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.
