Figure 3 shows a plot of H_{0} determinations using globular clusters over the past 30 years. Perhaps the most interesting aspect of this plot is the relative constancy of both the mean value (H_{0} = 72 km s^{-1} Mpc^{-1}) and the scatter (10 km s^{-1} Mpc^{-1}). While it would be silly to use this mean as an estimate of the Hubble constant, in a sense the scatter is probably a reasonable representation of the external errors, since it is dominated by the different assumptions that go into the calculation rather than the observational data themselves. This is probably why the scatter is nearly constant, although the observational precision has improved dramatically over the past 30 years. The quoted uncertainties appear to be relatively good estimates since they roughly match the scatter in the diagram.
Figure 3. Estimates of H_{0} based on the GCLF. Includes Sandage (1968), Racine (1968), de Vaucouleurs (1970, 1977), Hanes (1979), van den Bergh, Pritchet, & Grillmair (1985), van den Bergh (1985), Geisler & Forte (1990), Harris et al. (1991), Jacoby et al. (1992), Sandage & Tammann (1995), Baum et al. (1995), Whitmore et al. (1995), Forbes (1996a, b), Sandage & Tammann (1996), and Whitmore (1996). |
Until very recently the best available data set for estimating the Hubble constant was the study of the four Virgo galaxies NGC 4365, NGC 4472, NGC 4486, and NGC 4649 by Harris et al. (1991), and van den Bergh, Pritchet, & Grillmair (1985). These observations, which go roughly one mag past the turnover, led to estimates of H_{0} from 55 km s^{-1} Mpc^{-1} by Sandage and Tammann (1995) to 70 km s^{-1} Mpc^{-1} by Harris (1991).
The HST observations of the GCLF in M87 by Whitmore et al. (1995) reach more than two magnitudes beyond the turnover and provide a more secure exclusion of background/foreground objects. The position of M87 in the core of the Virgo cluster is another advantage. The resulting estimates for the Hubble constant range from H_{0} = 62 ± 9 km s^{-1} Mpc^{-1} by Sandage and Tammann (1996) to H_{0} = 78 ± 11 km s^{-1} Mpc^{-1} by Whitmore et al. (1995).
These two cases, which use the same data sets but result in an 25% spread in H_{0}, demonstrate that the major uncertainties are in the precepts made for the calculation (i.e. the local calibrators, expansion velocities, and extinction) rather than the intrinsic dispersion in the GCLF (i.e. 6% in distance estimation).
5.1. A new estimate of H_{0} using the Fornax cluster
Perhaps the best current estimate of the Hubble constant can be made using the seven galaxies (12 measurements) in the Fornax cluster. The weighted mean from Table 1 yields a value of m_{V} = 23.80 ± 0.07 mag. The compact size of the cluster makes the uncertainty due to position in the cluster negligible. In addition, the extinction is small (A_{V} = 0.00 mag; Burstein & Heiles 1984). HST observations of GCLFs for several galaxies in the Fornax clusters should supplement this sample in the near future.
The appropriate expansion velocity has not been as well studied for the Fornax cluster as for the Virgo cluster. Using V_{Fornax} = 1420 km s^{-1} (Freedman 1996), and M^{0}_{V} = -7.21 ± 0.26 mag (Section 3.1), yields a distance modulus m - M = 31.01 ± 0.27 mag and a Hubble constant H_{0} = 89 km s^{-1} Mpc^{-1}. If we use V_{Fornax} = 1398 km s^{-1} (Sandage & Tammann 1993) we find H_{0} = 88 km s^{-1} Mpc^{-1}, and for V_{Fornax} = 1338 km s^{-1} (Jerjen & Tammann 1993) the value is H_{0} = 84 km s^{-1} Mpc^{-1}.
Another approach is to offset from the Fornax cluster to the Coma cluster, assuming _{Virgo-Fornax}(m - M) = 0.00 ± 0.15 mag (see de Vaucouleurs 1993, Jerjen & Tammann 1993, Kohle et al. 1996, Blakeslee & Tonry 1996, Table 1), and _{Coma-Virgo}(m - M) = 3.71 ± 0.10 mag (see 3.4), and a velocity of the Coma cluster of 7188 km s^{-1} with an assumed uncertainty due to peculiar velocities of ± 250 km s^{1} (Lauer and Postman 1994). This leads to H_{0} = 82 ± 13 km s^{-1} Mpc^{-1}. For the present we consider this last estimate the most reliable, since a careful study of the peculiar velocity of the Fornax cluster remains to be done. Again, the main uncertainty is the Cepheid distance to the Virgo cluster and the Cephied zeropoint, both of which should improve in the near future.