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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]

The large separations between the oscillation frequencies of solar-like stars are measures of stellar mean density. The separations have been thought to be mostly constant in the observed range of frequencies. However, detailed investigation shows that they are not constant, and their variations are not random but have very strong diagnostic potential for our understanding of stellar structure and evolution. In this regard, frequencies of the minimum large separation are very useful tools. From these frequencies, in addition to the large separation and frequency of maximum amplitude, Yıldız et al. recently have developed new methods to find almost all the fundamental stellar properties. In the present study, we aim to find metallicity and helium abundances from the frequencies, and generalize the relations given by Yıldız et al. for a wider stellar mass range and arbitrary metallicity (Z) and helium abundance (Y). We show that the effect of metallicity is significant for most of the fundamental parameters. For stellar mass, for example, the expression must be multiplied by (Z/Z⊙)0.12. For arbitrary helium abundance, M ∝ (Y/Y⊙)0.25. Methods for determination of Z and Y from pure asteroseismic quantities are based on amplitudes (differences between maximum and minimum values of Δν) in the oscillatory component in the spacing of oscillation frequencies. Additionally, we demonstrate that the difference between the first maximum and the second minimum is very sensitive to Z. It also depends on νmin1/νmax and small separation between the frequencies. Such a dependence leads us to develop a method to find Z (and Y) from oscillation frequencies. The maximum difference between the estimated and model Z values is about 14 per cent. It is 10 per cent for Y. [ABSTRACT FROM AUTHOR]