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

Discovery of kHz Fluctuations in Centaurus X-3: Evidence for Photon Bubble Oscillations (PBO) and Turbulence in a High Mass X-ray Binary Pulsar

We report the discovery of kHz fluctuations, including quasi-periodic oscillations (QPO) at ~330 Hz and ~760 Hz and a broadband kHz continuum in the power density spectrum of the high mass X-ray binary pulsar Centaurus X-3. These observations of Cen X-3 were carried out with the Rossi X-ray Timing Explorer (RXTE). The fluctuation spectrum is flat from mHz to a few Hz, then steepens to $f^{-2}$ behavior between a few Hz and ~100 Hz. Above a hundred Hz, the spectrum shows the QPO features, plus a flat continuum extending to ~1200 Hz and then falling out to ~1800 Hz. These results, which required the co-adding three days of observations of Cen X-3, are at least as fast as the fastest known variations in X-ray emission from an accreting compact object (kHz QPO in LMXB sources) and probably faster since extension to ~1800 Hz is indicated by the most likely parameterization of the data. Multi-dimensional radiation hydrodynamics simulations of optically thick plasma flow onto the magnetic poles of an accreting neutron star show that the fluctuations at frequencies above 100 Hz are consistent with photon bubble turbulence and oscillations (PBO) previously predicted to be observable in this source. For a polar cap opening angle of 0.25 radians, we show that the spectral form above 100 Hz is reproduced by the simulations, including the frequencies of the QPO and the relative power in the QPO and the kHz continuum. This has resulted in the first model-dependent measurement of the polar cap size of an X-ray pulsar.Comment: received ApJ: April 1, 1999 accepted ApJ: September 1, 199

Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks: Electron-Positron Plasmas

We study the long term evolution of magnetic fields generated by a collisionless relativistic $e^+e^-$ shock which is initially unmagnetized. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are close to isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, with the non-propagating magnetic fields forming relatively isolated regions with transverse dimension $\sim 10-20$ skin depths. These structures decay in amplitude, with little sign of downstream merging. The fields start with magnetic energy density $\sim (0.1-0.2)$ of the upstream kinetic energy within the shock transition, but rapid downstream decay drives the fields to much smaller values, below $10^{-3}$ of equipartition after $10^3$ skin depths. In an attempt to construct a theory that follows field decay to these smaller values, we explore the hypothesis that the observed damping is a variant of Landau damping in an unmagnetized plasma. The model is based on the small value of the downstream magnetic energy density, which suggests that particle orbits are only weakly perturbed from straight line motion, if the turbulence is homogeneous. Using linear kinetic theory applied to electromagnetic fields in an isotropic, relativistic Maxwellian plasma, we find a simple analytic form for the damping rates, $\gamma_k$, in two and three dimensions for small amplitude, subluminous electromagnetic fields. We find that magnetic energy does damp due to phase mixing of current carrying particles as $(\omega_p t)^{-q}$ with $q \sim 1$. (abridged)Comment: 10 pages, 6 figures, accepted to ApJ; Downsampled version for arXiv. Full resolution figures available at http://astro.berkeley.edu/~pchang/full_res_weibel.pd