E4 Radiative Transfer and Opacity

Topic

The central element of this model is radiation intensity as it propagates through a medium that both absorbs and emits it.

The radiative transfer equation describes how this intensity changes along its path through the medium: absorption by the medium reduces it, while local emission from the medium itself replenishes it. Optical depth accumulates the total absorption the radiation has undergone up to a given point along its path; once this value exceeds unity, the medium becomes optically thick and radiation can no longer escape in a straight line—as happens within a star—whereas below this value, the medium is optically thin and radiation escapes almost unimpeded, as occurs in stellar coronae and nebulae.

The source function—defined as the ratio of the medium's emission to its absorption—equals the Planck function exactly when the medium is in local thermodynamic equilibrium; thus, achieving this equilibrium renders the source function indistinguishable from the Planck function at that point in the medium.

A star's visible atmosphere corresponds precisely to the optical depth where the continuum finishes forming; it is this specific optical depth that makes the entire star visible from the outside. Three opacity mechanisms dominate this process, combining to produce the medium's total opacity: photoionization (which sets the thresholds for spectral series), thermal bremsstrahlung, and free-electron scattering. The average of this total opacity—weighted according to the Planck function's temperature dependence—determines whether or not energy is transported through stellar interiors. Thus, ranging from the radiation intensity with which this document begins to the energy transport within stellar interiors with which it concludes—and encompassing optical depth, the source function, the star's visible atmosphere, radiative transfer, and opacity—these factors determine whether a given radiation intensity passes unimpeded through a thin medium or becomes trapped and thermalized in a thick medium, depending on the balance between absorption and emission imposed by that medium.

ID:3925