Fully Relativistic Derivation of the Thermal Sunyaev-Zel'dovich Effect

TL;DR

This paper provides the first fully relativistic derivation of the thermal Sunyaev-Zel'dovich effect, revealing small but systematic differences from traditional models, especially at high electron temperatures.

Contribution

It introduces a novel, fully relativistic derivation of the thermal Sunyaev-Zel'dovich effect using radiation spectrum formalism, improving upon classical approaches.

Findings

Small (<10%) differences in crossover frequency compared to traditional models

Energy increase at high electron cloud temperatures

Systematic relativistic corrections to the spectral distortion

Abstract

We present the first fully and inherently relativistic derivation of the thermal Sunyaev-Zel'dovich effect. This work uses the formalism historically used to compute radiation spectra emerging from inverse Thomson/Compton sources of x-ray radiation. Comparing our results to the traditional approach based on relativistically-corrected classical Kompaneets equation, we find small, but systematic differences. Most notable are the modest (< 10 %) differences in the crossover frequency where the spectral distortion due to the Sunyaev-Zel'dovich effect vanishes, and the energy increase of the distribution at high electron cloud temperatures.