The Globular Cluster - Dark Matter Halo Connection

Abstract: I present a simple phenomenological model for the observed linear scaling of the stellar mass in old globular clusters (GCs) with $z=0$ halo mass in which the stellar mass in GCs scales linearly with progenitor halo mass at $z=6$ above a minimum halo mass for GC formation. This model reproduces the observed $M_{\rm GCs}-M_{\rm halo}$ relation at $z=0$ and results in a prediction for the minimum halo mass at $z=6$ required for hosting one GC: $M_{\rm min}(z=6)=1.07 \times 10^9\,M_{\odot}$. Translated to $z=0$, the mean threshold mass is $M_{\rm halo}(z=0) \approx 2\times 10^{10}\,M_{\odot}$. I explore the observability of GCs in the reionization era and their contribution to cosmic reionization, both of which depend sensitively on the (unknown) ratio of GC birth mass to present-day stellar mass, $\xi$. Based on current detections of $z \gtrsim 6$ objects with $M_{1500} < -17$, values of $\xi > 10$ are strongly disfavored; this, in turn, has potentially important implications for GC formation scenarios. Even for low values of $\xi$, some observed high-$z$ galaxies may actually be GCs, complicating estimates of reionization-era galaxy ultraviolet luminosity functions and constraints on dark matter models. GCs are likely important reionization sources if $5 \lesssim \xi \lesssim 10$. I also explore predictions for the fraction of accreted versus in situ GCs in the local Universe and for descendants of systems at the halo mass threshold of GC formation (dwarf galaxies). An appealing feature of the model presented here is the ability to make predictions for GC properties based solely on dark matter halo merger trees.