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

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.

arXiv comment12 pages. Error in the interpretation of E. Wright's earlier results corrected. Accepted for publication in PRD

References in corpus (5)

• The Sunyaev-Zel'dovich Effect
• Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies
• Relativistic corrections to the Sunyaev-Zel'dovich effect
• The Non-Thermal Sunyaev-Zel'dovich Effect in Clusters of Galaxies
• Spectral distortion of cosmic background radiation by scattering on hot electrons. Exact calculations

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• SZ effects from annihilating dark matter in the Milky Way: smooth halo, subhalos and intermediate-mass-black-holes
• Effect of the non-thermal Sunyaev-Zel'dovich Effect on the temperature determination of galaxy clusters