On the Globular Cluster Initial Mass Function below 1 M

TLDR: In this article, the mass-luminosity (MF) distributions of globular clusters are transformed into mass functions (MFs) by means of mass luminosity relations that are consistent with all presently available data on the physical properties of low-mass, low-metallicity stars.

Abstract: Accurate luminosity functions (LFs) 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 LFs that rise continuously from an absolute I magnitude MI 6 to a peak at MI 8.5-9 and then drop with increasing MI. Transformation of the LFs into mass functions (MFs) by means of mass-luminosity (ML) relations that are consistent with all presently available data on the physical properties of low-mass, low-metallicity stars shows that all the LFs observed so far can be obtained from MFs having the shape of a lognormal distribution with characteristic mass mc = 0.33 ± 0.03 M☉ and standard deviation σ = 0.34 ± 0.04. In particular, the LFs 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 shows no statistically significant trend over a range of this last parameter of more than a factor of ~100. We conclude that the global MFs 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 the lognormal 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 initial mass function for this type of star in this mass range.