On the Compton scattering redistribution function in plasma

Compton scattering is the dominant opacity source in hot neutron stars, accretion discs around black holes and hot coronae. We collected here a set of numerical expressions of the Compton scattering redistribution functions (RFs) for unpolarized radiation, which are more exact than the widely used Kompaneets equation. The principal aim of this paper is the presentation of the RF by Guilbert, which is corrected for the computational errors in the original paper. This corrected RF was used in the series of papers on model atmosphere computations of hot neutron stars. We have also organized four existing algorithms for the RF computations into a unified form ready to use in radiative transfer and model atmosphere codes. The exact method by Nagirner & Poutanen was numerically compared to all other algorithms in a very wide spectral range from hard X-rays to radio waves. Sample computations of the Compton scattering RFs in thermal plasmawere done for temperatures corresponding to the atmospheres of bursting neutron stars and hot intergalactic medium. Our formulae are also useful to study the Compton scattering of unpolarized microwave background radiation in hot intracluster gas and the Sunyaev-Zeldovich effect. We conclude that the formulae by Guilbert and the exact quantum mechanical formulae yield practically the same RFs for gas temperatures relevant to the atmospheres of X-ray bursting neutron stars, T <= 10(8) K.