6 Discussion

One obvious limitation of the template method is that, as several leaks are included in each fit and their relative frequencies are not free parameters, the frequencies obtained at each l will not be completely independent of those for adjacent degrees. The method is also susceptible to variations in the relative power of the leaks, and does not make use of the leak information in fitting other spectra where the leak might be a target mode. However, a method of this kind may be useful for extending fitting into regions where the modes are only partly resolved from the leaks. This kind of technique is potentially applicable to data from any instrument which is sensitive to sufficiently high degrees that blending becomes problematic. It might be useful for data from SOI-MDI on board SOHO, for example. In tests, we obtained reasonably satisfactory results up to about l=190 or $\partial \nu /\partial l =1.3\Gamma$.In Fig. 14 we show the m-averaged spectrum for the l=150,n=7 multiplet, which illustrates the difficulty when the leak ridges come too close to the main one. This fit would probably have been rejected if we were applying the fitting scheme in a systematic manner.

  

Figure 14: The m-averaged spectrum (symbols) for the l=150,n=7 multiplet, with the attempted fit to a symmetric seven-peak model shown as the curve. This is not considered a good fit

Fitting the leaked ridges as single Lorentzian profiles is not strictly correct; for example, as noted above, each "$\delta l =\pm 1$ leak'' consists of two peaks with $\delta m=\pm 1$,and the "$\delta l=2$ ridges'' have three components with $\delta m = -2,0$,and 2, with relative strengths varying with m.

We have also ignored the asymmetry of the ridges in the data which, though clearly visible in the m-averaged spectra and $m-\nu$ diagrams, is not accounted for by the leakage-matrix calculations. Some of this asymmetry, which can be seen for instance in Fig. 12, is believed to arise from the neglected horizontal components of the motion in these low-order modes.

It should also be noted that a symmetrical Lorentzian profile may not be an adequate model for an individual peak because of the asymmetry introduced by the location of the excitation sources for the modes, as discussed, for example, by Abrams & Kumar (1996) and by Nigam  et al. (1998).

At higher degrees, the modes lose their global nature and the peaks for a given l become completely blended with their adjacent leaks. Under these conditions, the approach described above breaks down because the peaks in the template cannot be independently fitted even in the m-averaged spectrum. "Ridge fitting'' of a single unresolved peak at each m will give reliable results only if the shape of this compound peak accurately reflects the relative strengths of the unresolved components. To achieve this, knowledge of the leakage matrix would almost certainly be necessary.

Acknowledgements

This work utilizes data obtained by the Global Oscillation Network Group (GONG) project, managed by the National Solar Observatory, a Division of the National Optical Astronomy Observatories, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation. The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Obseratory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofisico de Canarias, and Cerro Tololo Interamerican Observatory. Our work is supported by the UK Particle Physics and Astronomy Research Council, through grant GR/J00588.