Numerical evolutions of nonlinear r-modes in neutron stars

Nonlinear evolution of the gravitational radiation ~GR! driven instability in the r-modes of neutron stars is studied by full numerical 3D hydrodynamical simulations. The growth of the r-mode instability is found to be limited by the formation of shocks and breaking waves when the dimensionless amplitude of the mode grows to about three in value. This maximum mode amplitude is shown by numerical tests to be rather insensitive to the strength of the GR driving force. Upper limits on the strengths of possible nonlinear mode-mode coupling are inferred. Previously unpublished details of the numerical techniques used are presented, and the results of numerous calibration runs are discussed.