Post-starburst galaxies can be identified via the presence of prominent Hydrogen Balmer absorption lines in their spectra. We present a comprehensive study of the origin of strong Balmer lines in a volume-limited sample of 189 galaxies with 0.01 < z < 0.05, log(M /M ) > 9.5 and projected axis ratio b/a > 0.32. We explore their structural properties, environments, emission lines and star formation histories, and compare them to control samples of star-forming and quiescent galaxies, and simulated galaxy mergers. Excluding contaminants, in which the strong Balmer lines are most likely caused by dust-star geometry, we find evidence for three different pathways through the post-starburst phase, with most events occurring in intermediate-density environments: (1) a significant disruptive event, such as a gas-rich major merger, causing a starburst and growth of a spheroidal component, followed by quenching of the star formation (70% of post-starburst galaxies at 9.5 < log(M /M ) < 10.5 and 60% at log(M /M ) > 10.5); (2) at 9.5 < log(M /M ) < 10.5, stochastic star formation in blue-sequence galaxies, causing a weak burst and subsequent return to the blue sequence (30%); (3) at log(M /M ) > 10.5, cyclic evolution of quiescent galaxies which gradually move towards the high-mass end of the red sequence through weak starbursts, possibly as a result of a merger with a smaller gas-rich companion (40%). Our analysis suggests that AGN are 'on' for 50% of the duration of the post-starburst phase, meaning that traditional samples of post-starburst galaxies with strict emission line cuts will be at least 50% incomplete due to the exclusion of narrow-line AGN.

We present the star formation histories of 39 galaxies with high quality rest-frame optical spectra at 0.5 < z < 1.3 selected to have strong Balmer absorption lines and/or Balmer break, and compare to a sample of spectroscopically selected quiescent galaxies at the same redshift. Photometric selection identifies a majority of objects that have clear evidence for a recent short-lived burst of star formation within the last 1.5 Gyr, i.e. "post-starburst" galaxies, however we show that good quality continuum spectra are required to obtain physical parameters such as burst mass fraction and burst age. Dust attenuation appears to be the primary cause for misidentification of post-starburst galaxies, leading to contamination in spectroscopic samples where only the [OII] emission line is available, as well as a small fraction of objects lost from photometric samples. The 31 confirmed post-starburst galaxies have formed 40-90% of their stellar mass in the last 1-1.5 Gyr. We use the derived star formation histories to find that the post-starburst galaxies are visible photometrically for 0.5-1 Gyr. This allows us to update a previous analysis to suggest that 25-50% of the growth of the red sequence at z∼1 could be caused by a starburst followed by rapid quenching. We use the inferred maximum historical star formation rates of several 100-1000 M /yr and updated visibility times to confirm that sub-mm galaxies are likely progenitors of post-starburst galaxies. The short quenching timescales of 100-200 Myr are consistent with cosmological hydrodynamic models in which rapid quenching is caused by the mechanical expulsion of gas due to an AGN.