  The first galaxies forming a few hundred million years after the Big Bang are
the key drivers of cosmic evolution and ideal laboratories to study theories of
galaxy formation. We here study the role of UV radiation in suppressing star
formation in primordial galaxies by destroying molecular hydrogen, the main
coolant in primordial gas and provide estimates of cold dense gas at the onset
of star formation. To accomplish this goal, we perform three dimensional
cosmological simulations of minihalos in different environments forming at $
z\sim 25$ by varying strength of background UV flux below the Lyman limit
between 0.01-1000 in units of $\rm J_{21}=10^{-21}~erg/cm^2/s/Hz/sr$.
Particularly, we include photo-detachment of $\rm H^-$, the self-shielding of
$\rm H_2$ which both were neglected in previous studies and use updated
reaction rates. Our results show that depending on the background level $\rm
H_2$ formation is suppressed, delaying gravitational collapse until halos reach
the atomic cooling limit. We find that the formation of cold dense molecular
gas and subsequently star formation gets delayed by 100 to 230 Myr depending on
the level of the background radiation and the growth history of the dark matter
halos. The fraction of dense self-shielded gas is a strong function of the
background flux and exponentially declines with the strength of incident UV
flux above $\rm J_{21} \geq 1$. We find that taking into account $\rm H_2$
self-shielding is crucial for accurately estimating the amount of cold dense
gas available for star formation.
