We present evidence that relativistic shocks propagating in unmagnetized plasmas can self-consistently accelerate particles. We use long-term two-dimensional particle-in-cell simulations to study the ...well-developed shock structure in unmagnetized pair plasma. The particle spectrum downstream of such a shock consists of two components: a relativistic Maxwellian, with a characteristic temperature set by the upstream kinetic energy of the flow, and a high-energy tail, extending to energies >100 times that of the thermal peak. This high-energy tall is best fitted as a power law in energy with index -2.4 plus or minus 0.1, modified by an exponential cutoff. The cutoff moves to higher energies with time of the simulation, leaving a larger power-law range. The number of particles in the tail is similar to 1% of the downstream population, and they carry similar to 10% of the kinetic energy in the downstream region. Investigating the trajectories of particles in the tail, we find that the energy gains occur as particles bounce between the upstream and downstream regions in the magnetic fields generated by the Weibei instability. We compare this mechanism to the first-order Fermi acceleration and set a lower limit on the efficiency of the shock acceleration process.
Relativistic collisionless shocks in electron-ion plasmas are thought to occur in the afterglow phase of gamma-ray bursts (GRBs) and in other environments where relativistic flows interact with the ...interstellar medium. A particular regime of shocks in an unmagnetized plasma has generated much interest for GRB applications. In this Letter, we present ab initio particle-in-cell simulations of unmagnetized relativistic electron-ion shocks. Using long-term 2.5-dimensional simulations with ion-electron mass ratios from 16 to 1000, we resolve the shock formation and reach a steady state shock structure beyond the initial transient. We find that even at high ion-electron mass ratios initially unmagnetized shocks can be effectively mediated by the ion Weibel instability with a typical shock thickness of similar to 20 ion skin depths. Upstream of the shock, the interaction with merging ion current filaments heats the electron component, so that the postshock flow achieves near-equipartition between the ions and electrons, with the electron temperature reaching 50% of the ion temperature. This energy exchange helps to explain the large electron energy fraction inferred from GRB afterglow observations.
We perform global particle-in-cell simulations of pulsar magnetospheres, including pair production, ion extraction from the surface, frame-dragging corrections, and high-energy photon emission and ...propagation. In the case of oblique rotators, the effects of general relativity increase the fraction of the open field lines that support active pair discharge. We find that the plasma density and particle energy flux in the pulsar wind are highly non-uniform with latitude. A significant fraction of the outgoing particle energy flux is carried by energetic ions, which are extracted from the stellar surface. Their energies may extend up to a large fraction of the open field line voltage, making them interesting candidates for ultra-high-energy cosmic rays. We show that pulsar gamma-ray radiation is dominated by synchrotron emission, produced by particles that are energized by relativistic magnetic reconnection close to the Y-point and in the equatorial current sheet. In most cases, the calculated light curves contain two strong peaks, which is in general agreement with Fermi observations. The radiative efficiency decreases with increasing pulsar inclination and increasing efficiency of pair production in the current sheet, which explains the observed scatter in Lγ versus . We find that the high-frequency cutoff in the spectra is regulated by the pair-loading of the current sheet. Our findings lay the foundation for quantitative interpretation of Fermi observations of gamma-ray pulsars.
The relativistic wind of obliquely rotating pulsars consists of toroidal stripes of opposite magnetic field polarity, separated by current sheets of hot plasma. By means of two- and three-dimensional ...particle-in-cell simulations, we investigate particle acceleration and magnetic field dissipation at the termination shock of a relativistic striped wind. At the shock, the flow compresses and the alternating fields annihilate by driven magnetic reconnection. Irrespective of the stripe wavelength Delta *l or the wind magnetization Delta *s (in the regime Delta *s 1 of magnetically dominated flows), shock-driven reconnection transfers all the magnetic energy of alternating fields to the particles, whose average Lorentz factor increases by a factor of Delta *s with respect to the pre-shock value. The shape of the post-shock spectrum depends primarily on the ratio Delta *l/(rL Delta *s), where rL is the relativistic Larmor radius in the wind. The spectrum becomes broader as the value of Delta *l/(rL Delta *s) increases, passing from a relativistic Maxwellian to a flat power-law tail with slope around --1.5, populated by particles accelerated by the reconnection electric field. Close to the equatorial plane of the wind, where the stripes are symmetric, the highest energy particles resulting from magnetic reconnection can escape ahead of the shock, and be injected into a Fermi-like acceleration process. In the post-shock spectrum, they populate a power-law tail with slope around --2.5, which extends beyond the flat component produced by reconnection. Our study suggests that the spectral break between the radio and the optical band in Pulsar Wind Nebulae can be a natural consequence of particle acceleration at the termination shock of striped pulsar winds.
The self-regulation of cosmic-ray (CR) transport in the interstellar and intracluster media has long been viewed through the lenses of linear and quasi-linear kinetic plasma physics. Such theories ...are believed to capture the essence of CR behavior in the presence of self-generated turbulence but cannot describe potentially critical details arising from the nonlinearities of the problem. We utilize the particle-in-cell numerical method to study the time-dependent nonlinear behavior of the gyroresonant streaming instabilities, self-consistently following the combined evolution of particle distributions and self-generated wave spectra in one-dimensional periodic simulations. We demonstrate that the early growth of instability conforms to the predictions from linear physics, but that the late-time behavior can vary depending on the properties of the initial CR distribution. We emphasize that the nonlinear stages of instability depend strongly on the initial anisotropy of CRs-highly anisotropic CR distributions do not efficiently reduce to Alfvénic drift velocities, owing to reduced production of left-handed resonant modes. We derive estimates for the wave amplitudes at saturation and the timescales for nonlinear relaxation of the CR distribution and then demonstrate the applicability of these estimates to our simulations. Bulk flows of the background plasma due to the presence of resonant waves are observed in our simulations, confirming the microphysical basis of CR-driven winds.
Magnetic reconnection is often invoked to explain the nonthermal radiation of relativistic outflows, including jets of active galactic nuclei (AGNs). Motivated by the largely unknown plasma ...composition of AGN jets, we study reconnection in the unexplored regime of electron-positron-proton (pair-proton) plasmas with large-scale two-dimensional particle-in-cell simulations. We cover a wide range of pair multiplicities (lepton-to-proton number ratio κ = 1-199) for different values of the all-species plasma magnetization ( = 1, 3, and 10) and electron temperature ( ). We focus on the dependence of the post-reconnection energy partition and lepton energy spectra on the hot pair plasma magnetization (i.e., the ratio of magnetic to pair enthalpy densities). We find that the post-reconnection energy is shared roughly equally between magnetic fields, pairs, and protons for 3. We empirically find that the mean lepton Lorentz factor in the post-reconnection region depends on , Θe, and as , for ≥ 1. The high-energy part of the post-reconnection lepton energy distributions can be described by a power law, whose slope is mainly controlled by for κ 3-6, with harder power laws obtained for higher magnetizations. We finally show that reconnection in pair-proton plasmas with multiplicities κ ∼ 1-20, magnetizations ∼ 1-10, and temperatures Θe ∼ 1-10 results in particle power-law slopes and average electron Lorentz factors that are consistent with those inferred in leptonic models of AGN jet emission.
The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as synchrotron radiation from electrons accelerated at the GRB external shock that propagates with relativistic velocities ...into the magnetized interstellar medium. By means of multi-dimensional particle-in-cell simulations, we investigate the acceleration performance of weakly magnetized relativistic shocks, in the magnetization range 0 lap sigma lap 10 super(-1). The pre-shock magnetic field is orthogonal to the flow, as genetically expected for relativistic shocks. We find that relativistic perpendicular shocks propagating in electron-positron plasmas are efficient particle accelerators if the magnetization is sigma lap 10 super(-3). Here, the acceleration process proceeds similarly for the two species, since the electrons enter the shock nearly in equipartition with the ions, as a result of strong pre-heating in the self-generated upstream turbulence. Our results can provide physically grounded inputs for models of non-thermal emission from a variety of astrophysical sources, with particular relevance to GRB afterglows.
We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations. We explore a range of inclination ...angles between the pre-shock magnetic field and the shock normal. We find that only magnetic inclinations corresponding to 'subluminal' shocks, where relativistic particles following the magnetic field can escape ahead of the shock, lead to particle acceleration. The downstream spectrum in such shocks consists of a relativistic Maxwellian and a high-energy power-law tail with exponential cutoff. For increasing magnetic inclination in the subluminal range, the high-energy tail accounts for an increasing fraction of particles (from ~1% to ~2%) and energy (from ~4% to ~12%). The spectral index of the power law increases with angle from -2.8 - 0.1 to -2.3 - 0.1. For nearly parallel shocks, particle energization mostly proceeds via the diffusive shock acceleration process; the upstream scattering is provided by oblique waves which are generated by the high-energy particles that escape upstream. For larger subluminal inclinations, shock-drift acceleration is the main acceleration mechanism, and the upstream oblique waves regulate injection into the acceleration process. For 'superluminal' shocks, self-generated shock turbulence is not strong enough to overcome the kinematic constraints, and the downstream particle spectrum does not show any significant suprathermal tail. As seen from the upstream frame, efficient acceleration in relativistic (Lorentz factor gamma 0 5) magnetized ( sigma 0.03) flows exists only for a very small range of magnetic inclination angles (34DG/ gamma 0), so relativistic astrophysical pair shocks have to be either nearly parallel or weakly magnetized to generate nonthermal particles. These findings place constraints on the models of pulsar wind nebulae, gamma-ray bursts, and jets from active galactic nuclei that invoke particle acceleration in relativistic magnetized shocks.
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