A Measurement of the Electromagnetic Luminosity of a Kerr Black Hole

By J. McKinney, Charles F. Gammie. 2004

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Some active galactic nuclei, microquasars, and gamma-ray bursts may be powered by the electromagnetic braking of a rapidly rotating black hole. We investigate this possibility via axisymmetric numerical simulations of a black hole surrounded by a magnetized plasma. The plasma is described by the equations of general relativistic magnetohydrodynamics, and the effects of radiation are neglected. The evolution is followed for 2000GM/c3, and the computational domain extends from inside the event horizon to typically 40GM/c2. We compare our results to two analytic steady state models, including the force-free magnetosphere of Blandford & Znajek. Along the way we present a self-contained rederivation of the Blandford-Znajek model in Kerr-Schild (horizon penetrating) coordinates. We find that (1) low-density polar regions of the numerical models agree well with the Blandford-Znajek model, (2) many of our models have an outward Poynting flux on the horizon in the Kerr-Schild frame, (3) none of our models have a net outward energy flux on the horizon, and (4) one of our models, in which the initial disk has net magnetic flux, shows a net outward angular momentum flux on the horizon. We conclude with a discussion of the limitations of our model, astrophysical implications, and problems to be addressed by future numerical experiments.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bac1dbe039742f7f0e48eb687413aaa78e95e6fc

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Citations in the corpus

Electromagnetic Extraction of Energy from Kerr Black Holes (2005, methodology): “FFDE/MHD simulations To solve a weakly magnetized thick disk around a Kerr black hole, McKinney and Gammie (2004) carried out numerical simulations of general-relativistic MHD, making references to (i) the BZ process and (ii) the Gammie model for a stationary, axisymmetric equatorial MHD inflow.”
The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105 (2006, background): “For many years, scientists have speculated that these jets are powered by BH spin via a Penrose-like process associated with magnetic fields (e.g., Blandford & Znajek 1977; Hawley & Balbus 2002; Meier 2003; McKinney & Gammie 2004).”
Spin, Accretion, and the Cosmological Growth of Supermassive Black Holes (2004, methodology): “However, the spin evolution parameter s(a/M) is different and can be represented reasonably well by the least squares linear fit s = 3.14− 3.30 a M (MHD disk), (15) (see Table 2 in McKinney & Gammie 2004).”
Stability of relativistic jets from rotating, accreting black holes via fully three-dimensional magnetohydrodynamic simulations (2008, methodology): “GRMHD simulations show that no strong jet emerges due to the accretion of higher multipole moments put initially withinthe disc (McKinney & Gammie 2004; McKinney & Narayan 2007a,b; c© 2009 RAS, MNRAS000, 1–6 Beckwith et al. 2008).”
MOMENTUM DRIVING: WHICH PHYSICAL PROCESSES DOMINATE ACTIVE GALACTIC NUCLEUS FEEDBACK? (2010, background): “The total energy output from these phases is considerable, but the accretion rates are thought to be low in these phases so the efficiencies of energy generation may be very high (cf. for a computation McKinney & Gammie 2004).”
Grand unification of AGN activity in the ΛCDM cosmology (2009, background): “Embedding such calculations in a fully general relativistic framework produces relativistic jets from the accretion flow, and the collima- c© 0000 RAS tion and jet power depend on the BH spin (McKinney & Gammie 2004; De Villiers et al. 2005; Hawley & Krolik 2006).”
ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics (2007, background): “…of the Blandford-Znajek mechanism for the extraction of rotational energy from a Kerr black hole (Komissarov 2001; Koide 2003; Komissarov 2004; McKinney & Gammie 2004; Komissarov 2005; McKinney 2005), the spin evolution of a black hole under the effect of different physical processes (Gammie…”
An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics (2006, background): “Other attractive examples include pulsar wind nebulae (Bucciantini et al. 2005), microquasars (Meier 2003; McKinney & Gammie 2004), X-ray binaries (Varnière, Rodriguez & Tagger 2002) and stellar core collapse in the context of general relativity (Bruenn 1985; Dimmelmeier, Font & Müller 2002).”
Hot Accretion Flows Around Black Holes (2014, methodology): “Representative results from 3D GRMHD simulations can be found in the series of early papers by De Villiers and collaborators (De Villiers et al. 2003, 2005; Hirose et al. 2004; Krolik et al. 2005) and Gammie and collaborators (Gammie et al. 2004, McKinney & Gammie 2004, McKinney 2006).”
THREE-DIMENSIONAL SIMULATIONS OF DYNAMICS OF ACCRETION FLOWS IRRADIATED BY A QUASAR (2007, background): “In fact, most magnetohydrodynamic simulations of accretion flows show outflows (e.g., Uchida & Shibata 1985; Stone & Norman 1994; Ouyed & Pudritz 1997; Hawley & Balbus 2002; Proga & Begelman 2003b; De Villier et al. 2004; McKinney & Gammie 2004, and references therein).”
Energy, momentum and mass outflows and feedback from thick accretion discs around rotating black holes (2013, background): “The jets on the other hand were relativistic and escaped easily, though carrying very little mass. Jets have been studied in detail by a number of authors (McKinney & Gammie 2004; De Villiers et al. 2005; McKinney 2006).”
General relativistic magnetohydrodynamical simulations of the jet in M 87 (2015, background): “Assuming that the jet power increases with BH spin asPj ∼ a2∗ (McKinney & Gammie 2004, Blandford & Znajek 1977), the discrepancy between halo and core jet power cannot be removed even if an extremely fastrotating BH (a∗ = 0.998) is assumed.”
Neutrino-dominated accretion flows as the central engine of gamma-ray bursts (2017, background): “…(2D or 3D) MHD simulations have investigated on how a large-scale vertical magnetic field evolves with an accretion disk and which configurations may power a jet (e.g., McKinney & Gammie 2004; Beckwith et al. 2008, 2009; McKinney & Blandford 2009), yet the analytic form of f (a∗) is still unclear.”
General relativistic magnetohydrodynamic simulations of magnetically choked accretion flows around black holes (2012, methodology): “BH x-ray binary QPOs are not seen (or are very weak) in the high-soft state that is typically associated with a thin disk dominated by MHD-MRI turbulence (Wijnands & van der Klis 1999; Remillard 2005; Rubio-Herrera & Lee 2005; Machida & Matsumoto 2008; Mondal et al. 2009).”
X-Ray Properties of Black-Hole Binaries (2006, background): “…scientists have speculated that these jets are powered by BH spin via something like the Penrose (1969) process, which allows energy to be milked from a spinning BH. Detailed models generally invoke magnetic fields (Blandford & Znajek 1977; Hawley & Balbus 2002; Meier 2003; McKinney & Gammie 2004).”
The black hole accretion code (2016, background): “, [17] with the purpose of stretching the grid radially and being able to concentrate resolution in the equatorial region.”
General relativistic magnetohydrodynamic simulations of the jet formation and large-scale propagation from black hole accretion systems (2006, methodology): “The Kerr metric in Kerr-Schild coordinates and the Jacobian transformation to Boyer-Lindquist coordinates are given in McKinney & Gammie (2004).”