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Astron. Astrophys. 345, 635-642 (1999)

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2. The model

Our model has three components, namely a quiet-sun, a facular and a spot contribution (see Paper II for details). In order to calculate fluxes, intensities and limb-dependent contrasts of each of these components, we employ Kurucz's ATLAS9 program with opacity distribution functions (ODFs). The program (as rewritten by J. B. Lester) and the ODFs were obtained through CCP7 (Collaborative Computing Project No. 7). Kurucz's solar model atmosphere was used to obtain the quiet-sun fluxes and intensities (Kurucz 1992a, 1992b, 1992c). Our approach to modelling solar irradiance variations, although in many ways similar to that taken by Fontenla et al. (1999), is also complementary to theirs. They model selected parts of the spectrum using NLTE and, where necessary partial redistribution, thus achieving much greater realism than our LTE approach. However, the simplification of LTE and the use of ODFs allows us to calculate the whole spectrum from 160 nm to 160 000 nm with a spectral resolution of better than 200 in the visible. Whereas in theory, we are able to calculate the solar spectrum down to about 10 nm, the discrepancies between the calculated and observed solar spectrum become prohibitively large below 160 nm, so that we do not consider this extreme UV region in our comparisons. The spot fluxes (from umbra and penumbra together) were calculated from a model atmosphere of 5150 K which in turn was interpolated from the Kurucz grid of model atmospheres. Using separate models for umbra and penumbra produced no significant changes in the emerging spectrum.

Rather than making up the facular model atmosphere from scratch, we used model P of Fontenla et al. (1993) (FAL P) as a starting point. Following very small modifications, this model had proved remarkably successful in our previous attempt to model the spectral irradiance variations (see Papers I and II).

The model as used in Papers I and II had to be further altered in order to be used with ATLAS9. The original hot chromosphere produced strong excess emission in the UV as well as emission reversals in all the Balmer lines and in numerous UV lines, due mainly to the simplification of LTE that we employ. We therefore truncated the atmosphere at about the temperature minimum and extrapolated down to lower temperatures (using ATLAS9). The resulting model was then further adjusted to improve the fits to the spectral irradiance variations (see Sect. 5.1) and to the VIRGO data (see Sect. 5.2). The modifications consisted mainly in a small temperature decrease in the deeper atmospheric layers, along with a flatter temperature gradient between optical depths 0.002 and 0.4 (i.e. column masses of 0.1 to 3). The original model P as well as our current facular model are shown in Fig. 1.

[FIGURE] Fig. 1a and b. The original and the modified facular models in comparison: a  the temperature as a function of column mass; b  the gas pressure as a function of temperature. The solid lines in both plots show model P as given in Fontenla et al. (1993) and the dashed lines show our current facular model. For comparison, Kurucz's solar model is also plotted using dotted lines.

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© European Southern Observatory (ESO) 1999

Online publication: April 19, 1999