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Abstract Black holes can launch powerful jets through the Blandford–Znajek process. This relies on enough plasma in the jet funnel to conduct the necessary current. However, in some low-luminosity active galactic nuclei, the plasma supply near the jet base may be an issue. It has been proposed that spark gaps—local regions with unscreened electric field—can form in the magnetosphere, accelerating particles to initiate pair cascades, thus filling the jet funnel with plasma. In this paper, we carry out 2D general relativistic particle-in-cell (GRPIC) simulations of the gap, including self-consistent treatment of inverse Compton scattering and pair production. We observe gap dynamics that is fully consistent with our earlier 1D GRPIC simulations. We find strong dependence of the gap power on the soft photon spectrum and energy density, as well as the strength of the horizon magnetic field. We derive physically motivated scaling relations, and applying to M87, we find that the gap may be energetically viable for the observed TeV flares. For Sgr A*, the energy dissipated in the gap may also be sufficient to power the X-ray flares. 

Abstract Rapid shear motion of magnetar crust can launch Alfvén waves into the magnetosphere. The dissipation of the Alfvén waves has been theorized to power the X-ray bursts characteristic of magnetars. However, the process by which Alfvén waves convert their energy to X-rays is unclear. Recent work has suggested that energetic fast magnetosonic (fast) waves can be produced as a byproduct of Alfvén waves propagating on curved magnetic field lines; their subsequent dissipation may power X-ray bursts. In this work, we investigate the production of fast waves by performing axisymmetric force-free simulations of Alfvén waves propagating in a dipolar magnetosphere. For Alfvén wave trains that do not completely fill the flux tube confining them, we find a fast wave dominated by a low frequency component with a wavelength defined by the bouncing time of the Alfvén waves. In contrast, when the wave train is long enough to completely fill the flux tube, and the Alfvén waves overlap significantly, the energy is quickly converted into a fast wave with a higher frequency that corresponds to twice the Alfvén wave frequency. We investigate how the energy, duration, and wavelength of the initial Alfvén wave train affect the conversion efficiency to fast waves. For modestly energetic star quakes, we see that the fast waves that are produced will become nonlinear well within the magnetosphere, and we comment on the X-ray emission that one may expect from such events. 

NICER has observed a few millisecond pulsars where the geometry of the X-ray-emitting hotspots on the neutron star have been analyzed in order to constrain the mass and radius from X-ray light-curve modeling. One example, PSR J0030 + 0451, has been shown to possibly have significant multipolar magnetic fields at the stellar surface. Using force-free simulations of the magnetosphere structure, it has been shown that the radio, X-ray, andγ-ray light curves can be modeled simultaneously with an appropriate field configuration. An even more stringent test is to compare predictions of the force-free magnetosphere model with observations of radio polarization. This paper attempts to reproduce the radio polarization of PSR J0030 + 0451 using a force-free magnetospheric solution. As a result of our modeling, we can reproduce certain features of the polarization well.