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

Liu, D.-B.; Chen, L.; Ling, J. J.; You, Junhan; Hua, Xin‐Min

doi:10.1051/0004-6361:20031765

Cited by 11 publications

(21 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this study, differing from the method used to obtain Eq. (4) by Liu et al (2004), we present a new extended Kompaneets equation ( 35) by expanding the distribution function in ∆p instead of ∆ν, which can be used to describe a more general Comptonization process, including down-and up-Comptonization, suitable for any case, hν kT e , hν kT e , and hν ∼ kT e . The condition hν kT e , under which the original Kompaneets equation (2) was derived, is no longer necessary for Eq.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Given the initial condition, i.e., the initial spectrum, and the diffusion timescale, we can solve Eq. ( 35) numerically by using the three-point finite difference method (Liu et al 2004). For simplicity, we assume that the X-ray source is stable with a time-independent spectrum f (x).…”

Section: Numerical Calculations For the Comptonization Of Gaussian Emission Lines: Comparison Of The Modified And Original Kompaneets Equmentioning

confidence: 99%

“…(4) the ratio of the second term in the numerator to the first term is (hν/m e c 2 )(hν/kT e ). When hν is large enough, as Liu et al (2004) argued, the second term in the numerator cannot be neglected. Hence in this paper we keep the second term.…”

Section: Introductionmentioning

confidence: 98%

“…The detailed consideration of the problem of energy transfer between the radiation and the medium is as important as that of the basic radiation mechanism, particularly in the X-ray band. With the rapid development of X-ray astronomy in recent years, it seems necessary to have an effective theory that describes the radiative transfer process (Kompaneets 1957;Illarionov et al 1979;Fabian et al 1995;Sunyaev & Titarchuk 1985;Titarchuk 1994;Hua et al 1997;Kazanas et al 1997;Misra & Kembhavi 1998;Zhang et al 2000;Liu et al 2004;Felten & Rees 1972;Miyamoto 1978). When high-energy photons go through the Research supported by the Strategic Priority Research Program of Chinese Academy of Sciences, Grant No.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modified form of the Kompaneets equation

Chen

Zhang

Gao

et al. 2021

A&A

View full text Add to dashboard Cite

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.

show abstract

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Numerical Calculations For the Comptonization Of Gaussian Emission Lines: Comparison Of The Modified And Original Kompaneets Equmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modified form of the Kompaneets equation

Chen

Zhang

Gao

et al. 2021

A&A

View full text Add to dashboard Cite

show abstract

“…Liu et al 11 explored Compton scattering with these same physical conditions. They have extended the traditional formulation of the Kompaneets equation to include relativistic effects.…”

Section: Fig 3 the Electron Energy Density (Green Curve) Declines Amentioning

confidence: 99%

A Practical Review of the Kompaneets Equation and its Application to Compton Scattering

Shirk¹

2006

View full text Add to dashboard Cite

In this study, we explore both inverse Compton and Compton scattering processes using the Chang and Cooper scheme to form a deterministic solution of the Kompaneets equation. We examine the individual terms of the Kompaneets equation and illustrate their effect on the equilibrium solution. We use two examples (a Gaussian line profile and a Planck profile) to illustrate the advective and diffusive properties of the Kompaneets operator. We also explore both inverse Compton scattering and Compton scattering, and discuss and illustrate the BoseEinstein condensation feature of the Compton scattering spectrum.

show abstract

Comptonisation

Courvoisier

2012

High Energy Astrophysics

View full text Add to dashboard Cite

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

Abstract: Abstract. The original Kompaneets equation fails to describe down-Comptonization, which is the most important radiative transfer process in hard X-ray and γ-ray astronomy, compared with up-Comptonization. In this paper, we improve our previous

Cited by 11 publications

References 13 publications

Modified form of the Kompaneets equation

Modified form of the Kompaneets equation

A Practical Review of the Kompaneets Equation and its Application to Compton Scattering

Comptonisation

Contact Info

Product

Resources

About