An axisymmetric, nonstationary electrodynamic model of the central engine in an active galactic nucleus

An axisymmetric, stationary model of the central engine in an active galactic nucleus has been investigated as the background of the Blandford-Znajek process, which consists of the supermassive black hole surrounded by a magnetized accretion disk. This model was reformulated and extended by Macdonald and Thorne, and their work forms the basis for our model. Our model, however, includes the secular effects of the mass accretion, and has nonstationary characteristics. In the first part we analyze the axisymmetric, nonstationary electrodynamics of the black hole. Under the assumption that the mass accretion is confined to the equatorial plane of the black hole our results suggest that, at the equatorial zone of the black hole, the angular velocity of the magnetic field lines anchored on the accreting matter must be close to that of the black hole. In the second part we analyze the axisymmetrie, nonstationary electrodynamics of a surrounding magnetized accretion disk in a similar way. Unlike the first part, we find that the power output due to the Blandford-Znajek process can be variable even on short time scales. This follows from the fact that the physical parameters of the accreting matter itself, rather than the boundary values at the event horizon of the black hole, appear in the power equation. This may explain the observed short-time-scale variability of active galactic nuclei. In the third part we analyze the rotation of the magnetic-field lines in our model. In the original axisymmetric, stationary model each magnetic field line must rotate with constant angular velocity which will exceed the speed of light far from the centre. Even though the field lines are purely mathematical entities, this condition sets a stringent physical constraint on the motion of the magnetic field lines and the particles on them. In this paper we show that we can remove this auxiliary constraint in our model by allowing nonstationary processes. As a result the magnetic field lines can be twisted and wound up in a region lying outside of the quasi-stationary magnetosphere of the black hole. We conclude that astrophysical jets are formed in that region due to the twisted and wound magnetic field lines powered by the Blandford-Znajek process and the other driving forces.