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 < MV >= −7.41 ± 0.11, σ(MV ) = 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 < MV >= −7.48 ± 0.11, σ(MV ) = 1.08 mag, h3 = 0.05± 0.05, and h4 = 0.13± 0.05. Subject headings: globular clusters: luminosity function