Abstract
Observations of galaxy luminosity function at high redshifts typically focus on fields of view of limited sizes preferentially containing bright sources. These regions possibly are overdense and hence biased with respect to the globally averaged regions. Using a semi-analytic model based on Choudhury & Ferrara (2006) which is calibrated to match a wide range of observations, we study the reionization and thermal history of the universe in overdense regions. The main results of our calculation are: (i) Reionization and thermal histories in the biased regions are markedly different from the average ones because of enhanced number of sources and higher radiative feedback. (ii) The galaxy luminosity function for biased regions is markedly different from those corresponding to average ones. In particular, the effect of radiative feedback arising from cosmic reionization is visible at much brighter luminosities. (iii) Because of the enhanced radiative feedback within overdense locations, the luminosity function in such regions is more sensitive to reionization history than in average regions. The effect of feedback is visible for absolute AB magnitude $M_{AB} \gtrsim -17$ at $z=8$, almost within the reach of present day observations and surely to be probed by JWST. This could possibly serve as an additional probe of radiative feedback and hence reionization at high redshifts.
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