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Astron. Astrophys. 332, 1082-1086 (1998)

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3. Inter-cycle variations of facular emission

Following Foukal & Lean (1990) we assume that the shorter-term variations of facular brightness (i.e. variations on time scales of days to years) are well described by [FORMULA]. This is a reasonable choice for irradiance reconstructions aiming to cover long periods, since only [FORMULA] of the other proxies is known to reproduce direct irradiance observations better, but possesses too short a record.

We search here for possible departures from the sunspot number record on time scales longer than a solar cycle by looking for common features in the other four proxies. This may help us to construct a more robust proxy from their combination. Hence we need to consider only the ratio of the cycle-averaged value of one of the other four proxies (let us generically call it [FORMULA]) to the cycle-averaged value of [FORMULA]:


The sum over i runs over all (or alternatively a part of) the points in a cycle, and n is the number of the cycle (n lies between 12 and 22).

For better comparison all values are normalized to the mean of the cycles that are common to all five proxies, namely 18-20, i.e. we introduce the normalized values [FORMULA]:


We have found that the results depend only insignificantly on the details of the normalization.

By changing the summation boundaries in Eq. (1), we are able to estimate the contribution from different parts of a cycle. Hence, we restrict the summation boundaries in Eq. (1) to values of [FORMULA] lying between two fixed boundaries, e.g. between 0-200, 0-400, 50-400 and 100-400 (cf. Paper I) and calculate an average over the four values for each cycle. The resulting ratios [FORMULA] are presented in Fig. 3, where [FORMULA] or 10.7. Note that the summation index i is ordered according to increasing [FORMULA], so that changing the summation boundaries is equivalent to summing over different horizontal intervals in Fig. 2. The results depend on the summation interval most strongly for [FORMULA] and [FORMULA], due to their non-linear dependence on [FORMULA]. This is reflected in the larger error bars for [FORMULA] and [FORMULA] in Fig. 3 which mark the standard deviations of [FORMULA] obtained by varying the summation boundaries. The inter-cycle variations of [FORMULA] and [FORMULA] are identical to those already seen in Paper I. The influence of restricting the summation over [FORMULA] can also be judged from Fig. 5 of that paper.

[FIGURE] Fig. 3. Inter-cycle variations of ratios of sunspot areas ([FORMULA], solid line), 10.7cm radio flux measurements ([FORMULA], dash dotted), white light facular areas ([FORMULA], dashed) and Ca II K-line plage areas ([FORMULA], dotted) to sunspot number. The ratios are normalized and averaged as described in the text.

On the whole, the ratios are constant to within 20%, except for [FORMULA]. Whereas [FORMULA], [FORMULA] and [FORMULA] in Fig. 3 exhibit approximately the same level of variation, the [FORMULA] show a factor of four larger fluctuations. Another striking feature is that all three proxies extending sufficiently far back, i.e. sunspot, facular and plage areas, show a prominent increase relative to [FORMULA] for cycle 16. The Ca II plage areas show an even stronger peak at cycle 19 which, however, is absent in the other proxies, as has already been pointed out by Foukal (1996). The peak of [FORMULA] at cycle 16 is the only feature that is common to all data sets.

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© European Southern Observatory (ESO) 1998

Online publication: March 30, 1998