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The interaction between Active Galactic Nuclei (AGN) 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 allow to observe AGN feeding and feedback processes at high accretion rates. We apply a spectroastrometric analysis to VLT MUSE NFM-AO observations of Mrk 1044, a nearby super-Eddington accreting NLS1. This allows us to map two ionised gas outflows traced by [O$\,$III] which have velocities of $-560\pm20\,{\rm km\:s}^{-1}$ and $-144 \pm 5 \,{\rm km\:s}^{-1}$. Both outflows are spatially unresolved and located close to the galaxy nucleus ($<1\,{\rm pc}$). They have gas densities higher than $10^5\,{\rm cm}^{-3}$, 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 unresolved multi-phase outflow. A kinematic analysis suggests that significant turbulence may be present in the ISM around the nucleus, which may lead to a condensation rain, potentially explaining the efficient feeding of Mrk 1044's AGN. We identify an additional ionised gas outflowing component that is spatially resolved. It has a velocity of $-211 \pm 22 \,{\rm km\:s}^{-1}$ and a projected size of $4.6 \pm 0.6 \,{\rm pc}$. Within the innermost 0.5" (160$\,{\rm pc}$) around the nucleus we detect modest star formation hidden by the beam-smeared emission from the outflow, which suggests that Mrk 1044's AGN phase set on recently. We estimate that the multi-phase outflow has been launched $<10^4 \,{\rm yrs}$ ago. It 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., Comment: 17 pages. 12 figures. Re-submitted to A&A after minor revision. Comments welcome

We investigate how cosmic web environment impacts the average properties of central galaxies in the Sloan Digital Sky Survey (SDSS). We analyse how the average specific star-formation rate, stellar age, metallicity and element abundance ratio [$\alpha$/Fe] of SDSS central galaxies depend on distance from the cosmic web nodes, walls and filaments identified by DisPerSE. In our approach we control for galaxy stellar mass and local density differentiated between field and group environment. Our results confirm the known trend whereby galaxies exhibit lower specific star-formation rates with decreasing distance to the cosmic web features. Furthermore, we show that centrals closer to either nodes, walls or filaments are on average older, metal richer and $\alpha$-enhanced compared to their equal mass counterparts at larger distances. The identified property gradients appear to have the same amplitude for central galaxies in the field as for those in groups. Our findings support a cosmic web quenching that stems from nurture effects, such as ram pressure stripping and strangulation, and/or nature effects linked to the intrinsic properties of the cosmic web., Comment: 15 pages, 7 figures, 4 tables, accepted for publication in MNRAS

We investigate how cosmic web environment impacts the average properties of central galaxies in the Sloan Digital Sky Survey (SDSS). We analyse how the average specific star-formation rate, stellar age, metallicity and element abundance ratio [$\alpha$/Fe] of SDSS central galaxies depend on distance from the cosmic web nodes, walls and filaments identified by DisPerSE. In our approach we control for galaxy stellar mass and local density differentiated between field and group environment. Our results confirm the known trend whereby galaxies exhibit lower specific star-formation rates with decreasing distance to the cosmic web features. Furthermore, we show that centrals closer to either nodes, walls or filaments are on average older, metal richer and $\alpha$-enhanced compared to their equal mass counterparts at larger distances. The identified property gradients appear to have the same amplitude for central galaxies in the field as for those in groups. Our findings support a cosmic web quenching that stems from nurture effects, such as ram pressure stripping and strangulation, and/or nature effects linked to the intrinsic properties of the cosmic web., Comment: 15 pages, 7 figures, 4 tables, accepted for publication in MNRAS