Scaling Laws in High-Energy Inverse Compton Scattering. II. Effect of Bulk Motions

TL;DR

This paper extends the scaling laws of inverse Compton scattering to include bulk motions of electrons, showing that the primary spectral features remain unaffected, which aids in analyzing high-energy astrophysical phenomena.

Contribution

It introduces a formalism for inverse Compton scattering with bulk motions and demonstrates the scaling law's robustness against such motions.

Findings

The probability distribution function maintains the same scaling law with bulk motions.

The spectral intensity function also follows the same scaling law.

Bulk motions have a minimal effect on the spectral intensity.

Abstract

We study the inverse Compton scattering of the CMB photons off high-energy nonthermal electrons. We extend the formalism obtained by the previous paper to the case where the electrons have non-zero bulk motions with respect to the CMB frame. Assuming the power-law electron distribution, we find the same scaling law for the probability distribution function P_{1,K}(s) as P_{1}(s) which corresponds to the zero bulk motions, where the peak height and peak position depend only on the power-index parameter. We solved the rate equation analytically. It is found that the spectral intensity function also has the same scaling law. The effect of the bulk motions to the spectral intensity function is found to be small. The present study will be applicable to the analysis of the X-ray and gamma-ray emission models from various astrophysical objects with non-zero bulk motions such as radio galaxies and astrophysical jets.