Isothermal Bondi Accretion in Two-component Jaffe Galaxies with a Central Black Hole

The fully analytical solution for isothermal Bondi accretion onto a black hole (MBH) at the center of two-component Jaffe galaxy models is presented. In a previous work, we provided the analytical expressions for the critical accretion parameter and the radial profile of the Mach number in the case of accretion onto an MBH at the center of a spherically symmetric one-component Jaffe galaxy model. Here we apply this solution to galaxy models where both the stellar and total mass density distributions are described by the Jaffe profile with different scale lengths and masses and to which a central MBH is added. For such galaxy models, all the relevant stellar dynamical properties can also be derived analytically. In these new models, the hydrodynamical and stellar dynamical properties are linked by imposing that the gas temperature is proportional to the virial temperature of the galaxy stellar component. The formulae that are provided allow one to evaluate all flow properties and are then useful for estimates of the scale radius and mass flow rate when modeling accretion onto MBHs at the center of galaxies. As an application, we quantify the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the MBH, under the hypothesis of classical Bondi accretion.