Stellar rotation formalisms of γ Doradus stars from gravity-mode period spacings

The oscillation frequencies of stars are used to constrain our theoretical models, from which we can derive stellar internal properties including rotation rates. The g-mode pulsations of γ Doradus stars are highly sensitive to the near-core regions. Two of the most common rotation formalisms, the second-order Perturbative Approach and the Traditional Approximation of Rotation, are compared to investigate their validity domains. We compute grids of 1-D γ Doradus models for (1,0) modes with the two rotation descriptions, using benchmark models instead of real stars to be the targets. Results show that the grids are generally capable of reproducing the benchmark to within observational uncertainties. However, the two formalisms disagree with each other at rotation rates beyond Omega/Omega_k=0.04. A method of distinguishing the formalisms without presupposing the stars’ rotation rates is successfully found: Their models diverge at periods longer than 2.5 days, given that the gradient of the period spacing is greater than -0.0122. The comparison results also reveal that our method of fitting period spacing series is not sufficient for taking rotational mixing effects fully into account. These findings offer potential for refining our current rotation theories with observational data, and contribute to the development of new techniques for improving modelling accuracies.