The discrepancy between dynamical and stellar masses in massive compact galaxies traces non-homology

TL;DR

This study investigates why dynamical masses are often underestimated in massive compact galaxies by revealing that non-homology effects cause the standard virial relation to break down, especially for more compact galaxies.

Contribution

It introduces a modified virial coefficient dependent on galaxy size and stellar mass, improving mass estimates for compact galaxies and addressing the mass discrepancy issue.

Findings

Mass discrepancy increases with galaxy compactness.

Homology assumption fails for compact galaxies.

Proposed virial coefficient accounts for non-homology effects.

Abstract

For many massive compact galaxies, their dynamical masses ($M_\mathrm{dyn} \propto \sigma^2 r_\mathrm{e}$) are lower than their stellar masses ($M_\star$). We analyse the unphysical mass discrepancy $M_\star / M_\mathrm{dyn} > 1$ on a stellar-mass-selected sample of early-type galaxies ($M_\star \gtrsim 10^{11} \ \mathrm{M_\odot}$) at redshifts $z \sim 0.2$ to $z \sim 1.1$. We build stacked spectra for bins of redshift, size and stellar mass, obtain velocity dispersions, and infer dynamical masses using the virial relation $M_\mathrm{dyn} \equiv K \ \sigma_\mathrm{e}^2 r_\mathrm{e} / G$ with $K = 5.0$; this assumes homology between our galaxies and nearby massive ellipticals. Our sample is completed using literature data, including individual objects up to $z \sim 2.5$ and a large local reference sample from the Sloan Digital Sky Survey (SDSS). We find that, at all redshifts, the discrepancy between $M_\star$ and $M_\mathrm{dyn}$ grows as galaxies depart from the present-day relation between stellar mass and size: the more compact a galaxy, the larger its $M_\star / M_\mathrm{dyn}$. Current uncertainties in stellar masses cannot account for values of $M_\star / M_\mathrm{dyn}$ above 1. Our results suggest that the homology hypothesis contained in the $M_\mathrm{dyn}$ formula above breaks down for compact galaxies. We provide an approximation to the virial coefficient $K \sim 6.0 \left[ r_\mathrm{e} / (3.185 \ \mathrm{kpc}) \right]^{-0.81} \left[ M_\star / (10^{11} \ \mathrm{M_\odot}) \right]^{0.45}$, which solves the mass discrepancy problem. A rough approximation to the dynamical mass is given by $M_\mathrm{dyn} \sim \left[ \sigma_\mathrm{e} / (200 \ \mathrm{km \ s^{-1}}) \right]^{3.6} \left[ r_\mathrm{e} / (3 \ \mathrm{kpc}) \right]^{0.35} 2.1 \times 10^{11} \ \mathrm{M_\odot}$.