Properties of the ionisation glitch

Aims. In the present paper, we aim to constrain the properties of the ionisation region of a star from the oscillation frequency variation (a so-called glitch) caused by rapid structural variations in this very region. In particular, we seek tof 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. Methods. Building on previous findings, 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 that in the slow trend accompanying the ionisation of hydrogen. This information can be directly expressed in terms of parameters related to the helium abundance, electronic degeneracy, and the extent of the ionisation region, respectively. Results. Using Bayesian inference, we show that substantial recovery of the properties at the origin of the glitch is possible. We find a degeneracy between the helium abundance and the electronic degeneracy, which particularly affects the helium estimate. Extending the method to cases where the glitch is subject to contamination (e.g., surface effects), we note the importance of the slow glitch trend associated with hydrogen ionisation. We propose the use of a Gaussian process to disentangle the frequency glitch from surface effects.