New light on the initial mass function of the Galactic Halo globular clusters

We present new constraints on the initial mass spectrum of the Galactic Old Halo globular clusters. This has remained poorly known so far, as both an initial power-law mass spectrum and an initial lognormal mass function could have evolved into the presently observed globular cluster mass distribution, making the initial contribution of now lost low-mass objects ill-determined. Our approach consists of comparing the evolution with time of both the radial mass density profile and the number density profile of the globular cluster system. Using the analytical expression established by Vesperini & Heggie for the temporal evolution of the mass of a globular cluster on a circular orbit in a stable Galactic potential, we evolve the mass and number density profiles of many putative globular cluster systems, each starting with a different initial cluster mass spectrum and initial cluster space density. We then compare the modelled profiles with those of the Old Halo cluster system in order to investigate which system(s) provide(s) the best consistency with the data. Specifically, we build on the following points: (i) the presently observed mass density profile and number density profile of the Old Halo cluster system show the same shape; (ii) assuming that globular clusters were initially distributed the same way in mass at all galactocentric distances, the mass and number density profiles had also the same shape initially; and (iii) according to our simulations, the mass density profile remains well preserved, irrespective of the initial cluster mass spectrum, while the temporal evolution of its number counterpart depends sensitively on initial conditions. We show that to obtain a mass density profile and a number density profile that are identical in shape, both initially and after a Hubble time of evolution, the globular cluster system must have been depleted in low-mass objects from the beginning. We deduce that the initial distribution in mass of the globular clusters was either a lognormal mass function, similar to that today, or a power-law mass spectrum with a slope congruent to -2 and truncated at large mass, say, around 105 M-circle dot. In contrast, a power-law mass spectrum with a similar slope but extending down to low cluster mass (i.e. a few thousand solar masses) seems to be ruled out.