arXiv subjects

A. Achterberg

Publications and source records attributed to A. Achterberg.

24 records · Page 2Linked to original sources

arXiv2004

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 m_e/m_p) 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.

astro-ph↗

arXiv2003

Magnetic field generation in relativistic shocks

We present an analytical estimate for the magnetic field strength generated by the Weibel instability in ultra-relativistic shocks in a hydrogen plasma. We find that the Weibel instability is, by itself, not capable of converting the kinetic energy of protons penetrating the shock front into magnetic field energy. Other (nonlinear) processes must determine the magnetic field strength in the wake of the shock.

astro-ph↗

arXiv2002

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 created at 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 ${\cal M}_{\rm psr} = 7/\sqrt{5}$, {\em independent} of the supernova explosion energy and pulsar velocity. The bow shock structure is shown to survive this break-through event.

astro-ph↗

arXiv2000

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.

astro-ph↗

arXiv2000

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 fronts to apply to shocks of arbitrarily high Lorentz factor. In agreement with the findings of Monte-Carlo simulations, we find 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 (where s=-d(ln f)/dp with f the Lorentz invariant phase-space density and p the momentum). This corresponds to a synchrotron index for uncooled electrons of a=0.62 (taking cooling into account a=1.12), where a=-d(ln F)/dn, F is the radiation flux and n 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 non-relativistic case the angular distribution is weighted more towards 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 ratio of Poynting to kinetic energy flux upstream is not small are less compressive and lead to larger values of $s$.

astro-ph↗

arXiv1999

Particle acceleration at oblique shocks and discontinuities of the density profile

In the theory of diffusive acceleration at oblique shock fronts the question of the existence of a discontinuity of energetic particle density is contentious. The resolution of this problem is interesting from a theoretical point of view, and potentially for the interpretation of observations of particle densities at heliospheric shocks and of high-resolution radio observations of the rims of supernova remnants. It can be shown analytically that an isotropic particle distribution at a shock front implies continuity of the particle density -- whether or not the shock is oblique. However, if the obliquity of the shock induces an anisotropy, a jump is permitted. Both semi-analytic computations and Monte-Carlo simulations are used to show that, for interesting parameter ranges, a jump is indeed produced, with accelerated particles concentrated in a precursor ahead of the shock front.

astro-ph↗