Comprehensive stellar seismic analysis

Aims: We develop a method that provides a comprehensive analysis of the oscillation spectra of solar-like pulsators. We define new seismic indicators that should be
as uncorrelated and as precise as possible and should hold detailed information about stellar interiors. This is essential to improve the quality of the results obtained
from asteroseismology as it will provide better stellar models which in turn can be used to refine inferences made in exoplanetology and galactic archeology.
Method: The presented method – WhoSGlAd – relies on Gram-Schmidt’s orthogonalisation process. A Euclidean vector subspace of functions is defined and the
oscillation frequencies are projected over an orthonormal basis in a specific order. This allows the obtention of independent coefficients that we combine to define
independent seismic indicators.
Results: The developed method has been shown to be stable and to converge efficiently for solar-like pulsators. Thus, detailed and precise inferences can be obtained
on the mass, the age, the chemical composition and the undershooting in the interior of the studied stars. However, attention has to be paid when studying the helium
glitch as there seems to be a degeneracy between the influence of the helium abundance and that of the heavy elements on the glitch amplitude. As an example, we
analyse the 16CygA (HD 186408) oscillation spectrum to provide an illustration of the capabilities of the method.