The IMACS Cluster Building Survey: IV. The Log-normal Star Formation History of Galaxies

We present here a simple model for the star formation history of galaxies that is successful in describing both the star formation rate density over cosmic time, as well as the distribution of specific star formation rates of galaxies at the current epoch, and the evolution of this quantity in galaxy populations to a redshift of z=1. We show first that the cosmic star formation rate density is remarkably well described by a simple log-normal in time. We next postulate that this functional form for the ensemble is also a reasonable description for the star formation histories of individual galaxies. Using the measured specific star formation rates for galaxies at z~0 from Paper III in this series, we then construct a realisation of a universe populated by such galaxies in which the parameters of the log-normal star formation history of each galaxy are adjusted to match the specific star formation rates at z~0 as well as fitting, in ensemble, the cosmic star formation rate density from z=0 to z=8. This model predicts, with striking fidelity, the distribution of specific star formation rates in mass-limited galaxy samples to z=1; this match is not achieved by other models with a different functional form for the star formation histories of individual galaxies, but with the same number of degrees of freedom, suggesting that the log-normal form is well matched to the likely actual histories of individual galaxies. We also impose the specific star formation rate versus mass distributions at higher redshifts from Paper III as constraints on the model, and show that, as previously suggested, some galaxies in the field, particularly low mass galaxies, are quite young at intermediate redshifts. As emphasized in Paper III, starbursts are insufficient ...[abridged]