Shape of the Crab Pulsar and its Period Fluctuations

Abstract

RICHARDS et al.¹ have recently recorded sinusoidal variations in the arrival times of radio pulses from NP 0532 with a period of about three months and an amplitude Δ_τ= 6 × 10⁻⁴ s. This effect can be interpreted in terms of genuine sinusoidal variations of the circular frequency of the Crab pulsar where Ω ≃ 200 s⁻¹, ω ≃ 10⁻⁶ s⁻¹, A ≃ 10⁻¹⁰. Equation (1) can be explained by the widely accepted oblique rotator model^2–4 simply by investigating an interesting consequence of the possible ellipticity of the neutron star. To account for the history and energy balance of the Crab Nebula³, an upper limit must be placed^4,5 to this ellipticity, such that the gravitational quadrupole radiation dominates the magnetic dipole radiation only in the early life of the pulsar. It turns out that the explanation given here for the anomalies in the pulse arrival times provides in the end an even stronger limit to the deviations from spherical symmetry allowed in a neutron star.