The calculation of line profiles in a stratified atmosphere.

Abstract

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The calculation of line profiles in a stratified atmosphere. Doherty, L. R. ; Hazen, M. L. ; Menzel, D. H. Abstract The acceptability of a model solar atmosphere depends upon the agreement of the observed and predicted line profiles or curves of growth, at different angles of the emergent beam. One calculates the specific intensity from Milne's familiar integral, in terms of a known source function. The dependence of the result upon changes of model may be difficult to determine and interpret physically when many variables are present and when each integration is a relatively laborious process. We have adopted a simplified model which allows for stratification of the absorbing material and for a wide variety of source functions. The final result appears in algebraic form, so that one can readily examine how the emergent radiation varies with alteration of the parameters of the model. The approximations that we have made are the following. I. We have reproduced the effect of stratification by taking the ratio of line-to-continuous absorption (Eddington's ~) as constant in a layer between two arbitrarily chosen values of the optical depth r. We can also obtain a simple result by taking ~ proportional to r/ (a + r) or 2. We have assumed a constant Doppler temperature throughout the absorbing layer. 3. We have represented the source function as a linear combination of exponential and power terms in the optical depth. Intensities computed under the assumptions ~tated in (I) show that the results for variable 71 may essentially be duplicated by a layer with 71 constant between selected optical depths. In other words, the results are not very sensitive to the detailed form of the stratification. From this fact we conclude that the layer model adequately represents the effects of stratification on profiles of absorption lines. We have also computed curves of growth and find that a layer extending from the surface to an optical depth about 0.5 provides the best fit to the empirical curves for Fei (Bell 1951) and Tii (Claas 1951). As might be expected, this curve also corresponds with the theoretical Schuster-Schwarzschild curve. We anticipate that this method will be particularly useful for source functions that depend on depth in a complicated manner, as in the chromosphere, or that vary over the disk, granulation and spots. This work has been supported by the Geophysics Research Directorate, Air Force Cambridge Research Center, under a contract with Harvard University. Bell, B. 1951, Harvard thesis. Claas, W. 1951, Rech. Astr. Obs. Utrecht 12, Part I. Harvard College Observatory, Cambridge, Mass. Publication: The Astronomical Journal Pub Date: September 1958 DOI: 10.1086/107752 Bibcode: 1958AJ.....63..305D full text sources ADS |