The state of globular clusters at birth: emergence from the gas-embedded phase

In this paper, we discuss the origin of the observed correlation between cluster concentration c and present-day mass function (PDMF) slope {\alpha} reported by De Marchi, Paresce & Pulone. This relation can either be reproduced from universal initial conditions combined with some dynamical mechanism(s) that alter(s) the cluster structure and mass function over time, or it must arise early on in the cluster lifetime, such as during the gas-embedded phase of cluster formation. Using a combination of Monte Carlo and N-body models for globular cluster evolution performed with the MOCCA and NBODY6 codes, respectively, we explore a number of dynamical mechanisms that could affect the observed relation. For the range of initial conditions considered here, our results are consistent with an universal initial binary fraction \approx 10% (which does not, however, preclude 100%) and an universal initial stellar mass function resembling the standard Kroupa distribution. Most of the dispersion observed in the c-{\alpha} relation can be attributed to two-body relaxation and Galactic tides. However, dynamical processes alone could not have reproduced the dispersion in concentration, and we require at least some correlation between the initial concentration and the total cluster mass. We argue that the origin of this trend could be connected to the gas-embedded phase of cluster evolution.