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The molecular gas in galaxies traces both the fuel for star formation and the processes that can enhance or suppress star formation. Observations of the molecular gas state can thus point to when and why galaxies stop forming stars. In this study, we present Atacama Large Millimeter/submillimeter Array observations of the molecular gas in galaxies evolving through the post-starburst phase. These galaxies have low current star formation rates (SFRs), regardless of the SFR tracer used, with recent starbursts ending within the last 600 Myr. We present CO (3–2) observations for three post-starburst galaxies, and dense gas HCN/HCO⁺/HNC (1–0) observations for six (four new) post-starburst galaxies. The post-starbursts have low excitation traced by the CO spectral-line energy distribution up to CO (3–2), more similar to early-type than starburst galaxies. The low excitation indicates that lower density rather than high temperatures may suppress star formation during the post-starburst phase. One galaxy displays a blueshifted outflow traced by CO (3–2). MaNGA observations show that the ionized gas velocity is disturbed relative to the stellar velocity field, with a blueshifted component aligned with the molecular gas outflow, suggestive of a multiphase outflow. Low ratios of HCO⁺/CO, indicating low fractions of dense molecular gas relative to the total molecular gas, are seen throughout post-starburst phase, except for the youngest post-starburst galaxy considered here. These observations indicate that the impact of any feedback or quenching processes may be limited to low excitation and weak outflows in the cold molecular gas during the post-starburst phase.

Post-starburst (PSB), or “E + A,” galaxies represent a rapid transitional phase between major, gas-rich mergers and gas-poor, quiescent, early-type galaxies. Surprisingly, many PSBs have been shown to host a significant interstellar medium (ISM), despite theoretical predictions that the majority of the star-forming gas should be expelled in active galactic nuclei– or starburst-driven outflows. To date, the resolved properties of this surviving ISM have remained unknown. We present high-resolution ALMA continuum and CO(2–1) observations in six gas- and dust-rich PSBs, revealing for the first time the spatial and kinematic structure of their ISM on sub-kpc scales. We find extremely compact molecular reservoirs, with dust and gas surface densities rivaling those found in (ultra)luminous infrared galaxies. We observe spatial and kinematic disturbances in all sources, with some also displaying disk-like kinematics. Estimates of the internal turbulent pressure in the gas exceed those of normal star-forming disks by at least 2 orders of magnitude, and rival the turbulent gas found in local interacting galaxies, such as the Antennae. Though the source of this high turbulent pressure remains uncertain, we suggest that the high incidence of tidal disruption events in PSBs could play a role. The star formation in these PSBs’ turbulent central molecular reservoirs is suppressed, forming stars only 10% as efficiently as starburst galaxies with similar gas surface densities. “The fall” of star formation in these galaxies was not precipitated by complete gas expulsion or redistribution. Rather, this high-resolution view of PSBs’ ISM indicates that star formation in their remaining compact gas reservoirs is suppressed by significant turbulent heating.