Magnetic Domination of Recollimation Boundary Layers in Relativistic Jets

We study the collimation of relativistic magnetohydrodynamic jets by the pressure of an ambient medium, in the limit where the jet interior loses causal contact with its surroundings. This follows up a hydrodynamic study in a previous paper, adding the effects of a toroidal magnetic field threading the jet. As the ultrarelativistic jet encounters an ambient medium with a pressure profile with a radial scaling of p ~ r^-eta where 2<eta<4, it loses causal contact with its surroundings and forms a boundary layer with a large pressure gradient. By constructing self-similar solutions to the fluid equations within this boundary layer, we examine the structure of this layer as a function of the external pressure profile. We show that the boundary layer always becomes magnetically dominated far from the source, and that in the magnetic limit, physical self-similar solutions are admitted in which the total pressure within the layer decreases linearly with distance from the contact discontinuity inward. These solutions suggest a `hollow cone' behavior of the jet, with the boundary layer thickness prescribed by the value of eta. In contrast to the hydrodynamical case, however, the boundary layer contains an asymptotically vanishing fraction of the jet energy flux.