A GAUSS-HERMITE EXPANSION OF THE GALACTIC GLOBULAR-CLUSTER LUMINOSITY FUNCTION

We decompose the luminosity function of Galactic globular clusters into a sum of the orthogonal Gauss-Hermite functions. This method quantifies the asymmetric third-order (h3) and symmetric fourth-order (h4) terms of the distribution while minimizing the effect of outliers in the data. For 138 Galactic globulars we obtain [M(v)] = -7.41 +/- 0.11, sigma(M(v)) = 1.24 mag, h3 = 0.02 +/- 0.05, and h4 = 0.06 +/- 0.05, i.e., the core of the distribution does not differ significantly from a Gaussian. For a low-metallicity subsample of 103 globular clusters with [Fe/H] < -0.8, we find [M(v)] = -7.48 +/- 0.11, sigma(M(v)) = 1.08 mag, h3 = 0.05 +/- 0.05, and h4 = 0.13 +/- 0.05.