Universal IMF versus dark halo response in early-type galaxies: breaking the degeneracy with the Fundamental Plane

We use the relations between aperture stellar velocity dispersion (Sigma(ap)), stellar mass (M-SPS) and galaxy size (R-e) for a sample of similar to 150 000 early-type galaxies from Sloan Digital Sky Survey/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We build lambda cold dark matter-based mass models that reproduce, by construction, the relations between galaxy size, light concentration and stellar mass, and use the spherical Jeans equations to predict Sigma(ap). Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median Sigma(ap) versus M-SPS relation is not possible with both a universal IMF and a universal dark halo response. Significant departures from a universal IMF and/or dark halo response are required, but there is a degeneracy between these two solutions. We show that this degeneracy can be broken using the strength of the correlation between residuals of the velocity-mass (delta log Sigma(ap)) and size-mass (delta log R-e) relations. The slope of this correlation, partial derivative(VR) equivalent to delta log Sigma(ap)/delta log R-e, varies systematically with galaxy mass from partial derivative(VR) similar or equal to -0.45 at M-SPS similar to 10(10) M-circle dot to partial derivative(VR) similar or equal to -0.15 at M-SPS similar to 10(11.6) M-circle dot. The virial Fundamental Plane (FP) has partial derivative(VR) = -1/2, and thus we find that the tilt of the observed FP is mass dependent. Reproducing this tilt requires both a non-universal IMF and a non-universal halo response. Our best model has mass-follows-light at low masses (M-SPS less than or similar to 10(11.2) M-circle dot) and unmodified Navarro, Frenk and White haloes at M-SPS similar to 10(11.5) M-circle dot. The stellar masses imply a mass-dependent IMF which is 'lighter' than Salpeter at low masses and 'heavier' than Salpeter at high masses.