Recollimation Boundary Layers in Relativistic Jets
  We study the collimation of relativistic hydrodynamic jets by the pressure of
an ambient medium in the limit where the jet interior has lost causal contact
with its surroundings. For a jet with an ultrarelativistic equation of state
and external pressure that decreases as a power of spherical radius, p \propto
r^(-eta), the jet interior will lose causal contact when eta > 2. However, the
outer layers of the jet gradually collimate toward the jet axis as long as eta
< 4, leading to the formation of a shocked boundary layer. Assuming that
pressure-matching across the shock front determines the shape of the shock, we
study the resulting structure of the jet in two ways: first by assuming that
the pressure remains constant across the shocked boundary layer and looking for
solutions to the shock jump equations, and then by constructing self-similar
boundary-layer solutions that allow for a pressure gradient across the shocked
layer. We demonstrate that the constant-pressure solutions can be characterized
by four initial parameters that determine the jet shape and whether the shock
closes to the axis. We show that self-similar solutions for the boundary layer
can be constructed that exhibit a monotonic decrease in pressure across the
boundary layer from the contact discontinuity to the shock front, and that the
addition of this pressure gradient in our initial model generally causes the
shock front to move outwards, creating a thinner boundary layer and decreasing
the tendency of the shock to close. We discuss trends based on the value of the
pressure power-law index eta.
