Millisecond X-Ray Pulsars in Low-mass X-Ray Binaries

The discovery of millisecond X-ray pulsars in low-mass X-ray binaries (LMXRBs) with the Rossi X-Ray Timing Explorer (RXTE) has resulted in the determination of the neutron star spin periods to be in a very narrow period range. Based on evolutionary models for LMXRBs, it is likely that these pulsars have accreted sufficient material to be at or close to their equilibrium spin periods. If this is the case, then the similar neutron star rotation periods over 2 orders of magnitudes in observed luminosity require a comparable magnetospheric radius in all these systems to give a similar spin period. This means that either there is a correlation between surface magnetic field strength and X-ray luminosity (BL$1{/}2{r X}$ --> for the commonly used magnetospheric scaling for a gas pressure dominated accretion disk) or, if the neutron star surface magnetic field is comparable in all cases, the magnetospheric radius is very weakly dependent on the accretion rate in the inner radiation-dominated disk relevant to this regime. We suggest that the anomalous case of Sco X-1, where there is an apparent change in the inferred neutron star spin period, may be understood in terms of the radiation-driven expansion of the neutron star photosphere by up to 30%.