Milne-Eddington Solutions for Relativistic Plane-Parallel Flows

TL;DR

This paper derives analytical solutions for radiative transfer in relativistic plane-parallel flows, such as accretion disk winds, revealing how radiation properties change with flow speed and relativistic effects.

Contribution

It provides the first analytical Milne-Eddington solutions for relativistic flows, extending classical static atmosphere models to relativistic regimes.

Findings

Radiation energy density, flux, and pressure are analytically obtained for relativistic flows.

Solutions reduce to classical Milne-Eddington in the static limit.

Emergent intensity is enhanced in the flow direction due to relativistic effects.

Abstract

Radiative transfer in a relativistic plane-parallel flow, e.g., an accretion disk wind, is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed, for the relativistically moving atmosphere we analytically obtain generalized Milne-Eddington solutions of radiative moment equations; the radiation energy density, the radiative flux, and the radiation pressure. In the static limit these solutions reduce to the traditional Milne-Eddington ones for the plane-parallel static atmosphere, whereas the source function nearly becomes constant as the flow speed increases. Using the analytical solutions, we analytically integrate the relativistic transfer equation to obtain the specific intensity. This specific intensity also reduces to the Milne-Eddinton case in the static limit, while the emergent intensity is strongly enhanced toward the flow direction due to the Doppler and aberration effects as the flow speed increases (relativistic peaking).