The Faber-Jackson relation and Fundamental Plane from halo abundance   matching
  The Fundamental Plane (FP) describes the relation between the stellar mass, size, and velocity dispersion of elliptical galaxies; the Faber-Jackson relation (FJR) is its projection onto {mass, velocity} space. In this work we redeploy and expand the framework of Desmond & Wechsler (2015) to ask whether abundance matching-based LCDM models that have shown success in matching the spatial distribution of galaxies are also capable of explaining key properties of the FJR and FP, including their scatter. Within our framework, agreement with the normalisation of the FJR requires haloes to expand in response to disc formation. We find that the tilt of the FP may be explained by a combination of the observed non-homology in galaxy structure and the variation in mass-to-light ratio produced by abundance matching with a universal initial mass function (IMF), provided that the anisotropy of stellar motions is taken into account. However, the predicted scatter around the FP is considerably increased by situating galaxies in cosmologically-motivated haloes due to variations in halo properties at fixed stellar mass, and appears to exceed that of the data. This implies that additional correlations between galaxy and halo variables may be required to fully reconcile these models with elliptical galaxy scaling relations. 
Harry Desmond and Risa H. Wechsler
astro-ph.GA astro-ph.CO