The Crustal Rigidity of a Neutron Star, and Implications for PSR 1828-11 and other Precession Candidates

Like the Earth, a neutron star (NS) can undergo torque-free precession because some piece ∆Id of its inertia tensor remains tied to the crust’s principal axes, as opposed to following the crust’s angular velocity vector. The (bodyframe) precession frequency νp is νs∆Id/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, ∆Id = b∆IΩ, where ∆IΩ 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 (1971) gives b ∼ 10 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 1828-11, 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