Collimating, relativistic, magnetic jets from rotating disks

The magnetic flux distribution is determined by the solution of the Grad-Shafranov equation. With differential rotation, i.e. the variation of the iso-rotation parameter, the shape of the light surface must be calculated in an iterative way. For the first time, we have calculated the force-free magnetic structure of truly two-dimensional, relativistic jets, anchored in a differentially rotating disk. Such an approach allows for a direct connection between parameters of the central source (mass, rotation) and the extension of the radio jet. We present an analytical estimate for the jet opening angle along the asymptotic branches of the light surface. In general, differential rotation of the iso-rotation parameter leads to an increase of the jet opening angle. Comparison to the M87 jet shows agreement in the collimation distance. We derive a light cylinder radius of the M87 jet of 50 Schwarzschild radii.