Salpeter Normalization of the Stellar Initial Mass Function for Massive Galaxies at z ~ 1

Abstract

The stellar initial mass function (IMF) is a key parameter for studying galaxy evolution. Here we measure the IMF mass normalization for a sample of 68 field galaxies in the redshift range 0.7-0.9 within the Extended Groth Strip. To do this we derive the total (stellar + dark matter) mass-to-light [(M/L)] ratio using axisymmetric dynamical models. Within the region where we have kinematics (about one half-light radius), the models assume (1) that mass follows light, implying negligible differences between the slope of the stellar and total density profiles, (2) constant velocity anisotropy (\beta _{z}\equiv 1-\sigma _z^2/\sigma _R^2=0.2), and (3) that galaxies are seen at the average inclination for random orientations (i.e., i = 60°, where i = 90° represents edge-on). The dynamical models are based on anisotropic Jeans equations, constrained by Hubble Space Telescope/Advanced Camera for Surveys imaging and the central velocity dispersion of the galaxies, extracted from good-quality spectra taken by the DEEP2 survey. The population (M/L) are derived from full-spectrum fitting of the same spectra with a grid of simple stellar population models. Recent dynamical modeling results from the ATLAS^3D project and numerical simulations of galaxy evolution indicate that the dark matter fraction within the central regions of our galaxies should be small. This suggests that our derived total (M/L) should closely approximate the stellar M/L. Our comparison of the dynamical (M/L) and the population (M/L) then implies that for galaxies with stellar mass M _* >~ 10¹¹ M _⊙, the average normalization of the IMF is consistent with a Salpeter slope, with a substantial scatter. This is similar to what is found within a similar mass range for nearby galaxies.