Mass distribution and orbital anisotropy of early-type galaxies: constraints from the mass plane

Abstract

Massive early-type galaxies are observed to lie on the mass plane (MP), a two-dimensional manifold in the space of effective radius Re, projected mass M p (measured via strong gravitational lensing) and projected stellar velocity dispersion σ e2 withinRe/2. The MP is less ‘tilted’ than the traditional Fundamental Plane, and the two have comparable associated scatter. This means that the dimensionless structure parameter ce2 = 2GM p /(Reσ 2 ) is a nearly universal constant in the range σ e2 = 175–400 km s −1 . This finding can be used to constrain the mass distribution and internal dynamics of early-type galaxies: in particular, we explore the dependence of ce2 on light profile, dark matter distribution, and orbital anisotropy for several families of spherical galaxy models. We find that a relatively wide class of models has values of ce2 in the observed range, because ce2 is not very strongly sensitive to the mass distribution and orbital anisotropy. The degree of fine-tuning required to match the small intrinsic scatter of ce2 depends on the considered family of models: if the total mass distribution is isothermal (∝ r −2 ), a broad range of stellar luminosity profile and anisotropy is consistent with the observations, while Navarro, Frenk & White dark matter haloes require more fine-tuning of the stellar mass fraction, luminosity profile and anisotropy. If future data can cover a broader range of masses, the MP could be seen to be tilted by the known non-homology of the luminosity profiles of early-type galaxies, and the value of any such tilt would provide a discriminant between models for the total mass–density profile of the galaxies.