Dynamos in Accretion Disks around Black Holes
The formation of relativistic jets in Active Galactic Nuclei
requires magnetic fields close to the central black hole of the order
kGauss. It is uncertain, whether advection of magnetic fields from
the parsec scale yields such strong fields in the innermost region.
Alternatively a dynamo operating in the accretion disk could provide
the fields. Close to a black hole a relativistic dynamo theory is
required.
The Gravitomagnetic Dynamo
The coupling of the gravitomagnetic potential of a rotating black hole with electromagnetic fields shows up in Maxwell's equations as extra induction term and current density. In axisymmetry those terms reduce to the shear of the poloidal electric and magnetic fields in the differential rotation of space. We have shown that the shear of the poloidal electric field appears as source term for the flux of the poloidal magnetic field in the axisymmetric dynamo problem. This implies that Cowling's anti-dynamo theorem does not hold in the Kerr metric. In numerical simulations of the kinematic problem, growing modes of this "gravitomagnetic dynamo" have so far not been found, however. They have only been verified analytically under assumptions, which seem hard to fulfill in a realistic situation.If, however, the accretion flow brings in magnetic field from the outer regions of the accretion disk, which is dominantly toroidal due to strong shear, the gravitomagnetic source term generates closed loops of poloidal magnetic field in the ergosphere (see figure below).
Poloidal magnetic field generated by the gravitomagnetic source, if dominantly toroidal magnetic field is steadily replenished at R=20. This simulation has been done with our 2D, implicit time-dependent Finite Elemente Code, solving the axisymmetric resistive MHD induction equation in the Kerr metric.
The {alpha}{Omega} dynamo in the Kerr metric
The turbulent {alpha}{Omega} dynamo is based on mean field MHD, which is not yet availlable in the relativistic context. I have made a heuristic ansatz for {alpha} and the turbulent diffusivity and run numerical simulations. I find that for realistic disk parameters there are growing oscillating modes of the dynamo. An example of a quadropole mode is shown below.
An oscillating growing quadrupolar eigenmode of a simple {alpha}{Omega} dynamo around a rotating black hole. The left panel shows the poloidal magnetic field. On the right is shown the poloidal current, which is proportional to the azimuthal magnetic field..
(Author: Ramon Khanna)
