The aim of this paper is to examine the effects of the horizontal turbulence in differentially rotating stars on the GSF instability and apply our results to pre-supernova models. For this purpose we derive the expression for the GSF instability with account of the thermal transport and smoothing of the mu-gradient by the horizontal turbulence. We apply the new expressions in numerical models of a 20 solar mass star. We show that if N^2_{Omega} < 0 the Rayleigh-Taylor instability cannot be killed by the stabilizing thermal and mu-gradients, so that the GSF instability is always there and we derive the corresponding diffusion coefficient. The GSF instability grows towards the very latest stages of stellar evolution. Close to the deep convective zones in pre-supernova stages, the transport coefficient of elements and angular momentum by the GSF instability can very locally be larger than the shear instability and even as large as the thermal diffusivity. However the zones over which the GSF instability is acting are extremely narrow and there is not enough time left before the supernova explosion for a significant mixing to occur. Thus, even when the inhibiting effects of the mu-gradient are reduced by the horizontal turbulence, the GSF instability remains insignificant for the evolution. We conclude that the GSF instability in pre-supernova stages cannot be held responsible for the relatively low rotation rate of pulsars compared to the predictions of rotating star models.
Several X-ray pulsars have been observed to experience torque reversals, which provide important observational clues to the interaction between the neutron star magnetic field and the accretion disk. We review the current models proposed for the torque reversals and discuss their viability based on the observations of the quasi-periodic oscillations (QPOs) in 4U 1626-67. Most of these models seem to be incompatible with the evolution of the QPO frequencies if they are interpreted in terms of the beat frequency model. We suggest that winds or outflows from the neutron star and the accretion disk may play an important role in accounting for the spin-down in disk-fed neutron stars.
It has been pointed out that the slope of the nuclear symmetry energy at saturation density ($L$) is a crucial quantity to determine the mass and width of neutron-star crusts. This letter intends to clarify the relation between $L$ and the core-crust transition. We confirm that the transition density is soundly correlated with $L$ despite differences in the nuclear models, and we propose a clear understanding of this correlation based on a generalized liquid drop model (GLDM). Using a large number of nuclear models, we evaluate the dispersion affecting the correlation between the transition pressure $P_t$ and $L$. Furthermore, from a detailed analysis it is shown that this correlation is weak due to a cancellation between different terms. We point out that the correlation between the isovector coefficients $K_{sym}$ and $L$ plays a crucial role in this discussion.
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