We investigate the temporal evolution of an axisymmetric magnetosphere around a rapidly rotating, stellar-mass black hole, applying a two-dimensional particle-in-cell simulation scheme. Adopting a homogeneous pair production, and assuming that the mass accretion rate is much less than the Eddington limit, we find that the black hole's rotational energy is preferentially extracted from the middle latitudes, and that this outward energy flux exhibits an enhancement that lasts approximately 160 dynamical time scales. It is demonstrated that the magnetohydrodynamic approximations cannot be justified in such a magnetically-dominated magnetosphere, because the Ohm's law completely breaks down, and because the charge-separated electron-positron plasmas are highly non-neutral. An implication is given regarding the collimation of relativistic jets.
The stationary axisymmetric force-free magnetosphere of a pulsar is studied analytically. The pulsar equation is solved in the region close to the magnetic axis. Proceeding from linearization of the current function in the axial region, we find the axial magnetic flux function valid at any altitude above the neutron star. This function is used as a starting approximation to develop series for the non-linear pulsar equation in the polar region. Taking into account the quasi-monopolar character of the pulsar magnetic flux at infinity, we obtain unique asymptotic series for the flux and current f…
A magnetar's magnetosphere gradually evolves by the injection of energy and helicity from the interior. Axisymmetric static solutions for a relativistic force-free magnetosphere with a power-law current model are numerically obtained. They provide information about the configurations in which the stored energy is large. The energy along a sequence of equilibria increases and becomes sufficient to open the magnetic field. A magnetic flux rope, in which a large amount of toroidal field is confined, is formed in the vicinity of the star, for states exceeding the open field energy. These states ar…
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 imitate 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 powe…
Magnetar magnetospheres gradually become twisted due to shearing by footpoint motion. The axisymmetric solutions for the force-free field with a power-law current model are calculated by taking into account general relativistic effects. Here we show how the magnetic energy and helicity are accumulated along a sequence of equilibria. In a strongly twisted case, a magnetic flux rope, in which a large amount of toroidal field is confined, detaches in the vicinity of the star. It is found this kind of magnetic field line structure is easily produced due to strong relativistic effects compared with…
A pseudo-spectral method with an absorbing outer boundary is used to solve a set of the time-dependent force-free equations. In the method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergencelessness of magnetic field is analytically enforced by a projection method. Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be well reproduced by our pseudo-spectral code. Further the method is used to present the time-dependent simulation of the force-free pulsar magneto…
Based on the exact dipolar solution of the pulsar equation the self-consistent two-fluid model of the pulsar magnetosphere is developed. We concentrate on the low-mass limit of the model, taking into account the radiation damping. As a result, we obtain the particle distributions sustaining the dipolar force-free configuration of the pulsar magnetosphere in case of a slight velocity shear of the electron and positron components. Over most part of the force-free region, the particles follow the poloidal magnetic field lines, with the azimuthal velocities being small. Close to the Y-point, howev…
The main issue of the pulsar magnetosphere is how the rotation power is converted into both particle beams which causes pulsed emissions, and a highly relativistic wind of electron-positron plasmas which forms surrounding nebulae shining in X-rays and TeV gamma-rays. As a sequel of the first paper (Wada & Shibata 2007), we carried out a three dimensional particle simulation for the axisymmetric global magnetosphere. We present the results of additional calculations, which are higher resolution model and higher pair creation rate cases, and a detailed analysis for the solution. We confined to d…
The self-consistent two-fluid model of the pulsar magnetosphere is considered. We concentrate on the case of vanishingly small inertia of the particles. Our approach allows to obtain the realistic particle distributions sustaining the force-free magnetic field configuration of a monopolar structure. The result differs substantially from the customary picture of the radial speed-of-light motion of massless particles. In our case, the electron and positron constituents follow slightly curved trajectories and are characterized by definite number densities and distinct velocities. The velocity shi…
We present the first self-consistent global simulations of pulsar magnetospheres with operating $e^\pm$ discharge. We focus on the simple configuration of an aligned or anti-aligned rotator. The star is spun up from zero (vacuum) state to a high angular velocity, and we follow the coupled evolution of its external electromagnetic field and plasma particles using the "particle-in-cell" method. A plasma magnetosphere begins to form through the extraction of particles from the star; these particles are accelerated by the rotation-induced electric field, producing curvature radiation and igniting …
We present solutions of force-free pulsar magnetospheres coupled with a uniform external magnetic field aligned with the dipole magnetic moment of the pulsar. The inclusion of the uniform magnetic field has the following consequences: The equatorial current sheet is truncated to a finite length, the fraction of field lines that are open increases, and the open field lines are confined within a cylindrical surface instead of becoming radial. A strong external magnetic field antiparallel to the dipole allows for solutions where the pulsar magnetic field is fully enclosed within an ellipsoidal su…
We present a global kinetic plasma simulation of an axisymmetric pulsar magnetosphere with self-consistent $e^\pm$ pair production. We use the particle-in-cell method and log-spherical coordinates with a grid size $4096\times 4096$. This allows us to achieve a high voltage induced by the pulsar rotation and investigate pair creation in a young pulsar far from the death line. We find the following. (1) The energy release and $e^\pm$ creation are strongly concentrated in the thin, Y-shaped current sheet, with a peak localized in a small volume at the Y-point. (2) The Y-point is shifted inward fr…
We examine the temporary evolution of axisymmetric magnetospheres around rapidly rotating black holes (BHs), by applying our two-dimensional particle-in-cell simulation code. Assuming a stellar-mass BH, we find that the created pairs fail to screen the electric field along the magnetic field, provided that the mass accretion rate is much small compared to the Eddington limit. Magnetic islands are created by reconnection near the equator and migrate toward the event horizon, expelling magnetic flux tubes from the BH vicinity during a large fraction of time. When the magnetic islands stick to th…
The recent detection of gravitational waves associated with a binary neutron star merger revives interest in interacting pulsar magnetospheres. Current models predict that a significant amount of magnetic energy should be released prior to the merger, leading to electromagnetic precursor emission. In this paper, we revisit this problem in the light of the recent progress in kinetic modeling of pulsar magnetospheres. We limit our work to the case of aligned magnetic moments and rotation axes, and thus neglect the orbital motion. We perform global two-dimensional axisymmetric particle-in-cell si…
We consider force-free magnetospheres around the extreme Kerr black hole. In this case there is no known exact analytic solution to force free electrodynamics which is stationary, axisymmetric and magnetically-dominated. However, any stationary, axisymmetric and regular force-free magnetosphere in extreme Kerr black hole approaches the same attractor solution in the near-horizon extreme Kerr (NHEK) limit with null electromagnetic field. We show that by moving away from the attractor solution in the NHEK region, one finds magnetically-dominated solutions in the extreme Kerr black hole with fini…
The stationary axisymmetric force-free magnetosphere of a pulsar is considered. We present an exact dipolar solution of the pulsar equation, construct the magnetospheric model on its basis and examine its observational support. The new model has toroidal rather than common cylindrical geometry, in line with that of the plasma outflow observed directly as the pulsar wind nebula at much larger spatial scale. In its new configuration, the axisymmetric magnetosphere consumes the neutron star rotational energy much more efficiently, implying re-estimation of the stellar magnetic field, $B_{\mathrm …
In this poster we present the structure of an axisymmetric, force-free magnetosphere of a twisted, aligned rotating dipole within a corotating plasma-filled magnetosphere. We explore various profiles for the twist. We find that as the current increases more field lines cross the light cylinder leading to more efficient spin-down. Moreover, we notice that the twist cannot be increased indefinitely and after a finite twist of about $π/2$ the field becomes approximately radial. This could have implications for torque variations of magnetars related to outbursts.
The equatorial current sheet in pulsar magnetospheres is often regarded as an ideal site for particle acceleration via relativistic reconnection. Using 2D spherical particle-in-cell simulations, we investigate particle acceleration in the axisymmetric pulsar magnetosphere as a function of the injected plasma multiplicity and magnetization. We observe a clear transition from a highly charge-separated magnetosphere for low plasma injection with little current and spin-down power, to a nearly force-free solution for high plasma multiplicity characterized by a prominent equatorial current sheet an…
Magnetars exhibit a variety of transient high-energy phenomena in the form of bursts, outbursts, and giant flares. It is a common belief that these events originate in the sudden release of magnetic energy due to the rearrangement of a twisted magnetic field. We present global models of a 3D Force-Free (FF) non-linear twisted magnetar magnetosphere. We solve the FF equations following the Grad-Rubin approach in a compactified spherical domain. Appropriate boundary conditions are imposed at the surface of the star for the current distribution and the magnetic field. Our implementation is tested…
The magnetospheres of magnetars are believed to be filled with electron-positron plasma generated by electric discharge. We present a first direct numerical experiment showing how the plasma is created in an axisymmetric closed magnetosphere. The $e^\pm$ discharge occurs in response to twisting of the magnetic field lines by a shear deformation of the magnetar surface, which launches electric currents into the magnetosphere. The simulation shows the formation of an electric "gap" with unscreened electric field ($\mathbf{E}\cdot \mathbf{B}\neq 0$) that continually accelerates particles along th…
We present PICsar -- a new Particle in Cell code geared towards efficiently simulating the magnetosphere of the aligned rotator. PICsar is a special relativistic, electromagnetic, charge conservative code that can be used to simulate arbitrary electromagnetics problems in axisymmetry. It features stretchable body-fitted coordinates that follow the surface of a sphere, simplifying the application of boundary conditions in the case of the aligned rotator; a radiation absorbing outer boundary, which allows a steady state to be set up dynamically and maintained indefinitely from transient initial …
Dynamics of charged matter in the oblique black hole magnetosphere is investigated. In particular, we adopt a model consisting of a rotating black hole embedded in the external large-scale magnetic field that is inclined arbitrarily with respect to the rotation axis. Breaking the axial symmetry appears to have profound consequences regarding the dynamics of particles and it also poses some methodological difficulties. In this contribution we discuss the applicability of the method of effective potential for the non-axisymmetric model and show that it may only be applied in the appropriate refe…
We present the first simulations of evolving, strongly twisted magnetar magnetospheres. Slow shearing of the magnetar crust is seen to lead to a series of magnetospheric expansion and reconnection events, corresponding to X-ray flares and bursts. The axisymmetric simulations include rotation of the neutron star and the magnetic wind through the light cylinder. We study how the increasing twist affects the spindown rate of the star, finding that a dramatic increase in spindown occurs. Particularly spectacular are explosive events caused by the sudden opening of large amounts of overtwisted magn…
Analytical solutions to force-free electrodynamics around black holes are fundamental for building simple models of accretion disk and jet dynamics. We present a (nonexhaustive) classification of complex highest-weight solutions to the force-free equations in the near-horizon region of the extremal Kerr black hole. Several classes of real magnetically dominated or null solutions, either axisymmetric or nonaxisymmetric, are described which admit finite energy and angular momentum with respect to the asymptotically flat observer. Subtleties related to the velocity of light surface in the near-ho…
Recent observations in X-ray and Gamma-ray suggest that the emission region of the pulsar magnetosphere can be multifold. In particular, the open-close boundary of the magnetic field, so-called the Y-point, can be the new candidate place where magnetic field energy converts into the plasma heat and/or flow energy. Here, we present a new Particle-in-Cell code, which can be applied to the Y-point of the pulsar magnetosphere in axisymmetric geometry. The electromagnetic solver is used in the two-dimensional grid points with the cylindrical coordinate (R, z), while the particle solver operates in …
Magnetar magnetospheres are believed to be strongly twisted, due to shearing of the stellar crust by internal magnetic stresses. We present time-dependent axisymmetric simulations showing in detail the evolution of relativistic force-free magnetospheres subjected to slow twisting through large angles. When the twist amplitude is small, the magnetosphere moves quasi-statically through a sequence of equilibria of increasing free energy. At some twist amplitude the magnetosphere becomes tearing-mode unstable to forming a resistive current sheet, initiating large-scale magnetic reconnection in whi…
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 obliqu…
Dynamics of charged particles in the vicinity of a rotating black hole embedded in the external large-scale magnetic field is numerically investigated. In particular, we consider a non-axisymmetric model in which the asymptotically uniform magnetic field is inclined with respect to the axis of rotation. We study the effect of inclination onto the prevailing dynamic regime of particle motion, i.e. we ask whether the inclined field allows regular trajectories or if instead, the deterministic chaos dominates the motion. In this contribution we further discuss the role of initial condition, partic…
We revisit the Blandford & Znajek (1977) process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity omega and the poloidal electric current I. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem, the inner `light surface' located inside the ergosphere, and the outer `light surface' which is the generalization of the pulsar light …
The magnetar magnetosphere is gradually twisted by shearing from footpoint motion, and stored magnetic energy also increases at the same time. When a state exceeds a threshold, flares/outbursts manifest themselves as a result of a catastrophic transition. Axisymmetric static solutions for a relativistic force-free magnetosphere with dipole--quadrupole mixed fields at the surface have been calculated. The quadrupole component represents a kind of magnetic-field irregularity at a small scale. Locally twisted models are constructed by limiting current flow regions, where the small part originates…
On the universality of the split monopole black hole magnetosphere
Columbia University（哥伦比亚大学）；Anton Pannekoek Institute（安东·潘内克研究所）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；University of Toronto（多伦多大学）；Perimeter Institute for Theoretical Physics（基础理论物理研究所）；Flatiron Institute（平顿研究所）
It has recently been demonstrated that self-consistent particle-in-cell simulations of low-obliquity pulsar magnetospheres in flat spacetime show weak particle acceleration and no pair production near the poles. We investigate the validity of this conclusion in a more realistic spacetime geometry via general-relativistic particle-in-cell simulations of the aligned pulsar magnetospheres with pair formation. We find that the addition of frame-dragging effect makes local current density along the magnetic field larger than the Goldreich-Julian value, which leads to unscreened parallel electric fi…
Based on the Lagrangian of the steady axisymmetric force-free magnetosphere (FFM) equation around Kerr black holes(KBHs), we find that the FFM equation can be rewritten in a new form as $f_{,rr} / (1-μ^{2}) + f_{,μμ} / Δ+ K(f(r,μ),r,μ) = 0$, where $μ= -\cosθ$. By coordinate transformation, the form of the above equation can be given by $s_{,yy} + s_{,zz} + D(s(y,z),y,z) = 0$. Based on the form, we prove finally that the Meissner effect is not possessed by a KBH-FFM with the condition where $dω/d A_ϕ \leqslant 0$ and $H_ϕ(dH_ϕ/dA_ϕ) \geqslant 0$, here $A_ϕ$ is the $ϕ$ component of the vector po…
We present a numerical model in which a cold pair plasma is ejected with relativistic speed through a polar cap region and flows almost radially outside the light cylinder. Stationary axisymmetric structures of electromagnetic fields and plasma flows are self-consistently calculated. In our model, motions of positively and negatively charged particles are assumed to be determined by electromagnetic forces and inertial terms, without pair creation and annihilation or radiation loss. The global electromagnetic fields are calculated by the Maxwell's equations for the plasma density and velocity, …
Black holes are known to launch powerful relativistic jets and emit highly variable gamma radiation. How these jets are loaded with plasma remains poorly understood. Spark gaps are thought to drive particle acceleration and pair creation in the black-hole magnetosphere. In this paper, we perform 2D axisymmetric general-relativistic particle-in-cell simulations of a monopole black-hole magnetosphere with a realistic treatment of inverse Compton scattering and pair production. We find that the magnetosphere can self-consistently fill itself with plasma and activate the Blandford-Znajek mechanism…
Context: The origin of ultra-rapid flares of very high-energy radiation from active galactic nuclei remains elusive. Magnetospheric processes, occurring in the close vicinity of the central black hole, could account for these flares. Aims: We aim to bridge the gap between simulations and observations by synthesizing gamma-ray lightcurves in order to characterize the activity of a black-hole magnetosphere, using kinetic simulations. Methods: We perform global axisymmetric two-dimensional general-relativistic particle-in-cell simulations of a Kerr black-hole magnetosphere. We include a self-cons…
There is observational evidence that the X-ray continuum source that creates the broad fluorescent emission lines in some Seyfert Galaxies may be compact and located at a few gravitational radii above the black hole. We consider the possibility that this compact source may be powered by small scale flux tubes near the black hole that are attached to the orbiting accretion disk. As a first step, this paper investigates the salient features of black hole magnetospheres that contain small scale, disk-hole linking "closed" flux tubes, using the force-free approximation in an axisymmetric setting. …
We explore superradiance for Alfvén waves (Alfvénic superradiance) in an axisymmetric rotating magnetosphere of a Kerr black hole within the force-free approximation. On the equatorial plane of the Kerr spacetime, the Alfvén wave equation is reduced to a one-dimensional Schrödinger-type equation by separating variables of the wave function and introducing a tortoise coordinate mapping the inner and outer light surfaces to $-\infty$ and $+\infty$, respectively, and we investigate a wave scattering problem for Alfvén waves. An analysis of the asymptotic solutions of the wave equation and the con…
We perform 2.5D axisymmetric simulations of the pulsar magnetosphere (aligned dipole rotator) using the charge conservative, relativistic, electromagnetic particle in cell code PICsar. Particle in cell codes are a powerful tool to use for studying the pulsar magnetosphere, because they can handle the force-free and vacuum limits and provide a self-consistent treatment of magnetic reconnection. In the limit of dense plasma throughout the magnetosphere, our solutions are everywhere in the force-free regime except for dissipative regions at the polar caps, in the current layers, and at the Y-poin…
We quantitatively study the stationary, axisymmetric, force-free magnetospheres of spinning (Kerr) black holes (BHs) and the conditions needed for relativistic jets to be powered by the Blandford-Znajek mechanism. These jets could be from active galactic nuclei, blazars, quasars, micro-quasars, radio active galaxies, and other systems that host Kerr BHs. The structure of the magnetosphere determines how the BH energy is extracted, e.g., via Blandford-Znajek mechanism, which converts the BH rotational energy into Poynting flux. The key assumption is the force-free condition, which requires the …
Strong gravity and magnetic fields are key ingredients that power processes of accretion and ejection near compact objects. While the particular mechanisms that operate here are still discussed, it seems that the presence of an ordered magnetic field is crucial for the acceleration and collimation of relativistic jets of electrically charged particles on superhorizon length scales. In this context, we further study the effect of a large-scale magnetic field on the dynamics of charged particles near a rotating black hole. We consider a scenario in which the initially neutral particles on regula…
We propose a new approach to find magnetically-dominated force-free magnetospheres around highly spinning black holes, relevant for models of astrophysical jets. Employing the near-horizon extreme Kerr (NHEK) limit of the Kerr black hole, any stationary, axisymmetric and regular force-free magnetosphere reduces to the same attractor solution in the NHEK limit with null electromagnetic field strength. We use this attractor solution as the universal starting point for perturbing away from the NHEK region in the extreme Kerr spacetime. We demonstrate that by going to second order in perturbation …
We study the effects of large scale magnetic fields on the dynamics of charged particles near a rotating black hole. We consider a scenario in which the initially neutral particles on geodesic orbits in the equatorial plane become ionized, and hence they are destabilized by the charging process. Fraction of charged particles are then accelerated out of the equatorial plane and then follow jet like trajectories with relativistic velocities. We explore non axisymmetric systems in which the magnetic field is inclined with respect to the black hole spin. We study the system numerically in order to…
We discuss stationary and axisymmetric trans-magnetosonic outflows in the magnetosphere of a rotating black hole (BH). Ejected plasma from the plasma source located near the BH is accelerated far away to form a relativistic jet. In this study, the plasma acceleration efficiency and conversion of fluid energy from electromagnetic energy are considered by employing the trans-fast magnetosonic flow solution derived by Takahashi & Tomimatsu (2008). Considering the parameter dependence of magnetohydrodynamical flows, we search for the parameters of the trans-magnetosonic outflow solution to the rec…
Magnetars are neutron stars characterized by strong surface magnetic fields generally exceeding the quantum critical value of 44.1 TeraGauss. High-energy photons propagating in their magnetospheres can be attenuated by QED processes like photon splitting and magnetic pair creation. In this paper, we compute the opacities due to photon splitting and pair creation by photons emitted anywhere in the magnetosphere of a magnetar. Axisymmetric, twisted dipole field configurations embedded in the Schwarzschild metric are treated. The paper computes the maximum energies for photon transparency that pe…
We investigate the dynamics and emission of a starved magnetospheric region (gap) formed in the vicinity of a Kerr black hole horizon, using a new, fully general relativistic particle-in-cell code that implements Monte Carlo methods to compute gamma-ray emission and pair production through the interaction of pairs and gamma rays with soft photons emitted by the accretion flow. It is found that when the Thomson length for collision with disk photons exceeds the gap width, screening of the gap occurs through low-amplitude, rapid plasma oscillations that produce self-sustained pair cascades, with…
The interaction of black holes with ambient magnetic fields is important for a variety of highly energetic astrophysical phenomena. We study this interaction within the force-free approximation in which a tenuous plasma is assumed to have zero inertia. Blandford and Znajek (BZ) used this approach to demonstrate the conversion of some of the black hole's energy into electromagnetic Poynting flux in stationary and axisymmetric single black hole systems. We adopt this approach and extend it to examine asymmetric and, most importantly, dynamical systems by implementing the fully nonlinear field eq…
We review electrodynamics of rotating magnetized neutron stars, from the early vacuum model to recent numerical experiments with plasma-filled magnetospheres. Significant progress became possible due to the development of global particle-in-cell simulations which capture particle acceleration, emission of high-energy photons, and electron-positron pair creation. The numerical experiments show from first principles how and where electric gaps form, and promise to explain the observed pulsar activity from radio waves to gamma-rays.
Accreting pulsars power relativistic jets, and display a complex spin phenomenology. These behaviours may be closely related to the large-scale configuration of the star's magnetic field, shaped by its interaction with the surrounding accretion disc. Here we present the first relativistic simulations of the interaction of a pulsar magnetosphere with an accretion flow. Our axisymmetric simulations treat the magnetospheric, or coronal, regions using a resistive extension of force-free electrodynamics. The magnetic field is also evolved inside the disc, which is a defined volume with a specified …
Recent advances in numerical algorithms and computational power have enabled first-principles simulations of pulsar magnetospheres using Particle-in-Cell (PIC) techniques. These ab-initio simulations seem to indicate that pair creation through photon-photon collision at the light cylinder is required to sustain the pulsar engine. However, for many rotation-powered pulsars pair creation operates effectively only near the stellar surface where magnetic field is high. How these "weak pulsars" fill their magnetospheres without efficient photon-photon pair conversion in the outer magnetosphere is s…
We present a model for high-energy emission sources generated by a standing magnetohydrodynamical (MHD) shock in a black hole magnetosphere. The black hole magnetosphere would be constructed around a black hole with an accretion disk, where a global magnetic field could be originated by currents in the accretion disk and its corona. Such a black hole magnetosphere may be considered as a model for the central engine of active galactic nuclei, some compact X-ray sources and gamma-ray bursts. The energy sources of the emission from the magnetosphere are the gravitational and electromagnetic energ…
