THE DYNAMO EFFECT IN MAGNETOHYDRODYNAMIC ACCRETION ONTO A ROTATING BLACK-HOLE

Active galactic nuclei are interesting astrophysical objects which con tain a supermassive black hole at the central region as an engine of t heir activity. Plasma accretion onto the black hole is the fundamental process for producing the high and variable x-ny luminosity from the central region, and the magnetic field is expected to-be a crucial com ponent in the accretion models to explain various observed features. T his motivates us to study general-relativistic effects in a black-hole magnetosphere, in particular, in relation to the important role of th e spinning motion. The stationary and axisymmetric magnetospheric stru cture based on the general-relativistic magnetohydrodynamic treatment under the assumption of infinite conductivity is briefly reviewed. We then turn to analyse the time evolution of axisymmetric magnetic field s in the vicinity of the black hole, taking into account the contribut ion of a finite magnetic diffusivity eta. Our approach is to solve the general-relativistic Maxwell equations supplemented by the generalize d Ohm's law for a given Velocity field of accreting and rotating plasm a. Numerical examples of time-dependent solutions which show self-exci tation of dipolar and quadrupolar modes of the poloidal magnetic field were recently given by Khanna and Camenzind. However, the validity of the dynamo action remains controversial. Here, we develop the analyti cal perturbation method under the approximation of small diffusivity e psilon equivalent to eta/cr(H) much less than 1, where r(H) is the bla ck-hole radius, and our analysis is limited to the narrow boundary reg ion (r-r(H))/r(H) = O(epsilon) very close to the black-hole surface. T he condition for growing multipolar seed fields is expressed by rotati on parameters. We discuss our simple analytical results in comparison with the numerical calculations.