r-Mode Instability Of Neutron Stars: Surprise and Speculation Several recent surprises appear dramatically to have improved the likelihood that the spin of rapidly rotating, newly formed neutron stars (and, possibly, of old stars spun up by accretion) is limited by an instability driven by gravitational waves. If so, the emitted waves may be observable by gravitational-wave detectors with the sensitivity of LIGO II. Although several possible ways to kill the instability have been suggested, it has so far survived them all.