Constraints on the star formation histories of galaxies from z ∼ 1 to 0

We present a new method to estimate the average star formation rate per unit stellar mass (SSFR) of a stacked population of galaxies. We combine the spectra of 600-1000 galaxies with similar stellar masses and parametrize the star formation history of this stacked population using a set of exponentially declining functions. The strength of the hydrogen Balmer absorption-line series in the rest-frame wavelength range 3750-4150 Å is used to constrain the SSFR by comparing with a library of models generated using the BC03 stellar population code. Our method, based on a principal component analysis, can be applied in a consistent way to spectra drawn from local galaxy surveys and from surveys at z ∼ 1, and is only weakly influenced by attenuation due to dust. We apply our method to galaxy samples drawn from Sloan Digital Sky Survey and DEEP2 to study the mass-dependent growth of galaxies from z ∼ 1 to 0. We find that (i) high-mass galaxies have lower SSFRs than low-mass galaxies and (ii) the average SSFR has decreased from z = 1 to 0 by a factor of ∼3-4, independent of galaxy mass. Additionally, at z ∼ 1, our average SSFRs are a factor of 2-2.5 lower than those derived from multiwavelength photometry using similar data sets. We then compute the average time <in units of the Hubble time, t_H(z)> needed by galaxies of a given mass to form their stars at their current rate. At both z = 0 and 1, this time-scale decreases strongly with stellar mass from values close to unity for galaxies with masses ∼10¹⁰ M_⊙, to more than 10 for galaxies more massive than 10¹¹ M_⊙. Our results are in good agreement with models in which active galactic nuclei feedback is more efficient at preventing gas from cooling and forming stars in high-mass galaxies.