Ion acceleration in non-relativistic astrophysical shocks

We explore the physics of shock evolution and particle acceleration in non-relativistic collisionless shocks using multidimensional hybrid simulations. We analyze a wide range of physical parameters relevant to the acceleration of cosmic rays (CRs) in astrophysical non-relativistic shock scenarios, such as in supernova remnant (SNR) shocks. We explore the evolution of the shock structure and particle acceleration efficiency as a function of Alfv\'enic Mach number and magnetic field inclination angle $\theta$. We show that there are fundamental differences between high and low Mach number shocks in terms of the electromagnetic turbulence generated in the pre-shock zone and downstream; dominant modes are resonant with the streaming CRs in the low Mach number regime, while both resonant and non-resonant modes are present for high Mach numbers. Energetic power law tails for ions in the downstream plasma can account for up to 15% of the incoming upstream flow energy, distributed over $\sim5$ of the particles in a power law with slope $-2\pm0.2$ in energy. The energy conversion efficiency (for CRs) peaks at $\theta=15^\circ$ to $30^\circ$ and $M_A=6$, and decreases for higher Mach numbers, down to $\sim2$ for $M_A=31$. Accelerated particles are produced by Diffusive Shock Acceleration (DSA) and by Shock Drift Acceleration (SDA) mechanisms, with the SDA contribution to the overall energy gain increasing with magnetic inclination. We also present a direct comparison between hybrid and fully kinetic particle-in-cell results at early times; the agreement between the two models justifies the use of hybrid simulations for longer-term shock evolution. In SNR shocks, particle acceleration will be significant for low Mach number quasi-parallel flows ($M_A < 30$, $\theta< 45$). This finding underscores the need for effective magnetic amplification mechanism in SNR shocks

Dissipative Pulsar Magnetosphere

Dissipative axisymmetric pulsar magnetosphere is calculated by a direct numerical simulation of the Strong-Field Electrodynamics equations. The magnetic separatrix disappears, it is replaced by a region of enhanced dissipation. With a better numerical scheme, one should be able to calculate the bolometric lightcurves for a given conductivity.Comment: 2 pages, 10 figures, minor changes for the journa

Impulsive acceleration of strongly magnetized relativistic flows

The definitive version can be found at: http://onlinelibrary.wiley.com/ Copyright Royal Astronomical SocietyThe strong variability of magnetic central engines of active galactic nuclei (AGNs) and gamma-ray bursts (GRBs) may result in highly intermittent strongly magnetized relativistic outflows. We find a new magnetic acceleration mechanism for such impulsive flows that can be much more effective than the acceleration of steady-state flows. This impulsive acceleration results in kinetic-energy-dominated flows that are conducive to efficient dissipation at internal magnetohydrodynamic shocks on astrophysically relevant distances from the central source. For a spherical flow, a discrete shell ejected from the source over a time t0 with Lorentz factor Γ∼ 1 and initial magnetization σ0=B20/4πρ0c2≫ 1 quickly reaches a typical Lorentz factor Γ∼σ1/30 and magnetization σ∼σ2/30 at the distance R0≈ct0. At this point, the magnetized shell of width Δ∼R0 in the laboratory frame loses causal contact with the source and continues to accelerate by spreading significantly in its own rest frame. The expansion is driven by the magnetic pressure gradient and leads to relativistic relative velocities between the front and back of the shell. While the expansion is roughly symmetric in the centre of the momentum frame, in the laboratory frame, most of the energy and momentum remains in a region (or shell) of width Δ∼R0 at the head of the flow. This acceleration proceeds as Γ∼ (σ0R/R0)1/3 and σ∼σ2/30 (R/R0)-1/3 until reaching a coasting radius Rc∼R0σ20, where the kinetic energy becomes dominant: Γ∼σ0 and σ∼ 1 at Rc. The shell then starts coasting and spreading (radially), its width growing as Δ∼R0(R/Rc), causing its magnetization to drop as σ∼Rc/R at R > Rc. Given the typical variability time-scales of AGNs and GRBs, the magnetic acceleration in these sources is a combination of the quasi-steady-state collimation acceleration close to the source and the impulsive (conical or locally quasi-spherical) acceleration farther out. The interaction with the external medium, which can significantly affect the dynamics, is briefly addressed in the discussion.Peer reviewe

Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks

We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic $e^+e^-$ shock. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are approximately isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, nonpropagating, and decaying. Using linear kinetic theory, we find a simple analytic form for these damping rates. Our theory predicts that overall magnetic energy decays like $(\omega_p t)^{-q}$ with $q \sim 1$, which compares favorably with simulations, but predicts overly rapid damping of short wavelength modes. Magnetic trapping of particles within the magnetic structures may be the origin of this discrepancy. We conclude that initially unmagnetized relativistic shocks in electron-positron plasmas are unable to form persistent downstream magnetic fields. These results put interesting constraints on synchrotron models for the prompt and afterglow emission from GRBs.Comment: 4 pages, 3 figures, contributed talk at the workshop: High Energy Phenomena in Relativistic Outflows (HEPRO), Dublin, 24-28 September 2007; Downsampled version for arXiv. Full resolution version available at http://astro.berkeley.edu/~pchang/proceedings.pd

On the Cosmic Ray Driven Firehose Instability

The role of the non-resonant firehose instability in conditions relevant to the precursors of supernova remnant shocks is considered. Using a second order tensor expansion of the Vlasov-Fokker-Planck equation we illustrate the necessary conditions for the firehose to operate. It is found that for very fast shocks, the diffusion approximation predicts that the linear firehose growth rate is marginally faster than its resonant counterpart. Preliminary hybrid MHD-Vlasov-Fokker-Planck simulation results using young supernova relevant parameters are presented.Comment: Contribution to the 6th International Symposium on High Energy Gamma-Ray Astronomy (Gamma2016), Heidelberg, Germany. To be published in the AIP Conference Proceeding

Acceleration in perpendicular relativistic shocks for plasmas consisting of leptons and hadrons

We investigate the acceleration of light particles in perpendicular shocks for plasmas consisting of a mixture of leptonic and hadronic particles. Starting from the full set of conservation equations for the mixed plasma constituents, we generalize the magneto-hydrodynamical jump conditions for a multi-component plasma, including information about the specific adiabatic constants for the different species. The impact of deviations from the standard model of an ideal gas is compared in theory and particle-in-cell simulations, showing that the standard-MHD model is a good approximation. The simulations of shocks in electron-positron-ion plasmas are for the first time multi-dimensional, transverse effects are small in this configuration and 1D simulations are a good representation if the initial magnetization is chosen high. 1D runs with a mass ratio of 1836 are performed, which identify the Larmor frequency \omega_{ci} as the dominant frequency that determines the shock physics in mixed component plasmas. The maximum energy in the non-thermal tail of the particle spectra evolves in time according to a power-law proportional to t^\alpha with \alpha in the range 1/3 < \alpha < 1, depending on the initial parameters. A connection is made with transport theoretical models by Drury (1983) and Gargate & Spitkovsky (2011), which predict an acceleration time proportional to \gamma and the theory for small wavelength scattering by Kirk & Reville (2010), which predicts a behavior rather as proportional to \gamma^2. Furthermore, we compare different magnetic field orientations with B_0 inside and out of the plane, observing qualitatively different particle spectra than in pure electron-ion shocks

Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks: Electron-Positron Plasmas

We study the long term evolution of magnetic fields generated by a collisionless relativistic $e^+e^-$ shock which is initially unmagnetized. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are close to isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, with the non-propagating magnetic fields forming relatively isolated regions with transverse dimension $\sim 10-20$ skin depths. These structures decay in amplitude, with little sign of downstream merging. The fields start with magnetic energy density $\sim (0.1-0.2)$ of the upstream kinetic energy within the shock transition, but rapid downstream decay drives the fields to much smaller values, below $10^{-3}$ of equipartition after $10^3$ skin depths. In an attempt to construct a theory that follows field decay to these smaller values, we explore the hypothesis that the observed damping is a variant of Landau damping in an unmagnetized plasma. The model is based on the small value of the downstream magnetic energy density, which suggests that particle orbits are only weakly perturbed from straight line motion, if the turbulence is homogeneous. Using linear kinetic theory applied to electromagnetic fields in an isotropic, relativistic Maxwellian plasma, we find a simple analytic form for the damping rates, $\gamma_k$, in two and three dimensions for small amplitude, subluminous electromagnetic fields. We find that magnetic energy does damp due to phase mixing of current carrying particles as $(\omega_p t)^{-q}$ with $q \sim 1$. (abridged)Comment: 10 pages, 6 figures, accepted to ApJ; Downsampled version for arXiv. Full resolution figures available at http://astro.berkeley.edu/~pchang/full_res_weibel.pd