Quantifying the AGN-driven outflows in ULIRGs (QUADROS) III: Measurements of the radii and kinetic powers of 8 near-nuclear outflows

As part of the QUADROS project to quantify the impact of AGN-driven outflows in rapidly evolving galaxies in the local universe, we present observations of 8 nearby ULIRGs ($0.04<z<0.2$) taken with the ISIS spectrograph on the $\mathit{\text{William}}\mathit{\text{Herschel}}\mathit{\text{Telescope}}$ (WHT), and also summarise the results of the project as a whole. Consistent with \cite{Rose2018}, we find that the outflow regions are compact (0.08 < $R_{[OIII]}$ < 1.5 kpc), and the electron densities measured using the [SII], [OII] trans-auroral emission-line ratios are relatively high (2.5 < log n${}_e$(cm${}^{-3}$) < 4.5, median log n${}_e$(cm${}^{-3})\sim 3.1$). Many of the outflow regions are also significantly reddened (median E(B-V) $\sim$ 0.5). Assuming that the de-projected outflow velocities are represented by the 5${}^{\mathrm{t}\mathrm{h}}$ percentile velocities ($v_{05}$) of the broad, blueshifted components of [OIII]$\lambda$5007, we calculate relatively modest mass outflow rates ($0.1<\dot{M}<20$ M${}_{\odot }$ yr${}^{-1}$, median $\dot{M}$ $\sim$ 2 M${}_{\odot }$ yr${}^{-1}$), and find kinetic powers as a fraction of the AGN bolometric luminosity ($\dot{F} = \dot{E}/L_{bol}$)intherange0.02<$\dot{F}$<3\mathrm{\%},median$\dot{F}$ $\sim$ 0.3 %). The latter estimates are in line with the predictions of multi-stage outflow models, or single-stage models in which only a modest fraction of the initial kinetic power of the inner disk winds is transferred to the larger-scale outflows. Considering the QUADROS sample as a whole, we find no clear evidence for correlations between the properties of the outflows and the bolometric luminosities of the AGN, albeit based on a sample that covers a relatively small range in $L_{bol}$. Overall, our results suggest that there is a significant intrinsic scatter in outflow properties of ULIRGs for a given AGN luminosity.