Globular clusters (GCs) in the Milky Way exhibit a well-observed bimodal distribution in core radii separating the so-called core-collapsed and non-core-collapsed clusters. Here, we use our Henon-type Monte Carlo code, CMC, to explore initial cluster parameters that map into this bimodality. Remarkably, we find that by varying the initial size of clusters (specified in our initial conditions in terms of the initial virial radius, $r_v$) within a relatively narrow range consistent with the measured radii of young star clusters in the local universe ($r_v approx 0.5-5$ pc), our models reproduce the variety of present-day cluster properties. Furthermore, we show that stellar-mass black holes (BHs) play an intimate role in this mapping from initial conditions to the present-day structural features of GCs. We identify best-fit models for three GCs with known observed BH candidates, NGC 3201, M22, and M10, and show that these clusters harbor populations of $sim 50-100$ stellar-mass BHs at present. As an alternative case, we also compare our models to the core-collapsed cluster NGC 6752 and show that this cluster likely contains few BHs at present. Additionally, we explore the formation of BH binaries in GCs and demonstrate that these systems form naturally in our models in both detached and mass-transferring configurations with a variety of companion stellar types, including low-mass main sequence stars, white dwarfs, and sub-subgiants.
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