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The Fundamental Plane (FP) describes the relation between the stellar mass,size, and velocity dispersion of elliptical galaxies; the Faber-Jacksonrelation (FJR) is its projection onto {mass, velocity} space. In this work weredeploy and expand the framework of Desmond & Wechsler (2015) to ask whetherabundance matching-based LCDM models that have shown success in matching thespatial distribution of galaxies are also capable of explaining key propertiesof the FJR and FP, including their scatter. Within our framework, agreementwith the normalisation of the FJR requires haloes to expand in response to discformation. We find that the tilt of the FP may be explained by a combination ofthe observed non-homology in galaxy structure and the variation inmass-to-light ratio produced by abundance matching with a universal initialmass function (IMF), provided that the anisotropy of stellar motions is takeninto account. However, the predicted scatter around the FP is considerablyincreased by situating galaxies in cosmologically-motivated haloes due tovariations in halo properties at fixed stellar mass, and appears to exceed thatof the data. This implies that additional correlations between galaxy and halovariables may be required to fully reconcile these models with ellipticalgalaxy scaling relations.

The Faber-Jackson relation and Fundamental Plane from halo abundance matching