Accreting neutron star spins and the equation of state

X-ray timing of neutron stars in low-mass X-ray binaries (LMXBs) with RXTE has since 1996 revealed several distinct high-frequency phenomena. Among these are oscillations during thermonuclear (type-I) bursts, which (in addition to persistent X-ray pulsations) are thought to trace the neutron star spin. Recent discoveries bring the total number of measured LMXB spin rates to 22. An open question is why the majority of the ~100 known neutron stars in LMXBs show neither pulsations nor burst oscillations. Recent observations suggest that persistent pulsations may be more common than previously thought, although detectable intermittently, and in some cases at very low duty cycles. For example, the 377.3 Hz pulsations in HETE J1900.1-2455 were only present in the first few months of it's outburst, and have been absent since (although X-ray activity continues). Intermittent (persistent) pulsations have since been detected in a further two sources. In two of these three systems the pulsations appear to be related to the thermonuclear burst activity, but in the third (Aql X-1) they are not. This phenomenon offers new opportunities for spin measurements in known systems. Such measurements can constrain the poorly-known neutron star equation of state, and neutron stars in LMXBs offer observational advantages over rotation-powered pulsars which make the detection of more rapidly-spinning examples more likely. Even so, spin rates of at least 50% faster than the present maximum appear necessary to give constraints stringent enough to discriminate between the various models. Although the future prospects for such rapidly-spinning objects do not appear optimistic, several additional observational approaches are possible for LMXBs.