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 .
( 2012 ) using the photometric binary populations as proxies for the true underlying distributions , in order to test the hypothesis that the data are consistent with an universal initial binary fraction near unity and the binary orbital parameter distributions of Kroupa ( 1995 ) .
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 ( 10 ^ { 4 } -10 ^ { 6 } M _ { \odot } pc ^ { -3 } ) , or low initial binary fractions ( \sim 5-10 % ) with a dominant hard binary component combined with moderate initial densities near their present-day values ( 10 ^ { 2 } -10 ^ { 3 } M _ { \odot } 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 contribute to reproducing the observed anti-correlation 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 .
( 2012 ) 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 _ { h } \propto M _ { clus } ^ { \alpha } with \alpha < 1/3 , corresponding to an initial correlation between cluster mass and density .