Toward fully compressible numerical simulations of stellar magneto-convection with the RAMSES code

Abstract

Context. Numerical simulations of magneto-convection have greatly expanded our understanding of stellar interiors and stellar magnetism. Recently, fully compressible hydrodynamical simulations of full-star models have demonstrated the feasibility of studying the excitation and propagation of pressure and internal gravity waves in stellar interiors, which would allow for a direct comparison with asteroseismological measurements. However, the impact of magnetic fields on such waves has not been taken into account yet in three-dimensional simulations. Aims. We conduct a proof of concept for the realization of three-dimensional, fully compressible, magneto-hydrodynamical numerical simulations of stellar interiors with the RAMSES code. Methods. We adapted the RAMSES code to deal with highly subsonic turbulence, typical of stellar convection, by implementing a well-balanced scheme in the numerical solver. We then ran and analyzed three-dimensional hydrodynamical and magneto-hydrodynamical simulations with different resolutions of a plane-parallel convective envelope on a Cartesian grid. Results. Both hydrodynamical and magneto-hydrodynamical simulations develop a quasi-steady, turbulent convection layer from random density perturbations introduced over the initial profiles. The convective flows are characterized by small-amplitude fluctuations around the hydrodynamical equilibrium of the stellar interior, which is preserved over the whole simulation time. Using our compressible well-balanced scheme, we were able to model flows with Mach numbers as low as ℳ ∼ 10−3, but even lower Mach number flows are possible in principle. In the magneto-hydrodynamical runs, we observe an exponential growth of magnetic energy consistent with the action of a small-scale dynamo. The weak seed magnetic fields are amplified to mean strengths of 37% relative to the kinetic equipartition value in the highest resolution simulation. Since we chose a compressible approach, we see imprints of pressure and internal gravity waves propagating in the stable regions above and beneath the convection zone. In the magneto-hydrodynamical case, we measured a deficit in acoustic and internal gravity wave power with respect to the purely hydrodynamical counterpart of 16% and 13%, respectively. Conclusions. The well-balanced scheme implemented in RAMSES allowed us to accurately simulate the small-amplitude, turbulent fluctuations of stellar (magneto-)convection. The qualitative properties of the convective flows, magnetic fields, and excited waves are in agreement with previous studies in the literature. The power spectra, profiles, and probability density functions of the main quantities converge with resolution. Therefore, we consider the proof of concept to be successful. The deficit of acoustic power in the magneto-hydrodynamical simulation shows that magnetic fields must be included in the study of pressure waves in stellar interiors. We conclude by discussing future developments.