Surface layer independent model fitting by phase matching: theory and application to HD49933 an HD177153 (aka Perky)

Aims. To describe the theory of surface layer independent model fitting by phase matching and to apply this to the stars HD49933 observed by CoRoT, and HD177153 (aka Perky), observed by Kepler Methods. We use theoretical analysis, phase shifts, and model fitting. Results. We define the inner and outer phase shifts of a frequency set of a model star and show that the outer phase shifts are (almost) independent of degree $\ell$, and that a function of the inner phase shifts (the phase function) collapses to an $\ell$ independent function of frequency in the outer layers. We then show how to use this result in a model fitting technique to find a best fit model to an observed frequency set by calculating the inner phase shifts of a model using the observed frequencies and determining the extent to which the phase function collapses to a single function of frequency in the outer layers. We give two examples applying this technique to the frequency sets of HD49933 observed by CoRoT and HD177153 (aka Perky) observed by Kepler, and compare our results with those of previous studies and show that they are compatible with those obtained using different techniques. We show that there can be many different models that fit the data within the errors and that better precision on the frequencies is needed to discriminate between the models. We compare this technique to that using the ratios of small to large separations, showing that in principle it is more accurate and avoids the problem of correlated errors in separation ratio fitting.Comment: 9 pages 15 figure

On the use of the average large separation in surface layer independent model fitting

The physics of the outer layers of a star are not well understood but these layers make a major contribution to the large separation. We quantify this using stellar models and show that the contribution ranges from 6\% from the outer 0.1\% of the radius to 30\% from the outer 5\%. and therefore argue that the large separation should not be used as a constraint on surface layer independent model fitting. The mass and luminosity are independent of the outer layers and can be used as constraints, the mass being determined from binarity or from surface gravity and radius. The radius can be used as a constraint but with enhanced error estimates. We briefly consider the determination of the large separation for $\alpha$ Cen A and find that mass derived from surface gravity is closer to the binary mass than that derived from the large separation.Comment: 4 pages, 6 figure

Anomalies in the Kepler Asteroseismic Legacy Project Data. A re-analysis of 16 Cyg A&B, KIC8379927 and 6 solar-like stars

I compare values of the frequencies, separation ratios, errors and covariance matrices from a new analysis of 9 solar-like stars with the Legacy project values reported by Lund et al and, for 16Cyg A&B and KIC8379927, with values derived by Davies et al. There is good agreement between my results (using Davies power spectra) and Davies's for these 3 stars, but no such agreement with the Legacy project results. My frequencies differ from the Legacy values, there are inconsistencies in the Legacy frequency covariance matrices which are not positive definite, and the Legacy errors on separation ratios are up to 40 times larger than mine and the values and upper limits derived from the Legacy frequency covariances. There are similar anomalies for 6 other solar-like stars: frequencies and separation ratio errors disagree and 2 have non positive definite covariance matrices. There are inconsistencies in the covariance matrices of 27 the 66 stars in the full Legacy set and problems with the ratio errors for the vast majority of these stars}Comment: 10 pages, 11 figure

On the use of the ratio of small to large separations in asteroseismic model fitting

Context. The use of ratios of small to large separations as a diagnostic of stellar interiors. Aims. To demonstrate that model fitting by comparing observed and model separation ratios at the same n values is in error, and to present a correct procedure. Methods. Theoretical analysis using phase shifts and numerical models. Results. We show that the separation ratios of stellar models with the same interior structure, but different outer layers, are not the same when compared at the same n values, but are the same when evaluated at the same frequencies by interpolation. The separation ratios trace the phase shift differences as a function of frequency not of n. We give examples from model fitting where the ratios at the same n values agree within the error estimates, but do not agree when evaluated at the same frequencies and the models do not have the same interior structure. The correct procedure is to compare observed ratios with those of models interpolated to the observed frequencies.Comment: 7 pages, 14 figures, 3 table

Inversions of Stellar Structure From Asteroseismic Data

peer reviewedThe advent of space-based photometry missions in the early 21st century enabled the application to asteroseismic data of advanced inference techniques until then restricted to the field of helioseismology. The high quality of the observations, the discovery of mixed modes in evolved solar-like oscillators and the need for an improvement in the determination of stellar fundamental parameters such as mass, radius and age led to the development of sophisticated modelling tools, amongst which seismic inversions play a key role. In this review, we will discuss the existing inversion techniques for the internal structure of distant stars adapted from helio-to asteroseismology. We will present results obtained for various Kepler targets, their coupling to other existing modelling techniques as well as the limitations of seismic analyses and the perspectives for future developments of these approaches in the context of the current TESS and the future PLATO mission, as well as the exploitation of the mixed modes observed in post-main sequence solar-like oscillators, for which variational formulations might not provide sufficient accuracy

CoRoT/ESTA-TASK 1 and TASK 3 comparison of the internal structure and seismic properties of representative stellar models: Comparisons between the ASTEC, CESAM, CLES, GARSTEC and STAROX codes

We compare stellar models produced by different stellar evolution codes for the CoRoT/ESTA project, comparing their global quantities, their physical structure, and their oscillation properties. We discuss the differences between models and identify the underlying reasons for these differences. The stellar models are representative of potential CoRoT targets. Overall we find very good agreement between the five different codes, but with some significant deviations. We find noticeable discrepancies (though still at the per cent level) that result from the handling of the equation of state, of the opacities and of the convective boundaries. The results of our work will be helpful in interpreting future asteroseismology results from CoRoT.Comment: 26 pages, 21 figures, accepted for publication in Astrophysics and Space Science, CoRoT/ESTA Volum

Detection of solar-like oscillations from Kepler photometry of the open cluster NGC 6819

Asteroseismology of stars in clusters has been a long-sought goal because the assumption of a common age, distance and initial chemical composition allows strong tests of the theory of stellar evolution. We report results from the first 34 days of science data from the Kepler Mission for the open cluster NGC 6819 -- one of four clusters in the field of view. We obtain the first clear detections of solar-like oscillations in the cluster red giants and are able to measure the large frequency separation and the frequency of maximum oscillation power. We find that the asteroseismic parameters allow us to test cluster-membership of the stars, and even with the limited seismic data in hand, we can already identify four possible non-members despite their having a better than 80% membership probability from radial velocity measurements. We are also able to determine the oscillation amplitudes for stars that span about two orders of magnitude in luminosity and find good agreement with the prediction that oscillation amplitudes scale as the luminosity to the power of 0.7. These early results demonstrate the unique potential of asteroseismology of the stellar clusters observed by Kepler.Comment: 5 pages, 4 figures, accepted by ApJ (Lett.