Clarifying the covariant formalism for the SZ effect due to relativistic non-thermal electrons

TL;DR

This paper reinterprets the covariant formalism for the relativistic Sunyaev-Zel'dovich effect caused by non-thermal electrons in galaxy clusters, framing it as a Boltzmann-like equation for better theoretical understanding.

Contribution

It clarifies and formalizes the covariant approach to the SZ effect, connecting Wright's empirical method to a Boltzmann equation framework.

Findings

Reinterpreted Wright's formalism as a Boltzmann-like equation.

Provided a covariant derivation for the relativistic SZ effect.

Enhanced theoretical understanding of non-thermal electron impacts.

Abstract

We derive the covariant formalism associated with the relativistic Sunyaev-Zel'dovich effect due to a non-thermal population of high energy electrons in clusters of galaxies. More precisely, we show that the formalism proposed by Wright in 1979, based on an empirical approach (and widely used in the literature) to compute the inverse Compton scattering of a population of relativistic electrons on CMB photons, can actually be re-interpreted as a Boltzmann-like equation, in the single scattering approximation.