Green's Function for the Linear Kompaneets Equation

Details Green's Function for the Linear Kompaneets Equation Green's Function for the Linear Kompaneets Equation

Jan 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997ap.....40...62n&link_type=abstract

Astrophysics, Volume 40, Issue 1, pp.62-76

Astronomy and Astrophysics

Astrophysics

Scientific paper

Green’s function for the linear Kompaneets equation is calculated; it is expressed in terms of a Whittaker function W2,iμ(Z) or a MacDonald function Kiμ(z) with a purely imaginary index. A method is proposed for calculating these functions. Langer’s asymptotic solution for large μ is refined in Cherry’s second approximation. With a series expansion for small values of the argument and the asymptotic form for large values, this approximation enables one to calculate Green’s function to five significant figures. Solutions of the Kompaneets equation will be used to estimate the accuracy of numerical methods and to calculate the evolution of the spectrum of a photon gas during Compton scattering, as well as the average frequencies and the dispersion of photon frequencies for different initial spectra.

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