Theory of Compton Scattering by Anisotropic Electrons

Abstract

Compton scattering plays an important role in various astrophysical objects such as accreting black holes and neutron stars, pulsars, and relativistic jets, clusters of galaxies as well as the early Universe. In most of the calculations it is assumed that the electrons have isotropic angular distribution in some frame. However, there are situations where the anisotropy may be significant due to the bulk motions, or anisotropic cooling by synchrotron radiation, or anisotropic source of seed soft photons. We develop here an analytical theory of Compton scattering by anisotropic distribution of electrons that can simplify significantly the calculations. Assuming that the electron angular distribution can be represented by a second order polynomial over cosine of some angle (dipole and quadrupole anisotropy), we integrate the exact Klein-Nishina cross-section over the angles. Exact analytical and approximate formulae valid for any photon and electron energies are derived for the redistribution functions describing Compton scattering of photons with arbitrary angular distribution by anisotropic electrons. The analytical expressions for the corresponding photon scattering cross-section on such electrons as well as the mean energy of scattered photons, its dispersion and radiation pressure force are also derived. We applied the developed formalism to the accurate calculations of the thermal and kinematic Sunyaev-Zeldovich effects for arbitrary electron distributions.

A fast and accurate method for computing the Sunyaev-Zel'dovich signal of hot galaxy clusters

“…These corrections have been investigated theoretically by several independent groups (e.g. Wright ; Rephaeli ; Challinor & Lasenby ; Itoh, Kohyama & Nozawa ; Nozawa, Itoh & Kohyama ; Sazonov & Sunyaev ; Molnar & Birkinshaw ; Enßlin & Kaiser ; Dolgov et al ; Shimon & Rephaeli ; Chluba, Hütsi & Sunyaev ; Poutanen & Vurm ), and various analytic approximations already provide a good description of the SZ signals in different ranges of temperature and frequency. However, a number of high‐resolution SZ experiments, including ALMA, CARMA, CCAT and MUSTANG, are underway or planned, promising a dramatic increase in sensitivities, spatial resolution and spectral coverage over the next few years.…”

Analytical study on the Sunyaev-Zeldovich effect for clusters of galaxies. II. Comparison of covariant formalisms

“…It is also found that the two formalisms give the same expression for the kinematical SZ effect in the Thomson limit. This will conclude that the existing formalisms [9,14,16] for the SZ effects for the CG are equivalent in the Thomson approximation. The present finding will establish a theoretical foundation for the analysis of the SZ effects for the CG.…”

“…On the other hand, there is yet another covariant formalism which also starts with the relativistic kinetic equation for photons [15,16]. Although the starting equations are same for the two covariant formalisms, the final expressions for the SZ effect differ significantly from each other.…”

“…In Sec. III, we then rewrite the redistribution functions of Poutanen and Vurm [16] formalism in the Thomson approximation. We will show that the redistribution functions in the two formalisms are identical.…”

Covariant Compton scattering kernel in general relativistic radiative transfer

“…Given the inherent algebraic complexity, and the number of calls required per scattering event, this will lead to significant loss of precision, in particular between cancellations of terms of similar value or of particular smallness (e.g. Poutanen & Vurm 2010).…”