On the Globular Cluster IMF Below 1 M⊙

Abstract

Accurate luminosity functions (LF) for a dozen globular clusters have now been measured at or just beyond their half-light radius using HST. They span almost the entire cluster main sequence (MS) below 0.75 M ⊙ . All these clusters exhibit LF that rise continuously from an absolute I magnitude M I ≃ 6 to a peak at M I ≃ 8.5−9 and then drop with increasing M I . Transformation of the LF into mass functions (MF) by means of the mass luminosity (ML) relations of Baraffe et al. (1997) and Cassisi et al. (1999) that are consistent with all presently available data on the physical properties of low mass, low metallicity stars shows that all the LF observed so far can be obtained from MF having the shape of a log-normal distribution with characteristic mass m c = 0.33 ± 0.03 M ⊙ and standard deviation σ = 1.81 ± 0.19. In particular, the LF of the four clusters in the sample that extend well beyond the peak luminosity down to close to the Hydrogen burning limit (NGC 6341, NGC 6397, NGC 6752, and NGC 6809) can only be reproduced by such distributions and not by a single power-law in the 0.1 − 0.6 M ⊙ range. After correction for the effects of mass segregation, the variation of the ratio of the number of higher to lower mass stars with cluster mass or any simple orbital parameter or the expected time to disruption recently computed for these clusters by Gnedin & Ostriker (1997) and Dinescu et al. (1999) shows no statistically significant trend over a range of this last parameter of more than a factor of ∼ 100. We conclude that the global MF of these clusters have not been measurably modified by evaporation and tidal interactions with the Galaxy and, thus, should reflect the initial distribution of stellar masses. Since 1 Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555 -2 -the log-normal function that we find is also very similar to the one obtained independently for much younger clusters and to the form expected theoretically, the implication seems to be unavoidable that it represents the true stellar IMF for this type of stars in this mass range.

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