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Pré-Publication, Document De Travail Année : 2008

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

Résumé

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 (but 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. Although this would tend to reconcile Wright's approach with the latest works on the relativistic corrections of the thermal SZ effect, we find that the squared matrix amplitude derived by Wright by applying a relativistic Lorentz boost on Chandrasekhar's non-relativistic formula is incorrect (it is not equivalent to the well-known Compton scattering squared matrix amplitude in the limit of relativistic incoming electrons and low energy photons). This has important consequences. In particular, this modifies the photon frequency transfer probability function $P(s,\beta)$, as computed by Wright, which was supposed to encode the full angular distribution of the inverse Compton scattering, and which is still widely used in non-thermal SZ computations.

Dates et versions

hal-00360925 , version 1 (12-02-2009)

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Celine Boehm, Julien Lavalle. Clarifying the covariant formalism for the SZ effect due to relativistic non-thermal electrons. 2008. ⟨hal-00360925⟩
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