The ages, metallicities and element abundance ratios of massive quenched galaxies at $z\simeq 1.6$

We investigate the stellar population properties of a sample of 24 massive quenched galaxies at identified in the COSMOS field with our Subaru/Multi-object Infrared Camera and Spectrograph 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 ?-to-iron element abundance ratio [?/Fe] are derived as , , and , respectively. If our sample of quenched galaxies at 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 , around which the bulk of stars in these galaxies have been formed. The measured [?/Fe] value indicates a star formation timescale of Gyr, which can be translated into a specific star formation rate of prior to quenching. Based on these findings, we discuss identifying possible progenitor star-forming galaxies at . 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 presented here.