Collimating, relativistic, magnetic jets from rotating disks - The axisymmetric field structure of relativistic jets and the example of the M 87 jet

We investigate the axisymmetric structure of collimating, relativistic, str ongly magnetized (force-free) jets. In particular, we include the different ial rotation of the foot points of the held lines in our treatment. The mag netic flux distribution is determined by the solution of the Grad-Shafranov equation and the regularity condition along the light surface. With differ ential rotation, i.e. the variation of the iso-rotation parameter Omega (F) , the shape of the light surface is not known a priori and must be calculat ed in an iterative way. For the first time, we have calculated the force-fr ee magnetic structure of truly two-dimensional, relativistic jets, anchored in a differentially rotating disk. Such an approach allows for a direct co nnection between parameters of the central source (mass, rotation) and the extension of the radio jet. In particular, this can provide a direct scalin g of the location of the asymptotic jet light cylinder in terms of the cent ral mass and the accretion disk magnetic flux distribution. We demonstrate that differentially rotating jets must be collimated to a smaller radius in terms of the light cylinder if compared to jets with rigid rotation. Also, the opening angle is smaller. Further we present an analytical estimate fo r the jet opening angle along the asymptotic branches of the light surface. In general, differential rotation of the iso-rotation parameter leads to a n increase of the jet opening angle. Our results are applicable for highly magnetized, highly collimated, relativistic jets from active galactic nucle i and Galactic superluminal jet sources. Comparison to the M 87 jet shows a greement in the collimation distance. We derive a light cylinder radius of the M 87 jet of 50 Schwarzschild radii.