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Title: RANDOM WALKS AND EFFECTIVE OPTICAL DEPTH IN RELATIVISTIC FLOW

We investigate the random walk process in relativistic flow. In the relativistic flow, photon propagation is concentrated in the direction of the flow velocity due to the relativistic beaming effect. We show that in the pure scattering case, the number of scatterings is proportional to the size parameter ξ ≡ L/l {sub 0} if the flow velocity β ≡ v/c satisfies β/Γ >> ξ{sup –1}, while it is proportional to ξ{sup 2} if β/Γ << ξ{sup –1}, where L and l {sub 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{sub a} is considerably smaller than the optical depth for scattering τ{sub s} (τ{sub a}/τ{sub s} << 1) and the flow velocity satisfies β≫√(2τ{sub a}/τ{sub s}), then the effective optical depth is approximated by τ{sub *} ≅ τ{sub 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 scatterings. The analytic expression is consistent with the results of the numerical simulations. Themore » expression derived in this study can be used to estimate the photon production site in relativistic phenomena, e.g., gamma-ray burst and active galactic nuclei.« less
Authors:
;  [1] ;  [2]
  1. Department of physics, Konan University, 8-9-1 Okamoto, Kobe, Hyogo 658-8501 (Japan)
  2. National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588 (Japan)
Publication Date:
OSTI Identifier:
22365845
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal Letters; Journal Volume: 787; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; COSMIC GAMMA BURSTS; COSMIC PHOTONS; GALAXY NUCLEI; GRAPH THEORY; MEAN FREE PATH; MONTE CARLO METHOD; PARTICLE PRODUCTION; RADIANT HEAT TRANSFER; RANDOMNESS; RELATIVISTIC RANGE; VELOCITY