Modelling the spin equilibrium of neutron stars in low‐mass X‐ray binaries without gravitational radiation

In this paper we discuss the spin equilibrium of accreting neutron stars in low-mass X-ray binaries (LMXBs). We demonstrate that, when combined with a naive spin-up torque, the observed data lead to inferred magnetic fields which are at variance with those of Galactic millisecond radio pulsars. This indicates the need for either additional spin-down torques (e.g. gravitational radiation) or an improved accretion model. We show that a simple consistent accretion model can be arrived at by accounting for radiation pressure in rapidly accreting systems (above a few per cent of the Eddington accretion rate). In our model the inner disc region is thick and significantly sub-Keplerian and the estimated equilibrium periods are such that the LMXB neutron stars have properties that accord well with the Galactic millisecond radio pulsar sample. The implications for future gravitational-wave observations are also discussed briefly.