The formation of globular clusters and their relation to the distribution of dark matter have long puzzled astronomers. One of the most recently-proposed globular cluster formation channels ties ancient star clusters to the large-scale streaming velocity of baryons relative to dark matter in the early Universe. These streaming velocities affect the global infall of baryons into dark matter halos, the high-redshift halo mass function, and the earliest generations of stars. In some cases, streaming velocities may result in dense regions of dark-matter-free gas that becomes Jeans unstable, potentially leading to the formation of compact star clusters. We investigate this hypothesis using cosmological hydrodynamical simulations that include a full chemical network and the formation and destruction of H$_2$, a process crucial for the formation of the first stars. We find that high-density gas in regions with significant streaming velocities -- which constitute approximately 1% of the Universe -- is indeed somewhat offset from the centers of dark matter halos, but this offset is typically significantly smaller than the virial radius. Gas outside of dark matter halos never reaches Jeans-unstable densities in our simulations. We postulate that low-level ($Z approx 10^{-3},Z_{odot}$) metal enrichment by Population III supernovae may enable cooling in the extra-virial regions, allowing gas outside of dark matter halos to cool to the CMB temperature and become Jeans-unstable. Follow-up simulations that include both streaming velocities and metal enrichment by Population III supernovae are needed to understand if streaming velocities provide one path for the formation of globular clusters in the early Universe.
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