2. Data and results
We use the sunspot data over the whole range of modern observations, starting from Carrington's (1853-1861) and Spörer's (1861-1894) data. To extend this record to the present day (i.e. 1874-1996), the data from the Greenwich Photoheliographic Results and the Solar Optical Observing Network have been combined 1. These data sets cover completely sunspot cycles 10 to 22 of which cycles 10 and 11 are taken from Carrington/Spörer data and cycles 12 to 22 from the Greenwich data. These long-term data have been used to analyse solar photospheric velocities by Pulkkinen & Tuominen (1998) where the data are also introduced in more detail.
An important feature connected with activity variations between cycles is the mean latitude of sunspots, taken as spatial averages over whole hemispheres or narrower latitude bands, and temporal averages over a cycle or shorter time range (n days). In practice, the shortest time range is about 10 days since sunspots are not always observed simultaneously at both hemispheres. The distribution over cycles 10 to 22 is given in Table 1. The latitude band with highest sunspot number is typically 10-15 degrees away from the equator, but the average latitude varies quite significantly as can be seen also in Fig. 1 where the cyclic averages have been computed from the whole hemispheric data. The rising activity during the first 60 years (cycles 14 to 19) of the 20th century is seen as higher latitudes of sunspots. Error bars (calculated as the mean error of the mean) being so small, the effect is rather strong and systematic, especially in the north. But the correlation between active cycles and high sunspot latitudes is not complete-the total cycle activity increased from cycle 12 to cycle 19 and then rapidly went down. For sunspot latitudes, they went higher up between cycles 14 and 22, as if there were a phase shift.
Table 1. The relative number of sunspot measurements at different latitude bands (given in degrees) and cycles. The sum of each column is 100. In the last row the beginning year of each cycle is written
As the mean latitude of sunspots, or the whole sunspot belt, is varying between cycles and hemispheres, their relative distance from the equator is changing too. This can be seen, when we calculate the latitude of the "magnetic equator" defined by sunspot latitudes. This is the sum ( is negative) of mean latitudes . An interesting pattern is seen in Fig. 2 where this sum is plotted as 10-day averages. In symmetric case this sum should be zero, but this band, although wide, is clearly moving up and down rather systematically. If this is fitted to a sinusoidal profile (solid line in Fig. 2), we get
where time t is measured in days, being Nov 8, 1853, the first measurement by Carrington. The period of this variation days, and the amplitude degrees. Fig. 3 shows the same as Fig. 2 but with 11 point smoothed average. The alternating pattern is even clearer, only with few outlying measurements denoting gaps between two sunspot cycles.
If we repeat the above procedure with yearly averages, the sinusoidal variation of Fig. 2 still appears to be present (Fig. 4). Here the error bars are simply sums of errors of and separately, so they may be exaggerated. Of course, we may compute the trigonometric fit, and then and . Here, days and the amplitude is degrees.
If we consider the error ranges for the coefficients over 10-day or yearly averages, we see that the two curves are compatible. Thus the sinusoidal form of the curve appears to be robust to the form of averaging employed.
© European Southern Observatory (ESO) 1999
Online publication: December 4, 1998