4 Power spectra

Figure 8 illustrates the various steps of the duty cycle improvement in the case of the year 1995. The two individual potassium instruments, Mark-1 and LOWL, obtain the excellent duty cycles of almost 29 and 24%, thanks to the exceptional quality of the Tenerife and Mauna Loa sites. However, these one-instrument time series are obviously very sensitive to the diurnal periodicity, and they both display a significant sidelobe structure around each p-mode peak. This sidelobe structure degrades the performance in two ways: first, the sidelobes are interfering with neighbouring peaks, and second, the peak itself is losing a large fraction of its power to the sidelobes and is reduced by a corresponding amount, so that the signal-to-noise ratio is dramatically reduced. The IRIS sodium network alone is doing only a little better in duty cycle, just above 35%. However the benefit of the better distribution in longitude is clearly visible, with a sidelobe structure already reduced by about a factor of 5. The IRIS⁺⁺ merging of the 3 time series provides a spectacular improvement, essentially all sidelobes being now invisible, at least at the scale of this plot. The repetitive music partial gap filling makes the final improvement, increasing the peaks by 40 percent more and cancelling extremely well the sidelobe structure.

It can be seen in Fig. 8 that the gap filled power spectra display a modulated background, at a period of about 67.5 $\mu$Hz, which is, of course, the inverse of 4 hours and the average distance between the pairs of modes of odd and even degrees. The fine tuning of the gap filling method consists of choosing the time lag so that the minima of this modulation are located in the central part of the noise between peaks, thus reducing the access to information only where there is no interesting information. However, this modulation must be taken into account when fitting the peak profiles. Fierry-Fraillon & Appourchaux (2001) have shown how to modify the simple Lorentz profile generally used as the asymptotic function in the fits in order to take the modulation into account, without any bias.

Next Fig. 9 compares the performance of IRIS⁺⁺ with GOLF (Global Oscillations of Low Frequencies) during a four-month run obtained during the summer of 1996. Exactly the same starting and ending dates have been selected in both data sets, to make the comparison meaningful. One can see that part of the background noise in the IRIS⁺⁺ spectrum comes from the residual window function. After gap filling, the IRIS⁺⁺ spectrum is still a little noisier than the GOLF one. The mode amplitudes are slightly different, because of the different duty cycles, and also because of the different monochromatic windows used by the two instruments. However, most of the p-mode information that is present in GOLF is also present in IRIS⁺⁺. Certainly, further benefits can be expected from a cross spectrum analysis of such independent (instrumentally speaking) data sets.