Radiative Precession of an Isolated Neutron Star

Abstract

Euler's equations of motion are derived exactly for a rigid, triaxial, internally frictionless neutron star spinning down electromagnetically in vacuo. It is shown that the star precesses, but not freely: its regular precession relative to the principal axes of inertia couples to the component of the radiation torque associated with the near-zone radiation fields and is modified into an anharmonic wobble. The wobble period τ_1 typically satisfies τ_1 < 10^{-2}τ_0, where τ_0 is the braking time-scale; the wobble amplitude evolves towards a constant non-zero value, oscillates, or decreases to zero, depending on the degree of oblateness or prolateness of the star and its initial spin state; and the (negative) angular frequency derivative dω/dt oscillates as well, exhibiting quasi-periodic spikes for triaxial stars of a particular figure. In light of these properties, a young, Crab-like pulsar ought to display fractional changes of order unity in the space of a few years in its pulse profile, magnetic inclination angle, and dω/dt. Such changes are not observed, implying that the wobble is damped rapidly by internal friction, if its amplitude is initially large upon crystallization of the stellar crust. If the friction is localized in the inner and outer crusts, the thermal luminosity of the neutron star increases by a minimum amount ΔL = 3*10^{31} (ε/ 10^{-12}) (ω/ 10^3 rad s^{-1})^2 (τ_d / 1 yr)^{-1} erg s^{-1}, where epsilon is the ellipticity and τ_d is the damping time-scale, with the actual value of ΔL determined in part by the thermal conduction time τ_cond. The increased luminosity is potentially detectable as thermal X-rays lasting for a time max(tau_d,tau_cond) following crystallization of the crust.