On the Universality of Energy Extraction from Black Hole Spacetimes

TL;DR

This study tests the universality of the Blandford-Znajek energy-extraction mechanism beyond Kerr GR by simulating 3D GRMHD accretion onto Johannsen-Psaltis black hole spacetimes with deviation parameters $(\epsilon_{3},\alpha_{13},\alpha_{22})$ (and $\alpha_{52}=0$). It demonstrates that the BZ jet power relation $\eta_{\rm BZ} \propto \phi_{\rm H}^2 \Omega_{\rm H}^2$ holds across Kerr and non-Kerr spacetimes, with horizon-frame-dragging enhancements from $\alpha_{22}$ allowing much stronger jets than Kerr at the same spin. However, there are strong degeneracies between spin $a$ and non-Kerr parameters in both jet power and horizon-scale shadow morphologies (quantified by $\delta$), meaning spin inferences based on jet power or images require independent measurements of $\Omega_{\rm H}$ and frame-dragging. The work argues that combining jet, accretion-rate and photon-ring observables, along with polarization-based probes of $\Omega_{\rm H}$, can help break these degeneracies and provide tests of Kerr-ness with current and future very-long-baseline interferometry.

Abstract

The launching of astrophysical jets provides the most compelling observational evidence for direct extraction of black hole (BH) spin energy via the Blandford-Znajek (BZ) mechanism. Whilst it is known that spinning Kerr BHs within general relativity (GR) follow the BZ jet power relation, the nature of BH energy extraction in general theories of gravity has not been adequately addressed. This study performs the first comprehensive investigation of the BZ jet power relation by utilizing a generalized BH spacetime geometry which describes parametric deviations from the Kerr metric of GR, yet recovers the Kerr metric in the limit that all deviation parameters vanish. Through performing and analyzing an extensive suite of three-dimensional covariant magnetohydrodynamics (MHD) simulations of magnetized gas accretion onto these generalized BH spacetimes we find that the BZ jet power relation still holds, in some instances yielding jet powers far in excess of what can be produced by even extremal Kerr BHs. It is shown that independent variation of the frame-dragging rate of the BH can enhance or suppress the effects of BH spin, and by extension of frame-dragging. This variation greatly enhances or suppresses the observed jet power and underlying photon ring image asymmetry, introducing a previously unexplored yet important degeneracy in BH parameter inference. Finally we show that sufficiently accurate measurements of the jet power, accretion rate and photon ring properties from supermassive BHs can potentially break this degeneracy, highlighting the need of independent investigations of BH frame-dragging from observations.

Figures (8)

• Figure 1: Top panel: Snapshot 3D rendering of a BH accreting gas and launching magnetized jets (GRMHD simulations of a JP BH with $\alpha_{22}=2$ and $a=0.9$, see text), together with a zoom-in view of the vicinity of the event horizon (inset). The diffuse material comprising the large-scale relativistic jet is shown in blue, with the extended denser accretion disk material shown in red and yellow. Tightly-wound magnetic field within the jet and counter-jet is indicated by the gray lines, with the BH event horizon denoted by the central dark sphere. Bottom panel: Corresponding ray-traced GRRT image of the upper panel's GRMHD snapshot as viewed at $86$ GHz (logarithmic color scale), together with the inset zoom-in view of the event horizon-scale structure, as viewed at the Event Horizon Telescope (EHT) frequency of $230$ GHz (linear color scale) for M87$^*$.
• Figure 2: Panel a demonstrates that the BZ mechanism accurately describes the outflow power for arbitrary non-Kerr BHs out to large horizon angular frequencies beyond even extremal Kerr BHs. This implies that the BZ power is a fundamental property of spinning BHs. The red shaded region indicates the predicted BZ power over a range of magnetic field shapes: $0.044 \leq k\leq 0.054$ from eqn. \ref{['eqn:BZ']}. Panel b shows that the outflow power can assume a large range of values given a particular BH spin within our model set. Panel c is similar to panel b, but now presents the deviation in mean BH shadow diameter with respect to the Schwarzschild value of $d_{\rm sh, Schw}=6\sqrt{3}~M$, hereafter $\delta :=d_{\rm sh}/d_{\rm sh, Schw}-1$. We also show the 2017 EHT measurements of M87* of $\delta=-0.01\pm0.17$EHTC+2019fPsaltis+2020Kocherlakota+2021, delineated as dashed lines. These plots illustrate the inherent degeneracies in BH spin inference from jet power estimates and shadow image size measurements when one relaxes the assumption that the spacetime geometry is described by a Kerr BH. See Sec. \ref{['sec:conclusion']} for more discussion on these degeneracies.
• Figure 3: Collection of three-image panel groups showing $86$ GHz M87* images (upper panels) and corresponding 230 GHz BH shadow images (both viewed at $i=163^{\circ}$, bottom left) and as viewed at $i=90^{\circ}$ (bottom right). From left to right, top to bottom, trios of panels represent: Schwarzschild BH, Kerr BH with $a=0.5$, JP BH with $\alpha_{13}=6$ and $a=0.5$, and a JP BH with $\alpha_{22}=8$ and $a=0.5$, respectively. Differences in jet size and power are evident between Schwarzschild and Kerr BHs at $86$ GHz. The JP BH with $\alpha_{13}=6$, in spite of having the same spin as the Kerr BH, has a significantly weaker jet and larger photon ring size. By contrast, the JP BH with $\alpha_{22}=8$ possesses a large $\Omega_{\rm H}$, enhancing the effects of frame dragging, giving rise to a more powerful and extended jet than the Kerr BH with identical spin. All panels show time-averaged images over the interval $20,000$ M -- $25,000$ M. The $86$ GHz image color scale is logarithmic and spans 5 orders of magnitude in specific intensity, whereas the $230$ GHz images are plotted on a linear scale and show the full range of specific intensity. All images are normalized to a maximum pixel intensity of unity.
• Figure 4: Breaking degeneracies in BH parameters. Left: The outflow power $\eta$ depends strongly on the horizon angular frequency $\Omega_{\rm H}$ for the Kerr and Non-Kerr JP $\alpha_{22}$ models. $\eta$ increases monotonically as $|\Omega_{\rm H}|$ increases both for prograde and retrograde BHs. Therefore, it is possible to constrain $|\Omega_{\rm H}|$ using measurements of the outflow efficiency from observations of jetted BHs. Right: Contours of $\Omega_{\rm H}$ (in colour) overlaid with contours of the shadow size deviation $\delta$ for JP $\alpha_{22}$ spacetimes. Independent measurements of $\Omega_{\rm H}$ and $\delta$ could place stringent constraints on the black hole spin $a$ and quadrapole moment $\alpha_{22}$. Forbidden solutions for the JP metric are shown by the gray-lined region.
• Figure 5: Time evolution of the accretion rate $\dot{M}$, the outflow power $P$, the square of the un-normalized horizon magnetic flux $\Phi_{\rm H}^2$ (which is essentially equivalent to the expected BZ power) and the 230 GHz flux for four different (non-)Kerr models. We also mention the ratio of the $1\sigma$ standard deviation and the mean $\mu$ for each curve as a measurement of the variability of each quantity for each model.