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Register a new userThe maximum energy of shock-accelerated electrons in a microturbulent magnetic field
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Relativistic shocks propagating into a medium with low magnetization are generated and sustained by small-scale but very strong magnetic field turbulence. This so-called microturbulence modifies the typical shock acceleration process, and in particular that of electrons. In this work we perform Monte Carlo (MC) simulations of electrons encountering shocks with microturbulent fields. The simulations cover a three-dimensional parameter space in shock speed, acceleration efficiency, and peak magnetic field strength. From these, a Markov Chain Monte Carlo (MCMC) method was employed to estimate the maximum electron momentum from the MC-simulated electron spectra. Having estimated this quantity at many points well-distributed over an astrophysically relevant parameter space, an MCMC method was again used to estimate the parameters of an empirical formula that computes the maximum momentum of a Fermi-accelerated electron population anywhere in this parameter space. The maximum energy is well-approximated as a broken power-law in shock speed, with the break occurring when the shock decelerates to the point where electrons can begin to escape upstream from the shock.
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The maximum energy to which cosmic rays can be accelerated at weakly-magnetised ultra-relativistic shocks is investigated. We demonstrate that for such shocks, in which the scattering of energetic particles is mediated exclusively by ion skin-depth scale structures, as might be expected for a Weibel-mediated shock, there is an intrinsic limit on the maximum energy to which particles can be accelerated. This maximum energy is determined from the requirement that particles must be isotropised in the downstream plasma frame before the mean field transports them far downstream, and falls considerably short of what is required to produce ultra-high-energy cosmic rays. To circumvent this limit, a highly disorganised field is required on larger scales. The growth of cosmic-ray induced instabilities on wavelengths much longer than the ion-plasma skin depth, both upstream and downstream of the shock, is considered. While these instabilities may play an important role in magnetic field amplification at relativistic shocks, on scales comparable to the gyroradius of the most energetic particles, the calculated growth-rates have insufficient time to modify the scattering. Since strong modification is a necessary condition for particles in the downstream region to re-cross the shock, in the absence of an alternative scattering mechanism, these results imply that acceleration to higher energies is ruled out. If weakly-magnetised ultra-relativistic shocks are disfavoured as high energy particle accelerators in general, the search for potential sources of ultra-high-energy cosmic rays can be narrowed.
It is widely believed that the maximum energy of synchrotron photons when electrons are accelerated in shocks via the Fermi process is about 50 MeV (in plasma comoving frame). We show that under certain conditions, which are expected to be realized in relativistic shocks of gamma-ray bursts, synchrotron photons of energy much larger than 50 MeV (comoving frame) can be produced. The requirement is that magnetic field should decay downstream of the shock front on a length scale that is small compared with the distance traveled by the highest energy electrons before they lose half their energy; photons of energy much larger than 50 MeV are produced close to the shock front whereas the highest Lorentz factor that electrons can attain is controlled by the much weaker field that occupies most of the volume of the shocked plasma.
The direct current (DC) electric field near the reconnection region has been proposed as an effective mechanism to accelerate protons and electrons in solar flares. A power-law energy spectrum was generally claimed in the simulations of electron acceleration by the reconnection electric field. However in most of the literature, the electric and magnetic fields were chosen independently. In this paper, we perform test-particle simulations of electron acceleration in a reconnecting magnetic field, where both the electric and magnetic fields are adopted from numerical simulations of the MHD equations. It is found that the accelerated electrons present a truncated power-law energy spectrum with an exponential tail at high energies, which is analogous to the case of diffusive shock acceleration. The influences of reconnection parameters on the spectral feature are also investigated, such as the longitudinal and transverse components of the magnetic field and the size of the current sheet. It is suggested that the DC electric field alone might not be able to reproduce the observed single or double power-law distributions.
Bow Shock Pulsar Wind Nebulae are a class of non-thermal sources, that form when the wind of a pulsar moving at supersonic speed interacts with the ambient medium, either the ISM or in a few cases the cold ejecta of the parent supernova. These systems have attracted attention in recent years, because they allow us to investigate the properties of the pulsar wind in a different environment from that of canonical Pulsar Wind Nebulae in Supernova Remnants. However, due to the complexity of the interaction, a full-fledged multidimensional analysis is still laking. We present here a simplified approach, based on Lagrangian tracers, to model the magnetic field structure in these systems, and use it to compute the magnetic field geometry, for various configurations in terms of relative orientation of the magnetic axis, pulsar speed and observer direction. Based on our solutions we have computed a set of radio emission maps, including polarization, to investigate the variety of possible appearances, and how the observed emission pattern can be used to constrain the orientation of the system, and the possible presence of turbulence.
We investigate axisymmetric steady solutions of (magneto)hydrodynamics equations that describe approximately accretion flows through a standing shock wave and discuss the effects of rotation and magnetic field on the revival of the stalled shock wave in supernova explosions. We develop a new powerful numerical method to calculate the 2-dimensional (2D) steady accretion flows self-consistently. We first confirm the results of preceding papers that there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution in spherical models. If a collapsing star has rotation and/or magnetic field, the accretion flows are no longer spherical owing to the centrifugal force and/or Lorentz force and the critical luminosity is modified.In fact we find that the critical luminosity is reduced by about 50% - 70% for rapid rotations and about 20% - 50% for strong toroidal magnetic fields, depending on the mass accretion rate. These results may be also interpreted as an existence of the critical specific angular momentum or critical magnetic field, above which there exists no steady solution and the standing shock wave will revive for a given combination of mass accretion rate and neutrino luminosity.
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