A wind model for high energy pulses

A solution to the sigma problem - that of finding a mechanism capable of converting Poynting energy flux to particle-borne energy flux in a pulsar wind - was proposed several years ago by Coroniti and Michel who considered a particular prescription for magnetic reconnection in a striped wind. This prescription was later shown to be ineffective. In this paper, we discuss the basic microphysics of the reconnection process and conclude that a more rapid prescription is permissible. Assuming dissipation to set in at some distance outside the light-cylinder, we compute the resulting radiation signature and find that the synchrotron emission of heated particles appears periodic, in general showing both a pulse and an interpulse. The predicted spacing of these agrees well with observation in the case of the Crab and Vela pulsars. Using parameters appropriate for the Crab pulsar - magnetization parameter at the light cylinder sigma_L = 6 x 10^4, Lorentz factor Gamma=250 - reasonable agreement is found with the observed total pulsed luminosity. This suggest that the high-energy pulses from young pulsars originate not in the co-rotating magnetosphere within the light cylinder (as in all other models) but from the radially directed wind well outside it.Comment: 6 pages, 2 figures. To appear in the Proceedings of the 270. WE-Heraeus Seminar on Neutron Stars, Pulsars and Supernova Remnants, Jan. 21-25, 2002, Physikzentrum Bad Honnef, eds W. Becker, H. Lesch & J. Truemper. Proceedings are available as MPE-Report 27

Particle Acceleration at Ultra-Relativistic Shocks and the Spectra of Relativistic Fireballs

We examine Fermi-type acceleration at relativistic shocks, and distinguish between the initial boost of the first shock crossing cycle, where the energy gain per particle can be very large, and the Fermi process proper with repeated shock crossings, in which the typical energy gain is of order unity. We calculate by means of numerical simulations the spectrum and angular distribution of particles accelerated by this Fermi process, in particular in the case where particle dynamics can be approximated as small-angle scattering. We show that synchrotron emission from electrons or positrons accelerated by this process can account remarkably well for the observed power-law spectra of GRB afterglows and Crab-like supernova remnants. In the context of a decelerating relativistic fireball, we calculate the maximum particle energy attainable by acceleration at the external blast wave, and discuss the minimum energy for this acceleration process and its consequences for the observed spectrum.Comment: To appear in Proceedings of the 5th Huntsville Gamma-Ray Burst Symposium. LaTeX, 6 pages, 2 figures, uses aipproc.sty and epsfi

An eigenfunction method for particle acceleration at ultra-relativistic shocks

We adapt and modify the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock front via the first-order Fermi process (Kirk, J.G., Schneider, P., Astrophysical Journal 315, 425 (1987)) to apply to shocks of arbitrarily high Lorentz factor. The power-law index of accelerated particles undergoing isotropic small-angle scattering at an ultrarelativistic, unmagnetized shock is found to be s=4.23 +/- 0.2 (where s=d\ln f/ d\ln p, with f the Lorentz-invariant phase-space density and p the momentum), in agreement with the results of Monte-Carlo simulations. We present results for shocks in plasmas with different equations of state and for Lorentz factors ranging from 5 to infinity.Comment: 4 pages, 2 figures, contribution to the Proceedings of the 5th Huntsville GRB Symposiu

Pulsar wind nebulae in supernova remnants

A spherically symmetric model is presented for the interaction of a pulsar wind with the associated supernova remnant. This results in a pulsar wind nebula whose evolution is coupled to the evolution of the surrounding supernova remnant. This evolution can be divided in three stages. The first stage is characterised by a supersonic expansion of the pulsar wind nebula into the freely expanding ejecta of the progenitor star. In the next stage the pulsar wind nebula is not steady; the pulsar wind nebula oscillates between contraction and expansion due to interaction with the reverse shock of the supernova remnant: reverberations which propagate forward and backward in the remnant. After the reverberations of the reverse shock have almost completely vanished and the supernova remnant has relaxed to a Sedov solution, the expansion of the pulsar wind nebula proceeds subsonically. In this paper we present results from hydrodynamical simulations of a pulsar wind nebula through all these stages in its evolution. The simulations were carried out with the Versatile Advection Code.Comment: 10 pages, 9 figures, submitted to Astronomy and Astrophysic

PrAGMATiC: a Probabilistic and Generative Model of Areas Tiling the Cortex

Much of the human cortex seems to be organized into topographic cortical maps. Yet few quantitative methods exist for characterizing these maps. To address this issue we developed a modeling framework that can reveal group-level cortical maps based on neuroimaging data. PrAGMATiC, a probabilistic and generative model of areas tiling the cortex, is a hierarchical Bayesian generative model of cortical maps. This model assumes that the cortical map in each individual subject is a sample from a single underlying probability distribution. Learning the parameters of this distribution reveals the properties of a cortical map that are common across a group of subjects while avoiding the potentially lossy step of co-registering each subject into a group anatomical space. In this report we give a mathematical description of PrAGMATiC, describe approximations that make it practical to use, show preliminary results from its application to a real dataset, and describe a number of possible future extensions

Pycortex: an interactive surface visualizer for fMRI.

Surface visualizations of fMRI provide a comprehensive view of cortical activity. However, surface visualizations are difficult to generate and most common visualization techniques rely on unnecessary interpolation which limits the fidelity of the resulting maps. Furthermore, it is difficult to understand the relationship between flattened cortical surfaces and the underlying 3D anatomy using tools available currently. To address these problems we have developed pycortex, a Python toolbox for interactive surface mapping and visualization. Pycortex exploits the power of modern graphics cards to sample volumetric data on a per-pixel basis, allowing dense and accurate mapping of the voxel grid across the surface. Anatomical and functional information can be projected onto the cortical surface. The surface can be inflated and flattened interactively, aiding interpretation of the correspondence between the anatomical surface and the flattened cortical sheet. The output of pycortex can be viewed using WebGL, a technology compatible with modern web browsers. This allows complex fMRI surface maps to be distributed broadly online without requiring installation of complex software