Salpeter normalization of the Stellar Initial Mass Function for massive galaxies at z~1

The stellar initial mass function (IMF) is a key parameter to study galaxy evolution. Here we measure the IMF mass normalization for a sample of 68 field galaxies in the redshift range 0.7 to 0.9 within the Extended Groth Strip. To do this we derive total (stellar + dark matter) mass-to-light [$(M/L)_{\rm dyn}$] using axisymmetric dynamical models. Within the region where we have kinematics (about one half-light radius), the models assume: (i) that mass-follows-light, implying negligible differences between the stellar and total density profiles; (ii) constant velocity anisotropy ($\beta_{\rm z}\equiv1-\sigma_z^2/\sigma_R^2=0.2$); (iii) that galaxies are seen at the average inclination for random orientations (i.e. $i=60^\circ$, where $i=90^\circ$ represents edge-on). The dynamical models are based on anisotropic Jeans equations, constrained by HST/ACS imaging and the central velocity dispersion of the galaxies, extracted from good-quality spectra taken by the DEEP2 survey. The population $(M/L)_{\rm pop}$ are derived from full-spectrum fitting of the same spectra with a grid of simple stellar population models. Recent dynamical modelling results by 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 suggest that our derived total $(M/L)_{\rm dyn}$ should closely approximate the stellar $M/L$. Our comparison of $(M/L)_{\rm dyn}$ and $(M/L)_{\rm pop}$ then imply that for galaxies with stellar mass $M_\odot \geq 10^{11}$ $M_{\odot}$, 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.