High‐Resolution Simulations of the Plunging Region in a Pseudo‐Newtonian Potential: Dependence on Numerical Resolution and Field Topology

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Abstract
New three-dimensional magnetohydrodynamic simulations of accretion disk dynamics in a pseudo-Newtonian Paczyński-Wiita potential are presented. These have finer resolution in the inner disk than any previously reported. Finer resolution leads to increased magnetic field strength, greater accretion rate, and greater fluctuations in the accretion rate. One simulation begins with a purely poloidal magnetic field, the other with a purely toroidal field. Compared to the poloidal initial field simulation, a purely toroidal initial field takes longer to reach saturation of the magnetorotational instability and produces less turbulence and weaker magnetic field energies. For both initial field configurations, magnetic stresses continue across the marginally stable orbit; measured in units corresponding to the Shakura-Sunyaev α-parameter, the stress grows from ~0.1 in the disk body to as much as ~10 deep in the plunging region. Matter passing the inner boundary of the simulation has ~10% greater binding energy and ~10% smaller angular momentum than it did at the marginally stable orbit. Both the mass accretion rate and the integrated stress fluctuate widely on a broad range of timescales.
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