Comptonization of photons near the photosphere of relativistic outflows

TL;DR

This paper models photon spectrum formation near the photosphere of relativistic outflows using a generalized Kompaneets equation, revealing spectral features consistent with Gamma Ray Burst observations.

Contribution

It introduces a generalized anisotropic Kompaneets equation for relativistic outflows and explores its implications for observed spectra, including the Band function.

Findings

Observed spectrum matches previous models.

For T∝r^{-2}, spectrum's low-energy index is approximately -1.

Results align with Gamma Ray Burst spectral observations.

Abstract

We consider the formation of photon spectrum at the photosphere of ultrarelativistically expanding outflow. We use the Fokker-Planck approximation to the Boltzmann equation, and obtain the generalized Kompaneets equation which takes into account anisotropic distribution of photons developed near the photosphere. This equation is solved numerically for relativistic steady wind and the observed spectrum is found in agreement with previous studies. We also study the photospheric emission for different temperature dependences on radius in such outflows. In particular, we found that for $T\propto r^{-2}$ the Band low energy photon index of the observed spectrum is $\alpha\simeq -1$, as typically observed in Gamma Ray Bursts.