The Close AGN Reference Survey (CARS) Tracing the circumnuclear star formation in the super-Eddington NLS1 Mrk 1044

Context. The interaction between active galactic nuclei (AGNs) and their host galaxies is scarcely resolved. Narrow-line Seyfert 1 (NLS1) galaxies are believed to represent AGN at early stages of their evolution and to allow one to observe feeding and feedback processes at high black hole accretion rates. Aims. We aim to constrain the properties of the ionised gas outflow in Mrk 1044, a nearby super-Eddington accreting NLS1. Based on the outflow energetics and the associated timescales, we estimate the outflow's future impact on the ongoing host galaxy star formation on different spatial scales. Methods. We applied a spectroastrometric analysis to observations of Mrk 1044's nucleus obtained with the adaptive-optics-assisted narrow field mode of the VLT/MUSE instrument. This allowed us to map two ionised gas outflows traced by [O III], which have velocities of -560 +/- 20 km s(-1) and -144 +/- 5 km s(-1). Furthermore, we used an archival spectrum from the Space Telescope Imaging Spectrograph on HST to identify two Ly-alpha absorbing components that escape from the centre with approximately twice the velocity of the ionised gas components. Results. Both [O III] outflows are spatially unresolved and located close to the AGN (<1 pc). They have gas densities higher than 10(5) cm(-3), which implies that the BPT diagnostic cannot be used to constrain the underlying ionisation mechanism. We explore whether an expanding shell model can describe the velocity structure of Mrk 1044's multi-phase outflow. In the ionised gas emission, an additional outflowing component, which is spatially resolved, is present. It has a velocity of -211 +/- 22 km s(-1) and a projected size of 4.6 +/- 0.6 pc. Our kinematic analysis suggests that significant turbulence is present in the interstellar medium around the nucleus, which may lead to a condensation rain, potentially explaining the efficient feeding of Mrk 1044's AGN. Within the innermost 0.5 '' (160 pc), we detect modest star formation hidden by the beam-smeared emission from the outflow. Conclusions. We estimate that the multi-phase outflow was launched <10(4) yr ago. Together with the star formation in the vicinity of the nucleus, this suggests that Mrk 1044's AGN phase started only recently. The outflow carries enough mass and energy to impact the host galaxy star formation on different spatial scales, highlighting the complexity of the AGN feeding and feedback cycle in its early stages.