Misleading variations in estimated rotational frequency splittings of solar p modes: Consequences for helioseismology and asteroseismology

The aim of this paper is to investigate whether there are any 11-yr or quasi-biennial solar-cycle-related variations in solar rotational splitting frequencies of low-degree solar p modes. Although no 11-yr signals were observed, variations on a shorter time-scale (similar to 2 yr) were apparent. We show that the variations arose from complications/artefacts associated with the realization noise in the data and the process by which the data were analysed. More specifically, the realization noise was observed to have a larger effect on the rotational splittings than accounted for by the formal uncertainties. When used to infer the rotation profile of the Sun these variations are not important. The outer regions of the solar interior can be constrained using higher degree modes. While the variations in the low-l splittings do make large differences to the inferred rotation rate of the core, the core rotation rate is so poorly constrained, even by low-l modes, that the different inferred rotation profiles still agree within their respective 1s uncertainties. By contrast, in asteroseismology, only low-l modes are visible and so higher l modes cannot be used to constrain the rotation profile of stars. Furthermore, we usually only have one data set from which to measure the observed low-l splitting. In such circumstances the inferred internal rotation rate of a main-sequence star could differ significantly from estimates of the surface rotation rate, hence leading to spurious conclusions. Therefore, extreme care must be taken when using only the splittings of low-l modes to draw conclusions about the average internal rotation rate of a star.