Open issues in probing interiors of solar-like oscillating main sequence stars: 2. Diversity in the HR diagram

We review some major open issues in the current modelling of low and intermediate mass, main sequence stars based on seismological studies. The solar case was discussed in a companion paper, here several issues specific to other stars than the Sun are illustrated with a few stars observed with CoRoT and expectations from Kepler data.Comment: GONG 2010 - SoHO 24, A new era of seismology of the Sun and solar-like stars, To be published in the Journal of Physics: Conference Series (JPCS

Estimating stellar mean density through seismic inversions

Determining the mass of stars is crucial both to improving stellar evolution theory and to characterising exoplanetary systems. Asteroseismology offers a promising way to estimate stellar mean density. When combined with accurate radii determinations, such as is expected from GAIA, this yields accurate stellar masses. The main difficulty is finding the best way to extract the mean density from a set of observed frequencies. We seek to establish a new method for estimating stellar mean density, which combines the simplicity of a scaling law while providing the accuracy of an inversion technique. We provide a framework in which to construct and evaluate kernel-based linear inversions which yield directly the mean density of a star. We then describe three different inversion techniques (SOLA and two scaling laws) and apply them to the sun, several test cases and three stars. The SOLA approach and the scaling law based on the surface correcting technique described by Kjeldsen et al. (2008) yield comparable results which can reach an accuracy of 0.5 % and are better than scaling the large frequency separation. The reason for this is that the averaging kernels from the two first methods are comparable in quality and are better than what is obtained with the large frequency separation. It is also shown that scaling the large frequency separation is more sensitive to near-surface effects, but is much less affected by an incorrect mode identification. As a result, one can identify pulsation modes by looking for an l and n assignment which provides the best agreement between the results from the large frequency separation and those from one of the two other methods. Non-linear effects are also discussed as is the effects of mixed modes. In particular, it is shown that mixed modes bring little improvement as a result of their poorly adapted kernels.Comment: Accepted for publication in A&A, 20 pages, 19 figure

Evidence for a temperature-induced spin-state transition of Co3+ in La2-xSrxCoO4

We study the magnetic susceptibility of mixed-valent La2-xSrxCoO4 single crystals in the doping range of 0.5<= x <= 0.8 for temperatures up to 1000 K. The magnetism below room temperature is described by paramagnetic Co2+ in the high-spin state and by Co3+ in the non-magnetic low-spin state. Above room temperature, an increase in susceptibility compared to the behavior expected from Co2+ is seen, which we attribute to a spin-state transition of Co3+. The susceptibility is analyzed by comparison to full-multiplet calculations for the thermal population of the high- and intermediate-spin states of Co3+

Oscillation mode frequencies of 61 main sequence and subgiant stars observed by Kepler

Solar-like oscillations have been observed by Kepler and CoRoT in several solar-type stars, thereby providing a way to probe the stars using asteroseismology. We provide the mode frequencies of the oscillations of various stars required to perform a comparison with those obtained from stellar modelling. We used a time series of nine months of data for each star. The 61 stars observed were categorised in three groups: simple, F-like and mixed-mode. The simple group includes stars for which the identification of the mode degree is obvious. The F-like group includes stars for which the identification of the degree is ambiguous. The mixed-mode group includes evolved stars for which the modes do not follow the asymptotic relation of low-degree frequencies. Following this categorisation, the power spectra of the 61 main sequence and subgiant stars were analysed using both maximum likelihood estimators and Bayesian estimators, providing individual mode characteristics such as frequencies, linewidths, and mode heights. We developed and describe a methodology for extracting a single set of mode frequencies from multiple sets derived by different methods and individual scientists. We report on how one can assess the quality of the fitted parameters using the likelihood ratio test and the posterior probabilities. We provide the mode frequencies of 61 stars (with their 1-sigma error bars), as well as their associated echelle diagrams.Comment: 83 pages, 17 figures, 61 tables, paper accepted by Astronomy and Astrophysic

Butterfly diagram of a Sun-like star observed using asteroseismology

Stellar magnetic fields are poorly understood but are known to be important for stellar evolution and exoplanet habitability. They drive stellar activity, which is the main observational constraint on theoretical models for magnetic field generation and evolution. Starspots are the main manifestation of the magnetic fields at the stellar surface. In this study we measure the variation of their latitude with time, called a butterfly diagram in the solar case, for the solar analogue HD 173701 (KIC 8006161). To that effect, we use Kepler data, to combine starspot rotation rates at different epochs and the asteroseismically determined latitudinal variation of the stellar rotation rates. We observe a clear variation of the latitude of the starspots. It is the first time such a diagram is constructed using asteroseismic data.Comment: 8 pages, 4 figures, accepted in A&A Letter

The CoRoT target HD 49933: 2- Comparison of theoretical mode amplitudes with observations

From the seismic data obtained by CoRoT for the star HD 49933 it is possible, as for the Sun, to constrain models of the excitation of acoustic modes by turbulent convection. We compare a stochastic excitation model described in Paper I (arXiv:0910.4027) with the asteroseismology data for HD 49933, a star that is rather metal poor and significantly hotter than the Sun. Using the mode linewidths measured by CoRoT for HD 49933 and the theoretical mode excitation rates computed in Paper I, we derive the expected surface velocity amplitudes of the acoustic modes detected in HD 49933. Using a calibrated quasi-adiabatic approximation relating the mode amplitudes in intensity to those in velocity, we derive the expected values of the mode amplitude in intensity. Our amplitude calculations are within 1-sigma error bars of the mode surface velocity spectrum derived with the HARPS spectrograph. The same is found with the mode amplitudes in intensity derived for HD 49933 from the CoRoT data. On the other hand, at high frequency, our calculations significantly depart from the CoRoT and HARPS measurements. We show that assuming a solar metal abundance rather than the actual metal abundance of the star would result in a larger discrepancy with the seismic data. Furthermore, calculations that assume the ``new'' solar chemical mixture are in better agreement with the seismic data than those that assume the ``old'' solar chemical mixture. These results validate, in the case of a star significantly hotter than the Sun and Alpha Cen A, the main assumptions in the model of stochastic excitation. However, the discrepancies seen at high frequency highlight some deficiencies of the modelling, whose origin remains to be understood.Comment: 8 pages, 3 figures (B-W and color), accepted for publication in Astronomy & Astrophysics. Corrected typo in Eq. (4). Updated references. Language improvement

Asteroseismic detection of latitudinal differential rotation in 13 Sun-like stars

The differentially rotating outer layers of stars are thought to play a role in driving their magnetic activity, but the underlying mechanisms that generate and sustain differential rotation are poorly understood. We report the measurement of latitudinal differential rotation in the convection zones of 40 Sun-like stars using asteroseismology. For the most significant detections, the stars' equators rotate approximately twice as fast as their mid-latitudes. The latitudinal shear inferred from asteroseismology is much larger than predictions from numerical simulations.Comment: 45 pages, 11 figures, 4 tables, published in Scienc

The underlying physical meaning of the νmax−νc\nu_{\rm max}-\nu_{\rm c} relation

Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum ($\nu_{\rm max}$) of solar-like oscillations and the cut-off frequency ($\nu_{\rm c}$). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called \emph{plateau} of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between $\nu_{\rm max}$ and $\nu_{\rm c}$, with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter.Comment: 8 pages, 11 figures. Accepted in A&