In Figs. 3 - 5we show surface plots of the average count rate per pixel, the resulting peak power at the most significant frequency and the most significant frequency above 1.5 mHz in the light curve of a pixel, for all datasets, as derived from time-series analyses without frequency binning (i.e., W=1). Our definition of significant power is the 99.9% confidence level. As can be seen not all pixels within a particular dataset show evidence of an oscillation. However, in some instances, although not in all datasets, individual pixels which do not show a clear wave-like behaviour, if added together, can sometimes show a periodicity in the 3-4 mHz range at the 99.9% confidence level. In most cases, those regions showing a clear oscillation are confined in size. Sometimes, it can be a single pixel, thus less than . In other instances, the spatial size can approach a few pixels.
In Fig. 6, we show the light-curve plus the resulting power spectrum for a group of 11 pixels (showing excess signal) from the central region of dataset 92712 (note that in this figure, two adjacent frequency bins were averaged, i.e., W=2). As can be clearly seen, excess signal at 3.0 and 3.7 mHz is present corresponding to periods of 330 sec and 270 sec respectively. These periods are similar to those derived by Drake et al. (1989). In dataset 92712, there is no evidence of flare-like activity, although in some datasets the observed periodicities are flare-like. As an example, we show in Fig. 7 the light-curve and power spectrum for dataset 92921. As can be clearly seen in the light-curve, there is a series of short duration bursts which are of a flare-like appearance. The time lag between these events ranges from 6 to 10 mins. This can also be seen from the power spectrum which shows peaks corresponding to these periods, plus a range of shorter periods in the range 2-4 mins.
In many datasets, as can be seen in Fig. 6, the 5 min. period has at least 9 cycles. However, this is not the case for the longer periods perhaps because our datasets are only of 44 min duration, thus a wave with a period approaching 10 mins. can have at most 4 cycles.
Our data comprise the light curves of pixels. In the power spectra of 738 light curves, (29%) statistically significant power peaks were found. In most of the cases significant power was found at multiple frequencies. Above 6-10 mHz the power, in general, varies around 2, the value expected from a (Poissonian) noise distribution. For each of the light curves containing significant power, we determined the frequency above 2 mHz at which the maximum power (peak power) was found. The distribution of the number of pixels with a peak power at a given frequency is shown in Fig. 8. Because three datasets were analyzed with a slightly different frequency grid we show these separately in Figs. 8b-8d while Fig. 8a is based on the twelve other datasets. Fig. 8a shows that for the majority of the datasets the most dominant powers are found in the 2-5 mHz range with a distinct maximum around 3 mHz. Only a few pixels have their peak power in the 6-10 mHz range. For most of the datasets the number of pixels with a peak power around 2 mHz is small. However, the data set shown in Fig. 8c contains a large number of pixels with peak powers at 2 mHz (8.3 min.). These pixels are often associated with flare-like brightnings and have high count rates.
For all datasets, we show in Fig. 9a the distribution of the peak powers as a function of frequency and in Fig. 9b the average count rate as a function of frequency. Note that these figures show a `vertical band' structure at certain frequencies because of the different frequency grid used for three datasets. Because the power is normalized according to Eq. (5), the 99.9% confidence level corresponds to about 23. This explains the minimum power level in the figure. Also, the power at which a data point is found is a direct measure of its significance level. Because we put our detection limit at the 99.9% confidence level, the powers shown in Fig. 9a are extremely significant. The strongest powers are found in the 2-5 mHz range although the magnitude of the power strongly varies. Between 6-10 mHz the distribution of the peak powers, in terms of their significance, is relatively flat.
The highest count rates are found for frequencies around 2 mHz and are associated with flare-like brightnings (Fig. 9b). Most pixels with significant power in the range 2-10 mHz have average count rates of 200-600 counts/second. However, between 2 and 5 mHz, the pixels show a larger spread of the count rate than above 5 mHz. Fig. 9c shows that there is a weak correlation between the count rate and the peak power in the sense that as the count rate increases the spread in the powers increases. This could, however, be a selection effect because low count rates are necessarily related to a relatively larger Poisson noise and lower (unnormalized) powers. On the other hand, Figs. 3 - 5 demonstrate that high count rates do not always result in the detection of significant peaks in the power spectrum. From this we conclude that there is no clear correlation between the presence of a significant period and the count rate.
© European Southern Observatory (ESO) 1997
Online publication: April 8, 1998