| Summary: | We present the evolution in the number density and stellar mass functions of photometrically selected post-starburst galaxies in the UKIDSSUltraDeep Survey,with redshifts of 0.5<z<2 and stellar masses log (M/M�) >10. We find that this transitionary species of galaxy is rare at all redshifts, contributing ∼5 per cent of the total population at z ∼ 2, to <1 per cent by z ∼ 0.5. By comparing the mass functions of quiescent galaxies to post-starburst galaxies at three cosmic epochs, we show that rapid quenching of star formation can account for
100 per cent of quiescent galaxy formation, if the post-starburst spectral features are visible for ∼250 Myr. The flattening of the low-mass end of the quiescent galaxy stellar mass function seen at z ∼ 1 can be entirely explained by the addition of rapidly quenched galaxies. Only
if a significant fraction of post-starburst galaxies have features that are visible for longer than 250 Myr, or they acquire new gas and return to the star-forming sequence, can there be significant growth of the red sequence from a slower quenching route. The shape of the mass function of these transitory post-starburst galaxies resembles that of quiescent galaxies at z ∼ 2, with a preferred stellar mass of log (M/M�) ∼10.6, but evolves steadily to resemble that of star-forming galaxies at z < 1. This leads us to propose a dual origin for post-starburst galaxies: (1) at z >/~ 2 they are exclusively massive galaxies that have formed the bulk of their stars during a rapid assembly period, followed by complete quenching of further star formation; (2) at z </~1 they are caused by the rapid quenching of gas-rich star-forming galaxies, independent of stellar mass, possibly due to environment and/or gas-rich major mergers.
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