The state of globular clusters at birth – II. Primordial binaries

In this paper, we constrain the properties of primordial binary populations in Galactic globular clusters. Using the mocca Monte Carlo code for cluster evolution, our simulations cover three decades in present-day total cluster mass. Our results are compared to the observations of Milone et al. using the photometric binary populations as proxies for the true underlying distributions, in order to test the hypothesis that the data are consistent with a universal initial binary fraction near unity and the binary orbital parameter distributions of Kroupa. With the exception of a few possible outliers, we find that the data are to first-order consistent with the universality hypothesis. Specifically, the present-day binary fractions inside the half-mass radius can be reproduced assuming either high initial binary fractions near unity with a dominant soft binary component as in the Kroupa distribution combined with high initial densities (104–106 M⊙ pc−3), or low initial binary fractions (∼5–10 per cent) with a dominant hard binary component combined with moderate initial densities near their present-day values (102–103 M⊙ pc−3). This apparent degeneracy can potentially be broken using the binary fractions outside the half-mass radius – only high initial binary fractions with a significant soft component combined with high initial densities can reproduce the observed anticorrelation between the binary fractions outside the half-mass radius and the total cluster mass. We further illustrate using the simulated present-day binary orbital parameter distributions and the technique first introduced in Leigh et al. that the relative fractions of hard and soft binaries can be used to further constrain both the initial cluster density and the initial mass–density relation. Our results favour an initial mass–density relation of the form $r_{\rm h} \propto M_{\rm clus}^{\alpha }$ with α < 1/3, corresponding to an initial correlation between cluster mass and density.