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Abstract

Context. The wealth of asteroseismic data for red-giant stars and the precision with which these data have been observed over the last decade calls for investigations to further understand the internal structures of these stars.

Aim. The aim of this work is to validate a method to measure the underlying period spacing, coupling term, and mode offset of pure gravity modes that are present in the deep interiors of red-giant stars. We subsequently investigate the physical conditions of the evanescent zone between the gravity mode cavity and the pressure mode cavity.

Methods. We implement an alternative mathematical description compared to what is used in the literature to analyse observational data and to extract the underlying physical parameters that determine the frequencies of mixed modes. This description takes the radial order of the modes explicitly into account, which reduces its sensitivity to aliases. Additionally, and for the first time, this method allows us to constrain the gravity mode offset ϵg for red-giant stars.

Results. We find that this alternative mathematical description allows us to determine the period spacing ΔΠ and the coupling term q for the dipole modes within a few percent of values found in the literature. Additionally, we find that ϵg varies on a star-by-star basis and should not be kept fixed in the analysis. Furthermore, we find that the coupling factor is logarithmically related to the physical width of the evanescent region normalised by the radius at which the evanescent zone is located. Finally, the local density contrast at the edge of the core of red-giant branch models shows a tentative correlation with the offset ϵg.

Conclusions. We are continuing to exploit the full potential of the mixed modes to investigate the internal structures of red-giant stars; in this case we focus on the evanescent zone. It remains, however, important to perform comparisons between observations and models with great care as the methods employed are sensitive to the range of input frequencies.