We are studying the slow (ṁ < 1) spherical accretion of a gas onto a supermassive (M ≈ 108M⊙) black hole in the presence of a strong tangled magnetic field. In the core with radius 2.5 rg < r < 10 rg protons are isotropized due to scattering in magnetic field, but are not thermalized since the characteristic time of pp — Coulomb scattering is less than the infall time. A proton moves in the electron gas with a friction due to pe — scattering, gradually transferring energy to electrons. The standard equations for the proton gas allow the virial regime of accretion when the kinetic energy of the proton is a function of a distance only Ek(r) = (2/5) mpc2 (rg/r). The model is relevant to the slow subsonic settling of matter onto the black hole, as, for example, in the upstream region after the shock standing at a distance r ∼ 20 rg (Mészàros and Ostriker 1983). Electrons are thermalized and are cooling predominantly by bremsstrahlung radiation. For ṁ ≲ 0.1 the core is transparent for bremsstrahlung photons. In agreement with Park (1990) the e+e− - pair production is found to be insignificant. The equilibrium between the energy release in pe — scattering and the bremsstrahlung radiation results in the almost isothermal core with the temperature Te ≈ 4 me, which slightly increases towards the inner edge of the core. The only role of magnetic field is the isotropization of the proton gas, as the synchrotron radiation is strongly self-absorbed. Therefore the model is insensitive to the precise value of H.
The role of electron heating physics in images and variability of the Galactic Centre black hole Sagittarius A*