7 Observational results

We first present results from the sunspot in active region 8951 as observed on 14 April 2000. In Fig. 7, using an MDI intensity-gram image, we show an enlarged region around the sunspot together with an overlay of a portion of the slit from the temporal series dataset s19932r00 showing its location at the beginning and end times of the observation. The MDI intensity-gram used was obtained from the file fd_-Ic_-01h.63844.0048.fits. The MDI intensity-gram observations were performed at 04:47:33, the same time approximately as the start time of the CDS temporal series observations of dataset s19332r00. In Fig. 8 we show CDS intensity rasters of size $60 \times 240$ arcsec² for different temperature lines along with a (low resolution) Kitt peak magnetogram. The CDS rasters were obtained from dataset s19331r00, with a starting time of 04:25 on the 14 April 2000. The low resolution Kitt Peak magnetogram (resolution $\sim$4 arcsec) with a start-time of 14:26:31 on the same day was thus obtained about 10 hours after the CDS observations. The thin rectangles over-plotted on these images show the location of the slit (for the s19332r00 dataset) at the beginning (the right one) and end of the temporal sequence (the left one). Pixel 67 is marked as a black box in all the images. The CDS rasters shown are the square-root images (i.e. the square root of the intensities has been taken to reduce the contrast between the most bright and dark values). A comparison of the raster images and the magnetogram clearly reveals that all the intensity enhancements are closely related with concentrated magnetic field regions.

The contours for the umbra and penumbra (in Figs. 7, 8) are plotted using the average value for the whole MDI intensity-gram as a guide. The penumbra is defined as the parts of the MDI intensity where the intensity falls below a factor of 1.5 that of the average, i.e. it is the average/1.5. The outer contour around the sunspot shows the contour of the average value, while the inner contour shows the contour of the average/1.5 values. The umbra is then defined as anything that is contained within this average/1.5 contour.

Figure 10: Wavelet results corresponding to the He  I 584 Å line in the s19332r00 dataset at pixel 67. Panels  a) and  b) represent intensity and velocity results respectively. The middle row left panels show the time frequency phase plot corresponding to the variations shown in the top panels. The middle row right hand panels show the average of the wavelet power spectrum over time, i.e. the global wavelet spectrum. The continuous dashed horizontal lines in the wavelet spectra indicate the lower cut off frequency. The lowest panels show the variation of the probability with time from the randomization test, with the dot-dash line indicating the 95% significance level.

Figure 11: Wavelet results corresponding to the O  V 629 Å line in the s19332r00 dataset at pixel 67. Representations are same as Fig. 10.

In order to show the spatial variation of the observed oscillation frequencies across the sunspot region we select the strongest line, i.e. O  V 629 Å. In Fig. 9 we plot the variation of the frequencies over a section of the observing slit. This section includes the umbra, penumbra and the adjacent regions. The top panel shows a contrast enhanced intensity map (X-T slice), obtained by removing the low frequency trend of the oscillations for each of the positions along the slit. The lower two left panels show the measured frequencies as a function of position along the slit (X-F slice) for velocity and intensity respectively. The crosses correspond to the primary maxima in the global wavelet spectra. The total number of counts in a pixel (summed counts) during the observation is shown in the right columns and is useful in identifying the location of the umbra of the sunspot. Note that pixel 67 is the brightest pixel across our slit (see right panel of Fig. 9). This pixel may correspond to a plume region. According to Maltby et al. (1999), locations that show $I > 5 \bar{I}$, where $\bar{I}$ is the average intensity in the sunspot area being investigated, can be considered as plumes in the sunspot umbra, if they also coincide with the location of an umbral region seen in, for example, a MDI intensity-gram. In the X-T slice, for portions of the image, roughly from 50-60 and then between 80-90 pixels along the slit there are brightenings and darkenings, representing longer period oscillations, which correspond to the penumbra and adjacent regions. The frequencies in these regions are typically in the 2-4 mHz range, whereas for the central part of the slit, roughly from pixels 60-75, there are many alternate dark and bright ridges, corresponding to the umbral oscillations, with frequencies of oscillation in the range 5.5-7 mHz, with most peaks at 6.2 mHz. Another point to note in the X-T image is that there is a drift in the ridges, a slanting from top to bottom, which is due to the solar rotational drift (i.e. a sit and stare effect), that is, the oscillating umbra source moves down along the slit as the Sun rotates under the slit. As mentioned before, the peak counts occur at pixel 67. Below we investigate this pixel in all three spectral lines, He I, O III and O V.

Figure 12: Wavelet results corresponding to the O  V 629 Å line in the s19336r00 dataset at pixel 67. Representations are the same as Fig. 10.

In Fig. 10 we show as a representative umbral oscillation, the power spectra analysis corresponding to the He  I 584 Å line at pixel location 67 (marked as a box in Fig. 8). In the wavelet spectrum, the dark contour regions show the locations of the highest powers. Only locations that have a probability greater than 95% are regarded as being real, i.e. not due to noise. Cross-hatched regions, on either side of the wavelet spectrum, indicate the "cone of influence'' (COI), where edge effects become important (see Torrence & Compo 1998). The dashed horizontal lines in the wavelet spectra indicate the lower frequency cut-off, in this instance 1.5 mHz. The results from the phase plots show that the He  I 584 Å intensity and velocity both show significant power in the 6.0-7.0 mHz range, for the periods between the 20-30th and 40-65th minutes of the observing sequence. From the overlay of the MDI intensity-gram and the slit location (Fig. 7) one can clearly see that this particular pixel was over the sunspot umbra between the time interval 20-65th minute of the observing sequence (for a total of 45 min). We should point out that the wavelet analysis has been carried out on relative intensity and velocity values and hence there is a lack of low frequency power in the wavelet spectrum plots. The global wavelet spectra (on the right of Figs. 10a, b, which are the average of the wavelet power spectrum over the entire observing period, show the strongest intensity and velocity power at 6.2 mHz ($\sim$161 s). This is printed out in Fig. 10 above the global wavelet plots, together with the probability estimate for the global wavelet power spectrum. In the lowest panels we show the variation of the probability level as estimated from the randomization test. Note that the statistical significance is calculated only for the maximum powers in the wavelet spectrum marked by the dotted white line in the dark patches. From these panels we can clearly see that the oscillations were significant in the period between the 20-30 and 40-65 min of the time sequence.

The O  III 599 Å line formed in the low-to-mid transition region, is rather faint and to increase the signal to noise ratio we binned over two pixels (67-68). The intensity wavelet shows power around 5.6 mHz and also some strong power around 3 mHz for the first 20 min. The slit was not positioned over the sunspot umbra for the first 20 min of the observing sequence and thus the first 20 min power corresponds to the umbra boundary. In the global wavelet the main power peak is at 5.6 mHz, but there is also a strong peak around 3 mHz, which corresponds to the first 20 min during which the penumbra rotates under the slit. The most significant oscillations take place during the time intervals between 20-25 and 45-50 min. For the O  III 599 Å line the velocity signal is too weak and hence the oscillations for this component are not reliable and so are not included in this analysis.

Now we turn our attention to the transition region O  V 629 Å line. Figure 11 shows the wavelet results for the same pixel location, 67, and dataset, s19332r00. Intensity and velocity both shows strong power around 6.7 mHz in the phase and global wavelet spectra. The O V oscillation is strong for the same time interval (as in He  I and O  III), namely between the 20-65 min, with a drop in significance for the time interval between 30-40 min of the sequence. From this one pixel located in the sunspot umbra we thus find that the average frequency of oscillation over the entire observing time for the O  V line is at 6.7 mHz (165 s), as estimated from the global wavelet spectrum.

Using the same techniques as before, we also examine the same sunspot $\sim$30 min later using dataset s19334r00. The results from this temporal series dataset are summarized in Table 4. For the central portion of the umbra we find that the global peaks show frequencies in the range 5.2-5.7 mHz for all the three lines observed and the lifetimes of the oscillations are between 10-20 min, very similar to the previous case of s19332r00. We concentrate on the same single pixel as before, namely pixel 67, in the umbra of the sunspot (plume). From Fig. 12 it is clear that the main oscillations in intensity and velocity, take place in a 5-60 min interval in the observing sequence, with most significant oscillations occurring in the 5-15 and 25-65 min intervals for intensity and the 20-55 min interval for the velocity (this can be confirmed by looking at the variation of probability in the lowest panels). The global peak for the intensity and velocity both appear at 6.2 mHz with a very high probability level. The results from the other lines from this dataset are given in Table 4. In Fig. 13, we show the overall spatial variations of the oscillations in O  V. In the X-T slice we can see faint light and dark ridges in the interval between pixels 60-75, where the central part, roughly between pixels 66-68 corresponds to the plume (where $I > 5 \bar{I}$, see rightmost panels). Once again a slow downward drift of the bright ridges may be seen in the X-T slice, which is a rotational effect due to the movement of the oscillating source down relative to the slit with time. The frequency distribution shows that the umbra oscillates in intensity and velocity in the 5-6.5 mHz range, with most oscillations occurring at 6.2 mHz.

Now we turn our attention to the study of the other active region, AR8963 over the period 19-20 April 2000 (see Table 3 for details). To save space, we do not show here detailed wavelet plots for individual dataset, rather we choose some selective pixel locations in each dataset (corresponding to the umbra of a sunspot) and summarize our results in the form of Table 4. We also list the duration of the oscillations, estimated as the periods of time different oscillation packets showed significant oscillations above the 95% significance level. This can be easily measured from a comparison of the wavelet phase plots and the variation of the probability level in the wavelet analysis (e.g. in Fig. 12). We just point out here some of the other additional features which we noticed for this active region. Firstly we should point out that this active region was much larger compared to the previous one with 12 beta type spots. In certain cases we found that the oscillation frequency changed during the observation which might indicate that a new oscillating region was rotating into the field of view of the CDS slit. For 20 April 2000 dataset, we also encountered a small flaring event which interfered with the measurement of the underlying higher frequency oscillations. It was noted that active region AR8963 had slightly evolved in comparison with the previous day (the flare was a result of that). In all the datasets corresponding to 20th April we find a wider distribution of frequency measured from the peak of the global wavelet spectrum, so we have listed the range of frequency over which the oscillation was most significant.