EDP Sciences
Free access
Volume 417, Number 2, April II 2004
Page(s) 381 - 389
Section Astrophysical processes
DOI http://dx.doi.org/10.1051/0004-6361:20031765

A&A 417, 381-389 (2004)
DOI: 10.1051/0004-6361:20031765

Evolution of X-ray spectra in down-Comptonization. A comparison of the extended Kompaneets equation with Monte Carlo simulation and the Ross-McCray equation

D.-B. Liu1, L. Chen1, J. J. Ling1, J. H. You1 and X. M. Hua2

1  Institute for Space and Astrophysics, Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, PR China
2  Laboratory for High Energy Astrophysics, NASA/GSFC Code 661, Greenbelt, Maryland 20771, USA

(Received 13 May 2003 / Accepted 18 November 2003 )

The original Kompaneets equation fails to describe down-Comptonization, which is the most important radiative transfer process in hard X-ray and $\gamma$-ray astronomy, compared with up-Comptonization. In this paper, we improve our previous derivation of the extended Kompaneets equation and present it more clearly. The new equation can be used to describe a more general Comptonization process, including up- and down-Comptonization, suitable for any case, $h\overline{\nu}\ll kT_{\mathrm e}$, $h\overline{\nu}\gg kT_{\mathrm e}$ and $h\overline{\nu}\sim kT_{\mathrm e}$. The condition of the original Kompaneets equation $h\overline{\nu}\ll kT_{\mathrm e}$ is no longer necessary. Using the extended equation, we give some typical solutions in X-ray astronomy, and compare them with those of the prevailing Monte Carlo simulations and the Ross-McCray equation. The excellent consistency between the extended Kompaneets equation and Monte Carlo simulation or Ross-McCray equation confirms the correctness of our extended Kompaneets equation. The numerical solution of the extended Kompaneets equation is less expensive in terms of computational time than the Monte Carlo simulation. Another advantage of the equation method is the simplicity and the clarity in physics. The potential applications in X-ray and $\gamma$-ray astronomy are also emphasized.

Key words: scattering -- radiative transfer -- methods: analytical -- X-rays, $\gamma$-rays: ISM

Offprint request: D.-B. Liu, dbliu@sjtu.edu.cn

© ESO 2004