Statistics – Computation
Scientific paper
May 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995apj...445...33r&link_type=abstract
The Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 445, no. 1, p. 33-36
Statistics
Computation
113
Background Radiation, Compton Effect, Cosmology, Critical Frequencies, Intergalactic Media, Microwaves, Relativistic Effects, Spectral Energy Distribution, Temperature Distribution, Computational Astrophysics, Electron Density (Concentration), Flux Density, Perturbation, Probability Theory, Relativistic Electron Beams
Scientific paper
The commonly used expressions for the cosmic microwave background intensity and temperature changes due to Compton scattering by hot gas in clusters of galaxies (the Sunyaev-Zel'dovich effect) are based on a solution to the Kompaneets nonrelativistic diffusion equation. These expressions are insufficiently accurate because of the high electron velocities and low scattering probability in the hot intracluster gas. The results of an improved relativistic treatment show significant deviations, at frequenices on the Wien side, from what is predicted from the Kompaneets-based calculation. Useful expressions are given which can be readily integrated to determine the exact magnitude of the effect at any frequency and gas temperature. An important feature of the relativistic spectral distribution of the intensity change is the dependence of the critical frequency -- where the effect vanishes -- on the gas temperature. This dependence must be taken into account in determinations of peculiar velocities of clusters from measurements of the kinematic Sunyaev-Zel'dovich effect.
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