Gravitational Radiation Limit on the Spin of Young Neutron Stars

A newly discovered instability in rotating neutron stars, driven bygravitational radiation reaction acting on the stars' $r$-modes, is shown hereto set an upper limit on the spin rate of young neutron stars. We calculate thetimescales for growth of linear perturbations due to gravitational radiationreaction, and for dissipation by shear and bulk viscosity, working to secondorder in a slow-rotation expansion within a Newtonian polytropic stellar model.The results are very temperature-sensitive: in hot neutron stars ($T>10^9$ K),the lowest-order $r$-modes are unstable, while in colder stars they are dampedby viscosity. These calculations have a number of interesting astrophysicalimplications. First, the $r$-mode instability will spin down a newly bornneutron star to a period close to the initial period inferred for the Crabpulsar, probably between 10 and 20 ms. Second, as an initially rapidly rotatingstar star spins down, an energy equivalent to roughly 1% of a solar mass isradiated as gravitational waves, which makes the process an interesting sourcefor detectable gravitational waves. Third, the $r$-mode instability rules outthe scenario whereby millisecond pulsars are formed by accretion-inducedcollapse of a white dwarf: the new star would be hot enough to spin down tomuch slower rates.Comment: 1 ps figur