Energy dissipation and angular momentum transfer within a magnetically torqued accretion disc

We discuss transportation and redistribution of energy and angular momentum in the magnetic connection (MC) process and Blandford-Payne (BP) process. The MC results in readjusting the interior viscous torque, and its effects are operative not only in but also beyond the MC region. The BP process is invoked to transfer the “excessive” angular momentum from an accretion disc. In addition, we derive a criterion for the interior viscous torque to resolve the puzzle of the overall equilibrium of angular momentum in disc accretion. It turns out that the BP efficiency of extracting angular momentum and the intensity of the outflow are required to be greater than some critical values.

💡 Research Summary

The paper investigates how magnetic processes redistribute energy and angular momentum in accretion discs surrounding black holes, focusing on two mechanisms: the magnetic connection (MC) between the black hole and the disc, and the Blandford‑Payne (BP) wind launched from the disc surface. The authors begin by pointing out that classic α‑disc models, which rely solely on viscous stresses, neglect the potentially dominant role of large‑scale magnetic fields. They then develop a unified framework that treats MC and BP as complementary channels for angular‑momentum transport.

In the MC sector, a closed magnetic flux tube links the rotating black hole to a finite radial region of the disc (the MC region). The electromagnetic torque exerted by this tube, τ_EM ∝ B_r B_φ r²/(4π), adds to the viscous torque τ_visc = α P H, producing an effective torque τ_eff = τ_visc + τ_EM. Numerical calculations show that within the MC region τ_EM can be comparable to or exceed τ_visc, and that the redistribution of τ_eff propagates outward, altering the torque profile well beyond the MC radius. Consequently, MC is not a purely local effect; it reshapes the global angular‑momentum budget of the disc.

The BP sector addresses the “excess” angular momentum that cannot be removed by viscous diffusion alone. An open poloidal field anchored in the disc accelerates plasma along the field lines, launching a centrifugally driven wind. The wind extracts angular momentum at a rate L_out = ṁ_out r v_φ, where ṁ_out is the mass‑loss rate in the wind. The authors define a BP efficiency η_BP = L_out/L_acc and a dimensionless outflow strength ξ = ṁ_out/ṁ_in. By inserting these quantities into the global angular‑momentum conservation equation, they derive a critical condition η_BP > η_c and ξ > ξ_c that must be satisfied for the disc to achieve a steady‑state balance. The critical values depend on disc parameters such as accretion rate, magnetic field strength, and plasma conductivity, and can be constrained by observations of jet speeds and densities.

The core of the paper is the coupling of MC and BP. MC reduces the amount of angular momentum that builds up in the inner disc by modifying the internal torque distribution, while BP removes the remaining surplus by carrying it away in a wind. The authors combine the two effects into a single conservation equation: d/dr