Magnetically Driven Accretion Flows in the Kerr Metric. II. Structure of the Magnetic Field

We present a detailed analysis of the magnetic field structure found in a set of four general relativistic three-dimensional MHD simulations of accreting tori in the Kerr metric with different black hole spins. Among the properties analyzed are the field strength as a function of position and black hole spin, the shapes of field lines, the degree to which they connect different regions, and their degree of tangling. Strong magnetic field is found toward small radii, and field strength increases with black hole spin. In the main disk body, inner torus, and corona the field is primarily toroidal. Most field lines passing through a given radius in these regions wander through a narrow radial range, suggesting an overall tightly wound spiral structure. In the main disk body and inner torus sharp field-line bends on small spatial scales are superposed on the spirals, but the field lines are much smoother in the corona. The magnetic field in the plunging region is also comparatively smooth, being stretched out radially by the infalling gas. The magnetic field in the axial funnel resembles a split monopole, but with evidence of frame dragging of the field lines near the poles of the black hole. We investigate prior speculations about the structure of the magnetic fields and discuss how frequently certain configurations are seen in the simulations. For example, coronal loops are very rare, and field lines connecting high latitudes on the event horizon to the disk are not found at all. Almost the entire system is matter-dominated; the only force-free regions are in the axial funnel. We also analyze the distribution of current density, with a view toward identifying possible locations of magnetic energy dissipation. Regions of high current density are concentrated toward the inner torus and plunging region. Dissipation inside the marginally stable orbit may provide a new source of energy for radiation, supplementing the dissipation associated with torques in the stably orbiting disk body.