1999ApJ...519L..77M

The two anomalous X-ray pulsars (AXPs) with well-sampled timing histories, 1E 1048.1-5937 and 1E 2259+586, are known to spin down irregularly, with ``bumps'' superposed on an overall linear trend. Here we show that if AXPs are nonaccreting magnetars, i.e., isolated neutron stars with surface magnetic fields B<sub>0</sub>≳10<sup>10</sup> T, then they spin down electromagnetically in exactly the manner observed, because of an effect called ``radiative precession.'' Internal hydromagnetic stresses deform the star, creating a fractional difference ε=(I₃-I₁)/I₁∼10^–8 between the principal moments of inertia I₁ and I₃; the resulting Eulerian precession couples to an oscillating component of the electromagnetic torque associated with the near-zone radiation fields, and the star executes an anharmonic wobble with period τ_pr∼2π/εΩ(t)∼10 yr, where Ω(t) is the rotation frequency as a function of time t. We solve Euler's equations for a biaxial magnet rotating in vacuo, show that the computed Ω(t) matches the measured timing histories of 1E 1048.1-5937 and 1E 2259+586, predict Ω(t) for the next 20 years for both objects, predict a statistical relation between <dΩ/dt> and τ_pr, to be tested as the population of known AXPs grows, and hypothesize that radiative precession will be observed in future X-ray timing of soft gamma-ray repeaters.