SPECIFIC FREQUENCIES OF GLOBULAR-CLUSTERS IN ELLIPTIC GALAXIES - A NEW TEST OF THE EXTRAGALACTIC DISTANCE SCALE

The specific frequencies of globular clusters in elliptical galaxies, S, being the ratio of their (extrapolated) total number, N(t), to the absolute luminosity of the galaxy, depend on the adopted distance scale. If the distance is derived from the redshift and some assumed value of h = H/100, the optimum value, h(m), may be derived for a sample of normal E galaxies covering a sufficient range of distances by finding the value of h (or of log h) which minimizes either the dispersion sigma(S) or sigma(log S) or, better, the relative dispersion F(S) = sigma(S)/[S]. Application to a sample of nine E galaxies for which Harris and van den Bergh calculated S for h = 0.50, 0.75, and 1.00, gives H(m) = (85 +/- 4) km s-1 Mpc-1. This is also the value which optimizes the agreement between the different methods and minimizes [S] = 4.7 +/- 0.7. The mean Hubble ratio predicted by the original short scale (EDS VII) for the same nine objects was [H*] = 87 +/- 3 (Appendix A). Because all nine objects are in the north Galactic hemisphere where the apparent Hubble ratio is known to be about 20%-30% less than in the south Galactic hemisphere, the corresponding all-sky average could be as high as H = 95, in close agreement with the short-scale value. An alternative use of the errors by means of linear relations and correlation coefficients with the Hubble modulus HM makes little difference to the solutions. The frequency function of 28 solutions is very nearly Gaussian with mode [H(m)] = 86 +/- 2 and dispersion sigma(H(m)) = 12 (Appendix B). A suggestion to use weighted means is tested, but although agreeing in the mean (84.5 +/- 6) with the unweighted solutions, it leads to a much larger scatter and is contraindicated (Appendix C). A larger, more precise and more homogeneous collection of counts, magnitudes, and extinction corrections over a bigger range of distances will be necessary to better evaluate the errors and potential precision of the method.