Exploring the chemical link between local ellipticals and their high-redshift progenitors

We present Keck/MOSFIRE K-band spectroscopy of the first mass-selected sample of galaxies at $z\sim2.3$. Targets are selected from the 3D-HST Treasury survey. The six detected galaxies have a mean [NII]$\lambda$6584/H$\alpha$ ratio of $0.27\pm0.01$, with a small standard deviation of 0.05. This mean value is similar to that of UV-selected galaxies of the same mass. The mean gas-phase oxygen abundance inferred from the [NII]/H$\alpha$ ratios depends on the calibration method, and ranges from 12+log(O/H)$_{gas}=8.57$ for the {Pettini} & {Pagel} (2004) calibration to 12+log(O/H)$_{gas}= 8.87$ for the {Maiolino} {et~al.} (2008) calibration. Measurements of the stellar oxygen abundance in nearby quiescent galaxies with the same number density indicate 12+log(O/H)$_{stars}= 8.95$, similar to the gas-phase abundances of the $z\sim2.3$ galaxies if the {Maiolino} {et~al.} (2008) calibration is used. This suggests that these high-redshift star forming galaxies may be progenitors of today's massive early-type galaxies. The main uncertainties are the absolute calibration of the gas-phase oxygen abundance and the incompleteness of the $z\sim2.3$ sample: the galaxies with detected H$\alpha$ tend to be larger and have higher star formation rates than the galaxies without detected H$\alpha$, and we may still be missing the most dust-obscured progenitors.