SQuIGG E: Spatially resolved NIRSpec Pa alpha reveals that the most CO-luminous, z about0.7 post-starburst galaxies exhibit falling---but still active---star formation behind optically thick dust

One of the fundamental uncertainties in the study of galaxies at the interface between star formation and quiescence--post-starburst galaxies--is their instantaneous star formation rate. While these galaxies appear quiescent in the rest UV-optical, many of the youngest systems are highly CO luminous, implying dense molecular gas, and potentially star formation. However, their instantaneous star formation rates have proved elusive, as measurements with rest-optical emission lines or UV-to-IR SED fitting yield order-of-magnitude uncertainty. Here, we present JWST/NIRSpec G395M/170LP integral field spectroscopy of the three most CO-luminous massive galaxies in the SQuIGG E survey, spatially resolving Pa α /Br γ /Br β to map the dust-corrected star formation rate. We find that these galaxies host star formation rates of 27-80 M yr-1, though about30-40% of the emission may arise from non-star-forming ionization (AGN or shocks), implied by high [FeII]/Pa α in central spaxels. We also find effective A Paα about1 and individual about700 pc spaxels with A Paα about2, implying significant dust obscuration of nebular regions that contribute little to the rest-optical lines. These galaxies are not consistent with total quiescence; the measured star formation rates place these galaxies on or above the main sequence. However, their star formation rates are significantly lower (about0.5-1 dex) than the peak star formation rates inferred from spectrophotometric fitting. We propose that the CO luminous post-starburst phase represents the last gasp of star formation in galaxies on the rapid quenching pathway, and that dust-obscured star formation, outflows, and (speculatively) an uncertain CO-to-H2 conversion reconcile their gas exhaustion with observed timescales of fading.