The influence of an inclined rotation axis on solar irradiance variations

Compared with Sun-like stars, the irradiance variations of the Sun over the solar cycle appear to be relatively small for its average activity level (Lockwood et al. 1992; Radick et al. 1998). It has been proposed that the special position of Earth-based observers in the ecliptic plane may give the impression of a subdued solar photometric variability (Schatten 1993). The aim of the present paper is to examine the influence on irradiance variations of a solar rotation axis inclined towards the observer. A three-component model is used to calculate relative flux variations of a given active-region distribution on the surface of the Sun as a function of inclination and wavelength. Wavelength-dependent intensity spectra are used to describe the contributions of the undisturbed photosphere, sunspots and faculae. The spectra result from models that have successfully been used to reproduce a host of solar data and thus represent realistic estimates of the radiative output from these solar features. We find that an inclined rotation axis increases the total solar irradiance variations maximally by 40%. The most probable value is approximately 6%. This is much less than that suggested by former studies, which were based on simple contrast functions. In the averaged Strömgren filters we estimate a most probable increase of the solar variability of 30%. In addition, we estimate the dependence of the flux in the chromospheric Ca II H&K lines on inclination. We find that the average chromospheric activity level depends only slightly on the inclination angle. The chromospheric variability of Sun-like stars, however, is significantly affected. Nonetheless, our results indicate that a different average inclination of stellar rotation axes relative to the observer cannot explain the discrepancy between the brightness variations of the Sun and Sun-like stars.