tokens: note that the good agreement of the TSI with the red filters is expected to be valid only for the rotational variability, which is dominated by spots. In contrast, the solar irradiance variability on the activity cycle timescale is given by the delicate balance between facular and spot components, and consequently has a very sophisticated spectral profile ( Shapiro et al. 2016 ; Witzke et al. 2018 ). Thus, values of slopes from Table 1 cannot be extrapolated from rotational to activity cycle timescales (see Shapiro et al. 2016 , for the detailed discussion). Fig. 3. R 30 in different filter systems compared to the TSI (black solid line) for a time span of 1000 days over solar cycle 22. Top panels : Kepler , CoRoT, and TESS. Middle panels : three Gaia passbands. Bottom panels : three VIRGO/SPM channels. See the main text for the definition of R 30 . Table 1. Slopes of the linear regressions in Fig. 4 . Table 2 lists the cycle-averaged values of R 30 for all passbands in mmag. Together, Fig. 4 , and Tables 1 and 2 show that the TSI is a passable representative for the variability on the solar rotation timescale as it would be observed in the TESS, Kepler , CoRoT, Gaia G , Gaia G RP , and VIRGO-red filters, but it noticeably underestimates the variability in G BP , VIRGO-green, and VIRGO-blue. Fig. 4. Linear regression between the R 30 values calculated with the TSI and with the solar light curves as they would be recorded in different filter systems. The values of the slope, s , are given in the legend. The black lines have a slope equal to 1. Several studies (see e.g. Basri et al. 2010 ; Harrison et al. 2012 ) have assumed that the amplitude of the rotational solar variability as it would be measured by Kepler is very close to the amplitude calculated for the combined green and red VIRGO/SPM light curves (in the following VIRGO/g+r). Here we test this hypothesis. The variability R 30 for Kepler compared to VIRGO/g+r is shown in Fig. 5 , which is limited to the same time interval as Fig. 3 . The two curves are remarkably similar to one another. To test the similarity quantitatively, we show the linear regression of R 30 between Kepler and VIRGO/g+r for four solar cycles (21–24) in Fig. 6 . The Pearson correlation coefficient is very high (0.999) and the slope deviates by only +0.8% of unity averaged over four solar cycles. While these calculations are related to the amplitude of the rotational variability, R 30 , we additionally calculate regressions between Kepler and Virgo light curves in Sect. 4 . We also directly connect the TSI and VIRGO/g+r rotational variability. The linear regression between R 30 in TSI and VIRGO/g+r results in a slope of 0.88 (±0.002) and a Pearson correlation coefficient of 0.995. Fig. 5. R 30 over cycle 22 for VIRGO/g+r and Kepler . Fig. 6. Linear regression between the R 30 calculated for VIRGO/g+r and for Kepler light curves. The black solid line represents a linear regression with slope = 1. 3. Correction for the
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