# Radiation hydrodynamics

Neal J. Turner (2011), Scholarpedia, 6(4):3648. | doi:10.4249/scholarpedia.3648 | revision #43469 [link to/cite this article] |

A fluid interacting with electromagnetic radiation gains or loses energy and momentum through the emission, absorption and scattering of photons. Radiation hydrodynamics is a set of techniques used to model the resulting flows. The intensity of the radiation field and the optical depth of the fluid determine many basic properties of the composite system, and are key factors to consider in choosing a modeling approach.

Other composite flows modeled using similar methods include neutrinos interacting with ordinary matter, as in core-collapse supernova explosions, and neutron transport in nuclear engineering.

## Contents |

## Types of Radiating Flows

The effects of the photons vary with the intensity of the radiation field. At low intensities the radiation affects the matter mostly through energy transport, causing cooling in some places and heating in others. The forces due to the radiation can be ignored. At somewhat higher intensities, the photons carry significant momentum, and accelerate the medium through which they pass. The effects produced include Poynting-Robertson drag and photon viscosity. At still higher intensities, the distinction between matter and radiation blurs, and the mass density changes through the transport of gamma-ray photons and the creation and annihilation of matter-antimatter particle pairs.

Approaches to radiation hydrodynamics also can be divided according to the optical depth of the flow. When the photon mean free path is much greater than the flow size, the system is optically thin. Emitted photons often can be assumed to escape with no further interactions. When the mean free path is much shorter than internal variations in the flow, the system is optically thick. The matter and radiation are well-coupled, the frequent interactions between the two components make the radiation approximately isotropic, and the transport of the radiation through the flow is often treated by a diffusion approximation. The intermediate regime, where photon mean free paths are similar to some of the scales in the fluid, can lead to large anisotropies in the radiation field and typically requires the most effort to treat properly. Approaches that have proven useful include, in order of increasing complexity, (1) the escape probability method, where the optical depth determines the chance an emitted photon interacts again with the material locally, (2) the flux-limited diffusion method, involving interpolation between the known solutions for optically-thick and thin atmospheres, and (3) the variable tensor Eddington factor method, where the radiation field is explicitly determined by solving the transfer equation along a set of rays.

## Example Applications

Damped acoustic waves: Mihalas D. & Mihalas B. W. 1984, Ap. J. 283, 469.

Radiating shocks: Sincell M. W., Gehmeyr M. & Mihalas D. 1999, Shock Waves 9, 391.

Solar convection: Stein R. F. & Nordlund \AA 1998, Ap. J. 499, 914.

Winds from massive stars: Owocki S. P., Castor J. I. & Rybicki G. B. 1988, Ap. J. 335, 914.

Neutron star accretion columns: Hsu J. J. L., Arons J. & Klein R. I. 1997, Ap. J. 478, 663.

Black hole accretion disks: Hirose S., Krolik J. H. & Stone J. M. 2006, Ap. J. 640, 901.

Protostellar collapse: Bodenheimer P., Yorke H. W., Rozyczka M. & Tohline J. E. 1990, Ap. J. 355, 651.

Photoevaporating protostellar disks: Richling S. & Yorke H. W. 2000, Ap. J. 539, 258.

## Further Reading

1. J. I. Castor (2004), Radiation Hydrodynamics. Cambridge University Press.

2. D. Mihalas & B. Weibel-Mihalas (1984), Foundations of Radiation Hydrodynamics. Oxford University Press. Dover Publications edition 1999.

3. J. M. Stone, D. Mihalas & M. L. Norman (1992), Ap. J. Suppl. 80, 819.