A Toy Model for the Magnetic Connection between a Black Hole and a Disk

Abstract

A magnetic field connecting a Kerr black hole to a disk rotating around it can extract energy and angular momentum from the black hole and transfer them to the disk if the black hole rotates faster than the disk. The energy can be dissipated and radiated away by the disk, which makes the disk shine without the need of accretion. In this paper we present a toy model for the magnetic connection: a single electric current flowing around a Kerr black hole in the equatorial plane generates a poloidal magnetic field which connects the black hole to the disk. The rotation of the black hole relative to the disk generates an electromotive force which in turn generates a poloidal electric current flowing through the black hole and the disk and produces a power on the disk. We will consider two cases: (1) The toroidal current flows on the inner boundary of the disk, which generates a poloidal magnetic field connecting the horizon of the black hole to a region of the disk {\it beyond} the inner boundary; (2) The toroidal current flows on a circle inside the inner boundary of the disk but outside the horizon of the black hole, which generates a poloidal magnetic field connecting a portion of the horizon of the black hole to the {\it whole} disk. We will calculate the power produced by the magnetic connection and the resulting radiation flux of the disk in the absence of accretion, and compare them with that produced by accretion.

arXiv comment9 pages, including 9 figures

References in corpus (5)

• Extracting energy from black holes: the relative importance of the Blandford-Znajek mechanism
• Accretion Disk Torqued by a Black Hole
• Extracting Energy from a Black Hole through Its Disk
• Extracting Energy from Accretion into Kerr Black Hole
• A Toy Model for Blandford-Znajek Mechanism

Cited by in corpus (10)

• General Relativistic Magnetohydrodynamic Simulations of Magnetically Choked Accretion Flows around Black Holes
• Simulations of Magnetized Disks Around Black Holes: Effects of Black Hole Spin, Disk Thickness, and Magnetic Field Geometry
• A magnetic reconnection model for quasi-periodic oscillations in black hole systems
• Magnetohydrodynamic Shocks in Non-Equatorial Plasma Flows around a Black Hole
• Evolution of Magnetic Fields around a Kerr Black Hole
• A Toy Model for Magnetic Connection in Black-Hole Accretion Disc
• BZ-MC-BP Model for Jet Production from Black Hole Accretion Disc
• Magnetic connection and current distribution in black hole accretion discs
• A model for 3:2 HFQPO pairs in black hole binaries based on cosmic battery
• Estimating the black hole mass of NGC1313 X-1 based on the spectral and timing properties