Generation of internal gravity waves by penetrative convection

Context. The rich harvest of seismic observations over the past decade provides evidence of angular momentum redistribution in stellar interiors that is not reproduced by current evolution codes. In this context, transport by internal gravity waves can play a role and could explain discrepancies between theory and observations.
Aims: The efficiency of the transport of angular momentum by waves depends on their driving mechanism. While excitation by turbulence throughout the convective zone has already been investigated, we know that penetrative convection into the stably stratified radiative zone can also generate internal gravity waves. Therefore, we aim at developing a semianalytical model to estimate the generation of IGW by penetrative plumes below an upper convective envelope. The formalism is developed with the purpose of being implemented in 1D stellar evolution codes.
Methods: We derive the wave amplitude considering the pressure exerted by an ensemble of plumes on the interface between the radiative and convective zones as source term in the equation of momentum. We consider the effect of a thermal transition from a convective gradient to a radiative one on the transmission of the wave into the radiative zone. The plume-induced wave energy flux at the top of the radiative zone is computed for a solar model and is compared to the turbulence-induced one.
Results: We show that, for the solar case, penetrative convection generates waves more efficiently than turbulence and that plume-induced waves can modify the internal rotation rate on shorter time scales. The result is solid since it holds despite a wide range of values considered for the parameters of the model. We also show that a smooth thermal transition significatively enhances the wave transmission compared to the case of a steep transition.
Conclusions: Driving by penetrative convection must be taken into account as much as turbulence-induced waves for the transport of internal angular momentum. We propose a simple prescription that has the advantage of being easily implementable into 1D stellar evolution codes. We expect this mechanism to work in evolved stars, which will be subject to future investigations.