A Toy Model for Blandford-Znajek Mechanism

Abstract

A toy model for the Blandford-Znajek mechanism is investigated: a Kerr black hole with a toroidal electric current residing in a thin disk around the black hole. The toroidal electric current generates a poloidal magnetic field threading the black hole and disk. Due to the interaction of the magnetic field with remote charged particles, the rotation of the black hole and disk induces an electromotive force, which can power an astrophysical load at remote distance. The power of the black hole and disk is calculated. It is found that, for a wide range of parameters specifying the rotation of the black hole and the distribution of the electric current in the disk, the power of the disk exceeds the power of the black hole. The torque provided by the black hole and disk is also calculated. The torque of the disk is comparable to the torque of the black hole. As the disk loses its angular momentum, the mass of the disk gradually drifts towards the black hole and gets accreted. Ultimately the power comes from the gravitational binding energy between the disk and the black hole, as in the standard theory of accretion disk, instead of the rotational energy of the black hole. This suggests that the Blandford-Znajek mechanism may be less efficient in extracting energy from a rotating black hole with a thin disk. The limitations of our simple model and possible improvements deserved for future work are also discussed.

arXiv comment16 pages, 4 figures. Accepted for publication in Physical Review D

References in corpus (5)

• Are Gamma-Ray Bursts in Star Forming Regions?
• Extracting energy from black holes: the relative importance of the Blandford-Znajek mechanism
• Efficiency of Magnetized Thin Accretion Disks in the Kerr Metric
• Magnetized Accretion Inside the Marginally Stable Orbit around a Black Hole
• The Blandford-Znajek mechanism and emission from isolated accreting black holes

Cited by in corpus (30)

• The Physics of Gamma-Ray Bursts and Relativistic Jets
• Accretion Disk Torqued by a Black Hole
• Chaotic motion of Charged Particles in an Electromagnetic Field Surrounding a Rotating Black Hole
• Constraining the Type of Central Engine of GRBs with Swift Data
• Extracting Energy from a Black Hole through Its Disk
• Hyperaccreting Black Hole as Gamma-Ray Burst Central Engine. II. Temporal evolution of central engine parameters during Prompt and Afterglow Phases
• Neutron Star Mergers and How to Study Them
• Black hole Spin in Sw J1644+57 and Sw J2058+05
• Issues in the Blandford-Znajek Process for GRB Inner Engine
• Signature of a New-Born Black Hole from the Collapse of a Supra-massive Millisecond Magnetar
• GRB 211211A: a Prolonged Central Engine under a Strong Magnetic Field Environment
• Black hole central engine for ultra-long gamma-ray burst 111209A and its associated supernova 2011kl
• Long duration gamma-ray bursts: hydrodynamic instabilities in collapsar disks
• Black Hole Magnetospheres Around Thin Disks Driving Inward and Outward Winds
• The Second Plateau in X-ray Afterglow Providing Additional Evidence for Rapidly Spinning Magnetars as the GRB Central Engine
• What can we learn about GRB from the variability timescale related correlations?
• Giant X-ray and optical Bump in GRBs: evidence for fall-back accretion model
• A Toy Model for the Magnetic Connection between a Black Hole and a Disk
• Acceleration of electric current-carrying string loop near a Schwarzschild black hole immersed in an asymptotically uniform magnetic field
• Constraining Properties of GRB Central Engines with X-ray flares
• Making Clean Energy with a Kerr Black Hole: a Tokamak Model for Gamma-Ray Bursts
• Evolution of Black Holes in the Galaxy
• GRB 111209A/SN 2011kl: Collapse of a supramassive magnetar with r-mode oscillation and fall-back accretion onto a newborn black hole
• Black holes with current loops revisited
• Toy model for a two-dimensional accretion disk dominated by Poynting flux
• Special supernova signature from BH-NS/BH progenitor systems
• Two Dimensional Poynting Flux Dominated Flow onto a Schwarzschild Black Hole
• Estimates of the early EM emission from compact binary mergers
• On the Theory of Gamma Ray Bursts and Hypernovae: The Black Hole Soft X-ray Transient Sources
• EP241113a: dissipative photospheric emission from a dirty fireball