### Abstract

We derive from first principles the equations which govern the behavior of small-amplitude fluctuations in a homogeneous and isotropic radiating fluid. Products of the fluctuating quantities are shown to obey a wave-energy conservation law from which it follows that all perturbations must ultimately decay in time. Under fairly general circumstances the governing equations may be solved through the use of integral transforms which affords an accounting of the various wave modes supported by the radiating fluid. In addition to the familiar radiatively modified acoustic mode, the radiation-diffusion mode, the radiative-relaxation mode, and the isotropization and exchange modes which constitute the discrete spectrum of the differential equation, we find a continuous spectrum of wave modes associated with the "collisionless" nature of the photons on time-scales short compared to the photon lifetime. This continuous spectrum is eliminated if an Eddington approximation is used to close the heirarchy of equations that relate the fluctuating angular moments of the radiation field. Quantitative results are obtained for the simple case in which the opacity may be regarded as being independent of the frequency of the photon and the source function may be approximated by the (local) Planck function.

Original language | English |
---|---|

Pages (from-to) | 879-901 |

Number of pages | 23 |

Journal | Astrophysical Journal |

Volume | 456 |

Issue number | 2 PART I |

DOIs | |

Publication status | Published - 1 Jan 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

- Hydrodynamics
- Radiative transfer
- Sun: oscillations
- Waves

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*456*(2 PART I), 879-901. https://doi.org/10.1086/176704

**Waves in radiating fluids.** / Bogdan, T. J.; Knölker, M.; MacGregor, K. B.; Kim, E. J.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 456, no. 2 PART I, pp. 879-901. https://doi.org/10.1086/176704

}

TY - JOUR

T1 - Waves in radiating fluids

AU - Bogdan, T. J.

AU - Knölker, M.

AU - MacGregor, K. B.

AU - Kim, E. J.

PY - 1996/1/1

Y1 - 1996/1/1

N2 - We derive from first principles the equations which govern the behavior of small-amplitude fluctuations in a homogeneous and isotropic radiating fluid. Products of the fluctuating quantities are shown to obey a wave-energy conservation law from which it follows that all perturbations must ultimately decay in time. Under fairly general circumstances the governing equations may be solved through the use of integral transforms which affords an accounting of the various wave modes supported by the radiating fluid. In addition to the familiar radiatively modified acoustic mode, the radiation-diffusion mode, the radiative-relaxation mode, and the isotropization and exchange modes which constitute the discrete spectrum of the differential equation, we find a continuous spectrum of wave modes associated with the "collisionless" nature of the photons on time-scales short compared to the photon lifetime. This continuous spectrum is eliminated if an Eddington approximation is used to close the heirarchy of equations that relate the fluctuating angular moments of the radiation field. Quantitative results are obtained for the simple case in which the opacity may be regarded as being independent of the frequency of the photon and the source function may be approximated by the (local) Planck function.

AB - We derive from first principles the equations which govern the behavior of small-amplitude fluctuations in a homogeneous and isotropic radiating fluid. Products of the fluctuating quantities are shown to obey a wave-energy conservation law from which it follows that all perturbations must ultimately decay in time. Under fairly general circumstances the governing equations may be solved through the use of integral transforms which affords an accounting of the various wave modes supported by the radiating fluid. In addition to the familiar radiatively modified acoustic mode, the radiation-diffusion mode, the radiative-relaxation mode, and the isotropization and exchange modes which constitute the discrete spectrum of the differential equation, we find a continuous spectrum of wave modes associated with the "collisionless" nature of the photons on time-scales short compared to the photon lifetime. This continuous spectrum is eliminated if an Eddington approximation is used to close the heirarchy of equations that relate the fluctuating angular moments of the radiation field. Quantitative results are obtained for the simple case in which the opacity may be regarded as being independent of the frequency of the photon and the source function may be approximated by the (local) Planck function.

KW - Hydrodynamics

KW - Radiative transfer

KW - Sun: oscillations

KW - Waves

UR - http://www.scopus.com/inward/record.url?scp=21844484772&partnerID=8YFLogxK

U2 - 10.1086/176704

DO - 10.1086/176704

M3 - Article

VL - 456

SP - 879

EP - 901

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2 PART I

ER -