Differential rotation, radiative equilibrium, and local hydrodynamic stability in stellar interiors

• Main Author: Caleo, Andrea
• Other Authors: Balbus, Stephen
• Published: University of Oxford 2016
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730197

The problem of angular momentum transport in the radiative zone of the Sun and other stars is currently one of the most discussed in stellar astrophysics. A wide range of local and global instabilities acting in differentially rotating stars have been studied and incorporated in stellar evolutionary codes. In this thesis, I revisit two of the hydrodynamic processes that are thought to operate, namely the Eddington-Sweet (ES) circulation and a global motion induced by the Goldreich-Schubert-Fricke (GSF) instability, and investigate stellar models in which these mechanisms are suppressed. In particular: The data from helioseismology show that the upper radiative zone of the Sun is in near-uniform rotation, but they have a significant uncertainty. I discuss the possibility of patterns of differential rotation compatible with the constraint of perfect radiative equilibrium, which implies the absence of ES circulation. I show that this constraint leads to a set of ordinary differential equations for the stellar rotation profile, which are solved numerically. I find that these models can be quite close to uniform rotation, and compatible with the data from helioseismology. I investigate the dynamical stability of these models. It is shown that while a naive approach would suggest that the GSF instability would distrupt the rotation of these stars, this does not happen in reality. I present a study of the local stability of stratified, weakly magnetized, differentially rotating uids to non-axisymmetric perturbations with finite heat conductivity, kinematic viscosity, and resistivity. The models are found to be locally stable under rather general circumstances. Even if the molecular viscosity is very small compared to the heat conductivity, it suffices to suppress the GSF instability. I examine the onset of the GSF instability in the core of red giant stars, where, according to recent observations, strong differential rotation may be present. I derive constraints on the amount of shear necessary for the GSF instability to operate at different depths, and show that very strong shear is required. In general, the effectiveness of the GSF instability in transporting angular momentum is currently overstated.