Using seismic inversions to obtain an internal mixing processes indicator for main-sequence solar-like stars

Determining accurate and precise stellar ages is a major problem in astrophysics. These determinations are either obtained through empirical relations or model-dependent approaches. Currently, seismic modelling is one of the best ways of providing accurate ages. However, current methods are affected by simplifying assumptions concerning mixing processes. In this context, providing new structural indicators which are less model-dependent and more sensitive to such processes is crucial. We build a new indicator for core conditions on the main sequence, which should be more sensitive to structural differences and applicable to older stars than the indicator t presented in a previous paper. We also wish to analyse the importance of the number and type of modes for the inversion, as well as the impact of various constraints and levels of accuracy in the forward modelling process that is used to obtain reference models for the inversion. First, we present a method to obtain new structural kernels and use them to build an indicator of central conditions in stars and test it for various effects including atomic diffusion, various initial helium abundances and metallicities, following the seismic inversion method presented in our previous paper. We then study its accuracy for 7 different pulsation spectra including those of 16CygA and 16CygB and analyse its dependence on the reference model by using different constraints and levels of accuracy for its selection We observe that the inversion of the new indicator using the SOLA method provides a good diagnostic for additional mixing processes in central regions of stars. Its sensitivity allows us to test for diffusive processes and chemical composition mismatch. We also observe that octupole modes can improve the accuracy of the results, as well as modes of low radial order.Comment: Accepted for publication in Astronomy and Astrophysic

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&

Instability strips of main sequence B stars: a parametric study of iron enhancement

The discovery of beta Cephei stars in low metallicity environments, as well as the difficulty to theoretically explain the excitation of the pulsation modes observed in some beta Cephei and SPB stars, suggest that the iron opacity ``bump'' provided by standard models could be underestimated. We investigate, by means of a parametric study, the effect of a local iron enhancement on the location of the beta Cephei and SPB instability strips.Comment: 2 pages, to appear in the proceedings of "Vienna Workshop on the Future of Asteroseismology", September 20-22, 200

Constraints on the structure of 16 Cyg A and 16 Cyg B using inversion techniques

Constraining mixing processes and chemical composition is a central problem in stellar physics as their impact on stellar age determinations leads to biases in our studies of stellar evolution, galactic history and exoplanetary systems. In two previous papers, we showed how seismic inversion techniques could offer strong constraints on such processes by pointing out weaknesses in theoretical models. We now apply our technique to the solar analogues 16CygA and 16CygB, being amongst the best targets in the Kepler field to test the diagnostic potential of seismic inversions. The combination of various seismic indicators helps to provide more constrained and accurate fundamendal parameters for these stars. We use the latest seismic, spectroscopic and interferometric observational constraints in the litterature for this system to determine reference models independently for both stars. We carry out seismic inversions of the acoustic radius, the mean density and a core conditions indicator. We note that a degeneracy exists for the reference models. Namely, changing the diffusion coefficient or the chemical composition within the observational values leads to 5% changes in mass, 3% changes in radius and up to 8% changes in age. We use acoustic radius and mean density inversions to improve our reference models then carry out inversions for a core conditions indicator. Thanks to its sensitivity to microscopic diffusion and chemical composition mismatches, we are able to reduce the mass dispersion to 2%, namely [0.96, 1.0] M_sun, the radius dispersion to 1%, namely [1.188, 1.200] R_sun and the age dispersion to 3%, namely [7.0, 7.4] Gy, for 16CygA. For 16CygB, we can check the consistency of the models but not reduce independently the age dispersion. Nonetheless, assuming consistency with the age of 16CygA helps to further constrain its mass and radius.Comment: Submitted to Astronomy and Astrophysic

Instability strips of SPB and beta Cephei stars: the effect of the updated OP opacities and of the metal mixture

The discovery of $\beta$ Cephei stars in low metallicity environments, as well as the difficulty in theoretically explaining the excitation of the pulsation modes observed in some $\beta$ Cephei and hybrid SPB-$\beta$ Cephei pulsators, suggest that the ``iron opacity bump'' provided by stellar models could be underestimated. We analyze the effect of uncertainties in the opacity computations and in the solar metal mixture, on the excitation of pulsation modes in B-type stars. We carry out a pulsational stability analysis for four grids of main-sequence models with masses between 2.5 and 12 $\rm M_\odot$ computed with OPAL and OP opacity tables and two different metal mixtures. We find that in a typical $\beta$ Cephei model the OP opacity is 25% larger than OPAL in the region where the driving of pulsation modes occurs. Furthermore, the difference in the Fe mass fraction between the two metal mixtures considered is of the order of 20%. The implication on the excitation of pulsation modes is non-negligible: the blue border of the SPB instability strip is displaced at higher effective temperatures, leading to a larger number of models being hybrid SPB-$\beta$ Cephei pulsators. Moreover, higher overtone p-modes are excited in $\beta$ Cephei models and unstable modes are found in a larger number of models for lower metallicities, in particular $\beta$ Cephei pulsations are also found in models with Z=0.01.Comment: Accepted for publication in MNRAS Letter

Theoretical seismic properties of pre-main sequence gamma Doradus pulsators

Context. gamma Doradus (gamma Dor) are late A and F-type stars pulsating with high order gravity modes (g-modes). The existence of different evolutionary phases crossing the gamma Dor instability strip raises the question of the existence of pre-main sequence (PMS) gamma Dor stars. Aims. We intend to study the differences between the asteroseismic behaviour of PMS and main sequence (MS) gamma Dor pulsators as it is predicted by the current theory of stellar evolution and stability. Methods. We explore the adiabatic and non-adiabatic properties of high order g-modes in a grid of PMS and MS models covering the mass range 1.2 Msun < Mstar < 2.5 Msun. Results. We derive the theoretical instability strip (IS) for the PMS gamma Dor pulsators. This IS covers the same effective temperature range as the MS gamma Dor one. Nevertheless, the frequency domain of unstable modes in PMS models with a fully radiative core is larger than in MS models, even if they present the same number of unstable modes. Moreover, the differences between MS and PMS internal structures are reflected on the average values of the period spacing as well as on the dependence of the period spacing on the radial order of the modes, opening the window to the determination of the evolutionary phase of gamma Dor stars from their pulsation spectra.Comment: 9 pages, 17 figures, accepted for publication in A&

Can an underestimation of opacity explain B-type pulsators in the SMC?

Slowly Pulsating B and $\beta$ Cephei are $\kappa$ mechanism driven pulsating B stars. That $\kappa$ mechanism works since a peak in the opacity due to a high number of atomic transitions from iron-group elements occurs in the area of $\log T \approx 5.3$. Theoretical results predict very few SPBs and no $\beta$ Cep to be encountered in low metallicity environments such as the Small Magellanic Cloud. However recent variability surveys of B stars in the SMC reported the detection of a significant number of SPB and $\beta$ Cep candidates. Though the iron content plays a major role in the excitation of $\beta$ Cep and SPB pulsations, the chemical mixture representative of the SMC B stars such as recently derived does not leave room for a significant increase of the iron abundance in these stars. Whilst abundance of iron-group elements seems reliable, is the opacity in the iron-group elements bump underestimated? We determine how the opacity profile in B-type stars should change to excite SPB and $\beta$ Cep pulsations in early-type stars of the SMC.Comment: 5 pages, 7 figures, to appear under electronic form in : Proceedings of the 4th HELAS International Conference: Seismological Challenges for Stellar Structur

A new seismic analysis of Alpha Centauri

Models of alpha Cen A & B have been computed using the masses determined by Pourbaix et al. (2002) and the data derived from the spectroscopic analysis of Neuforge and Magain (1997). The seismological data obtained by Bouchy and Carrier (2001, 2002) do help improve our knowledge of the evolutionary status of the system. All the constraints are satisfied with a model which gives an age of about 6 Gyr for the binary.Comment: to be published in Astronomy and Astrophysic

Theoretical power spectra of mixed modes in low mass red giant stars

CoRoT and Kepler observations of red giant stars revealed very rich spectra of non-radial solar-like oscillations. Of particular interest was the detection of mixed modes that exhibit significant amplitude, both in the core and at the surface of the stars. It opens the possibility of probing the internal structure from their inner-most layers up to their surface along their evolution on the red giant branch as well as on the red-clump. Our objective is primarily to provide physical insight into the physical mechanism responsible for mixed-modes amplitudes and lifetimes. Subsequently, we aim at understanding the evolution and structure of red giants spectra along with their evolution. The study of energetic aspects of these oscillations is also of great importance to predict the mode parameters in the power spectrum. Non-adiabatic computations, including a time-dependent treatment of convection, are performed and provide the lifetimes of radial and non-radial mixed modes. We then combine these mode lifetimes and inertias with a stochastic excitation model that gives us their heights in the power spectra. For stars representative of CoRoT and Kepler observations, we show under which circumstances mixed modes have heights comparable to radial ones. We stress the importance of the radiative damping in the determination of the height of mixed modes. Finally, we derive an estimate for the height ratio between a g-type and a p-type mode. This can thus be used as a first estimate of the detectability of mixed-modes