5.7 A new millennium for low-degree helioseismology

Starting around the turn of the century, there was a move towards more collaborations and comparisons between different projects in an effort to understand the systematic errors and better constrain the solar core dynamics. By this time, multi-year observations were available from GONG and the SOHO instruments, as well as good-quality observations from BiSON stretching back to 1991.

Chaplin et al. (1999) combined the LOWL higher-degree splittings with the very precise low-frequency BiSON splittings for the lowest-degree modes, and concluded that the data were consistent either with rigid rotation or with a slight downturn in the rotation rate in the core (the latter being at best a 1-σ result); on the other hand, Corbard et al. (1998b) had used a very similar analysis of GOLF and MDI data to deduce a slight increase in the rotation rate below 0.25 R⊙, but García et al. (2003), also using MDI and GOLF data, obtained rather low splitting values from a 2243-day time series and tentatively concluded that they could rule out a high rotation rate in the core.

Eff-Darwich et al. (2002Jump To The Next Citation Point), following on from the work of Eff-Darwich and Korzennik (1998), again combined BiSON, GOLF, GONG and MDI data and found a very small downturn in rotation in the core, while Couvidat et al. (2003) found a flat rotation profile down to 0.2R ⊙ using combined GOLF, MDI and LOWL data.

Fletcher et al. (2003) investigated the problem of fitting the poorly-resolved higher-frequency low-degree mode splittings to integrated-sunlight observations such as those from BiSON. Using genetic fitting algorithms, they were able to reduce, though not eliminate, the bias towards higher splittings for these fits. They also found, in common with previous work, a strong anticorrelation between the estimated splitting value and its formal error, which would tend to cause overestimated splittings to be more heavily weighted in inversions.

García et al. (2004) considered two years of “sun-as-a-star” observations from early in the solar cycle, obtained from GOLF, GONG, MDI, VIRGO and BiSON, and were able to extract not only sectoral splittings but also a3 and a5 coefficients from the data, suggesting that it may be possible to infer differential rotation even in stars from which we will never have resolved data.

Chaplin et al. (2004) used artificial data to address the question the detectability of a rotation-rate gradient in the core. They concluded that, based on the best available data from ten years of observations, the difference between the rotation rate at 0.1 R⊙ and 0.35R ⊙ would be detectable only if it exceeded 110 nHz.

Chaplin et al. (2006) carried out an exhaustive “hare-and-hounds” exercise, in which one participant (the “hare” supplies the same set of artificial data to the others, the “hounds,” who then apply their various fitting methods without knowing the “true” answer, and compare the results. They obtained good agreement between the different techniques for l = 1, but systematic differences for the l > 1 splittings, which are attributed to different assumptions about the relative heights and spacing of the non-sectoral (|m | < l) components.

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