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Asteroseismology using space-based telescopes is vital to our understanding of stellar structure and evolution. CoRoT, Kepler , and TESS space telescopes have detected large numbers of solar-like oscillating evolved stars. Solar-like oscillation frequencies have an important role in the determination of fundamental stellar parameters; in the literature, the relations between the two is established by the so-called scaling relations. In this study, we analyse data obtained from the observation of 15 evolved solar-like oscillating stars using the Kepler and ground-based telescopes. The main purpose of the study is to determine very precisely the fundamental parameters of evolved stars by constructing interior models using asteroseismic parameters. We also fit the reference frequencies of models to the observational reference frequencies caused by the He  ii ionization zone. The 15 evolved stars are found to have masses and radii within ranges of 0.79–1.47 M⊙ and 1.60–3.15 R ⊙, respectively. Their model ages range from 2.19 to 12.75 Gyr. It is revealed that fitting reference frequencies typically increase the accuracy of asteroseismic radius, mass, and age. The typical uncertainties of mass and radius are ∼3–6 and ∼1–2 per cent, respectively. Accordingly, the differences between the model and literature ages are generally only a few Gyr. [ABSTRACT FROM AUTHOR]

Recently, by analysing the oscillation frequencies of 90 stars, Yıldız, Çelik Orhan & Kayhan have shown that the reference frequencies (νmin0, νmin1, and νmin2) derived from glitches due to He  ii ionization zone have very strong diagnostic potential for the determination of their effective temperatures. In this study, we continue to analyse the same stars and compute their mass, radius, and age from different scaling relations including relations based on νmin0, νmin1, and νmin2. For most of the stars, the masses computed using νmin0 and νmin1 are very close to each other. For 38 stars, the difference between these masses is less than 0.024 M |$\odot$| . The radii of these stars from νmin0 and νmin1 are even closer, with differences of less than 0.007 R |$\odot$| . These stars may be the most well known solar-like oscillating stars and deserve to be studied in detail. The asteroseismic expressions we derive for mass and radius show slight dependence on metallicity. We therefore develop a new method for computing initial metallicity from this surface metallicity by taking into account the effect of microscopic diffusion. The time dependence of initial metallicity shows some very interesting features that may be important for our understanding of chemical enrichment of Galactic Disc. According to our findings, every epoch of the disc has its own lowest and highest values for metallicity. It seems that rotational velocity is inversely proportional to 1/2 power of age as given by the Skumanich relation. [ABSTRACT FROM AUTHOR]

So-called scaling relations based on oscillation frequencies have the potential to reveal the mass and radius of solar-like oscillating stars. In the derivation of these relations, it is assumed that the first adiabatic exponent at the surface (Γ1s) of such stars is constant. However, by constructing interior models for the mass range 0.8-1.6 M⊙, we show that 1s is not constant at stellar surfaces for the effective temperature range with which we deal. Furthermore, the well-known relation between large separation and mean density also depends on Γ1s. Such knowledge is the basis for our aim of modifying the scaling relations. There are significant differences between masses and radii found from modified and conventional scaling relations. However, a comparison of predictions of these relations with the non-asteroseismic observations of Procyon A reveals that new scaling relations are effective in determining the mass and radius of stars. In the present study, solar-like oscillation frequencies of 89 target stars (mostly Kepler and CoRoT) were analysed. As well as two new reference frequencies (νmin1 and νmin2) found in the spacing of solar-like oscillation frequencies of stellar interior models, we also take into account νmin0. In addition to the frequency of maximum amplitude, these frequencies have a very strong diagnostic potential in the determination of fundamental properties. The present study applies the derived relations from the models to the solar-like oscillating stars, and computes their effective temperatures using purely asteroseismic methods. There are in general very close agreements between effective temperatures from asteroseismic and nonasteroseismic (spectral and photometric) methods. For the Sun and Procyon A, for example, the agreement is almost total. [ABSTRACT FROM AUTHOR]