Recollimation Boundary Layers in Relativistic Jets

TL;DR

This paper investigates the structure and collimation of relativistic jets influenced by ambient pressure, focusing on boundary layers and shock formation, with models that include constant and gradient pressure solutions.

Contribution

It introduces self-similar boundary-layer solutions with pressure gradients, expanding understanding of jet collimation and shock behavior in relativistic hydrodynamics.

Findings

Boundary layers form when eta < 4, leading to jet collimation.

Pressure gradients across the boundary layer affect shock position and thickness.

Constant-pressure solutions depend on four initial parameters.

Abstract

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.