The Virial Relation and Intrinsic Shape of Elliptical Galaxies

Early-type galaxies (ETGs) are supposed to follow the virial relation M ~ sigma^2 * R_e, with M being the galaxy mass, sigma being the stellar velocity dispersion, and R_e being the (2D) effective radius. I apply this relation to (a) the ATLAS3D sample and (b) the sample of Saglia et al. (2016). The two datasets reveal a statistically significant tilt of the empirical relation relative to the theoretical virial relation such that M ~ (sigma^2 * R_e)^0.92 with zero intrinsic scatter. This tilt disappears when replacing R_e with the semi-major axis of the projected half-light ellipse, a. Accordingly, a, not R_e, is the correct proxy for the scale radius of ETGs. By geometry, this implies that early-type galaxies are axisymmetric and oblate in general, in agreement with recent results from modeling based on kinematics and light distributions.