Tracing AGN Feedback Power with Cool/Warm Outflow Densities: Predictions and Observational Implications

Winds launched at the scale of the accretion disc or dusty torus in Active Galactic Nuclei (AGN) are thought to drive energy-conserving outflows that shape galaxy evolution. The key signature of such outflows, the presence of a hot ($T \gtrsim 10^9 , \rm K$), shocked wind component, is hard to detect directly. Observations of AGN outflows typically probe a separate outflow phase: cool/warm gas with $T \lesssim 10^5 , \rm K$. Here, we show that the density of cool outflowing gas scales with AGN luminosity, serving as an indirect diagnostic of the elusive hot, shocked wind. We use hydrodynamic simulations with the moving-mesh code AREPO to target the interaction between a small-scale AGN wind of speed $\approx 10^4 , \rm km , s^{-1}$ and galactic discs containing an idealised, clumpy interstellar medium (ISM). Through a new refinement scheme targeting rapidly-cooling, fast-moving gas, our simulations reach a resolution of $\lesssim 0.1 , \rm pc$ in the cool, outflowing phase. We extract an ensemble of cool clouds from the AGN-driven outflows produced in our simulations, finding that their densities increase systematically with AGN wind power and AGN luminosity. Moreover, the mass distribution and internal properties of these cloudlets appear to be insensitive to the initial properties of the ISM, and shaped mainly by the dynamics of radiative, turbulent mixing layers. The increase in cool outflow density with kinetic wind power and AGN luminosity has profound implications for observational estimates of outflow rates and their scaling with AGN luminosity. Depending on the available outflow and density tracers, observationally-derived outflow rates may be overestimated by orders of magnitude.

💡 Research Summary

This paper investigates how the density of the cool (T ≤ 2 × 10⁴ K) outflowing gas in active galactic nuclei (AGN) can serve as an indirect tracer of the hot, shocked wind component that is otherwise extremely difficult to detect. The authors employ the moving‑mesh hydrodynamics code AREPO together with a novel “BOLA” (Boundary Layer for AGN) wind injection scheme that launches an isotropic, ultra‑fast wind (v_wind ≈ 10⁴ km s⁻¹) from a spherical surface of radius 10 pc at the centre of a model galaxy. The wind’s kinetic power is tied directly to the AGN bolometric luminosity (L_AGN = 10⁴³–10⁴⁷ erg s⁻¹), ensuring that the injected momentum flux follows L_AGN/c.

The galactic disc is initialized as a two‑phase, clumpy interstellar medium (ISM) with a mean total number density of 5 cm⁻³, a total gas mass of 1.4 × 10⁹ M_⊙, and a fractal distribution of cold clumps (T ≈ 10⁴ K) generated via the PyFC package. The clump size spectrum spans 40–333 pc, reproducing observed ISM fractality. The hot background is set to n = 10⁻² cm⁻³ and T = 10⁷ K, and the whole system is in pressure equilibrium.

A key methodological advance is a refinement scheme that targets only the rapidly cooling, high‑Mach number gas that makes up the outflowing cool clouds. While the default AREPO refinement maintains a target cell mass of 100 M_⊙, the new algorithm reduces the target mass by a factor β whenever (i) the cell mass exceeds a cooling mass scale M_cool, or (ii) the local Mach number exceeds a threshold. This yields an effective resolution of ≲ 0.1 pc in the cool phase, allowing the authors to resolve cloud radii down to a few parsecs and capture the formation and destruction of cloudlets within the turbulent mixing layer between the wind and the ambient ISM.

The simulations reveal several robust trends. First, the mean number density of the cool gas clouds (n_cg) scales approximately linearly with L_AGN. For L_AGN = 10⁴⁴ erg s⁻¹, n_cg ≈ 40 cm⁻³; for L_AGN = 10⁴⁶ erg s⁻¹, n_cg ≈ 400 cm⁻³. This indicates that more powerful AGN winds compress the cooling gas more efficiently, producing denser cloudlets. Second, the mass and size distribution of the clouds is remarkably insensitive to the initial ISM parameters (mean density, clump size spectrum). Across all runs, cloud radii are ≤ 10 pc and masses lie in the range 10³–10⁵ M_⊙, suggesting that the properties of the turbulent, radiatively cooling mixing layer dominate cloud formation rather than the pre‑existing ISM structure. Third, while the hot wind bubble expands primarily via thermal pressure (energy‑conserving), the cool clouds are accelerated mainly by ram pressure from the wind. Consequently, the cool phase carries only ∼1 % of the total kinetic energy, implying a low coupling efficiency between the hot bubble and the dense phase.

These findings have profound observational implications. Most observational estimates of outflow mass‑loss rates (Ṁ_out) rely on emission‑line diagnostics (e.g.,