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

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4. A combined proxy

In an attempt to obtain a more reliable and robust proxy of the long-term behavior of facular emission over the last 11 activity cycles we combine together the ratios of all four proxies to [FORMULA]. Their different estimated reliabilities are taken into account by weighting the [FORMULA] curves accordingly. Hence the [FORMULA] curves are combined by calculating


where the weight [FORMULA] is set to zero if [FORMULA] and therefore [FORMULA] is not available for cycle number n.

The main problem with this approach is that assigning a weight to each proxy is relatively subjective. We have therefore tested how strongly Q depends on the choice of weights, subject to the following general restrictions. The time-series of white-light faculae is considered to be the least reliable and is consequently given the smallest weight: we always set [FORMULA]. Full-disk measurements of [FORMULA] radio flux, on the other hand, are given the largest weight ([FORMULA]). Weights to sunspot and plage area measurements are placed between these two extremes.

The tested weights, together with the resulting strengths of cycles 16 and 19 relative to the mean of cycles 18, 19 and 20 ([FORMULA] and [FORMULA], respectively), are listed in Table 1. The corresponding [FORMULA] curves are plotted in Fig. 4.


Table 1. Weights used to combine the four facular proxies. [FORMULA], [FORMULA], [FORMULA] and [FORMULA] are the weights for, respectively, white light faculae, sunspot areas, Ca K plage areas and 10.7cm radio flux. [FORMULA] and [FORMULA] indicate the strength (relative to the mean of cycles 18, 19 and 20) of cycle 16 and 19, respectively.

[FIGURE] Fig. 4. Inter-cycle variations of the ratio, Q, of the combined proxy relative to [FORMULA]. The various curves correspond to the weights given in Table 1.

The general shape of the Q curve is relatively insensitive to the exact choice of weights (at least within the above general restrictions on the relative weights). In particular, the dominance of cycle 16 is seen for all sets of weights we have tested. In view of the merits and demerits of the various data sets we have chosen [FORMULA] for our final proxy. This choice results in a Q curve that lies well inside the extremes we have found. The long-term variation of this proxy relative to [FORMULA] is plotted in Fig. 5. The error bars take into account uncertainties introduced by changing the boundary conditions in Eq. (1) and the uncertainty in the weights [FORMULA].

[FIGURE] Fig. 5. Ratio, Q, of the final combined proxy of long-term facular emission to [FORMULA] over the last 11 activity cycles. The presented curve results from a combination of all four proxies using the weights [FORMULA]. It shows a prominent increase of facular emission relative to that by [FORMULA] during cycle 16.

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© European Southern Observatory (ESO) 1998

Online publication: March 30, 1998