_I,Vega = −8.1 mag and σ = 1.1 mag; Miller & Lotz 2007), then our limit includes ~22% of the total number. This discrepancy is one of the main systematic uncertainties in our analysis. We emphasize, however, that changing the assumed GCLF does not affect the significance of our result, just the inferred total number of GCs. Given that the depth of our data is not sufficient to measure the GCLF parameters directly, we choose to assume the brighter GCLF, seen in giant ellipticals, as this will give us a lower estimate for the number of GCs in any given area. The numbers could be higher by ~80% in regions where the GCLF for dwarf ellipticals is more representative.

We also introduce a broad color cut of 0.6 < (g − I) < 1.5 that should include all old globular clusters. This color range is based on the transformed g–z colors of GCs in the ACS Virgo Cluster Survey (ACSVCS; Côté et al. 2004; Peng et al. 2006) and mainly eliminates distant, compact red galaxies. The ages of extragalactic GCs across all metallicities are primarily old (>5 Gyr), especially those associated with massive early-type galaxies (e.g., Peng et al. 2004; Puzia et al. 2005; Beasley et al. 2008; Woodley et al. 2010), so this color range should include all bona fide GCs.

NGC 4874 has previously been observed to have a large number of globular clusters (Blakeslee & Tonry 1995; Harris et al. 2000, 2009). It has also been shown to have a GC system whose spatial profile is shallower and more extended than those for other elliptical galaxies (Harris et al. 2009). Could the GCs that we see filling the cluster core simply be the extended GC system of NGC 4874? The situation is complicated by the fact that the core of the cluster contains not one but two giant ellipticals, the other being NGC 4889, as well as many other member galaxies.

In Figure 5, we show the radial distribution of GCs in the cluster core, centered on NGC 4874. For each bin in radius, we sum up the number of observed GC candidates in unmasked regions, subtract the expected contribution of GCs from other Coma galaxies (shown as the dotted line in Figure 5), and subtract the global background level (dot-dashed line), leaving what should be the NGC 4874 and IGC population. We determine the mean completeness of the sample within the annulus and extrapolate the total number of GCs assuming the M87 GCLF as described above. We then sum the total observed, unmasked area within the annulus to determine the surface number density of GCs. The random errors in each bin are derived from the Poisson errors for the number of candidate GCs as well as from the Poisson error in the background, added in quadrature.

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This profile, tabulated in Table 1, represents our best estimate of the radial surface density distribution of the GC system surrounding NGC 4874, uncontaminated by the GC systems of other cluster members. Perhaps the most interesting feature of this profile is a marked inflection at R ~ 200 kpc, beyond which the GC surface number density decreases much more slowly with radius. We interpret this flattening of the profile as the region where a large and extended population of IGCs starts to dominate the GCs directly associated with NGC 4874. The significance of this detection is extremely high, as the background level is shown in Figure 5 by the horizontal dot-dashed line at the bottom, with the estimated error of the background denoted as the shaded gray region. The inferred IGC surface density is a factor ~7 over the background. Another point of comparison is with the modeled surface density of remaining unmasked galactic GCs, shown as the dotted line, which also has already been subtracted from our total GC profile. The overall surface density of GCs in this cluster profile is well above the surface density of masked galactic GCs (by a factor 4–7), and thus the GCs we see are likely to be truly intergalactic. We have also found that our results do not change significantly if we only use data from the eastern or western half of the Coma core.

A single Sérsic profile, normally a good fit to the surface density profiles of GC systems, is not sufficient to describe the data for the central Coma cluster GCs. Instead, we fit a model combining a Sérsic profile and a constant. It is likely that the IGCs have a radially decreasing density profile (although the simulations of Bekki & Yahagi 2006 suggest that they can also have a flat density distribution within the central few hundred kiloparsecs), but the data only allow us to measure their mean surface density. The solid line in Figure 5 traces the best-fit model, and the dashed line that follows it until large radii is the best-fit Sérsic component. The fitted surface density of IGCs is 0.055 ± 0.002 kpc⁻², which is a 19σ detection over the background, 0.00845 ± 0.001 kpc⁻², assuming Poisson random errors. As we discuss in Section 4 and Appendix A.3, we also need to account for systematic uncertainties from our modeling, but they do not affect the main conclusion, which is high significance of the detection. We list the best-fit parameters in Table 2.

Although we cannot determine the shape of the IGC component's density profile, one constraint is that it must fall rapidly after the limits of our data. The mean distance of the three fields we are using to measure the background is shown as the vertical arrow at 1.3 Mpc. Therefore, the GC surface density must fall to zero, or at least the level of the dashed line, by this distance. A steep falloff like this favors a low n Sérsic profile for the IGCs (n = 1–2), similar to the ICL profiles in Seigar et al. (2007) and X-ray gas in galaxy clusters (Demarco et al. 2003), but lower (i.e., steeper in the outer regions) than dark matter halo density profiles (Merritt et al. 2006). However, at these radii, it may not make as much sense to speak of a circularly symmetric GC radial profile and it would be more useful to map in two dimensions the spatial distribution of GCs.

We use our radial spatial density profile to estimate the total number of GCs in the cluster core, which we define to be the extent of our data. Integrating this profile for R < 520 kpc gives a remarkable 70000 ± 1300 GCs, with the IGC component dominating the GC population beyond 150 kpc. As listed in Table 2, the number of GCs belonging to NGC 4874's "Sérsic component" out to this radius is ≈23, 000, leaving a remaining 47, 000 ± 1600 (random) ⁺⁴⁰⁰⁰₋₅₀₀₀ (systematic) to be IGCs. There are over twice as many IGCs as there are GCs from the Sérsic component, resulting in an IGC fraction of the entire central GC system of ~70%.

With a measurement of NGC 4874's luminosity, we can calculate an "intrinsic" specific frequency for the galaxy. Harris et al. (2009) use a luminosity of M_V = −23.46 (adjusted to D = 100 Mpc), but surface brightness profiles from SDSS imaging (J. Lucey 2010, private communication) and KPNO 4 m CCD imaging (R. Marzke 2010, private communication) show the galaxy to be substantially brighter. Measurements of the total r-band luminosity from mosaicked SDSS frames gives a value of r = 10.23 (M_r = −24.77, assuming E(B − V) = 0.009 from Schlegel et al. 1998), which includes a 0.32 mag extrapolation using the best-fit Sérsic profile for the light beyond R = 7'. The mean color of the galaxy is g − r ≈ 0.8 mag, which produces M_V = −24.47 using the Lupton 2005 transformation derived by matching SDSS photometry to Peter Stetson's published photometry for stars.²³

With this, we calculate an "intrinsic" specific frequency for NGC 4874 of S_N = 3.7 ± 0.1 (the errors are purely from the total numbers of GCs and do not include errors in the luminosity).²⁴ This value is very much in line with the those of non-cD, giant early-type galaxies in the Virgo and Fornax clusters.

If we assume that all GCs (including IGCs) are part of the NGC 4874 system and that we are not missing any luminosity from the galaxy, then this would give the specific frequency within 520 kpc a higher value of S_N = 11.4 ±  0.2, a value similar to those measured for some cD galaxies. Another interpretation, which we discuss later, is that the specific frequency of the system is the lower, more normal value, but that the IGCs are tracing a large amount of intracluster starlight that is unaccounted for.

A relevant comparison for the GCs is to the surface brightness profile of the field starlight of NGC 4874. In Figure 6, we plot the light profile in circular apertures around NGC 4874 from two independent data sets (with arbitrary normalization). As mentioned in the previous section, the first is from measurements using SDSS r-band imaging (J. Lucey 2011, in preparation) and the second uses imaging from the Mosaic-I camera on the KPNO 4 m telescope (R. Marzke 2010, private communication). Both profiles are in good agreement in the inner regions (R < 20 kpc), but start to diverge in the outer regions due to differences in the sky measurements. The difference between the two profiles is at the level of 2% of the sky.

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In the regions beyond 100 kpc, we also plot the surface brightness profile of the "intracluster background light" in the Coma cluster as determined photographically by Thuan & Kormendy (1977), transforming from $\mathcal {G}$ to r magnitudes using an offset of $(\mathcal {G}-r)=0.37$ mag, based on a (B − V) = 0.7 mag, their published transformation from $\mathcal {G}$ to Thuan–Gunn r (Thuan & Gunn 1976), and then an offset to SDSS r (Fukugita et al. 1995). This profile appears to match the SDSS photometry at R ~ 100 kpc but then continues with a shallower slope.

It is clear that at large radii (R>100 kpc), the determination of the sky is crucial to the measurement of the ICL. To illustrate this, we shade in the regions corresponding to a change in sky determination of ±2% of the sky level around the KPNO and SDSS measured profiles. Although there is no evidence for a "break" in the measured surface brightness profiles akin to what we see in the GCs, the surface brightness profile in the regions where IGCs dominate GC counts is entirely dependent on the determination of the sky level to better than 1% and thus is difficult to quantify.

We can use these profiles to calculate the "local" specific frequency of the outer GCs, although any calculation is highly uncertain due to sky subtraction for the surface photometry. Nevertheless, we can take these surface brightness profiles at face value to see if the calculated values are reasonable. Assuming that the surface brightness at R = 200 kpc is μ_r ≈ 26.2 mag (following the Thuan & Kormendy profile) and using V − r = 0.2 mag for old metal-poor stellar populations, then μ_V(200 kpc) ≈ 26.4 mag. Given the IGC surface density at these radii (46 arcmin⁻²), we estimate S_N(200 kpc) = 5. If we assume the profile derived from SDSS data, however, then μ_V(200 kpc) ≈ 27.5 mag, resulting in S_N(200 kpc) = 13. We emphasize that the surface photometry is extremely uncertain at these radii and the upper error bar on this number is essentially unconstrained. The local values of S_N at these kinds of radii have previously been reported to be quite high (Tamura et al. 2006 in M87 and Rhode & Zepf 2001 for NGC 4472), but those measurements are equally uncertain for similar reasons.

In the inner regions, there is a notable divergence between the GCs and the galaxy light. The galaxy does not show the prominent core within 10 kpc that the GC system does, only displaying a flattening in the profile at a smaller radius.

Perhaps the most relevant local comparison for the NGC 4874/Coma cluster GC system is that of M87 in the Virgo cluster. In Figure 7, we show the GC radial surface density profiles of the two GC systems. The outer M87 profile is taken from the data of McLaughlin (1999) and Tamura et al. (2006), while the central regions of the profile are from the ACSVCS data shown in Peng et al. (2008). We note that the physical resolution of the Coma HST data is very competitive with ground-based Virgo observations (01 resolution at Coma distance is equivalent to 06 resolution at Virgo distance), but obviously cannot match the ACSVCS observations of M87. None of the Virgo data sets go as far out in physical radius as our Coma data, but they still provide a useful comparison. The two GC systems profiles are similar in the range of intermediate radii (20–100 kpc), but differences appear in the very inner and outer regions. Most noticeably, the Coma GC systems display a very pronounced core within 10 kpc, which does not appear to be present in the Virgo system except perhaps within 1 kpc. This deficit of GCs at the center of NGC 4874 is also evident in the analysis of Harris et al. (2009). This core could be the result of dynamical friction destroying GCs at the center of NGC 4874.

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The core in the GC profile, and the divergence from the M87 GC profile, is most evident within 10 kpc. Could this be due to unaccounted observational incompleteness? The four innermost radial bins (R < 3.5 kpc) have the largest errors and shallowest observations because of the bright galaxy light (completeness of the GCLF is ≈25% in these bins). There are multiple reasons, however, why we believe these lower surface densities to be real. The radius at which the core becomes apparent, 20'', is large for HST imaging. Even excluding the inner 10'' (4.8 kpc), the difference in slope between the two GC profiles is still apparent. Also, the completeness tests we apply also take into account incompleteness due to imperfect profile subtraction and thus is a true measure of the completeness in these radial annuli. In order to turn the M87 GC profile into the Coma GC profile through a systematic overestimation of the completeness, the completeness would have to be overestimated by nearly an order of magnitude. Lastly, this deficit of GCs relative to the galaxy light profile was also independently found by Harris et al. (2009) using HST/WFPC2 data (see their Figure 6).

In the outer regions the M87 profile follows the single-Sérsic fit out to the limits of the data. The Virgo data, however, only reaches a radius of 130 kpc, and thus would not be sensitive to the kind of IGC population we see in Coma. In fact, if the Coma data had the same physical radial extent, it would have been very difficult to detect the IGC population. More deep, wide-field imaging of the area around M87, such as the Next Generation Virgo Survey,²⁵ will be necessary to detect or place more stringent limits on a population of IGCs in Virgo.

For old GCs, the broadband color is an indicator of metallicity. The color distributions of extragalactic GC systems have been studied extensively with HST (e.g., Larsen et al. 2001; Peng et al. 2006) and are often bimodal in nature (Gebhardt & Kissler-Patig 1999), especially in massive early-type galaxies. In Figure 8, we plot the color distribution of bright GCs (applying a magnitude limit of g < 25 mag for higher signal-to-noise ratio (S/N)) in the unmasked regions of the Coma cluster core. The color distribution of all GCs shows the typical bimodality seen in extragalactic GC systems, displaying a prominent peak of blue (metal-poor) GCs with (g − I) ≈ 0.9 and a red (metal-rich) peak with (g − I) ≈ 1.15.

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We plot the color distributions divided by distance from the center of NGC 4874—those within 50 kpc (galactic GCs) and those outside of 130 kpc (predominantly IGCs). We use the Kaye's Mixture Model (KMM; McLachlan & Basford 1988; Ashman et al. 1994) implementation of the expectation-maximization (EM) method to fit two Gaussians with the same standard deviation to the GC color distributions of each sample. Both the galactic and intergalactic GCs are much better described by bimodal distributions in color than by a single Gaussian with p-values less than 0.001. The inner blue GCs, however, have a much redder mean color—(g − I) = 0.94 as opposed to (g − I) = 0.89 for GCs in the outer regions—such that they are nearly merged with the red GCs (g − I) = 1.18. The metal-poor GCs are either quite red or there is a substantial population of GCs at intermediate color. It could also be the sign of a significant radial color gradient within the blue GC subpopulation (e.g., Harris 2009; Liu et al. 2011). This gradient could be in metallicity or in age, reminiscent of younger metal-poor GCs in Local Volume dIrr galaxies (Sharina et al. 2005; Georgiev et al. 2008, 2009), although the colors of the blue GCs are not so blue as to require very young ages. The inner regions also have equal numbers of blue and red GCs where the fraction of red GCs is f_red = 0.51.

The generally red colors of the inner GCs was noted by Harris et al. (2009), who used their WFPC2 data to show that the inner regions of the GC system had a high (50%) fraction of red GCs. Using the larger ACS coverage of our survey, however, we see that the total GC system around NGC 4874 is dominated by blue GCs. In the outer sample plotted in Figure 8, the IGC population is dominated by blue GCs with a blue-to-red ratio of 4:1, (f_red = 0.2) although the fraction of red GCs is still significant. Even measuring only the Sérsic component of the GC subpopulations, the NGC 4874 GCs are dominated by blue GCs, with the red GCs being more spatially concentrated. The radius at which the surface density of blue and red GCs are equal is R ≈ 40 kpc. Thus, like the giant ellipticals in the Virgo cluster (Peng et al. 2008), the GC system of NGC 4874 as well as the IGC population, is dominated by blue GCs.

The mean colors of the blue and red outer GCs are (g − I) = 0.89 and 1.22, respectively. The blue peak has a typical color for the GC systems of galaxies with masses at or below L* (Peng et al. 2006). The red peak, however, is still fairly red, having nearly the same mean color as the inner GCs around NGC 4874. We caution that some of these red GCs may be from the large metal-rich GC system of NGC 4889 and other more massive cluster members.

We can do a simple test to see if the red GCs beyond 130 kpc are associated with luminous galaxies. We calculate the distance from each GC to the nearest luminous (M_B < −17) galaxy and compare the mean shortest distance for the red and blue GCs. We find that there is no significant difference between these two populations. The median shortest distance for red GCs is 75'' and that for blue GCs is 74'', with the biweight Gaussian sigmas of each distribution being 35''. The spatial behavior of the red and blue GCs beyond 130 kpc are identical and is consistent with a population of IGCs mostly uncorrelated with nearby galaxies.

The existence of intracluster starlight and globular clusters has for decades been considered important, but always difficult to observe. Recently, as observations have improved and theory has shown that intracluster stellar populations are an essential feature of galaxy–galaxy and galaxy–cluster tidal interactions, there is increased interest in quantifying its properties: total mass, spatial distribution, metallicity, and kinematics. We have shown that with HST, a direct detection of IGCs is a clean way to measure one component of intracluster stellar populations in nearby galaxy clusters.

Only a small fraction of the total or stellar mass is in the form of old globular clusters. The total mass fraction in GCs appears to be relatively constant across galaxies and galaxy clusters (McLaughlin 1999; Blakeslee 1999). Because of the variation in the stellar mass-to-light ratio across galaxy mass, however, the specific frequency (or stellar mass fraction) can vary widely. Massive ellipticals and dwarf galaxies can have the highest S_N, and galaxies with luminosities around L* have the lowest S_N. The stellar mass fraction in early-type galaxies ranges from ~0.2% to a few percent (Peng et al. 2008).

We do not know the fraction of stellar mass that is in the form of IGCs, but we can make reasonable assumptions. One possibility is that the IGCs originate from low-mass dwarf galaxies that are tidally disrupted. The S_N of such a population can vary and can depend on the clustercentric radius (Peng et al. 2008), but if we assume that dwarfs in the cluster center will have high specific frequencies, then we can reasonably assume S_N,IGC = 8, which is similar to the S_N values for high-S_N dEs at the center of the Virgo cluster (Miller & Lotz 2007; Seth et al. 2004; Peng et al. 2008), the GC systems of even lower mass dwarfs (e.g., Puzia & Sharina 2008), and for Virgo cluster IGCs (Williams et al. 2007).

Such a value for the specific frequency of the IGC population would imply a total ICL luminosity within 520 kpc of M_V = −24.4 mag, an amount of starlight equal to the whole of NGC 4874. Spread out uniformly over this entire area, this luminosity would have a mean surface brightness of μ_V,ICL = 27 mag arcsec⁻², which is still challenging for surface photometry, but detectable in the best observations (Mihos et al. 2005). If we assume M/L_V = 1.7, a value typical of cluster dEs, then this corresponds to a stellar mass of $\mathcal {M}_{{\rm ICL}}\approx 9\times 10^{11} \;\mathcal {M}_{\odot }$.

Assuming a lower specific frequency like S_N,IGC = 1.5, as is more common for L* early-type galaxies or low-S_N dEs and dS0s in the outskirts of the Virgo cluster, would imply a higher luminosity for the ICL. Conversely, assuming a very high specific frequency like that in M87 or the highest S_N dwarfs, S_N,IGC = 12, would imply a lower ICL luminosity. The inferred ICL luminosities, surface brightnesses, masses, and central ICL fractions for these three assumed values of S_N,IGC are listed in Table 3. These values bracket the range of "local" S_N we calculate from the outer surface brightness profiles of NGC 4874 in Section 5.3. Deeper, systematically controlled photometry of the intracluster region will be the best way to set a meaningful limit on the S_N of the IGC population.

Table 3. ICL Luminosity, Surface Brightness, Mass, and Fraction (R < 520 kpc) as a Function of S_N,IGC

SN,IGC	MV,ICL	μV,ICL	$\mathcal {M}_{{\rm ICL}}$	$\frac{\mathcal {L}_{{\rm ICL}}}{(\mathcal {L}_{N4874+{\rm ICL}})}$
	(mag)	(mag arcsec−2)	($10^{11} \;\mathcal {M}_\odot$)
1.5	−26.2	25.2	50	0.8
8	−24.4	27.0	9	0.5
12	−24.0	27.4	6	0.4

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We have also calculated these values using the total luminosity in GCs, which is more robust than the total number because most of the luminosity in GCs is brighter than the mean of the GCLF (Harris 1991). Using typical values for the stellar luminosity fraction (0.2%–1.2%) from Peng et al. (2008), we arrive at very similar numbers to those in Table 3.

All of these inferred luminosities and masses are larger than those previously inferred from direct measurement of the low surface brightness ICL in Coma. Both Gregg & West (1998) and Adami et al. (2005) estimate a value of M_R ≈ −22, which for an old stellar population is roughly M_V ≈ −21.5. However, their values were the result of combining the luminosities of individual ICL sources. The 1% detection limit of the Adami et al. (2005) study is quoted as μ_V = 25.8, which is much shallower than what is required if S_N,IGC 2. It is likely that these previous studies were sensitive to overdense regions in the ICL, but not to the overall population of intracluster stars.

When considering only the IGC and NGC 4874 GC system (equivalent to BCG+ICL measurements), we find that the IGCs make up ~70% of the total "central" GC system. Although more difficult, we can also estimate the IGC fraction for all GCs in the cluster core, including the GCs belonging to cluster member galaxies. We do this in two ways. First, we can calculate this number only for those areas that we have observed. We assume the IGC surface density to be the fitted value in Table 2. We can subtract the surface density of IGCs from our data and what remains is the "galactic" GC population in the observed areas. Using this metric, we find that roughly ~30% of the observed GCs belong to the intracluster population. This number does not account for the GCs close to galaxies that were missed by our detection algorithm, so it can be considered an upper limit over the area observed.

The main drawback of limiting to the observed area, however, is that we do not observe large portions of the cluster core, including the other massive elliptical, NGC 4889. Another method is to apply the GC system modeling previously described to estimate the total number of GCs within 520 kpc that belong to galaxies. When we do this, we find that the IGCs make up ~45% of the GCs in the Coma cluster core (this fraction is higher because our observed area includes NGC 4874, depressing the IGC fraction). This number is naturally more uncertain because a large fraction of the galaxies are unobserved.

Given the assumptions in the previous section, we can infer that approximately half of the stellar luminosity associated with the "central" system (NGC 4874 and the ICL) is in the ICL. Because the ICL is likely to be more metal-poor and have a lower mass-to-light ratio than the stars at the center of NGC 4874, this translates to about one-third of the stellar mass being in the ICL. We would expect that the IGC fraction should be higher than the ICL fraction, because most of the stellar mass is in L* galaxies that have low S_N, whereas the specific frequency of the IGC population is likely to be high. This is why we find that the IGC fraction of the "central" system is ~70%, but that the likely ICL fractions in Table 3 are closer to 50%.

All of these numbers imply a high ICL fraction in the cluster, but are consistent with expectations from observations and simulations for the core of a massive, rich cluster such as Coma (e.g. Willman et al. 2004; Sommer-Larsen et al. 2005; Yang et al. 2009; Puchwein et al. 2010). Seigar et al. (2007) find a central ICL fraction of 60%–80% around cD galaxies, and Purcell et al. (2007) expect similar ICL fractions from simulations of tidal stripping.

Previous studies of extragalactic GC systems have also suggested that there is a roughly constant ratio between the total number or mass of GCs in a system and the total dynamical or baryonic mass (e.g., Blakeslee 1999; McLaughlin 1999; Peng et al. 2008; Spitler & Forbes 2009). If this is the case, than the IGC fraction may be more representative of the total mass fraction in the diffuse component of the galaxy cluster.

Both theory and simulations suggest that an intracluster stellar component is a natural result of many physical process that shape galaxies in the cluster environment. Galaxy–galaxy tidal interactions (e.g., Gallagher & Ostriker 1972; Moore et al. 1998; Stanghellini et al. 2006), tidal forces as galaxies orbit through the cluster gravitational potential (e.g., Merritt 1984; Gnedin 2003), tidal "preprocessing" within infalling galaxy groups (Rudick et al. 2006), tidal destruction of low mass galaxies (Lopez-Cruz et al. 1997), and tidal tails that escape from merging galaxies (e.g., Murante et al. 2007) are all plausible mechanisms to liberate stars and GCs from the gravitational potential of their host galaxy. The problem is in trying to distinguish between these mechanisms and determine what combination produces the observed intracluster stellar populations.

Based on previous ICL studies in Coma, the specific frequency of the IGC population is not likely to be very low, otherwise its associated ICL would already have been detected at relatively high S/N. One straightforward possibility is that the GCs originate mainly from disrupted dwarf galaxies, which can have high specific frequencies. Dwarf galaxies, having low masses and surface mass densities, are prone to be destroyed by interactions with other galaxies and with the cluster potential. If we assume S_N,IGC = 8, then the inferred IGC population would require the disruption of ~2300 dwarf galaxies with M_V = −16.

Simulations suggest, however, that the ICL originates from stars in L* galaxies rather than from dwarfs (Willman et al. 2004; Bekki & Yahagi 2006; Purcell et al. 2007) and that a significant fraction of the ICL is first liberated in dynamically cold streams possibly thrown off from merger remnants (Rudick et al. 2009). ICL production mechanisms that depend on galaxy–galaxy interactions appear to be able to produce the right amount of intracluster mass (early calculations by Gallagher & Ostriker 1972 of stars stripped from L* galaxies during close encounters predicted that the total ICL mass in the Coma cluster should be approximately $10^{12} \;\mathcal {M}_\odot$, a number quite close to what we infer from the IGCs).

Galaxy–galaxy harassment, however, is expected to produce a more centrally concentrated IGC/ICL component than, for instance, interactions from with the mean cluster tidal field (Merritt 1984), because the cross section for galaxy–galaxy interaction is strongly peaked at the cluster center. We unfortunately cannot determine the full spatial density profile of the IGCs as our observations only reach R = 520 kpc. What we do measure in the IGC dominated regime (150 < R < 520 kpc), however, is consistent with a flat profile and shows no sign of being very centrally concentrated.

Early-type galaxies near L* have a nearly universally low specific frequency, with S_N ≈ 2 (Peng et al. 2008). If these kinds of galaxies were entirely disrupted to supply the necessary IGCs, it would imply a relatively high ICL surface brightness. What is more likely is that it is predominantly the halos of these galaxies that are stripped, and that the stellar halos have higher local S_N. A prediction of this scenario would be the presence of a large number of intermediate-luminosity galaxies in the cluster core that have relatively few GCs and compact GC systems. These galaxies might be detectable as outliers in the color–magnitude relation for early-type galaxies.

The color distribution of the IGCs also provides a clue. Although the IGCs are mostly blue, 20% of the IGCs are still red. This appears contrary to the simulations of Bekki & Yahagi (2006), which predicted a single metal-poor peak for the GCs with few metal-rich IGCs. The red IGCs we observe have a mean color consistent with the red GC populations found in the more massive early-type galaxies rather than in the dwarfs (Larsen et al. 2001; Peng et al. 2006). The fraction of red IGCs is also slightly higher than that in dwarfs. For Virgo early-type dwarfs with M_V −18, the mean fraction of red GCs is only 10%, and many have zero red GCs. Producing this many red IGCs solely from the disruption of low mass galaxies would be difficult. Stripping of GCs from the halos of more massive galaxies (M_V ≈ −19) might be a more natural mechanism for producing the IGC population, although the stripping could not be too efficient, otherwise the ICL might be too red (c.f. the blue ICL color seen in Virgo by Rudick et al. 2010).

Mergers of these galaxies could also cause some metal-rich GCs to escape into intracluster space, although we are not able to differentiate between merging and stripping. Dissipational merging, with star formation, could also produce IGCs within gaseous tidal tails (e.g., Knapp et al. 2006), although for this mechanism to be important it would have to happen early in the formation of the cluster.

Although it is likely that dwarf galaxy disruption does play a role in supplying IGCs, the non-negligible fraction of red IGCs indicates that stripping and merging of intermediate-mass galaxies contributes a significant fraction of the population. Unfortunately, we do not currently have sufficient data to derive the full spatial profile of the IGC population itself, which would help determine the originating galaxy population, differentiate between merging, galaxy–galaxy interactions, and galaxy–cluster interactions, and also test whether the IGC radial density follows the overall mass density. More ACS imaging within the core and at larger radii would be extremely useful for this purpose.

We first generate masks around bright galaxies in and around all of our fields. We define masked galaxies to be those with 200'' of an ACS field center and with g₀ < 18 (M_g < −17) as observed in the SDSS Data Release 6 (DR6) catalog. To be conservative, we choose all galaxies that meet these criteria, although nearly all at these bright magnitudes are cluster members. We are required to use a catalog external to our ACS survey because some large galaxies not observed by ACS, but just off the edge of a field, can contribute GCs to our observations.

For each galaxy, excluding the two giants NGC 4874 and 4889, we use as a crude measure of galaxy size the radius that encloses 50% of the Petrosian light (R_p.50). After experimenting with various mask sizes, we liberally mask an area corresponding to a circular aperture with a radius of 8R_p,50. For a Sérsic profile with n = 2, this would mask 99% of the galaxy light. Even if the GC systems were twice the size of the galaxies, this would still mask ~92% of the GC system. For three of the larger galaxies, the SDSS sizes are not reliable, so we manually adjusted the mask size. For NGC 4889, IC 4045, and 4908 we used mask radii of 230'', 68'', and 160'', respectively.

For NGC 4889 in particular, the GC system is so large that a simple masking will not eliminate the contribution of its GCs. This is also the case for a few other bright galaxies. There is also the possibility that smaller but more numerous GC systems from the many dwarf galaxies in the cluster are contributing to the observed distribution of GCs. To account for this, we have simulated the composite GC distribution we would expect from the known galaxies in Coma.

We start with the Coma cluster galaxy catalog of Eisenhardt et al. (2007), who published UBVRIzJHK_s photometry for Coma galaxies covering a region well matched to our cluster core mosaic. For this purpose, their catalog is superior to the SDSS data because Eisenhardt et al. (2007) specifically measured photometry of the Coma galaxies, many of which are too large for the SDSS pipeline to handle properly. Their catalog is complete to M_V < −16 mag and extends to M_V < −14 mag. We use their Tables 1 and 2 as the basis for our simulated GC systems. We assume that each galaxy in their catalog has a GC system that is circularly symmetric and has a radial number density distribution that follows a Sérsic (1968) profile with index n = 2, which is a good fit to the GC spatial density profiles of the Virgo giant ellipticals M87 and M49. The one exception to this is NGC 4889, for which it seems clear from Figure 3 that its associated GC systems are not spherical. For this galaxy, we assume that the spatial density distribution follows a Sérsic profile along the geometric mean radius, $\langle r \rangle = \sqrt{ab}$, where a and b are the major and minor axes, respectively. The ellipticity of NGC 4889 is = 0.379 (Jorgensen et al. 1992), although we find that its GC systems are better described with higher ellipticity and use = 0.6. For this galaxy, we do not need to model its GCs but can use the observed radial distribution of GCs from the WFPC2 observations of Harris et al. (2009).

We then estimate the GC specific frequency, S_N, for each galaxy based on its absolute V magnitude, M_V. We use a linear interpolation of the Virgo early-type galaxy S_N data presented in Table 3 of Peng et al. (2008), giving us an estimate of the total number of GCs in each galaxy. Although we do not make any adjustments for morphological type, most cluster members in the core are early types similar to the galaxies analyzed in Peng et al. (2008), and early types also generally have higher S_N than late-types.

Lastly, we determine an effective radius, R_e, for the GC system, also assuming that it scales with galaxy M_V. We used a second-order polynomial fit between R_e and M_V in which GC systems of more luminous galaxies are larger. We derived this relation using the GC systems of 100 Virgo cluster galaxies observed in the ACSVCS (Côté et al. 2004; Jordán et al. 2009). This survey observed early-type galaxies with a wide range of luminosities (−22 < M_B < −15). The spatial density profiles were fit with Sérsic profiles to derive the effective radius of the GC systems as a function of galaxy luminosity. The details of this relation and its derivation will appear in a subsequent paper (E. W. Peng et al. 2011, in preparation). The spatial extent of GC systems is generally larger than that of the stars and is consistent with previous measurements showing that the local S_N for giant ellipticals increases with galactocentric radius. With this estimate of R_e, we can then infer the contribution of GCs from galactic systems as a function of position in the central mosaic of observations.

Using the same spatial grid shown in Figure 4, we estimate the total number of GCs expected in each cell from all of the galaxies in the Eisenhardt et al. (2007) catalog (not including NGC 4874). We correct this number for the total observed area—accounting for unobserved and masked area—and the local GCLF completeness. For each cell, we thus have an estimate of the total number of observed GCs that could be contributed by the GC systems of known cluster galaxies.

We then use this simulated distribution of GCs to statistically subtract the contribution from "galactic" GCs. In each cell, we sample a Poisson distribution about the expected value, and then assign each GC a random position in the cell. Additionally, we mask regions around all the known galaxies, as described above, with the results shown in Figure 9. We do expect that some galactic GCs will contribute to the apparent intergalactic GC population, especially GCs from the other gE, NGC 4889, but the expected number and spatial distribution of the galactic GCs (i.e., concentrated around the galaxies) do not agree with the spatial uniformity and overall large numbers of GCs observed throughout the cluster core.

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We also note that although our modeling of GC systems only extends to galaxies with M_V < −14 mag, this is unlikely to bias our final result. While it is true that S_N does tend to rise at lower luminosities, and some individual dEs have high S_N, the mean value is not very high. As shown by Miller & Lotz (2007) and Peng et al. (2008), dEs and dSphs have a very wide range of S_N, with some being high but many others quite ordinary or near zero. The mean S_N for dwarfs in the magnitude range that concerns us is ~2. Studies of Local Group dwarfs show that at fainter than a certain luminosity (M_B ≈ −10), dSphs do not appear to have GCs.

The technique we use to account for the unmasked galactic GCs introduces a systematic uncertainty into our analysis. We can quantify this effect by varying the assumed parameters over a wide range of acceptable values. We detail this in this section, but our main point is that our conclusions are not particularly sensitive to the specific parameters assumed for the modeling of galactic GC systems, because if Coma early-type galaxies have the same range of specific frequencies as Virgo early-type galaxies, then there are simply not enough galactic GCs to account for all the GCs that we observe.

We have produced a range of plausible galactic GC populations, varying the Sérsic n index of the assumed profiles, the effective radius, R_e, and the specific frequencies of the galaxies, S_N. By varying the Sérsic index from n = 1.0 to n = 4.0 (exponential to de Vaucouleurs), the inferred number of IGCs varies from 47, 000 to 44, 000. The exponential profile is steepest in the outer regions and so gives the highest estimate for the IGC population. If we assume that all galactic GC systems have the shallower outer profiles of a de Vaucouleurs profile, then our inferred IGC population is smaller by ~3000 GCs. This effect is only at the peak-to-peak level of 6%–7% and is small enough to justify our choice of a single Sérsic index for our GCS models. A single n = 2 model gives us an inferred population of 46, 500 IGCs, so we take the systematic error here to be (⁺⁵⁰⁰_−3,000).

By varying the specific frequency, we affect the total number of galactic GCs. Our modeling uses the S_N–L relationship from Peng et al. (2008). Although there is no evidence that S_N for normal galaxies is different in the Coma cluster, we can make the assumption that S_N is systematically different from Virgo by ±20%. Doing so would change the number of IGCs by ±2000. This does not appreciably alter the significance of the detection. We include this in the systematic error budget.

We can also test the dependence of inferred IGC numbers on the effective radii of the GC systems. We can assume that the R_e of GC systems in Coma are a factor of two larger or smaller for a given galaxy luminosity than for their counterparts in Virgo (a fairly extreme assumption). If the GC systems are larger, the number of unmasked galactic GCs is increased and the number of IGCs will go down. Using this assumption in our modeling, the total number of IGCs changes by ±3000. Once again, the overall effect on the significance of our detection is rather small.

Given that our systematic errors are comparable to or larger than our Poisson errors (which are at the level of ±1600 GCs), it is important to include these in the error budget. Nevertheless, it is clear that the details of the modeling do not affect the conclusion that there is a significant detection of IGCs in the Coma core. By combining the estimated errors independently and in quadrature, we estimate that there is a combined systematic error of ⁺⁴⁰⁰⁰₋₅₀₀₀ IGCs. The inferred number of IGCs is thus 47, 000 ± 1600 (random) ⁺⁴⁰⁰⁰₋₅₀₀₀ (systematic).

There are three outer ACS fields that we do not use for our background estimate because they are near larger Coma galaxies. Assuming that these fields have few or no IGCs, they present the opportunity to test the validity of our methodology. This test is not ideal, because NGC 4839 is a giant elliptical galaxy that is the dominant member of its subgroup, and our assumptions are most valid when we can average over many galaxies rather than be dominated by a luminous single galaxy. Nevertheless, we can apply the technique used to model the core region and check for consistency. Similar to NGC 4889, for which there are published measurements and no need to infer from scaling relations, we use the known S_N for NGC 4839 (Marín-Franch & Aparicio 2002), although for every other parameter and for all other galaxies in the region, we use our scaling relations. We take the same approach to modeling and masking as was done in the core, although since the Eisenhardt et al. (2007) catalog does not cover this region, we use an equivalent cut with SDSS. For each field, after subtracting the modeled GC population and the estimated background from the total counts, we should expect to have numbers statistically equivalent to zero. For these three fields, we obtain residual counts of 13 ± 9, 3 ±  11, and 10 ±  13, where the errors do not include the systematic errors as discussed above. We can assume that the systematic errors contribute roughly equally (or more) to the error budget. These numbers are satisfyingly consistent with zero, within the random and systematic errors. The predicted values do skew positive (with large errors), but this is likely a reflection of our systematic error, and is consistent with what we discuss in Appendix A.3. Over three fields, the residual is marginally significant over random errors, 26 ± 19 or when corrected for the full GCLF, 0.007 ± 0.005 kpc⁻². This is still 8× smaller than our measured IGC surface density, so any systematic residual at this level would not affect the significance of our measurement. Even if we were to adjust our model to increase the predicted number of GCs so as to match these fields, the impact on our result and the IGCs numbers would be small and within our quoted errors. Thus, we are reassured that our GC subtraction procedure and estimation of our uncertainties is robust.