In this chapter, we have presented the study of long period oscillations in two parts. In the first part, we analysed three eight-hour datasets of the microwave emission generated over three different sunspots, recorded with the Nobeyama Radiohelio- graph at 17 GHz. The main findings of this part are as follows:
1. Significant long period (P ≈16-88 min) oscillatory components are present in the time signals of all three analysed sunspots.
2. In each of the spectra of the sunspots, there are at least two such components. In general, these components are found to have higher power than the three minute oscillations. The periodicities are: AR10105: P1 = 57±12 min,
Figure 3.18: Top panel: final G-band time series after detrending. Bottom panel: Scargle periodogram computed from the final signal. The dashed horizontal line indicates the 99% significance level.
Figure 3.19: Top panel: final Ca II H time series after detrending. Bottom panel: Scargle periodogram computed from the final signal.
Figure 3.20: Top panel: final NoRH time series after detrending. Middle panel: Scargle periodogram computed from the final signal. Bottom panel: Morlet wavelet power spectrum computed from the final signal.
P2 = 31±6 min; AR10330: P1 = 88−+1621 min, P2 = 37+8−11 min; AR10673: P1 = 27±16 min,P2 = 16±4 min.
3. The periodicities stay constant during the observing intervals, without any significant drift.
4. The spatial distribution of the oscillations shows, in general, (for both fre- quency ranges of AR10330 (∆f1= 0.292-0.833 mHz, ∆f2 = 0.133-0.292 mHz) and for frequency range ∆f2 = 0.206-0.417 mHz of AR10105) regions of en- hanced power in the umbral regions.
Figure 3.21: Top row: the period (left) and amplitude (right) maps for AR10923 from the G-band data, after filtering to keep frequencies in the range ∆f = 0.107- 0.237 mHz. Frequencies in the periodmap have been normalised to the maximum value in the map and amplitudes are displayed on a logarithmic scale. Bottom row: the correlation (left) and lag (right) maps. Lags have been normalised toP = 45.5 min.
Figure 3.22: Top row: the period (left) and amplitude (right) maps for AR10923 from the Ca II H data, after filtering to keep frequencies in the range ∆f = 0.133- 0.256 mHz. Frequencies in the periodmap have been normalised to the maximum value in the map and amplitudes are displayed on a logarithmic scale. Bottom row: the correlation (left) and lag (right) maps. Lags have been normalised to P = 40 min.
Figure 3.23: The first image in the G-band datacube showing the regions of quiet Sun studied to test for the artificial nature of the periodicity. The solar limb is towards the left of the image.
5. There are regions of the sunspots that coherently oscillate both in phase and in anti-phase with the chosen master pixel. The typical size of the coherently oscillating regions is about 25 pixels. For frequency ranges ∆f1 = 0.417-0.833 mHz of AR10105 and ∆f2 of AR10330, there are two regions of almost equal size that oscillate in anti-phase with each other. For frequency range ∆f2 of AR10105, a region of in-phase oscillation (with the master pixel) is found in the centre of the sunspot and is surrounded by regions oscillating in anti-phase. A sharp spatial transition between the different regions of coherent oscillation is seen in all cases.
In the second part, we attempted the study of the oscillations in a single sunspot, but made use of optical observations (in Ca II H and G-band, using Hinode/SOT) as well as microwave data. The periods found were as follows: Ca II H: 80.21+21−7 min; G-band: 91.27+23−10min and microwave: 128+26−21 min. Above, shorter periods (in the rangeP ≈16-60 min) were observed with NoRH and the periodogram generated from the Ca II signal shows the possible presence of peaks around 40 and 60 min. Wavelet analysis for the microwave data again revealed the presence of the oscillation throughout the observation period. The lack of significant spectral peaks close to these periodicities in quiet Sun regions in the optical wavelengths may suggest that
Figure 3.24: Top two rows: the time series from the quiet Sun regions (G-band). Bottom two rows: the Scargle periodograms for the time series in the top two rows. The dashed lines show the 99% significance levels and the red lines mark the 91 min period that was found in the sunspot signal.
Figure 3.25: Top two rows: the time series from the quiet Sun regions (Ca II H). Bottom two rows: the Scargle periodograms for the time series in the top two rows. The dashed lines show the 99% significance levels and the red lines mark the 80 min period that was found in the sunspot signal.
the oscillations are not artificial.
The nature of the detected long period oscillations in sunspots is still not re- vealed. In the following, we discuss possible options. The observed periodicities are close to the periods of candidate spectral peaks associated with g-modes: e.g. 22-26 min and about 75 min (Garc´ıa et al. 2008) and the sunspot magnetic flux tubes can operate as waveguides, channelling signals of g-modes from deeper regions. This is just a hypothesis, as flux tubes are known to act as waveguides (see, e.g.Nakariakov & Verwichte 2005). Thus, one possible interpretation of the observed periodicities is their association with the leakage of g-modes, but this scenario requires a solid theoretical foundation. Also, the observed anti-phase oscillations in different parts of the sunspots do not seem to support this interpretation.
The observed patterns of fluctuations are also consistent with the shallow sunspot model ofSolov’ev & Kirichek(2008). In this model a cylindrical magnetic flux tube has a finite depth of L ∼ 3 Mm below the solar surface, where it termi- nates. The flow around the structure and close to its boundary is mainly vertically downwards for depths smaller than L, and becomes a mostly horizontal flow below the depthL (Zhao et al. 2001). For such a configuration, radially structured fluc- tuations (that is fluctuations with a certain azimuthal symmetry) could be excited at the bottom of the flux tube and propagate vertically to generate patterns, such as these observed in figure3.10. It has been shown, using the variational principle, that the periods of such oscillations vary from 40-200 minutes (Solov’ev & Kirichek 2008), in agreement with periods detected in this work.