Radiativetransfer

Radiative transfer is the study of how electromagnetic radiation propagates through a medium in which absorption, emission, and scattering modify the radiation field. It is a foundational concept in astrophysics, planetary science, atmospheric physics, and remote sensing, enabling the interpretation of spectra, images, and radiative energy balances in stars, planets, and interstellar and intergalactic media.

The core of radiative transfer is the radiative transfer equation, which describes the change of the specific intensity Iν along a path. In its common form, dIν/ds = -αν Iν + jν + scattering terms, where αν is the absorption coefficient and jν is the emission coefficient. In optical-depth form, dIν/dτν = Iν - Sν, with Sν = jν/αν the source function. When scattering is important, Sν becomes non-local and depends on direction, frequency, and the surrounding radiation field.

Solving the equation requires boundary conditions and often numerical methods. In local thermodynamic equilibrium (LTE), the source function reduces to the Planck function Bν(T). Non-LTE models treat level populations explicitly and include scattering and non-thermal emission, making the problem more complex and computationally demanding.

Opacity and emissivity vary with frequency, temperature, density, and composition, leading to line and continuum formation. In optically thick regions the diffusion approximation applies; in optically thin layers radiation escapes more freely. Radiative transfer also governs radiative cooling and heating balances and radiative equilibrium in atmospheres and cosmology.

Common numerical approaches include the discrete ordinates method, Feautrier method, and short- or long-characteristics schemes. Radiative transfer codes model stellar and planetary atmospheres and interpret spectra and energy transport in diverse astrophysical and atmospheric contexts.