Large amplitude behavior of the bulk viscosity of dense matter

We study the bulk viscosity of dense matter, taking into account nonlinear effects that arise in the large amplitude 'supra-thermal' region where the deviation of the chemical potentials from chemical equilibrium fulfills . This regime is relevant to unstable modes, such as r-modes, which grow in amplitude until saturated by nonlinear effects. We study the damping due to direct and modified Urca processes in hadronic matter, and due to non-leptonic weak interactions in strange quark matter. We give general results valid for an arbitrary equation of state of dense matter and find that the viscosity can be strongly enhanced by supra-thermal effects. Our study confirms previous results on quark matter and shows that the nonlinear enhancement is even stronger in the case of hadronic matter. Our results can be applied to calculations of the r-mode-induced spin-down of fast-rotating neutron stars, where the spin-down time will depend on the saturation amplitude of the r-mode.