We investigate the stellar population properties of a sample of 24 massive quenched galaxies at 1.25 < z _ { \text { 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 ( \text { age } / \text { Gyr } ) = 0.04 _ { -0.08 } ^ { +0.10 } , \text { [ Z / H ] } = 0.24 _ { -0.14 } ^ { +0.20 } , and \text { [ $ \alpha$ / 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 _ { \text { 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 \text { 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 .