Properties of the ionisation glitch II. Seismic signature of the structural perturbation

TL;DR

This paper develops a model-independent seismic method to analyze ionisation regions in stars, enabling estimation of helium abundance and other properties from oscillation frequency variations, with Bayesian inference and Gaussian processes to handle degeneracies and surface effects.

Contribution

It introduces a new seismic analysis technique that avoids stellar model calibration, using structural perturbations and Bayesian inference to estimate ionisation region properties.

Findings

Successful recovery of ionisation region properties from oscillation data.

Identification of degeneracy between helium abundance and electronic degeneracy.

Effective disentanglement of glitch signals from surface effects using Gaussian processes.

Abstract

In the present paper, we aim to constrain the properties of the ionisation region in a star from the oscillation frequency variation (a so-called glitch) caused by rapid structural variations in this very region. In particular, we seek to avoid the use of calibration based on stellar models thus providing a truly independent estimate of these properties. These include both the helium abundance and other physical quantities that can have a significant impact on the oscillation frequencies such as the electronic degeneracy parameter or the extent of the ionisation region. Taking as a starting point our first paper, we applied structural perturbations of the ionisation zone to the wave equation for radial oscillations in an isentropic region. The resulting glitch model is thus able to exploit the information contained in the fast frequency oscillation caused by the helium ionisation but also in the slow trend accompanying that of hydrogen. This information can directly be expressed in terms of parameters related respectively to the helium abundance, electronic degeneracy and extent of the ionisation region. Using a Bayesian inference, we show that a substantial recovery of the properties at the origin of the glitch is possible. A degeneracy between the helium abundance and the electronic degeneracy is found to exist, which particularly affects the helium estimate. Extending the method to cases where the glitch is subject to contamination (e.g. surface effects), we noted the importance of the slow glitch trend associated with hydrogen ionisation. We propose using a Gaussian process to disentangle the frequency glitch from surface effects.