Cluster analysis of the space-time distribution of sunspot groups during solar cycle no. 20

Cluster analysis (a Bayesian iteration procedure) was used to study the space-time distribution of sunspot groups in the time interval from 1965 to 1977. (Data were taken from the Greenwich and Debrecen Heliographic Results.) The distribution proved to be significantly non-random for the 8–10 groups cluster^–1 (gr cl^–1) level of clustering. Convincing evidence also favours non-random behaviour for other levels of clustering from the lowest (3–4 gr cl^–1) up to the highest ( 150 gr cl^–1) level. The rotation rate of the non-random pattern is generally slightly lower than the Carrington rate.The 8–10 gr cl^–1 level, crudely corresponding to the sunspot nests investigated earlier, was studied in more detail. The cycle- and latitude-averaged rotational rate of the nests is slightly ( 1%) but significantly lower than the Carrington rate. Their differential rotation is strongly reduced: the cycle-averaged rotational rate varies only by 2–3% within the sunspot belt. A slight but significant bimodality is seen in the differential rotation curve: the intermediate latitudes ( 10°–20°) show a somewhat slower rotation than both the equatorial and the higher latitude regions. This might be explained by a time-dependence of the rotation rate coupled with the butterfly diagram.     

DEPENDENCE OF ROTATION VELOCITY OF INDIVIDUAL SUNSPOTS ON THEIR LIFETIME

By using a large number (452) of individual sunspots or individual sunspots with small spots around them, taken from the Greenwich Photoheliographic Results (GPR) for the years 1964–1976 that cover solar cycle No. 20, it is shown that the rotation velocity of the sunspots varies with their lifetimes. This investigation indicates that at the equator, the rotation rate for the last three days (of the lifetime) is about 1.3% slower than that over the whole lifetime and about 0.5% slower than during the first three days, but this is reversed at high and low latitudes, and the difference is much larger in the northern hemisphere than in the southern hemisphere. These results confirm to the fact that the rotation rate of the solar layers increases with depth.