Radiative Transfer in Accretion-Disk Winds

TL;DR

This paper analytically and numerically investigates radiative transfer in accretion disk winds, revealing how wind velocity influences emergent intensity and limb-darkening effects, especially under relativistic conditions.

Contribution

It provides a detailed analysis of radiative transfer in accretion-disk winds, highlighting the velocity-dependent limb-darkening effect caused by wind motion and Doppler effects, extending previous static models.

Findings

Emergent intensity shows velocity-dependent limb-darkening due to wind motion.

For small velocities, the atmosphere resembles static cases with standard limb-darkening.

At high velocities, the flow reaches terminal speed, and velocity-dependent limb-darkening dominates.

Abstract

Radiative transfer equation in an accretion disk wind is examined analytically and numerically under the plane-parallel approximation in the subrelativistic regime of $(v/c)^1$, where $v$ is the wind vertical velocity. Emergent intensity is analytically obtained for the case of a large optical depth, where the flow speed and the source function are almost constant. The usual limb-darkening effect, which depends on the direction cosine at the zero-optical depth surface, does not appear, since the source function is constant. Because of the vertical motion of winds, however, the emergent intensity exhibits the {\it velocity-dependent} limb-darkening effect, which comes from the Doppler and aberration effects. Radiative moments and emergent intensity are also numerically obtained. When the flow speed is small ($v \leq 0.1c$), the radiative structure resembles to that of the static atmosphere, where the source function is proportional to the optical depth, and the usual limb-darkening effect exists. When the flow speed becomes large, on the other hand, the flow speed attains the constant terminal one, and the velocity-dependent limb-darkening effect appears. We thus carefully treat and estimate the wind luminosity and limb-darkening effect, when we observe an accretion disk wind.