5 Discussion

Bogart (1982) investigated autcorrelation functions of daily Sunspot Numbers for the period 1850-1977, obtaining a distinct period at 27 days. Since the persistence of this periodicity lasted for about 8-12 solar rotations, which is distinctly longer than the lifetimes of sunspots, Bogart (1982) concluded that this outcome provides evidence for the existence of "active longitudes" on the Sun. The idea that solar activity phenomena (sunspots, flares, etc.) are not uniformly distributed in longitude but preferentially occur at certain longitude intervals was already suspected by Carrington (1863), and has been systematically studied since the 1960s (e.g., Trotter & Billings 1962; Warwick 1965; Bumba & Howard 1965). In later studies it became clear that these "active longitudes" usually do not extend over both hemispheres, and the terms "active zones" and "complexes of activity" are often used instead.

In the present analysis, studying the period 1975-2000, we obtained a similar outcome for the autocorrelation function of the daily Sunspot Numbers as Bogart (1982). On the other hand, the supplementary analysis of the hemispheric Sunspot Numbers reveals that the persistent 27 day period occurs only for the northern hemisphere. The autocorrelation function of the southern Sunspot Numbers is strongly attenuated after 3 periods, which matches with the lifetimes of long-lived sunspot groups. The autocorrelation function derived from the northern Sunspot Numbers shows a stable periodicity up to 15 periods. This outcome provides strong evidence that during the considered period a preferred zone of activity was present at the northern hemisphere rigidly rotating with 27 days, whereas the behavior of the southern hemisphere is mainly dominated by individual long-lived sunspot groups, which are not (or only weakly) grouped at preferred longitude intervals.

Bai (1987) studied the occurrence of major solar flares during 1980-1985, and found evidence for a very prominent active zone in the northern hemisphere, in which almost half of the flares of the northern hemisphere took place (see his Fig. 3), and a second (but weaker) one separated by $\sim$180$^\circ$. In the periodograms, we find a highly significant peak at $\sim$13.3 days, which gives indication for a second active zone $180^\circ$ apart. Such a peak was noticed too, e.g., by Bogart (1982). Bai (1987) reports also evidence for two active zones in the southern hemisphere, but with a distinctly less pronounced activity than the major northern active zone. In the present study we do not find evidence for an active zone in the southern hemisphere. A possible explanation is that the hemispheric Sunspot Numbers, which represent a quantity averaged over a whole hemisphere, are less sensitive to the detection of active zones than the binning of solar activity phenomena in longitude intervals, as done by Bai (1987).

The 27 day Bartels rotation is a very prominent period with respect to the occurrence of geomagnetic disturbances, and it is supposed to be relevant for the large scale solar magnetic fields (e.g. Balthasar & Schüssler 1984). From the distribution of daily Sunspot Numbers and sunspot groups in the Bartels rotation of 27 days, Balthasar & Schüssler (1983, 1984) inferred evidence for preferred Bartels longitudes of activity, which may even cover a whole hemisphere. These preferred hemispheres were found to alternate with the 22 year magnetic cycle. The present data set (1975-2000) is too short to draw any conclusion with respect to the 22 year magnetic cycle. However, it is worth noting that during the considered period the total activity is higher in the southern hemisphere (see Fig. 5), but the northern hemisphere shows a distinctly more systematic behavior in the rotational recurrence of activity (see Fig. 8), very probably dominated by one or two preferred active zones. For solar cycle 21, a cyclic behavior of the N-S asymmetry with a phase shift between both hemispheres can be inferred from the cumulative Sunspot Numbers (Fig. 5) as well as directly from Fig. 3, whereas no cyclic behavior is indicated for solar cycle 22. Nevertheless, a cyclic behavior in the N-S asymmetry of solar activity for the last 8 solar cycles was recently reported by Vernova et al. (2002), using the so-called "vectorial sunspot area", which more strongly emphasizes the systematic, longitudinally asymmetric sunspot activity compared to the stochastic, longitudinally evenly distributed component than the normal sunspot areas and Sunspot Numbers.

The study of N-S asymmetries of solar activity and the analysis of the rotational behavior separately for the northern and southern hemisphere is particularly relevant, as it is related to the solar dynamo and the generation of magnetic fields. Antonucci et al. (1990) investigated the rotation of photospheric magnetic fields during solar cycle 21, and obtained a dominant period of 26.9 days for the northern and 28.1 days for the southern hemisphere. The spectral power was concentrated in a few well-defined regions with a rather wide extent in latitude. On average, these regions were found to lie near the sunspot differential curve, but the latitudinal extent was not consistent with the standard differential curve. From these findings, Antonucci et al. (1990) concluded that the emergence of photospheric magnetic field tracers is organized in a large-scale pattern with different rotation periods in both hemispheres.

The rotation rates for the magnetic fields of the northern and southern hemisphere reported by Antonucci et al. (1990) coincide well with the present study of hemispheric Sunspot Numbers, in which we found an enhanced PSD at $\sim$27 days with a rigid rotation for the northern hemisphere, and $\sim$28 days for the southern hemisphere. Thus, a strong correlation of the underlying large-scale magnetic fields and the rotation of sunspots is suggested. It has to be noted that Nesme-Ribes et al. (1993), who analyzed sunspots observed on spectroheliograms during solar cycle 21, came to an opposite conclusion, since the 28 days period in the southern hemisphere could not be reproduced. In this regard, it has to be stressed that the rotational behavior of the solar surface is sensitive to various factors, such as, for instance the used tracers (e.g., old versus young sunspots) as well as the phase of the solar cycle (e.g., Balthasar et al. 1986; Nesme-Ribes et al. 1993; Pulkkinen & Tuominen 1998, and references therein).

The existence of significant N-S asymmetries in the occurrence of solar activity and in the rotational behavior provides strong evidence that the magnetic field systems originating in the two hemispheres are only weakly coupled (see also Antonucci et al. 1990). Another feature that gives indications for a weak coupling of the hemispheric activities and the related magnetic field evolution within the course of a solar cycle is the double-peaked cycle maximum known since Gnevyshev (1963), which is supposed to be related to the solar magnetic field reversal (e.g., Feminella & Storini 1997; Bazilevskaya et al. 2000, and references therein). From Fig. 4 it can be seen that the Gnevyshev gap is more pronounced by considering the northern and southern Sunspot Numbers (or sunspot areas) separately and it does not necessarily take place at the same time and with the same strength in both hemispheres.

In principle, studies of the N-S asymmetry of solar activity provide constraints on solar dynamo theories. In addition to the 11 year sunspot cycle, the 22 year magnetic cycle, the presence of grand sunspot minima, the butterfly diagram and phase-amplitude correlations, a reliable dynamo theory should be able to explain the weak coupling between the hemispheres and the existence of significant N-S asymmetries in the occurrence of solar activity as well as in the rotational behavior. Ossendrijver et al. (1996) have shown that a mean field dynamo model with stochastic fluctuations of $\alpha$ can reproduce observed N-S asymmetries in solar activity. A probable candidate for the origin of these stochastic fluctuations are giant convective cells that extend sufficiently deep into the convection zone (Ossendrijver et al. 1996). The existence of giant cells was first suggested by Bumba & Howard (1965), but their subsequent history was quite controversial (see Hathaway et al. 2000). Recently, Beck et al. (1998) reported evidence for long-lived giant velocity cells on the solar surface that extend 40-50$^\circ$ in longitude but less than $10^{\circ}$ in latitude. The magnetic fields of solar activity are generated at the bottom of the convection zone, and long-lived cells connected to this layer could explain the persistence of solar activity at the same location (Beck et al. 1998). Thus, giant convective cells possibly provide the physical link between the solar interior and active zones at the solar surface, whose existence has been established for various solar activity phenomena and for various solar cycles. To account for the observational effects, these active zones must not be significantly disrupted by differential rotation up to several years. On the other hand, as suggested by Balthasar & Schüssler (1983), the rigid 27 days rotation does not necessarily represent any material motion but may result from the phase velocity of a dynamo-produced large-scale solar magnetic structure.