The Crustal Rigidity of a Neutron Star and Implications for PSR B1828−11 and Other Precession Candidates

Abstract

Like the Earth, a neutron star (NS) can undergo torque-free precession because some piece ΔId of its inertia tensor remains tied to the crust's principal axes, as opposed to following the crust's angular velocity vector. The (body frame) precession frequency νp is νsΔId/IC, where νs is the NS's spin frequency and IC is the moment of inertia associated with the crustal nuclei, plus any component of the star tightly coupled to the crust over a timescale less than the spin period. For a spinning NS with a relaxed crust, ΔId = bΔIΩ, where ΔIΩ is the rotational oblateness of a fluid star rotating at spin frequency Ω and b is the NS's rigidity parameter. A previous estimate of b by Baym & Pines gives b ~ 10-5 for typical NS parameters. Here we calculate the rigidity parameter b and show that it is ~40 times smaller than the Baym-Pines estimate. We apply this result to PSR B1828-11, an isolated pulsar whose correlated timing residuals and pulse shape variations provide strong evidence for precession with a 511 day period. We show that this precession period is ~250 times shorter than one would expect, assuming that (1) the crust is relaxed (except for the stresses induced by the precession itself) and (2) the NS possesses no other source of stress that would deform its figure (e.g., a strong magnetic field). We conclude that the crust must be under significant stress to explain the precession period of PSR B1828-11; such stress arises naturally as the star spins down. Assuming that crustal shear stresses do set the precession period, the star's reference angular velocity (roughly, the spin at which the crust is most relaxed) is ≈40 Hz (i.e., ≈ times faster than today's spin), and the weighted average of the crust's present spin-down strain is ≃ 5 × 10-5. We briefly describe the implications of our improved b calculation for other precession candidates.