  Early quiescent galaxies at z~2 are known to be remarkably compact compared
to their nearby counterparts. Possible progenitors of these systems include
galaxies that are structurally similar, but are still rapidly forming stars.
Here, we present Karl G. Jansky Very Large Array (VLA) observations of the
CO(1-0) line towards three such compact, star-forming galaxies at z~2.3,
significantly detecting one. The VLA observations indicate baryonic gas
fractions >~5 times lower and gas depletion times >~10 times shorter than
normal, extended massive star-forming galaxies at these redshifts. At their
current star formation rates, all three objects will deplete their gas
reservoirs within 100Myr. These objects are among the most gas-poor objects
observed at z>2, and are outliers from standard gas scaling relations, a result
which remains true regardless of assumptions about the CO-H2 conversion factor.
Our observations are consistent with the idea that compact, star-forming
galaxies are in a rapid state of transition to quiescence in tandem with the
build-up of the z~2 quenched population. In the detected compact galaxy, we see
no evidence of rotation or that the CO-emitting gas is spatially extended
relative to the stellar light. This casts doubt on recent suggestions that the
gas in these compact galaxies is rotating and significantly extended compared
to the stars. Instead, we suggest that, at least for this object, the gas is
centrally concentrated, and only traces a small fraction of the total galaxy
dynamical mass.
