Metallicity-Dependent quenching of Star Formation at High Redshift in
  Small Galaxies
  [abridged] The star formation rates (SFR) of low-metallicity galaxies depend
sensitively on the gas metallicity, because metals are crucial to mediating the
transition from intermediate-temperature atomic gas to cold molecular gas, a
necessary precursor to star formation. We study the impact of this effect on
the star formation history of galaxies. We incorporate metallicity-dependent
star formation and metal enrichment in a simple model that follows the
evolution of a halo main progenitor. Our model shows that including the effect
of metallicity leads to suppression of star formation at redshift z>2 in dark
halos with masses <~ 10^11 Msun, with the suppression becoming near total for
halos below ~10^9.5-10 Msun. We find that at high redshift the SFR cannot catch
up with the gas inflow rate (IR), because the SFR is limited by the free-fall
time, and because it is suppressed further by a lack of metals. As a result, in
each galaxy the SFR is growing in time faster than the IR, and the integrated
cosmic SFR density is rising with time. The suppressed in situ SFR at high z
makes the growth of stellar mass dominated by ex situ SFR which implies that
the specific SFR (sSFR) remains constant with time. The intensely accreted gas
at high z is accumulating as an atomic gas reservoir. This provides additional
fuel for star formation in 10^10 - 10^12 Msun halos at z ~ 1-3, which allows
the SFR to exceed the instantaneous IR, and may enable an even higher outflow
rate. At z<1, following the natural decline in IR with time due to the
universal expansion, the SFR and sSFR are expected to drop. We specify the
expected dependence of sSFR and metallicity on stellar mass and redshift. At a
given z, and below a critical mass, these relations are predicted to be flat
and rising respectively. Our model predictions qualitatively match some of the
puzzling features in the observed star formation history.
