Blandford-Znajek Mechanism Research Articles

Timelike geodesic currents in the stationary, axisymmetric, force-free magnetosphere of a Kerr black hole

The structural properties of geodesic currents in an ambient Kerr background is studied from an analytical point of view. The geodesics in the congruence correspond to charged particles that carry energy and angular momentum from the black hole through the Blandford-Znajek mechanism. It is shown that the resulting magnetosphere naturally satisfies the Znajek regularity condition. Particular attention is paid here to the energy extracted by matter currents rather than by electromagnetic Poynting fluxes.

Hyperaccretion after the Blandford-Znajek Process: A New Model for GRBs with X-Ray Flares Observed in Early Afterglows

We propose a three-stage model with Blandford-Znajek (BZ) and hyperaccretion process to interpret the recent observations of early afterglows of Gamma-Ray Bursts (GRBs). In the first stage, the prompt GRB is powered by a rotating black hole (BH) invoking the BZ process. The second stage is a quiet stage, in which the BZ process is shut off, and the accretion onto the BH is depressed by the torque exerted by the magnetic coupling (MC) process. Part of the rotational energy transported by the MC process from the BH is stored in the disk as magnetic energy. In the third stage, the MC process is shut off when the magnetic energy in the disk accumulates and triggers magnetic instability. At this moment, the hyperaccretion process may set in, and the jet launched in this restarted central engine generates the observed X-ray flares. This model can account for the energies and timescales of GRBs with X-ray flares observed in early afterglows.

Extended monopole solution of the Blandford-Znajek mechanism: Higher order terms for a Kerr parameter

The Blandford-Znajek mechanism, by which the rotational energy of a black hole is extracted through electromagnetic fields, is one of the promising candidates as an essential process of the central engine of active compact objects such as gamma-ray bursts. The only known analytical solution of this mechanism is the perturbative monopole solution for Kerr parameter a up to the second order terms. In order to apply the Blandford-Znajek mechanism to rapidly rotating black holes, we try to obtain the perturbation solution up to the fourth order. As a result, we find that the fourth order terms of the vector potential diverge at infinity, and this implies that the perturbation approach breaks down at a large distance from the black hole. Although there are some uncertainties about the solution due to the unknown boundary condition at infinity for the fourth order terms, we can derive the evaluation of the total energy flux extracted from the black hole up to fourth order of a without any ambiguity. Furthermore, from the comparison between the numerical solution, which is valid for 0<a<1, and the fourth order solution, we find that the fourth order solution reproduces the numerical result better than the second order solution.more » At the same time, since the fourth order solution does not match well with the numerical result at large a, we conclude that more higher order terms are required to reproduce the numerical result.« less

Energy Extraction from a Rotating Black Hole by Magnetic Reconnection in the Ergosphere

We investigate mechanisms of energy extraction from a rotating black hole in terms of negative energy at infinity. In addition to the Penrose process through particle fission, the Blandford-Znajek mechanism by magnetic tension, and the magnetohydrodynamic Penrose process, we examine energy extraction from a black hole caused by magnetic reconnection in the ergosphere. The reconnection redistributes the angular momentum efficiently to yield the negative energy at infinity. We derive a condition for the process to operate in a simple situation, where the plasma is incompressible and the magnetic energy is converted completely to the plasma kinetic energy locally. Astrophysical situations of magnetic reconnection around the black holes are also discussed.

Blandford-Znajek Mechanism versus Penrose Process

During the three decades since its theoretical discovery the Blandford-Znajek process of extracting the rotational energy of black holes has become one of the foundation stones in the building of modern relativistic astrophysics. However, it is also true that for a long time its physics was not well understood, as evidenced by the controversy that surrounded it since 1990s. Thanks to the efforts of many theorists during the last decade the state of affairs is gradually improving. In this lecture I attempt to explain the key ingredients of this process in more or less systematic, rigorous, and at the same time relatively simple fashion. A particular attention is paid to the similarities and differences between the Blandford-Znajek and Penrose processes. To this purpose I formulate the notion of energy counter flow. The concept of horizon membrane is replaced with the concept of vacuum as an electromagnetically active medium. The effect of negative phase velocity of electromagnetic waves in the black hole ergosphere is also discussed.

Stellar explosions powered by the Blandford–Znajek mechanism

Abstract In this Letter, we briefly describe the first results of our numerical study on the possibility of magnetic origin of relativistic jets of long-duration gamma-ray bursters within the collapsar scenario. We track the collapse of massive rotating stars on to a rotating central black hole using axisymmetric general relativistic magnetohydrodynamic code that utilizes a realistic equation of state of stellar matter, and takes into account the cooling associated with emission of neutrinos and the energy losses due to dissociation of nuclei. The neutrino heating is not included. We describe the solution for one particular model where the progenitor star has magnetic field B= 3 × 1010 G. The solution exhibits strong explosion driven by the Poynting-dominated jets whose power exceeds 2 × 1051 erg s−1. The jets originate mainly from the black hole, and they are powered via the Blandford–Znajek mechanism.

A simplified model of jet power from active galactic nuclei

Aims. A simplified model of jet power from active galactic nuclei is proposed in which the relationship between jet power and disk luminosity is discussed by combining disk accretion with two mechanisms of extracting energy magnetically from a black hole accretion disk, i.e., the Blandford-Payne (BP) and the Blandford-Znajek (BZ) processes. Methods. By including the BP process into the conservation laws of mass, angular momentum and energy, we derive the expressions of the BP power and disk luminosity, and the jet power is regarded as the sum of the BZ and BP powers. Results. We find that the disk radiation flux and luminosity decrease because a fraction of the accretion energy is channelled into the outflow/jet in the BP process. It is found that the dominant cooling mode of the accretion disk is determined mainly by how the poloidal magnetic field decreases with the cylindrical radius of the jet. By using the parameter space we found, which consists of the black hole spin and the self-similar index of the configuration of the poloidal magnetic field frozen in the disk, we were able to compare the relative importance of the following quantities related to the jet production: (1) the BP power versus the disk luminosity, (2) the BP power versus the BZ power, and (3) the jet power versus the disk luminosity. In addition, we fit the jet power and broad-line region luminosity of 11 flat-spectrum radio quasars (FSRQs) and 17 steep-spectrum radio quasars (SSRQs) based on our model.

The BZ–MC–BP model for jet production from a black hole accretion disc

ABSTRACT Three energy mechanisms invoking large-scale magnetic fields are incorporated ina model to interpret jet production in black hole (BH) systems, i.e., the Blandford-Znajek(BZ) ,the magneticcoupling(MC) andBlandford-Panye(BP)processes.Theseenergy mechanisms can coexist in BH accretion disc based on the magnetic field con-figurations constrained by the screw instability, provided that the BH spin and thepower-law index indicating the variation of the magnetic field at an accretion disc aregreater than some critical values. In this model the jets are driven by the BZ processin the Poynting flux regime and by the BP process in the hydromagnetic regime, beingconsistent with the spine/sheath jet structure observed in BH sources of stellar andsupermassive size.Key words: accretion, accretion discs — black hole physics — magnetic field — jetproduction 1 INTRODUCTIONAs is well known, jets exist in many astronomical cases, suchas active galactic nuclei, quasars and young stellar objects.Different theoretical models have been proposed for acceler-ation and collimation of jets, which can be divided into twomain regimes. Energy and angular momentum are carried byboth the electromagnetic field and the kinetic flux of mat-ter in the hydromagnetic regime, and those are carried pre-dominantly by the electromagnetic field in the Poynting fluxregime (Ustyugova et al. 2000; Lovelace et al. 2002). Bland-ford & Znajek (1977) proposed firstly that jets from AGNscan be powered by a rotating black hole (BH) with a largescale magnetic field threading its horizon. Later, Blandford& Payne (1982, hereafter BP82) suggested that an outflowof matter can be driven centrifugally by large-scale mag-netic fields anchored at the disc surface. These two mech-anisms are usually referred to the BZ and BP processes,respectively. As argued in BP82, an outflow of matter canbe driven centrifugally from the disc, provided that the an-gle of the poloidal magnetic field with the normal of discsurface is greater than a critical value, i.e., α

The ‘Meissner effect’ and the Blandford—Znajek mechanism in conductive black hole magnetospheres

Abstract The expulsion of axisymmetric magnetic fields from the event horizons of rapidly rotating black holes has been seen as an astrophysically important effect that may significantly reduce or even nullify the efficiency of the Blandford–Znajek mechanism of powering the relativistic jets in active galactic nuclei and gamma-ray bursts. However, this Meissner-like effect is seen in the vacuum solutions of black hole electrodynamics, whereas the Blandford–Znajek mechanism is concerned with plasma-filled magnetospheres. In this Letter we argue that conductivity dramatically changes the properties of axisymmetric electromagnetic solutions – even for a maximally rotating Kerr black hole, the magnetic field is pulled inside the event horizon. Moreover, the conditions resulting in an outgoing Poynting flux in the Blandford–Znajek mechanism exist not on the event horizon but everywhere within the black hole ergosphere. Thus, the ‘Meissner effect’ is unlikely to be of interest in the astrophysics of black holes, at least not in the way this has been suggested so far. These conclusions are supported by the results of time-dependent numerical simulations that used three different computer codes. The test problems involve black holes with the rotation parameter ranging from a = 0.999 to a = 1. The pure electrodynamic simulations deal with the structure of conductive magnetospheres of black holes placed in a uniform-at-infinity magnetic field (Wald's problem) and the magnetohydrodynamic simulations are used to study the magnetospheres arising in the problem of disc accretion.

Models for jet power in elliptical galaxies: a case for rapidly spinning black holes

The power of jets from black holes are expected to depend on both the spin of the black hole and the structure of the accretion disk in the region of the last stable orbit. We investigate these dependencies using two different physical models for the jet power: the classical Blandford-Znajek (BZ) model and a hybrid model developed by Meier. In the BZ case, the jets are powered by magnetic fields directly threading the spinning black hole while in the hybrid model, the jet energy is extracted from both the accretion disk as well as the black hole via magnetic fields anchored to the accretion flow inside and outside the hole's ergosphere. The hybrid model takes advantage of the strengths of both the Blandford-Payne and BZ mechanisms, while avoiding the more controversial features of the latter. We develop these models more fully to account for general relativistic effects and to focus on advection-dominated accretion flows (ADAF) for which the jet power is expected to be a significant fraction of the accreted rest mass energy. We apply the models to elliptical galaxies, in order to see if these models can explain the observed correlation between the Bondi accretion rates and the total jet powers. For typical values of the disk viscosity parameter alpha~0.04-0.3 and mass accretion rates consistent with ADAF model expectations, we find that the observed correlation requires j>0.9; i.e., it implies that the black holes are rapidly spinning. Our results suggest that the central black holes in the cores of clusters of galaxies must be rapidly rotating in order to drive jets powerful enough to heat the intracluster medium and quench cooling flows.

A model of the light curves of gamma-ray bursts

An extreme Kerr black hole (BH) surrounded by a precessing disk is invoked to explain the light curves of gamma-ray bursts (GRBs) based on the coexistence of the Blandford-Znajek (BZ) and the magnetic coupling (MC) processes. The overall shape of the light curves and the duration of GRBs are interpreted by the evolution of the half-opening angle of the magnetic flux on the BH horizon, and the complex temporal structures are modulated by the precession and nutation of the jet powered by the BZ process. The time profile of the emission exhibits a fast rise and a slow decay due to the effect of the evolution of the half-opening angle. The light curves of several GRBs are well fitted by this model with only six free parameters.

Correlation between 3 : 2 QPO Pairs and Jets in Black Hole X‐Ray Binaries

We argue, following our earlier works (the CEBZMC model), that the phenomenon of twin peak high frequency quasi-periodic oscillations (QPOs) observed in black hole X-ray binaries is caused by magnetic coupling (MC) between accretion disk and black hole (BH). Due to MC, two bright spots occur at two separate radial locations r_{in} and r_{out} at the disk surface, energized by a kind of the Blandford-Znajek mechanism (BZ). We assume, following the Kluzniak-Abramowicz QPO resonance model, that Keplerian frequencies at these two locations are in the 3:2 ratio. With this assumption, we estimate the BH spins in several sources, including GRO J1655-40, GRS 1915+105, XTE J1550-564, H1743-322 and Sgr A*. We give an interpretation of the jet line in the hardness-intensity plane discussing the parameter space consisting of the BH spin and the power-law index for the variation of the large-scale magnetic field in the disk. Furthermore, we propose a new scenario for the spectral state transitions in BH X-ray binaries based on fluctuation in densities of accreting plasma from a companion star.

Screw Instability of Magnetic Field and Gamma‐Ray Bursts in Type Ib/c Supernovae

A toy model for gamma-ray burst supernovae (GRB-SNe) is discussed by considering the effects of screw instability of magnetic field in black hole (BH) magnetosphere. The screw instability in the Blandford-Znajek (BZ) process (henceforth SIBZ) can coexist with the screw instability in the magnetic coupling (MC) process (henceforth SIMC). It turns out that both SIBZ and SIMC occur inevitably, provided that the following parameters are greater than some critical values, i.e., (i) the BH spin, (ii) the power-law index describing the magnetic field at the disk, and (iii) the vertical height of the astrophysical load above the equatorial plane of the rotating BH. The features of several GRBs are well fitted. In our model the durations of the long GRBs depend on the evolve time of the half-opening angle. A small fraction of energy is extracted from the BH via the BZ process to power a GRB, while a large fraction of energy is extracted from the BH via the MC process to power an associated supernova. In addition, the variability time scales of tens of msec in the light curves of the GRBs are fitted by two successive flares due to SIBZ.

A New Model for Gamma-Ray Burst Powered by the Blandford-Znajek Process

A new model for gamma-ray bursts (GRBs) is discussed by considering the coexistence of the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process, in which the half-open angle θ BZ of the open magnetic flux on the horizon is determined by the mapping relation between the angular coordinate on the horizon and the radial coordinate on the disk with the assumption that the closed magnetic flux penetrating the disk takes precedence over the open magnetic flux. The GRB is powered by the BZ process with the duration identified as the lifetime of open magnetic flux on the horizon. The powers and torques of the BZ and MC processes are derived by using an improved equivalent circuit. It is shown that the BH is slowed down strongly by the MC process, resulting in a greater average power than other models for GRBs powered by the BZ process. It turns out that the data of several GRBs are well fitted by our model.

A New Approach to Black hole Spin in X-Ray Binaries

A new approach of detecting the black hole spin in x-ray binaries isproposed based on the model of the coexistence of the Blandford–Znajek(BZ) and magnetic coupling (MC) processes, inwhich the BZ process is used to power the jet emissions from x-raybinaries, and high frequency quasi-periodic oscillations (QPOs)are explained by a rotating hotspot in the inner region of theaccretion disc surrounding a fast-spinning black hole. It is shown thatthe black hole spins of several x-ray binaries (XTE J1550-564, GROJ1665-40 and GRS 1915+105) can be constrained in a rather narrowrange, provided that QPOs and jets coexist in these sources.

Total and Jet Blandford-Znajek Power in the Presence of an Accretion Disk

A rotating black hole probably powers ultrarelativistic jets in gamma-ray bursts, relativistic jets from some active galactic nuclei, and jets from some black hole x-ray binaries. Prior estimates of the power output of a black hole have assumed an infinitely thin disk, a magnetic field based upon a slowly rotating black hole, and have not self-consistently determined the geometry or magnitude of the magnetic field for a realistic accretion disk. We provide useful formulae for the total and jet Blandford-Znajek (BZ) power and efficiency as determined self-consistently from general relativistic magnetohydrodynamic numerical models. Of all jet mechanisms, we suggest that only the BZ mechanism is able to produce an ultrarelativistic jet.

Effects of Screw Instability on Extracting Energy from aRotating Black Hole

Magnetic extraction of energy from a rotating black hole(BH) is discussed in the coexistence of the Blandford–Znajek (BZ)process and the magnetic coupling (MC) process by considering theeffects of the screw instability of the magnetic field. It isshown that the screw instability affects the configuration of themagnetosphere and the evolution characteristics of the BH,augmenting the energy extracted in the BZ and MC processes. Inaddition, the observed energy and duration of several gamma-raybursts can be fitted well by virtue of our model.

Observations of the Blandford-Znajek process and the magnetohydrodynamic Penrose process in computer simulations of black hole magnetospheres

In this paper we report the results of axisymmetric relativistic magnetohydrodynamic (MHD) simulations for the problem of a Kerr black hole immersed in a rarefied plasma with ‘uniform’ magnetic field. The long-term solution shows properties that are significantly different from those of the initial transient phase studied recently by Koide. The topology of magnetic field lines within the ergosphere is similar to that of the split-monopole model with a strong current sheet in the equatorial plane. Closer inspection reveals a system of isolated magnetic islands inside the sheet and ongoing magnetic reconnection. No regions of negative hydrodynamic ‘energy at infinity’ are seen inside the ergosphere and the so-called MHD Penrose process does not operate. However, the rotational energy of the black hole continues to be extracted via the purely electromagnetic Blandford‐Znajek mechanism. In spite of this, no strong relativistic outflows from the black hole are seen to be developing. Combined with results of other recent simulations, our results signal a potential problem for the standard MHD model of relativistic astrophysical jets should they be found at distances as small as a few tens of gravitational radii from the central black hole. Ke yw ords: black hole physics ‐ magnetic fields ‐ methods: numerical.

An Electromagnetic Model for Jet Power from an AdvectionDominated Accretion Flow around a Rotating Black Hole

We discuss jet production from an advection dominated accretionflow (ADAF) around a rotating black hole (BH) in an electromagneticregime. An analytical expression for the jet power is derivedby using an equivalent circuit in the BH magnetosphere. It turns outthat a large fraction of jet powers is contributed from the innerregion of the ADAF, and the jet power depends sensitively on thedegree to which the flow is advection-dominated. In addition, weuse our model to fit the strong jet powers of several BL Lacobjects, which cannot be explained by virtue of the BZ process.

A model of rotating hotspots for the 3 : 2 frequency ratio of high-frequency quasi-periodic oscillations in black hole X-ray binaries

We propose a model to explain a puzzling 3:2 frequency ratio of high frequency quasi-periodic oscillations (HFQPOs) in black hole (BH) X-ray binaries, GRO J1655-40, GRS 1915+105 and XTE J1550-564. In our model a non-axisymmetric magnetic coupling (MC) of a rotating black hole (BH) with its surrounding accretion disc coexists with the Blandford-Znajek (BZ) process. The upper frequency is fitted by a rotating hotspot near the inner edge of the disc, which is produced by the energy transferred from the BH to the disc, and the lower frequency is fitted by another rotating hotspot somewhere away from the inner edge of the disc, which arises from the screw instability of the magnetic field on the disc. It turns out that the 3:2 frequency ratio of HFQPOs in these X-ray binaries could be well fitted to the observational data with a much narrower range of the BH spin. In addition, the spectral properties of HFQPOs are discussed. The correlation of HFQPOs with jets from microquasars is contained naturally in our model.