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Astron. Astrophys. 341, L43-L46 (1999)

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3. Discussion

Our main result is that the "magnetic equator" of the Sun displays a long term variation between north and south latitudes. The magnetic equator is defined by the average of the signed value of the latitude of each sunspot (positive for north, negative for south). From the data since 1853, the form of this variation appears to be well approximated by a sinusoidal curve with a period of about 90 years and an amplitude of 1.3 degrees. Since the average latitudinal distance from the equator of the main activity belts is around 15-17 degrees, this is a striking variation. Onto this long-term variation, is superimposed a highly irregular signal with an amplitude that can be over 10 times greater. Carbonell, Oliver & Ballester (1993) considered the signal of the asymmetry to have a dominant noisy component, a periodic (12.1 years) signal and a long-term trend. Our 90 year signal would correspond to this long-term trend. It is important to note that our measure of north-south asymmetry via latitudinal variation differs from the measure usually adopted, where the activity measures are totalled in each hemisphere separately and then compared. The usual index is [FORMULA] where N and S are the total activity counts in the northern and southern hemispheres. Such a measure loses all information about the latitudinal variation of the sunspots and, as far as we can tell, our result is novel in this aspect.

This result appears to confirm other evidence pointing to a 90 year cycle, such as variation in cycle length (Lassen & Friis-Christensen 1995). The variation in latitude can be explained as a mixed parity mode in which a quadrupolar component is oscillating with this period. The well-defined sinusoidal form of the time series curve would seem to indicate that the quadrupolar component is frequency-locked to the dominant dipolar mode in the manner described in Brooke et al. (1998). We can see this by examining the formulas used in the aforementioned work, for example a modified version of their formula (8)


Here b represents the toroidal component of the quadrupolar field and [FORMULA] represents the toroidal component of the dipolar field, the [FORMULA] notation indicating that this is considerably weaker. We use a matrix notation where the upper row represents the field in the northern hemisphere and the lower the field in the southern hemisphere at a given latitude. The period at which the components are locked is represented as [FORMULA], this would be several times longer than an individual solar cycle. If we postulate that the level of activity in the magnetic activity belts is a measure of the absolute value of the total toroidal field [FORMULA] (where [FORMULA] and [FORMULA] indicate the signed values of the quadrupolar and dipolar components of the toroidal field), then we see that [FORMULA] is larger in the northern hemisphere at time t and larger in the southern hemisphere at time [FORMULA]. If we multiplied [FORMULA] by the (signed) latitude representing the activity belt then this weighted average latitude would oscillate about zero. The above argument is of course schematic, for instance we have to add that the latitude at which the field values are given by (2) will be migrating with time. However it does indicate a possible mechanism to account for the variation in the "magnetic equator" as defined as the weighted average of the two activity belts. We are preparing a more extended version of this argument for subsequent publication.

A possible alternative explanation of the oscillations in the "magnetic equator" would be systematic errors in coordinate measuring, perhaps due to a precession of the Sun's magnetic field or rotational axis. Precession of the rotation axis can immediately be ruled out since such an effect would be immediately seen over one rotational period, by tracking a long-lived spot group. In addition, the Earth's precession period is 26,000 years and it is hardly conceivable that the Sun would precess
in 90 years. A precession of the Sun's magnetic axis about the rotational axis would be observed as a thickening of the activity belts due to rotation. Essentially the activity belts where the majority of spots are observed would be inclined to the equator, thus the spots would appear to be distributed over a wider range of latitude. The effects of precession would be, in effect, hidden by the Sun's rotation. Thus we consider the measurements correct and the effect genuine.

The latitudinal distribution of sunspots separately is also interesting. The mean latitude wanders higher up as the century proceeds. It is puzzling that the apparent correlation between high sunspot latitudes and active cycles is no longer valid at the less active cycles 20 to 22. It will be seen in the next decades whether the mean sunspot latitude will come lower following the descending solar activity, or another new "period" will be discovered. We note here that if the latitudinal distribution of the spots is different in each hemisphere, this provides an alternative mechanism for the effect in Fig. 2 to the arguments about weighted averages presented above, thus this is another important avenue of investigation.

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© European Southern Observatory (ESO) 1999

Online publication: December 4, 1998