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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., Comment: 5 pages, 4 figures, published in A&A

Context. Asteroseismic studies showed that cores of post main-sequence stars rotate slower than theoretically predicted by stellar models with purely hydrodynamical transport processes. Recent studies on main sequence stars, particularly Gamma Doradus ($\gamma$ Dor) stars, revealed their internal rotation rate for hundreds of stars, offering a counterpart on the main sequence for studies of angular momentum transport. Aims. We investigate whether such a disagreement between observed and predicted internal rotation rates is present in main sequence stars by studying angular momentum transport in $\gamma$ Dor stars. Furthermore, we test whether models of rotating stars with internal magnetic fields can reproduce their rotational properties. Methods. We compute rotating models with the Geneva stellar evolution code taking into account meridional circulation and the shear instability. We also compute models with internal magnetic fields using a general formalism for transport by the Tayler-Spruit dynamo. We then compare these models to observational constraints for $\gamma$ Dor stars that we compiled from the literature, combining so the core rotation rates, projected rotational velocities from spectroscopy, and constraints on their fundamental parameters. Results. We show that combining the different observational constraints available for $\gamma$ Dor stars enable to clearly distinguish the different scenarios for internal angular momentum transport. Stellar models with purely hydrodynamical processes are in disagreement with the data whereas models with internal magnetic fields can reproduce both core and surface constraints simultaneously. Conclusions. Similarly to results obtained for subgiant and red giant stars, angular momentum transport in radiative regions of $\gamma$ Dor stars is highly efficient, in good agreement with predictions of models with internal magnetic fields., Comment: Accepted for publication in Astronomy & Astrophysics. 16 pages, 17 figures, 1 appendix

Asteroseismic measurements of the internal rotation rate in evolved stars pointed out to a lack of angular momentum (AM) transport in stellar evolution models. Several physical processes in addition to hydrodynamical ones were proposed as candidates for the missing mechanism. Nonetheless, no current candidate can satisfy all the constraints provided by asteroseismology. We revisit the role of a candidate process whose efficiency scales with the contrast between the rotation rate of the core and the surface which was proposed to be related to the azimuthal magneto-rotational instability (AMRI) by Spada et al. We compute stellar evolution models of low- and intermediate-mass stars with the parametric formulation of AM transport proposed by Spada et al. until the end of the core-helium burning for low- and intermediate-mass stars and compare our results to the latest asteroseismic constraints available in the post main sequence phase. Both hydrogen-shell burning stars in the red giant branch and core-helium burning stars of low- and intermediate-mass in the mass range $1 M_{\odot} \lesssim M \lesssim 2.5 M_{\odot}$ can be simultaneously reproduced by this kind of parametrisation. Given current constraints from asteroseismology, the core rotation rate of post-main sequence stars seems to be well explained by a process whose efficiency is regulated by the internal degree of differential rotation in radiative zones., Comment: Accepted for publication in Astronomy & Astrophysics. 10 pages, 10 figures, 1 appendix

Thanks to asteroseismology, constraints on the core rotation rate are available for hundreds of low- and intermediate-mass stars in evolved phases. Current physical processes tested in stellar evolution models cannot reproduce the evolution of these core rotation rates. We investigate the efficiency of the internal angular momentum redistribution in red giants during the hydrogen shell and core-helium burning phases based on the asteroseismic determinations of their core rotation rates. We compute stellar evolution models with rotation and model the transport of angular momentum by the action of a sole dominant diffusive process parametrized by an additional viscosity. We constrain the values of this viscosity to match the mean core rotation rates of red giants and their behaviour with mass and evolution along the red giant branch and in the red clump. For red giants in the hydrogen shell-burning phase the transport of angular momentum must be more efficient in more massive stars. The additional viscosity is found to vary by approximately two orders of magnitude in the mass range M $\sim$ 1 - 2.5 M$_{\odot}$. As stars evolve along the red giant branch, the efficiency of the internal transport of angular momentum must increase for low-mass stars (M $\lesssim$ 2 M$_{\odot}$) and remain approximately constant for slightly higher masses (2.0 M$_{\odot}$ $\lesssim$ M $\lesssim$ 2.5 M$_{\odot}$). In red-clump stars, the additional viscosities must be an order of magnitude higher than in younger red giants of similar mass during the hydrogen shell-burning phase. In combination with previous efforts, we obtain a clear picture of how the physical processes acting in stellar interiors should redistribute angular momentum from the end of the main sequence until the core-helium burning phase for low- and intermediate-mass stars to satisfy the asteroseismic constraints., Comment: 10 pages, 12 figures, 1 table. Accepted for publication in A&A