Spin‐up of Low‐Luminosity, Low‐Mass X‐Ray Binaries

We examine the spin-up of low luminosity, low mass X-ray binaries (LMXBs) tomillisecond pulsars (MSPs). In the conventional spin-up model of the Ghosh &Lamb type, where the stellar magnetic field interacts with the Keplerianaccretion disk, MSPs could be produced from LMXBs if their magnetic field B <10^{8}({\dot M}/10^{16}g/s)^{1/2}G, where {\dot M} is the mass accretion rate.However, for {\dot M} < {\dot M}_c ~ 10^{16}g/s accretion is likely to occurvia a quasi-spherical flow with a sub-Keplerian rotation. The sub-Keplerianrotation rate is smaller than the Keplerian rate by a factor ~2-10. As aconsequence, the spin-up of LMXBs produces pulsars with spin periods longer bya factor ~2-10 than those with a Keplerian accretion disk. The observed MSPscould be produced only for B < 10^7G even when {\dot M}\sim {\dot M}_c ~10^{16}g/s. This suggests that the low luminosity LMXBs with {\dot M} < {\dotM}_c would not be able to spin-up to the observed MSPs. This rules out anyundetected populations of persistent, low luminosity LMXBs and potentially asignificant fraction of the atoll sources as a possible source population ofthe observed MSPs. If a large number of undetected, persistent, low luminosityLMXBs do exist, they could produce MSPs near the pulsar death line withintrinsic electromagnetic luminosity <~ 10^{30} erg/s. The observed MSPs couldpossibly arise from a population of soft x-ray transients (SXTs) containingneutron stars although this is not supported by current estimates of theoutburst rate or numbers of such systems. Accretion induced collapse of lowmagnetic field white dwarfs remains a possible channel for MSP formation.Comment: 12 pages LaTeX (uses aaspp4.sty) plus two figures (Postscript) Accepted for publication in ApJ (September, 1998