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

Two dimensional numerical simulations of Supercritical Accretion Flows revisited

We study the dynamics of super-Eddington accretion flows by performing two-dimensional radiation-hydrodynamic simulations. Compared with previous works, in this paper we include the $T_{\theta\phi}$ component of the viscous stress and consider various values of the viscous parameter $\alpha$. We find that when $T_{\theta\phi}$ is included, the rotational speed of the high-latitude flow decreases, while the density increases and decreases at the high and low latitudes, respectively. We calculate the radial profiles of inflow and outflow rates. We find that the inflow rate decreases inward, following a power law form of $\dot{M}_{\rm in}\propto r^s$. The value of $s$ depends on the magnitude of $\alpha$ and is within the range of $\sim 0.4-1.0$. Correspondingly, the radial profile of density becomes flatter compared with the case of a constant $\dot{M}(r)$. We find that the density profile can be described by $\rho(r)\propto r^{-p}$, and the value of $p$ is almost same for a wide range of $\alpha$ ranging from $\alpha=0.1$ to $0.005$. The inward decrease of inflow accretion rate is very similar to hot accretion flows, which is attributed to the mass loss in outflows. To study the origin of outflow, we analyze the convective stability of slim disk. We find that depending on the value of $\alpha$, the flow is marginally stable (when $\alpha$ is small) or unstable (when $\alpha$ is large). This is different from the case of hydrodynamical hot accretion flow where radiation is dynamically unimportant and the flow is always convectively unstable. We speculate that the reason for the difference is because radiation can stabilize convection. The origin of outflow is thus likely because of the joint function of convection and radiation, but further investigation is required.Comment: 16 pages, 13 figures, accepted for publication in Ap

Magnetothermal and magnetorotational instabilities in hot accretion flows

In a hot, dilute, magnetized accretion flow, the electron mean-free path can be much greater than the Larmor radius, thus thermal conduction is anisotropic and along magnetic field lines. In this case, if the temperature decreases outward, the flow may be subject to a buoyancy instability (the magnetothermal instability, or MTI). The MTI amplifies the magnetic field, and aligns field lines with the radial direction. If the accretion flow is differentially rotating, the magnetorotational instability (MRI) may also be present. Using two-dimensional, time-dependent magnetohydrodynamic simulations, we investigate the interaction between these two instabilities. We use global simulations that span over two orders of magnitude in radius, centered on the region around the Bondi radius where the infall time of gas is longer than the growth time of both the MTI and MRI. Significant amplification of the magnetic field is produced by both instabilities, although we find that the MTI primarily amplifies the radial component, and the MRI primarily the toroidal component, of the field, respectively. Most importantly, we find that if the MTI can amplify the magnetic energy by a factor $F_t$, and the MRI by a factor $F_r$, then when the MTI and MRI are both present, the magnetic energy can be amplified by a factor of $F_t \cdot F_r$. We therefore conclude that amplification of the magnetic energy by the MTI and MRI operates independently. We also find that the MTI contributes to the transport of angular momentum, because radial motions induced by the MTI increase the Maxwell (by amplifying the magnetic field) and Reynolds stresses. Finally, we find that thermal conduction decreases the slope of the radial temperature profile. The increased temperature near the Bondi radius decreases the mass accretion rate.Comment: 8 pages, 9 figures, accepted by MNRA