  Supersonically Induced Gas Objects (SIGOs) are a class of early Universe
objects that have gained attention as a potential formation route for globular
clusters. SIGOs have only recently begun to be studied in the context of
molecular hydrogen cooling, which is key to characterizing their structure and
evolution. Studying the population-level properties of SIGOs with molecular
cooling is important for understanding their potential for collapse and star
formation, and central for addressing whether SIGOs can survive to the present
epoch. Here, we investigate the evolution of SIGOs before they form stars,
using a combination of numerical and analytical analysis. For example, we study
various timescales important to the evolution of SIGOs at a population level in
the presence of molecular cooling. Revising the previous formulation for the
critical density of collapse for SIGOs allows us to show that their prolateness
tends to act as an inhibiting factor to collapse. We find that simulated SIGOs
are limited by artificial two-body relaxation effects that tend to disperse
them, an effect of their limited resolution. We expect that SIGOs in nature
will be longer-lived compared to our simulations. Further, the fall-back
timescale on which SIGOs fall into nearby dark matter halos, potentially
producing a globular-cluster-like system, is frequently longer than their
cooling timescale and the collapse timescale on which they shrink through
gravity. Therefore, some SIGOs have time to cool and collapse outside of halos
despite initially failing to exceed the critical density, even without
considering metal line cooling. From this analysis we conclude that SIGOs
should form stars outside of halos in non-negligible stream velocity patches in
the Universe.
