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 ( ap ), stellar mass (M SPS ) and galaxy size (R e ) for a sample of 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 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 ap . Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median 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 ( log ap ) and size-mass ( log R e ) relations. The slope of this correlation, VR log ap / log R e , varies systematically with galaxy mass from VR -0.45 at M SPS 10 10 M to VR -0.15 at M SPS 10 11.6 M . The virial Fundamental Plane (FP) has VR = -1/2, and thus we find that the tilt of the observed FP is mass dependent. Reproducing this tilt requires both a nonuniversal IMF and a non-universal halo response. Our best model has mass-follows-light at low masses (M SPS 10 11.2 M ) and unmodified Navarro, Frenk and White haloes at M SPS 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.