The robustness of inferred envelope and core rotation rates of red giant stars from asteroseismology

Context. Rotation is an important phenomenon influencing stellar structure and evolution, however, it has not been adequately modelled thus far. Therefore, accurate estimates of internal rotation rates are valuable for constraining stellar evolution models. Aims. We aim to assess the accuracy of asteroseismic estimates of internal rotation rates and how they depend on the fundamental stellar parameters. Methods. We applied the recently developed extended-multiplicative optimally localised averages (eMOLA) inversion method, to infer localised estimates of internal rotation rates of synthetic observations of red giants. We searched for suitable reference stellar models, following a grid-based approach, and we assessed the robustness of the resulting inferences with respect to the choice of reference model. Results. We find that matching the mixed-mode pattern between the observation and the reference model is an important criterion for selecting suitable reference models. We propose (i) selecting a set of reference models based on the correlation between the observed rotational splittings and the mode-trapping parameter; (ii) computing the rotation rates for all these models; and (iii) using the average value obtained across the whole set as the estimate of the internal rotation rates. We find that the effect of a near surface perturbation in the synthetic observations on the rotation rates estimated based on the correlation between the observed rotational splittings and the mode-trapping parameter is negligible. Conclusions. We conclude that when using an ensemble of reference models that are selected by matching the mixed-mode pattern, the input rotation rates can be recovered across a range of fundamental stellar parameters such as mass, mixing-length parameter, and composition. Further, red giant rotation rates determined in this way are also independent of any near-surface perturbation of the stellar structure.