Today I worked out what hypotheses we are testing with the K+A environment research.
(1) Post-starburst galaxies lie in the same range of environments as "all" or "ordinary" galaxies.
(2) Post-starburst galaxies lie in the same range of environments as bulge-dominated or "early-type" galaxies.These hypotheses were both ruled out by Quintero et al and by Blake et al; in fact hypothesis (1) was very unlikely from the start, since no spectrally or morphologically selected subsample has the same environment distribution as "all" the galaxies ("all" doesn't really have a meaning here).
Indeed, both Quintero et al and Blake et al concluded that the mean or typical environments of K+As is the same as those of disk-dominated or "spiral" or star-forming galaxies. We already know, from work like Blanton et al, that star formation is the galaxy property most tied to environment. This leads to two new hypotheses
(3-weak) Post-starburst galaxies lie in the same range of environments as disk-dominated or "spiral" galaxies.
(3-strong) Post-starburst galaxies, at every measure of A-star excess (A/K), lie in the same range of environments as the subsample of disk-dominated or "spiral" galaxies that has the same value of A/K.
Our results confirm hypothesis (3-strong): Of all the star-formation-rate indicators, it is A-star excess that predicts the environment distribution, not H-alpha (since K+As have none by definition). This fits in with the idea that A/K evolves on timescales that are long like dynamical times.
The only statistically significant deviations we find from (3-strong) are at very small physical scales, where the dynamical time is likely shorter than the lifetime of an A star.