Constraints on the evolutionary mechanisms of massive galaxies since $z sim 1$ from their velocity dispersions

Several authors have reported that the dynamical masses of massive compact galaxies ($M_star gtrsim 10^{11} mathrm{M_odot}$, $r_mathrm{e} sim 1 mathrm{kpc}$), computed as $M_mathrm{dyn} = 5.0 sigma_mathrm{e}^2 r_mathrm{e} / G$, are lower than their stellar masses $M_star$. In a previous study from our group, the discrepancy is interpreted as a breakdown of the assumption of homology that underlie the $M_mathrm{dyn}$ determinations. Here, we present new spectroscopy of six redshift $z approx 1.0$ massive compact ellipticals from the Extended Groth Strip, obtained with the 10.4 m Gran Telescopio Canarias. We obtain velocity dispersions in the range $161-340 mathrm{km s^{-1}}$. As found by previous studies of massive compact galaxies, our velocity dispersions are lower than the virial expectation, and all of our galaxies show $M_mathrm{dyn} < M_star$ (assuming a Salpeter initial mass function). Adding data from the literature, we build a sample covering a range of stellar masses and compactness in a narrow redshift range $mathit{z approx 1.0}$. This allows us to exclude systematic effects on the data and evolutionary effects on the galaxy population, which could have affected previous studies. We confirm that mass discrepancy scales with galaxy compactness. We use the stellar mass plane ($M_star$, $sigma_mathrm{e}$, $r_mathrm{e}$) populated by our sample to constrain a generic evolution mechanism. We find that the simulations of the growth of massive ellipticals due to mergers agree with our constraints and discard the assumption of homology.

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

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 $M_mathrm{dyn} sim left[ sigma_mathrm{e} / (200 mathrm{km s^{-1}}) right]^{3.6} left[ r_mathrm{e} / (3 mathrm{kpc}) right]^{0.35} 2.1 times 10^{11} mathrm{M_odot}$.