We present Keck-I MOSFIRE near-infrared spectroscopy for a sample of 13 compact star-forming galaxies ( SFGs ) at redshift 2 \leq z \leq 2.5 with star formation rates of SFR \sim 100 M _ { \odot } y ^ { -1 } and masses of log ( M/M _ { \odot } ) \sim 10.8 .
Their high integrated gas velocity dispersions of \sigma _ { int } = 230 ^ { +40 } _ { -30 } km s ^ { -1 } , as measured from emission lines of H \alpha and [ O iii ] , and the resultant M _ { \star } - \sigma _ { int } relation and M _ { \star } - M _ { dyn } all match well to those of compact quiescent galaxies at z \sim 2 , as measured from stellar absorption lines .
Since log ( M _ { \star } /M _ { dyn } ) = -0.06 \pm 0.2 dex , these compact SFGs appear to be dynamically relaxed and more evolved , i.e. , more depleted in gas and dark matter ( < 13 ^ { +17 } _ { -13 } % ) than their non-compact SFG counterparts at the same epoch .
Without infusion of external gas , depletion timescales are short , less than \sim 300 Myr .
This discovery adds another link to our new dynamical chain of evidence that compact SFGs at z \gtrsim 2 are already losing gas to become the immediate progenitors of compact quiescent galaxies by z \sim 2 .