## 3. Frequencies error bars resultsThe theoretical frequencies error-bars are based on Eq. (6) (Toutain and Appourchaux, 1994): being the linewidth of the mode, We took this quantity as reference for the comparisons. ## 3.1. IRIS data, sidelobesFigs. 4 and 5 show a comparison between the former theoretical
error-bars and the computed ones, computed on the 1990 dataset of the
IRIS data with a bin in the spectral density of
Hz. In all the cases, all the errors range from
Hz to Hz. All the curves show a frequency
dependence, related to the presence of the linewidth in the numerator
of Eq. 6. Nevertheless, the error-bar curves are
The presence of sidelobes of one day in the spectral density biases
the measurement of the linewidths above 3.7 mHz, affecting both the
computed and theoretical curves in the same way, so that they continue
to match, up to 4.2 mHz. The presence of the daily sidelobes, taken
into account by the fit, also affects the quality of the result in
degrading by a small amount the frequency of a given peak, but in
degrading its immediate neighbours at about 11.57 and degrade themselves reciprocally, although is more affected, being of poorer SNR, and degrades . Subsequently, we expect as a general trend to have smaller error bars on and than on the two others, and this is actually the case. As to the hypothesis of the gain in precision afforded by the multiplets, there is a difference between Fig. 4 and 5. For , the relation seems verified and the MC numbers are closer to the of Eq. 7than to . It is not the case for or 3 where the MC values are closer to . We think that the precision in the central frequency of a multiplet can benefit from independent determinations on each component only when those components are unambiguously identified by the fit for most of our 400 statistical realisations. The situation is then easier for because of its high relative amplitude and the cleanliness of its surroundings, than for , affected by the left sidelobe of . Also we shall see that the split components do interfere each other in the complex space, leading to interferences in the spectral density that can wipe out completely one or several components of the multiplet. The higher the number of components, the higher the probability of interferences leading to a misidentification of the individual components by the fit. ## 3.2. GONG data, no sidelobesFrom Figs. 4 and 5, it is not clear which effect plays the major role, although we suspect that the sidelobe pollution has a stronger effect than the 'blurring' of the splitting. For this reason, we also performed MC simulations using 1 month of GONG data with a 98% duty cycle and a better SNR than the IRIS data (but a lower resolution). Fig. 6a-c shows the difference between MC and theoretical uncertainties for singlet, doublet and triplet modes. In this case, free from sidelobes, we can really size the effect of the splitting on the error bars: we move from an almost perfect match for to a significant discrepancy for the doublet and triplet modes. We conclude from this that no gain in precision is to be expected from the split nature of a peak and that error-bars computed from an formula are a good guideline for all the modes. Fig. 7 shows one example of two possibles realizations of a doublet generated with the same set of initial parameters, and one can see that a maximum likelihood fit will give two incompatible values of splitting, and that the frequency determination will be greatly affected.
© European Southern Observatory (ESO) 1998 Online publication: April 15, 1998 |