On the convective instability of hot radiative accretion flows

How many fraction of gas available at the outer boundary can finally fall onto the black hole is an important question. It determines the observational appearance of accretion flows, and is also related with the evolution of black hole mass and spin. Previous two-dimensional hydrodynamical simulations of hot accretion flows find that the flow is convectively unstable because of its inward increase of entropy. As a result, the mass accretion rate decreases inward, i.e., only a small fraction of accretion gas can fall onto the black hole, while the rest circulates in the convective eddies or lost in convective outflows. Radiation is usually neglected in these simulations. In many cases, however, radiative cooling is important. In the regime of the luminous hot accretion flow (LHAF), radiative cooling is even stronger than the viscous dissipation. In the one dimensional case, this implies that the inward increase of entropy will become slower or the entropy even decreases inward in the case of an LHAF. We therefore expect that convective instability becomes weaker or completely disappears when radiative cooling is important. To examine the validity of this expectation, in this paper we perform two-dimensional hydrodynamical simulations of hot accretion flows with strong radiative cooling. We find that compared to the case of negligible radiation, convection only becomes slightly weaker. Even an LHAF is still strongly convectively unstable, its radial profile of accretion rate correspondingly changes little. We find the reason is that the entropy still increases inward in the two-dimensional case.Comment: moderately revised, one figure added; 11 pages, 10 figures; accepted by MNRA

Does the circularization radius exist or not for low angular momentum accretion?

If the specific angular momentum of accretion gas at large radius is small compared to the local Keplerian value, one usually believes that there exists a "circularization radius" beyond which the angular momentum of accretion flow is almost a constant while within which a disk is formed and the angular momentum roughly follows the Keplerian distribution. In this paper, we perform numerical simulations to study whether the picture above is correct in the context of hot accretion flow. We find that for a steady accretion flow, the "circularization radius" does not exist and the angular momentum profile will be smooth throughout the flow. However, for transient accretion systems, such as the tidal disruption of a star by a black hole, a "turning point" should exist in the radial profile of the angular momentum, which is conceptually similar to the "circularization radius". At this radius, the viscous timescale equals the life time of the accretion event. The specific angular momentum is close to Keplerian within this radius, while beyond this radius the angular momentum is roughly constant.Comment: 5 pages, 2 figures, accepted by MNRA

On the role of initial and boundary conditions in numerical simulations of accretion flows

We study the effects of initial and boundary conditions, taking two-dimensional hydrodynamical numerical simulations of hot accretion flow as an example. The initial conditions considered include a rotating torus, a solution expanded from the one-dimensional global solution of hot accretion flows, injected gas with various angular momentum distributions, and the gas from a large-scale numerical simulation. Special attention is paid to the radial profiles of the mass accretion rate and density. Both can be described by a power-law function, $\dot{M}\propto r^s$ and $\rho\propto r^{-p}$. We find that if the angular momentum is not very low, the value of $s$ is not sensitive to the initial condition and lies within a narrow range, 0.47\la s \la 0.55. However, the value of $p$ is more sensitive to the initial condition and lies in the range 0.48\la p \la 0.8. The diversity of the density profile is because different initial conditions give different radial profiles of radial velocity due to the different angular momentum of the initial conditions. When the angular momentum of the accretion flow is very low, the inflow rate is constant with radius. Taking the torus model as an example, we have also investigated the effects of inner and outer boundary conditions by considering the widely adopted "outflow" boundary condition and the "mass flux conservation" condition. We find that the results are not sensitive to these two boundary conditions.Comment: 10 pages, 15 figures, accepted by MNRA