Ab Initio Pulsar Magnetosphere: Three-Dimensional Particle-in-Cell Simulations of Oblique Pulsars

Abstract

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 accelerated 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 ≤ 40 • 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.

Electrodynamics of Pulsar Magnetospheres

“…The 3D simulations of inclined rotators (Philippov et al 2015a) show a similar mechanism of sustaining the wobbling current sheet predicted by the 3D force-free simulations of Spitkovsky (2006). A snapshot of the inclined rotator with χ = 60 o is shown in Figure 8.…”

“…The aligned rotator has the maximum dissipated fraction of about 20%. The dissipation rate then decreases monotonically with increasing inclination to about 2.5% for χ = 90 o (Philippov et al 2015a). The dissipated Poynting flux is not lost numerically, but instead it is self-consistently channelled into particle kinetic energy and non-thermal radiation.…”

“…Self-consistent simulations of e ± discharge showing how the magnetosphere is filled with plasma were first performed for an aligned rotator (Chen and Beloborodov 2014) and then for an inclined rotator (Philippov et al 2015a). They demonstrated that the main particle accelerator in pulsars is the Y-shaped current sheet.…”

“…Cerutti et al (2015) did not implement e ± creation in the magnetosphere and instead injected a mildly relativistic HE radiative efficiency Fig. 9 Top: Dissipated fraction of the total radial Poynting flux L (converted to nonthermal particles and radiation) within a sphere of radius r = 2R LC as a function of the pulsar inclination, as reported by global PIC studies (Philippov and Spitkovsky 2014;Chen and Beloborodov 2014;Cerutti et al 2015;Philippov et al 2015a;Belyaev 2015a). The values from Cerutti et al (2015) and Belyaev (2015a) are for their highest particle injection solutions (closest to force-free); lower particle injection leads to more dissipation (20-50%).…”

“…Belyaev (2015a) implemented e ± creation proportionally to the local E . Philippov et al (2015a) assumed instantaneous local pair creation by any particle reaching a fixed threshold Lorentz factor γ thr . Chen and Beloborodov (2014) performed the most detailed simulation that followed the propagation of curvature gamma-rays and their conversion to pairs.…”