What curves Δ𝜈?

Abstract

What curves Δ𝜈? S. Hekker, Y. Elsworth, S. Basu, F. Ahlborn, L. Buchele, F. Espinoza-Rojas Stars are to first order described as spheres of gas. They do however deviate somewhat from homogenous spheres of ideal gas and these deviations are imprinted in their normal oscillation modes. One of these imprinted features is that the large frequency separation, Δ𝜈, in solar-like oscillators is not constant: it is curved as a function of frequency. Two questions arise naturally 1) what in the structure of the star is responsible for this second order variation of Δ𝜈, and 2) how does the variation depend on global properties of the star like mass and age. We analyse a few thousand red-giant stars to derive empirical relations between 𝛼 (the curvature coefficient) and Δ𝜈. Comparing these empirical relations with those obtained from stellar evolution models shows that a) the 𝛼 - Δ𝜈 relation for red-giant branch stars is mass dependent, and b) that the 𝛼 - Δ𝜈 relations obtained from the models differ from the empirical ones. We also calculate sensitivity kernels for 𝛼 that allow us to determine the regions responsible for the curvature.This will provide important insights for improving the physics in our models and reconciling the difference between the empirical 𝛼 - Δ𝜈 relationships and those based on models.