Excitation of stellar p-modes by turbulent convection: 1. Theoretical formulation

Stochatic excitation of stellar oscillations by turbulent convection is investigated and an expression for the power injected into the oscillations by the turbulent convection of the outer layers is derived which takes into account excitation through turbulent Reynolds stresses and turbulent entropy fluctuations. This formulation generalizes results from previous works and is built so as to enable investigations of various possible spatial and temporal spectra of stellar turbulent convection. For the Reynolds stress contribution and assuming the Kolmogorov spectrum we obtain a similar formulation than those derived by previous authors. The entropy contribution to excitation is found to originate from the advection of the Eulerian entropy fluctuations by the turbulent velocity field. Numerical computations in the solar case in a companion paper indicate that the entropy source term is dominant over Reynold stress contribution to mode excitation, except at high frequencies.Comment: 14 pages, accepted for publication in A&

Excitation of non-radial stellar oscillations by gravitational waves: a first model

The excitation of solar and solar-like g modes in non-relativistic stars by arbitrary external gravitational wave fields is studied starting from the full field equations of general relativity. We develop a formalism that yields the mean-square amplitudes and surface velocities of global normal modes excited in such a way. The isotropic elastic sphere model of a star is adopted to demonstrate this formalism and for calculative simplicity. It is shown that gravitational waves solely couple to quadrupolar spheroidal eigenmodes and that normal modes are only sensitive to the spherical component of the gravitational waves having the same azimuthal order. The mean-square amplitudes in case of stationary external gravitational waves are given by a simple expression, a product of a factor depending on the resonant properties of the star and the power spectral density of the gravitational waves' spherical accelerations. Both mean-square amplitudes and surface velocities show a characteristic R^8-dependence (effective R^2-dependence) on the radius of the star. This finding increases the relevance of this excitation mechanism in case of stars larger than the Sun.Comment: 8 pages, to be published in MNRAS (in press); corrected typo

Period spacings in red giants II. Automated measurement

The space missions CoRoT and Kepler have provided photometric data of unprecedented quality for asteroseismology. A very rich oscillation pattern has been discovered for red giants, including mixed modes that are used to decipher the red giants interiors. They carry information on the radiative core of red giant stars and bring strong constraints on stellar evolution. Since more than 15,000 red giant light curves have been observed by Kepler, we have developed a simple and efficient method for automatically characterizing the mixed-mode pattern and measuring the asymptotic period spacing. With the asymptotic expansion of the mixed modes, we have revealed the regularity of the gravity-mode pattern. The stretched periods were used to study the evenly space periods with a Fourier analysis and to measure the gravity period spacing, even when rotation severely complicates the oscillation spectra. We automatically measured gravity period spacing for more than 6,100 Kepler red giants. The results confirm and extend previous measurements made by semi-automated methods. We also unveil the mass and metallicity dependence of the relation between the frequency spacings and the period spacings for stars on the red giant branch. The delivery of thousands of period spacings combined with all other seismic and non-seismic information provides a new basis for detailed ensemble asteroseismology.Comment: 13 pages, 13 figure

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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.Comment: 12 pages, accepted for publication in A&

Excitation of solar-like oscillations across the HR diagram

We extend semi-analytical computations of excitation rates for solar oscillation modes to those of other solar-like oscillating stars to compare them with recent observations. Numerical 3D simulations of surface convective zones of several solar-type oscillating stars are used to characterize the turbulent spectra as well as to constrain the convective velocities and turbulent entropy fluctuations in the uppermost part of the convective zone of such stars. These constraints, coupled with a theoretical model for stochastic excitation, provide the rate 'P' at which energy is injected into the p-modes by turbulent convection. These energy rates are compared with those derived directly from the 3D simulations. The excitation rates obtained from the 3D simulations are systematically lower than those computed from the semi-analytical excitation model. We find that Pmax, the excitation rate maximum, scales as (L/M)^s where s is the slope of the power law and L and M are the mass and luminosity of the 1D stellar model built consistently with the associated 3D simulation. The slope is found to depend significantly on the adopted form of the eddy time-correlation ; using a Lorentzian form results in s=2.6, whereas a Gaussian one gives s=3.1. Finally, values of Vmax, the maximum in the mode velocity, are estimated from the computed power laws for Pmax and we find that Vmax increases as (L/M)^sv. Comparisons with the currently available ground-based observations show that the computations assuming a Lorentzian eddy time-correlation yield a slope, sv, closer to the observed one than the slope obtained when assuming a Gaussian. We show that the spatial resolution of the 3D simulations must be high enough to obtain accurate computed energy rates.Comment: 14 pages ; 7 figures ; accepted for publication in Astrophysics & Astronom

Solar-like oscillation amplitudes and line-widths as a probe for turbulent convection in stars

Excitation of solar-like oscillations is attributed to turbulent convection and takes place at the upper-most part of the outer convective zones. Amplitudes of these oscillations depend on the efficiency of the excitation processes as well as on the properties of turbulent convection. We present past and recent improvements on the modeling of those processes. We show how the mode amplitudes and mode line-widths can bring information about the turbulence in the specific cases of the Sun and Alpha Cen A.Comment: 9 pages ; 3 figures ; invited talk given during the Symposium no. 239 "Convection in Astrophysics", International Astronomical Union., held 21-25 August, 2006 in Prague, Czech Republi