Universal IMF vs dark halo response in early-type galaxies: breaking the degeneracy with the fundamental plane

Abstract: We use the relations between aperture stellar velocity dispersion (\sigma_ap), stellar mass (M_sps), and galaxy size (R_e) for a sample of \sim 150,000 early-type galaxies from SDSS/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We build LCDM 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 vs M_sps relation is not possible with {\it 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, d_vr \equiv \Delta log \sigma_ap/\Delta log R_e, varies systematically with galaxy mass from d_vr \simeq -0.45 at M_sps \sim 10^{10}M_sun, to d_vr \simeq -0.15 at M_sps \sim 10^{11.6} M_sun. The virial fundamental plane (FP) has d_vr=-1/2, and thus we find the tilt of the observed FP is mass dependent. Reproducing this tilt requires {\it 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_sun) and unmodified NFW haloes at M_sps \sim 10^{11.5} M_sun. The stellar masses imply a mass dependent IMF which is "lighter" than Salpeter at low masses and "heavier" than Salpeter at high masses.