General relativistic magnetohydrodynamic simulations of Blandford–Znajek jets and the membrane paradigm

Abstract

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, while ignoring the accretion disk leads to a further ∼ 50% overestimate. Simply reducing the standard BZ jet power prediction by 60% gives a good fit to our simulation data. Our second result is to show that the membrane formulation of the BZ model correctly describes the physics underlying simulated jets: torques, dissipation, and electromagnetic fields on the horizon. This provides intuitive yet rigorous pictures for the black hole energy extraction process. Third, we compute the effective resistance of the load region and show that the load and the black hole achieve near perfect impedance matching. Taken together, these results increase our confidence in the BZ model as the correct description of jets observed from astrophysical black holes.We re-derive this equation in Appendix A. The assumption Ω F /Ω H = 1/2 gives maximum jet efficiency. We refer to the BZ model with this assumption as the standard BZ model. Equation (1) c 0000 RAS

Black hole Meissner effect and entanglement

“…The geometrical interpretation of the black hole Meissner effect relies on the fact that the length of the throat blows up in the extremal limit. This is the geometrical manifestation of (14). We have derived this fact from the KMS property of the Hartle-Hawking vacuum at low Hawking-Unruh temperatures.…”

“…The standard model of spin-powered jets [11] requires magnetic fields threading the horizon [12]. The jets are powered by magnetic torques acting on the horizon [13,14]. There is observational evidence for near-extremal Kerr black holes in our galaxy [44][45][46].…”

“…The standard model of black hole jets [11] requires magnetic fields threading the horizon [12]. The fields torque the horizon and extract its rotational energy (according to the membrane paradigm [13,14]). So if the Meissner effect expels the field, then the jets will be quenched [12,[15][16][17].…”

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

“…Blandford & Payne 1982;Königl 1989;Field & Rogers 1993;Blackman et al 2001;Lynden-Bell 2006;Blackman & Pessah 2009;Pudriz et al 2012;Penna et al 2013). Accreting systems typically exhibit a continuum spectrum and luminosity best explained by matter accreting onto a central object falling deeper into a potential well and thereby releasing positive kinetic energy in the form of radiation or jet outflows.…”

Testing the membrane paradigm with holography

“…a very small distance from the event horizon [2]. In the astrophysical context, this membrane approximation has been applied to the study of the magnetosphere of a black hole surrounded by a magnetized accretion disk [3] and jets [4]; see [5] for many more applications and further references. More recent interest in the membrane paradigm has been stimulated by the discovery of holography [6][7][8] and what eventually became known as the fluid-gravity duality [9,10]; see [11] for a review of the membrane paradigm in this context.…”