Astrophysics (Index)About

equation of radiative transfer

(RTE, transfer equation, radiative transfer equation)
(equation describing energy transfer by EMR)

An equation of radiative transfer (or radiative transfer equation or RTE or transfer equation) is an equation that describes radiative transfer, the transfer of energy by electromagnetic radiation (EMR) through a gas or plasma, taking into account the absorption and emission of photons by the gas particles. Such equations are used in modeling stars and in modeling the effect of planetary atmospheres on EMR. The equations generally represent the EMR along a beam, in this case, beam meaning the EMR directed along some straight line, including whatever EMR is added and/or removed along the way, as long as it is EMR following that line. Such an equation can be put in many forms, one general form being:

rate of change in intensity
= rate of emission due to excitation
- rate of absorption
- rate of scattering of photons out of the beam
+ rate of scattering of photons into the beam
+ rate of generated EMR (within stars, that due to fusion)

In this form, each term's "rate" is a rate over distance along the beam, specifically its differential (i.e., the above represents a differential equation). Some of the terms are functions of intensity and/or of density, and some incorporate opacity.

If each term can be calculated (or its value looked up in a pre-calculated table), the equation can be used to create tractable stellar-structure models. Some forms of the equation may combine some of these terms, e.g., considering the effects of scattering as part of the emission and absorption terms. Some common approximating assumptions: equilibrium (no change over time, thermodynamic equilibrium or local thermodynamic equilibrium), an approximation of the composite of all wavelengths (gray atmosphere, using the Rosseland mean opacity), a directional component (Eddington approximation) and/or that variation in the medium is along a single dimension (plane-parallel atmosphere).

Further reading:

Referenced by pages:
absorption coefficient
radiative transfer (RT)
source function (S)