Electron densities from [S II] lines significantly overestimate the impact of ionised AGN outflows

TL;DR

This work compares two electron-density diagnostics for AGN-driven ionised outflows in 48 nearby QSO2s, using a robust Monte Carlo spectral-fitting approach to derive densities from both the transauroral lines and the [S II] 6717/6731 doublet. It finds that transauroral densities are systematically higher (≈0.8 dex) than those from [S II], implying lower outflow masses when TR is used, and demonstrates that a simple correction of +$0.75$ dex to [S II] densities aligns the two methods for this sample. The authors advocate using the transauroral diagnostic for kinematic outflow studies and provide a sample-specific correction when TR data are unavailable, enabling more accurate estimates of outflow energetics for current and future large spectroscopic surveys. These results have significant implications for assessing the role of AGN feedback in galaxy evolution by refining a key quantity: the electron density that sets outflow mass and energy budgets.

Abstract

To explain the properties of the local galaxy population, theoretical models require active galactic nuclei (AGN) 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 ($n_e$) of ionised 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 ionised 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 $\mathrm{log}_{10}(n_{e\mathrm{,\, outflow}}\mathrm{ [cm}^{-3}\mathrm{]}) = \mathrm{log}_{10}(n_{e\mathrm{,[S\,II]}}\mathrm{ [cm}^{-3}\mathrm{]}) + 0.75(\pm0.07)$ 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.

Figures (9)

• Figure 1: Spectral fit to the flux-normalised, de-redshifted spectrum of the QSO2 J1405+40 that was produced using our fitting routine. The observed spectrum is represented by the solid black line, with $1\sigma$ flux uncertainties shown in shaded grey; the overall fit to the spectrum is shown as a solid red line; the emission-line model is shown as a dashed-dotted blue line, and the stellar-continuum fit (see Section \ref{['section: spectral_fitting: stellar_continuum_modelling']} and Figure \ref{['fig: stellar_continuum_fit']}) is shown as a dashed orange line. The full wavelength range of the spectrum is shown in the top panel (in which the flux axis is shown logarithmically for presentation purposes); the other panels show the fits to key emission lines used in our analysis along with the $\mathrm{[O\,II]}\lambda\lambda4959,5007$ doublet and H$\alpha+\mathrm{[N\,II]}\lambda\lambda6548,6583$ lines that we include to better constrain the fits. Here, the emission-line models have been offset to the level of the continuum for presentation purposes.
• Figure 2: The variation of the [S II](6717/6731) flux ratio with electron density, as modelled using the PyNeb module for an electron temperature of $T_e=15\mathrm{,}000$ K (black line); the shaded grey area shows the values of the ratio between $8000<T_e<22000$ K. The solid red lines indicate the measured ratio with $1\sigma$ uncertainties for each object in the sample at its corresponding electron-density value.
• Figure 3: Example transauroral-line-ratio ($TR$) grid for an ionising-source spectral index of $\alpha=1.5$, an ionisation parameter of $\mathrm{log}U=-3.00$, and solar-metallicity gas; the black points represent the line ratios predicted by this photoionisation model for gas of different electron densities ($2.00<\mathrm{log}_{10}(n_e\mathrm{[cm}^{-3}])<6.00$) and colour-excess values ($0.01<E(B-V)<1.00$). The blue shaded regions contain 67 per cent of the Monte Carlo realisations for each object in our sample.
• Figure 4: Non-parametric velocity width ($W_{80}$; the velocity width containing 80 per cent of the total line flux) distribution for the $\mathrm{[O\,III]}\lambda5007$ emission-line profiles in our sample. The dashed yellow line corresponds to a line width of $400$ km s$^{-1}$, above which the profiles can be considered to have a significant non-rotational component (see Bessiere2024).
• Figure 5: Two-dimensional histogram of electron densities measured by the transauroral-line-technique ($TR$) and [S II](6717/6731) flux ratio for the 10,000 Monte Carlo realisations for each object in the QSOFEED sample; one-dimensional histograms for the densities derived from each method are shown above and to the right. The black contours contain 10, 30, 50, 70, and 90 per cent of all realisations for the entire sample, while the grey shaded regions contain 67 per cent of the realisations for individual objects. The solid red line represents the one-to-one relation between densities measured with each technique --- it can be seen that the majority of the realisations fall below this line, indicating that the $TR$ method systematically produces values that are $\sim$0.8 dex higher than the [S II] ratio.