Magnetic field lines entering the event horizon of a rapidly spinning black hole can slow down its rotation, acting like rubber bands that are dragged along with it. This theoretical concept is well known as the Blandford/Znajek process. While the model is appealing for its clarity in simple equilibrium solutions of magnetic fields around black holes, it was unclear whether and how it operates in highly dynamic scenarios. One such scenario is the accretion of a tube of magnetic flux onto a black hole, as an alternative to the continuous build-up of large-scale magnetic structures. In this research, we extend earlier results from 2D simulations and show that episodes of an efficiently operating Blandford/Znajek process emerge in carefully modeled 3D magnetospheres. By finding optimal sizes for the accreted magnetic flux tubes, we relate the variability of efficient energy extraction from the central black hole to astronomical observations. For a black hole like the one at the center of the galaxy M87, we estimate variability time scales of several days to weeks for polarity reversals during the accretion of magnetic loops.

Research summary

• We devised a way to feed magnetic loops onto a rapidly spinning black hole by adding current-driven layers and resistive transition regions around an in-situ accretion disk model in a force-free Kerr magnetosphere.
• In a parameter study, we examined the dynamics of magnetic loops of different extensions and accretion velocities falling onto the central object. For counter-rotating accretion disks with an innermost circular orbit at some distance from the event horizon, we identified an ideal loop geometry for launching efficient Blandford/Znajek episodes.
• Our main argument for efficient energy extraction relies on comparing the time scales of the disk rotation and of the black hole rotation. As field lines slip across the event horizon, they need sufficient time to wind up and produce a jet-like structure. With insufficient time, failed jet structures tip over onto the disk and do not fuel a powerful striped jet with each accreted loop in three dimensions.
• Even in 3D and in an extremely dynamic environment, where many assumptions of the original derivation of the Blandford/Znajek process do not hold, ideal conditions are reached at the event horizon whenever efficient outflows occur. We conclude that the process can operate quite universally in arbitrary geometries whenever a rapidly spinning black hole immersed in a force-free magnetosphere emits outgoing Poynting flux, that is, electromagnetic energy flux.

Visualizing science

During the accretion of a magnetic flux tube, the magnetosphere around a rapidly spinning Kerr black hole becomes highly ordered, and jet-like structures of outgoing Poynting flux, shown as ribbons, emerge. Once the polarity of the infalling magnetic field, shown as color density, changes, the extended structure is lost. An inefficient phase of magnetospheric re-polarization then replaces the efficient Blandford/Znajek episode. This process repeats and produces pulses of efficient energy extraction from the central black hole. Scaled to a black hole like the one at the center of the galaxy M87 and assuming the ideal loop geometry identified in this work, the pulses last several days to weeks.

Collaborative results

J. F. Mahlmann, A. Levinson, M. Á. Aloy, Striped Blandford/Znajek jets from advection of small-scale magnetic field, Monthly Notices of the Royal Astronomical Society, Volume 494, Issue 3, May 2020, Pages 4203–4225, https://doi.org/10.1093/mnras/staa943