The Virial Relation and Intrinsic Shape of Early-Type Galaxies

Abstract

Early-type galaxies (ETGs) are supposed to follow the virial relation $M=k_e{\sigma }_{\ast }^2{R}_e/G$, with $M$ being the mass, ${\sigma }_{\ast }$ 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 $⟨k_e⟩=5.15\pm 0.09$ and $⟨k_e⟩=4.01\pm 0.18$, 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 $M\propto ({\sigma }_{\ast }^2{R}_e{)}^{0.92}$. 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.

arXiv comment6 pages, 3 figures; to appear in JKAS (submitted 2016 July 19; accepted 2016 September 26). v2: Minor typos corrected. v3: Improved comparison to results by ATLAS3D Collaboration, discussion amended

References in corpus (13)

• The Atlas3D project -- I. A volume-limited sample of 260 nearby early-type galaxies: science goals and selection criteria
• The SAURON project - IV. The mass-to-light ratio, the virial mass estimator and the fundamental plane of elliptical and lenticular galaxies
• The Atlas3D project - XV. Benchmark for early-type galaxies scaling relations from 260 dynamical models: mass-to-light ratio, dark matter, Fundamental Plane and Mass Plane
• Structure and Kinematics of Early-Type Galaxies from Integral-Field Spectroscopy
• A Revised Parallel-Sequence Morphological Classification of Galaxies: Structure and Formation of S0 and Spheroidal Galaxies
• The SINFONI Black Hole Survey: The Black Hole Fundamental Plane revisited and the paths of (co-) evolution of supermassive black holes and bulges
• Discriminating Between the Physical Processes that Drive Spheroid Size Evolution
• The luminosity and stellar mass Fundamental Plane of early-type galaxies
• The Atlas3D project - XXIV. The intrinsic shape distribution of early-type galaxies
• Major Merging: The Way to Make a Massive, Passive Galaxy
• A More Fundamental Plane
• The Universal Faber-Jackson Relation
• The MOND Fundamental Plane

Cited by in corpus (2)

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