Pulsar winds and other burning questions of astrophysics

This thesis concerns physical processes that are powered or strongly affected by the rapid rotation of neutron stars. In the first part, we study the interaction of relativistic outflows from rotation-powered pulsars with surrounding supernova remnants. We describe results from time-dependent numerical modeling of the collisionless reverse shock terminating the pulsar wind in the Crab Nebula. We treat the upstream relativistic wind as composed of ions and electron-positron plasma embedded in a toroidal magnetic field. The relativistic cyclotron instability of the ion ring downstream of the leading shock in the pairs launches propagating magnetosonic waves with periodicity on the order of the ion Larmor time. Compressions in the magnetic field and pair density associated with these waves, as well as their propagation speed, semi-quantitatively reproduce the behavior of the wisp and ring features described in recent observations obtained using the Hubble Space Telescope and the Chandra X-Ray Observatory. By matching the model to the data we constrain the energetics and composition of the pulsar wind in the Crab Nebula.; We then turn to the question of formation of pulsar winds, and present results of the first self-consistent numerical model of the outer magnetosphere of a pulsar. Using the relativistic 3D “particle-in-cell” method we are able to follow magnetospheric plasma through the light cylinder into the wind zone for arbitrary magnetic inclination angles. For aligned rotators we confirm the “disk-dome” charge-separated structure of the magnetosphere and find that this configuration is unstable to a 3D nonaxisymmetric diocotron instability. This instability allows plasma to move across the field lines and approach the corotating Goldreich-Julian solution within several rotation periods. We also perform simulations of the oblique rotators and demonstrate the formation of the spiral “striped wind” in the equatorial direction and show that the star with pair formation forms wind outflow driven by electromgnetic pressure of the inclined dipole.; Finally, we consider the influence of stellar rotation on ignition and propagation of thermonuclear burning in the ocean of an accreting, rapidly rotating neutron star in a low-mass X-ray binary during a type I X-ray burst. We use both analytical arguments and numerical simulations of simplified models for ocean burning. We find a new regime for the spreading of a nuclear burning front, where the flame is carried along a coherent shear flow across the front with the width equal to the Rossby radius. Using this result we present a model for the global evolution of ignition and burning during a type I X-ray burst.