Dark Matter Contraction and the Stellar Content of Massive Early-Type Galaxies: Disfavoring “Light” Initial Mass Functions

We use stellar dynamics, strong lensing, stellar population synthesis models, and weak lensing shear measurements to constrain the dark matter (DM) profile and stellar mass in a sample of 53 massive early-type galaxies. We explore three DM halo models (unperturbed Navarro, Frenk, and White (NFW) halos and the adiabatic contraction models of Blumenthal and Gnedin) and impose a model for the relationship between the stellar and virial mass (i.e., a relationship for the star formation efficiency as a function of halo mass). We show that, given our model assumptions, the data clearly prefer a Salpeter-like initial mass function (IMF) over a lighter IMF (e.g., Chabrier or Kroupa), irrespective of the choice of DM halo. In addition, we find that the data prefer at most a moderate amount of adiabatic contraction (Blumenthal adiabatic contraction is strongly disfavored) and are only consistent with no adiabatic contraction (i.e., an NFW halo) if a mass-dependent IMF is assumed, in the sense of a more massive normalization of the IMF for more massive halos.