(ed.). Gravitational waves (IOP, 2001)(422s).

78 Source calculations,,3 .3, ORJ 7.Figure 7.1. The balance of viscous and gravitational radiation effects in the r-modes isillustrated in a diagram of rotation speed, showing the ratio of the maximum period P kto the rotation period P versus the temperature of the star. The solid curve indicates theboundary between viscosity-dominated and radiation-dominated behaviour: stars abovethe line are unstable. The dashed curves illustrate possible nonlinear evolution histories asa young neutron star cools.that become important as the modes grow. This could only be done with anumerical simulation, which some groups are now working on. However, it ispossible to make simple estimates analytically.We characterize the initial configuration with just two paramters: the uniformangular velocity , and the amplitude α of the r-modes perturbation. The star isassumed to cool at the accepted cooling rate for neutron stars, independently ofwhether it is affected by the r-mode instability or not. The star is assumed tolose angular momentum to gravitational radiation at a rate given by the linearradiation field, with its large amplitude α. This loss is taken to drive the starthrough a sequence of equilibrium states of lower and lower angular momentum.Details of this approximation are in [31], here we report only the results. The