Stationary models of relativistic magnetohydrodynamic jets

Highly relativistic jets are most probably driven by strong magnetic fields and are launched from the accretion disk surrounding a central black hole. In this paper we review some of our recent results considering the two-dimensional magnetic field structure and the dynamics of collimating relativistic jets. Applying the stationarity assumption enables us to calculate global solutions of the relevant MHD equations. We discuss solutions of the Grad-Shafranov equation obtained in a general relativistic context applying the 3+1 formalism for Kerr geometry. These solutions extend from the inner light surface around the Kerr black hole to the asymptotic regime of a cylindrically collimated jet with a finite radius. In a further step, we include differential rotation of the foot points of the field lines. Considering the general relativistic MHD wind equation, we investigate the dynamics of the collimating jet, in particular the effects of Kerr metric on the acceleration. Temperature and density follow a power law. Having at hand a relativistic MHD jet solution, we calculate the thermal optically thin X-ray spectrum for the innermost hot part of the jet. Doppler shift and boosting is taken into account. For microquasars we obtain a jet X-ray luminosity 10^33 erg/s. Iron emission lines are clearly visible.