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{k}\mathrm{p}\mathrm{c}$$),computedas$M_$\mathrm{d}\mathrm{y}\mathrm{n}$ = 5.0 \ \sigma_$\mathrm{e}$^2 r_$\mathrm{e}$ / G$,arelowerthantheirstellarmasses$M_\star$. In a previous study from our group, the discrepancy is interpreted as a breakdown of the assumption of homology that underlie the $M_{\mathrm{d}\mathrm{y}\mathrm{n}}$ determinations. Here, we present new spectroscopy of six redshift $z\approx 1.0$ massive compact ellipticals from the Extended Groth Strip, obtained with the 10.4 m Gran Telescopio Canarias. We obtain velocity dispersions in the range $161-340
$\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$$. As found by previous studies of massive compact galaxies, our velocity dispersions are lower than the virial expectation, and all of our galaxies show $M_{\mathrm{d}\mathrm{y}\mathrm{n}}<M_{\star }$ (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 $z\approx \mathit{1.0}$. 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.