Stochastic excitation of waves in magnetic stars

Context. Stellar oscillations are key to unravelling stellar properties, such as their mass, radius, and age. This in turn enables us to date and characterize their exoplanetary systems. The amplitudes of acoustic (p-) modes in solar-like stars are intrinsically linked to their convective turbulent excitation source, which in turn is influenced by magnetism. In the observations of the Sun and stars, the mode amplitudes are modulated following their magnetic activity cycles: the higher the magnetic field, the lower the mode amplitudes. When the magnetic field is strong, it can even inhibit acoustic modes, which are not detected in most of the solar-like stars that are strongly magnetically active. Magnetic fields are known to freeze convection when they stronger than a critical value: the so-called on-off approach is used in the literature. Aims. We investigate the impact of magnetic fields on the stochastic excitation of acoustic modes. Methods. First, we generalise the forced-wave equation formalism, including the effects of magnetic fields. Second, we assess how convection is affected by magnetic fields using results from the magnetic mixing-length theory. Results. We provide the source terms of the stochastic excitation, including a new magnetic source term and the Reynolds stresses. We derive scaling laws for the mode amplitudes that take both the driving and the damping into account. These scalings are based on the inverse Alfvén dimensionless parameter: The damping increases with the magnetic field and reaches a saturation threshold when the magnetic field is strong. The driving of the modes diminishes when the magnetic field becomes stronger and the turbulent convection is weaker. Conculsions. As expected from the observations, we find that a stronger magnetic field diminishes the resulting mode amplitudes. The evaluation of the inverse Alfvén number in stellar models provides a means for estimating the expected amplitudes of acoustic modes in magnetically active solar-type stars.