Modified Form Of The Kompaneets Equation Possible Application To The Distortion Of High-Temperature Blackbody And Cmb Spectra

Comptonization is a very important phenomenon in astrophysics. The Kompaneets equation describes the Comptonization process in up-Comptonization (h (nu) over bar << kT(e)), while it fails in describing the down-Comptonization (h (nu) over bar >> kT(e)), which is the most important radiative transfer process in hard X-ray and gamma-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 h (nu) over bar << kT(e), h (nu) over bar >> kT(e), and h (nu) over bar similar to kT(e). 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 di fferences are displayed for down-Comptonization. Based on this extended equation, the modified Sunyaev-Zel'dovich e ffect 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.