5 Multiplet splittings

As pointed out by Winget et al. (1994) and Vuille et al. (2000), the observed triplets in the 1900 and 1994 data sets had splittings ranging from 6.5 $\mu$Hz from the "external'' modes (such as k=17) to 3.6 $\mu$Hz for the "internal'' modes k=8 and 9. Winget et al. interpreted these splittings to be the result of radial differential rotation, and Kawaler et al. (1999) examined this interpretation in more detail. An examination of the frequencies found in the 2000 data set, shown in Table 9, shows that the multiplet structure is much harder to discern, since the k=10 through 20 modes typically have only one multiplet member with a large amplitude. The obvious multiplet members have frequencies that agree with the 1990 data, except for the 16^- mode, where there is a $+10.234~\mu$Hz shift in the 2000 data.

Figure 13: Peaks around k=10 in the 1990 (solid line) and 2000 (dashed line) transforms.

Note that the k=10 mode identified at $2027~{\rm\mu Hz}$ is different than the $1994~{\rm\mu Hz}$ identified by Winget et al. (1994) in the 1990 data. However, the peak they identified is not the highest peak in that region of the Fourier transform (see Fig. 13). Our analysis of the 1990 data has statistically significant k=10peaks close to $1999~\mu$Hz and 2008 $\mu$Hz.

The only modes with obvious multiplet structure are the k=9 mode, which still shows an obvious 3.6 $\mu$Hz split triplet, and the k=8 mode, which shows two peaks that are consistent with $2\times 3.6~\mu$Hz separation.

In Table 11 we have a peak 3.3 $\mu$Hz from the k=15, m=1mode that we have not seen before; we call it the 15^b mode. We are not certain whether this is another member of the k=15 multiplet (analogous to the 15^a mode in the 1994 WET data) or if it is something else. The 1994 data set also presented a large peak 4.4 $\mu$Hz from k=15, m=0, which we call the 15^a mode, in addition to the $m=\pm 1$ components. We have not seen this 15^a mode in any other data set other than the 1994 WET run. The identity of the "extra subcomponents'' remains an unsolved mystery.