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The Initial Mass Function (IMF) for massive galaxies can be constrained bycombining stellar dynamics with strong gravitational lensing. However, thismethod is limited by degeneracies between the density profile of dark matterand the stellar mass-to-light ratio. In this work we reduce this degeneracy bycombining weak lensing together with strong lensing and stellar kinematics. Ouranalysis is based on two galaxy samples: 45 strong lenses from the SLACS surveyand 1,700 massive quiescent galaxies from the SDSS main spectroscopic samplewith weak lensing measurements from the Hyper Suprime-Cam survey. We use aBayesian hierarchical approach to jointly model all three observables. We fitthe data with models of varying complexity and show that a model with a radialgradient in the stellar mass-to-light ratio is required to simultaneouslydescribe both galaxy samples. This result is driven by a subset of stronglenses with very steep total density profile, that cannot be fitted by modelswith 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 decreasesdramatically the inferred IMF normalisation, compared to previous lensing-basedstudies, with the exact value depending on the assumed dark matter profile. Themain effect of strong lensing selection is to shift the stellar massdistribution towards the high mass end, while the halo mass and stellar IMFdistribution at fixed stellar mass are not significantly affected.

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