Frequency ratio method for seismic modeling ofγDoradus stars

Abstract

A method for obtaining asteroseismological information of a γ Doradus oscillating star showing at least three pulsation frequencies is presented. This method is based on a first-order asymptotic g -mode expression, in agreement with the internal structure of γ Doradus stars. The information obtained is twofold: 1) a possible identification of the radial order n and degree $\ell$ of observed frequencies (assuming that these have the same $\ell$), and 2) an estimate of the integral of the buoyancy frequency (Brunt-Vaisala) weighted over the stellar radius along the radiative zone. The accuracy of the method as well as its theoretical consistency are also discussed for a typical γ Doradus stellar model. Finally, the frequency ratios method has been tested with observed frequencies of the γ Doradus star HD 12901. The number of representative models verifying the complete set of constraints (the location in the HR diagram, the Brunt-Vaisala frequency integral, the observed metallicity and frequencies and a reliable identification of n and $\ell$) is drastically reduced to six.