Examining early-type galaxy scaling relations using simple dynamical models

Abstract

We use dynamical models that include bulk rotation, velocity dispersion anisotropy and both stars and dark matter to explore the conditions that give rise to the early-type galaxy scaling relations referred to as the Fundamental Plane (FP) and Manifold (FM). The modelled scaling relations generally match the observed relations and are remarkably robust to all changes allowed within these models. The empirical relationships can fail beyond the parameter ranges where they were calibrated and we discuss the nature of those failures. Because the location of individual models relative to the FP and FM is sensitive to the adopted physical scaling of the models, unconstrained rescaling produces a much larger scatter about the scaling relations than that observed. We conclude that only certain combinations of scaling values, which define the physical radial and kinematic scale of the model, produce low scatter versions of the FP and FM. These combinations further result in reproducing a condition observed previously for galaxies, $r_c ρ_0 = $ constant, where $r_c$ is the scaling radius and $ρ_0$ is the central density. As such, we conclude that this empirical finding and global galaxy scaling relations are not independent and that finding the physical cause of one should lead to the solution to the other. Although our models are strictly for pressure supported galaxies, these results may well hold generally because the central density constraint was first identified in dwarf spheroidals but later extended to rotating giant galaxies and the FM applies to galaxies of any morphological type and luminosity class.

12 pages, 9 figures