Astron. Astrophys. 335, L97-L100 (1998)

3. Analysis

We analyse the temporal and spatial variations of the velocity and magnetogram signals throughout the active region, but concentrate here on selected positions, such as the sunspot umbrae which show significant oscillations of the magnetogram signal.

In the temporally averaged magnetogram, we define regions that have a magnetogram signal above a certain threshold. Then, the magnetic (or velocity) signal is averaged at each time step over the chosen region. The averaging is done in order to increase the signal-to-noise ratio. Fig. 2 shows the temporal variation of such averaged signals for the leading spot with a threshold level of  G. All these points lie within the umbra. Oscillations are clearly present in velocity and seem likely in the magnetogram signal, although the noise is larger. The two curves differ in phase by .

Fig. 2. Magnetogram and velocity signals as a function of time. The signal shown here corresponds to the average of the points having a magnetogram signal larger than 1800 G in the spot to the right in Fig. 1 (leading spot).

Next, power spectra of these spatially averaged regions are computed. Before computing the power spectrum of any pixel or region, we remove the long-term evolution by subtracting a 3rd order polynomial fit to the considered time series. Fig. 3 shows examples of power spectra. The plots to the left display the power spectra obtained in the biggest umbra of the following spot. There the signal was averaged over all pixels for which the time-averaged magnetogram signal was smaller than -1600 G. The plots to the right correspond to the umbra of the leading spot using a contour level of 1800 G. (Note that these contour levels do not correspond to the brightness contours drawn in Fig. 1. The extremal values of the magnetogram signal amount to -1730 G in the following sunspot and 1960 G in the leading sunspot.) The horizontal lines correspond to the 99% confidence levels determined according to Groth (1975).

Fig. 3. Power spectra of the magnetogram signal (upper panels) and Doppler shift (lower panels) for the two largest umbrae of the region. The dashed lines represent the 99% confidence levels. In the lower right panel this level is so low that it cannot be distinguished from the zero line.

The 5 minute (3.2 mHz) oscillations appear clearly in the velocity power spectra of both spots, but only in the power spectrum of the magnetogram signal of the leading spot. For the following spot the magnetic peak lies at 5.9 mHz.

It appears that the oscillations seen in the magnetogram strongly favor those positions that show the strongest magnetogram signal, but which need not correspond to the darkest region of the sunspot (although there is a certain, incomplete overlap between the two). The magnetic power in the rest of the sunspot is much lower though not completely absent (see below).

We have also averaged over other regions. For example, we find that no significant oscillations of the magnetogram signal are detected when the averaging is carried out over the darkest parts of the umbra. This does not necessarily mean that no magnetogram oscillations are present, but rather that they cannot be coherent over that region.

Fig. 4 shows the power of the magnetogram signal oscillations at 3.2 mHz (upper frame) and 5.9 mHz (lower frame). Here the signal has been spatially smoothed over pixels before computing the power spectra in order to reduce the noise. The purpose of this figure is to show that these oscillations are not cospatial and that the sites of strong power are very localised. If a slit is placed randomly through an umbra, then it can easily miss the magnetic oscillations sites. This may explain why Lites et al. (1998) saw no such oscillations. The phase shifts observed between the magnetogram and velocity signals in the regions of strong power in Fig. 4a typically range between and .

Fig. 4. Map of the power in the oscillations of the magnetogram signal at two different frequencies: 3.2 mHz (top) and 5.9 mHz (bottom).

The following sunspot is composed of different umbrae. Three of these have regions with magnetic field strength lower than -1600 G. It appears that the velocity and magnetogram signals of these 3 umbral regions are not oscillating in phase. Furthermore, the magnetogram signal oscillation frequencies of the different umbrae are not the same: the 5.9 mHz oscillation is seen only in the largest umbra.

© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998
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