The Virial Relation and Intrinsic Shape of Early-Type Galaxies

TL;DR

This paper investigates the virial relation in early-type galaxies, finding that the intrinsic shape is consistent with axisymmetric, oblate structures, and confirms the virial relation's role in determining galaxy mass with zero intrinsic scatter.

Contribution

It demonstrates that the galaxy mass plane aligns with the virial relation when using the semi-major axis, confirming the oblate shape of early-type galaxies and clarifying the role of geometry in the virial factor.

Findings

The virial relation shows a tilt that disappears when using the semi-major axis.

The mass plane of ETGs has zero intrinsic scatter, indicating a fundamental relation.

Early-type galaxies are generally axisymmetric and oblate.

Abstract

Early-type galaxies (ETGs) are supposed to follow the virial relation $M = k_e \sigma_*^2 R_e / G$, with $M$ being the mass, $\sigma_*$ being the stellar velocity dispersion, $R_e$ 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 ATLAS3D sample of Cappellari et al. (2013) and (b) the sample of Saglia et al. (2016) gives ensemble-averaged factors $\langle k_e\rangle =5.15\pm0.09$ and $\langle k_e\rangle =4.01\pm0.18$, 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 $M\propto(\sigma_*^2R_e)^{0.92}$. 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 $(1-\epsilon) \propto M^{0.12}$, with $\epsilon$ being the ellipticity and $R_e = a\sqrt{1-\epsilon}$. 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.