Scaling Laws in High-Energy Inverse Compton Scattering

TL;DR

This paper derives and analyzes scaling laws in high-energy inverse Compton scattering for nonthermal electrons, providing analytical solutions that relate spectral features to the electron distribution's power-law index, aiding astrophysical emission modeling.

Contribution

It introduces a new scaling law for the probability distribution and spectral intensity functions in high-energy inverse Compton scattering, with analytical solutions based on power-law electron distributions.

Findings

Peak height and position depend only on the power index parameter.

Analytical solutions for the rate equations are obtained.

Scaling laws apply to X-ray and gamma-ray emission models.

Abstract

Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the inverse Compton scattering process for high-energy nonthermal electrons. Assuming the power-law electron distribution, we find a scaling law in the probability distribution function P_1(s), 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 scaling law, where the peak height and peak position depend only on the power index parameter. The present study will be particularly important to the analysis of the X-ray and gamma-ray emission models from various astrophysical objects such as radio galaxies and supernova remnants.