Abstract
Context.Solar gravity modes (gmodes) are buoyancy waves that are trapped in the solar radiative zone and have been very difficult to detect at the surface. Solargmodes would complement solar pressure modes (pmodes) in probing the central regions of the Sun, for example the rotation rate of the core.Aims.A detection ofgmodes using changes in the large frequency separation ofpmodes has recently been reported. However, it is unclear howpandgmodes interact. The aim of this study is to evaluate to what extentgmodes can perturb the frequencies ofpmodes.Methods.We computed the first-order perturbation to globalp-mode frequencies due to a flow field and perturbations to solar structure (e.g. density and sound speed) caused by agmode. We focused on long-periodgmodes and assumed that theg-mode perturbations are constant in time. The surface amplitude ofgmodes is assumed to be 1 mm s−1, which is close to the observational limit set by Doppler observations.Results.Gravity modes do perturbp-mode frequencies to first order if the harmonic degree of thegmode is even and if its azimuthal order is zero. The effect is extremely small. For dipole and quadrupolepmodes, all frequency shifts are smaller than 0.1 nHz, or 2 × 10−8in relative numbers. This is because the relative perturbation to solar structure quantities caused by agmode of realistic amplitude is of the order of 10−6–10−5. Additionally, we find that structural changes dominate over advection. Surprisingly, the interaction ofgandpmodes takes place to a large part near the surface, wherepmodes spend most of their propagation times andgmodes generate the largest relative changes to solar structure. This is due to the steep density stratification, which compensates the evanescent behaviour ofgmodes in the convection zone.Conclusions.It appears to be impossible to detectgmodes solely through their signature inp-mode frequency shifts. Whethergmodes leave a detectable signature inp-mode travel times under a given observational setup remains an open question.
Highlights
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
Using observations of pressure modes (p modes), helioseismology has been very successful in determining solar interior structure and differential rotation in the convection zone and in most of the radiative zone
P modes are most sensitive to relative changes to solar structure close to the surface
Summary
Using observations of pressure modes (p modes), helioseismology has been very successful in determining solar interior structure and differential rotation in the convection zone and in most of the radiative zone (see, e.g. Howe 2009; Aerts et al 2010; Basu 2016). A possible signature of g modes in the p-mode frequency signal has been studied previously by Kennedy et al (1993), Lou (2001), and Scherrer & Gough (2019) In these studies, the g-mode period was assumed to be much longer than the p-mode period, and the perturbation to solar structure caused by a g mode was assumed to be time-independent on shorter temporal scales. Böning et al.: Signature of solar g modes in first-order p-mode frequency shifts
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