CONTEXT. Gamma Doradus stars (hereafter gamma Dor stars) are known to exhibit gravity- and/or gravito-intertial modes that probe the inner stellar region near the convective core boundary. The non-equidistant spacing of the pulsation periods is an observational signature of the stars evolution and current internal structure and is heavily influenced by rotation. AIMS. We aim to constrain the near-core rotation rates for a sample of gamma Dor stars, for which we have detected period spacing patterns. METHODS. We combined the asymptotic period spacing with the traditional approximation of stellar pulsation to fit the observed period spacing patterns using chi-squared optimisation. The method was applied to the observed period spacing patterns of a sample of stars and used for ensemble modelling. RESULTS. For the majority of stars with an observed period spacing pattern we successfully determined the rotation rates and the asymptotic period spacing values, though the uncertainty margins on the latter were typically large. This also resulted directly in the identification of the modes corresponding with the detected pulsation frequencies, which for most stars were prograde dipole gravity and gravito-inertial modes. The majority of the observed retrograde modes were found to be Rossby modes. We further discuss the limitations of the method due to the neglect of the centrifugal force and the incomplete treatment of the Coriolis force. CONCLUSION. Despite its current limitations, the proposed methodology was successful to derive the rotation rates and to identify the modes from the observed period spacing patterns. It forms the first step towards detailed seismic modelling based on observed period spacing patterns of moderately to rapidly rotating gamma Dor stars.
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