An analysis of negative radiative feedback from resident stars in minihalos is performed. It is found that the most effective mechanism to suppress star formation is provided by infrared photons from resident stars via photo-detachment of ${rm H^-}$. It is shown that a stringent upper bound on (total stellar mass, metallicity) of ($sim 1000{rm M_odot}$, $-3.3pm 0.2$) in any newly minted atomic cooling halo can be placed, with the actual values possibly significantly lower. This has both important physical ramifications on formation of stars and supermassive black seeds in atomic cooling halos at high redshift, pertaining to processes of low temperature metal cooling, dust formation and fragmentation, and direct consequences on the faint end galaxy luminosity function at high redshift and cosmological reionization. The luminosity function of galaxies at the epoch of reionization may be substantially affected due to the combined effect of a diminished role of minihalos and an enhanced contribution from Pop III stars in atomic cooling halos. Upcoming results on reionization optical depth from Planck High-Frequency Instrument data may provide a significant constraint on and a unique probe of this star formation physical process in minihalos. As a numerical example, in the absence of significant contributions from minihalos with virial masses below $1.5times 10^{8}{rm M_odot}$ the reionization optical depth is expected to be no greater than $0.065$, whereas allowing for minihalos of masses as low as ($10^7{rm M_odot}$, $10^{6.5}{rm M_odot}$) to form stars unconstrained by this self-regulation physical process, the reionization optical depth is expected to exceed $(0.075,0.085)$, respectively.
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