On the minimum spin period of accreting pulsars

TL;DR

This paper investigates why neutron stars in low-mass X-ray binaries do not spin faster than 730 Hz by analyzing the effects of disc-magnetosphere interaction, star deformation, and gravitational waves on their maximum spin rate.

Contribution

It combines models of disc-magnetosphere interaction, star deformation, and gravitational wave emission to explain the observed spin frequency cutoff in neutron stars.

Findings

Maximum spin frequency is reduced by disc-magnetosphere interaction.

Star's moment of inertia change further limits spin rate.

Gravitational wave torque significantly influences spin equilibrium.

Abstract

The distribution of the spin frequencies of neutron stars in low-mass X-ray binaries exhibits a cut-off at 730 Hz, below the break-up frequency (mass-shedding limit) of neutron stars. The absence of the sub-millisecond pulsars presents a problem, given that these systems are older than the spin-up timescale. We confront models of disc-magnetosphere interaction near torque equilibrium balanced by the torque due to gravitational wave emission. We note that field lines penetrating the disc beyond the inner radius reduce the maximum rotation frequency of the star, a result well-known since the seminal work of Ghosh & Lamb. We show that the polar cap area corresponds to about half the neutron star surface area at the cut-off frequency if the inner radius is slightly smaller than the corotation radius. We then include the change in the moment of inertia of the star due to the accretion of mass and find that this effect further reduces the maximum rotation frequency of the star. Finally, we include the torque due to gravitational wave emission and calculate its contribution to the torque equilibrium. Our results suggest that all three processes are significant at the cut-off frequency, and all of them must be considered in addressing the absence of sub-millisecond pulsars.