4.4 Calibration

The calibration of the method reduces, in essence, to determining the absolute turnover magnitude M₀ and GCLF dispersion independently in as many galaxies as possible, with the Milky Way GCLF as the fundamental starting point. We do not suppose that either M₀ or are ``universal'' (identical) in all galaxies, although such assumptions were sometimes made of necessity in the earlier history of the subject. The basic requirement of the method is simply that the shape parameters (M₀, ) must behave regularly along the Hubble sequence of galaxies, i.e., that they do not differ unpredictably between galaxies of the same type.

The full job of calibrating the GCLF self-consistently is not yet complete, though much recent progress has been made. For the GCLFs in giant ellipticals, the dispersion falls consistently in the range 1.4 ± 0.1 magnitudes (Harris et al. 1988b; Geisler and Forte 1990; Harris et al. 1991). For the Local Group galaxies (the Milky Way, M31, and the dwarf ellipticals), a smaller value 1.2 ± 0.2 provides a better match, but the samples (particularly in M31) need to be improved and augmented further; see Harris (1991), Racine (1991), and Reed et al. (1992).

For the fundamental calibrating GCLF sample in the Milky Way, the turnover luminosity is at M_B⁰ = -6.8 ± 0.17. In M31, the turnover may be ~ (0.2 ± 0.2) mag more luminous, depending on the exact Local Group distance scale adopted and also on the still-uncertain degree of incompleteness in the faint half of the M31 halo cluster sample (Racine 1991; Reed et al. 1992). Among four Virgo giant ellipticals including the high-specific-frequency M87 system (van den Bergh et al. 1985; Harris et al. 1991), the intrinsic differences in M₀ from galaxy to galaxy are ± 0.2 mag or less. A direct match between M₀(spirals) and M₀(ellipticals) has not yet been made, e.g., by comparing the GCLFs in elliptical and disk galaxies that are known beforehand to be in the same group and thus at the same distance from us to the necessary precision. However, on elementary external grounds, for any distance scale H₀ in the range 50-100 km s^-1 Mpc^-1 the difference M₀ between the Local Group Sb spirals and the Virgo giant E's must be less than half a magnitude (Harris 1987b, 1991). The essential argument is shown in Figure 8, which contains the currently measured M_B⁰ values for 13 galaxies of all types: four Local Group dwarfs, M31, and the Milky Way (Harris 1987b; Harris et al. 1991); two large ellipticals in the Leo group, NGC 3377 (Harris 1990) and NGC 3379 (Pritchet and van den Bergh 1985b); NGC 1399 in the Fornax cluster (Geisler and Forte 1990; Bridges et al. 1991); and the four Virgo ellipticals mentioned above (van den Bergh et al. 1985; Harris et al. 1991). For the five giant E's, the values plotted in the figure assume Fornax and Virgo distances corresponding to H₀ = 75. The near-constancy of the turnover magnitude over more than a factor of 4000 in parent galaxy luminosity is remarkable; excluding the four dwarfs, the unweighted average from the nine remaining large galaxies is < M_B⁰ > = -6.6 with an rms scatter of ± 0.26 magnitude.

Figure 8. Estimated turnover luminosities MB0 for 13 galaxies, plotted against total galaxy luminosity. The filled circles include six Local Group members (the Milky Way, M31, and the four dwarfs: NGC 147, 185, 205, and Fornax), plus the Leo ellipticals NGC 3377 and 3379, whose distance of d = (10 ± 1) Mpc is well established by the PN and SBF techniques (Ciardullo et al. 1989; Tonry et al. 1989). The open circles include four Virgo members (NGC 4365, 4472, 4486, 4649) and the central giant elliptical in the Fornax cluster, NGC 1399; note that for these, we assume d = 17 Mpc to derive the distances and turnover luminosityes.

Refining the trend of M₀ with parent galaxy type will require cluster photometry in several more galaxies with independently established distances (see below). The zeropoint of the GCLF luminosity scale depends primarily on the Population II RR Lyrae scale which sets the distances to the Milky Way globulars. It then depends secondarily on near-field extragalactic standard candles including Cepheid and RR Lyrae variables (for M31).