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 { H ^ { - } } .
It is shown that a stringent upper bound on ( total stellar mass , metallicity ) of ( \sim 1000 { 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 } { 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 } { M _ { \odot } } , 10 ^ { 6.5 } { 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 .