6 Observations and data reduction

For these observations we have used the normal incidence spectrometer ( NIS) (Harrison et al. 1995), which is one of the components of the Coronal Diagnostic Spectrometer ( CDS) on-board the Solar Heliospheric Observatory (SoHO). The data discussed here were selected from the observing period 14 April and 19-20 April 2000. The observations were performed for two different active regions. The details of the observations including pointing and start times are summarized in Table 3. Two different CDS sequences were run, one temporal series sequence called CHROM_-N6 and another raster sequence called CHROM_-N5. Temporal series datasets of $\sim$85 min duration were obtained for the three lines of He  I 584 Å ( $\log~ T = 4.6$), O  III 599 Å ( $\log~ T= 5.0$) and O  V 629 Å ( $\log~ T=5.4$) using exposure times of 25 s and the $2 \times 240$ arcsec² slit. The CDS pixels in the y direction (i.e. spatial resolution) are of size 1.68 arcsec. In the raster sequence the $2 \times 240$ slit was moved 30 times in steps of 2 arcsec so as to build up $60 \times 240$ arcsec² raster images within a duration of 24 min. For this sequence the lines used were: He  I 584 Å ( $\log~ T = 4.6$), O  III 599 Å ( $\log~ T= 5.0$), O  V 629 Å ( $\log~ T=5.4$), Ca  X 574 Å ( $\log~ T=5.8$), and Mg  IX 368 Å ( $\log~ T=6.0$).

In order to get good time resolution the rotational compensation was switched off (sit-and-stare mode) and so it becomes important to calculate the lowest possible frequency we can detect from this long time sequence after taking the solar rotation into account (see Doyle et al. 1998 for details). We estimate that the maximum effect of the sit and stare mode on the resulting power, for all datasets would be a spreading of the frequencies by around 1.5 mHz, depending on the size of the source. For all our sunspots, whose sizes are several arcsec and which have (well-defined) primary oscillating frequencies much above 3 mHz, the effect of the sit and stare is not considered to be important.

The fitting of the different CDS lines was done using a single Gaussian as the lines were found to be generally symmetric. Details on the CDS reduction procedure, plus the wavelet analysis, may be found in O'Shea et al. (2001). Before applying the wavelet analysis we first removed the trend of the data (i.e. the very lowest frequency oscillations) using a 30 point running average. By dividing the results of this running average (or trend) into the original data and subtracting a value of one we obtained the resulting detrended data used in the analysis. Fludra (2001) have shown that this method is very efficient in removing the low frequency background oscillation. The statistical significance of the observed oscillations was estimated using a Monte Carlo or randomization method. The advantage of using a randomization test is that it is distribution free or nonparametric, i.e. it is not limited or constrained by any specific noise models, such as Poisson, Gaussian etc. We follow the method of Fisher randomization as outlined in Nemec & Nemec (1985), performing 250 random permutations to calculate the probability levels. The levels displayed here are the values of $(1-p) \times 100$, where p is the proportion of the permutations that show a null test result (see O'Shea et al. 2001). We choose a value of 95% as the lowest acceptable probability level. Occasionally the estimated p value can have a value of zero, i.e. there being an almost zero chance that the observed time series oscillations could have occurred by chance. In this case, and following Nemec & Nemec (1985), the 95% confidence interval can be obtained using the binomial distribution, and is given by 0.0 < p < 0.01, that is, the probability ( $(1-p) \times 100$) in this case is between 99-100%. The velocity values presented in this paper are relative velocities, that is, they are calculated relative to an averaged profile, obtained by summing over all pixels along the slit and all time frames.

Figure 9: Frequencies measured as a function of spatial position along the slit (X-F slice) for the O  V 629 Å line (left panels) and the s19332r00 dataset. The right panels show the total number of counts in a pixel (summed counts) over the observation time.