Stochastic excitation of non-radial modes I. High-angular-degree p modes

Turbulent motions in stellar convection zones generate acoustic energy, part of which is then supplied to normal modes of the star. Their amplitudes result from a balance between the efficiencies of excitation and damping processes in the convection zones. We develop a formalism that provides the excitation rates of non-radial global modes excited by turbulent convection. As a first application, we estimate the impact of non-radial effects on excitation rates and amplitudes of high-angular-degree modes which are observed on the Sun. A model of stochastic excitation by turbulent convection has been developed to compute the excitation rates, and it has been successfully applied to solar radial modes (Samadi & Goupil 2001, Belkacem et al. 2006b). We generalize this approach to the case of non-radial global modes. This enables us to estimate the energy supplied to high-($\mathrm{\ell }$) acoustic modes. Qualitative arguments as well as numerical calculations are used to illustrate the results. We find that non-radial effects for $p$ modes are non-negligible:

• for high-$n$ modes (i.e. typically $n>3$) and for high values of $\mathrm{\ell }$; the power supplied to the oscillations depends on the mode inertia.
• for low-$n$ modes, independent of the value of $\mathrm{\ell }$, the excitation is dominated by the non-diagonal components of the Reynolds stress term. We carried out a numerical investigation of high-$\mathrm{\ell }$ $p$ modes and we find that the validity of the present formalism is limited to $\mathrm{\ell }<500$ due to the spatial separation of scale assumption. Thus, a model for very high-$\mathrm{\ell }$ $p$-mode excitation rates calls for further theoretical developments, however the formalism is valid for solar $g$ modes, which will be investigated in a paper in preparation.