Self-consistent models of spherical accretion onto black holes. I. One-temperature solutions

Spherically symmetric, steady state accretion onto a black hole is considered for various dimensionless accretion rates ṁ (≡ Mc²/L_E, where Ṁ is the accretion rate and L_E is the Eddington luminosity). Models are constructed by iteratively integrating relativistic hydrodynamic and radiation moment equations with bremsstrahlung and Comptonization as the main radiative processes. Electrons and ions are assumed to be coupled completely. The effects of preheating, and the shock that may result, are also considered. At least one type of self-consistent model is found for any ṁ, self-consistency meaning that the gas at all radii is heated by the radiation it produces. Two sets of models (characterized by different temperatures) were found in the range 3 ≲ ṁ ≲ 100. The dimensionless luminosity l (≡ L/L_E) is 5.8 × 10^-5ṁ² for ṁ ≪ 1. Lowtemperature models (T ≃ 10⁴ K), which exist for ṁ ≳ 0.1, have l ≃ 7 × 10^-10ṁln (10⁸/ṁ); high-temperature models, which exist for 3 ≲ ṁ ≲ 100, have 3 × 10^-4 ≲ l ≲ 3 × 10^-2. The ṁ = 100 model has the highest luminosity of all: l = 2.6 × 10^-2. High-ṁ models have correct mean photon energies for AGNs. Because of the effects of preheating, no steady state high-temperature self-consistent solution exists for 0.1 ≲ ṁ ≲ 3 without a shock, and none exists for ṁ ≲ 100 regardless of the presence or absence of a shock. The calculations also suggest that the high-temperature ṁ > 1 model is unstable at a fixed accretion rate.