The Initial Mass Function of Low-Mass Stars in Globular Clusters

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Abstract
We compare deep I-band luminosity functions of two globular clusters (NGC 6397 and NGC 6656) that have similar metal content but have experienced very different dynamical histories, both in terms of internal dynamics and as a result of different interactions with the Galactic tidal field. Their luminosity functions measured at the half-mass radius are indistinguishable from one another within the statistical errors over a range of more than 5 mag. They both show an increase with decreasing luminosity up to a peak at MI 8.5 and then drop all the way to the detection limit. We use the presently available theoretical mass-luminosity relations to convert these luminosity functions into mass functions and show that they all share one basic feature, namely, an exponential rise with decreasing mass down to about ~0.2 M☉ followed by a plateau. We conclude that an initial mass function that flattens out and possibly drops below ~0.2 M☉ is the only viable hypothesis for the low metallicity globular clusters studied so far.