On neutron star structure and the millisecond pulsar

Abstract

The recently discovered millisecond pulsar¹ (PSR1937 + 214) has been observed to be rotating close to the limit of dynamic instability for a neutron star. In spite of its extremely rapid rotation, the present measurements of the period derivative^2,3 put a stringent upper limit on the energy loss from gravitational radiation, thus requiring that the quadrupole moment be quite small. The pulsar must also be rotating below the critical frequency at which its equilibrium configuration would become non-axisymmetric, since the lifetime of this configuration against decay by gravitational radiation is very short. This critical frequency, given by the theory of rotating ellipsoids⁴, imposes a more severe restriction on the rotation rate than the break-up frequency and may be used to set a lower limit, 〈ρ〉 > 2 × 10¹⁴ g cm⁻³, on the density of the star. If the mass is 0.5–1.5 M_⊙, several of the stiffer neutron star equations of state may be ruled out, and the radius should be <16 km. The condition for axisymmetry also imposes an upper limit on the rotation rate to which neutron stars may be spun up by accretion disks in binary systems, a model recently proposed for the evolution of the millisecond pulsar⁵.