The magnetic field assumed in our models is normalized either to β = 100, which means thermally dominated accretion flows, or to β = 1, which means actually quite strong magnetization and equilibrium ratio of the magnetic and gas pressures. The gas pressure is set by the solution of the Bondi transonic accretion flow, which is our initial condition for the simulation. Only if the magnetic pressure does not add a high contribution to this flow structure can we safely assume that the solution holds, and the gas falls supersonically to the black hole downstream of the sonic point, ultimately reaching the speed of light at the black hole horizon. We perturb this flow in time, by adding a slow rotation to the gas; hence, our sonic point is moving, and the shape of the sonic surface is disturbed. However, when the magnetic pressure is substantially large, the initial solution for the transonic accretion may not be a good approximation. Already at the beginning, multiple critical points might exist in the flow. The possible existence of shocks in low angular momentum flows connected with the presence of multiple critical points in the phase space has been studied from different points of view during the past 30 yr. However, the theoretical works that describe the fundamental properties of the low angular momentum accretion and that usually treat the steady solution of the equations have so far been carried out only for nonmagnetized and usually also nonviscous flows (Abramowicz & Zurek 1981; Abramowicz & Chakrabarti 1990; Das 2002; Das & Czerny 2012). Hydrodynamical models of the low angular momentum accretion flows have been studied already in two and three dimensions, e.g., by Proga & Begelman (2003) and Janiuk et al. (2008, 2009). In those simulations, a single, constant value of the specific angular momentum was assumed, while the variability of the flows occurred owing to, e.g., nonspherical or nonaxisymmetric distribution of the matter. The level of this variability was also dependent on the adiabatic index (see also Palit et al. 2019). However, these studies considered nonmagnetized flow only, which limits the applicability of these models to observational data and to the stellar evolution and presupernova studies (Heger et al. 2005). The range of strength of the magnetic field varies from very low values in the interstellar medium to extremely high values of ∼ 1015 G in the magnetars, which are extremely magnetized neutron stars. During the accretion process, the magnetic field in the star is likely to be amplified in the innermost region of the black hole, so a negligible amount of magnetic field in those regions, where the shock and the sonic point could be located, is thus not anticipated. The only method, however, to describe the effect of strong magnetic fields in the context of transonic accretion with low angular momentum is via numerical simulations, because no analytic solution of this problem exists, to the best of our knowledge. Hence, setting up the initial condition with strong magnetic fields overimposed on the slowly rotating transonic Bondi flow is a simple but working approach that we make here.
Citation: Abramowicz & Zurek 1981
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