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Asteroseismic large frequency separations possess great diagnostic value.However, their expressions as scaling relations are predicated on homologyarguments which may not hold in general, resulting in mass- andtemperature-dependent deviations. The first-order asymptotic expressions, whichshould in principle account for this structural evolution, also deviate morefrom fitted frequency-separation estimates than do the simple scalingrelations, and exhibit qualitatively different behavior. We present a modifiedasymptotic estimator, and show that these discrepancies can be accounted for bythe evolution of the acoustic turning points of the asteroseismic mode cavity,which is typically neglected in first-order asymptotic analysis. This permitsus to use a single expression to accurately estimate the large frequencyseparations of main-sequence, ascending red giant branch, and red clump stellarmodels, except at transition points between two asymptotic regimes during thesubgiant phase of evolution, where the WKB approach fails. The existence ofsuch transition points provides theoretical justification for separatelycalibrated scaling relations for stars in different evolutionary stages.

Explaining Deviations from the Scaling Relationship of the Large Frequency Separation