Time dependent monochromatic scattering of radiation in one dimensional media: Analytical and numerical solutions |
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| Authors: | D I Nagirner S L Kirusheva |
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| Institution: | (1) V. V. Sobolev Institute of Astronomy, St. Petersburg State University, Russia |
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| Abstract: | In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact
solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic scattering
for sources with an arbitrary spatial distribution and an arbitrary time variation of their power. The Lax-Wendroff method
seems to be the most suitable. Because it is assumed that radiation delay is caused by the finite speed of light, the following
difficulty arises when the numerical method is used: the region of variation of the variables (position τ and time t) is triangular (the inequality τ ≤ t). This difficulty is overcome by expanding the unknown functions in series in terms of small values of the time and position.
By comparing the numerical and exact solutions for a point source with a given time dependence for its power and with pure
scattering, the number of steps in the variables required to obtain a desired accuracy is estimated. This numerical method
can be used to calculate the intensity and polarization of the radiation from sources in the early universe during epochs
close to the recombination epoch.
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Translated from Astrofizika, Vol. 51, No. 1, pp. 109–123 (February 2008). |
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| Keywords: | radiation scattering time dependent |
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