The Profile of a Narrow Line after Single Scattering by Maxwellian Electrons: Relativistic Corrections to the Kernel of the Integral Kinetic Equation

Abstract

The photon frequency distribution that results from single Compton scattering of monochromatic radiation on thermal electrons is derived in the mildly relativistic limit. Algebraic expressions are given for (1) the photon redistribution function, K(ν, Ω → ν ′ , Ω ′ ), and (2) the spectrum produced in the case of isotropic incident radiation, P(ν → ν ′ ). The former is a good approximation for electron temperatures kT e ∼ < 25 keV and photon energies hν ∼ < 50 keV, and the latter is applicable when hν(hν/m e c 2 ) ∼ < kT e ∼ < 25 keV, hν ∼ < 50 keV. Both formulae can be used for describing the profiles of X-ray and low-frequency lines upon scattering in hot, optically thin plasmas, such as present in clusters of galaxies, in the coronae of accretion disks in X-ray binaries and active galactic neclei (AGNs), during supernova explosions, etc. Both formulae can also be employed as the kernels of the corresponding integral kinetic equations (direction-dependent and isotropic) in the general problem of Comptonization on thermal electrons. The K(ν, Ω → ν ′ , Ω ′ ) kernel, in particular, is applicable to the problem of induced Compton interaction of anisotropic low-frequency radiation of high brightness temperature with free electrons in the vicinity of powerful radiosources and masers. Fokker-Planck-type expansion (up to fourth order) of the integral kinetic equation with the P(ν → ν ′ ) kernel derived here leads to a generalization of the Kompaneets equation. We also present (1) a simpler kernel that is necessary and sufficient to derive the Kompaneets equation and (2) an expression for the angular function for Compton scattering in a hot plasma, which includes temperature and photon energy corrections to the Rayleigh angular function.

XMM-Newton observations of SS 433 I. EPIC spectral analysis

“…The break energy turns out to be around 7.1 keV, the low energy power law rises with energy (Γ 1 ∼ −1.0); the high energy part is rather steep (Γ 2 ∼ 4.0), however, the parameters are usually not well determined in the fits. This spectral form is reminiscent of an emission line Compton down-scattered by colder material with moderate (τ ∼ 5) optical depth (Sunyaev & Titarchuk 1980, Sazonov & Sunyaev 2000. The number of photons in this scattered component is about 10−15 times higher than the number of photons of the observed iron line, indicating that we are seeing the scattered light from the innermost hot jet, otherwise hidden by the disc material.…”

Cosmological hydrogen recombination: influence of resonance and electron scattering

“…see Fig. 8), so that no big difference is expected when more correctly using a scattering Kernel-approach (Syunyaev 1980;Sazonov & Sunyaev 2000), which accurately takes both the Doppler effect and electron recoil into account.…”

Green's function of the cosmological thermalization problem – II. Effect of photon injection and constraints

“…At z 200, when matter and radiation thermally decouple, the last term is further suppressed. We furthermore mention that for very small, but nonzero, y-parameter one can alternatively replace the δ-function using the Compton scattering kernel (Sazonov & Sunyaev 2000). The free-free absorption optical depth can be calculated using the results from CosmoRec (Chluba & Thomas 2011) for the ionization history and approximations for the free-free Gaunt factors from Itoh et al (2000).…”