Bulk viscosity, r-modes, and the early evolution of neutron stars

Abstract

We discuss the effect of nonlinear bulk viscosity and the associated reheating on the evolution of newly born, rapidly rotating neutron stars with r-modes destabilized through the Chandrasekhar-Friedman-Schutz (CFS) mechanism. Bulk viscosity in these stars is due to the adjustment of the relative abundances of different particle species as the density of a fluid element is perturbed. It becomes nonlinear when the chemical potential difference $δμ$, measuring the chemical imbalance in the fluid element, becomes larger than the temperature $T$, which is generally much smaller than the Fermi energy. From this scale on, the bulk viscosity increases much faster with $δμ$ than predicted by the usual, linear approximation. This provides a potential saturation mechanism for stellar oscillation modes at a small to moderate amplitude. In addition, bulk viscosity dissipates energy, which can lead to neutrino emission, reheating of the star, or both. This is the first study to explicitly consider these effects in the evolution of the r-mode instability. For stars with little or no hyperon bulk viscosity, these effects are not strong enough to prevent the r-modes from growing to amplitudes $α\sim 1$ or higher, so other saturation mechanisms will probably set in earlier. The reheating effect makes spin-down occur at a higher temperature than would otherwise be the case, in this way possibly avoiding complications associated with a solid crust or a core superfluid. On the other hand, stars with a substantial hyperon bulk viscosity and a moderate magnetic field saturate their mode amplitude at a low value, which makes them gravitational radiators for hundreds of years, while they lose angular momentum through gravitational waves and magnetic braking.