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.
We perform first-principles relativistic particle-in-cell simulations of aligned pulsar magnetosphere. We allow free escape of particles from the surface of a neutron star and continuously populate the magnetosphere with neutral pair plasma to imitat
e pair production. As pair plasma supply increases, we observe the transition from a charge-separated electrosphere solution with trapped plasma and no spin-down to a solution close to the ideal force-free magnetosphere with electromagnetically-dominated pulsar wind. We calculate the magnetospheric structure, current distribution and spin-down power of the neutron star. We also discuss particle acceleration in the equatorial current sheet.
The current state of the art in pulsar magnetosphere modeling assumes the force-free limit of magnetospheric plasma. This limit retains only partial information about plasma velocity and neglects plasma inertia and temperature. We carried out time-de
pendent 3D relativistic magnetohydrodynamic (MHD) simulations of oblique pulsar magnetospheres that improve upon force-free by retaining the full plasma velocity information and capturing plasma heating in strong current layers. We find rather low levels of magnetospheric dissipation, with less than 10% of pulsar spindown energy dissipated within a few light cylinder radii, and the MHD spindown that is consistent with that in force-free. While oblique magnetospheres are qualitatively similar to the rotating split-monopole force-free solution at large radii, we find substantial quantitative differences with the split-monopole, e.g., the luminosity of the pulsar wind is more equatorially concentrated than the split-monopole at high obliquities, and the flow velocity is modified by the emergence of reconnection flow directed into the current sheet.
The magnetosphere of a rotating pulsar naturally develops a current sheet beyond the light cylinder (LC). Magnetic reconnection in this current sheet inevitably dissipates a nontrivial fraction of the pulsar spin-down power within a few LC radii. We
develop a basic physical picture of reconnection in this environment and discuss its implications for the observed pulsed gamma-ray emission. We argue that reconnection proceeds in the plasmoid-dominated regime, via an hierarchical chain of multiple secondary islands/flux ropes. The inter-plasmoid reconnection layers are subject to strong synchrotron cooling, leading to significant plasma compression. Using the conditions of pressure balance across these current layers, the balance between the heating by magnetic energy dissipation and synchrotron cooling, and Amperes law, we obtain simple estimates for key parameters of the layers --- temperature, density, and layer thickness. In the comoving frame of the relativistic pulsar wind just outside of the equatorial current sheet, these basic parameters are uniquely determined by the strength of the reconnecting upstream magnetic field. For the case of the Crab pulsar, we find them to be of order 10 GeV, $10^{13} cm^{-3}$, and 10 cm, respectively. After accounting for the bulk Doppler boosting due to the pulsar wind, the synchrotron and inverse-Compton emission from the reconnecting current sheet can explain the observed pulsed high-energy (GeV) and VHE (~100 GeV) radiation, respectively. Also, we suggest that the rapid relative motions of the secondary plasmoids in the hierarchical chain may contribute to the production of the pulsar radio emission.
We address the question of whether numerical particle-in-cell (PIC) simulations and laboratory laser-plasma experiments can (or will be able to, in the near future) model realistic gamma-ray burst (GRB) shocks. For this, we compare the radiative cool
ing time, t_cool, of relativistic electrons in the shock magnetic fields to the microscopic dynamical time of collisionless relativistic shocks -- the inverse plasma frequency of protons, omega_pp^{-1}. We obtain that for t_cool*omega_pp^{-1}lesssim ~few hundred, the electrons cool efficiently at or near the shock jump and are capable of emitiing away a large fraction of the shock energy. Such shocks are well-resolved in existing PIC simulations; therefore, the microscopic structure can be studied in detail. Since most of the emission in such shocks would be coming from the vicinity of the shock, the spectral power of the emitted radiation can be directly obtained from finite-length simulations and compared with observational data. Such radiative shocks correspond to the internal baryon-dominated GRB shocks for the conventional range of ejecta parameters. Fermi acceleration of electrons in such shocks is limited by electron cooling, hence the emitted spectrum should be lacking a non-thermal tail, whereas its peak likely falls in the multi-MeV range. Incidentally, the conditions in internal shocks are almost identical to those in laser-produced plasmas; thus, such GRB-like plasmas can be created and studied in laboratory experiments using the presently available Petawatt-scale laser facilities. An analysis of the external shocks shows that only the highly relativistic shocks, corresponding to the extremely early afterglow phase, can have efficient electron cooling in the shock transition. We emphasize the importance of radiative PIC simulations for further studies.
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 distrib
utions 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.
