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

TL;DR

This study investigates how initial and boundary conditions influence the results of two-dimensional hydrodynamical simulations of hot accretion flows, revealing that initial conditions significantly affect density profiles but not the mass accretion rate's radial dependence.

Contribution

It systematically analyzes the impact of various initial and boundary conditions on accretion flow simulations, highlighting the robustness of the mass accretion rate profile against boundary condition choices.

Findings

Mass accretion rate slope $s$ is insensitive to initial conditions, within 0.47 to 0.55.

Density profile slope $p$ varies with initial conditions, between 0.48 and 0.8.

Results are not sensitive to different boundary conditions such as outflow or mass flux conservation.

Abstract

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.