Massive post-starburst galaxies at z > 1 are compact proto-spheroids
We investigate the relationship between the quenching of star formation and the structural transformation of massive galaxies, using a large sample of photometrically-selected post-starburst galaxies in the UKIDSS UDS field. We find that post-starburst galaxies at high-redshift ($z>1$) show high S\'ersic indices, significantly higher than those of active star-forming galaxies, but with a distribution that is indistinguishable from the old quiescent population. We conclude that the morphological transformation occurs before (or during) the quenching of star formation. Recently quenched galaxies are also the most compact; we find evidence that massive post-starburst galaxies (M$_{\ast}> 10^{10.5} ~$M$_{\odot}$) at high redshift ($z>1$) are on average smaller than comparable quiescent galaxies at the same epoch. Our findings are consistent with a scenario in which massive passive galaxies are formed from three distinct phases: (1) gas-rich dissipative collapse to very high densities, forming the proto-spheroid; (2) rapid quenching of star formation, to create the "red nugget" with post-starburst features; (3) a gradual growth in size as the population ages, perhaps as a result of minor mergers.