Initial conditions for globular clusters and assembly of the old globular cluster population of the Milky Way

By comparing the outcome of N-body calculations that include primordial residual-gas expulsion with the observed properties of 20 Galactic globular clusters (GCs) for which the stellar mass function (MF) has been measured, we constrain the time-scale over which the gas of their embedded cluster counterparts must have been removed, the star formation efficiency the progenitor cloud must have had and the strength of the tidal field the clusters must have formed in. The three parameters determine the expansion and mass loss during residual-gas expulsion. After applying corrections for stellar and dynamical evolution, we find birth cluster masses, sizes and densities for the GC sample and the same quantities for the progenitor gas clouds. The pre-cluster cloud-core masses were between 105 and 107 M(circle dot) and half-mass radii were typically below 1 pc and reach down to 0.2 pc. We show that the low-mass present day MF (PDMF) slope, initial half-mass radius and initial density of clusters correlate with cluster metallicity, unmasking metallicity as an important parameter driving cluster formation and the gas expulsion process. This work predicts that PD low-concentration clusters should have a higher binary fraction than PD high-concentration clusters. Since the oldest GCs are early residuals from the formation of the Milky Way (MW) and the derived initial conditions probe the environment in which the clusters formed, we use the results as a new tool to study the formation of the inner GC system of the Galaxy. We achieve time-resolved insight into the evolution of the pre-MW gas cloud on short time-scales (a few hundred Myr) via cluster metallicities. The results are shown to be consistent with a contracting and self-gravitating cloud in which fluctuations in the pre-MW potential grow with time. An initially relatively smooth tidal field evolved into a grainy potential within a dynamical time-scale of the collapsing cloud.