A MAXIMUM-LIKELIHOOD ANALYSIS OF GLOBULAR-CLUSTER LUMINOSITY DISTRIBUTIONS IN THE VIRGO ELLIPTICALS

We have formulated a model to represent globular cluster luminosity functions (GCLFs) in distant galaxies by means of maximum-likelihood statistics. This model simultaneously accounts for the presence of a contaminating background population, incompleteness at faint magnitudes, and photometric measurement error. We apply this model to observational data sets for the three Virgo giant elliptical galaxies NGC 4365, 4472, and 4649, to derive accurate new values for the GCLF peak and dispersion. With a Virgo core distance modulus of (m-M)V = 30.95 +/- 0.25, we obtain GCLF turnover luminosities for the three gEs as follows: M(V)0 = -7.12 +/- 0.36 and sigma(t) = 1.52 +/- 0.13 (NGC 4365), M(V)0 = -7.03 +/- 0.27 and sigma(t) = 1.30 +/- 0.07 (NGC 4472), and M(V)0 = -7.18 +/- 0.27 and sigma(t) = 1.15 +/- 0.07 (NGC 4649). Accordingly, the unweighted average of these GCLF parameter estimates are [M(V)0] = -7.11 +/- 0.3 and [sigma(t)] = 1.32 +/- 0.09. Comparing with similar maximum-likelihood parameter estimates for M31 and the Milky Way, we obtain mean differences DELTAM(V)0 = -0.31 +/- 0.33 mag and DELTAsigma(t) = -0.36 +/- 0.13 mag, in the sense that the GCLFs in the giant ellipticals are slightly less luminous at the turnover but with significantly large functional dispersion.