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[abridged] The star formation rates (SFR) of low-metallicity galaxies dependsensitively on the gas metallicity, because metals are crucial to mediating thetransition from intermediate-temperature atomic gas to cold molecular gas, anecessary precursor to star formation. We study the impact of this effect onthe star formation history of galaxies. We incorporate metallicity-dependentstar formation and metal enrichment in a simple model that follows theevolution of a halo main progenitor. Our model shows that including the effectof metallicity leads to suppression of star formation at redshift z>2 in darkhalos with masses <~ 10^11 Msun, with the suppression becoming near total forhalos below ~10^9.5-10 Msun. We find that at high redshift the SFR cannot catchup with the gas inflow rate (IR), because the SFR is limited by the free-falltime, and because it is suppressed further by a lack of metals. As a result, ineach galaxy the SFR is growing in time faster than the IR, and the integratedcosmic SFR density is rising with time. The suppressed in situ SFR at high zmakes the growth of stellar mass dominated by ex situ SFR which implies thatthe specific SFR (sSFR) remains constant with time. The intensely accreted gasat high z is accumulating as an atomic gas reservoir. This provides additionalfuel for star formation in 10^10 - 10^12 Msun halos at z ~ 1-3, which allowsthe SFR to exceed the instantaneous IR, and may enable an even higher outflowrate. At z<1, following the natural decline in IR with time due to theuniversal expansion, the SFR and sSFR are expected to drop. We specify theexpected dependence of sSFR and metallicity on stellar mass and redshift. At agiven z, and below a critical mass, these relations are predicted to be flatand rising respectively. Our model predictions qualitatively match some of thepuzzling features in the observed star formation history.

Metallicity-Dependent quenching of Star Formation at High Redshift in Small Galaxies