A Critical Evaluation of Recent Claims Concerning Solar Rotation

Abstract

Fossat et al. (2017) recently reported detecting rotational splitting of g modes indirectly via the interaction with p modes observed directly by the GOLF instrument on SOHO. They concluded that the core of the Sun is rotating 3.8 ± 0.1 times faster than the surrounding radiative envelope. This is startling, partly because such rapid rotation almost contradicts direct inferences from the p-mode rotational splitting inferred from the same data. Moreover, the inferred amplitudes of the g modes appear to exceed the upper bound reported by Appourchaux et al. (2010). It is also suspect because the theory of the procedure implies that the principal modes claimed to have been measured should be undetectable. We point out that there are other interpretations: one leads to a core rotation about twice faster than the surrounding envelope; another, to a core rotating more slowly than the envelope. Here we also report on an independent assessment of the Fossat et al. analysis by applying their procedure to different representations of the GOLF data, expanding on Schunker et al. (2018). We also analyze seismic data obtained from LOI and MDI (both also on SOHO), from HMI (on SDO) and from the ground-based BiSON and GONG, and found the evidence reported by Fossat et al. not to be robust. We also illustrate that merely fitting model spectra to observations, which Fossat et al. do to support their g-mode detections and as Fossat & Schmider (2018) do for extracting additional g-mode splittings, is not necessarily reliable. We are therefore led to doubt the claim.

Signature of solargmodes in first-orderp-mode frequency shifts

“…Measuring such a small effect would require an extremely long observation time. Our results are in broad agreement with the estimates obtained by Scherrer & Gough (2019).…”

“…The harmonic degree l g of the g mode has to be even, the azimuthal order m g of the g mode has to be zero, and the harmonic degree l g of the g mode has to be smaller than or equal to twice the harmonic degree of the p mode (l g ≤ 2l p ). The condition that the harmonic degree of the g mode has to be even has been previously obtained by Kennedy et al (1993) and Scherrer & Gough (2019).…”

“…Kennedy et al (1993) and Scherrer & Gough (2019) have found previously that only g modes of even harmonic degree produce a p-mode frequency shift at first order, see also Gough (1993) for perturbations to solar structure that preserve hydrostatic equilibrium. Although Scherrer & Gough (2019) do not note a selection rule regarding m g , it can be derived using their framework of degenerate perturbation theory, where both the g mode and rotation where treated as perturbations to the solar model. This can be seen by considering the coupling matrix that leads to the perturbed p-mode eigenfunctions and perturbed pmode frequencies at first order.…”

“…They found that the signal reported by Fossat & Schmider (2018) would be due to relative frequency shifts of the order of 10 −5 , which would correspond to a g-mode amplitude of 50 cm s −1 and which is much higher than the observational upper limit on g-mode amplitudes (for a review, see Appourchaux et al 2010). Both Kennedy et al (1993) and Scherrer & Gough (2019) found that only g modes with even harmonic degrees can couple to p modes to leading order.…”

“…The effect of aspherical perturbations on p-mode frequencies has been studied by Gough (1993), on which Kennedy et al (1993) and Scherrer & Gough (2019) are based. The aforementioned work was done under the assumption that the perturbation to solar structure preserves hydrostatic equilibrium.…”