Stochastic excitation of nonradial modes II. Are solar asymptotic gravity modes detectable?

Detection of solar gravity modes remains a major challenge to our understanding of the innerparts of the Sun. Their frequencies would enable the derivation of constraints on the core physical properties while their amplitudes can put severe constraints on the properties of the inner convective region. Our purpose is to determine accurate theoretical amplitudes of solar g modes and estimate the SOHO observation duration for an unambiguous detection. We investigate the stochastic excitation of modes by turbulent convection as well as their damping. Input from a 3D global simulation of the solar convective zone is used for the kinetic turbulent energy spectrum. Damping is computed using a parametric description of the nonlocal time-dependent convection-pulsation interaction. We then provide a theoretical estimation of the intrinsic, as well as apparent, surface velocity. Asymptotic g-mode velocity amplitudes are found to be orders of magnitude higher than previous works. Using a 3D numerical simulation, from the ASH code, we attribute this to the temporal-correlation between the modes and the turbulent eddies which is found to follow a Lorentzian law rather than a Gaussian one as previously used. We also find that damping rates of asymptotic gravity modes are dominated by radiative losses, with a typical life-time of $3 times 10^5$ years for the $ell=1$ mode at $ u=60 mu$Hz. The maximum velocity in the considered frequency range (10-100 $mu$Hz) is obtained for the $ell=1$ mode at $ u=60 mu$Hz and for the $ell=2$ at $ u=100 mu$Hz. Due to uncertainties in the modeling, amplitudes at maximum i.e. for $ell=1$ at 60 $mu$Hz can range from 3 to 6 mm s$^{-1}$.

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-($ell$) 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 $ell$; the power supplied to the oscillations depends on the mode inertia. - for low-$n$ modes, independent of the value of $ell$, the excitation is dominated by the non-diagonal components of the Reynolds stress term. We carried out a numerical investigation of high-$ell$ $p$ modes and we find that the validity of the present formalism is limited to $ell < 500$ due to the spatial separation of scale assumption. Thus, a model for very high-$ell$ $p$-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.