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 (SFH) of galaxies that is successful in describing both the star formation rate density (SFRD) over cosmic time, as well as the distribution of specific star formation rates (sSFRs) 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 SFRD 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 SFHs of individual galaxies. Using the measured sSFRs for galaxies at z similar to 0 from Paper III in this series, we then construct a realization of a universe populated by such galaxies in which the parameters of the log-normal SFH of each galaxy are adjusted to match the sSFRs at z similar to 0 as well as fitting, in ensemble, the cosmic SFRD from z = 0 to z = 8. This model predicts, with striking fidelity, the distribution of sSFRs in mass-limited galaxy samples to z = 1; this match is not achieved by other models with a different functional form for the SFHs 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 sSFR 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 to explain the enhanced sSFRs in intermediate redshift galaxies; we show here that a model using only smoothly varying log-normal SFHs for galaxies, which allows for some fraction of the population to have peak star formation at late times, does however fully explain the observations. Finally, we show that this model, constrained in detail only at redshifts z < 1, also produces the main sequence of star-formation observed at 1.5 < z < 2.5, again suggesting that the log-normal SFHs are a close approximation to the actual histories of typical galaxies.