Physics
Scientific paper
Mar 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...307..665k&link_type=abstract
Astronomy and Astrophysics, v.307, p.665-685
Physics
27
Accretion, Accretion Disks, Black Hole Physics, Mhd, Relativity
Scientific paper
We develop the kinematic theory of axisymmetric dynamo action in the innermost part of an accretion disk around a rotating black hole. The problem is formulated in the 3+1 split of Kerr spacetime. It turns out that the gravitomagnetic field of the hole gives rise to a dynamo current for the the poloidal magnetic field without any need of turbulent plasma motions even in axisymmetry. We show that Cowling's theorem does not apply in the Kerr metric. This gravitomagnetic dynamo effect (ω-effect) requires finite diffusivity and is enhanced by anomalous or turbulent magnetic diffusivity. The reformulation of the problem in the framework of mean field magnetohydrodynamics introduces the familiar α-effect. The dynamo equations are formally identical with their classical equivalents (i.e. equations for the α{OMEGA} dynamo in flat space), augmented by the general relativistic ω-effect-term as source. We have carried out time-dependent numerical simulations of the dynamo in a turbulent differentially rotating accretion disk using a finite element code with implicit time-stepping. The advection of the magnetic field with the plasma is fully included. Solutions are discussed for extremely and less rapidly rotating black holes. We observe growing dipolar, quadrupolar and mixed modes, the second being, however, dominant. A common feature of all our simulations of the ω{OMEGA} dynamo is that it will finally build up a stellar like magnetosphere around the black hole, which blends into the outer disk field topology in a transition region. This finding enforces the analogy in the models of jet formation in AGN and YSOs. An interesting feature occurs for less rapidly rotating holes. The frame dragging effect introduces a boundary layer in the plasma rotation, where the plasma is prone to resistive magnetohydrodynamical instabilities such as the rippling mode or the tearing mode and thus the boundary layer has to be regarded as a potential site of particle acceleration. We also present a simulation of the αω{OMEGA} dynamo. For a heuristic description of α in the 3+1 split of Kerr spacetime, the ω-effect is dominated by the α-effect. For the same parameters as in the simulations of the ω{OMEGA} dynamo, the αω{OMEGA} dynamo behaves much more dynamically. The simulation shows radially and vertically oscillating dipolar, quadrupolar and mixed modes.
Camenzind Max
Khanna Rajesh
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