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Dynamical Simulations of the First Globular Clusters

Tidally limited star clusters are started on nearly circular orbits in the dark matter sub-halos present at high redshift and evolved with an n-body code augmented with gravitational interactions in the clusters. The tidally removed stars and the remaining high redshift clusters from a redshift 8 start are more concentrated than the dark matter, as expected. However, the subset of stars from the clusters that began in the lower mass sub-halos have a distribution somewhat more extended than the dark matter halo, with a mean galactic radius of about 60 kpc inside 150 kpc. The clusters from low mass sub-halos, those with a peak circular velocity of $ 12-18$ \kms, also produce most of the population's thin stellar streams. The dependence of the stellar population distribution on sub-halo mass is not seen in simulations that start clusters at lower redshift. The half mass radii of the clusters are set by the tidal fields of the initial cluster orbits, which leads to the average half mass radius decreasing with increased redshift of formation. Starting clusters at greater than redshift 4 leads to cluster half mass radii approximately as seen in the Milky Way, with lower redshifts leading to clusters that are too large. If extremely metal poor globular clusters were preferentially formed in high redshift, low mass, dwarf galaxies, then the clusters should be spread nearly uniformly over the dark halo, along with their tidally removed stars.