Rotation in stellar interiors: General formulation and an asteroseismic-calibrated transport by the Tayler instability

Context: Asteroseismic measurements of the internal rotation of evolved stars indicate that at least one unknown efficient angular momentum (AM) transport mechanism is needed in stellar radiative zones. Aims: We investigate the impact of AM transport by the magnetic Tayler instability as a possible candidate for such a missing mechanism. Methods: We derived general equations for AM transport by the Tayler instability to be able to test different versions of the Tayler-Spruit (TS) dynamo. Results: These general equations highlight, in a simple way, the key role played by the adopted damping timescale of the azimuthal magnetic field on the efficiency of the resulting AM transport. Using this framework, we first show that the original TS dynamo provides an insufficient coupling in low-mass red giants that have a radiative core during the main sequence (MS), as was found previously for more massive stars that develop a convective core during the MS. We then derived a new calibrated version of the original TS dynamo and find that the damping timescale adopted for the azimuthal field in the original TS dynamo has to be increased by a factor of about 200 to correctly reproduce the core rotation rates of stars on the red giant branch (RGB). This calibrated version predicts no correlation of the core rotation rates with the stellar mass for RGB stars in good agreement with asteroseismic observations. Moreover, it correctly reproduces the core rotation rates of clump stars similarly to a revised prescription proposed recently. Interestingly, this new calibrated version of the TS dynamo is found to be in slightly better agreement with the core rotation rates of sub-giant stars, while simultaneously better accounting for the evolution of the core rotation rates along the RGB compared to the revised dynamo version. These results were obtained with both the Geneva and the MESA stellar evolution codes.