Nonlinear decay of r modes in rapidly rotating neutron stars

We investigate the dynamics of r modes at amplitudes in the nonlinear regime for rapidly but uniformly rotating neutron stars with a polytropic equation of state. For this, we perform three-dimensional relativistic hydrodynamical simulations, making the simplifying assumption of a fixed spacetime. To excite r modes, we linearly scale exact eigenfunctions to large amplitudes. We find that for initial dimensionless amplitudes around three, r modes decay on time scales around ten oscillation periods, while at amplitudes of order unity, they are stable over the evolution time scale. Together with the decay, a strong differential rotation develops, conserving the total angular momentum, with angular velocities in the range 0.5 ... 1.2 of the initial one. We evolved two models with different rotation rates and found slower decay for the more rapidly rotating one. We present r-mode eigenfunctions and frequencies, and compare them to known analytic results for slowly rotating Newtonian stars. As a diagnostic tool, we discuss conserved energy and angular momentum for the case of a fixed axisymmetric background metric and introduce a measure for the energy of nonaxisymmetric fluid oscillation modes.