Black Hole Magnetosphere Research Articles

Synthetic gamma-ray light curves of Kerr black hole magnetospheric activity from particle-in-cell simulations

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. Our aim is to bridge the gap between simulations and observations by synthesizing gamma-ray light curves in order to characterize the activity of a black hole magnetosphere, using kinetic simulations. Methods. We performed global axisymmetric 2D general-relativistic particle-in-cell simulations of a Kerr black hole magnetosphere. We included a self-consistent treatment of radiative processes and plasma supply, as well as a realistic magnetic configuration, with a large-scale equatorial current sheet. We coupled our particle-in-cell code with a ray-tracing algorithm in order to produce synthetic light curves. Results. These simulations show a highly dynamic magnetosphere, as well as very efficient dissipation of the magnetic energy. An external supply of magnetic flux is found to maintain the magnetosphere in a dynamic state, otherwise the magnetosphere settles in a quasi-steady Wald-like configuration. The dissipated energy is mostly converted to gamma-ray photons. The light curves at low viewing angle (face-on) mainly trace the spark gap activity and exhibit high variability. On the other hand, no significant variability is found at high viewing angle (edge-on), where the main contribution comes from the reconnecting current sheet. Conclusions. We observe that black hole magnetospheres with a current sheet are characterized by a very high radiative efficiency. The typical amplitude of the flares in our simulations is lower than is detected in active galactic nuclei. These flares could result from the variation in parameters external to the black hole.

Matter Density Distribution of General Relativistic Highly Magnetized Jets Driven by Black Holes

Abstract High-resolution very long baseline interferometry (VLBI) radio observations have resolved the detailed emission structures of active galactic nucleus jets. General relativistic magnetohydrodynamic (GRMHD) simulations have improved the understanding of jet production physics, although theoretical studies still have difficulty constraining the origin and distribution of jetted matter. We construct a new steady, axisymmetric GRMHD jet model to obtain approximate solutions of black hole (BH) magnetospheres, and examine the matter density distribution of jets. By assuming fixed poloidal magnetic field shapes that mimic force-free analytic solutions and GRMHD simulation results and assuming constant poloidal velocity at the separation surface, which divides the inflow and outflow, we numerically solve the force balance between the field lines at the separation surface and analytically solve the distributions of matter velocity and density along the field lines. We find that the densities at the separation surface in our parabolic field models roughly follow in the far zone from the BH, where r ss is the radius of the separation surface. When the BH spin is larger or the velocity at the separation surface is smaller, the density at the separation surface becomes concentrated closer to the jet edge. Our semianalytic model, combined with radiative transfer calculations, may help us interpret the high-resolution VLBI observations and understand the origin of jetted matter.

On the Heating of AGN Magnetospheres

The Langmuir–Landau-Centrifugal Drive (LLCD), which can effectively “convert” gravitational energy into particles, is explored as a driving mechanism responsible for the extreme thermal luminosity acquired by some active galactic nuclei (AGN). For this purpose, we consider equations governing the process of heating of AGN magnetospheres. In particular, we examine the Fourier components of the momentum equation, the continuity equation and the Poisson equation in the linear approximation and estimate the growth rate of the centrifugally excited electrostatic waves and the increment of the Langmuir collapse. It is shown that the process of energy pumping is composed of three stages: in the first stage the energy is efficiently transferred from rotation to the electrostatic modes. In due course of time, the second regime-the Langmuir collapse-occurs, when energy pumping is even more efficient. This process is terminated by the Landau damping, when enormous energy is released in the form of heat. We show that the magnetospheres of the supermassive black holes with luminosities of the order of 1045−46 erg/s can be heated up to 106−10 K.

Force-free magnetosphere attractors for near-horizon extreme and near-extreme limits of Kerr black hole

We propose a new approach to find magnetically-dominated force-free (FF) 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 FF 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 theory, it is possible to find magnetically dominated magnetospheres around the extreme Kerr black hole. Furthermore, we consider the near-horizon near-extreme Kerr (near-NHEK) limit that provides access to a different regime of highly spinning black holes. Also in this case we find a novel FF attractor, which can be used as the universal starting point for a perturbative construction of FF magnetospheres. Finally, we discuss the relation between the NHEK and near-NHEK attractors.

Computational general relativistic force-free electrodynamics

General relativistic force-free electrodynamics is one possible plasma-limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. The amazing images of black hole (BH) shadows from the Galactic Center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. We aim at providing a tool to numerically model the dynamics of such fields in magnetospheres around compact objects, such as BHs and neutron stars. To do so, we probe their role in the formation of high energy phenomena such as magnetar flares and the highly variable teraelectronvolt emission of some active galactic nuclei. In this work, we present numerical strategies capable of modeling fully dynamical force-free magnetospheres of compact astrophysical objects. We provide implementation details and extensive testing of our implementation of general relativistic force-free electrodynamics in Cartesian and spherical coordinates using the infrastructure of the EINSTEINTOOLKIT. The employed hyperbolic/parabolic cleaning of numerical errors with full general relativistic compatibility allows for fast advection of numerical errors in dynamical spacetimes. Such fast advection of divergence errors significantly improves the stability of the general relativistic force-free electrodynamics modeling of BH magnetospheres.

Flares in the Galactic Centre – I. Orbiting flux tubes in magnetically arrested black hole accretion discs

ABSTRACT Recent observations of Sgr A* by the GRAVITY instrument have astrometrically tracked infrared (IR) flares at distances of ∼10 gravitational radii (rg). In this paper, we study a model for the flares based on 3D general relativistic magnetohydrodynamic (GRMHD) simulations of magnetically arrested accretion discs (MADs) that exhibit violent episodes of flux escape from the black hole magnetosphere. These events are attractive for flare modelling for several reasons: (i) the magnetically dominant regions can resist being disrupted via magnetorotational turbulence and shear; (ii) the orientation of the magnetic field is predominantly vertical as suggested by the GRAVITY data; and (iii) the magnetic reconnection associated with the flux eruptions could yield a self-consistent means of particle heating/acceleration during the flare events. In this analysis, we track erupted flux bundles and provide distributions of sizes, energies, and plasma parameter. In our simulations, the orbits tend to circularize at a range of radii from ${\sim} 5\hbox{ to }40\, r_{\rm g}$. The magnetic energy contained within the flux bundles ranges up to ${\sim} 10^{40}\,\rm erg$, enough to power IR and X-ray flares. We find that the motion within the magnetically supported flow is substantially sub-Keplerian, in tension with the inferred period–radius relation of the three GRAVITY flares.

Comprehensive Analysis of Magnetospheric Gaps around Kerr Black Holes Using 1D GRPIC Simulations

Abstract Spark gaps are likely the source of plasma in active black hole (BH) magnetospheres. In this paper, we present results of 1D general relativistic particle-in-cell simulations of a starved BH magnetosphere with a realistic treatment of inverse-Compton scattering and pair production, for a broad range of conditions, run times longer than in previous studies, and different setups. We find that following the initial discharge, the system undergoes gradual evolution over prolonged time until either restoring the vacuum state or reaching a state of quasiperiodic oscillations, depending on the spectral shape and luminosity of the ambient radiation field. The oscillations occur near the null charge surface in cases where the global magnetospheric current is in the direction defined by the product of the asymptotic Goldreich–Julian charge density and the radial velocity, while they occur near the boundary of the simulation box when it is the opposite direction (return current). Their amplitude and the resultant luminosity of TeV photons emitted from the gap depend sensitively on the conditions; for the cases studied here the ratio of TeV luminosity to the Blandford–Znajek power ranges from 10−5 to 10−2, suggesting that strong flares may be generated by moderate changes in disk emission. We also examined the dependence of the solution on the initial number of particles per cell (PPC) and found convergence for PPC of about 50 for the cases examined. At lower PPC values the pair multiplicity is found to be artificially high, affecting the solution considerably.

Gap-type Particle Acceleration in the Magnetospheres of Rotating Supermassive Black Holes

Abstract 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.

Multidimensional Simulations of Ergospheric Pair Discharges around Black Holes.

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 Letter, 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. A highly time-dependent spark gap opens near the inner light surface, which injects pair plasma into the magnetosphere. These results may account for the high-energy activity observed in active galactic nuclei and explain the origin of plasma at the base of the jet.

Properties of Trans-fast Magnetosonic Jets in Black Hole Magnetospheres

Abstract Traveling across several orders of magnitude in distance, relativistic jets from strong gravity regions to asymptotic flat spacetime regions are believed to consist of several general relativistic magnetohydrodynamic (GRMHD) processes. We present a semianalytical approach for modeling the global structures of a trans-fast magnetosonic relativistic jet, which should be ejected from a plasma source near a black hole in a funnel region enclosed by dense accreting flow and a disk corona around the black hole. Our model consistently includes the inflow and outflow part of the GRMHD solution along the magnetic field lines penetrating the black hole horizon. After the rotational energy of the black hole is extracted electromagnetically by the negative energy GRMHD inflow, the huge electromagnetic energy flux propagates from the inflow to the outflow region across the plasma source, and in the outflow region, the electromagnetic energy converts to the fluid kinetic energy. Eventually, the accelerated outflow must exceed the fast magnetosonic wave speed. We apply the semianalytical trans-fast magnetosonic flow model to the black hole magnetosphere for both parabolic and split-monopole magnetic field configurations and discuss the general flow properties, that is, jet acceleration, jet magnetization, and the locations of some characteristic surfaces of the black hole magnetosphere. We have confirmed that, at large distances, the GRMHD jet solutions are in good agreement with the previously known trans-fast special relativistic magnetohydrodynamic jet properties, as expected. The flexibility of the model provides a prompt and heuristic way to approximate the global GRMHD trans-fast magnetosonic jet properties.

Black hole magnetospheres in the Born–Infeld theory

We study the force-free electrodynamics on rotating black holes in the Born–Infeld (BI) effective theory. The stream equation describing a steady and axisymmetric magnetosphere is derived. From its near-horizon behavior, we obtain the modified Znajek regularity condition, with which we find that the horizon resistivity in the BI theory is generally not a constant. As expected, the outer boundary condition far away from the hole remains unchanged. In terms of the conditions at both boundaries, we derive the perturbative solution of split monopole in the slow rotation limit. It is interesting to realize that the correction to the solution relies not only on the parameter in the BI theory, but also on the radius (or the mass) of the hole. We also show that the quantum effects can undermine the energy extraction process of the magnetosphere in the nonlinear theory and the extraction rate gets the maximum in the Maxwell theory.

The structure of magnetically dominated energy-extracting black hole magnetospheres: Dependencies on field line angular velocity

Abstract If a magnetically dominated magnetosphere is to extract a black hole’s rotational energy and transmit it to distant regions, then the inner light surface of that magnetosphere must lie within the ergoregion. That inner light surface condition limits the angular velocity of magnetic field lines. We take the distribution of magnetic field line angular velocity on the horizon to be a useful proxy for inner light surface location and study how different distributions affect the structure of energy-extracting magnetospheres. Within magnetospheres that exhibit differential field line bending towards both the azimuthal axis and the equatorial plane, we find that the total Poynting flux energy directed outward along the azimuthal axis can vary by over a factor of 100 for a single value of black hole spin.

GR-MHD Disk Winds and Jets from Black Holes and Resistive Accretion Disks

Abstract We perform GR-MHD simulations of outflow launching from thin accretion disks. As in the nonrelativistic case, resistivity is essential for the mass loading of the disk wind. We implemented resistivity in the ideal GR-MHD code HARM3D, extending previous works for larger physical grids, higher spatial resolution, and longer simulation time. We consider an initially thin, resistive disk orbiting the black hole, threaded by a large-scale magnetic flux. As the system evolves, outflows are launched from the black hole magnetosphere and the disk surface. We mainly focus on disk outflows, investigating their MHD structure and energy output in comparison with the Poynting-dominated black hole jet. The disk wind encloses two components—a fast component dominated by the toroidal magnetic field and a slower component dominated by the poloidal field. The disk wind transitions from sub- to super-Alfvénic speed, reaching velocities ≃0.1c. We provide parameter studies varying spin parameter and resistivity level and measure the respective mass and energy fluxes. A higher spin strengthens the B ϕ -dominated disk wind along the inner jet. We disentangle a critical resistivity level that leads to a maximum matter and energy output for both, resulting from the interplay between reconnection and diffusion, which in combination govern the magnetic flux and the mass loading. For counterrotating black holes the outflow structure shows a magnetic field reversal. We estimate the opacity of the innermost accretion stream and the outflow structure around it. This stream may be critically opaque for a lensed signal, while the axial jet funnel remains optically thin.

Black hole magnetosphere with small-scale flux tubes – II. Stability and dynamics

ABSTRACT In some Seyfert galaxies, the hard X-rays that produce fluorescent emission lines are thought to be generated in a hot corona that is compact and located at only a few gravitational radii above the supermassive black hole. We consider the possibility that this X-ray source may be powered by small-scale magnetic flux tubes attached to the accretion disc near the black hole. We use three-dimensional, time-dependent, special relativistic, force-free simulations in a simplified setting to study the dynamics of such flux tubes as they get continuously twisted by the central compact star/black hole. We find that the dynamical evolution of the flux tubes connecting the central compact object and the accretion disc is strongly influenced by the confinement of the surrounding field. Although differential rotation between the central object and the disc tends to inflate the flux tubes, strong confinement from surrounding field quenches the formation of a jet-like outflow, as the inflated flux tube becomes kink unstable and dissipates most of the extracted rotational energy relatively close to the central object. Such a process may be able to heat up the plasma and produce strong X-ray emission. We estimate the energy dissipation rate and discuss its astrophysical implications.

Black hole magnetosphere with small-scale flux tubes

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 find that the extent of the closed zone is a result of the balance between the black hole spin induced twist in the closed zone and the confinement pressure of the external (open) field of the disk. The maximal extent of the closed zone, for a typical external confinement, is usually a few gravitational radii. The pressure competition between the closed zone and the external confinement could in principle lead to interesting dynamics and dissipation relevant for the compact X-ray corona.

Very High-Energy Emission from the Direct Vicinity of Rapidly Rotating Black Holes

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 rotationally induced Goldreich–Julian density. In such a charge-starved magnetosphere, an electric field arises along the magnetic field lines to accelerate charged leptons into ultra-relativistic energies, leading to an efficient TeV emission via an inverse-Compton (IC) process, spending a portion of the extracted hole’s rotational energy. In this review, we summarize the stationary lepton accelerator models in black hole magnetospheres. We apply the model to super-massive black holes and demonstrate that nearby low-luminosity active galactic nuclei are capable of emitting detectable gamma-rays between 0.1 and 30 TeV with the Cherenkov Telescope Array.

Magnetosphere structure of a Kerr black hole: Marginally force-free equatorial boundary condition

The role of equatorial boundary condition in the structure of a force-free black hole magnetosphere was rarely discussed, since previous studies have been focused on the field lines entering the horizon. However, recent high-accuracy force-free electrodynamics (FFE) simulations \cite{East2018} show that there are both field lines entering the horizon and field lines ending up on the equatorial current sheet within the ergosphere for asymptotic uniform field configuration. For the latter field lines, the equatorial boundary condition is well approximated being marginally force-free, i.e., $B^2-E^2\approx 0$, where $B$ and $E$ are the magnetic and electric field strength, respectively. In this paper, we revisit the uniform field solution to the Kerr BH magnetosphere structure and investigate the role of the marginally force-free equatorial boundary condition. We find this boundary condition plays an important role in shaping the BH magnetosphere in various aspects, including the shape of the light surface, the near-horizon field line configuration and the source of the Poynting flux. We also propose an algorithm for numerically solving the Grad-Shafranov equation and self-consistently imposing the marginally force-free equatorial condition. As a result, we find a good agreement between our numerical solutions and the high-accuracy FFE simulations. We also discuss the applicability of the marginally force-free boundary condition and the numerical algorithm proposed in this paper for general magnetic field configurations.

Physics of Pair Producing Gaps in Black Hole Magnetospheres

Abstract 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 an unscreened electric field can exist in the black hole magnetosphere, accelerating particles and producing high-energy gamma-rays that can create e ± 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 ± pairs and high-energy radiation. If this gap is operating at the base of the jet in M87, we expect an intermittency on the order of a few r g /c, which coincides with the timescale of the observed TeV flares from the same object. For Sagittarius A* the gap electric field can potentially grow to change the global magnetospheric structure, which may explain the lack of a radio jet at the center of our galaxy.

Existence of steady gap solutions in rotating black hole magnetospheres

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 electric current which is determined, in reality, by the global properties of the magnetosphere. In this paper we map the parameter regime in which steady gap solutions exist, using a steady-state gap model in Kerr geometry, and show that such solutions are allowed only under restrictive conditions that may not apply to most astrophysical systems. We further argue that even the allowed solutions are inconsistent with the global magnetospheric structure. We conclude that magnetospheric gaps are inherently intermittent, and point out that this may drastically change their emission properties.

Lepton Acceleration in the Vicinity of the Event Horizon: Very High Energy Emissions from Supermassive Black Holes

Abstract Around a rapidly rotating black hole (BH), when the plasma accretion rate is much less than the Eddington rate, the radiatively inefficient accretion flow (RIAF) cannot supply enough MeV photons that are capable of materializing as pairs. In such a charge-starved BH magnetosphere, the force-free condition breaks down in the polar funnels. Applying the pulsar outer-magnetospheric lepton accelerator theory to supermassive BHs, we demonstrate that a strong electric field arises along the magnetic field lines in the direct vicinity of the event horizon in the funnels, that the electrons and positrons are accelerated up to 100 TeV in this vacuum gap, and that these leptons emit copious photons via inverse-Compton (IC) processes between 0.1 and 30 TeV for a distant observer. It is found that these IC fluxes will be detectable with Imaging Atmospheric Cherenkov Telescopes, provided that a low-luminosity active galactic nucleus is located within 1 Mpc for a million-solar-mass central BH or within 30 Mpc for a billion-solar-mass central BH. These very high energy fluxes are beamed in a relatively small solid angle around the rotation axis because of the inhomogeneous and anisotropic distribution of the RIAF photon field and show an anticorrelation with the RIAF submillimeter fluxes. The gap luminosity depends little on the 3D magnetic field configuration, because the Goldreich–Julian charge density, and hence the exerted electric field, is essentially governed by the frame-dragging effect, not by the magnetic field configuration.