THE VIRIAL RELATION AND INTRINSIC SHAPE OF EARLY-TYPE GALAXIES

Early-type galaxies (ETGs) are supposed to follow the virial relation M = k(e)sigma*R-2(e)/G, with M being the mass, sigma* being the stellar velocity dispersion, Re being the effective radius, G being Newton's constant, and k(e) being the virial factor, a geometry factor of order unity. Applying this relation to (a) the ATLAS(3D) sample of Cappellari et al. (2013) and (b) the sample of Saglia et al. (2016) gives ensemble averaged factors (ke) = 5.15 +/- 0.09 and (k(e)) = 4.01 +/- 0.18, respectively, with the difference arising from different definitions of effective velocity dispersions. The two datasets reveal a statistically significant tilt of the empirical relation relative to the theoretical virial relation such that M alpha (sigma*R-2(e))(0.92) This tilt disappears when replacing R-e with the semi-major axis of the projected half-light ellipse, a. All best-fit scaling relations show zero intrinsic scatter, implying that the mass plane of ETGs is fully determined by the virial relation. Whenever a comparison is possible, my results are consistent with, and confirm, the results by Cappellari et al. (2013). The difference between the relations using either a or R-e arises from a known lack of highly elliptical high-mass galaxies; this leads to a scaling (1 - epsilon) alpha M-0.12, with epsilon being the ellipticity and R-e = a root 1 - epsilon. 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 published results from modeling based on kinematics and light distributions.