The radiation hydrodynamics of relativistic shear flows

TL;DR

This paper develops a method to analyze radiation-matter interactions in relativistic shear flows, deriving a covariant energy-momentum tensor that bridges viscous and streaming regimes, applicable to various astrophysical contexts.

Contribution

It introduces a self-similar velocity profile and a covariant radiation energy-momentum tensor for relativistic shear flows, enabling analysis without specific velocity profiles.

Findings

Derived a simple, conserved scattering model at the $ au a1 1$ surface.

Formulated an approximate energy-momentum tensor interpolating between viscous and streaming limits.

Provided a covariant framework for analyzing general radiation-dominated relativistic shear flows.

Abstract

We present a method for analyzing the interaction between radiation and matter in regions of intense, relativistic shear that can arise in many astrophysical situations. We show that there is a simple velocity profile that should be manifested in regions of large shear that have "lost memory" of their boundary conditions, and we use this self-similar velocity profile to construct the surface of last scattering, or $\tau \simeq 1$ surface, as viewed from any comoving point within the flow. We demonstrate that a simple treatment of scattering from this $\tau \simeq 1$ surface exactly conserves photon number, and derive the rate at which the radiation field is heated due to the shear present in the flow. The components of the comoving radiation energy-momentum tensor are calculated, and we show that they have relatively simple, approximate forms that interpolate between the viscous (small shear) and streaming (large shear) limits. We put our expression for the energy-momentum tensor in a covariant form that does not depend on the explicit velocity profile within the fluid and, therefore, represents a natural means for analyzing general, radiation-dominated, relativistic shear flows.