BASS XXXI: Outflow scaling relations in low redshift X-ray AGN host galaxies with MUSE

Ionised gas kinematics provide crucial evidence of the impact that active galactic nuclei (AGN) have in regulating star formation in their host galaxies. Although the presence of outflows in AGN host galaxies has been firmly established, the calculation of outflow properties such as mass outflow rates and kinetic energy remains challenging. We present the [OIII]5007 ionised gas outflow properties of 22 z$<$0.1 X-ray AGN, derived from the BAT AGN Spectroscopic Survey using MUSE/VLT. With an average spatial resolution of 1" (0.1-1.2 kpc), the observations resolve the ionised gas clouds down to sub-kiloparsec scales. Resolved maps show that the [OIII] velocity dispersion is, on average, higher in regions ionised by the AGN, compared to star formation. We calculate the instantaneous outflow rates in individual MUSE spaxels by constructing resolved mass outflow rate maps, incorporating variable outflow density and velocity. We compare the instantaneous values with time-averaged outflow rates by placing mock fibres and slits on the MUSE field-of-view, a method often used in the literature. The instantaneous outflow rates (0.2-275 $M_{\odot}$ yr$^{-1}$) tend to be 2 orders of magnitude higher than the time-averaged outflow rates (0.001-40 $M_{\odot}$ yr$^{-1}$). The outflow rates correlate with the AGN bolometric luminosity ($L_{\rm bol}\sim$ 10$^{42.71}$-10$^{45.62}$ erg/s) but we find no correlations with black hole mass (10$^{6.1}$-10$^{8.9}$ M$_{\odot}$), Eddington ratio (0.002-1.1) and radio luminosity (10$^{21}$-10$^{26}$ W/Hz). We find the median coupling between the kinetic energy and $L_{\rm bol}$ to be 1%, consistent with the theoretical predictions for an AGN-driven outflow.