Simulations of magnetized discs around black holes: effects of black hole spin, disc thickness and magnetic field geometry

Abstract

The standard general relativistic model of a razor-thin accretion disk around\na black hole, developed by Novikov & Thorne (NT) in 1973, assumes the shear\nstress vanishes at the radius of the innermost stable circular orbit (ISCO) and\nthat, outside the ISCO, the shear stress is produced by an effective turbulent\nviscosity. However, astrophysical accretion disks are not razor-thin, it is\nuncertain whether the shear stress necessarily vanishes at the ISCO, and the\nmagnetic field, which is thought to drive turbulence in disks, may contain\nlarge-scale structures that do not behave like a simple local scalar viscosity.\nWe describe three-dimensional general relativistic magnetohydrodynamic\nsimulations of accretion disks around black holes with a range of spin\nparameters, and we use the simulations to assess the validity of the NT model.\nOur fiducial initial magnetic field consists of multiple (alternating polarity)\npoloidal field loops whose shape is roughly isotropic in the disk in order to\nmatch the isotropic turbulence expected in the poloidal plane. For a thin disk\nwith an aspect ratio |h/r| ~ 0.07 around a non-spinning black hole, we find a\ndecrease in the accreted specific angular momentum of 2.9% relative to the NT\nmodel and an excess luminosity from inside the ISCO of 3.5%. The deviations in\nthe case of spinning black holes are of the same order. In addition, the\ndeviations decrease with decreasing |h/r|. We therefore conclude that\nmagnetized thin accretion disks in x-ray binaries in the thermal/high-soft\nspectral state ought to be well-described by the NT model, especially at\nluminosities below 30% of Eddington where we expect a very small disk thickness\n|h/r| <~ 0.05. We also discuss how the stress and the luminosity inside the\nISCO depend on the assumed initial magnetic field geometry. (abridged)\n