Abstract
Context. Determining the properties of solar-like oscillating stars can be subject to many biases. A particularly important example is the helium-mass degeneracy, where the uncertainties regarding the internal physics can cause a poor determination of both the mass and surface helium content. Accordingly, an independent helium estimate is needed to overcome this degeneracy. A promising way to obtain such an estimate is to exploit the so-called ionisation glitch, that is, the deviation from the asymptotic oscillation frequency pattern caused by the rapid structural variation in the He ionisation zones. Aims. Although it is progressively becoming more sophisticated, the glitch-based approach faces problems inherent to its current modelling such as the need for calibration using realistic stellar models. This requires a physical model of the ionisation region that explicitly involves the parameters of interest, such as the surface helium abundance, Ys. Methods. Through a thermodynamic treatment of the ionisation region, an analytical approximation for the first adiabatic exponent Γ1 is presented. Results. The induced stellar structure is found to depend on only three parameters, including the surface helium abundance Ys and the electron degeneracy ψCZ in the convective region. The model thus defined allows a wide variety of structures to be described, and it is in particular able to approximate a realistic model in the ionisation region. The modelling work we conducted enables us to study the structural perturbations causing the glitch. More elaborate forms of perturbations than those that are usually assumed are found. It is also suggested that there might be a stronger dependence of the structure on the electron degeneracy in the convection zone and on the position of the ionisation region rather than on the amount of helium itself. Conclusions. When analysing the ionisation glitch signature, we emphasise the importance of having a relation that can take these additional dependences into account.
Highlights
Asteroseismology, i.e. the study of resonant modes in stars, reveals information on the physical properties of the layers that the wave passes through on its way to the surface
We propose a physical model of the ionisation region that allows us to derive a semi-analytic description of the structural perturbation caused by a change in abundances
We focused on introducing a physical model of the ionisation region that depends on only a few parameters in order to study its properties
Summary
Asteroseismology, i.e. the study of resonant modes in stars, reveals information on the physical properties of the layers that the wave passes through on its way to the surface. In the case of a large number of frequencies being available like that of the Sun, inversion techniques highlight significant discrepancies and solar models are forced to compromise between inconsistent abundances, densities or convective zone (CZ) depths (Basu & Antia 2004; Asplund et al 2009; Serenelli et al 2009) In addition to these processes directly involving the composition, one must face additional uncertainties surrounding the near-surface region, namely surface effects (Christensen-Dalsgaard et al 1988). This effect is not specific to the ionisation regions, the latter have benefited from numerous treatments, being both the most pronounced glitch and a potential marker of the helium abundance (Perez Hernandez & Christensen-Dalsgaard 1994; Lopes et al 1997) From this point on, many studies (Monteiro et al 1994; Basu et al 1994; Monteiro & Thompson 1998, 2005; Gough 2002; Houdek & Gough 2007) considered various shapes of structural perturbations to analytically derive the expected frequency shifts. The last part of the article will be dedicated to our conclusions
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