Instability windows and evolution of rapidly rotating neutron stars

We consider an instability of rapidly rotating neutron stars in low-mass X-ray binaries (LMXBs) with respect to excitation of r-modes (which are analogous to Earth's Rossby waves controlled by the Coriolis force). We argue that finite temperature effects in the superfluid core of a neutron star lead to a resonance coupling and enhanced damping (and hence stability) of oscillation modes at certain stellar temperatures. Using a simple phenomenological model we demonstrate that neutron stars with high spin frequency may spend a substantial amount of time at these `resonance' temperatures. This finding allows us to explain puzzling observations of hot rapidly rotating neutron stars in LMXBs and to predict a new class of hot, non-accreting, rapidly rotating neutron stars, some of which may have already been observed and tentatively identified as quiescent LMXB (qLMXB) candidates. We also impose a new theoretical limit on the neutron star spin frequency, explaining the cut-off spin frequency ~730 Hz, following from the statistical analysis of accreting millisecond X-ray pulsars. Besides explaining the observations, our model provides a new tool to constrain superdense matter properties comparing measured and theoretically predicted resonance temperatures.