The ages, metallicities and element abundance ratios of massive quenched
  galaxies at z~1.6
  We investigate the stellar population properties of a sample of 24 massive
quenched galaxies at $1.25<z_\mathrm{spec}<2.09$ identified in the COSMOS field
with our Subaru/MOIRCS near-IR spectroscopic observations. Tracing the stellar
population properties as close to their major formation epoch as possible, we
try to put constraints on the star formation history, post-quenching evolution,
and possible progenitor star-forming populations for such massive quenched
galaxies. By using a set of Lick absorption line indices on a rest-frame
optical composite spectrum, the average age, metallicity [Z/H], and
$\alpha$-to-iron element abundance ratio [$\alpha$/Fe] are derived as
$\log(\mathrm{age}/\mathrm{Gyr})=0.04_{-0.08}^{+0.10}$,
$\mathrm{[Z/H]}=0.24_{-0.14}^{+0.20}$, and
$[\alpha/\mathrm{Fe}]=0.31_{-0.12}^{+0.12}$, respectively. If our sample of
quenched galaxies at $\langle z \rangle = 1.6$ is evolved passively to $z=0$,
their stellar population properties will align in excellent agreement with
local counterparts at similar stellar velocity dispersions, which qualifies
them as progenitors of local massive early-type galaxies. Redshift evolution of
stellar population ages in quenched galaxies combined with low redshift
measurements from the literature suggests a formation redshift of $z_\mathrm{f}
\sim 2.3$ around which the bulk of stars in these galaxies have been formed.
The measured [$\alpha$/Fe] value indicates a star formation timescale of
$\lesssim 1$ Gyr, which can be translated into a specific star formation rate
of $\simeq 1\,\mathrm{Gyr}^{-1}$ prior to quenching. Based on these findings,
we discuss identifying possible progenitor star-forming galaxies at $z \simeq
2.3$. We identify normal star-forming galaxies, i.e, those on the star-forming
main sequence, followed by a rapid quenching event, as likely precursors of the
quenched galaxies at $\langle z \rangle = 1.6$ presented here.
