Understanding the structural scaling relations of early-type galaxies

We use a large suite of hydrodynamical simulations of binary galaxy mergers to construct and calibrate a physical prescription for computing the effective radii and velocity dispersions of spheroids. We implement this prescription within a semi-analytic model embedded in merger trees extracted from the Bolshoi Lambda cold dark matter N-body simulation, accounting for spheroid growth via major and minor mergers and disc instabilities. We find that without disc instabilities, our model does not predict sufficient numbers of intermediate-mass early-type galaxies in the local Universe. Spheroids also form earlier in models with spheroid growth via disc instabilities. Our model correctly predicts the normalization, slope, and scatter of the low-redshift size-mass and Fundamental Plane relations for early-type galaxies. It predicts a degree of curvature in the Faber-Jackson relation that is not seen in local observations, but this could be alleviated if higher mass spheroids have more bottom-heavy initial mass functions. The model also correctly predicts the observed strong evolution of the size-mass relation for spheroids out to higher redshifts, as well as the slower evolution in the normalization of the Faber-Jackson relation. We emphasize that these are genuine predictions of the model since it was tuned to match hydrodynamical simulations and not these observations.