Luminosity Functions for Globular Clusters

Abstract

We present theoretical mass-luminosity relations and luminosity functions (LFs) for globular cluster stars, from luminosities above the horizontal branch down to the minimum luminosity of hydrogen-burning stars. The LFs are available for metal mass fraction Z from Z = 10-4 to Z = 4 × 10-3, in the Johnson V band and in the Bessell-Cousins I band, and are based on tracks especially computed for this program, with the input physics of the models developed recently by D'Antona et al., Mazzitelli et al., and D'Antona & Mazzitelli. Two typical comparisons with observations are presented and discussed: (1) comparisons and statistical analysis with the LFs of the lower giant branch, turnoff region, and upper main sequence of several globular clusters from low to high metallicity, (2) derivation of the initial mass function (IMF) for the stars below the turnoff for several globular clusters for which Hubble Space Telescope data are available. In the first analysis we find that, for relatively large metallicities (Z ≥ 10-3) a good fit between theoretical and observed LFs can be found, although a simple χ2 statistical analysis shows that it is not possible to derive a strongly preferred age (or, equivalently, distance modulus) from the LF comparison. The fit with lower metallicity [Z ~ (1-2) × 10-4] LFs is less good but statistically acceptable. The main result is that the difference between observed and theoretical LFs of low-metallicity clusters reported by VandenBerg, Bolte, & Stetson appears to be much reduced in present models, and we give the possible reason why this happens and its consequences for the important parameter of the helium core mass at the flash. In the second application, we explore the effect of varying age and distance modulus on the mass function derived for a globular cluster. Distance moduli corresponding to the long distance scale (and relatively low ages) seem to be preferred based on these comparisons. The resulting index of the IMF is smaller than with a lower distance modulus, and generally an insignificant amount of mass in brown dwarfs is predicted if the IMF is extrapolated below the hydrogen-burning limit.