We present the analysis of the ALMA CO(2−1) emission line and the underlying 1.2 mm continuum of Mrk 509 with spatial resolution of ∼270 pc. This local Seyfert 1.5 galaxy, optically classified as a spheroid, is known to host an ionised disc, a starburst ring, and ionised gas winds on both nuclear (ultra-fast outflows) and galactic scales. From CO(2−1) we estimate a molecular gas reservoir of MH2 = 1.7 × 109 M⊙, located within a disc of size ∼5.2 kpc, with Mdyn = (2.0 ± 1.1) × 1010 M⊙ inclined at 44 ± 10 deg. The molecular gas fraction within the disc is μgas = 5%, consistent with that of local star-forming galaxies with similar stellar mass. The gas kinematics in the nuclear region within r ∼ 700 pc, that is only marginally resolved at the current angular resolution, suggests the presence of a warped nuclear disc. Both the presence of a molecular disc with ongoing star formation in a starburst ring, and the signatures of a minor merger, are in agreement with the scenario where galaxy mergers produce gas destabilisation, feeding both star formation and AGN activity. The spatially resolved Toomre Q-parameter across the molecular disc is in the range Qgas = 0.5 − 10, and shows that the disc is marginally unstable across the starburst ring, and stable against fragmentation at nucleus and in a lopsided ring-like structure located inside of the starburst ring. We find complex molecular gas kinematics and significant kinematics perturbations at two locations, one within 300 pc of the nucleus and one 1.4 kpc away close to the region with high Qgas, that we interpret as molecular winds with velocity v98 = 200 − 250 km s−1. The total molecular outflow rate is in the range 6.4−17.0 M⊙ yr−1 for the optically thin and thick cases, respectively. The molecular wind total kinetic energy is consistent with a multiphase momentum-conserving wind driven by the AGN with Ṗof/Ṗrad in the range 0.06−0.5. The spatial overlap of the inner molecular wind with the ionised wind, and their similar velocity suggest a cooling sequence within a multiphase wind driven by the AGN. The second outer molecular wind component overlaps with the starburst ring, and its energy is consistent with a supernova-driven wind arising from the starburst ring.

We present the first systematic study of the molecular gas and star formation efficiency in a sample of ten narrow-line Seyfert 1 galaxies selected to have X-ray Ultra Fast Outflows and, therefore, to potentially show AGN feedback effects. CO observations were obtained with the IRAM 30m telescope in six galaxies and from the literature for four galaxies. We derived the stellar mass, star formation rate, AGN and FIR dust luminosities by fitting the multi-band spectral energy distributions with the CIGALE code. Most of the galaxies in our sample lie above the main sequence (MS) and the molecular depletion time is one to two orders of magnitude shorter than the one typically measured in local star-forming galaxies. Moreover, we found a promising correlation between the star formation efficiency and the Eddington ratio, as well as a tentative correlation with the AGN luminosity. The role played by the AGN activity in the regulation of star formation within the host galaxies of our sample remains uncertain (little or no effect? positive feedback?). Nevertheless, we can conclude that quenching by the AGN activity is minor and that star formation will likely stop in a short time due to gas exhaustion by the current starburst episode.