Signature of solargmodes in first-orderp-mode frequency shifts

Abstract

Context. Solar gravity modes (g modes) are buoyancy waves that are trapped in the solar radiative zone and have been very difficult to detect at the surface. Solar g modes would complement solar pressure modes (p modes) in probing the central regions of the Sun, for example the rotation rate of the core. Aims. A detection of g modes using changes in the large frequency separation of p modes has recently been reported. However, it is unclear how p and g modes interact. The aim of this study is to evaluate to what extent g modes can perturb the frequencies of p modes. Methods. We computed the first-order perturbation to global p-mode frequencies due to a flow field and perturbations to solar structure (e.g. density and sound speed) caused by a g mode. We focused on long-period g modes and assumed that the g-mode perturbations are constant in time. The surface amplitude of g modes is assumed to be 1 mm s −1 , which is close to the observational limit set by Doppler observations. Results. Gravity modes do perturb p-mode frequencies to first order if the harmonic degree of the g mode is even and if its azimuthal order is zero. The effect is extremely small. For dipole and quadrupole p modes, all frequency shifts are smaller than 0.1 nHz, or 2 × 10 −8 in relative numbers. This is because the relative perturbation to solar structure quantities caused by a g mode of realistic amplitude is of the order of 10 −6 to 10 −5 . Additionally, we find that structural changes dominate over advection. Surprisingly, the interaction of g and p modes takes place to a large part near the surface, where p modes spend most of their propagation times and g modes generate the largest relative changes to solar structure. This is due to the steep density stratification, which compensates the evanescent behaviour of g modes in the convection zone.Conclusions. It appears to be impossible to detect g modes solely through their signature in p-mode frequency shifts. Whether g modes leave a detectable signature in p-mode travel times under a given observational setup remains an open question.

Amplitude of solar gravity modes generated by penetrative plumes

“…Indeed, the result was shown to be very sensitive to the parameters of the time series considered in the analysis, as the start time, and somehow appears to be an artifact of the methodology. Theoretical studies on the coupling between acoustic and gravity modes reinforced the fragility of this result (Scherrer & Gough 2019;Böning et al 2019). At the time of writing, no robust detection of the solar gravity modes has therefore been unequivocally confirmed yet.…”

Amplitude of solar gravity modes generated by penetrative plumes

“…The result was shown to be very sensitive to the parameters of the time series considered in the analysis (e.g., the start time), and appears to be an artifact of the methodology. Theoretical studies of the coupling between acoustic and gravity modes reinforced the fragility of this result (Scherrer & Gough 2019;Böning et al 2019). At the time of writing no robust detection of the solar gravity modes has therefore been unequivocally confirmed.…”

Solar structure and evolution

“…Also, the physical effects that might introduce the g-mode signal in the acoustic-mode properties are so far unclear. Indeed, although already Kennedy et al (1993) proposed this type of analysis they noted that the coupling between the modes is such that to leading order the p-mode frequencies are insensitive to g modes of odd degree (see also Gough, 1993), in conflict with the inferences of Fossat et al This was analysed in more detail by Böning et al (2019) and Scherrer and Gough (2019). Furthermore, Scherrer and Gough confirmed and extended the results of Schunker et al (2018) and tried, and failed, to find a similar signal in the MDI and HMI data; they also noted that the inferred rapid rotation of the solar core is difficult to reconcile with the constraints obtained from extensive analyses of well-observed solar acoustic modes (see Section 5.1.4).…”