Black hole - accretion disc systems are the central engines of relativistic jets from stellar to galactic scales. We numerically quantify the unsteady outgoing Poynting flux through the horizon of a rapidly spinning black hole endowed with a rotating accretion disc. The disc supports small-scale, concentric, flux tubes with zero net magnetic flux. Our General Relativistic force-free electrodynamics simulations follow the accretion onto the black hole over several hundred dynamical timescales in 3D. For the case of counter-rotating accretion discs, the average process efficiency reaches up to $\left\langleε\right\rangle\approx 0.43$, compared to a stationary energy extraction by the Blandford/Znajek process. The process efficiency depends on the cross-sectional area of the loops, i.e. on the product $l\times h$, where $l$ is the radial loop thickness and $h$ its vertical scale height. We identify a strong correlation between efficient electromagnetic energy extraction and the quasi-stationary setting of ideal conditions for the operation of the Blandford/Znajek process (e.g. optimal field line angular velocity and fulfillment of the so-called Znajek condition). Remarkably, the energy extraction operates intermittently (alternating episodes of high and low efficiency) without imposing any large-scale magnetic field embedding the central object. Scaling our results to supermassive black holes, we estimate that the typical variability timescale of the system is of the order of days to months. Such timescales may account for the longest variability scales of TeV emission observed, e.g. in M87.
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.
Gamma-ray bursts (GRBs) are believed to be powered by the electromagnetic extraction of spin energy from a black hole endowed with a magnetic field supported by electric currents in a surrounding disk (Blandford & Znajek 1977). A generic feature of this mechanism is that, under certain fairly general assumptions, the energy loss rate decays exponentially. In this work, we are looking precisely for such exponential decay in the lightcurves of long duration GRBs observed with the XRT instrument on the Swift satellite. We found out that almost 30 % of XRT lightcurves show such behavior before the…
We propose a two-component jet model consistent with the observations of several gamma ray bursts (GRBs) and active galactic nuclei (AGNs). The jet consists of inner and outer components, and they are supposed to be driven by the Blandford-Znajek (BZ) and Blandford-Payne (BP) processes, respectively. The baryons in the BP jet is accelerated centrifugally via the magnetic field anchored in the accretion disk. The BZ jet is assumed to be entrained a fraction of accreting matter leaving the inner edge of the accretion disk, and the baryons are accelerated in the conversion from electromagnetic en…
We provide a semi-analytic comparison between the Blandford-Znajek (BZ) and the magnetic reconnection power for accreting black holes in the curved spacetime of a rotating black hole. Our main result is that for a realistic range of astrophysical parameters, the reconnection power may compete with the BZ power. The field lines anchored close to or on the black hole usually evolve to open field lines in general relativistic magnetohydrodynamic (GRMHD) simulations. The BZ power is dependent on the black hole spin while magnetic reconnection power is independent of it for the force-free magnetic …
The interaction of large scale magnetic fields with the event horizon of rotating black holes (the Blandford-Znajek [1977] mechanism) forms the basis for some models of the most relativistic jets. We explore a scenario in which the central inward "plunging" region of the accretion flow enhances the trapping of large scale poloidal field on the black hole. The study is carried out using a fully relativistic treatment in Kerr spacetime, with the focus being to determine the spin dependence of the Blandford-Znajek effect. We find that large scale magnetic fields are enhanced on the black hole com…
Long-duration gamma-ray bursts (GRBs) are generally related to the core-collapse of massive stars. In the collapsar scenario, a rotating stellar-mass black hole (BH) surrounded by a hyperaccretion disk has been considered as one of the plausible candidates of GRB central engines. In this paper, we work on a sample including 146 long GRBs with significant jet break features in the multi-band afterglows. The jet opening angles can be then obtained by the jet break time. By asumming GRB jets powered by Blandford-Znajek (BZ) mechanism in the BH hyperaccretion system, we analyze the distributions o…
According to the Blandford-Znajek mechanism, black hole jets are powered by the rotational energy of the compact object. In this work, we consider the possibility that the metric around black holes may not be described by the Kerr solution and we study how this changes the Blandford-Znajek model. If the Blandford-Znajek mechanism is responsible for the formation of jets, the estimate of the jet power in combination with another measurement can test the nature of black hole candidates and constrain possible deviations from the Kerr solution. However, this approach might become competitive with …
Collapse of massive stars may result in formation of accreting black holes in their interior. The accreting stellar matter may advect substantial magnetic flux onto the black hole and promote release of its rotational energy via magnetic stresses (the Blandford-Znajek mechanism). In this paper we explore whether this process can explain the stellar explosions and relativistic jets associated with long Gamma-ray-bursts. In particularly, we show that the Blandford-Znajek mechanism is activated when the rest mass-energy density of matter drops below the energy density of magnetic field in the ver…
The Blandford-Znajek monopole is a conjectured solution of force-free electrodynamics in the vicinity of a slowly rotating Kerr black hole, supposedly defined as a perturbation in small angular momentum. It is used to argue for the extraction of energy from rotating black holes by the Blandford-Znajek process. We set up a careful analysis of the perturbative definition of the Blandford-Znajek monopole, showing in particular that the regime in which it is defined allows to use the technique of matched asymptotic expansions. Our conclusion is that the Blandford-Znajek monopole, as it is defined,…
Under the assumption that a Gamma-ray Burst (GRB) is ultimately produced by a Blandford-Znajek (BZ) jet from a highly spinning black hole BH, we put limits on the magnetic field and BH mass needed to power observed long and short GRBs. For BHs in the range of $2-10 M_{\odot}$ (for long GRBs) and $0.5-4 M_{\odot}$ (for short GRBs), we find magnetic fields in the range of $5x10^{14} \lesssim B \lesssim 10^{17}$ G are needed to power the observed GRBs. Under the simple assumption of flux conservation, we estimate the magnetic fields of the progenitor systems for both long and short GRBs, finding …
The Blandford-Znajek mechanism has long been regarded as a key ingredient in models attempting to explain powerful jets in AGNs, quasars, blazzars etc. In such mechanism, energy is extracted from a rotating black hole and dissipated at a load at far distances. In the current work we examine the behaviour of the BZ mechanism with respect to different boundary conditions, revealing the mechanism robustness upon variation of these conditions. Consequently, this work closes a gap in our understanding of this important scenario.
A neutrino-dominated accretion flow (NDAF) around a rotating stellar-mass black hole (BH) is one of the plausible candidates for the central engine of gamma-ray bursts (GRBs). Two mechanisms, i.e., Blandford-Znajek (BZ) mechanism and neutrino annihilation process, are generally considered to power GRBs. Using the analytic solutions from Xue et al. (2013) and ignoring the effects of the magnetic field configuration, we estimate the BZ and neutrino annihilation luminosities as the functions of the disk masses and BH spin parameters to contrast the observational jet luminosities of GRBs. The resu…
The Blandford-Znajek process, the steady electromagnetic energy extraction from a rotating black hole, is widely believed to work for driving relativistic jets, although it is still under debate where the electric current is driven. We address this issue analytically by investigating the time-dependent state in the Boyer-Lindquist and Kerr-Schild coordinate systems. This analysis suggests that a non-ideal magnetohydrodynamic region is required in the time-dependent state, while not in the steady state.
Recently, it was claimed that accretion of electric charge by a black hole rotating in an aligned external magnetic field results in a "dead" vacuum magnetosphere, where the electric field is totally screened, no vacuum breakdown is possible, and the Blandford-Znajek mechanism cannot operate King & Pringle (2021). Here we study in details the properties of the Wald(1974) solution for electrically charged black holes discussed in that paper. Our results show that the claim is erroneous as in the solution with the critical charge $q_0=2aB_0$ there exists a drop of electrostatic potential along a…
Recently it has been observed that the scaling of jet power with black hole spin in galactic X-ray binaries is consistent with the predictions of the Blandford-Znajek (BZ) jet model. These observations motivate us to revisit the BZ model using general relativistic magnetohydrodynamic simulations of magnetized jets from accreting (h/r ~ 0.3), spinning (0 < a_* < 0.98) black holes. We have three main results. First, we quantify the discrepancies between the BZ jet power and our simulations: assuming maximum efficiency and uniform fields on the horizon leads to a ~10% overestimate of jet power, w…
The Blandford-Znajek mechanism is the continuous extraction of energy from a rotating black hole via plasma currents flowing on magnetic field lines threading the horizon. In the discovery paper, Blandford and Znajek demonstrated the mechanism by solving the equations of force-free electrodynamics in a perturbative expansion valid at small black hole spin. Attempts to extend this perturbation analysis to higher order have encountered inconsistencies.We overcome this problem using the method of matched asymptotic expansions, taking care to resolve all of the singular surfaces (light surfaces) i…
From a spacetime perspective, the dynamics of magnetic field lines of force-free electromagnetic fields can be rewritten into a quite similar form for the dynamics of strings, i.e., dynamics of "field sheets". Using this formalism, we explicitly show that the field sheets of stationary and axisymmetric force-free electromagnetic fields have identical intrinsic properties to the world sheets of rigidly rotating Nambu-Goto strings. Thus, we conclude that the Blandford-Znajek process is kinematically identical to an energy-extraction mechanism by the Nambu-Goto string with an effective magnetic t…
The Blandford-Znajek theory (1977) is generally studied to understand the generation of powerful relativistic jets. However, it could also give important insights about the feedback between a rotating black hole, its ergosphere, and a surrounding accretion disk. The energy flow between these systems could be understood by studying the BZ power as a function of a slip factor, which in turn is defined as a function of the angular velocity of the black hole and the angular velocity of the magnetic field lines (generally anchored to the disk). The distinct stages could explain the different types …
Spinning black holes tend to expel magnetic fields. In this way they are similar to superconductors. It has been a persistent concern that this black hole "Meissner effect" could quench jet power at high spins. This would make it impossible for the rapidly rotating black holes in Cyg X-1 and GRS 1915+105 to drive Blandford-Znajek jets. We give a simple geometrical argument why fields which become entirely radial near the horizon are not expelled by the Meissner effect and may continue to power jets up to the extremal limit. A simple and natural example is a split-monopole field. We stress that…
We consider the Blandford-Znajek process of electromagnetic extraction of energy from a general axially symmetric asymptotically flat slowly rotating black hole. Using the general parametrization of the black-hole spacetime we construct formulas for the flux of the magnetic field and the rate of energy extraction, which are valid not only for the Kerr spacetime, but also for its arbitrary axially symmetric deformations. We show that in the dominant order these quantities depend only on a single deformation parameter, which relates the spin frequency of a black hole with its rotation parameter.
The superradiant scattering of Alfvén waves (Alfvénic superradiance) in a forcefree magnetosphere is discussed to reveal the relationship between the Blandford-Znajek (BZ) process and superradiance. For simplicity, we consider a four-dimensional rotating black string spacetime of which each $z=\text{const}$ slice is a Bañados-Teitelboim-Zanelli solution as an analogy of the equatorial plane of the Kerr spacetime. Then, it is confirmed that the condition for Alfvénic superradiance coincides with that for the BZ process, and the wave amplification can be very large due to a resonant scattering f…
The Blandford-Znajek (BZ) mechanism describes a physical process for the energy extraction from a spinning black hole (BH), which is believed to power a great variety of astrophysical sources, such as active galactic nuclei (AGNs) and Gamma ray bursts (GRBs). The only known analytic solution to the BZ mechanism is a split monopole perturbation solution up to $O(a^2)$, where $a$ is the spin parameter of a Kerr black hole. In this paper, we extend the monopole solution to higher order $\sim O(a^4)$. We carefully investigate the structure of the BH magnetosphere, including the angular velocity of…
Neutrino-dominated accretion flow (NDAF) around a rotating stellar-mass black hole (BH) is one of the plausible candidates for the central engines of gamma-ray bursts (GRBs). Because the time-variant and anisotropic emission of neutrinos from NDAFs leads to GRB variability, NDAFs can be regarded as the sources of the strong gravitational waves (GWs). We calculate the dependences of the GW strains on both the BH spin and the accretion rate. We demonstrate that for typical GRBs with either single pulse or multiple pulses, the GWs from NDAFs might be detected at a distance of $\sim 100$ kpc/$\sim…
We study the metric backreaction of mass and angular momentum accretion on black holes. We first develop the formalism of monopole and dipole linear gravitational perturbations around the Schwarzschild black holes in the Eddington-Finkelstein coordinates against the generic time-dependent matters. We derive the relation between the time dependence of the mass and angular momentum of the black hole and the energy-momentum tensors of accreting matters. As a concrete example, we apply our formalism to the Blandford-Znajek process around the slowly rotating black holes. We find that the time depen…
Blandford and Znajek discovered a process by which a spinning black hole can transfer rotational energy to a plasma, offering a mechanism for energy and jet emissions from quasars. Here we describe a version of this mechanism that operates with only vacuum electromagnetic fields outside the black hole. The setting, which is not astrophysically realistic, involves either a cylindrical black hole or one that lives in 2+1 spacetime dimensions, and the field is given in simple, closed form for a wide class of metrics. For asymptotically Anti-de Sitter black holes in 2+1 dimensions the holographic …
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…
One of the mechanisms widely considered for driving relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts is the electromagnetic extraction of the rotational energy of a central black hole, i.e., the Blandford-Znajek process, although the origin of the electromotive force in this process is still under debate. We study this process as the steady unipolar induction in the Kerr black hole magnetosphere filled with a collisionless plasma screening the electric field (the D field) along the magnetic field (the B field), i.e., D dot B = 0. We extend the formulatio…
Magnetic fields connecting the immediate environs of rotating black holes to large distances appear to be the most promising mechanism for launching relativistic jets, an idea first developed by Blandford and Znajek in the mid-1970s. To enable an understanding of this process, we provide a brief introduction to dynamics and electromagnetism in the spacetime near black holes. We then present a brief summary of the classical Blandford-Znajek mechanism and its conceptual foundations. Recently, it has become possible to study these effects in much greater detail using numerical simulation. After d…
Jets launched by active galactic nuclei (AGN) are believed to play a significant role in shaping the properties of galaxies and provide an energetically viable mechanism through which galaxies can become quenched. Here we present a novel AGN feedback model, which we have incorporated into the AREPO code, that evolves the black hole mass and spin as the accretion flow proceeds through a thin $α$-disc which we self-consistently couple to a Blandford-Znajek jet. We apply our model to the central region of a typical radio-loud Seyfert galaxy embedded in a hot circumgalactic medium (CGM). We find t…
Blandford-Znajek (BZ) mechanism has usually been studied in the literature for accretion with considerably high angular momentum leading either to the formation of a cold Keplerian disc, or a hot and geometrically thick sub-Keplerian flow as described within the framework of ADAF/RIAF. However, in nearby elliptical galaxies, as well as for our own Galactic centre, accretion with very low angular momentum is prevalent. Such quasi-spherical strongly sub-Keplerian accretion has complex dynamical features and can accommodate stationary shocks. In this letter, we present our calculation for the max…
Blandford-Znajek process, the steady electromagnetic energy extraction from a rotating black hole (BH), is widely believed to work for driving relativistic jets in active galactic nuclei, gamma-ray bursts and Galactic microquasars, although it is still under debate how the Poynting flux is causally produced and how the rotational energy of the BH is reduced. We generically discuss the Kerr BH magnetosphere filled with a collisionless plasma screening the electric field along the magnetic field, extending the arguments of Komissarov and our previous paper, and propose a new picture for resolvin…
Recent Very Long Baseline Interferometry observations of the relativistic jet in the M87 radio galaxy at 43 GHz show gradual relativistic acceleration of the plasma and suggest a linear dependence of Lorentz factor on jet radius at scales up to 8 marcsec (0.65 pc) from the core (2.5 marcsec in projection). General analysis of integrals of motion being unaltered along the jet and reflecting fundamental conservation laws shows that the above dependence implies a polytropic equation of state with index 4/3. The inferred value of the polytropic index appears independent of the exact nature of forc…
Recent general relativistic MHD simulations have suggested that relativistic jets from active galactic nuclei (AGNs) have been powered by rotational energy of central black holes. Some mechanisms of extraction of black hole rotational energy have been proposed, like the Penrose process, Blandford-Znajek mechanism, MHD Penrose process, and superradiance. The Blandford-Znajek mechanism is the most promising mechanism for the engines of the relativistic jets from AGNs. However, an intuitive interpretation of this mechanism with causality is not clarified yet, while the Penrose process has a clear…
The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas $et~al.$ put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations. Building on this, we revisit the BZ perturbative expansion, and extend the per…
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 …
Transitions to high mass accretion rates in black hole X-ray binaries are associated with the ejection of powerful, relativistically-moving jets. The mechanism powering such events is thought to be linked to tapping of the angular momentum (spin) of the black hole, the rate of accretion through the disc or some combination of the two. We can attempt to discriminate between these possibilities by comparing proxies for jet power with spin estimates. Due to the small number of sources reaching Eddington rates and have therefore been suggested to act as 'standard candles', there has been much rece…
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 …
Despite their potential importance for understanding astrophysical jets, physically realistic exact solutions for magnetospheres around Kerr black holes have not been found, even in the force-free approximation. Instead approximate analytical solutions such as the Blandford-Znajek (split-)monopole, as well as numerical solutions, have been constructed. In this paper we consider a new approach to the analysis and construction of such magnetospheres. We consider force-free electrodynamics close to the rotation axis of a magnetosphere surrounding a Kerr black hole assuming axisymmetry. This is th…
We explore the connection between black hole spin and AGN power by addressing the consequences underlying the assumption in the recent literature that the gap region between accretion disks and black holes is fundamental in producing strong, spin-dependent, horizon-threading magnetic fields. Under the additional assumption that jets and outflows in AGN are produced by the Blandford-Znajek and Blandford-Payne mechanisms, we show that maximum jet/outflow power is achieved for accretion onto black holes having highly retrograde spin parameter, an energetically excited yet unstable gravitomagnetic…
Supermassive black holes (SMBH) are essential for the production of jets in radio-loud active galactic nuclei (AGN). Theoretical models based on Blandford & Znajek extract the rotational energy from a Kerr black hole, which could be the case for NGC1052, to launch these jets. This requires magnetic fields of the order of $10^3\,$G to $10^4\,$G. We imaged the vicinity of the SMBH of the AGN NGC1052 with the Global Millimetre VLBI Array and found a bright and compact central feature, smaller than 1.9 light days (100 Schwarzschild radii) in radius. Interpreting this as a blend of the unresolved j…
We have performed a series of numerical experiments aimed at studying the activation of Kerr black holes (BHs) by advection of small scale magnetic fields. Such configurations may potentially give rise to the formation of quasi-striped Blandford-Znajek jets. It can also lead to enhanced dissipation and generation of plasmoids in current sheets formed in the vicinity of the BH horizon, which may constitute a mechanism to power the hard X-ray emission seen in many accreting BH systems (a la lamppost models). Our analysis suggests that formation of quasi-striped jets with significant power may be…
A disk-corona model for fitting low/hard (LH) state of associated steady jet of black hole X-ray binaries (BHXBs) is proposed based on the large-scale magnetic field configuration of the coexistence of the Blandford-Znajek (BZ) and Blandford-Payne (BP) processes,where the magnetic field configuration for the BP process is determined by the requirement of energy conversion from Poynting energy flux into kinetic energy flux in the jet. It is found that corona current is crucial to guarantee the consistency of the jet launching from accretion disk. The relative importance of the BZ to BP processe…
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…
Supermassive black holes are found at the centers of most galaxies and their inspiral is a natural outcome when galaxies merge. The inspiral of these systems is of utmost astrophysical importance as prodigious producers of gravitational waves and in their possible role in energetic electromagnetic events. We study such binary black hole coalescence under the influence of an external magnetic field produced by the expected circumbinary disk surrounding them. Solving the Einstein equations to describe the spacetime and using the force-free approach for the electromagnetic fields and the tenuous …
University of Amsterdam（阿姆斯特丹大学）；Dutch Institute for Emergent Phenomena (DIEP)（荷兰涌现现象研究所）；Institute for Advanced Study, University of Amsterdam（阿姆斯特丹大学高等研究院）；Anton Pannekoek Institute（安东·潘内科克研究所）
We investigate the launching mechanism of relativistic jets from black hole sources, in particular the strong winds from the surrounding accretion disk. Numerical investigations of the disk wind launching - the simulation of the accretion-ejection transition - have so far almost only been done for non-relativistic systems. From these simulations we know that resistivity, or magnetic diffusivity, plays an important role for the launching process. Here, we extend this treatment to general relativistic magnetohydrodynamics (GR-MHD) applying the resistive GR-MHD code rHARM. Our model setup conside…
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 fit the most updated broadband spectral energy distribution from radio to X-rays for NGC 4258 with a coupled accretion-jet model that surrounding a Kerr black hole (BH), where both the jet and the warped H_2O maser disk are assumed to be triggered by a spinning BH through Blandford-Znajek mechanism and Bardeen-Petterson effect respectively. The accretion flow consists with an inner radiatively inefficient accretion flow (RIAF) and an outer truncated standard thin disk, where the transition radius R_tr~3*10^3Rg for NGC 4258 based on the width and variability of its narrow Fe K$α$ line. The h…
