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Astron. Astrophys. 328, 670-681 (1997)

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3. Monthly sunspot group data

Our data set refers to the sunspot group time-series reconstructed by Hoyt et al. (1994). Details on the reconstruction, the comparison between different observers, the comparison between the Wolf sunspot number can be found in Hoyt and Schatten (1992 a,b) and Hoyt et al. (1994). Let us stress the advantage of using sunspot groups rather than the Wolf number.

A sunspot group has a physical meaning: it is the manifestation of an east-west magnet produced by the stretching of a initial poloidal north-south field under the effect of non uniform solar rotation. In the simplest case, a single magnet appears at a given place, with two sunspots being the poles of the magnets. The Wolf number is defined as ten times the number of sunspot groups plus the number of individual sunspots, with a correction factor depending on the observer. This was done by Wolf in order to smooth out fluctuations. It is evident that the activity index established by Wolf is more empirical.

The time-series he reconstructed is not homogeneous: he used compilations of magnetic aurorae to fill up certain observational gaps. In our case, we used only direct solar observations and we included all 17th century data (Hoyt et al. 1994). Some observational gaps still exist, especially in the mid 18th century. However, our time-series is more complete and homogeneous than Wolf's reconstruction. One may argue that a bias will arise in the time-series due to the improvment of the telescopes since Galilei's time. It has been shown that the bias, if any, would be small and would not change the counts significantly (Ribes and Nesme-Ribes, 1993). By extending the time-series back to the Maunder minimum, we have included the only currently available example of a grand minimum in solar activity. Certain properties of the Maunder minimum have already been discussed by Nesme-Ribes et al. (1994), in terms of the north-south asymmetry of sunspot group number and sunspot rotation. These authors surmised that the onset of the Maunder minimum was fairly rapid. The updated time-series displayed in Fig. 2 clearly shows that the beginning of the Maunder minimum was indeed very abrupt.

[FIGURE] Fig. 2. Monthly mean number of sunspot groups (1610 - 1994).

Maunder minimum-type events have also been observed in stellar activity by Soon et al. (1994). For those stars entering the Maunder minimum phase, the activity decline is sharp (a transition time comparable with one period of activity). However, stellar information is obviously much noisier than solar data. For example, the contrast between a normal solar activity cycle and the Maunder minimum is about [FORMULA] to [FORMULA]. Such a large contrast could hardly be observed by the stellar magnetic index. Therefore, it is not always clear to what extent one can identify stellar quiet episodes with the solar Maunder minimum. Stellar Maunder minimum-type events should be rather compared with the Dalton minimum observed on the Sun at the end of the 18th century.

The choice of the time-averaging interval is also a relevant question. The lifetime of each sunspot varies from a few hours up to a full solar rotation. The leading sunspot (which appears first on the east limb) is of longer duration than the following one. So a 1-month averaging corresponds to the average lifetime of a sunspot group.

There are a certain number of gaps in the available monthly sunspot group record prior to the 19th century. Assuming that the lack of sunspot groups over this period was due to a lack of observations, we interpolated to fill these gaps: if isolated months without observations are preceded and followed by months with observations, we apply a linear best fit over four months apart and prescribe the corresponding value to the month without observations. If there is only one month with observation in the center of the gap, we extend the interpolation fit to the next three monthly data. We interpolate gaps of greater than one year with a linear best fit based on eight months of data. In the interpolation process we go from short gaps to longer, basing longer-range interpolations on the shorter.

The longest data gap is about 2.5 years, around 1750, i.e. a period of normal solar activity. This gap is 4.4 times shorter than the main period of solar activity. As similar long-lasting observational gaps are relatively isolated, we believe that our interpolation method does not lead to drastic artificial changes in the data set.

The results of our interpolation are shown in Fig. 3a and informations on time intervals of interpolation and durations are shown in Fig. 3b. Although some uncertainties due to inhomogeneous historical records and observing techniques, the accuracy of the time-series is quite high. It has been shown by Ribes and Nesme-Ribes (1993) that the Maunder minimum was thoroughly observed by Picard and coworkers. So the rapid onset of the Maunder minimum (Figs. 2 and 3a) is likely to be a real phenomenon.

[FIGURE] Fig. 3. Interpolated monthly mean number of sunspot groups (1610 - 1994); a interpolated data, b indicator of gaps in data - small negative values correspond to gaps less then 1 year, large ones correspond to gaps longer then 1 year, c one example of a statistical noise time-series produced by a generator of white noise using the real dispersion of data
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© European Southern Observatory (ESO) 1997

Online publication: March 26, 1998