Toward a Better Understanding of Cosmic Chronometers: Stellar Population
  Properties of Passive Galaxies at Intermediate Redshift
  We take advantage of the publicly available LEGA-C spectroscopic survey to
measure the stellar population properties of 140 individual massive and passive
galaxies at $z\sim0.7$. We develop and publicly release PyLick, a flexible
python code to measure UV to near-IR spectral indices. With PyLick we study the
H/K ratio as a new diagnostic based on the pseudo-Lick CaII H and K indices,
and find that a cut in ${\rm H/K}<1.1$ can be used jointly with other criteria
to select (or verify the purity of) samples of passive galaxies. By combining
photometric and spectroscopic criteria, we select a reliable sample of
passively evolving galaxies. We constrain single-burst stellar ages,
metallicities $\mathrm{[Z/H]}$, and $\mathrm{[\alpha/Fe]}$ with an optimized
set of Lick indices, exploring in detail the robustness of our measurement
against different combinations. Even without imposing cosmological priors, the
derived ages follow a clear trend compatible with the expected cosmological
aging of the Universe. We observe no significant redshift evolution for the
metal abundance with respect to the values derived at $z=0$, with median
$\mathrm{[Z/H]}=0.08\pm0.18$ and $\mathrm{[\alpha/Fe]}=0.13\pm0.11$. Finally,
we find positive correlations between $\log\mathrm{age}$, $\mathrm{[Z/H]}$,
$\mathrm{[\alpha/Fe]}$ and the stellar velocity dispersion, with slopes of
($0.48\pm0.14$), ($0.26\pm0.17$), and ($0.23\pm0.11$), respectively; the small
scatter of $<0.2$ dex points to rather homogeneous and short star formation
histories. Overall, these results confirm and extend low-redshift findings of a
mass-downsizing evolution. This work further strengthens the possibility of
selecting pure samples of passive galaxies to be exploited reliably as cosmic
chronometers to place independent cosmological constraints.
