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

Abstract

For many massive compact galaxies, their dynamical masses ($M_{\mathrm{dyn}}\propto \ddot{I}{ƒ}^2{r}_{\mathrm{e}}$) 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 $M_{\mathrm{dyn}}\equiv K\ddot{I}{ƒ}_{\mathrm{e}}^2{r}_{\mathrm{e}}/G$ 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 $M_{\mathrm{dyn}}\sim {\left[\ddot{I}{ƒ}_{\mathrm{e}}/(200\mathrm{km}{\mathrm{s}}^{-1})\right]}^{3.6}{\left[r_{\mathrm{e}}/(3\mathrm{kpc})\right]}^{0.35}2.1\times 10^{11}{\mathrm{M}}_{\odot }$.

15 pages, 15 figures, 2 tables. Updated to match the published version in MNRAS