We present first-principles relativistic particle-in-cell simulations of the oblique pulsar magnetosphere with pair formation. The magnetosphere starts to form with particles extracted from the surface of the neutron star. These particles are acceler
ated by surface electric fields and emit photons capable of producing electron-positron pairs. We inject secondary pairs at locations of primary energetic particles, whose energy exceeds the threshold for pair formation. We find solutions that are close to the ideal force-free magnetosphere, with the Y-point and current sheet. Solutions with obliquities $lt 40^{circ}$ do not show pair production in the open field line region, because the local current density along magnetic field is below the Goldreich-Julian value. The bulk outflow in these solutions is charge separated, and pair formation happens in the current sheet and return current layer only. Solutions with higher inclinations show pair production in the open field line region, with high multiplicity of the bulk flow and the size of pair-producing region increasing with inclination. We observe the spin-down of the star to be comparable to MHD model predictions. The magnetic dissipation in the current sheet ranges between 20% for the aligned rotator and 3% for the orthogonal rotator. Our results suggest that for low obliquity neutron stars with suppressed pair formation at the light cylinder, the presence of phenomena related to pair activity in the bulk of the polar region, e.g., radio emission, may crucially depend on the physics beyond our simplified model, such as the effects of curved space-time or multipolar surface fields.
The Crab Nebula was formed after the collapse of a massive star about a thousand years ago, leaving behind a pulsar that inflates a bubble of ultra-relativistic electron-positron pairs permeated with magnetic field. The observation of brief but brigh
t flares of energetic gamma rays suggests that pairs are accelerated to PeV energies within a few days; such rapid acceleration cannot be driven by shocks. Here, it is argued that the flares may be the smoking gun of magnetic dissipation in the Nebula. Using 2D and 3D particle-in-cell simulations, it is shown that the observations are consistent with relativistic magnetic reconnection, where pairs are subject to strong radiative cooling. The Crab flares may highlight the importance of relativistic magnetic reconnection in astrophysical sources.
The discovery of rapid synchrotron gamma-ray flares above 100 MeV from the Crab Nebula has attracted new interest in alternative particle acceleration mechanisms in pulsar wind nebulae. Diffuse shock-acceleration fails to explain the flares because p
article acceleration and emission occur during a single or even sub-Larmor timescale. In this regime, the synchrotron energy losses induce a drag force on the particle motion that balances the electric acceleration and prevents the emission of synchrotron radiation above 160 MeV. Previous analytical studies and 2D particle-in-cell (PIC) simulations indicate that relativistic reconnection is a viable mechanism to circumvent the above difficulties. The reconnection electric field localized at X-points linearly accelerates particles with little radiative energy losses. In this paper, we check whether this mechanism survives in 3D, using a set of large PIC simulations with radiation reaction force and with a guide field. In agreement with earlier works, we find that the relativistic drift kink instability deforms and then disrupts the layer, resulting in significant plasma heating but few non-thermal particles. A moderate guide field stabilizes the layer and enables particle acceleration. We report that 3D magnetic reconnection can accelerate particles above the standard radiation reaction limit, although the effect is less pronounced than in 2D with no guide field. We confirm that the highest energy particles form compact bunches within magnetic flux ropes, and a beam tightly confined within the reconnection layer, which could result in the observed Crab flares when, by chance, the beam crosses our line of sight.
It is generally accepted that astrophysical sources cannot emit synchrotron radiation above 160 MeV in their rest frame. This limit is given by the balance between the accelerating electric force and the radiation reaction force acting on the electro
ns. The discovery of synchrotron gamma-ray flares in the Crab Nebula, well above this limit, challenges this classical picture of particle acceleration. To overcome this limit, particles must accelerate in a region of high electric field and low magnetic field. This is possible only with a non-ideal magnetohydrodynamic process, like magnetic reconnection. We present the first numerical evidence of particle acceleration beyond the synchrotron burnoff limit, using a set of 2D particle-in-cell simulations of ultra-relativistic pair plasma reconnection. We use a new code, Zeltron, that includes self-consistently the radiation reaction force in the equation of motion of the particles. We demonstrate that the most energetic particles move back and forth across the reconnection layer, following relativistic Speiser orbits. These particles then radiate >160 MeV synchrotron radiation rapidly, within a fraction of a full gyration, after they exit the layer. Our analysis shows that the high-energy synchrotron flux is highly variable in time because of the strong anisotropy and inhomogeneity of the energetic particles. We discover a robust positive correlation between the flux and the cut-off energy of the emitted radiation, mimicking the effect of relativistic Doppler amplification. A strong guide field quenches the emission of >160 MeV synchrotron radiation. Our results are consistent with the observed properties of the Crab flares, supporting the reconnection scenario.
The recent discovery of day-long gamma-ray flares in the Crab Nebula, presumed to be synchrotron emission by PeV (10^{15} eV) electrons in milligauss magnetic fields, presents a strong challenge to particle acceleration models. The observed photon en
ergies exceed the upper limit (~100 MeV) obtained by balancing the acceleration rate and synchrotron radiation losses under standard conditions where the electric field is smaller than the magnetic field. We argue that a linear electric accelerator, operating at magnetic reconnection sites, is able to circumvent this difficulty. Sufficiently energetic electrons have gyroradii so large that their motion is insensitive to small-scale turbulent structures in the reconnection layer and is controlled only by large-scale fields. We show that such particles are guided into the reconnection layer by the reversing magnetic field as they are accelerated by the reconnection electric field. As these electrons become confined within the current sheet, they experience a decreasing perpendicular magnetic field that may drop below the accelerating electric field. This enables them to reach higher energies before suffering radiation losses and hence to emit synchrotron radiation in excess of the 100 MeV limit, providing a natural resolution to the Crab gamma-ray flare paradox.
