A Relativistic Formula for the Multiple Scattering of Photons
Abstract
We have discovered analytical expressions for the probability density function (PDF) of photons that are multiply scattered in relativistic flows, under the assumption of isotropic and inelastic scattering. These expressions characterize the collective dynamics of these photons, ranging from freestreaming to diffusion regions. The PDF, defined within the light cone to ensure the preservation of causality, is expressed in a threedimensional space at a constant time surface. This expression is achieved by summing the PDFs of photons that have been scattered n times within fourdimensional spacetime. We have confirmed that this formulation accurately reproduces the results of relativistic Monte Carlo simulations. We found that the PDF in threedimensional space at a constant time surface can be represented in a separable variable form. We demonstrate the behavior of the PDF in the laboratory frame across a wide range of Lorentz factors for the relativistic flow. When the Lorentz factor of the fluid is low, the behavior of scattered photons evolves sequentially from free propagation to diffusion, and then to dynamic diffusion, where the mean effective velocity of the photons equates to that of the fluid. On the other hand, when the Lorentz factor is large, the behavior evolves from anisotropic ballistic motion, characterized by a mean effective velocity approaching the speed of light, to dynamic diffusion.
 Publication:

The Astrophysical Journal
 Pub Date:
 May 2024
 DOI:
 10.3847/20418213/ad409b
 arXiv:
 arXiv:2405.10484
 Bibcode:
 2024ApJ...967L..10T
 Keywords:

 Radiative processes;
 Radiative transfer;
 Relativity;
 Relativistic fluid dynamics;
 Astrophysical fluid dynamics;
 Active galactic nuclei;
 Gammaray astronomy;
 Gammaray bursts;
 Supernova dynamics;
 Supernova neutrinos;
 Cosmic rays;
 Accretion;
 2055;
 1335;
 1393;
 1389;
 101;
 16;
 628;
 629;
 1664;
 1666;
 329;
 14;
 Astrophysics  High Energy Astrophysical Phenomena;
 Condensed Matter  Statistical Mechanics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 The version accepted by ApJ Letters