  Metal poor globular clusters (MPGCs) are a unique probe of the early
universe, in particular the reionization era. Systems of globular clusters in
galaxy clusters are particularly interesting as it is in the progenitors of
galaxy clusters that the earliest reionizing sources first formed. Although the
exact physical origin of globular clusters is still debated, it is generally
admitted that globular clusters form in early, rare dark matter peaks (Moore et
al. 2006; Boley et al. 2009). We provide a fully numerical analysis of the
Virgo cluster globular cluster system by identifying the present day globular
cluster system with exactly such early, rare dark matter peaks. A popular
hypothesis is that that the observed truncation of blue metal poor globular
cluster formation is due to reionization (Spitler et al. 2012; Boley et al.
2009; Brodie & Strader 2006); adopting this view, constraining the formation
epoch of MPGCs provides a complementary constraint on the epoch of
reionization. By analyzing both the line of sight velocity dispersion and the
surface density distribution of the present day distribution we are able to
constrain the redshift and mass of the dark matter peaks. We find and quantify
a dependence on the chosen line of sight of these quantities, whose strength
varies with redshift, and coupled with star formation efficiency arguments find
a best fitting formation mass and redshift of $\simeq 5 \times 10^8
\rm{M}_\odot$ and $z\simeq 9$. We predict $\simeq 300$ intracluster MPGCs in
the Virgo cluster. Our results confirm the techniques pioneered by Moore et al.
(2006) when applied to the the Virgo cluster and extend and refine the analytic
results of Spitler et al. (2012) numerically.
