Abstract
Supersonically induced gas objects (SIGOs), are structures with little to no dark-matter component predicted to exist in regions of the universe with large relative velocities between baryons and dark matter at the time of recombination. They have been suggested to be the progenitors of present-day globular clusters. Using simulations, SIGOs have been studied on small scales (around 2 Mpc) where these relative velocities are coherent. However, it is challenging to study SIGOs using simulations on large scales due to the varying relative velocities at scales larger than a few Mpc. Here, we study SIGO abundances semi-analytically: using perturbation theory, we predict the number density of SIGOs analytically, and compare these results to small-box numerical simulations. We use the agreement between the numerical and analytic calculations to extrapolate the large-scale variation of SIGO abundances over different stream velocities. As a result, we predict similar large-scale variations of objects with high gas densities before reionization that could possibly be observed by JWST. If indeed SIGOs are progenitors of globular clusters, then we expect a similar variation of globular cluster abundances over large scales. Significantly, we find that the expected number density of SIGOs is consistent with observed globular cluster number densities. As a proof-of-concept, and because globular clusters were proposed to be natural formation sites for gravitational wave sources from binary black-hole mergers, we show that SIGOs should imprint an anisotropy on the gravitational wave signal on the sky, consistent with their distribution.