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

The r-modes 79evolution turns out to have three phases.(a) Initially the angular velocity of the hot rapidly rotating neutron star isnearly constant, evolving on the viscous timescale 1/τ v , while the amplitudeα grows exponentially on the gravitational radiation timescale 1/τ GR .(b) After a short time nonlinear effects become important and stop the growth ofthe amplitude α. Most of the initial angular momentum of the star is radiatedaway by gravitational radiation. The star spins down and evolves to a pointwhere the angular velocity and the temperature is sufficiently low that ther-mode is stable.(c) Finally gravitational radiation and viscosity damp out the r-mode and drivethe star into its final equilibrium configuration.This may take about a year, a timescale governed by the cooling time of thestar. During this year, the star would radiate away most of its angular momentumand rotational kinetic energy. This could be a substantial fraction of a solar massin energy.7.2.3 Detection of r-mode radiationThe large amount of energy radiated into the r-modes makes them attractive fordetection, but detection will not be trivial. The r-mode event occurs at the rateof supernovae: some fraction (hopefully large) of all supernovae leave behind arapidly spinning neutron star that spins down over a one-year period. This meanswe should have sufficient sensitivity to reach the Virgo Cluster (20 Mpc distance).Estimates [31] suggest that a neutron star in the Virgo Cluster could be detectedby second generation of LIGO and VIRGO gravitational-wave detectors with anamplitude signal-to-noise of about eight, provided one can use matched filtering(exact template matching).It will not be easy to use matched filtering, since one must follow all cyclesof the signal as the star spins down, and we will not know this well because ofmany uncertainties: initial temperature, initial spin distribution, detailed physicsof viscosity, and so on. However, it would be helpful to have a parametrizedmodel to take account of the uncertainties, so that we could look for a significantfit to one or more of the parameters.In addition, it is likely that, if a significant proportion of all neutron starswent through the r-mode instability, then the universe has been filled by theirradiation. There should be a background with an energy density gw that is agood fraction of the closure density. Its lower frequency limit should be around200 Hz in the rest frame of the star. When we see radiation cosmologically, itslower frquency limit will indicate the epoch at which star formation began.It is clear that the discovery of this new source of gravitational waves willopen several prospects for astronomy. Observations could be used as supernovaedetectors, revealing supernovae hidden in clouds of dust, identifying them about ayear after they are formed. The existence of the radiation raises several prospects