Angular momentum transfer and the size���mass relation in early-type galaxies

Abstract

Early-type galaxies (ETGs) define a narrow strip in the size–mass plane because of the observed correlation between the effective radius Reff and the total stellar mass M★. When expressed in logarithmic units, a linear relation, log Reff∝γ log M★, is indeed observationally found, but the slope γ deviates from the canonical γ= 1/2 value which can be naively predicted for a spherically symmetric isotropic system. We propose here that a transfer of angular momentum to the stellar component induces an anisotropy in the velocity space, thus leading to a modified distribution function (DF). Assuming an Osipkov–Merritt like anisotropic DF, we derive an analytic relation between the slope γ of the size–mass relation and the slope α of the angular momentum term in the DF. With this simple model, we are then able to recover the observed γ value provided α is suitably set. It turns out that an anisotropy profile which is tangential inside ∼0.6ra and radial outside, with ra the anisotropy radius, is able to reproduce the observed size–mass relation observed for massive (M★≥ 2 × 1010h−1 M⊙) elliptical galaxies.