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 ($h_3$) and symmetric fourth-order ($h_4$) terms of the distribution while minimizing the effect of outliers in the data. For 138 Galactic globulars we obtain $ =-7.41\pm0.11$, $σ(M_V)=1.24$ mag, $h_3=0.02\pm 0.05$, and $h_4=0.06 \pm 0.05$, {\em 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 $ =-7.48\pm0.11$, $σ(M_V)=1.08$ mag, $h_3=0.05 \pm 0.05$, and $h_4=0.13 \pm 0.05$.
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