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.Comment: 7 pages, 3 figures, accepted for publication in A&

A more accurate numerical scheme for diffusive shock acceleration

We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using Stochastic Differential Equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that contains a shock of finite width and a varying diffusivity of the cosmic rays, where the diffusivity decreases across the shock. We compare the results for the slope of the momentum distribution with those obtained from a perturbation analysis valid for finite but small shock width. These calculations show that this scheme, although computationally more expensive, provides a significantly better performance than the Cauchy-Euler type schemes that were proposed earlier in the case where steep gradients in the cosmic ray diffusivity occur. For constant diffusivity the proposed scheme gives similar results as the Cauchy-Euler scheme.Comment: 9 pages, 2 figures. Published in MNRA

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

We consider the acceleration of charged particles at the ultra-relativistic shocks, with Lorentz factors \Gamma_s >> 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 \Gamma_s^2 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 re-isotropise 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 10^{18.5} - 10^{20.5} eV, by the blast wave. We propose, however, 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.Comment: Accepted for MNRAS (Letters), with minor revisions. LaTeX, 5 pages, uses mn.st

Evolution of Magnetic Fields in Supernova Remnants

Supernova remnants (SNR) are now widely believed to be a source of cosmic rays (CRs) up to an energy of 1 PeV. The magnetic fields required to accelerate CRs to sufficiently high energies need to be much higher than can result from compression of the circumstellar medium (CSM) by a factor 4, as is the case in strong shocks. Non-thermal synchrotron maps of these regions indicate that indeed the magnetic field is much stronger, and for young SNRs has a dominant radial component while for old SNRs it is mainly toroidal. How these magnetic fields get enhanced, or why the field orientation is mainly radial for young remnants, is not yet fully understood. We use an adaptive mesh refinement MHD code, AMRVAC, to simulate the evolution of supernova remnants and to see if we can reproduce a mainly radial magnetic field in early stages of evolution. We follow the evolution of the SNR with three different configurations of the initial magnetic field in the CSM: an initially mainly toroidal field, a turbulent magnetic field, and a field parallel to the symmetry axis. Although for the latter two topologies a significant radial field component arises at the contact discontinuity due to the Rayleigh-Taylor instability, no radial component can be seen out to the forward shock. Ideal MHD appears not sufficient to explain observations. Possibly a higher compression ratio and additional turbulence due to dominant presence of CRs can help us to better reproduce the observations in future studies.Comment: 5 pages, 3 figures. To appear in conference proceedings of "Magnetic Fields in the Universe II" (2008), RevMexA

Nonthermal X-ray emission from young Supernova Remnants

The cosmic-ray spectrum up to the knee ($E\sim 10^{15}$ eV) is attributed to acceleration processes taking place at the blastwaves which bound supernova remnants. Theoretical predictions give a similar estimate for the maximum energy which can be reached at supernova remnant shocks by particle acceleration. Electrons with energies of the order $\sim 10^{15}$ eV should give a nonthermal X-ray component in young supernova remnants. Recent observations of SN1006 and G347.3-0.5 confirm this prediction. We present a method which uses hydrodynamical simulations to describe the evolution of a young remnant. These results are combined with an algorithm which simultaneously calculates the associated particle acceleration. We use the test particle approximation, which means that the back-reaction on the dynamics of the remnant by the energetic particles is neglected. We present synchrotron maps in the X-ray domain, and present spectra of the energies of the electrons in the supernova remnant. Some of our results can be compared directly with earlier semi-analytical work on this subject by Reynolds [1].Comment: 4 pages, 2 figures, contribution proceedings of poster presented at the 11th Annual Astrophysics Conference in Maryland, to appear in Young Supernova Remnants, ed. by S. S. Holt and U. Hwang (AIP

Branching on multi-aggregated variables

open5siopenGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, DomenicoGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, Domenic

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