Abstract:

The models of radiatively inefficient accretion flow (RIAF) are used to explain the observations of the hot gas that surrounds Sgr A* and the supermassive black holes of elliptical galaxies. The direct numerical simulations of RIAFs have shown that convection is a general feature in such accretion flows. In this paper, we analytically investigate time evolution of RIAFs in the presence of convection. The convection turbulent will be responsible to transport of angular momentum and energy. We consider the cases of inward and outward transports of angular momentum by convection. To estimate strength of convection diffusion, we use mixing length theory and introduce the convection parameter α_c in analogy to α-prescription of standard theory of accretion discs. We apply a wide range of viscosity parameter, α = 0.001–0.3, to study the influences of viscosity on the strength of convection parameter. We found that the results critically depend on the parametrized magnitude of viscosity and the transport direction of angular momentum by convection. As, with magnitude of viscosity, the gas density decreased and the radial infall velocity increased. The unlike to these physical variables, the convection parameter does not show a regular behaviour with respect to different ranges of viscosity parameter. But, in the both cases of inward and outward angular momentum transfer, the convection becomes important in accreting gas if the viscosity parameter is sufficiently small, α ≲ 0.1, else the convection becomes weaker than viscosity throughout the accreting gas.