GLOBULAR CLUSTER SYSTEMS IN BRIGHTEST CLUSTER GALAXIES: A NEAR-UNIVERSAL LUMINOSITY FUNCTION?

In this paper, we present the first results of photometry for GCs in seven BCG galaxies, all of which are examples of the largest galaxies that exist in the present-day universe. Each of these was already known from previous deep ground-based imaging to contain a rich GC population (Harris et al. 1995; Bridges et al. 1996; Blakeslee et al. 1997). Our targets, listed in Table 1 in order of increasing distance, were imaged during program GO-12238 (PI: Harris) with the exception of the F814W exposures for the three European Space Observatory (ESO) galaxies, which came from program GO-10429 (PI: Blakeslee). The table lists in successive columns the galaxy ID, the Abell cluster for which it is the central BCG, coordinates, redshift of the galaxy cz normalized to the cosmic background (CBR) reference frame, apparent distance modulus, foreground extinction (from NED on the Landolt scale), and V-band luminosity, where V_T is taken from NED. All the foreground extinctions are small and have no effect on the following analysis. Throughout the following discussion, we adopt a distance scale of H₀ = 70 km s⁻¹ Mpc⁻¹. The uncertainties in the conversion to the CBR frame and possible motion of the BCG relative to the Abell cluster center may make the true cz differ by up to ∼400 km s⁻¹, or 0.05–0.10 in distance modulus depending on distance.

Table 1. Basic Parameters for BCGs in the Survey

Galaxy	Cluster	R.A.	Decl.	cz	(m − M)I	AI	$M_V^T$
				(km s−1)
NGC 7720	A2634	23:38:29	+27:01:53	8714	35.61	0.107	−23.35
NGC 6166	A2199	16:28:38	+39:33:06	9125	35.60	0.017	−23.7
UGC 9799	A2052	15:16:44	+07:01:18	10500	35.95	0.056	−23.1
UGC 10143	A2147	16:02:17	+15:58:29	10741	35.99	0.047	−23.0
ESO509-G008	A1736	13:26:44	−27:26:22	10848	36.06	0.079	−23.35
ESO383-G076	A3571	13:47:28	−32:51:54	11832	36.24	0.082	−24.1
ESO444-G046	A3558	13:27:57	−31:29:44	14345	36.65	0.075	−23.8

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The primary camera for all targets was the Advanced Camera for Surveys (ACS)/Wide Field Camera (WFC), with the Wide Field Camera 3 (WFC3) being used in parallel; exposures in both cameras were through the F475W and F814W filters. In choosing these targets, to save orbits we took advantage of the long exposures in F814W of the three ESO galaxies that were already in the HST archive. The luminosities of these giant galaxies are comparable with or even higher than the two brightest BCGs whose GC systems have previously been studied to similar depth, namely, NGC 4874 in Coma and NGC 4696 in Centaurus (Harris 2009a).

In Table 2, we summarize the raw exposure data for the ACS/WFC pointings, including the total exposure times and the limiting magnitudes that resulted. Two or more orbits were used for each filter, subdivided into sequences of half-orbit exposures. The total exposures were designed to reach a limit in absolute magnitude close to the expected GCLF turnover point at M_{V, 0} ≃ −7.3, M_{I, 0} ≃ −8.4 and thus to secure the largest possible GC sample sizes within the limits of the program.

Preprocessing consisted of CTE correction on the raw images (Anderson & Bedin 2010), and then use of the standard Multidrizzle package to generate a combined image in each filter that kept the native pixel scale of 005.

Photometry was carried out with the standard tools in SourceExtractor (Bertin & Arnouts 1996) and DAOPHOT (Stetson 1987) in its IRAF implementation, including aperture photometry (phot) and then point-spread-function (PSF) fitting through allstar. All PSFs were empirically generated from stars on the target fields, with anywhere from 60 to 160 individual stars on each frame. Finding bright, isolated candidate PSF stars was easily done, since our targets are all moderately high-latitude fields that are completely uncrowded in any absolute sense.

Each target galaxy was found, as expected, to be surrounded by many thousands of clusters. Virtually all of the individual GCs appear starlike: since our target systems are in the distance range 125–205 Mpc, a typical GC effective radius of ∼3 pc corresponds to an angular size in the range 0003–0005, far below the 01 resolution of the telescope and safely in the "unresolved" category according to the criteria in Harris (2009a). The direct advantage for our photometry is that the GCs are therefore easily distinguished from the faint, nonstellar background galaxies that constitute the main source of sample contamination.

In the last column of Table 2, we also give the radial range $R(\rm min) - R(\rm max)$ from galaxy center covered by the ACS field. This R(max) is determined both by the distance to the galaxy and its placement relative to the center of the ACS/WFC field of view. The innermost radii sampled for any of the galaxies are typically ∼20 arcsec, corresponding to R(min) ∼ 10–20 kpc depending on distance; at smaller radii, the object detection and photometry are more severely limited by the higher surface brightness of the central galaxy. These numbers show that the bulk of our GC sample is drawn from the mid- to outer-halo regions of these supergiant galaxies.

The calibration of our data is in the VEGAMAG system, and uses the most recent filter-based zeropoints given on the HST webpages to define the F475W and F814W natural magnitudes. For the purposes of the present discussion and ease of comparison with previous work (e.g., Harris et al. 2006; Harris 2009a), we use conventional (B, I) magnitudes converted from (F475W, F814W) defined by the transformations in Saha et al. (2011). Using the reddening corrections for each galaxy from the NED database (listed in Table 1), we convert the preliminary color–magnitude distributions to absolute magnitude M_I and intrinsic color (B − I)₀.

Figure 1 shows the color–magnitude diagrams for all seven galaxies. The huge GC populations around each one are evident, and to first order the distributions in luminosity and color are similar. To quantify the limits of the photometry, we carried out an extensive series of artificial star tests on every field through daophot/addstar. The limiting magnitudes quoted in Table 2 (not de-reddened and in the natural filter-based VEGAMAG scale) for each field and filter are the levels at which the artificial star tests show that the completeness of detection falls to 50%. At levels ≳ 0.5 mag brighter, the completeness approaches 100%. We find that within the radial range R ≳ 20 kpc that contains the vast majority of our measured GCs, the surface brightness of the BCG itself has fallen to low enough levels that the limiting magnitudes do not depend noticeably on R. As noted above, crowding effects are also negligible in this same radial range. It is worth noting that this situation is in strong contrast to imaging of much closer galaxies such as the Virgo members at d ≃ 16 Mpc (e.g., Peng et al. 2008), where the ACS field of view covers a maximum radius of only R ∼ 10 kpc and the surface brightness gradient of the central galaxy across the detector is more of a concern.

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In Figure 2, we show the trend of photometric measurement uncertainties for each galaxy, plotted as a function of absolute magnitude M_F814W ≃ M_I. The exposure times were planned to yield fairly uniform limits in absolute magnitude, so these curves are similar for all galaxies in the sample. As will be seen below, the uncertainties in the F814W magnitudes are ≲ 0.1 mag for all levels brighter than the GCLF turnover, implying that the ≃ 1.3 mag intrinsic width of the GCLF is negligibly broadened by photometric scatter.

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Any field contamination of the GC samples is due to sparsely distributed foreground stars and a few very small, faint unresolved background galaxies. To gauge the level of contamination, we used the offset WFC3 fields, placed on relatively galaxy-free locations in the outskirts of the galaxy cluster. After the same photometric procedure, rejection of nonstellar objects, and rejection of objects with extreme colors (see below), we found that the residual contamination (and thus its effects on the measured GC LFs) was negligible at any level brighter than the limiting magnitudes of the survey.

The CMDs generally show evidence for broad bimodal or multimodal distributions in the GC colors. A more extensive discussion will be given in following papers that concentrate on the color–magnitude and spatial distributions.

To reduce the contamination of our sample, we select only objects within the dereddened color range 1.0 < (B − I)₀ < 2.3. A cutoff at the blue end eliminates any objects bluer than the minimum metallicity known for GCs ([Fe/H] < −2.5) (see Harris 2009a). Translation from (B − I)₀ to metallicity [Fe/H] here assumes the linear relation (B − I)₀ = 2.158 + 0.375 [Fe/H] (Harris et al. 2006). The red end cut is based on empirical increase of contaminants in the parallel background fields, which are more frequent at colors redder than the GC sequences. In the case of ESO444, we have also cross-correlated our objects with the catalog of nucleated dwarf galaxies identified by John Blakeslee in program GO-10429. We found only four objects in common and eliminated those. The 002 angular resolution limit above which we could reliably identify nonstellar objects (see Harris 2009a) corresponds to a linear resolution of ∼20 pc at the average distance of our BCG targets. This limit is not low enough to distinguish many or most UCDs from luminous GCs, so our sample is likely to include some UCDs at the high-L end (see the discussion in Section 4).

Figure 3 shows the resulting GCLFs for each of the seven BCGs. At the lowest plotted luminosity, L_I = 10⁵ L_☉ (which is closely similar to the fiducial GCLF turnover luminosity), three systems are complete to at least 50% at that level and the others are essentially complete to ∼100%.

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We fit a log-normal (Gaussian in log L) distribution to the GCLF in the I band

$$\begin{equation} {dN \over d\log {L}} = N_{0}\, \exp {\left[ -{(\log {L}-\log {L_0})^{2} \over 2\sigma _{L}^{2}}\right]}, \end{equation} \tag{ 1 }$$

for clusters within a chosen range L_min < L_I < L_max described below. (NB: by log  we denote logarithm base-10.) To convert M_I to L_I, we adopt M_I(☉) = 4.08. The free parameters are the turnover (peak) luminosity L₀ and the Gaussian dispersion σ_L, while N₀ is constrained by the total number of clusters.

We bin the data evenly spaced in log L and, for consistency, we use the same bin size for all seven systems in the survey. We have experimented with varying the bin size from 0.01 dex to 0.1 dex and calculated the average χ² per number of degrees of freedom (n_dof) of individual galaxy fits. It is defined as

$$\begin{equation} \chi ^2 = \sum _i {(N_{i,\rm obs} - N_{\rm exp}(L_i | L_{0},\sigma _{L},N_{0}))^2 \over (\Delta N_{i,\rm obs})^2}, \end{equation} \tag{ 2 }$$

where N_{i, obs} is the observed and completeness-corrected number of clusters in bin i, N_exp is the expected number from the fitting function above, and $\Delta N_{i,\rm obs} = N_{i,\rm obs}^{1/2}$ is the Poisson counting uncertainty. The number of degrees of freedom is the number of bins minus 3, accounting for L₀, σ_L, and N₀. The minimum χ²/n_dof occurs at δlog L = 0.02 dex, which we adopt for our analysis. This choice also results in a statistically optimum number of bins $\approx N_{\rm tot}^{1/2}$.

Limiting the range of luminosity for constraining the fit parameters is necessary because at low L the cluster counts are incomplete in both B and I, and at high L the log-normal function does not account for any superluminous clusters that form an extended tail to the LF (see Section 4 below). We have varied log L_min (in Solar units) from 5.0 to 5.3 in steps of 0.1, and calculated χ²/n_dof for each system. Values of 5.1 and 5.2 gave similar fits for most galaxies, and therefore we adopt log L_min = 5.1 to include more clusters in our analysis. This limit is also conservatively brighter (by about 1 mag) than the I-band completeness limit of the photometry, but is near the B-band limit for the reddest GCs. For one system (ESO509) we found that lowering log L_min to 4.7 gave the most robust fit.

The upper L_max to the fitted range is determined by an iterative procedure. First, we set L_max → ∞ and find the best-fitting log-normal function for all clusters above L_min. Given this fit, we define L_max as the limit above which the integrated GCLF predicts only 10 clusters:

$$\begin{equation} \int _{L_{\mathrm{max}}}^{\infty } \frac{dN_{\rm exp}}{dL} \, dL = 10. \end{equation} \tag{ 3 }$$

The number 10 was chosen based on empirical comparison with the high-L tail of the observed GCLF so that small number statistics in the uppermost L bins would not unduly influence the fit. Integrating Equation (1) gives an explicit non-linear relation for L_max:

$$\begin{equation} N_{0}\, \sigma _{L}\, \sqrt{\frac{\pi }{2}}\, \mathrm{erfc}{\left(\frac{\log {L_{\mathrm{max}}}-\log {L_0}}{\sqrt{2}\, \sigma _{L}}\right)} = 10. \end{equation} \tag{ 4 }$$

For a given combination (L₀, σ_L, N₀), we solve this equation numerically and use the new value of L_max to repeat the GCLF fit. This process is iterated until L_max varies by less than 1%. The values of L_max are determined for each system individually. Clearly, L_max is not a fixed boundary because it will be higher for galaxies with larger total populations N₀. However, defining it this way ensures that we will be fitting the fiducial Gaussian function over the luminosity range where the number of clusters per bin is satisfactorily large. In Figure 1, we show the adopted L_min and L_max levels for each galaxy.

The best-fit parameters (L₀, σ) for individual fits to each GC system are listed in Table 3. The 68% confidence error bars, Δlog L₀ and Δσ_L, are calculated at Δχ² = 1. The table also lists the de-reddened 50% completeness limits L_{I, lim}, which are fainter than our adopted lower cut for all systems. The fraction of missing (undetected) clusters between L_min and the peak of the GCLF, L₀, relative to that expected from the fit, ranges between 18% and 29%. We conclude that our samples are complete enough in the chosen luminosity range for accurate fitting to be carried out.

Table 3. Luminosity Function Parameters

Galaxy	N(LI > L0)	NSL	log Lmax	log LI, lim	log L0	Δlog L0	σL	ΔσL	χ2/(ndof)	$\chi ^2_{\rm g} /(n_{\mathrm{dof}})$	PKS, g
NGC 7720	4372	16	6.73	4.7	5.15	0.04	0.52	0.02	105/(79)	121/(74)	0.011
NGC 6166	6043	10	6.81	4.7	5.09	0.04	0.55	0.02	96/(83)	119/(78)	0.0007
UGC 9799	4765	18	6.85	4.9	5.26	0.02	0.51	0.01	74/(85)	69/(80)	0.91
UGC 10143	3674	24	6.79	5.0	5.25	0.03	0.52	0.02	83/(82)	77/(77)	0.29
ESO509-G008	2857	18	6.72	4.6	5.07	0.03	0.58	0.02	116/(99)	97/(75)	0.86
ESO383-G076	5217	29	6.84	4.7	5.30	0.02	0.49	0.01	93/(84)	74/(79)	0.72
ESO444-G046	7083	24	6.97	4.8	5.34	0.02	0.49	0.01	165/(91)	115/(86)	0.023
All (global fit)			7.14		5.24	0.01	0.52	0.01	204/(100)

Notes. (1) N_SL is the observed number of "superluminous" objects with L_I > L_max. (2) L_max is the luminosity above which the log-normal fit predicts 10 clusters (see the text). (3) L_{I, lim} is the 50% completeness limit. (4) L₀, σ_L, and χ² of the log-normal fit are calculated in the luminosity range from 10^5.1 L_☉ to L_max, with the individual value of L_max for each galaxy. (5) $\chi ^2_{\rm g}$ and P_{KS, g} of the global fit are calculated over the range L₀–L_max.

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The observed number of clusters above the peak (shown in the second column in the table) can be roughly doubled to estimate the total expected population of the GC system, assuming the log-normal GCLF is symmetric. The total number of clusters per galaxy therefore ranges from about 6000 to over 14,000. The currently detected number of GCs above the 50% completeness limit for all seven systems is 47,910 and the number of clusters above L_I = 10⁵ L_☉ is 43,783. This sample represents the largest single data set of GCs in the literature, an order of magnitude larger, for example, than the total number of GCs brighter than the turnover in the Virgo survey (Jordán et al. 2007).

Table 3 also lists the χ² of the Gaussian fit and the number of degrees of freedom, n_dof. For each system, the ratio of the two is between 0.87 and 1.8, which indicates that the log-normal is an appropriate fitting function for these largest GC systems.

The values of peak luminosity and the width for the seven systems are remarkably similar to each other; unweighted direct means of the two quantities are 〈logL₀〉 = 5.21 ± 0.04 and 〈σ_L〉 = 0.52 ± 0.01. The observed rms scatter in log L₀ is ±0.10 dex; the expected ∼0.03 dex scatter due simply to distance uncertainties (see Section 2 above) does not contribute significantly to that. In short, we have no evidence that the seven LFs differ systematically from each other in any major way.

To further examine this universality, we combine the clusters from all seven galaxies and perform a global log-normal fit to this combined sample. For consistency, we keep the same lower limit L_min, but calculate L_max as described above. The last row of Table 3 lists the parameters of this global fit: log L_{0, g} = 5.24, σ_{L, g} = 0.52 dex. As expected, they fall in the middle of the range for the individual systems and are not significantly different from the unweighted mean values. The best-fit dispersion is equivalent to σ_g = 1.30 mag.

Figure 4 shows the confidence intervals of the global fit parameters. As was pointed out long ago by Hanes & Whittaker (1987), the two parameters of the fit are partially correlated if (as is the case here) the data do not reach clearly fainter than the turnover point (the true L₀). Thus, for example, an overestimated σ leads to a fainter estimated L₀. Nevertheless, the extremely large statistical size of our database allows us to determine the parameters fairly precisely.

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In the second last column of Table 3, we quantify how well this global GCLF matches each individual system by evaluating the goodness of fit $\chi ^2_{\rm g}$ (without solving for the parameters separately, but simply adopting log L₀ = 5.24 and σ = 0.52). The fit is calculated in the range of luminosity between L_{0, g} and each galaxy's L_max. We find that the quality of the global fit is scarcely worse than the fits optimized to each individual galaxy. Last, we also perform a Kolmogorov–Smirnov (KS) test and calculate the probability P_{KS, g} (calculated over the same range as $\chi ^2_{\rm g}$ and listed in the last column) that the observed cluster samples were drawn from the same global distribution. Table 3 shows that at least six systems have P_{KS, g} > 1%, which means they are not inconsistent with the universal GCLF. We note, of course, that these P_{KS, g} values cannot be as large as similar ones calculated one-by-one (where we would be testing only the hypothesis that each individual LF adequately matches the log-normal model). The KS probability is low for one galaxy (NGC 6166), primarily because of the somewhat steeper downturn of the LF at high luminosities.

In summary, we find that our data for these seven galaxies are consistent with a "universal" lognormal GCLF shape for BCG-type systems. Visually the global fit is indistinguishable from the individual fits. The red lines in Figure 3 overplot the global fit on the histograms of observed cluster numbers, adjusting only the normalization to the actual size of the GC system.

Several comparisons can be made for GCLF fits in other giant ellipticals. Peng et al. (2009), using the same F814W bandpass for extremely deep HST data around M87, find log L₀ = 5.06 ± 0.02 and σ_I = 0.55 ± 0.02 dex with an excellent fit to a log-normal model (see their Figure 8). Harris et al. (2009) studied the GCLFs of the Coma cluster galaxies and for a composite LF of five gE's found σ_L = 0.59 dex, log L₀ ≃ 5.0 (transformed from the V band), and again a good match to the log-normal model. These Coma data do not have as large a total GC sample and do not reach quite as faint in absolute magnitude as our present BCG sample, so the correlation noted above between the turnover point and dispersion may partly explain why the fitted L₀ is a bit fainter and σ_L a bit broader than we find.

The seven BCGs studied here can be added to the trends of GCLF turnover and dispersion with host galaxy luminosity, as defined from the many lower-luminosity galaxies in Virgo and Fornax (Villegas et al. 2010). The results are shown in Figure 5. In the top panel, $M_{\star }^{\rm gc}$ is the GC mass corresponding to the GCLF turnover luminosity, calculated with a stellar mass-to-light ratio from the Into & Portinari (2013) relations. For the Virgo and Fornax galaxies imaged with HST/ACS, the (g − z) color index was used, whereas for the seven BCGs the color index is (B − I). The error bars in $M_{\star }^{\rm gc}$ for the BCGs (for which only the bright half of the GCLF is measured) are inevitably larger than for the much nearer Virgo and Fornax members (for which almost the entire run of the GCLF was measured and the turnover is more precise). The trend derived by Villegas et al. (2010) is Δσ/ΔM_z = −0.10 ± 0.01; it is clear that the BCGs continue this trend smoothly upward.

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The lower panel of Figure 5 shows the same trend for the GCLF dispersion. Both parameters are plotted against galaxy stellar mass $M_{\star }^{\rm gal}$, again derived from the Into & Portinari (2013) color–(M/L) relations. Again, the BCGs continue upward along very much the same trend defined by the smaller galaxies. In both panels, weighted best-fit lines are shown for an assumed linear relation (solid line) and a quadratic relation (dashed line); these are scarcely different, and in either case indicate that the BCGs belong to the same family as other smaller galaxies.

The GCLF dispersion σ has also been measured for various giant galaxies at distances ∼100 Mpc and beyond from surface brightness fluctuation analysis. Though this method is not strictly comparable to fully resolved photometry of GCs, the results are consistent with the data listed above. Blakeslee et al. (1997), from a ground-based imaging survey of BCGs, determined 〈σ_L〉 = 0.57 dex (1.42 ± 0.02 mag) for 14 such galaxies with low internal uncertainties on σ. Overall, an empirical picture emerges in which the intrinsic width of the GCLF (for large galaxies) is consistently in the range σ_L = 0.52–0.55 dex.

We have also briefly investigated how the GCLF might change with projected galactocentric distance R. In Figure 6, the best-fit solutions for turnover luminosity L₀ and dispersion σ_L are plotted against R in kiloparsecs. For each galaxy the R range was broken into eight to nine rather narrow zones, a subdivision that was permitted by the very large statistical sample sizes (the relative numbers of clusters in each zone are indicated by the error bar sizes in the upper panel of the figure). We note that although formal solutions were carried out for the regions R ≲ 20 kpc, these should be given little weight: in these inner zones the numbers of clusters per bin are ≲ 100 with few faint GCs, and the gradually increasing background light from the central galaxy begins to affect the limiting magnitude of the photometry particularly in the F814W band.

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In the range R ≳ 20 kpc, the limiting magnitudes remain uniform (see discussion above) and the (L₀, σ_L) fits are more reliable. In all seven galaxies, a consistent pattern for L₀ to decrease weakly with R is evident, with an estimated power-law slope L₀ ∼ R^−0.2. The best-fit dispersion, however, remains nearly constant with R at σ_L ≃ 0.4. For comparison, the "global fit" for the dispersion, summing over all radii, is the somewhat larger value of σ_L ≃ 0.5. Given that L₀ shows a shallow dependence on R, the solutions within very restricted radial zones are expected to give smaller σ than the global average.

Regarding GCLF dependence on halo location, not much exists in the previous literature as a basis for comparison. In most cases, the GCLF has been quoted as a single solution for the GC population over the entire galaxy, or measured over a relatively small radial range determined by detector size so that systematic changes in R are not easy to see. In addition, few GCLF studies penetrate outward to the very large galactocentric distances that we have studied here. However, for the Milky Way, the analysis of Harris (2001, see particularly Figure 40 and Table 9 therein) does show a shallow outward decrease of the GCLF turnover luminosity for R ≳ 6 kpc, with a very similar dependence L₀ ∼ R^−0.2 to that found for our BCGs. By contrast, Tamura et al. (2006) and Jordán et al. (2007) find little change in the turnover luminosity out to R ∼ 40 kpc for the Virgo giant M87. Bassino et al. (2008) similarly find no strong change in L₀ over 8–60 kpc for the Antlia giants NGC 3258 and 3268.

The simplest interpretation of a gradient in L₀ is a similarly shallow trend in mean GC mass, but L₀ is also influenced by other factors such as metallicity and dynamical evolution. The latter possibility seems unlikely, since dynamical evolution processes should be relatively ineffective at such enormous distances in the halo at reshaping the GCLF (Gnedin & Ostriker 1997; Fall & Zhang 2001b; Vesperini 2001). However, the shallow downward gradient may at least partly be explained as a byproduct of a metallicity gradient in the GC system. That is, in many large galaxies the mean GC metallicity decreases outward (e.g., Geisler et al. 1996; Rhode & Zepf 2004; Bassino et al. 2006; Harris 2009a, 2009b; Liu et al. 2011). When we couple this trend with the observation that the GCLF turnover also becomes fainter in the smaller galaxies in which almost all the GCs are metal-poor (Jordán et al. 2007; Villegas et al. 2010), then we would expect to find a net decrease in L₀ going further outward into the progressively more metal-poor halo (and if this argument is correct, a steeper metallicity gradient in the GC system should go along with a steeper gradient in L₀). However, for a fixed mean GC turnover mass, the I-band luminosity of the turnover is almost independent of metallicity (see the models of Ashman et al. 1995). A possible implication of the trend we see is therefore that the metal-richer GCs should be systematically more massive than the metal-poor ones. These issues will be discussed more completely in a later paper containing the metallicity distribution function measurements more explicitly.

As a final point in this section, we can ask how valid is the Gaussian LF model in the first place. This simple (two-parameter) and extremely well-known functional form has been used as a quick and convenient descriptor of the GCLF for many decades, but it does not clearly result from any underlying physical theory for the formation and evolution of a globular cluster system (GCS). Other simple forms have been tried, the most notable of which is probably the "evolved Schechter function" introduced by Jordán et al. (2007) to fit the GCLFs in the Virgo galaxies. Harris et al. (2009) applied it to the Coma giants as well. This function is asymmetric and thus is preferable as a match for the entire luminosity range of GCLF because the GCLF is observed to decline more steeply on the faint side of the turnover L₀ than on the much more easily observable bright side. It also makes a logical link to the dynamical evolution of the GCS where an assumed initial power-law LF changes into the present-day form by preferential destruction of the lower-mass clusters (e.g., see the discussions of Vesperini 2001 and Jordán et al. 2007). However, for the great majority of cases in the literature (see Harris et al. 2013 for a catalog), the range L > L₀ is the only part covered by the observations, and over this high-luminosity range both functions do well at matching the empirical data (see Harris et al. 2009 for a specific comparison in the Coma cluster galaxies). More importantly, for the present discussion, either functional form leads to our major conclusion that the present-day GCLFs in BCG systems have a near-universal shape.