Physics of Rotation Powered Pulsars and Their Nebulae
This letter is my progress report for the Astrophysics Theory grant. The first goal of the research supported by this grant is to produce a time dependent theory of the unsteady relativistic collisionless shock wave terminating the relativistic wind from a pulsar, and compare the predicted surface brightness fluctuations to Hubble Space Telescope observations of the wisps in the Crab Nebula. The second goal is to model the production of electron-positron pairs over the polar caps of rotation powered pulsars, and use the results to predict the heating of the surface due to particle trapping and bombardment of the atmosphere at the base of the polar field lines. We have succeeded in creating a one dimensional hybrid code, in which the electron-positron pairs incident on the shock structure are modeled as a relativistic, adiabatic, ideal MHD fluid, while the heavy ions are treated as particles using a particle-in-cell algorithm. The electromagnetic fields are evaluated from the currents and charge densities in the pairs and the ions, while the particles and the fluid accelerate in response to the computed self-consistent electromagnetic fields. The results are promising, in that the underlying ion cyclotron instability generates finite amplitude, propagating magnetosonic waves in the pairs, whose wavelengths and frequencies, when translated into physical units, are comparable to the observed running waves of brightness observed by HST near the Crab pulsar. The code is undergoing a number of tests, to assure us that this preliminary correspondence is not an artifact. In the coming year, the observational appearance of the models will be computed and compared to the HST observations of the Crab now in hand, and used to predict the HST results which will be obtained the year after next. WE also developed a one dimensional cascade theory for pair creation over pulsars' polar caps. A linear integral equation describing the synchrotron cascade has been derived and solved by iterative techniques, in the case when a high energy electron moving parallel to a star centered dipole magnetic field initiates the cascade through curvature gamma ray emission.