On the Spin-Down of Intermittent Pulsars

Magnetospheres of pulsars are thought to be filled with plasma, and variations in plasma supply can affect both pulsar emission properties and spin-down rates. A number of recently discovered "intermittent" pulsars switch between two distinct states: an "on", radio-loud state, and an "off", radio-quiet state. Spin-down rates in the two states differ by a large factor, $\sim 1.5-2.5$, which is not easily understood in the context of current models. In this Letter we present self-consistent numerical solutions of "on" and "off" states of intermittent pulsar magnetospheres. We model the "on" state as a nearly ideal force-free magnetosphere with abundant magnetospheric plasma supply. The lack of radio emission in the "off" state is associated with plasma supply disruption that results in lower plasma density on the open field lines. We model the "off" state using nearly vacuum conditions on the open field lines and nearly ideal force-free conditions on the closed field lines, where plasma can remain trapped even in the absence of pair production. The toroidal advection of plasma in the closed zone in the "off" state causes spin-downs that are a factor of $\sim 2$ higher than vacuum values, and we naturally obtain a range of spin-down ratios between the "on" and "off" states, $\sim 1.2-2.9$, which corresponds to a likely range of pulsar inclination angles of $30{-}90^\circ$. We consider the implications of our model to a number of poorly understood but possibly related pulsar phenomena, including nulling, timing noise, and rotating radio transients.Comment: 6 pages, 4 figures, submitted to ApJ Letter

Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks

We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic $e^+e^-$ shock. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are approximately isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, nonpropagating, and decaying. Using linear kinetic theory, we find a simple analytic form for these damping rates. Our theory predicts that overall magnetic energy decays like $(\omega_p t)^{-q}$ with $q \sim 1$, which compares favorably with simulations, but predicts overly rapid damping of short wavelength modes. Magnetic trapping of particles within the magnetic structures may be the origin of this discrepancy. We conclude that initially unmagnetized relativistic shocks in electron-positron plasmas are unable to form persistent downstream magnetic fields. These results put interesting constraints on synchrotron models for the prompt and afterglow emission from GRBs.Comment: 4 pages, 3 figures, contributed talk at the workshop: High Energy Phenomena in Relativistic Outflows (HEPRO), Dublin, 24-28 September 2007; Downsampled version for arXiv. Full resolution version available at http://astro.berkeley.edu/~pchang/proceedings.pd

A distance formula related to a family of projections orthogonal to their symmetries

Let u be a hermitian involution, and e an orthogonal projection, acting on the same Hilbert space. We establish the exact formula, in terms of the norm of eue, for the distance from e to the set of all orthogonal projections q from the algebra generated by e,u, and such that quq=0.Comment: 6 pages, 1 figur

Simulations of Ion Acceleration at Non-relativistic Shocks. I. Acceleration Efficiency

We use 2D and 3D hybrid (kinetic ions - fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasi-parallel configurations (i.e., when the background magnetic field is almost aligned with the shock normal) and, for large sonic and Alfv\'enic Mach numbers, produces universal power-law spectra proportional to p^(-4), where p is the particle momentum. The maximum energy of accelerated ions increases with time, and it is only limited by finite box size and run time. Acceleration is mainly efficient for parallel and quasi-parallel strong shocks, where 10-20% of the bulk kinetic energy can be converted to energetic particles, and becomes ineffective for quasi-perpendicular shocks. Also, the generation of magnetic turbulence correlates with efficient ion acceleration, and vanishes for quasi-perpendicular configurations. At very oblique shocks, ions can be accelerated via shock drift acceleration, but they only gain a factor of a few in momentum, and their maximum energy does not increase with time. These findings are consistent with the degree of polarization and the morphology of the radio and X-ray synchrotron emission observed, for instance, in the remnant of SN 1006. We also discuss the transition from thermal to non-thermal particles in the ion spectrum (supra-thermal region), and we identify two dynamical signatures peculiar of efficient particle acceleration, namely the formation of an upstream precursor and the alteration of standard shock jump conditions.Comment: 21 pages, 14 figures, Minor changes reflecting the version accepted to Ap

Ab-initio pulsar magnetosphere: three-dimensional particle-in-cell simulations of axisymmetric pulsars

We perform first-principles relativistic particle-in-cell simulations of aligned pulsar magnetosphere. We allow free escape of particles from the surface of a neutron star and continuously populate the magnetosphere with neutral pair plasma to imitate pair production. As pair plasma supply increases, we observe the transition from a charge-separated electrosphere solution with trapped plasma and no spin-down to a solution close to the ideal force-free magnetosphere with electromagnetically-dominated pulsar wind. We calculate the magnetospheric structure, current distribution and spin-down power of the neutron star. We also discuss particle acceleration in the equatorial current sheet.Comment: 6 pages, 5 figures, published in ApJ Letter

Laser Shaping and Optimization of the Laser-Plasma Interaction

The physics of energy transfer between the laser and the plasma in laser wakefield accelerators is studied. We find that wake excitation by arbitrary laser shapes can be parameterized using the total pulse energy and pulse depletion length. A technique for determining laser profiles that produce the required plasma excitation is developed. We show that by properly shaping the longitudinal profile of the driving laser pulse, it is possible to maximize both the transformer ratio and the wake amplitude, achieving optimal laser-plasma coupling. The corresponding family of laser pulse shapes is derived in the nonlinear regime of laser-plasma interaction. Such shapes provide theoretical upper limit on the magnitude of the wakefield and efficiency of the accelerating stage by allowing for uniform photon deceleration inside the laser pulse. We also construct realistic optimal pulse shapes that can be produced in finite-bandwidth laser systems and propose a two-pulse wake amplification scheme using the optimal solution.Comment: 12 pages, 5 figures, contributed to the Advanced Accelerator Concepts 2000 worksho

Synthetic Spectra from PIC Simulations of Relativistic Collisionless Shocks

We extract synthetic photon spectra from first-principles particle-in-cell simulations of relativistic shocks propagating in unmagnetized pair plasmas. The two basic ingredients for the radiation, namely accelerated particles and magnetic fields, are produced self-consistently as part of the shock evolution. We use the method of Hededal & Nordlund (2005) and compute the photon spectrum via Fourier transform of the electric far-field from a large number of particles, sampled directly from the simulation. We find that the spectrum from relativistic collisionless shocks is entirely consistent with synchrotron radiation in the magnetic fields generated by Weibel instability. We can recover the so-called "jitter'' regime only if we artificially reduce the strength of the electromagnetic fields, such that the wiggler parameter K = qB lambda/mc^2 becomes much smaller than unity ("B" and "lambda" are the strength and scale of the magnetic turbulence, respectively). These findings may place constraints on the origin of non-thermal emission in astrophysics, especially for the interpretation of the hard (harder than synchrotron) low-frequency spectrum of Gamma-Ray Bursts.Comment: 5 pages, 3 figures, submitted to ApJ Letter