Compton scattering from isotropic electrons

Brinkmann, W.

doi:10.1016/0022-4073(84)90068-2

Cited by 9 publications

(9 citation statements)

References 7 publications

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“…The integrals in equation (2-18) can be calculated analytically (Brinkmann 1984;NP94) to obtain a fully general expression for R ph (x, x 1 , γ 1 ) valid in all regimes (see Appendix B). This is an alternative form of the function derived by Jones (1968).…”

Section: Compton Scattering 241 Compton Scattering Of Photonsmentioning

confidence: 99%

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Time-Dependent Modeling of Radiative Processes in Hot Magnetized Plasmas

Vurm

Poutanen

2009

ApJ

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Numerical simulations of radiative processes in magnetized compact sources such as hot accretion disks around black holes, relativistic jets in active galaxies and gamma-ray bursts are complicated because the particle and photon distributions span many orders of magnitude in energy, they also strongly depend on each other, the radiative processes behave significantly differently depending on the energy regime, and finally due to the enormous difference in the time-scales of the processes. We have developed a novel computer code for the time-dependent simulations that overcomes these problems. The processes taken into account are Compton scattering, electron-positron pair production and annihilation, Coulomb scattering as well as synchrotron emission and absorption. No approximation has been made on the corresponding rates. For the first time, we solve coupled integro-differential kinetic equations for photons and electrons/positrons without any limitations on the photon and lepton energies. A numerical scheme is proposed to guarantee energy conservation when dealing with synchrotron processes in electron and photon equations. We apply the code to model nonthermal pair cascades in the blackbody radiation field, to study the synchrotron self-absorption as particle thermalization mechanism, and to simulate time evolution of stochastically heated pairs and corresponding synchrotron self-Compton photon spectra which might be responsible for the prompt emission of gamma-ray bursts. Good agreement with previous works is found in the parameter regimes where comparison is feasible, with the differences attributable to our improved treatment of the microphysics.Vurm & Poutanen diative transport. Various approximations invoked to simplify the treatment of radiative processes at the same time limit the range of their applicability. One commonly employed approximation concerns Compton scattering, which is assumed to take place in the Thomson regime (e.g. Ghisellini et al. 1998, hereafter GHS98) and is accounted for by a simple cooling term in the electron equation. This sets two restrictions that the photon energy in the electron rest frame is smaller than the electron rest mass and the average photon energy is much lower than the electron kinetic energy. Otherwise all photons would not contribute to electron cooling, the higher energy ones being downscattered via Compton scattering. This means that one is unable to treat cases when Comptonization approaches saturation, which may be relevant at high compactnesses, and to study electron heating by external radiation. Other works account for Klein-Nishina corrections to the electron cooling rate, but still neglect the diffusive nature of the process when electron and photon energies are comparable (Coppi 1992;Moderski et al. 2005;Pe'er & Waxman 2005), which works towards establishing an equilibrium Maxwellian distribution. Another useful approximation, when the integral terms describing Compton scattering are accounted for, is to consider ultrarelativistic electrons and very l...

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Section: Compton Scattering 241 Compton Scattering Of Photonsmentioning

confidence: 99%

“…The angle-averaged function was obtained by Jones (1968), but the presented expressions are very cumbersome and the loss of accuracy occurs for small photon energies and large electron energies. An alternative function given by Brinkmann (1984) and NP94 does not suffer from these problems. We use here the latter expressions.…”

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confidence: 99%

Time-Dependent Modeling of Radiative Processes in Hot Magnetized Plasmas

Vurm

Poutanen

2009

ApJ

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“…It should be noted that the angular integrals in Eq. (30) were performed by Brinkmann [21] and also by Nagirner and Poutanen [22]. The source function is related to the change of the photon occupation number by…”

Section: Equvalence Between Two Formalisms In the Thomson Approxmentioning

confidence: 99%

Analytical study on the Sunyaev-Zeldovich effect for clusters of galaxies. II. Comparison of covariant formalisms

2010

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We study a covariant formalism for the Sunyaev-Zeldovich effects developed in the previous papers by the present authors, and derive analytic expressions for the redistribution functions in the Thomson approximation. We also explore another covariant formalism recently developed by Poutanen and Vurm. We show that the two formalisms are mathematically equivalent in the Thomson approximation which is fully valid for the cosmic microwave background photon energies. The present finding will establish a theoretical foundation for the analysis of the Sunyaev-Zeldovich effects for the clusters of galaxies.PACS numbers: 95.30. Cq,95.30.Jx,98.65.Cw,98.70.Vc

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“…Belmont 2009). An alternative derivation to that kernel was given by Brinkmann (1984) and Nagirner & Poutanen (1994, NP94 hereafter), who showed how to extend numerical scheme to cover all photon and electron energies of interest in astrophysical sources.…”

Section: Introductionmentioning

confidence: 99%

Theory of Compton Scattering by Anisotropic Electrons

Poutanen¹,

Vurm²

2010

ApJS

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Compton scattering plays an important role in various astrophysical objects such as accreting black holes and neutron stars, pulsars, and relativistic jets, clusters of galaxies as well as the early Universe. In most of the calculations it is assumed that the electrons have isotropic angular distribution in some frame. However, there are situations where the anisotropy may be significant due to the bulk motions, or anisotropic cooling by synchrotron radiation, or anisotropic source of seed soft photons. We develop here an analytical theory of Compton scattering by anisotropic distribution of electrons that can simplify significantly the calculations. Assuming that the electron angular distribution can be represented by a second order polynomial over cosine of some angle (dipole and quadrupole anisotropy), we integrate the exact Klein-Nishina cross-section over the angles. Exact analytical and approximate formulae valid for any photon and electron energies are derived for the redistribution functions describing Compton scattering of photons with arbitrary angular distribution by anisotropic electrons. The analytical expressions for the corresponding photon scattering cross-section on such electrons as well as the mean energy of scattered photons, its dispersion and radiation pressure force are also derived. We applied the developed formalism to the accurate calculations of the thermal and kinematic Sunyaev-Zeldovich effects for arbitrary electron distributions.

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Compton scattering from isotropic electrons

Cited by 9 publications

References 7 publications

Time-Dependent Modeling of Radiative Processes in Hot Magnetized Plasmas

Time-Dependent Modeling of Radiative Processes in Hot Magnetized Plasmas

Analytical study on the Sunyaev-Zeldovich effect for clusters of galaxies. II. Comparison of covariant formalisms

Theory of Compton Scattering by Anisotropic Electrons

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