Theoretical seismology in 3D: nonlinear simulations of internal gravity waves in solar-like stars

Abstract

Context. Internal gravity waves (IGWs) are studied for their impact on the angular momentum transport in stellar radiation zones and the information they provide about the structure and dynamics of deep stellar interiors. We present the first 3D nonlinear numerical simulations of IGWs excitation and propagation in a solar-like star. Aims. The aim is to study the behavior of waves in a realistic 3D nonlinear time-dependent model of the Sun and to characterize their properties. Methods. We compare our results with theoretical and 1D predictions. It allows us to point out the complementarity between theory and simulation and to highlight the convenience, but also the limits, of the asymptotic and linear theories. Results. We show that a rich spectrum of IGWs is excited by the convection, representing about 0.4% of the total solar luminosity. We study the spatial and temporal properties of this spectrum, the effect of thermal damping, and nonlinear interactions between waves. We give quantitative results for the modes' frequencies, evolution with time and rotational splitting, and we discuss the amplitude of IGWs considering different regimes of parameters. Conclusions. This work points out the importance of high-performance simulation for its complementarity with observation and theory. It opens a large field of investigation concerning IGWs propagating nonlinearly in 3D spherical structures. The extension of this work to other types of stars, with different masses, structures, and rotation rates will lead to a deeper and more accurate comprehension of IGWs in stars.

On Differential Rotation and Overshooting in Solar-like Stars

“…Given that the convective and radiative zones are nonlinearly and dynamically coupled, internal waves can easily be excited by the pummeling of convective plumes on top of the radiative interior Alvan et al 2014). The Brunt-Väisälä frequency N of the models are very close to that deduced from 1-D stellar models computed with the CESAM code (Morel 1997;Brun et al 2002, see Figure 4).…”

“…It drops off exponentially with depth in order to avoid a large inward heat flux in the stable zone (see Miesch et al 2000;Brun et al 2011;Alvan et al 2014). Of course there is some arbitrariness in choosing the exact shape and amplitude of our diffusivity profiles and we optimize their profiles such as to limit their influence on the results reported here.…”

“…We choose instead to focus our study on convection and the generation and maintenance of the large-scale mean flows and how they vary as a function of spectral type. As shown in Alvan et al (2014), fully spherical models are more adequate to realistically model internal waves and gravity modes, but they are much more expensive to run, which makes a comprehensive parameter study impractical.…”

Origin and Evolution of Magnetic Field in PMS Stars: Influence of Rotation and Structural Changes

“…The 3D full sphere simulations of the evolution of solartype stars during the PMS to the ZAMS presented here are computed with the ASH code (Clune et al 1999;Brun et al 2004;Alvan et al 2014). This code evolves the Lantz-Braginski-Roberts (LBR) form of the anelastic MHD equations for a conductive plasma in a rotating sphere (Jones et al 2011).…”

“…Moreover, except for the first one, all our models have two zones with a convective envelope and a radiative core. Since our models are full-sphere, boundary conditions only have to be imposed at the surface of the star and regularization of the solution is done at the center of the star, as described in Alvan et al (2014). The velocity boundary conditions are impenetrable and torque-free:…”