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

TL;DR

This paper clarifies that in asteroseismic model fitting, separation ratios should be compared at the same frequencies, not at the same n values, to accurately diagnose stellar interior structures.

Contribution

It demonstrates the correct method for comparing separation ratios in asteroseismology, emphasizing interpolation at the same frequencies rather than at the same n values.

Findings

Ratios at same n values can be misleading for interior structure inference.

Comparison at the same frequencies accurately reflects interior differences.

Interpolation is essential for correct model fitting in asteroseismology.

Abstract

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.