### Abstract

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 0 if the flow velocity β ≡ v/c satisfies β/Γ ≫ ξ^{-1}, while it is proportional to ξ^{2} if β/Γ ≪ ξ^{-1}, where 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 τa is considerably smaller than the optical depth for scattering τs (τa/τs ≪ 1) and the flow velocity satisfies , then the effective optical depth is approximated by τ* ≃ τa(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.

Original language | English |
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Article number | L4 |

Journal | Astrophysical Journal Letters |

Volume | 787 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 May 20 |

Externally published | Yes |

### Keywords

- gamma-ray burst: general
- radiative transfer
- relativistic processes
- scattering

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal Letters*,

*787*(1), [L4]. https://doi.org/10.1088/2041-8205/787/1/L4