Black hole Limits Redefined: Extreme Efficiency in Black Hole Jets

Abstract

Relativistic jets from black holes can extract energy not only from accretion but also directly from the black hole's spin, as described by the Blandford-Znajek mechanism. A longstanding question is whether magnetic flux can accumulate near the event horizon to such an extent that it halts accretion entirely, enabling energy extraction purely from spin. Previous studies have shown that accretion persists through instabilities and that jet power only modestly exceeds the accretion energy budget, yet some observational results suggest much higher efficiencies. Here we present state-of-the-art general relativistic magnetohydrodynamic (GRMHD) simulations that sustain a quasi-steady magnetically arrested disk state for approximately 10,000 dynamical times, during which accretion is globally suppressed across the full azimuthal extent. In this regime, jet power exceeds the accretion energy input by more than two orders of magnitude, demonstrating a previously unachieved level of efficiency. These results challenge conventional assumptions about the limits of black hole energy extraction and suggest a new framework for interpreting powerful jet systems. Our findings raise important questions about the long-term stability of such states and the fundamental limits of the Blandford-Znajek process.

Figures (10)

• Figure 1: Left Panels: Upper panel: evolution of the mass accretion measured across the black hole event horizon. Middle panel: evolution of the magnetic flux accreted onto the black hole. Lower panel: evolution of the normalized magnetic flux accumulated on the black-hole horizon. Right panels: Upper panel: the power of the jet. Lower panel: the efficiency of the jet for each magnetically arrested disk model. The dashed lines correspond to the average of the quantity from 1,500 $t_{\rm g}$ (2,000 $t_{\rm g}$ for the right one) till 10,000 $t_{\rm g}$.
• Figure 2: A 2D slice of the simulation at the equatorial plane showing rest-mass density at 6,000 $t_{\rm g}$. Left panel: model MAD.S.36 and Right panel: the extreme model MAD.S.7. The accretion disk in the extreme model has been expelled continuously for more than 3,000 dynamical times.
• Figure 3: A 2D slice of the simulation at constant azimuthal $\phi=180^o$ (left panel) and $\phi=0^o$ (right panel) for the extreme model MAD.S.7 at 5,000 $t_{\rm g}$. Left panel depicts the rest mass density whereas the right panel the magnetization $\sigma$.
• Figure 4: Left panel: Black hole spin versus the normalized magnetic flux at the event horizon. To match the results of Narayan2022 (green dots), the flux values from our simulations have been rescaled by a factor of $\sqrt{4\pi}$ (see Methods for details). The dashed blue line shows the fit from the green dots. Right panel: Black hole spin versus the efficiency from our simulations and that of Narayan2022 in green. The dashed blue line represents the BZ6 model prediction for jet power (equation 10 in Tchekhovskoy2010), calculated by inserting the magnetic flux fitting function $\phi_{\rm fit}(a_*)$, which is taken from the left hand panel into the theoretical expression.
• Figure 5: Magnetic flux $\Phi$ integrated across r in the initial time.