Evidence for radial variations in the stellar mass-to-light ratio of massive galaxies from weak and strong lensing

The Initial Mass Function (IMF) for massive galaxies can be constrained by combining stellar dynamics with strong gravitational lensing. However, this method is limited by degeneracies between the density profile of dark matter and the stellar mass-to-light ratio. In this work we reduce this degeneracy by combining weak lensing together with strong lensing and stellar kinematics. Our analysis is based on two galaxy samples: 45 strong lenses from the SLACS survey and 1,700 massive quiescent galaxies from the SDSS main spectroscopic sample with weak lensing measurements from the Hyper Suprime-Cam survey. We use a Bayesian hierarchical approach to jointly model all three observables. We fit the data with models of varying complexity and show that a model with a radial gradient in the stellar mass-to-light ratio is required to simultaneously describe both galaxy samples. This result is driven by a subset of strong lenses with very steep total density profile, that cannot be fitted by models with no gradient. Our measurements are unable to determine whether $M_*/L$ gradients are due to variations in stellar population parameters at fixed IMF, or to gradients in the IMF itself. The inclusion of $M_*/L$ gradients decreases dramatically the inferred IMF normalisation, compared to previous lensing-based studies, with the exact value depending on the assumed dark matter profile. The main effect of strong lensing selection is to shift the stellar mass distribution towards the high mass end, while the halo mass and stellar IMF distribution at fixed stellar mass are not significantly affected.