The method that we developed has been validated both on simulated and real data. The difficulty of optimisation has been overcome, and we are able to measure the correlation coefficient and the modes parameters. An estimation of the uncertainties of such measurements can be obtained by the Cramér-Rao bound. Although very preliminary, the first results on the few analysed modes show a significant anti-correlation in the excitation of modes with same geometry, but opposite phase. If confirmed, this could have consequences on our view of the excitation mechanism. For instance, it would definitively rule out the possibility of self-excitation of these modes. We have also demonstrated that a correlation on the excitation of split modes affects the shape of the power spectrum and modifies value of the rotational splitting. Such an effect should be measured in order to recover the true rotation profile. More generally, parametric representation is perfectly adapted for the analysis of the helioseismic data and could be used not only for correlation estimation, but also for other purposes like measurement of asymmetries or frequency variation.
Reliable results have been obtained on a pair of modes, allowing the estimation of excitation correlation between l=1, , or between two l=0 modes. For more complicated patterns, we will probably need to constrain the dynamical parameters estimation (e.g. impose the same width and the same separation in triplets l=2, as is generally done in Lorentz fitting procedure). Our evaluation of the uncertainties on the measured correlation has also to be improved, in particular to take into account the uncertainties on the dynamical parameters of the modes.
Up to now, the method is only valid for continuous data, and therefore can be applied to GOLF data. This work is still to be done, when the difficulty in the treatment of triplets or quadruplets will be solved. In the future, we would like to improve our procedure in order to be able to analyse non-continuous data such as IRIS or BiSON. The difficulty lies in the filtering of the data, necessary to isolate the considered modes. Some solutions to this problem are presently envisioned.
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