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We investigate the stellar population properties of a sample of 24 massivequenched galaxies at $1.25<z_\mathrm{spec}<2.09$ identified in the COSMOS fieldwith our Subaru/MOIRCS near-IR spectroscopic observations. Tracing the stellarpopulation properties as close to their major formation epoch as possible, wetry to put constraints on the star formation history, post-quenching evolution,and possible progenitor star-forming populations for such massive quenchedgalaxies. By using a set of Lick absorption line indices on a rest-frameoptical 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 ofquenched galaxies at $\langle z \rangle = 1.6$ is evolved passively to $z=0$,their stellar population properties will align in excellent agreement withlocal counterparts at similar stellar velocity dispersions, which qualifiesthem as progenitors of local massive early-type galaxies. Redshift evolution ofstellar population ages in quenched galaxies combined with low redshiftmeasurements 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 rateof $\simeq 1\,\mathrm{Gyr}^{-1}$ prior to quenching. Based on these findings,we discuss identifying possible progenitor star-forming galaxies at $z \simeq2.3$. We identify normal star-forming galaxies, i.e, those on the star-formingmain sequence, followed by a rapid quenching event, as likely precursors of thequenched galaxies at $\langle z \rangle = 1.6$ presented here.

The ages, metallicities and element abundance ratios of massive quenched galaxies at z~1.6