DIFFERENTIALLY ROTATING RELATIVISTIC MAGNETIC JETS - ASYMPTOTIC TRANS-FIELD FORCE-BALANCE INCLUDING DIFFERENTIAL ROTATION

Highly collimated jets are observed in various astronomical objects, a s active galactic nuclei, galactic high energy sources, and also young stellar objects. There is observational indication that these jets or iginate in accretion disks, and that magnetic fields play an important role for the jet collimation and plasma acceleration. The rapid disk rotation close to the central object leads to relativistic rotational velocities of the magnetic field lines. The structure of these axisymm etric magnetic flux surfaces follows from the trans-field force-balanc e described by the Grad-Schluter-Shafranov equation. In this paper, we investigate the asymptotic field structure of differentially rotating magnetic jets, widening the study by Appl & Camenzind (1993a,b). In g eneral, our results show that, with the same current distribution, dif ferentially rotating jets are collimated to smaller jet radii as compa red with jets with rigidly rotating field. Differentially rotating jet s need a stronger net poloidal current in order to collimate to the sa me asymptotic radius. Current-free solutions are not possible for diff erentially rotating disk-jet magnetospheres with cylindrical asymptoti cs. We present a simple analytical relation between the poloidal curre nt distribution and magnetic field rotation law. A general relation is derived for the current strength for jets with maximum differential r otation and minimum differential rotation. Analytical solutions are al so given in the case of a field rotation leading to a degeneration of the light cylinder. By linking the asymptotic solution to a Keplerian accretion disk, 'total expansion rates' for the jets, and also the flu x distribution at the foot points of the flux surfaces are derived. La rge poloidal currents imply a strong opening of flux surfaces, a stron ger gradient of field rotation leads to smaller expansion rates. There is indication that AGN jet expansion rates are less than in the case of protostellar jets. High mass AGN seem to have larger jet expansion rates than low mass AGN.