The Moment Method in Relativistic Radiative Transfer

Anderson, Johan; Spiegel, E. A.

doi:10.1086/151265

Cited by 61 publications

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“…12) is essentially the same as the moment formalism derived by Anderson and Spiegel. 1) We note that the second-rank tensor M αβ is equal to the energymomentum tensor for one of the radiation components.…”

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confidence: 99%

Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity

Shibata

Kiuchi

Sekiguchi

et al. 2011

Progress of Theoretical Physics

245

313

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A truncated moment formalism for general relativistic radiation hydrodynamics, based on Thorne's moment formalism, is derived. The fluid rest frame is chosen to be the fiducial frame for defining the radiation moments. Then, zeroth-, first-, and second-rank radiation moments are defined from the distribution function with a physically reasonable assumption for it in the optically thin and thick limits. The source terms are written, focusing specifically on the neutrino transfer and neglecting higher harmonic angular dependence of the reaction angle. Finally, basic equations for a truncated moment formalism for general relativistic radiation hydrodynamics in a closed covariant form are derived assuming a closure relation among the radiation stress tensor, energy density, and energy flux, and a variable Eddington factor, which works well. We note that only electron neutrinos can be degenerate in general. For antielectron neutrinos, μ c < 0 and for muon and tau neutrinos, μ c = 0, when these neutrinos are in thermal equilibrium with matter. Thus, these are not degenerate in general.

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confidence: 99%

Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity

Shibata

Kiuchi

Sekiguchi

et al. 2011

Progress of Theoretical Physics

245

313

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“…Although the observed spectra are characterized by a broken power-law shape [11], these properties have not been reproduced accurately in the numerical works of the relativistic hydrodynamics. Analytical and numerical solutions for the equation of radiative transfer in relativistic flows can be obtained by various methods [12,13]; in particular, some authors have developed the method to solve the problem statistically by Monte Carlo (MC) technique [14,15], which has been adopted for the problem in the context of radiative transport in supernova explosions [16,17]. Since some observations indicate spectra with a thermal component [18], radiative transport for thermal photons produced by photospheric emission is regarded as the feasible model, and the feature of the spectra in GRBs was interpreted by overlapping thermal spectra for some components of various angles of photons escaped from the photosphere due to different observed time [19].…”

Section: Introductionmentioning

confidence: 99%

Identical algorithm of radiative transfer across ultrarelativistic shock in different inertial frames

Ishii

Ohnishi

Nagakura

et al. 2015

High Energy Density Physics

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“…So far, the radiative transfer in curved spacetime was investigated by many authors (e.g. Lindquist 1966;Anderson& Spiegel 1972;Schmid-Burgk 1978;Thorne 1981;Schinder 1988;Turolla & Nobili 1988;Anile & Romano 1992;Cardall & Mezzacappa 2003;Park 2006;Takahashi 2007bTakahashi , 2008De Villiers 2008;Farris et al 2008).…”

Section: Introductionmentioning

confidence: 99%

Anisotropic radiation field and trapped photons around the Kerr black hole

Takahashi¹,

Takahashi²

2010

A&A

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Aims. In order to understand the anisotropic properties of local radiation field in the curved spacetime around a rotating black hole, we investigate the appearance of a black hole seen by an observer located near the black hole. When the black hole is in front of a source of illumination the black hole casts shadow in the illumination. Accordingly, the appearance of the black hole is called the black hole shadow. Methods. We first analytically describe the shape of the shadow in terms of constants of motion for a photon seen by the observer in the locally non-rotating reference frame (LNRF). Then, we newly derive the useful equation for the solid angle of the shadow. In a third step, we can easily plot the apparent image of the black hole shadow. Finally, we also calculate the ratio of the photon trapped by the hole and the escape photon to the distant region for photons emitted near the black hole. Results. From the shape and the size of the black hole shadow, we can understand the signatures of the curved spacetime; i.e., the mass and spin of the black hole. Our equations for the solid angle of the shadow has technical advantages in calculating the photon trapping ratio. That is, this equation is computationally very easy, and gives extremely precise results. This is because this equation is described by the one-parameter integration with given values of the spin and location for the black hole considered. After this, the solid angle can be obtained without numerical calculations of the null geodesics for photons.

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The Moment Method in Relativistic Radiative Transfer

Cited by 61 publications

References 0 publications

Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity

Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity

Identical algorithm of radiative transfer across ultrarelativistic shock in different inertial frames

Anisotropic radiation field and trapped photons around the Kerr black hole

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