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

Experimentally Observed Instability of a Laminar Ekman Flow in a Rotating Basin

In studying the axi-symmetric flow induced by source-sink distributions in a rotating cylindrical basin in the absence of radial barriers, a highly organized pattern of instability has been observed in the laminar Ekman layer along the bottom of the basin. The instability manifests itself in the form of almost perfectly concentric cylindrical sheets or curtains of water which rise as sharply defined vertical jets from the Ekman layer and penetrate the entire depth of fluid. A less sharply defined downward motion between the curtains completes the circulation celis thus developed. At some maximum critical radius, the curtains usually disappear, and the flow at larger radii is a stable, laminar Ekman flow. Quantitative observations of ring spacing and critical radius are reported for experiments in which angular velocity, flow rate, viscosity and total depth of water were varied over experimentally available ranges

Magnetar Driven Bubbles and the Origin of Collimated Outflows from GRBs

We model the interaction between the wind from a newly formed rapidly rotating magnetar and the surrounding progenitor. In the first few seconds after core collapse the magnetar inflates a bubble of plasma and magnetic fields behind the supernova shock, which expands asymmetrically because of the pinching effect of the toroidal magnetic field, as in PWNe, even if the host star is spherically symmetric. The degree of asymmetry depends on the ratio of the magnetic energy to the total energy in the bubble. We assume that the wind by newly formed magnetars inflating these bubbles is more magnetized than for PWNe. We show that for a magnetic to total power supplied by the central magnetar $\sim 0.1$ the bubble expands relatively spherically while for values greater than 0.3, most of the pressure in the bubble is exerted close to the rotation axis, driving a collimated outflow out through the host star. This can account for the collimation inferred from observations of long-duration gamma-ray bursts (GRBs). Given that the wind magnetization increases in time, we thus suggest that the magnetar-driven bubble initially expands relatively spherically (enhancing the energy of the associated supernova) while at late times it becomes progressivelymore collimated (producing the GRB). Similar processes may operate in more modestly rotating neutron stars to produce asymmetric supernovae and lower energy transients such as X-ray flashes.Comment: Proceeding of the conference "Astrophysics of Compact Objects", 1-7 July, Huangshan, Chin

Time Variability in the X-ray Nebula Powered by Pulsar B1509-58

We use new and archival Chandra and ROSAT data to study the time variability of the X-ray emission from the pulsar wind nebula (PWN) powered by PSR B1509-58 on timescales of one week to twelve years. There is variability in the size, number, and brightness of compact knots appearing within 20" of the pulsar, with at least one knot showing a possible outflow velocity of ~0.6c (assuming a distance to the source of 5.2 kpc). The transient nature of these knots may indicate that they are produced by turbulence in the flows surrounding the pulsar. A previously identified prominent jet extending 12 pc to the southeast of the pulsar increased in brightness by 30% over 9 years; apparent outflow of material along this jet is observed with a velocity of ~0.5c. However, outflow alone cannot account for the changes in the jet on such short timescales. Magnetohydrodynamic sausage or kink instabilities are feasible explanations for the jet variability with timescale of ~1.3-2 years. An arc structure, located 30"-45" north of the pulsar, shows transverse structural variations and appears to have moved inward with a velocity of ~0.03c over three years. The overall structure and brightness of the diffuse PWN exterior to this arc and excluding the jet has remained the same over the twelve year span. The photon indices of the diffuse PWN and possibly the jet steepen with increasing radius, likely indicating synchrotron cooling at X-ray energies.Comment: accepted to ApJ, 14 pages, 8 figure

Pair-production multiplicities in rotation-powered pulsars

We discuss the creation of electron-positron cascades in the context of pulsar polar cap acceleration models and derive several useful analytic and semi-analytic results for the spatial extent and energy response of the cascade. Instead of Monte Carlo simulations, we use an integro- differential equation which describes the development of the cascade energy spectrum in one space dimension quite well, when it is compared to existing Monte Carlo models. We reduce this full equation to a single integral equation, from which we can derive useful results, such as the energy loss between successive generations of photons and the spectral index of the response. We find that a simple analytic formula represents the pair cascade multiplicity quite well, provided that the magnetic field is below 10^12 Gauss, and that an only slightly more complex formula matches the numerically-calculated cascade at all other field strengths. Using these results, we find that cascades triggered by gamma rays emitted through inverse Compton scattering of thermal photons from the neutron star's surface, both resonant and non-resonant, are important for the dynamics of the polar cap region in many pulsars.Comment: to appear in ApJ; 19 pages, 18 figure

Thermal emission from low-field neutron stars

We present a new grid of LTE model atmospheres for weakly magnetic (B<=10e10G) neutron stars, using opacity and equation of state data from the OPAL project and employing a fully frequency- and angle-dependent radiation transfer. We discuss the differences from earlier models, including a comparison with a detailed NLTE calculation. We suggest heating of the outer layers of the neutron star atmosphere as an explanation for the featureless X-ray spectra of RX J1856.5-3754 and RX J0720.4-3125 recently observed with Chandra and XMM.Comment: 8 pages A&A(5)-Latex, 6 Figures, A&A in press. The model spectra presented here are available as XSPEC tables at http://www.astro.soton.ac.uk/~btg/outgoing/nsspec

Polarization Sweeps in Rotation Powered Pulsars

We re-examine the characteristic polarization angle sweep of rotation-powered pulsars and calculate the expected deviations from this sweep caused by aberrational effects and by polar-cap current flow. We find that in addition to the previously known phase shift of the entire sweep by $\Delta \Phi = -4 r/R_L$, aberration shifts the polarization angle itself by $\Delta \Psi = -(10/3) (r/R_L) \cos \alpha$. Similarly, current flow above the polar cap shifts the polarization sweep by $\Delta \Psi = (10/3) (r/R_L) (J/J_{GJ}) \cos \alpha$, potentially providing a method of directly measuring the magnitude of the current. The competition between these two effects produces a potentially observable signature in the polarization angle sweep. Although these effects may appear similar to orthogonal mode shifts, they are an independent phenomenon with distinct observational characteristics.Comment: 23 pages, 8 figures; accepted by Ap

Magnetic Confinement, MHD Waves, and Smooth Line Profiles in AGN

In this paper, we show that if the broad line region clouds are in approximate energy equipartition between the magnetic field and gravity, as hypothesized by Rees, there will be a significant effect on the shape and smoothness of broad emission line profiles in active galactic nuclei. Line widths of contributing clouds or flow elements are much wider than their thermal widths, due to the presence of non-dissipative MHD waves, and their collective contribution produce emission line profiles broader and smoother than would be expected if a magnetic field were not present. As an illustration, a simple model of isotropically emitting clouds, normally distributed in velocity, is used to show that smoothness can be achieved for less than 80,000 clouds and may even be as low as a few hundred. We conclude that magnetic confinement has far reaching consequences for observing and modeling active galactic nuclei.Comment: to appear in MNRA