Probing the star formation history using the redshift evolution of luminosity functions

We present a self-consistent, semi-analytical ΛCDM model of star formation and reionization. For the cosmological parameters favored by the WMAP data, our models consistently reproduce the electron scattering optical depth to reionization, redshift of reionization and the observed luminosity functions (LF) and hence the star formation rate (SFR) density at 3 ≤ z ≤ 6 for a reasonable range of model parameters. While simple photoionization feedback produces the correct shape of LF at z = 6, for z = 3 we need additional feedback that suppresses star formation activities in halos with 10 . (M/M⊙) . 10. Models with prolonged continuous star formation activities are preferred over those with short bursts as they are consistent with the existence of a Balmer break in considerable fraction of observed galaxies even at z ∼ 6. The halo number density evolution from the standard ΛCDM structure formation model that fits LF up to z = 6 is consistent with the upper limits on z ≃ 7 LF and source counts at 8 ≤ z ≤ 12 obtained from the Hubble Ultra Deep Field (HUDF) observations without requiring any dramatic change in the nature of star formation. However, to reproduce the observed LF at 6 ≤ z ≤ 10, obtained from the near-IR observations around strong lensing clusters, we need a strong evolution in the initial mass function, reddening correction and the mode of star formation at z & 8. We show that low mass molecular cooled halos, which may be important for reionizing the universe, are not detectable in the present deep field observations even if a considerable fraction of its baryonic mass goes through a star burst phase. However, their presence and contribution to reionization can be inferred indirectly from the redshift evolution of the luminosity function in the redshift range 6 ≤ z ≤ 12. In our model calculations, the contribution of low mass halos to global SFR density prior to reionization reveals itself in the form of second peak at z ≥ 6. However this peak will not be visible in the observed SFR density as a function of z as most of these galaxies have luminosity below the detection threshold of various ongoing deep field surveys. Accurately measuring the LF at high redshifts can be used to understand the nature of star formation in the dark ages and probe the history of reionization.