2014ApJ...787L...4S

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/l₀ if the flow velocity β ≡ v/c satisfies β/Γ {Gt} ξ^–1, while it is proportional to ξ² if β/Γ {Lt} ξ^–1, where L and l₀are 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_ais considerably smaller than the optical depth for scattering τ_s(τ_a/τ_s{Lt} 1) and the flow velocity satisfies β ≫ sqrt(2τ_a/τ_b), then 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 scatterings. The analytic expression is consistent with the results of the numerical simulations. The 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.