Unification Model of Active Galactic Nuclei by Photoionization Equilibrium Calculation Based on Radiative Hydrodynamic Simulations

To investigate the origin of the dependence of the covering factor on the Eddington ratio suggested by X-ray observations, we examined the angular distribution of HI and HII based on two-dimensional radiative hydrodynamic simulations. To calculate the Compton-thin covering factor $C_{22}$ and Compton-thick covering factor $C_{24}$ of HI alone, we performed one-dimensional photoionization equilibrium calculations with the XSTAR code based on radiative hydrodynamic simulations. The results obtained are as follows. (1) The Compton-thin covering factor $C_{22}$ of HI and HII is independent of the Eddington ratio and is approximately $70%$, while $C_{22}$ of HI alone is also independent of the Eddington ratio and is approximately $30%$. (2) The Compton-thick covering factor $C_{24}$ of HI has the same value as $C_{22}$ of HI. (3) Our $C_{24}$ is consistent with that obtained from X-ray observations. (4) Our $C_{22}$ agrees with that obtained from X-ray observations in a high Eddington ratio, while our $C_{22}$ is smaller than that from X-ray observations in a low Eddington ratio. (5) To explain the difference between $C_{22}$ obtained from theoretical calculations and that inferred from X-ray observations, a Compton-thin gas is required in regions extending at least $10~\mathrm{pc}$ beyond the current computational regions.

💡 Research Summary

The paper investigates why the covering factor (CF) of active galactic nuclei (AGN) appears to depend on the Eddington ratio in X‑ray observations. The authors combine two‑dimensional axisymmetric radiative hydrodynamic (RHD) simulations with one‑dimensional photo‑ionization equilibrium calculations using the XSTAR code to derive the angular distribution of neutral hydrogen (HI) and ionized hydrogen (HII) and to compute the Compton‑thin (C22) and Compton‑thick (C24) covering factors.

The RHD simulations, originally performed by Kudoh et al. (2024), model a dusty gas disk around a 10⁷ M⊙ supermassive black hole with a dust‑to‑gas mass ratio of 1 %. Four Eddington ratios are explored: log R_Edd = –3, –2, –1, and 0. The computational domain spans 10⁻⁴–2 pc in radius and ±2 pc in height. The simulations produce a dense equatorial structure (log n_H ≈ 8 cm⁻³) and a lower‑density outflow (log n_H ≈ 4 cm⁻³). Averaged over several snapshots, the hydrogen column density N_H reaches 10²² cm⁻² at polar angles of ~50° for the low‑Eddington cases and ~40° for the highest Eddington case, while N_H exceeds 10²⁵ cm⁻² between 65°–75°, indicating an almost fully neutral region at higher inclinations.

To assess the ionization state, the authors run XSTAR on each simulation cell, treating each cell as a slab illuminated by the spectrum emerging from the inner cell. The spectral energy distribution (SED) consists of a Shakura‑Sunyaev accretion‑disk component (assumed isotropic) and a power‑law corona with photon index Γ = 0.32 log R_Edd + 2.27. The ionization parameter ξ = L/(n_H r²) is computed, and the fractions of HI and HII are obtained. The key outcome is that the total gas (HI + HII) yields a Compton‑thin covering factor C22 ≈ 70 % independent of the Eddington ratio, whereas neutral gas alone gives C22 ≈ 30 % and, because the same neutral zones also exceed the 10²⁴ cm⁻² threshold, C24 (HI) ≈ 30 % as well.

When compared with the large X‑ray sample analyzed by Ricci et al. (2017a,b), the theoretical C24 matches observations across all Eddington ratios. The theoretical C22 matches the observed high‑Eddington‑ratio values (30–40 %) but falls short of the observed low‑Eddington‑ratio values (80–90 %). The authors attribute this discrepancy to the limited spatial extent of their simulations (≤ 2 pc). They argue that an additional Compton‑thin gas component extending at least 10 pc beyond the simulated region would raise the theoretical C22 to the observed levels for low Eddington ratios.

The study demonstrates that incorporating photo‑ionization equilibrium into radiation‑driven fountain models provides a physically grounded estimate of AGN torus covering factors. However, the reliance on 2‑D axisymmetry, isotropic disk emission, and a truncated computational domain are acknowledged limitations. Future work should involve fully three‑dimensional simulations with larger spatial scales to capture the extended, low‑density gas that likely contributes to the observed covering factors, thereby refining the connection between AGN feeding, feedback, and the observed X‑ray obscuration statistics.