Abstract
Motivated by recent observations of the star formation rate density function out to z~7, we describe a simple model for the star formation rate density function at high redshift based on the extended Press-Schechter formalism. This model postulates a starburst following each major merger, lasting for a time t_SF and converting at most f_star of galactic gas into stars. We include a simple physical prescription for supernovae feedback that suppresses star formation in low mass galaxies. Constraining t_SF and f_star to describe the observed star formation rate density at high redshifts, we find that individual starbursts were terminated after a time t_SF~10^7 years. This is comparable to the main-sequence lifetimes of supernova progenitors, indicating that high redshift starbursts are quenched once supernovae feedback had time to develop. High redshift galaxies convert ~10% of their mass into stars for galaxies with star formation rates above ~1 solar mass per year, but a smaller fraction for lower luminosity galaxies. Our best fit model successfully predicts the observed relation between star formation rate and stellar mass at z>~4, while our deduced relation between stellar mass and halo mass is also consistent with data on the dwarf satellites of the Milky Way. We find that supernovae feedback lowers the efficiency of star formation in the lowest mass galaxies and makes their contribution to reionization small. As a result, photo-ionization feedback on low mass galaxy formation does not significantly affect the reionization history. Using a semi-analytic model for the reionization history, we infer that approximately half of the ionizing photons needed to complete reionization have already been observed in star-forming galaxies.
Highlights
The galaxy luminosity function is the primary observable that must be reproduced by any successful model of galaxy formation
A complication that arises when modelling the luminosity function is that models predict a star formation rate, which must be converted to a luminosity assuming an initial mass function (IMF) for the stars
Ψobs(SF Ri, f,max, tSF, z) is the observed star formation rate density measured at redshift z, with uncertainty in dex of σSF R(SF Ri)
Summary
The galaxy luminosity function is the primary observable that must be reproduced by any successful model of galaxy formation. A complication that arises when modelling the luminosity function is that models predict a star formation rate, which must be converted to a luminosity assuming an initial mass function (IMF) for the stars. While this calculation is straightforward, of more importance is the potential contribution of reddening. As a result there is a dust correction which is both luminosity and redshift dependent and difficult to reproduce from first principles reliably in a simple model This renders theoretical studies of the luminosity function difficult to interpret.
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