The Origin Of The Gaussian Initial Mass Function of Old Globular Cluster Systems: Impact Of The Residual Star Forming Gas Removal

Mathematics – Probability

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Scientific paper

Evidence favouring a Gaussian cluster initial mass function (IMF) similar to that today for systems of old globular clusters (GC) has accumulated over recent years. We show that a bell-shaped cluster mass function may be the imprint of expulsion from the protocluster of the leftover star forming gas due to supernova activity. Owing to the corresponding weakening of its gravitational potential, the protocluster retains a fraction only of its newly formed stars. The mass fraction of bound stars extends from zero to unity depending on the star formation efficiency (SFE) achieved by the protoglobular cloud. We investigate how such wide variations affect the mapping of the protoglobular cloud mass function to the GC IMF. We assume that the protoglobular cloud mass spectrum obeys a power-law with spectral index between -2.5 and -1.5, as is observed for giant molecular clouds in the Local Group. Following convolution with an SFE probability distribution, we account for gas removal and derive the cluster initial mass (function) by combining each SFE value to the corresponding fraction of stars remaining bound to the protocluster. Although our simulations were started with power-law cloud mass distributions, the newly formed gas-free bound star clusters show bell-shaped mass functions, that is, little memory of the cloud mass distribution is retained. If the GC IMF is actually a bell-shape/Gaussian similar to that today, then the origin of the universal cluster mass at the present-day turnover is locked into the cluster formation process. We show that the turnover universality would originate mostly from a common value among galaxies for the lower mass limit of the protoglobular clouds, possibly with second-order variations driven by differences in the slope of the cloud mass spectrum, that of the SFE distribution, as well as by differences in the gas removal time-scale.

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