The Goldreich-Schubert-Fricke (GSF) instability is a rotational instability that is thought to contribute to the transfer of angular momentum in differentially rotating stars. It has been included in recent codes of stellar evolution in a diffusion-like approximation, under the assumption that the kinematic viscosity ν is unimportant for the development of the instability. As noted previously by other authors, for most stellar applications this may not be a valid approximation. We discuss this issue in detail, solving the dispersion relation of the perturbed modes for realistic values of ν in the bulk of the radiative zone of the Sun and of three red giant stars at various evolutionary stages. We find that the GSF instability is triggered only in layers of extremely strong shear. In a simple case study, we also investigate the effect of a small deviation from axisymmetry or a small background magnetic field. We find that, like the viscosity, these have a stabilising effect. We conclude that this instability is probably far less efficient in transporting angular momentum than is often assumed, and may not even be present.

It is well known that the combination of barotropic rotation and radiative equilibrium are mutually incompatible in stars. The Sun's internal rotation is far from barotropic, however, which allows at least the theoretical possibility that the Sun's thermal balance is one of radiative equilibrium in the region of the tachocline near the outer boundary of the radiative zone. We show here that (i) the constraint of radiative equilibrium leads to a straightforward ordinary differential equation for the Sun's rotation profile, and (ii) solutions of this equation can be found that, to within current levels of accuracy, closely resemble the rotation profile deduced from helioseismology. More generally, we calculate how large a baroclinic deviation from uniform rotation is required to maintain radiative equilibrium without meridional circulation throughout the bulk of the radiative zone. Very little deviation is required, well below detectability. The feasibility of radiative equilibrium for the tachocline suggests that the issue of a spreading boundary layer may be less severe than previously thought.

Barotropic rotation and radiative equilibrium are mutually incompatible in stars. The issue is often addressed by allowing for a meridional circulation, but this is not devoid of theoretical complications. Models of rotation in the Sun which maintain strict radiative equilibrium, making use of the observation that the Sun is not in a state of barotropic rotation, have recently been suggested. To investigate the dynamical behaviour of these solutions, we study the local stability of stratified, weakly magnetized, differentially rotating fluids to non-axisymmetric perturbations. Finite heat conductivity, kinematic viscosity, and resistivity are present. The evolution of local embedded perturbations is governed by a set of coupled, ordinary differential equations with time-dependent coefficients. Two baroclinic models of rotation for the upper radiative zone and tachocline are studied: (i) an interpolation based on helioseismology data, (ii) a theoretical solution directly compatible with radiative equilibrium. The growth of the local Goldreich-Schubert-Fricke instability appears to be suppressed, largely because of the viscosity. An extensive exploration of wavenumber space is carried out, with and without a magnetic field. Although we easily find classical local instabilities when they ought formally to be present, for the Sun the analysis reveals neither unstable solutions, nor even solutions featuring a large transient growth. We have not ruled out larger scale or nonlinear instabilities, nor have we rigorously proven local stability. But rotational configurations in close agreement with observations, generally thought to be vulnerable to the classic local Goldreich-Schubert-Fricke instability, do appear to be locally stable under rather general circumstances.

A distinguishing trait of the three known Galactic recurrent novae with the shortest orbital periods, T Pyx, IM Nor, and CI Aql, is that their optical decline time-scales are significantly longer than those of the other recurrent systems. On the other hand, some estimates of the mass of the ejecta, the velocity of the ejecta, and the duration of the soft X-rays emission of these systems are of the order of those of the other recurrent systems and the fast classical novae. We put forth a tentative explanation of this phenomenon. We propose that in these systems part of the material transferred from the companion during the first few days of the eruption remains within the Roche lobe of the white dwarf, preventing the radiation from ionizing the ejecta of the system and increasing the optical decline time-scale. We explain why this phenomenon is more likely in systems with a high mass transfer rate and a short orbital period. Finally, we present a schematic model that shows that the material transferred from the companion is sufficient to absorb the radiation from the white dwarf in these systems, ultimately supporting this scenario as quantitatively realistic.