  Observations have revealed massive (logM*/Msun>11) galaxies that were already
dead when the universe was only ~2 Gyr. Given the short time before these
galaxies were quenched, their past histories and quenching mechanism(s) are of
particular interest. In this paper, we study star formation histories (SFHs) of
24 massive galaxies at 1.6<z<2.5. A deep slitless spectroscopy + imaging data
set collected from multiple Hubble Space Telescope surveys allows robust
determination of their spectral energy distributions and SFHs with no
functional assumption on their forms. We find that most of our massive galaxies
had formed > 50% of their extant masses by ~1.5 Gyr before the time of observed
redshifts, with a trend where more massive galaxies form earlier. Their
stellar-phase metallicities are already compatible with those of local
early-type galaxies, with a median value of logZ*/Zsun=0.25 and scatter of
~0.15dex. In combination with the reconstructed SFHs, we reveal their rapid
metallicity evolution from z~5.5 to ~2.2 at a rate of ~0.2dex/Gyr in log
Z*/Zsun. Interestingly, the inferred stellar-phase metallicities are, when
compared at half-mass time, ~0.25dex higher than observed gas-phase
metallicities of star forming galaxies. While systematic uncertainties remain,
this may imply that these quenched galaxies have continued low-level star
formation, rather than abruptly terminating their star formation activity, and
kept enhancing their metallicity until recently.
