Fundamental properties of solar-like oscillating stars from frequencies of minimum $\Delta \nu$: I. Model computations for solar composition

TL;DR

This study reveals that the minima in the large frequency separation of solar-like oscillations, linked to the He II ionization zone, serve as precise diagnostics for determining fundamental stellar properties such as mass, radius, and age.

Contribution

It introduces a new method using minima in the large frequency separation to accurately infer stellar parameters and develops an asteroseismic diagram for stellar structure and evolution analysis.

Findings

Identified two minima in the large frequency separation linked to the He II ionization zone.

Established relations between these minima and stellar properties like mass and radius.

Developed a new asteroseismic diagram for predicting stellar structure and evolution.

Abstract

Low amplitude is the defining characteristic of solar-like oscillations. The space projects $Kepler$ and $CoRoT$ give us a great opportunity to successfully detect such oscillations in numerous targets. Achievements of asteroseismology depend on new discoveries of connections between the oscillation frequencies and stellar properties. In the previous studies, the frequency of the maximum amplitude and the large separation between frequencies were used for this purpose. In the present study, we confirm that the large separation between the frequencies has two minima at two different frequency values. These are the signatures of the He {\small II} ionization zone, and as such have very strong diagnostic potential. We relate these minima to fundamental stellar properties such as mass, radius, luminosity, age and mass of convective zone. For mass, the relation is simply based on the ratio of the frequency of minimum $\Delta \nu$ to the frequency of maximum amplitude. These frequency comparisons can be very precisely computed, and thus the mass and radius of a solar-like oscillating star can be determined to high precision. We also develop a new asteroseismic diagram which predicts structural and evolutionary properties of stars with such data. We derive expressions for mass, radius, effective temperature, luminosity and age in terms of purely asteroseismic quantities. For solar-like oscillating stars, we now will have five very important asteroseismic tools (two frequencies of minimum $\Delta \nu$, the frequency of maximum amplitude, and the large and small separations between the oscillation frequencies) to decipher properties of stellar interior astrophysics.