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Abstract We write down the force-free electrodynamics equations in dipole coordinates and solve for axisymmetric normal modes corresponding to Alfvénic perturbations in the magnetosphere of a neutron star. We show that a single Alfvén wave propagating on dipole field lines spontaneously sources a fast magnetosonic (fms) wave at the next order in the perturbation expansion, without needing three-wave interaction. The frequency of the sourced fms wave is twice the original Alfvén wave frequency, and the wave propagates spherically outward. The properties of the outgoing fms wave can be computed exactly using the usual devices of classical electrodynamics. We extend the calculation to the closed zone of a rotating neutron star magnetosphere, and show that the Alfvén wave also sources a spherical fms wave but at the same frequency as the primary Alfvén wave. 

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. 

Abstract Instabilities in a neutron star can generate Alfvén waves in its magnetosphere. Propagation along the curved magnetic field lines strongly shears the wave, boosting its electric current j A . We derive an analytic expression for the evolution of the wavevector k and the growth of j A . In the strongly sheared regime, j A may exceed the maximum current j 0 that can be supported by the background e ± plasma. We investigate these charge-starved waves, first using a simplified two-fluid analytic model, then with first-principles kinetic simulations. We find that the Alfvén wave is able to propagate successfully even when κ ≡ j A / j 0 ≫ 1. It sustains j A by compressing and advecting the plasma along the magnetic field lines with an increasing Lorentz factor, γ ≳ κ 1/2 . The simulations show how plasma instabilities lead to gradual dissipation of the wave energy. Our results suggest that an extremely high charge-starvation parameter κ ≳ 10 4 may be required in order for this mechanism to power the observed fast radio bursts (FRBs) from SGR 1935+2154. However, cosmological FRBs with much higher luminosities are unlikely to be a result of charge-starvation. 

Abstract The most common form of magnetar activity is short X-ray bursts, with durations from milliseconds to seconds, and luminosities ranging from 10³⁶–10⁴³erg s⁻¹. Recently, an X-ray burst from the galactic magnetar SGR 1935+2154 was detected to be coincident with two fast radio burst (FRB) like events from the same source, providing evidence that FRBs may be linked to magnetar bursts. Using fully 3D force-free electrodynamics simulations, we show that such magnetar bursts may be produced by Alfvén waves launched from localized magnetar quakes: a wave packet propagates to the outer magnetosphere, becomes nonlinear, and escapes the magnetosphere, forming an ultra-relativistic ejecta. The ejecta pushes open the magnetospheric field lines, creating current sheets behind it. Magnetic reconnection can happen at these current sheets, leading to plasma energization and X-ray emission. The angular size of the ejecta can be compact, ≲1 sr if the quake launching region is small, ≲0.01 sr at the stellar surface. We discuss implications for the FRBs and the coincident X-ray burst from SGR 1935+2154.