Applicability of the Fourier convolution theorem to the analysis of late-type stellar spectra

Solar flux and intensity measurements were obtained at Sacramento Peak Observatory to test the validity of the Fourier convolution method as a means of analyzing the spectral line shapes of late-type stars. Analysis of six iron lines near 6200A shows that, in general, the convolution method is not a suitable approximation for the calculation of the flux profile. The convolution method does reasonably reproduce the line shape for some lines which appear not to vary across the disk of the sun, but does not properly calculate the central line depth of these lines. Even if a central depth correction could be found, it is difficult to predict, especially for stars other than the sun, which lines have nearly constant shapes and could be used with the convolution method. Therefore, explicit disk integrations are promoted as the only reliable method of spectral line analysis for late-type stars. Several methods of performing the disk integration are investigated. Although the Abt (1957) prescription appears suitable for the limited case studied, methods using annuli of equal area, equal flux, or equal width (Soberblom, 1980) are considered better models. The model that is the easiest to use and most efficient computationally is the equal area model. Model atmosphere calculations yield values for the microturbulence and macroturbulence similar to those derived by observers. Since the depth dependence of the microturbulence is ignored in the calculations, the intensity profiles at disk center and the limb do not match the observed intensity profiles with only one set of velocity parameters. Use of these incorrectly calculated intensity profiles in the integration procedure to obtain the flux profile leads to incorrect estimates of the solar macroturbulence