The short-term periodicities of the flare index (FI) which is roughly proportional to thetotal energy emitted by the flare, are investigated in detail using Fourier transform (FT)
for the full-disc and for the northern and the southern hemispheres of the Sun separatelyover the epoch of almost 4 cycles (1966-2002) which covers 13392 days. Figure 1 shows the power spectra of the three time series of FI calculated for the 289-771 nHz (15-40 days)range with 0.24 nHz interval. The uncertainty in each frequency is +- 0.4 nHz due to the 36.5-year data length. The dashed lines indicate the false alarm probability significancelevels. In this figure, there are several pronounced power peaks whose significances are enough high. These are at 25.6, 27.0, 30.2 days for the full-disc, 27.0 days for the northernhemisphere and 27.5 and 33.8 days for the southern hemisphere. Since commonly used FT is not able to disclose the possible changes in the periodicities over the period studied,the wavelet transform (WT) was applied to search for temporal variability. The wavelet transform results show that the occurence of periodicities of flare index power is highlyintermittent in time. All three FI time series show that the major periods, obtained by Fourier transform are localised in short time intervals (typically up to half of a year).A comparison of the results of the FT and the time-period WT of the flare index time series has clarified the importance of different periodicities, whether they are or are notthe harmonics of the basic ones, as well as the temporal location of their occurrence. Because we found that the modulation of the flare index due to the 27-day solar rotationis more pronounced during the declining portion of solar cycle than during the rising portion. Our results show that 27-day modulation seems 27.5-day in the southern hemi-sphere of the Sun. There is a possibility that some parts of an active region move rapidly forward or backward with respect to the mean rotation rate of the Sun, to give spacingsdifferent from 27 days. This can be checked only by an actual image comparison.
The fundamental period proposed by Bai and Sturrock (1991) was reported as 25.5-day. In our analysis, we found this value as 25.6 days. This periodicity operates mainly during maximum phases of solar cycles only short time intervals. However, Zi,eba et al.(2001) found the rotation rate of the "active longitudes" in the rising phase of cycle 23 as equal to 26.0+-0.3 days. Recently, Bai (2003) studied longitude distributions of majorflares in a coordinate system rotating about the solar axis, using the rotation period as a free parameter. And he concluded that, the idea of 25.5 days is a fundamental period ofthe Sun is well supported by data. However, its clock mechanism is still unknown. The differences between the results of the different authors can be explain that because ofthe non-sinusoidal nature of the variation of some activities (e.g., square waveform shape
of an X-ray source), a broad fundamental frequency will appear in the power spectra(Bouwer, Pap, and Donnelly, 1990).
To conclude that the problem of solar periodicities is still open and needs new obser-vational data. Therefore, the solution of the observed solar periodicities should be sought in a complicated Sun's magnetic system which generates in the different solar data thecompound set of solar periodicities.