Numerical Simulation of Hot Accretion Flows (I): A Large Radial Dynamical Range and the Density Profile of Accretion Flow

TL;DR

This paper extends the radial dynamical range of hot accretion flow simulations to four orders of magnitude, confirming that the accretion rate and density profiles follow specific power laws, aligning well with observations of Sgr A* and NGC 3115.

Contribution

It introduces a two-zone simulation approach to achieve a larger radial range, providing more accurate density and accretion rate profiles for hot accretion flows.

Findings

Radial profiles follow power laws with specific exponents.

Profiles are consistent across different magnetic field conditions.

Results match observational data for Sgr A* and NGC 3115.

Abstract

Numerical simulations of hot accretion flow have shown that the mass accretion rate decreases with decreasing radius; consequently the density profile of accretion flow becomes flatter compared to the case of a constant accretion rate. This result has important theoretical and observational implications. However, because of technical difficulties, the radial dynamic range in almost all previous simulations usually spans at most two orders of magnitude. This small dynamical range, combined with the effects of boundary conditions, makes the simulation results suspectable. Especially, the radial profiles of density and accretion rate may not be precise enough to be used to compare with observations. In this paper we present a "two-zone" approach to expand the radial dynamical range from two to four orders of magnitude. We confirm previous results and find that from $r_s$ to $ 10^4r_s$ the radial profiles of accretion rate and density can be well described by $\dot{M}(r)\propto r^s$ and $\rho\propto r^{-p}$. The values of (s, p) are (0.48, 0.65) and (0.4, 0.85), for viscous parameter $\alpha=0.001$ and 0.01, respectively. We have looked up numerical simulation works in the literature and found that the values of $s$ and $p$ are all similar, no matter a magnetic field is included or not and what kind of initial conditions are adopted. The density profile we obtain is in good quantitative agreement with that obtained from the detailed observations and modeling to Sgr A* and NGC 3115. The origin of such a accretion rate profile will be investigated in a subsequent paper.