The influence of an inclined rotation axis on solar irradiance variations

Abstract

Abstract. 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.

Stellar Chromospheric Activity

“…Equally interesting are the activity-variability plots on the right side of Figure 15; the Sun has a vigorous chromospheric cycle relative to its closest stellar analogs (upper right) but is photometrically sedate (lower right). Radick et al (1998) found that this discrepancy could not be due to inclination effects (i.e., that a sample of randomly inclined stars might appear more photometrically variable than the Sun), a result corroborated by Knaack et al (2001).…”

AsteroFLAG: First results from hare‐and‐hounds Exercise #1

“…We also allowed for the effect of the angle of inclination of the star, having assumed the active-region signal was confined within certain bands of stellar latitude, using the work of Knaack et al (2001) as a guide. We assumed the timescale of the active-region signal scaled with the period of rotation of the star.…”

The place of the Sun among the Sun-like stars

“…The rms 20 variability of these stars is calculated, employing the approach described in Sect. 3 and Appendix A and the Knaack et al (2001) dependency of the 11-year variability on the angle between the solar rotation axes and the direction to the observer. For every set we calculated the mean rms 20 variability of the stars in the set, so for every pair of V LT and V 11 parameters we have a distribution of mean rms 20 variabilities.…”

“…B.1 we plot the long-term solar variability V LT as a function of the mean solar variability (rms 20 ) given by the stellar data, for two values of the 11-year variability V 11 . The inclination effect was calculated according to Knaack et al (2001). Let us note, however, that the positions of the Sun-like stars in Fig.…”

“…Schatten (1993) suggested that the special position of the Earth-based observer who sees the Sun from its equatorial plane can reduce the variability of solar brightness. However, detailed calculations showed that the equatorial position of the observer leads to only a 30% (most probable value) decrease in the solar variability and does not affect the mean level of the chromospheric activity (Knaack et al 2001). The out-of-ecliptic measurements of the Sun are needed to validate the model and accurately assess the effects from the hemispherical asymmetry of the density flux (Vieira et al 2012).…”