THE RELATIONSHIP BETWEEN νmax AND AGE t FROM ZAMS TO RGB-TIP FOR LOW-MASS STARS

Stellar age is an important quantity in astrophysics, which is useful for many fields both in the universe and galaxies. It cannot be determined by direct measurements, but can only be estimated or inferred. We attempt to find a useful indicator of stellar age, which is accurate from the zero-age main sequence to the tip of red giant branch for low-mass stars. Using the Yale Rotation and Evolution Code (YREC), a grid of stellar models has been constructed. Meanwhile, the frequency of maximum oscillations' power νmax and the large frequency separation Δν are calculated using the scaling relations. For the stars, the masses of which are from 0.8 M☉ to 2.8 M☉, we can obtain the νmax and stellar age by combing the scaling relations with the four sets of grid models (YREC, Dotter et al., Marigo et al., and YY isochrones). We find that νmax is tightly correlated and decreases monotonically with the age of the star from the main sequence to the red giant evolutionary stages. Moreover, we find that the line shapes of the curves in the Age versus νmax diagram, which is plotted by the four sets of grid models, are consistent for red giants with masses from 1.1 M☉ to 2.8 M☉. For red giants, the differences of correlation coefficients between Age and νmax for different grid models are minor and can be ignored. Interestingly, we find two peaks that correspond to the subgiants and bump of red giants in the Age versus νmax diagram. By general linear least-squares, we make the polynomial fitting and deduce the relationship between log(Age) and log(νmax) in red giants' evolutionary state.