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Fundamental properties of Kepler and CoRoT targets: III. Tuning scaling relations using the first adiabatic exponent

So called scaling relations have the potential to reveal the mass and radius of solar-like oscillating stars, based on oscillation frequencies. In derivation of these relations, it is assumed that the first adiabatic exponent at the surface (Gamma_1s) of such stars is constant. However, by constructing interior models for the mass range 0.8-1.6 Msun, we show that Gamma_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 Gamma_1s. Such knowledge is the basis for our aim of modifying scaling relations. There are significant differences between masses and radii found from modified and conventional scaling relations. However, 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 (nu_min1 and nu_min2) found in the spacing of solar-like oscillation frequencies of stellar interior models, we also take into account nu_min0. In addition to the frequency of maximum amplitude, these frequencies have very strong diagnostic potential for determination of fundamental properties. The present study involves the application of 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 non-asteroseismic (spectral and photometric) methods. For the Sun and Procyon A, for example, the agreement is almost total.