Fundamental properties of Kepler and CoRoT targets – IV. Masses and radii from frequencies of minimum Δν and their implications

Recently, by analysing the oscillation frequencies of 90 stars, Yildiz, \c{C}elik Orhan & Kayhan have shown that the reference frequencies ($\nu_{\rm min0}$, $\nu_{\rm min1}$ and $\nu_{\rm min2}$) derived from glitches due to He {\scriptsize 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 $\nu_{\rm min0}$, $\nu_{\rm min1}$ and $\nu_{\rm min2}$. For most of the stars, the masses computed using $\nu_{\rm min0}$ and $\nu_{\rm min1}$ are very close to each other. For 38 stars, the difference between these masses is less than 0.024 ${\rm M}_\odot$. The radii of these stars from $\nu_{\rm min0}$ and $\nu_{\rm min1}$ are even closer, with differences of less than 0.007 ${\rm R}_\odot$. 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.