  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 ($\sim 1000{\rm M_\odot}$, $-3.3\pm 0.2$)
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 $1.5\times 10^{8}{\rm M_\odot}$ 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.
