An implicit integral method to solve selected radiative transfer problems. I - Non-LTE line formation

Details An implicit integral method to solve selected radiative transfer problems. I - Non-LTE line formation An implicit integral method to solve selected radiative transfer problems. I - Non-LTE line formation

Jun 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...409..830s&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 409, no. 2, p. 830-840.

Statistics

Computation

15

Integrals, Line Spectra, Radiative Transfer, Stellar Radiation, Nuclear Models, Stellar Atmospheres

Scientific paper

In this paper we present a new method to solve those radiative transfer problems where the scattering term in the source function, i.e., the frequency-integrated mean intensity J(phi), is independent of both frequencies and directions. This particular form of the source function, together with an implicit description of the evolution of the specific intensities incoming to an individual layer from the neighboring ones, allows one to solve implicitly the radiative transfer equation layer by layer. Consequently, J(phi) can be expressed as an explicit function of the (as yet unknown) specific intensities without any need to solve numerically a system of equations or to invert matrices. In this way, the global problem is reduced to a series of one-layer two-point boundary problems. The resulting algorithm is the representation of the actual physical process. This, together with the fact that it does not require a matricial formalism, brings about self-evident advantages in terms of reliability and numerical accuracy, as well as computational time and memory storage. As an application, the instance of the spectral line formation in a two-level atomic model is considered.

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