The detection of rapidly variable gamma-ray emission in active galactic nuclei has generated renewed interest in magnetospheric particle acceleration and emission scenarios. In order to explore its potential, we study the possibility of steady gap acceleration around the null surface of a rotating black hole magnetosphere. We employ a simplified (1D) description along with the general relativistic expression of Gauss's law, and we assume that the gap is embedded in the radiation field of a radiatively inefficient accretion flow. The model is used to derive expressions for the radial distribution of the parallel electric field component, the electron and positron charge density, the particle Lorentz factor, and the number density of $γ$-ray photons. We integrate the set of equations numerically, imposing suitable boundary conditions. The results show that the existence of a steady gap solution for a relative high value of the global current is in principle possible if charge injection of both species is allowed at the boundaries. We present gap solutions for different choices of the global current and the accretion rate. When put in context, our results suggest that the variable very high energy $γ$-ray emission in M87 could be compatible with a magnetospheric origin.
In this paper, we provide exact solutions for the extraction of energy from a rotating black hole via both the electromagnetic Poynting flux and matter currents. By appropriate choice of a radially independent poloidal function $Λ(θ)$, we find solutions where the dominant outward energy flux is along the polar axis, consistent with a jet-like collimated outflow, but also with a weaker flux of energy along the equatorial plane. Unlike all the previously obtained solutions (Blandford & Znajek (1977), Menon & Dermer (2005)), the magnetosphere is free of magnetic monopoles everywhere.
We study the effects of frame-dragging on the structure of force-free magnetospheres around rotating black holes. For slowly rotating black holes, analytic explorations often focus on transforming an exact force-free solution applicable to a static black hole into a solution approximately applicable to a slowly-rotating black hole via perturbations in black hole spin. We show that the single perturbed monopolar solution most commonly arrived at using such techniques is in fact a separatrix between two broad classes of solutions: those with poloidal magnetic fields that bend upwards towards the…
Electron-positron cascade in magnetospheres of supermassive Kerr black holes and the origin of relativistic AGN jets
University of Kansas（堪萨斯大学）；Massachusetts Institute of Technology（麻省理工学院）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文中心）
Neutron stars are compact objects rotating at high speed, up to a substantial fraction of the speed of light (up to 20\% for millisecond pulsars) and possessing ultra-strong electromagnetic fields (close to and sometimes above the quantum critical field of \numprint{4.4e9}~\SIunits{\tesla}). Moreover, due to copious $e^\pm$ pair creation within the magnetosphere, the relativistic plasma surrounding the star is forced into corotation up to the light cylinder where the corotation speed reaches the speed of light. The neutron star electromagnetic activity is powered by its rotation which becomes …
A novel model of particle acceleration in the magnetospheres of rotating active galactic nuclei (AGN) is constructed.The particle energies may be boosted up to $10^{21}$eV in a two step mechanism: In the first stage, the Langmuir waves are centrifugally excited and amplified by means of a parametric process that efficiently pumps rotational energy to excite electrostatic fields. In the second stage, the electrostatic energy is transferred to particle kinetic energy via Landau damping made possible by rapid "Langmuir collapse". The time-scale for parametric pumping of Langmuir waves turns out t…
The IceCube neutrino observatory measures the diffuse flux of high-energy astrophysical neutrinos by means of various techniques, and there exists a mild tension between spectra obtained in different analyses. The spectrum derived from reconstruction of muon tracks is harder than that from cascades, dominated by electron and tau neutrinos. If confirmed, this tension may provide a clue to the origin of these neutrinos, which remains uncertain. Here we investigate the possibility that this tension may be caused by the change of the flavor content of astrophysical neutrinos with energy. We assume…
We find a class of twisted and differentially rotating neutron star magnetospheres that do not have a light cylinder, generate no wind and thus do not spin-down. The magnetosphere is composed of embedded differentially rotating flux surfaces, with the angular velocity decreasing as $Ω\propto 1/r$ (equivalently, becoming smaller at the foot-points closer to the axis of rotation). For each given North-South self-similar twist profile there is a set of self-similar angular velocity profiles (limited from above) with a "smooth", dipolar-like magnetic field structure extending to infinity. For spin…
Under conditions prevailing in certain classes of compact astrophysical systems, the active magnetosphere of a rotating black hole becomes charge-starved, giving rise to formation of a spark gap in which plasma is continuously produced. The plasma production process is accompanied by curvature and inverse Compton emission of gamma rays in the GeV-TeV band, that may be detectable by current and future experiments. The properties of the gap emission have been studied recently using a fully general relativistic model of a local steady gap. However, this model requires artificial adjustment of the…
In rotating magnetospheres planted on compact objects, there usually exist lightcylinders (LC), beyond which the rotation speed of the magnetic field lines exceeds the speed of light. The LC is a close analog to the horizon in gravity, and is a casual boundary for charged particles that are restricted to move along the magnetic field lines. In this work, it is proposed that there should be Hawking-like radiation of charged particles from the LC of a rotating magnetosphere from the point of view of tunneling by using the field sheet metric.
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 structure of force-free, steady and axisymmetric magnetosphere of a neutron star (NS) is governed by the Grad-Shafranov (GS) equation, which is a second-order differential equation but degrades to first-order on the light surface (LS). The key to numerically solving the GS equation is to enable magnetic field lines smoothly cross the LS, and crossing a straight LS in flat spacetime has been a well-studied problem. But the numerical algorithm implementation becomes complicate in the presence of a bent LS, e.g. in curved spacetime, since there is no suitable computation grid adapted to it. W…
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…
Accreting supermassive black holes can now be observed at the event-horizon scale at mm wavelengths. Current predictions for the image rely on hypotheses (fluid modeling, thermal electrons) which might not always hold in the vicinity of the black hole, so that a full kinetic treatment is in order. In this letter, we describe the first 3D global general-relativistic particle-in-cell simulation of a black-hole magnetosphere. The system displays a persistent equatorial current sheet. Synthetic images are computed by ray-tracing synchrotron emission from nonthermal particles accelerated in this cu…
Supermassive stars (SMSs) of mass $\gtrsim 10^5 M_\odot$ are candidates for seeds of supermassive black holes found in the center of many massive galaxies. We simulate the gravitational collapse of a rigidly rotating SMS core including nuclear burning effects in axisymmetric numerical-relativity simulation. We find that for realistic initial conditions, the nuclear burning does not play an important role. After the collapse, a torus surrounding a rotating black hole is formed and a fraction of the torus material is ejected. We quantitatively study the relation between the properties of these o…
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…
Abridged. Fast rotating and self-gravitating astrophysical objects suffer strong deformations from centrifugal forces. If moreover they are magnetized, they generate an electromagnetic wave that is perturbed accordingly. When stellar objects are also surrounded by an ideal plasma, a magnetosphere is formed. We study the electromagnetic configuration of a force-free magnetosphere encompassing an ideal spheroidal rotating conductor as an inner boundary. We put special emphasize to millisecond period neutron star magnetospheres, those showing a significant oblate shape. Force-free solutions are c…
Plasma magnetosphere surrounding rotating magnetized neutron star in the braneworld has been studied. For the simplicity of calculations Goldreich-Julian charge density is analyzed for the aligned neutron star with zero inclination between magnetic field and rotation axis. From the system of Maxwell equations in spacetime of slowly rotating star in braneworld, second-order differential equation for electrostatic potential is derived. Analytical solution of this equation indicates the general relativistic modification of an accelerating electric field and charge density along the open field lin…
We investigate the conditions for radio emission in rotating and oscillating magnetars, by focusing on the main physical processes determining the position of their death-lines in the P-\dot{P} diagram, i.e. of those lines that separate the regions where the neutron star may be radio-loud or radio-quiet. After using the general relativistic expression for the electromagnetic scalar potential in the magnetar magnetosphere, we find that larger compactness parameters of the star as well as larger inclination angles between the rotation axis and the magnetic moment produce death-lines well above t…
We construct hydromagnetic neutron star equilibria which allow for a non-zero electric current distribution in the exterior. The novelty of our models is that the neutron star's interior field is in equilibrium with its magnetosphere, thus bridging the gap between previous work in this area which either solves for the interior assuming a vacuum exterior or solves for the magnetosphere without modelling the star itself. We consider only non-rotating stars in this work, so our solutions are most immediately applicable to slowly-rotating systems such as magnetars. Nonetheless, we demonstrate that…
Motivated by the measured velocity profile of the M87 jet using the KVN and VERA Array (KaVA) by Park et al. indicating that the starting position of the jet acceleration is farther from the central engine of the jet than predicted in general relativistic magnetohydrodynamic simulations, we explore how to mitigate the apparent discrepancy between the simulations and the KaVA observation. We use a semi-analytic jet model proposed by Tomimatsu and Takahashi. consistently solving the trans-magnetic field structure but neglecting any dissipation effects. By comparing the jet model with the observe…
Very high energy (VHE; >100 GeV) gamma-rays are expected to be emitted from the vicinity of super-massive black holes (SMBH), irrespective of their activity state. In the magnetosphere of rotating SMBH, efficient acceleration of charged particles can take place through various processes. These particles could reach energies up to E~10^{19}eV. VHE gamma-ray emission from these particles is then feasible via leptonic or hadronic processes. Therefore passive systems, where the lack of a strong photon field allows the VHE gamma-rays to escape, are expected to be detected by Cherenkov telescopes. W…
We examine if an efficient particle acceleration takes place by a magnetic-field-aligned electric field near the light cylinder in a rotating neutron star magnetosphere. Constructing the electric current density with the actual motion of collision-less plasmas, we express the rotationally induced, Goldreich-Julian charge density as a function of position. It is demonstrated that the 'light cylinder gap', which emits very high energy photons via curvature process by virtue of a strong magnetic-field-aligned electric field very close to the light cylinder, will not arise in an actual pulsar magn…
We study the magnetosphere of a slowly rotating magnetized neutron star subject to toroidal oscillations in the relativistic regime. Under the assumption of a zero inclination angle between the magnetic moment and the angular momentum of the star, we analyze the Goldreich-Julian charge density and derive a second-order differential equation for the electrostatic potential. The analytical solution of this equation in the polar cap region of the magnetosphere shows the modification induced by stellar toroidal oscillations on the accelerating electric field and on the charge density. We also find…
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…
This is the second paper in a series where we examine the physics of pair producing gaps in low-luminosity accreting supermassive black hole systems. In this paper, we carry out time-dependent self-consistent fully general relativistic 1D PIC simulations of the gap, including full inverse Compton scattering and photon tracking. Similar to the previous paper, we find a highly time-dependent solution where a macroscopic vacuum gap can open quasi-periodically, producing bursts of $e^\pm$ pairs and high energy radiation. We present the light curve, particle and photon spectra from this process. Us…
The main contribution to the pulsar power can be calculated by assuming a rotating magnetically-dominated magnetosphere described by the force-free approximation. Although this simple model has been used thoroughly to study pulsar magnetospheres in the flat spacetime regime, only few works have considered the relativistic corrections introduced by the curvature and frame-dragging effects induced by a rotating neutron star. Here we revisit the problem and describe pulsar magnetospheres within full General Relativity, quantifying the corrections as a function of the angular velocity, the compact…
In some low-luminosity accreting supermassive black hole systems, the supply of plasma in the funnel region can be a problem. It is believed that a local region with unscreened electric field can exist in the black hole magnetosphere, accelerating particles and producing high energy gamma-rays that can create $e^{\pm}$ pairs. We carry out time-dependent self-consistent 1D PIC simulations of this process, including inverse Compton scattering and photon tracking. We find a highly time-dependent solution where a macroscopic gap opens quasi-periodically to create $e^{\pm}$ pairs and high energy ra…
When a black hole accretes plasmas at very low accretion rate, an advection-dominated accretion flow (ADAF) is formed. In an ADAF, relativistic electrons emit soft gamma-rays via Bremsstrahlung. Some MeV photons collide with each other to materialize as electron-positron pairs in the magnetosphere. Such pairs efficiently screen the electric field along the magnetic field lines, when the accretion rate is typically greater than 0.03-0.3% of the Eddington rate. However, when the accretion rate becomes smaller than this value, the number density of the created pairs becomes less than the rotation…
Quasi-spherical subsonic accretion onto slowly rotating magnetized NS is considered, when the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasi-static shell. The shell mediates the angular momentum transfer to/from the rotating NS magnetosphere by large-scale convective motions, which lead to an almost iso-angular-momentum rotation law inside the shell. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instability while taking cooling into account. The settling re…
We revisit secular stability against quasi-radial collapse for rigidly rotating supermassive stars (SMSs) in general relativity. We suppose that the SMSs are in a nuclear-burning phase and can be modeled by polytropic equations of state with the polytropic index $n_p$ slightly smaller than $3$. The stability is determined in terms of the turning-point method. We find a fitting formula of the stability condition for the plausible range of $n_p$ ($2.95 \alt n_p \alt 3$) for SMSs. This condition reconfirms that, while non-rotating SMSs with mass $\sim 10^5M_\odot$--$10^6M_\odot$ may undergo a gen…
We consider the curvature emission properties from relativistic particles streaming along magnetic field lines and co-rotating with pulsar magnetosphere. The co-rotation affects the trajectories of the particles and hence the emission properties, especially the polarization. We consider the modification of the particle velocity and acceleration due to the co-rotation. Curvature radiation from a single particle is calculated using the approximation of a circular path to the particle trajectory. Curvature radiation from particles at a given height actually contains the contributions from particl…
We study tidal disruption events of rotating stars by a supermassive black hole in a galactic nucleus by using a smoothed-particle hydrodynamics (SPH) code. We compare mass infall rates of tidal-disruption debris of a non-rotating and of a rotating star when they come close to the supermassive black hole. Remarkably the mass distribution of debris bound to the black hole as a function of specific energy shows clear difference between rotating and non-rotating stars, even if the stellar rotation is far from the break-up limit. The debris of a star whose initial spin is parallel to the orbital a…
It is a well-known fact that compact gravitating objects admit bound state configurations for massive bosonic fields. In this work we describe a new class of superradiant instabilities of axion bound states in neutron star magnetospheres. The instability arises from the mixing of axion and photon modes in the magnetic field of the neutron star which extract energy from the rotating magnetosphere. Unlike for black holes, where the dissipation required for superradiance is provided by an absorbative horizon, the non-hermitian dynamics in this paper come from the resistivity in the stellar magnet…
The annular gap model under a rotating dipole field approximation: simulating gamma-ray light curve
Guizhou Normal University（贵州师范大学）；Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University（贵州师范大学贵州省射电天文与数据处理重点实验室）；Guizhou University（贵州大学）；School of Physics and Electronic Science, Guizhou Normal University（贵州师范大学物理科学与电子科学学院）；Guizhou Radio Astronomical Observatory（贵州射电天文台）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
We investigate the structure of the steady-state force-free magnetosphere around a Kerr black hole in various astrophysical settings. The solution Psi(r,theta) depends on the distributions of the magnetic field line angular velocity omega(Psi) and the poloidal electric current I(Psi). These are obtained self-consistently as eigenfunctions that allow the solution to smoothly cross the two singular surfaces of the problem, the Inner Light Surface (ILS) inside the ergosphere, and the Outer Light Surface (OLS), which is the generalization of the pulsar light cylinder. Magnetic field configurations…
The mechanism by which the radiation received from obliquely rotating neutron stars is generated remains an open question half a century after the discovery of pulsars. In contrast, considerable progress has recently been made in determining the structure of the magnetosphere that surrounds these objects: numerical computations based on the force-free, magnetohydrodynamic and particle-in-cell formalisms have now established that the magnetosphere of an oblique rotator entails a current sheet outside its light cylinder whose rotating distribution pattern moves with linear speeds exceeding the s…
We study the dynamics of merging compact binaries near a rotating supermassive black hole (SMBH) in a hierarchical triple configuration. We include various general relativistic effects that couple the inner orbit, the outer orbit and the spin of the SMBH. During the orbital decay due to gravitational radiation, the inner binary can encounter an "apsidal precession resonance" and experience eccentricity excitation. This resonance occurs when the apsidal precession rate of the inner binary matches that of the outer binary, with the precessions driven by both Newtonian interactions and various po…
A theoretical model for quasi-spherical subsonic accretion onto slowly rotating magnetized neutron stars is constructed. In this model the accreting matter subsonically settles down onto the rotating magnetosphere forming an extended quasi-static shell. This shell mediates the angular momentum removal from the rotating neutron star magnetosphere during spin-down episodes by large-scale convective motions. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere. The settling regime of accretion can be realized for moderate accretion rates $\dot…
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…
While the motion of particles near a rotating, electrically-neutral (Kerr), and charged (Kerr--Newman) black hole is always strictly regular, a perturbation in the gravitational or the electromagnetic field generally leads to chaos. The transition from regular to chaotic dynamics is relatively gradual if the system preserves axial symmetry, whereas non-axisymmetry induces chaos more efficiently. Here we study the development of chaos in an oblique (electro-vacuum) magnetosphere of a magnetized black hole. Besides the strong gravity of the massive source represented by the Kerr metric we consid…
We analyze the dynamical evolution of a perturbed force-free magnetosphere of a rotating black hole, which is described by the Blandford-Znajek solution in the stationary limit. We find that the electromagnetic field perturbations can be classified into two categories: "trapped modes" and "traveling waves". The trapped modes are analogous to the vacuum (without plasma) electromagnetic quasinormal modes in rotating black hole spacetimes, but with different eigenfrequencies and wave functions, due to their coupling with the background electromagnetic field and current. The traveling waves propag…
The centrifugal acceleration is due to the rotating poloidal magnetic field in the magnetosphere creates the electric field which is orthogonal to the magnetic field. Charged particles with finite cyclotron radii can move along the electric field and receive energy. Centrifugal acceleration pushes particles to the periphery, where their azimuthal velocity reaches the light speed. We have calculated particle trajectories by numerical and analytical methods. The maximum obtained energies depend on the parameter of the particle magnetization $ κ$, which is the ratio of rotation frequency of magne…
The discovery of quasars at increasingly large cosmological redshifts may favor "direct collapse" as the most promising evolutionary route to the formation of supermassive black holes. In this scenario, supermassive black holes form when their progenitors - supermassive stars - become unstable to gravitational collapse. For uniformly rotating stars supported by pure radiation pressure and spinning at the mass-shedding limit, the critical configuration at the onset of collapse is characterized by universal values of the dimensionless spin and radius parameters $J/M^2$ and $R/M$, independent of …
In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. Thus, it is important for numerical simulations of black hole magnetospheres to minimize the …
We explore the structure of a dipole-type vacuum field of a slowly rotating magnetic star near the horizon of a supermassive black hole, where the structure of field lines becomes highly distorted by effects of strong gravity. Such a situation may occur near a neutron star in the final stages of a plunging trajectory into a galactic center. We solve Maxwell's equations in the Rindler approximation for the rotating conducting source of dipolar magnetic field arbitrarily inclined with respect to the axis of rotation. For the fixed inclination angle we calculate the field including the radiative …
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.
Acceleration of protons in the active galactic nuclei is considered. The largest energy is achieved by protons during centrifugal acceleration in the magnetosphere of the central machine. When the proton accelerated in the magnetosphere of a black hole approaches light cylinder surface, acceleration occurs mainly in the azimuthal direction, i.e. the acceleration is centrifugal. In this paper the acceleration of a proton having smaller synchrotron losses compared to the electron is considered. As a proton experiences the highest energy increase while accelerating near the light surface, a parti…
