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 (σap), stellar mass (MSPS), and galaxy size (Re) for a sample of ∼ 150000 early-type galaxies from SDSS/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We buildCDM 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 σap. Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median σap vs MSPS 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 (�logσap) and size-mass (�logRe) relations. The slope of this correlation, ∂VR ≡ �logσap/�logRe, varies systematically with galaxy mass from ∂VR ≃ −0.45 at MSPS ∼ 10 10 M⊙, to ∂VR ≃ −0.15 at MSPS ∼ 10 11.6 M⊙. The virial fundamental plane (FP) has ∂VR = −1/2, and thus we find 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 (MSPS ∼ 10 11.2 M⊙) and unmodified NFW haloes at MSPS ∼ 10 11.5 M⊙. The stellar masses imply a mass dependent IMF which is "lighter" than Salpeter at low masses and "heavier" than Salpeter at high masses.