4 Results and discussion

Most of the calculated periodograms have been obtained from radio observations (SVC and RRE time series calculated for seven different frequencies), but the ISN and MMF data were also analysed. The final periodograms obtained when all the main sinusoidal signals given in Tables 2 and 3 are subtracted from the original data are presented in Figs. 4-7. Careful examination of these periodograms shows that many periods having a formal significance level near 30% are seen in time series coming from different observational data. This fact allow us to suggest that even those periods could be real.

Taking into account all the information about the periods found obtained with the three different approaches to the data described in Sect.3, we prepare Table 4 for the minimum, and Table 5 for the rising phase, which bring together information about characteristic periodicities (lines) observed in these phases of the solar cycle 23 (we use the spectroscopic term "line" for the mean period calculated from the periods observed in various time series, which, as we suppose, represent the same characteristic periodicity). As two time series were created from the radio data at each frequency, we use two successive rows in the radio data columns to separate periods observed in SVC and RRE radio time series. The exact frequencies of the detected periods were found with a 1 nHz resolution in the vicinity of peaks seen in periodograms constructed from normalized power values on the grid of the independent frequencies appropriate to the given window. In all the figures, the points marked in the presented periodograms are situated in the places resulting from the grid of the independent frequencies, while the solid lines are drawn from the power values computed every 1 nHz. To discribe in some measure a "strength" of the line we introduced so called the importance number of the line. This number shows how large is support for this line from all the analysed time series. It is calculated according to the following rule. The each letter "a" in the line description columns (Cols. 12-14) gives for the importance number "5", the letter "b" gives "3" , and the letter "c" only "1". It is only one line with the importance number "5" in Tables 4 and 5. There are a few lines with a smaller importance number than "5" recognised in the analysed data, but we do not include them in Tables 4 and 5. However, it is important to notice that some of the lines included in Tables 4 and 5 can be unreal in a sense that they are created from periods which in fact belong to two different but neighboring lines. For such a case the calculated mean period is somewhere between the periods of these two neighboring, unknown lines. The probability of such a situation increses for lines having long periods and large values of $\Delta f$ (Col. 10, second row).

To aid in further discussion of the lines we have prepared Fig. 8, which shows all the lines present in Tables 4 and 5. The level of darkness in this 3D graph illustrate the importance number of the lines. A close look at Fig. 8 shows a clear difference among the 18 lines observed in the minimum and the 22 lines found in the rising phase of solar sunspot activity cycle. Although the 9 lines have almost the same periods in both the phases, the strength (measured indirectly by the importance number) of nearly all the 18 lines change, indicating that perhaps the physical mechanisms responsible for them also change with the solar phase. From Fig. 8 it is evident that the lines in the rising phase gather into three groups:

1.

Magnetic lines: all lines with periods shorter than 16 days. They have small importance numbers and were included on our list only because of very high peaks observed at these short periods in the MMF (mean magnetic field) time series. In the minimum, only one line (13 $.\!\!^{\rm d}$5) from this group is enough strong to be present in Fig. 8, but in the minimum MMF periodogram (see Fig. 6) some of them are easily seen;

2.

Rotational lines: all lines with periods inside the 25-34 days time interval of the Sun's rotation. The three lines from this group are visible in the minimum. The line 27 $.\!\!^{\rm d}$3 has the largest importance number and results probably from the rotation of such solar phenomena as new solar cycle sunspots as well as the long-lived coronal streamer structure observed during the 1996 minimum (Lewis et al. 1999). In the rising phase the period of this line shifts to 27 $.\!\!^{\rm d}$7. The next two lines 29 $.\!\!^{\rm d}$1 and 30 $.\!\!^{\rm d}$3 are stronger in the minimum than in the rising phase. This additionally supports the supposition that they are associated with some medium, and large scale magnetic structures (coronal neutral sheet, global neutral lines) which dominate in the minimum and then decline (Lantos et al. 1992; Lantos 1999). In the rising phase four new lines appear (25 $.\!\!^{\rm d}$2, 26 $.\!\!^{\rm d}$0, 26 $.\!\!^{\rm d}$8, 31 $.\!\!^{\rm d}$8). Three have periods shorter than those discussed above. One of them, having a period of 26 $.\!\!^{\rm d}$0, is the third dominant line of this phase. We suppose that this line is strongly connected with eruption of new active-region magnetic fields emerging within the complexes of activity "active longitudes" (Bumba & Howard 1969; Ruzmaikin 1998) and its period may be identified with a fundamental period of unknow Sun's clock which value is freqeuntly taken as equal to 25 $.\!\!^{\rm d}$5 or 25 $.\!\!^{\rm d}$8 (Bai & Sturrock 1993; Bai 1994);

3.

Activity lines: all lines with periods longer than 75 days. We propose this name as the strongest 151 days line in this group is thought to be related to the well known periodicity near l54 days seen mainly in the occurrence of high energy solar flares at the maximum of the solar sunspot activity. It is interesting to notice that this line is also observed in the minimum, but with a small importance number and only in the radio time series.

In the minimum, the distribution of the line periods in the investigated time window is much more uniform. There are 5 lines with periods shorter than 25 days but only one belongs to magnetic lines. Within an accuracy of $\pm0\hbox{$.\!\!^{\rm d}$ }3$ all of them were noted before in various time series (Hughes & Kesteven 1981; Pap et al. 1990). The lines with mean periods $13\hbox{$.\!\!^{\rm d}$ }6$ and $23\hbox{$.\!\!^{\rm d}$ }2$ are the most interesting. They belong to the group of 9 lines which are observed in both phases of the solar cycle investigated. Although in our data their importance numbers are not large, they were recognised as the dominant periods in the SMM/ACRIM total irradiance data for the years 1980-1988 (see Pap et al. 1990). A very intriguing group of lines is formed by 4 lines (39, 43, 48, 58 days) also observed in the minimum. All these lines are seen only in the time series which were obtained from the radio data, except for one with period 58 days also observed in the ISN data. Among them only the line at 39 days is also present in the rising phase, although a small shift of its period is visible. Coming to longer periods we see that most of them are present in both investigated phase of the solar cycle. However, in the rising phase we observed more lines and all of them are stronger than those in the minimum. In the minimum, the strongest line in this group has period 75 days. However, in the rising phase this line is more weaker. It is not clear if it should be correlated with periods 73-78 days observed by some authors (Bai & Sturrock 1991; Bai 1992a; Özgüç & Ataç 1994) mainly in flare activity during the maximum of a solar cycle. We suppose that this line could be important if it is a real harmonic of the best known line with period near 154 days. It is important to notice that all of them were mentioned before in various analyses (Lean & Brueckner 1989; Pap et al. 1990; Bai & Sturrock 1991; Kile & Cliver 1991; Antalová 1999).

Many previous studies by a number of authors have resulted in a wide range of solar periodicities, which are not easy to explain. This indicates that the problem of solar periodicities is still open and more systematic efforts should be undertaken. Here, we do not want to discuss all possible causes of the observed periods, but we want to present a suggestion which may be of help in further investigations.

Recently Oliver et al. (1998) proposed that the periodic emergence of magnetic flux, manifested as sunspots, triggers the near 158 day periodicity in high-energy solar flares. As different magnetic features have different rates of rotation (Gilman 1974; van Tend & Zwaan 1976; Erofeev 1999) we think that a periodic emergence and a constant conversion of various magnetic structures explain the origin of the observed lines and their transformation with the phase of solar cycle 23. The main arguments supporting this idea are as follows:

1.

There is a clear difference between the lines obtained in the minimum and in the rising phase. The lines characterictic for the minimum are probaly connected with both the short-lived small-scale magnetic fields which originate fairly high in the convective zone (Golub et al. 1981; Rivin 1999) and large-scale fields structures like coronal holes, coronal neutral sheet, global neutral lines. All these small and large scale magnetic fields dominate in the minimum phase of solar cycle (Golub et al. 1981; Wang et al. 1996; Lantos 1999);

2.

In the rising phase a new distinct rotational line at 26.0 days is seen. This period is equal to the rotation rate of the active longitudes (zones) at 30$^\circ$ (where the new flux appeared) determined from SOHO/MDI magnetograms by Benevolenskaya et al. (1999). They found in the northeren hemisphere the rotation rate 446.6 $\pm$ 1.7 nHz and 444.8 $\pm$ 1.6 nHz in the southern one, while our value for the whole Sun data is 444.4 $\pm$ 4 nHz. Also the rotation rate of the equatorial zons equal 461.8 nHz from SOHO observations is almost the same as the period 25 $.\!\!^{\rm d}$2 (459.5 nHz) seen in our radio data (see Table 5);

3.

The line at 151 days is in the rising phase very prominent. This period is connected by Bogart (1982), Bai (1987) and Oliver et al. (1998) with strong, long-lived active regions giving most of the energetic solar events. This regions are generated by the emergence within the "active longitudes" magnetic tubes formed in the dynamo located at the base of the convection zone (Golub et al. 1981; Benevolenskaya et al. 1999; Rivin 1999). We also observe in the rising phase ISN periodogram periods such as 13 $.\!\!^{\rm d}$1or 23 $.\!\!^{\rm d}$8, which were linked with the "active longitudes" and active centers in deep layers by Bai (1987).