We investigate the random walk process in relativistic flow. In the relativistic flow, photon propagation is concentrated in the directions of the flow velocity due to relativistic beaming effect. We show that, in the pure scattering case, the number of scatterings is proportional to the size parameterwhere L and l 0 are the size of the system in the observer frame and the mean free path in the comoving frame, respectively. We also examine the photon propagation in the scattering and absorptive medium. We find that, if the optical depth for absorption τ a is considerably smaller than the optical depth for scattering τ s (τ a /τ s ≪ 1) and the flow velocity satisfies β ≫ 2τ a /τ s , the effective optical depth is approximated by τ * ≃ τ a (1 + β)/β. Furthermore, we perform Monte Carlo simulations of radiative transfer and compare the results with the analytic expression for the number of scattering. The analytic expression is consistent with the results of the numerical simulations. The expression derived in this Letter can be used to estimate the photon production site in relativistic phenomena, e.g., gamma-ray burst and active galactic nuclei.
The Chacaltaya air shower array has continued to be used for the accumulation of muon-poor air showers in an attempt to find evidence of gamma rays in the primary cosmic radiation. A progress report is given here, and some upper limits to the intensities are presented for possible point sources and for galactic and isotropic backgrounds.
We investigate the fraction of metal nuclei in the relativistic jets of gamma-ray bursts associated with core-collapse supernovae. We simulate the fallback in jet-induced explosions with two-dimensional relativistic hydrodynamics calculations and the jet acceleration with steady, radial, relativistic magnetohydrodynamics calculations, and derive detail nuclear composition of the jet by postprocessing calculation. We found that if the temperature at the jet launch site is above 4.7 × 10 9 K, quasi-statistical equilibrium (QSE) is established and heavy nuclei are dissociated to light particles such as 4 He during the acceleration of the jets. The criterion for the survival of metal nuclei is written in terms of the isotropic jet luminosity as L iso j < ∼ 3.9 × 10 50 (R i /10 7 cm) 2 (1 + σ i ) erg s −1 , where R i and σ i are the initial radius of the jets and the initial magnetization parameter, respectively. If the jet is initially dominated by radiation field (i.e., σ i ≪ 1) and the isotropic luminosity is relatively high (L iso j > ∼ 4 × 10 52 ergs −1 ), the metal nuclei cannot survive in the jet. On the other hand, if the jet is mainly accelerated by magnetic field (i.e., σ i ≫ 1), metal nuclei initially contained in the jet can survive without serious dissociation even for the case of high luminosity jet. If the jet contains metal nuclei, the dominant nuclei are 28 Si, 16 O, and 32 S and the mean mass number can be A ∼ 25.
We develop a time-dependent multi-group multidimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids involved in, e.g., gammaray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) that evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with a ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed frame approach; the source function is evaluated in the comoving frame whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated with various test problems and comparisons with results of a relativistic Monte Carlo code. These validations confirm that the code correctly calculates intensity and its evolution in the computational domain. The code enables us to obtain an Eddington tensor that relates first and third moments of intensity (energy density and radiation pressure) and is frequently used as a closure relation in radiation hydrodynamics calculations. 6 The emission from a relativistic flow is also interesting for, e.g., active galactic nuclei (AGN).
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