2 research outputs found
The profile of a narrow line after single scattering by Maxwellian electrons: relativistic corrections to the kernel of the integral kinetic equation
The frequency distribution of photons in frequency 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(nu,Omega -> nu',Omega'), and (2) the spectrum
produced in the case of isotropic incident radiation, P(nu -> nu'). The former
is a good approximation for electron temperatures kT_e < 25 keV and photon
energies hnu < 50 keV, and the latter is applicable when hnu(hnu/m_ec^2) < kT_e
< 25 keV, hnu < 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 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(nu,Omega -> nu',Omega') 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(nu -> nu') kernel derived here leads to a generalization of
the Kompaneets equation. We further 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.Comment: 29 pages, 17 figures, accepted for publication in ApJ, uses
emulateapj.sty, corrects misprints in previous astro-ph versio