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

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2. Proxies of facular emission

We only consider indicators of solar activity that have been monitored for at least 40 years. These are: 1. the Zürich relative sunspot number ([FORMULA]); 2. sunspot areas ([FORMULA]); 3. 10.7cm radio flux measurements ([FORMULA]); 4. Ca II plage areas ([FORMULA]) and 5. white light facular areas ([FORMULA]). The various indices are available for the following periods: Daily values of [FORMULA] from 1818 to the present 1, [FORMULA] from 1874 to the present, [FORMULA] from 1947 to the present, [FORMULA] from 1915 to 1984 and [FORMULA] from 1906 to 1976. We take the [FORMULA] values from the Greenwich observatory record prior to 1976 and from other observatories since then (we use the combined and calibrated data set described in Paper I). The facular measurements obtained prior to 1906 are incomplete and of lower quality and hence have not been used.

It is difficult to decide which of these proxies to choose as a unique representative of facular brightness since each of them suffers from its own particular shortcoming. In the past [FORMULA] has often been considered to be better than, say, [FORMULA] because the latter did not correlate so well with a well-established facular proxy, such as [FORMULA]. In Paper I we showed that this was mainly due to a flawed [FORMULA] data set. The corrected [FORMULA] time series correlates almost as well with [FORMULA] as [FORMULA].

To better compare the time-series of [FORMULA] to the other four proxies we plot their auto-correlation functions in Fig. 1 for the year 1968 during the maximum of solar cycle 20. The shapes of the auto-correlation functions of [FORMULA], [FORMULA], [FORMULA] and [FORMULA] (upper panel) look very similar and are dominated by the solar rotation period around 27 days. The peaks have about equal widths in all four proxies, suggesting that they are tracking features of similar life-time. Note the anti-correlation present at a lag of around 12-14 days, which suggests an absence of active longitudes separated by [FORMULA] during the analyzed period.

[FIGURE] Fig. 1. Autocorrelation functions of the five investigated proxies for the year 1968 during the maximum of solar cycle 20. The shapes of the autocorrelation functions of [FORMULA], [FORMULA], [FORMULA] and [FORMULA] (a) look very similar and are dominated by the 27 day rotation of the Sun. The auto-correlation function of [FORMULA] (b) shows a completely different behavior, mainly because the visibility of white light faculae is restricted to locations near the solar limb.

In contrast, the auto-correlation function of [FORMULA] behaves rather differently (lower panel; see Brown & Evans 1980 and Foukal 1993 for more on [FORMULA]). Firstly, the central peak of the [FORMULA] autocorrelation is much narrower than of the other proxies (half width of  0.9 days versus  3-5 days), indicating that most faculae are detected only for a short time (1-2 days) near the limb (although the most prominent may well be followed over significant fractions of the disc). This is due to the limited visibility of white light faculae at the center of the solar disc and the influence of foreshortening near the limb. Secondly, the secondary maxima exhibited by the autocorrelation of [FORMULA] are lower than of the other proxies except [FORMULA]. Both the above facts, together with the expectation that faculae live just as long as, e.g., Ca plages, indicate that many faculae went undetected during at least one of their limb passages in the Greenwich record. This is easily possible due to their low contrast and fragmented morphology. The sum of the above features makes us give the Greenwich facular areas the lowest weight among the five considered proxies. We stress, however, that our conclusions are not affected by this choice.

Another comparison between the proxies is shown in Fig. 2, which shows a scatter-plot for cycle 18 of each of the other four facular proxies versus [FORMULA]. The proxies [FORMULA] and [FORMULA] depend non-linearly on [FORMULA], while [FORMULA] and [FORMULA] are linearly related. The quadratic terms of the fits through the [FORMULA] vs. [FORMULA] and [FORMULA] vs. [FORMULA] plots are significant at the 14 [FORMULA] level. Interestingly, total (i.e. disc integrated) Ca K core brightness varies linearly with [FORMULA]. Taken together with the non-linear relationship seen in Fig. 2 a this means that the relationship between Ca K full disk brightness and [FORMULA] is non-linear, with larger areas of plage having a greater brightness density.

[FIGURE] Fig. 2. Scatter-plots for cycle 18 of daily values of four potential facular proxies versus [FORMULA]. a Plage areas measured in the Ca II K-line. b Areas of white-light limb faculae. c Sunspot areas. d Full disk measurements of 10.7cm radio flux. The solid curves are quadratic (upper frames) and linear (lower frame) regressions.

We know little about the cycle-to-cycle variation of this non-linear relationship between [FORMULA] and Ca K brightness. Furthermore, the [FORMULA] record ends at an unfortunate time, with less than half a cycle's overlap with direct irradiance measurements. Finally, the Ca plage areas partly suffer from poor calibration, since many of the older photographic plates are uncalibrated although this may be largely countered by the relatively high contrast of Ca plage areas. These factors somewhat reduce the reliability or usefulness of [FORMULA], although we believe not to the level of [FORMULA]. Another point seen in Fig. 2 is that the scatter exhibited by [FORMULA] relative to [FORMULA] (or to the other proxies for that matter) is larger than of the other proxies. This also supports the low weight we have given [FORMULA].

The sunspot areas are well measured, but, again, the relationship between total facular brightness and spot area may itself show a cycle-to-cycle dependence. Also, on short scales [FORMULA] reproduces irradiance residuals less well than [FORMULA].

10.7cm flux is probably the best facular proxy of those considered, being free of subjectivity in the measurements and obtaining a large contribution from plages and the network (Tapping 1987), although sunspots also contribute significantly (Tapping & Harvey 1994). In addition, models that reconstruct solar irradiance using 10.7cm flux reproduce the observations made with the ACRIM instrument (Willson & Hudson, 1991) better than models using [FORMULA] or [FORMULA] as facular proxies (as mentioned above, [FORMULA] is not available for a sufficient length of time to test it against ACRIM as stringently). 10.7cm flux is only available for a relatively short period of time, however, which is not long enough to be of interest for climate studies. We therefore need to combine all the proxies to obtain a more reliable long-term record.

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© European Southern Observatory (ESO) 1998

Online publication: March 30, 1998