Random walks and effective optical depth in relativistic flow

Sanshiro Shibata, Nozomu Tominaga, Masaomi Tanaka

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 ξ2 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 languageEnglish
Article numberL4
JournalAstrophysical Journal Letters
Volume787
Issue number1
DOIs
Publication statusPublished - 2014 May 20
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Fingerprint Dive into the research topics of 'Random walks and effective optical depth in relativistic flow'. Together they form a unique fingerprint.

  • Cite this