Amplitude of solar gravity modes generated by penetrative plumes

¹ STAR Institute, Université de Liège, 19C Allée du 6 Août, 4000 Liège, Belgium
e-mail: charly.pincon@uliege.be
² Université Paris-Sud, Institut d’Astrophysique Spatiale, UMR 8617, CNRS, Bâtiment 121, 91405 Orsay Cedex, France
³ Observatoire de Genève, Université de Genève, 51 Ch. Des Maillettes, 1290 Sauverny, Switzerland

Received: 27 November 2020
Accepted: 3 March 2021

Abstract

Context. The observation of gravity modes is expected to give us unprecedented insights into the inner dynamics of the Sun. Nevertheless, there is currently no consensus on their detection. Within this framework, predicting their amplitudes is essential to guide future observational strategies and seismic studies.

Aims. While previous estimates considered convective turbulent eddies as the driving mechanism, our aim is to predict the amplitude of low-frequency asymptotic gravity modes generated by penetrative convection at the top of the radiative zone.

Methods. A generation model previously developed for progressive gravity waves was adapted to the case of resonant gravity modes. The stellar oscillation equations were analyzed considering the plume ram pressure at the top of the radiative zone as the forcing term. The plume velocity field was modeled in an analytical form.

Results. We obtain an analytical expression for the mode energy. It is found to depend critically on the time evolution of the plumes inside the generation region. Using a solar model, we then compute the apparent surface radial velocity of low-degree gravity modes as would be measured by the GOLF instrument, in the frequency range 10 µHz ≤ ν ≤  100 µHz. In the case of a Gaussian plume time evolution, gravity modes turn out to be undetectable because of too small surface amplitudes. This holds true despite a wide range of values considered for the parameters of the model. In the other limiting case of an exponential time evolution, plumes are expected to drive gravity modes in a much more efficient way because of a much higher temporal coupling between the plumes and the modes than in the Gaussian case. Using reasonable values for the plume parameters based on semi-analytical models, the apparent surface velocities in this case are one order of magnitude lower than the 22-year GOLF detection threshold and lower than the previous estimates considering turbulent pressure as the driving mechanism, with a maximum value of 0.05 cm s⁻¹ for ℓ = 1 and ν ≈ 100 µHz. When accounting for uncertainties on the plume parameters, the apparent surface velocities in the most favorable plausible case become comparable to those predicted with turbulent pressure, and the GOLF observation time required for a detection at ν ≈ 100 µHz and ℓ = 1 is reduced to about 50 yr.

Conclusions. Penetrative convection can drive gravity modes in the most favorable plausible case as efficiently as turbulent pressure, with amplitudes slightly below the current detection threshold. When detected in the future, the measurement of their amplitudes is expected to provide information on the plume dynamics at the base of the convective zone. In order to make a proper interpretation, this potential nevertheless requires further theoretical improvements in our description of penetrative plumes.