Precession of Isolated Neutron Stars II: Magnetic Fields and Type II Superconductivity

We consider the physics of free precession of a rotating neutron star with an oblique magnetic field. We show that if the magnetic stresses are large enough, then there is no possibility of steady rotation, and precession is inevitable. Even if the magnetic stresses are not strong enough to prevent steady rotation, we show that the minimum energy state is one in which the star precesses. Since the moment of inertia tensor is inherently triaxial in a magnetic star, the precession is periodic but not sinusoidal in time, in agreement with observations of PSR 1828-11. However, the problem we consider is {\it not} just precession of a triaxial body. If magnetic stresses dominate, the amplitude of the precession is not set just by the angle between the rotational angular velocity and any principal axis, which allows it to be small without suppressing oscillations of timing residuals at harmonics of the precession frequency. We argue that magnetic distortions can lead to oscillations of timing residuals of the amplitude, period, and relative strength of harmonics observed in PSR 1828-11 if magnetic stresses in its core are about 200 times larger than the classical Maxwell value for its dipole field, and the stellar distortion induced by these enhanced magnetic stresses is about 100-1000 times larger than the deformation of the neutron star's crust. Magnetic stresses this large can arise if the core is a Type II superconductor, or from toroidal fields $\sim 10^{14}$ G if the core is a normal conductor. The observations of PSR 1828-11 appear to require that the neutron star is slightly prolate.Comment: 40 pages, 1 figure. Discussion added on vortex pinning and compatibility with glitch models. References added and corrected. Typo corrected (Eq. 58

Non-equilibrium effects in steady relativistic e+e−γe^+e^-\gamma winds

We consider an ultra-relativistic wind consisting of electron-positron pairs and photons with the principal goal of finding the asymptotic Lorentz factor $\gamma_{\infty}$ for zero baryon number. The wind is assumed to originate at radius $r_i$ where it has a Lorentz factor $\gamma_i$ and a temperature $T_i$ sufficiently high to maintain pair equilibrium. As $r$ increases, $T$ decreases and becomes less than the temperature corresponding to the electron mass $m_e$, after which non-equilibrium effects become important. Further out in the flow the optical depth $\tau$ drops below one, but the pairs may still be accelerated by the photons until $\tau$ falls below $\sim 2\times10^{-5} \gamma_{i}^{3/4}$. Radiative transfer calculations show that only at this point do the radiation flux and pressure start to deviate significantly from their blackbody values. The acceleration of the pairs increases $\gamma$ by a factor $\sim 45$ as compared to its value at the photosphere; it is shown to approach \gamma_{\infty} \sim 1.4\times 10^3 (r_i/10^6\mbox{cm})^{1/4} \gamma_{i}^{3/4} T_i/m_e.Comment: 41 pages, 9 figures. Submitted to MNRA