Relativistic corrections to the Kompaneets equation

Nozawa, Satoshi; Kohyama, Yasuharu

doi:10.1016/j.astropartphys.2014.07.008

Cited by 9 publications

(10 citation statements)

References 18 publications

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“…Their expansion series (16) contains, in fact, the (7/10)ǫ 2 term included by Ross et al (1978), and their results are valid for both up and downscattering. Their results were extended in further studies by Itoh, Kohyama, & Nozawa (1998), Brown & Preston (2012) and Nozawa & Kohyama (2015), who confirmed the correctness of the results of Challinor & Lasenby (1998). However, their equation is a fourth-order partial differential equation and the obtained series is only asymptotic.…”

Section: Kinetic Equations For Compton Scatteringsupporting

confidence: 57%

“…Then, treated Compton scattering using either integral or differential form depending on the value of the fractional photon energy change. Challinor & Lasenby (1998), Itoh et al (1998), Brown & Preston (2012) and Nozawa & Kohyama (2015) also applied their results to the Sunyaev-Zeldovich effect. Without relativistic corrections, the Kompaneets equation (including the stimulated scattering term) only allows us to determine the Compton parameter, y ≡ 4θτ, of the medium (hot gas with kT e ∼ 10 keV in a cluster of galaxies) upscattering the cosmic microwave background radiation (Zeldovich & Sunyaev 1969).…”

Section: Kinetic Equations For Compton Scatteringmentioning

confidence: 99%

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Spectral and temporal properties of Compton scattering by mildly relativistic thermal electrons

Zdziarski

Szanecki

Poutanen

et al. 2020

Monthly Notices of the Royal Astronomical Society

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We have obtained new solutions and methods for the process of thermal Comptonization. We modify the solution to the kinetic equation of Sunyaev & Titarchuk to allow its application up to mildly relativistic electron temperatures and optical depths > ∼ 1. The solution can be used for spectral fitting of X-ray spectra from astrophysical sources. We also have developed an accurate Monte Carlo method for calculating spectra and timing properties of thermal-Comptonization sources. The accuracy of our kinetic-equation solution is verified by comparison with the Monte Carlo results. We also compare our results with those of other publicly available methods. Furthermore, based on our Monte Carlo code, we present distributions of the photon emission times and the evolution of the average photon energy for both up and downscattering.

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Section: Kinetic Equations For Compton Scatteringsupporting

confidence: 57%

Section: Kinetic Equations For Compton Scatteringmentioning

confidence: 99%

Spectral and temporal properties of Compton scattering by mildly relativistic thermal electrons

Zdziarski

Szanecki

Poutanen

et al. 2020

Monthly Notices of the Royal Astronomical Society

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“…Other extensions to Kompaneets can be found elsewhere that account for relativistic effects (Sazonov & Sunyaev 1998;Challinor & Lasenby 1998;Nagirner et al 1997;Challinor & Lasenby 1998;Brown & Preston 2012;Nozawa & Kohyama 2015), high temperatures (Sampson 1959;Xie et al 2010;Garain & …”

Section: E2 Thermal Comptonization Via Kompaneets Scatteringmentioning

confidence: 99%

Double Compton and Cyclo-Synchrotron in Super-Eddington Discs, Magnetized Coronae, and Jets

McKinney

Chluba

Wielgus

et al. 2017

Mon. Not. R. Astron. Soc.

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We present an extension to the general relativistic radiation magnetohydrodynamic code HARMRAD to account for emission and absorption by thermal cyclo-synchrotron, double Compton, bremsstrahlung, low-temperature OPAL opacities as well as Thomson and Compton scattering. We approximate the radiation field as a Bose-Einstein distribution and evolve it using the radiation number-energy-momentum conservation equations in order to track photon hardening. We perform various simulations to study how these extensions affect the radiative properties of magnetically-arrested disks accreting at Eddington to super-Eddington rates. We find that double Compton dominates bremsstrahlung in the disk within a radius of r ∼ 15r g (gravitational radii) at a hundred times the Eddington accretion rate, and within smaller radii at lower accretion rates. Double Compton and cyclo-synchrotron regulate radiation and gas temperatures in the corona, while cyclo-synchrotron regulates temperatures in the jet. Interestingly, as the accretion rate drops to Eddington, an optically thin corona develops whose gas temperature of T ∼ 10 9 K is ∼ 100 times higher than the disk's black body temperature. Our results show the importance of double Compton and synchrotron in super-Eddington disks, magnetized coronae, and jets.

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“…This equation is a nonlinear partial differential equation that, in astrophysics, is used to model the diffusion of photons in a plasma made up of electrons [25]. We will decomposed the nonlinear terms of this equation using the Adomian polynomials and then, in combination with the use of the Laplace transform, we will obtain an algorithm to solve the problem subject to initial conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Plot of the exact solution given by Eq (25). for (x, t) ∈ (0, 5] × [0, 0.004] The plot of the exact solution given by(25) appears above the plot of the approximate solution given in(24).…”

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confidence: 97%

Solution of the Nonlinear Kompaneets Equation Through the Laplace-Adomian Decomposition Method

González-Gaxiola

Chávez

Bernal-Jáquez

2016

Int. J. Appl. Comput. Math

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The Kompaneets equation is a nonlinear partial differential equation that plays an important role in astrophysics as it describes the spectra of photons in interaction with a rarefied electron gas. In spite of its importance, exact solution to this nonlinear equation are rarely found in literature. In this work, we solve this equation and present a new approach to obtain the solution by means of the combined use of the Adomian decomposition method and the Laplace transform (LADM). Besides, we illustrate our approach solving two examples in which, two initial photon distributions, well known in astrophysics, are given. We compare the behaviour of the solutions obtained with the only exact solutions given in the literature for the non-relativistic case. Our results indicate that LADM is highly accurate and can be considered a very useful and valuable method.

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Relativistic corrections to the Kompaneets equation

Cited by 9 publications

References 18 publications

Spectral and temporal properties of Compton scattering by mildly relativistic thermal electrons

Spectral and temporal properties of Compton scattering by mildly relativistic thermal electrons

Double Compton and Cyclo-Synchrotron in Super-Eddington Discs, Magnetized Coronae, and Jets

Solution of the Nonlinear Kompaneets Equation Through the Laplace-Adomian Decomposition Method

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