A. Achterberg

Particle acceleration by ultrarelativistic shocks: theory and simulations

We consider the acceleration of charged particles near ultrarelativistic shocks, with Lorentz factor . We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultrarelativistic shocks is a power law, , with a nearly universal value for the slope of this power law. We confirm that the ultrarelativistic equivalent of the Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurrence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle around the shock normal. We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount: . This limits the energy change per shock crossing cycle to , except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor for those particles that are scattered back across the shock into the upstream region.

First year performance of the IceCube neutrino telescope

The first sensors of the IceCube neutrino observatory were deployed at the South Pole during the austral summer of 2004-05 and have been producing data since February 2005. One string of 60 sensors buried in the ice and a surface array of 8 ice Cherenkov tanks took data until December 2005 when deployment of the next set of strings and tanks began. We have analyzed these data, demonstrating that the performance of the system meets or exceeds design requirements. Times are determined across the whole array to a relative precision of better than 3 nanoseconds, allowing reconstruction of muon tracks and light bursts in the ice, of air-showers in the surface array and of events seen in coincidence by surface and deep-ice detectors separated by up to 2.5 km.

Particle Acceleration at Ultrarelativistic Shocks: An Eigenfunction Method

We extend the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock front to apply to shocks of arbitrarily high Lorentz factor. In agreement with the findings of Monte Carlo simulations, we find that the index of the power-law distribution of accelerated particles, which undergo isotropic diffusion in angle at an ultrarelativistic, unmagnetized shock, is s = 4.23 ± 0.01 (where s = -d ln f/d ln p with f the Lorentz invariant phase-space density and p the momentum). This corresponds to a synchrotron index for uncooled electrons of α = 0.62 (taking cooling into account α = 1.12), where α = -d ln Fνα/d ln α, Fν is the radiation flux, and ν is the frequency. We also present an approximate analytic expression for the angular distribution of accelerated particles, which displays the effect of particle trapping by the shock: compared with the nonrelativistic case the angular distribution is weighted more toward the plane of the shock and away from its normal. We investigate the sensitivity of our results to the transport properties of the particles and the presence of a magnetic field. Shocks in which the parameter σ (the ratio of Poynting to kinetic energy flux) upstream is not small are less compressive and lead to larger values of s.

Ultra-high-energy cosmic ray acceleration by relativistic blast waves

We consider the acceleration of charged particles at the ultrarelativistic shocks, with Lorentz factors Γs≫1 relative to the upstream medium, arising in relativistic fireball models of gamma-ray bursts (GRBs). We show that for Fermi-type shock acceleration, particles initially isotropic in the upstream medium can gain a factor of order Γs2 in energy in the first shock-crossing cycle, but that the energy gain factor for subsequent shock-crossing cycles is only of order 2, because for realistic deflection processes particles do not have time to become isotropic upstream before recrossing the shock. We evaluate the maximum energy attainable and the efficiency of this process, and show that for a GRB fireball expanding into a typical interstellar medium, these exclude the production of ultra-high-energy cosmic rays (UHECRs), with energies in the range 1018.5--1020.5 eV, by the blast wave. However, we propose that in the context of neutron-star binaries as the progenitors of GRBs, relativistic ions from the pulsar-wind bubbles produced by these systems could be accelerated by the blast wave. We show that if the known binary pulsars are typical, the maximum energy, efficiency, and spectrum in this case can account for the observed population of UHECRs.

Pulsar wind nebulae in supernova remnants - Spherically symmetric hydrodynamical simulations

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 rst 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.

Magnetic field generation in relativistic shocks - An early end of the exponential Weibel instability in electron-proton plasmas

We discuss magnetic field generation by the proton Weibel instability in relativistic shocks, a situation that applies to the external shocks in the fireball model for Gamma-ray Bursts, and possibly also to internal shocks. Our analytical estimates show that the linear phase of the instability ends well before it has converted a significant fraction of the energy in the proton beam into magnetic energy: the conversion efficiency is much smaller (of order me/mp) in electron-proton plasmas than in pair plasmas. We find this estimate by modelling the plasma in the shock transition zone with a waterbag momentum distribution for the protons and with a background of hot electrons. For ultra-relativistic shocks we find that the wavelength of the most efficient mode for magnetic field generation equals the electron skin depth, that the relevant nonlinear stabilization mechanism is magnetic trapping, and that the presence of the hot electrons limits the typical magnetic field strength generated by this mode so that it does not depend on the energy content of the protons. We conclude that other processes than the linear Weibel instability must convert the free energy of the protons into magnetic fields.

The Weibel instability in relativistic plasmas. I. Linear theory

Aims. We discuss the linear theory of the Weibel instability in a relativistic plasma driven by ultra-relativistic beams, describing the physics of the generation of magnetic fields in the ultra-relativistic shocks associated with Gamma Ray Bursts (GRBs). We perform a detailed analysis of the linear dispersion relation for the benefit of non-linear calculations that we discuss in the companion paper. Methods. We use a covariant approach, where the linear response of the beam-plasma system is determined from the polarization tensor. This tensor relates the four-current density to the four-potential of the electromagnetic field. Showing that two approaches, one based on a fluid model and one on a kinetic description that uses a waterbag distribution for the phase-space density of the beam particles, yield essentially the same result, we compare our results to those obtained by other approaches. We mainly consider the symmetric case of two counterstreaming (but otherwise identical) beams. Results. We show that the effect of an asymmetry in the beam densities is small for typical parameters, and briefly discuss the effect of an ambient magnetic field. The dispersion relation of the Weibel instability driven by ultra-relativistic beams is rather insensitive to the model used to describe the plasma. The properties of the instability, such as the growth rate and the range of unstable wavelengths, are governed by only two parameters: the ratio of the plasma frequency squared of the beam and hot background plasma, and a “Mach number”, which is essentially the ratio of the beam momentum and the momentum associated with thermal velocity (∼sound speed) in the beam plasma. We also show that, at least for the parameters associated with the ultra-relativistic shocks in GRBs, the influence of the magnetic field is small, and the results for an unmagnetized plasma can be used. Conclusions.

Forming a constant density medium close to long gamma-ray bursts

Aims. The progenitor stars of long Gamma-Ray Bursts (GRBs) are thought to be Wolf-Rayet stars, which generate a massive and energetic wind. Nevertheless, about 25 percent of all GRB afterglows light curves indicate a constant density medium close to the exploding star. We explore various ways to produce this, by creating situations where the wind termination shock arrives very close to the star, as the shocked wind material has a nearly constant density. Methods. Typically, the distance between a Wolf-Rayet star and the wind termination shock is too large to allow afterglow formation in the shocked wind material. Here, we investigate possible causes allowing for a smaller distance: A high density or a high pressure in the surrounding interstellar medium (ISM), a weak Wolf-Rayet star wind, the presence of a binary companion, and fast motion of the Wolf-Rayet star relative to the ISM. Results. We find that all four scenarios are possible in a limited parameter space, but that none of them is by itself likely to explain the large fraction of constant density afterglows. Conclusions. A low GRB progenitor metallicity, and a high GRB energy make the occurrence of a GRB afterglow in a constant density medium more likely. This may be consistent with constant densities being preferentially found for energetic, high redshift GRBs.

The Search for Muon Neutrinos from Northern Hemisphere Gamma-Ray Bursts with AMANDA

The Search for Muon Neutrinos from Northern Hemisphere Gamma-Ray Bursts with AMANDA The IceCube Collaboration This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or The Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or The Regents of the University of California.

Interaction of high-velocity pulsars with supernova remnant shells

Hydrodynamical simulations are presented of a pulsar wind emitted by a supersonically moving pulsar. The pulsar moves through the interstellar medium or, in the more interesting case, through the supernova remnant createdat its birth event. In both cases there exists a three-fold structure consisting of the wind termination shock, contact discontinuity and a bow shock bounding the pulsar wind nebula. Using hydrodynamical simulations we study the behaviour of the pulsar wind nebula inside a supernova remnant, and in particular the interaction with the outer shell of swept up interstellar matter and the blast wave surrounding the remnant. This interaction occurs when the pulsar breaks out of the supernova remnant. We assume the remnant is in the Sedov stage of its evolution. Just before break-through, the Mach number associated with the pulsar motion equals M p s r = 7/ 5, independent of the supernova explosion energy and pulsar velocity. The bow shock structure is shown to survive this break-through event.