The stellar and dark matter distributions in elliptical galaxies from the ensemble of strong gravitational lenses

We derive the average mass profile of elliptical galaxies from the ensemble of 161 strong gravitational lens systems selected from several surveys, assuming that the mass profile scales with the stellar mass and effective radius of each lensing galaxy. The total mass profile is well fitted by a power-law ρ(r) \propto r^γwith best-fit slope γ= -2.11+/-0.05. The decomposition of the total mass profile into stellar and dark matter distributions is difficult due to a fundamental degeneracy between the stellar initial mass function (IMF) and the dark matter fraction f_DM. We demonstrate that this IMF-f_DM degeneracy can be broken by adding direct stellar mass fraction measurements by quasar microlensing observations. Our best-fit model prefers the Salpeter IMF over the Chabrier IMF, and a smaller central dark matter fraction than that predicted by adiabatic contraction models.

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