Electron densities from [S ii] lines significantly overestimate the impact of ionized AGN outflows

To explain the properties of the local galaxy population, theoretical models require active galactic nuclei (AGNs to inject energy into host galaxies, thereby expelling outflows of gas that would otherwise form stars. Observational tests of this scenario rely on determining outflow masses, which requires measuring the electron density ($n_\mathrm{ e}$) of ionized gas. However, recent studies have argued that the most commonly used diagnostic may underestimate electron densities (and hence overestimate outflow masses) by several orders of magnitude, casting doubt as to whether ionized AGN-driven outflows can provide the impact needed to reconcile observations with theory. Here, we investigate this by applying two different electron–density diagnostics to Sloan Digital Sky Survey (SDSS) spectroscopy of the Quasar Feedback (QSOFEED) sample of 48 nearby type-2 quasars. Accounting for uncertainties, we find that outflow masses implied by the transauroral-line electron-density diagnostic are significantly lower than those produced by the commonly-used ‘strong-line’ [S ii](6717/6731) method, indicating a different origin of these emission lines and suggesting that these doubts are justified. Nevertheless, we show that it is possible to modify the [S ii](6717/6731) electron–density diagnostic for our sample by applying a correction of $\mathrm{log}_{10}(n_{e\mathrm{,\, outflow}}\mathrm{ [cm}^{-3}\mathrm{]}) = \mathrm{log}_{10}(n_{e\mathrm{,[S\, II]}}\mathrm{ [cm}^{-3}\mathrm{]}) + 0.75(\pm 0.07)$ to account for this, which results in values that are statistically consistent with those produced using the transauroral-line method. The techniques that we present here will be crucial for outflow studies in the upcoming era of large spectroscopic surveys, which will also be able to verify our results and broaden this method to larger samples of AGN of different types.