2019MNRAS.484.1724B

The mass-accretion rate is a key parameter in accretion disc theory, determining the accretion mode of black holes. In large-scale cosmological simulations of galaxy formation and evolution, the Bondi radius can be at most marginally resolved. In these simulations, the Bondi accretion formula is always used to estimate the black hole accretion rate. The Bondi solution is too simple, however, and does not represent the real accretion process. We perform simulations at the parsec scale of a hot accretion flow irradiated by a low-luminosity active galactic nucleus (AGN). We perform 77 simulations with varying density and temperature at the outer boundary (10 parsec). Our aim is to find a formula to calculate the real black hole accretion rate based on the gas density and temperature at the parsec scale. We define the Eddington accretion rate to be {dot}M_ Edd_=10L Edd_/c^2, with L_Edd and c the Eddington luminosity and speed of light respectively, and set the black hole mass to be 10⁸M^_☉, where M_☉ is the solar mass. We find that the black hole accretion rate can be expressed as {dot}M_ BH_/{dot}M_ Edd_=10^–3.11 (ρ_0/10^–22 g cm^–3)^1.36 (T_0/10⁷ K⁾-1.9^, where ρ₀ and T₀ are the density and temperature at the parsec scale, respectively. We find that the formula can accurately predict the luminosity of observed low-luminosity AGNs (with black hole mass ∼10⁸M^_☉). This formula can be used in subgrid models in large-scale cosmological simulations with a black hole mass of ∼10⁸M^_☉.