NUMERICAL SIMULATION OF HOT ACCRETION FLOWS. I. A LARGE RADIAL DYNAMICAL RANGE AND THE DENSITY PROFILE OF ACCRETION FLOW

Numerical simulations of hot accretion flow, both hydrodynamical and magnetohydrodynamical, have shown that the mass accretion rate decreases with decreasing radius; consequently, the density profile of accretion flow becomes flatter than in 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 suspect. In particular, the radial profiles of density and inflow 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(4)r(s) the radial profiles of accretion rate and density can be well described by (M) over dot(r) alpha r(s) and rho alpha r(-p). The values of (s, p) are (0.48, 0.65) and (0.4, 0.85) for the viscous parameters alpha = 0.001 and alpha = 0.01, respectively. More precisely, the accretion rate is constant (i.e., s = 0) within similar to 10r(s), but beyond 10r(s) we have s = 0.65 and 0.54 for alpha = 0.001 and 0.01, respectively. We find that the values of both s and p are similar in all numerical simulation works irrespective of whether a magnetic field is included or not and what kind of initial conditions are adopted. Such an apparently surprising common result can be explained by the most recent version of the adiabatic inflow-outflow model. The density profile we obtain is in good quantitative agreement with that obtained from the detailed observations and modeling of Sgr A* and NGC 3115. The origin and implications of such a profile will be investigated in a subsequent paper.