1,340 research outputs found
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&
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
Jets as diagnostics of the circumstellar medium and the explosion energetics of supernovae: the case of Cas A
We present hydrodynamical models for the Cassiopeia A (Cas A) supernova
remnant and its observed jet / counter-jet system. We include the evolution of
the progenitor's circumstellar medium, which is shaped by a slow red supergiant
wind that is followed by a fast Wolf-Rayet (WR) wind.
The main parameters of the simulations are the duration of the WR phase and
the jet energy. We find that the jet is destroyed if the WR phase is
sufficiently long and a massive circumstellar shell has formed. We therefore
conclude that the WR phase must have been short (a few thousand yr), if present
at all. Since the actual jet length of Cas A is not known we derive a lower
limit for the jet energy, which is ~10^{48} erg. We discuss the implications
for the progenitor of Cas A and the nature of its explosion.Comment: 9 pages, 5 figures, ApJ accepted. Version with high resolution
figures available at http://www.phys.uu.nl/~schure/CasA_jet.pd
Magnetic field generation in relativistic shocks
Linear theory of the Weibel instability cannot explain magnetic field generation in relativistic shock fronts in electron-proton plasmas. The fireball model for Gamma-ray Burst afterglows requires a magnetic field in similar shock
fronts between the fireball and the surrounding matter to explain the detected nonthermal afterglow radiation. We consider an analytical model of pre-shock protons
penetrating the hot post-shock electron plasma. The linear Weibel instability produces magnetic fields through
self-enhancing current channels. Perturbations with a
length-scale comparable to the electron skin depth reach the highest magnetic field before the linear theory breaks down. The electrons quench the linear proton instability
so that it cannot randomize the proton velocity distribution and only converts a small fraction of the available kinetic energy of the protons into magnetic fields. We conclude that the linear Weibel instability that dominates in pair plasmas is relatively unimportant in electron-proton plasmas and that non-linear processes are
probably much more important
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
Cosmic-ray energy spectrum and composition up to the ankle - the case for a second Galactic component
We have carried out a detailed study to understand the observed energy
spectrum and composition of cosmic rays with energies up to ~10^18 eV. Our
study shows that a single Galactic component with subsequent energy cut-offs in
the individual spectra of different elements, optimised to explain the observed
spectra below ~10^14 eV and the knee in the all-particle spectrum, cannot
explain the observed all-particle spectrum above ~2x10^16 eV. We discuss two
approaches for a second component of Galactic cosmic rays -- re-acceleration at
a Galactic wind termination shock, and supernova explosions of Wolf-Rayet
stars, and show that the latter scenario can explain almost all observed
features in the all-particle spectrum and the composition up to ~10^18 eV, when
combined with a canonical extra-galactic spectrum expected from strong radio
galaxies or a source population with similar cosmological evolution. In this
two-component Galactic model, the knee at ~ 3x10^15 eV and the second knee at
~10^17 eV in the all-particle spectrum are due to the cut-offs in the first and
second components, respectively. We also discuss several variations of the
extra-galactic component, from a minimal contribution to scenarios with a
significant component below the ankle (at ~4x10^18 eV), and find that
extra-galactic contributions in excess of regular source evolution are neither
indicated nor in conflict with the existing data. Our main result is that the
second Galactic component predicts a composition of Galactic cosmic rays at and
above the second knee that largely consists of helium or a mixture of helium
and CNO nuclei, with a weak or essentially vanishing iron fraction, in contrast
to most common assumptions. This prediction is in agreement with new
measurements from LOFAR and the Pierre Auger Observatory which indicate a
strong light component and a rather low iron fraction between ~10^17 and 10^18
eV.Comment: Added Table 4; Published in A&A, 595 (2016) A33 (Highlight paper
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 .Comment: Minor additions on publicatio
On the Structure and Scale of Cosmic Ray Modified Shocks
Strong astrophysical shocks, diffusively accelerating cosmic rays (CR) ought
to develop CR precursors. The length of such precursor is believed to
be set by the ratio of the CR mean free path to the shock speed,
i.e., , which is formally
independent of the CR pressure . However, the X-ray observations of
supernova remnant shocks suggest that the precursor scale may be significantly
shorter than which would question the above estimate unless the
magnetic field is strongly amplified and the gyroradius is strongly
reduced over a short (unresolved) spatial scale. We argue that while the CR
pressure builds up ahead of the shock, the acceleration enters into a strongly
nonlinear phase in which an acoustic instability, driven by the CR pressure
gradient, dominates other instabilities (at least in the case of low
plasma). In this regime the precursor steepens into a strongly nonlinear front
whose size scales with \emph{the CR pressure}as , where is the scale of
the developed acoustic turbulence, and is the ratio of CR to gas
pressure. Since , the precursor scale reduction may be strong
in the case of even a moderate gas heating by the CRs through the acoustic and
(possibly also) the other instabilities driven by the CRs.Comment: EPS 2010 paper, to appear in PPC
Induced Scattering and Two-Photon Absorption of Alfven Waves with Arbitrary Propagation Angles
The equation for temporary evolution of spectral energy of collisionless
Alfven waves is derived in framework of weak turbulence theory. The main
nonlinear processes for such conditions are induced scattering and two quantum
absorption of Alfven waves by thermal ions. The equation for velocity
distribution of thermal particles is derived that describes diffusion in
momentum space due to this nonlinear processes. Comparison is done with the
results of another authors. Results obtained are qualitatively differ from the
ones obtained for the case of Alfven waves propagation along mean magnetic
field.Comment: 8 page
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