Spitzer-MIPS 24 micron and ground-based observations of the rich galaxy cluster Abell 851 at z=0.41 are used to derive star formation rates from the mid-IR 24 micron and from [O II] 3727 emission. Many cluster galaxies have SFR(24 um)/SFR([O II]) >> 1, indicative of star formation highly obscured by dust. We focus on the substantial minority of A851 cluster members where strong Balmer absorption points to a starburst on a 10^{8-9} year timescale. As is typical, A851 galaxies with strong Balmer absorption occur in two types: with optical emission (starforming), and without (post-starburst). Our principal result is the former, so-called e(a) galaxies, are mostly detected (9 out of 12) at 24 um -- for these we find typically SFR(24 um)/SFR([O II]) ~ 4. Strong Balmer absorption and high values of SFR(24 um)/SFR([O II]) both indicate moderately active starbursts and support the picture that e(a) galaxies are the active starbursts that feed the post-starburst population. While 24 um detections are frequent with Balmer-strong objects (even 6 out of 18 of the supposedly post-starburst galaxies are detected) only 2 out of 7 of the continuously starforming `e(c) galaxies (with weak Balmer absorption) are detected -- for them, SFR(24 um)/SFR([O II]) ~ 1. Their optical spectra resemble present-epoch spirals that dominate todays universe; we strengthen this association by that SFR(24 um)/SFR([O II]) ~ 1 is the norm today. That is, not just the amount of star formation, but its mode, has evolved strongly from z ~ 0.4 to the present. By fitting spectrophotometric models we measure the strength and duration of the bursts to quantify the evolutionary sequence from active- to post-starburst, and to harden the evidence that moderately active starbursts are the defining feature of starforming cluster galaxies at z ~ 0.4.
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