Abstract

Stochastic excitation of gravity waves by overshooting convection in solar-type stars

¹ Observatoire Midi-Pyrénées, 14 avenue Edouard Belin, 31400 Toulouse, France
² Nordic Institute for Theoretical Physics, Blegdamsvej 17, 2100 Copenhagen, Denmark
³ Theoretical Astrophysics Center, and Astronomical Observatory, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
⁴ Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI48823, USA

Gravity waves propagating in the radiative zones of solar-type stars have been recently invoked in connection with major problems of stellar structure, such as the dependence of the lithium abundance on the spectral type for some main-sequence stars (the so-called Li-dip problem) or the quasi-solid rotation of Sun's radiative interior revealed by helioseismology. Indeed, these waves are expected to transport energy, angular momentum or chemicals over long distances in radiative zones of stars and, up to now, this kind of transport was ignored by the standard stellar model. There remains the problem of their excitation since, unlike pulsating white dwarfs, for example, a k-mechanism based on hydrogen and helium ionization zones is not applicable here.
One possibility concerns the excitation by overshooting convection from neighboring convection zones. Strong downward plumes are known to penetrate substantial distances into the adjacent stable zone so that internal gravity waves can be randomly generated. Using high-resolution two-dimensional simulations of compressible convection, we investigated in details this excitation mechanism. One of the main difficulties of this problem lies in the correct detection of gravity wave events in the bottom radiative zone. We therefore proposed a new technique allowing us to measure rigorously both the spectrum and amplitudes of excited g-modes.
This method is based on a combination of projections of each convection simulation onto the anelastic sub-space built from the solutions of the associated linear eigenvalue problem and time-frequency diagrams of the resulting projection coefficients. Its main advantage, compared to the classical detection method based on (k,

)-diagrams of the wholesimulation, is that the random nature of the excitation is now well taken into account. As a consequence, real spectra and amplitudes of stochastically excited g-modes are reached and not only their "mean" values over the full simulation.
As a pedagogical test, we will first present the application of this new detection technique to the g-mode oscillations of an isothermal atmosphere and then, we will focus on results obtained from our 2D numerical simulations of a three-layer model, consisting of a convective zone embedded between two stable ones.