Luminosity functions for globular clusters

We present theoretical mass-luminosity relations and luminosity functions ( LFs) for globular cluster stars, from luminosities above the horizontal bra nch down to the minimum luminosity of hydrogen-burning stars. The LFs are a vailable for metal mass fraction Z from Z = 10(-4) to Z = 4 x 10(-3), in th e 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 & M azzitelli. Two typical comparisons with observations are presented and disc ussed: (1) comparisons and statistical analysis with the LFs of the lower g iant branch, turnoff region, and upper main sequence of several globular cl usters from low to high metallicity, (2) derivation of the initial mass fun ction (IMF) for the stars below the turnoff for several globular clusters f or which Hubble Space Telescope data are available. In the first analysis we find that, for relatively large metallicities (Z g reater than or equal to 10(-3)) a good fit between theoretical and observed LFs can be found, although a simple chi(2) statistical analysis shows that it is not possible to derive a strongly preferred age (or, equivalently, d istance modulus) from the LF comparison. The fit with lower metallicity [Z - (1-2) x 10(-4)] LFs is less good but statistically acceptable. The main r esult-is that the difference between observed and theoretical LFs of low-me tallicity clusters reported by VandenBerg, Bolte, & Stetson appears to be m uch reduced in present models, and we give the possible reason why this hap pens and its consequences for the important parameter of the helium core ma ss at the flash. in the second application, we explore the effect of varyin g age and distance modulus on the mass function derived for a globular clus ter. Distance moduli corresponding to the "long" distance scale (and relati vely low ages) seem to be preferred based on these comparisons. The resulti ng index of the IMF: is smaller than with a lower distance modulus, and gen erally an insignificant amount of mass in brown dwarfs is predicted if the IMF is extrapolated below the hydrogen-burning limit.