In this paper, I will review the theory behind the gravitational wave (GW) driven r-mode instability in rapidly rotating neutron stars (NSs) and discuss which constraints can be derived from observations of spins and temperatures in low mass X-ray binaries (LMXBs). I will discuss how a standard, 'minimal' NS model is not consistent with the data, and discuss some of the additional physical mechanisms that could reconcile theory with observations. In particular, I will focus on additional forms of damping due to exotic cores and on strong mutual friction due to superfluid vortices cutting through superconducting flux tubes, and examine the repercussions these effects could have on the saturation amplitude of the mode. Finally I will also discuss the possibility that oscillations due to r-modes may have been recently observed in the X-ray light curves of two LMXBs.
Saturation of thef-mode instability in neutron stars. II. Applications and results