Estimating the helium glitch acoustic depth

Abstract

In the past decade, space missions, such the CoRoT, Kepler and TESS, have provided the asteroseismic community with a vast amount of observations, of unprecedented quality. This gave the opportunity to stellar astrophysicists, to study the stellar interiors of a large variety of pulsating stars. Amongst them, are the solar-like stars, that are low-mass main-sequence stars, reaching up to 2.3 Solar Masses. During the main-sequence phase, the solar-like stars are stable, and they present frequencies that are very regular, which is most obvious in a power spectrum. Nevertheless, there are some departures from that equidistance, to which we refer as the smooth part, and one of the reasons for that, are the glitches. The glitches are due to sharp variations, on the internal structure of the stars, which introduce an oscillatory feature, as a function of the frequency, in the oscillation spectrum. Solar-like stars experience mostly two glitches, the helium glitch, for which our study is about, and the convection zone glitch. The former is located in the second ionization zone of helium, quite close to the stellar surface, and the latter, is located in the transition region between the convective envelope and the radiation zone. The study of those glitches is important, because they provide information about their respective regions, which further helps constrain the internal structure of a star. The amplitude of the helium glitch, is directly linked to the helium abundance, in that area and, since that area is very close to the surface, and convection dominates there, it provides information about the surface helium abundance. This is the only way to obtain that value, because the stellar surface of solar-like stars, does not have the required temperature for the excitation of helium, and thus, few or no emission lines can be obtained spectroscopically. There exists a number of methods that use the observed frequencies, and derive seismic constraints, which are used to derive information about the stellar structure, through stellar modeling. The one that we used for our analysis, is the Whole Spectrum and Glitches Adjustment (WhoSGlAd). It uses both the smooth part of the spectrum, along with the glitches part, to derive seismic indicators, as little correlated as possible. The accuracy of those indicators, allows them to be used as constraints by minimization techniques, in order to retrieve precise values about global quantities, as is the mass, the age and the chemical composition. In the case of WhoSGlAd, one of the constraints that is used is the helium glitch amplitude, but for its value we need to know the helium acoustic depth. When we work with observations this value is not available and so, we have to derive it by a model, to estimate the helium acoustic depth, which takes time and it is inconvenient, since it makes the results model dependent. In this study, we propose a method, that uses a linear relation, in order to derive this acoustic depth, which uses only observed quantities and so, makes the procedure much faster. We prove the efficiency and the accuracy of that method, by using both models and observations. This means that it does not make any sacrifices in the precision of WhoSGlAd. Moreover, since this method is linear, and uses only observables, it can be implemented in already existing codes, and provide results much faster. The method, as a result of the assumed linear formulation, does not apply to cases that are not linear. This occurs in cases beyond the main sequence, or with convective cores. This can happen for example, for the case of stars ≥1.2 solar masses, for some chemical compositions.