TY - JOUR

T1 - The general relativistic equations of radiation hydrodynamics in the viscous limit

AU - Coughlin, Eric R.

AU - Begelman, Mitchell C.

N1 - Publisher Copyright:
© 2014. The American Astronomical Society. All rights reserved.

PY - 2014/12/20

Y1 - 2014/12/20

N2 - We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.

AB - We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.

KW - Radiation: Dynamics

KW - Radiative transfer

KW - Relativistic processes

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U2 - 10.1088/0004-637X/797/2/103

DO - 10.1088/0004-637X/797/2/103

M3 - Article

AN - SCOPUS:84916612987

VL - 797

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

M1 - 103

ER -