On the efficiency of the Blandford-Znajek mechanism for low angular momentum relativistic accretion

Blandford-Znajek (BZ) mechanism has usually been studied in the literature for accretion with considerably high angular momentum leading either to the formation of a cold Keplerian disc, or a hot and geometrically thick sub-Keplerian flow as described within the framework of ADAF/RIAF. However, in nearby elliptical galaxies, as well as for our own Galactic centre, accretion with very low angular momentum is prevalent. Such quasi-spherical strongly sub-Keplerian accretion has complex dynamical features and can accommodate stationary shocks. In this letter, we present our calculation for the maximum efficiency obtainable through the BZ mechanism for complete general relativistic weakly rotating axisymmetric flow in the Kerr metric. Both shocked and shock free flow has been studied in detail for rotating and counter rotating accretion. Such study has never been done in the literature before. We find that the energy extraction efficiency is low, about 0.1%, and increases by a factor 15 if the ram pressure is included. Such an efficiency is still much higher than the radiative efficiency of such optically thin flows. For BZ mechanism, shocked flow produces higher efficiency than the shock free solutions and retrograde flow provides a slightly larger value of the efficiency than that for the prograde flow.

💡 Research Summary

The paper investigates how efficiently the Blandford‑Znajek (BZ) mechanism can extract rotational energy from a Kerr black hole when the surrounding accretion flow has very low angular momentum. Most previous studies of BZ have assumed a high‑angular‑momentum, Keplerian or thick ADAF/RIAF disc that supplies a strong, ordered magnetic field. In contrast, the authors consider a quasi‑spherical, weakly rotating, axisymmetric flow described by the full general‑relativistic equations in the Kerr metric. The flow is taken to be inviscid, adiabatic, and characterized by four parameters: the relativistic Bernoulli constant (E), the specific angular momentum (\lambda), the adiabatic index (\gamma), and the black‑hole spin (a). Solving the relativistic Euler and continuity equations yields a set of first‑order differential equations for the radial three‑velocity (u(r)) and the sound speed (c_s(r)). Depending on the parameter values, the flow can possess up to three critical (sonic) points. When a centre‑type critical point lies between two saddle points, the Rankine‑Hugoniot shock conditions can be satisfied, producing a stationary shock. The authors therefore study both shock‑free (single‑sonic) and shocked (multi‑sonic) solutions, for prograde (co‑rotating) and retrograde (counter‑rotating) flows.

The BZ power is written as
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