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Abstract
Comptonization is a very important phenomenon in astrophysics. The Kompaneets equation describes the Comptonization process in up-Comptonization (hν̄ ≪ kTe), while it fails in describing the down-Comptonization (hν̄ ≫ kTe), which is the most important radiative transfer process in hard X-ray and γ-ray astronomy. In this study we extend the Kompaneets equation to a new modified equation which works in a more general Comptonization process, including up- and down-Comptonization, suitable for the cases hν̄ ≪ kTe, hν̄ ≫ kTe, and hν̄ ∼ kTe. Numerical solutions for the evolution behavior of Gaussian emission lines show excellent agreement between the classical equations and our new equation for up-Comptonization, while the big differences are displayed for down-Comptonization. Based on this extended equation, the modified Sunyaev-Zel’dovich effect is investigated. Instead, some typical calculated results for up- and down-Comptonization in X-ray astronomy are compared between the new equation and the Kompaneets equation. The potential applications of the extended equation in astrophysics are also highly emphasized for further study.
Highlights
Radiative transfer for photons passing through a plasma is an important topic in both astrophysics and radiation physics
We note the specialty of the radiative transfer in X-ray band: for an almost fully ionized plasma at high temperature, which often occurs in high-energy astrophysics, the dominant mechanism of energy exchange between radiation and plasma is nonelastic photon-electron scattering
We note that our extended Kompaneets equation is better than the Kompaneets equation in describing the Comptonization of high-energy photons passing through “cold” electron plasma, which is of great significance in hard X-ray and γ-ray astronomy
Summary
Radiative transfer for photons passing through a plasma (i.e., photon-electron scattering) is an important topic in both astrophysics and radiation physics. We note the specialty of the radiative transfer in X-ray band: for an almost fully ionized plasma at high temperature, which often occurs in high-energy astrophysics, the dominant mechanism of energy exchange between radiation and plasma is nonelastic photon-electron scattering. This special transfer mechanism in Xray astronomy is known as Comptonization. The Kompaneets equation is applicable when the photon energy hν kTe mec2 It fails in describing the Comptonization of highenergy photons passing through electron plasma, which is the most important radiative transfer process in hard X-ray and γray astronomy. Additional Comptonization figures of the spectrum under various conditions can be found in Appendix A
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