Prograde and Retrograde Black Holes: Whose Jet is More Powerful?

Abstract: The outflow efficiency (eta) from black hole (BH) accretion disc systems is known to depend upon both the BH spin (a) and the amount of large-scale magnetic flux threading the BH and disc. Semi-analytical flux-trapping models suggest retrograde BHs should trap much more large-scale magnetic flux near the BH leading to much higher eta than for prograde BHs. We self-consistently determine the amount of large-scale magnetic flux trapped by rapidly spinning (a = -0.9 and 0.9) BHs using global 3D time-dependent non-radiative general relativistic magnetohydrodynamic simulations of thick (h/r ~ 0.3-0.6) discs. We find that BH-trapped flux builds up until it is strong enough to disrupt the inner accretion disc. Contrary to prior flux-trapping models, which do not include the back-reaction of magnetic flux on the disc, our simulations show prograde BHs trap more magnetic flux, leading to about 3 times higher eta than retrograde BHs for |a| = 0.9. Both spin orientations can produce highly efficient jets, eta ~ 100%, with increasing eta for increasing disc thickness. The similarity of eta for prograde and retrograde BHs makes it challenging to infer the sign of BH spin based on jet energetics alone.

• The paper finds that prograde black holes exhibit jet efficiency (~102% for a=0.9) nearly three times greater than retrograde BHs (~34%) due to enhanced magnetic flux trapping.
• Using global 3D GRMHD simulations of thick, non-radiative accretion discs, the study challenges conventional flux-trapping models by incorporating magnetic back-reaction.
• The results offer a robust framework for interpreting AGN and BHB jet observations, emphasizing the critical roles of black hole spin, disc thickness, and magnetic influences.

Analysis of Jet Power from Prograde and Retrograde Black Holes

The paper authored by Alexander Tchekhovskoy and Jonathan C. McKinney investigates the difference in jet power arising from prograde and retrograde black holes (BHs) under the influence of large-scale magnetic fields. Using global 3D general relativistic magnetohydrodynamic (GRMHD) simulations, this study challenges prevailing semi-analytical flux-trapping models that suggest enhanced jet power emanating from retrograde BHs as compared to prograde counterparts.

The research primarily deploys simulations of thick, non-radiative accretion discs to explore the nuances of the outflow efficiency ($\eta$), which is intrinsically linked to the spin of the BH ($a$) and the magnetic flux threading through the BH-disc system.

Key Findings

1. Flux Trapping and Magnetic Flux Saturation: Contrary to predictions, the simulations reveal that prograde BHs effectuate higher magnetic flux trapping compared to retrograde BHs. This is primarily attributed to the inclusion of magnetic flux back-reaction on the disc, which is absent in flux-trapping models. Consequently, prograde BHs demonstrate an approximate threefold increase in energy outflow efficiency ($\eta$) compared to retrograde BHs.
2. Efficiency and Spin Orientation: The results depict a challenging scenario for inferring the sign of BH spin based solely on energetics due to the realization that both spin orientations can yield highly efficient jets. For instance, for $a=0.9$, a prograde BH exhibited an efficiency $\sim102\%$, significantly surpassing the $\sim34\%$ efficiency noted for its retrograde counterpart.
3. Influence of Disc Thickness: The study notes that disc thickness is a pivotal factor, with thicker discs exhibiting greater efficiency. This suggests that $\eta$ increases with disc thickness, notwithstanding the spin orientation.
4. Magnetically Arrested Discs (MADs): The authors focus on the MAD state where the accretion of large magnetic flux leads to the disc being magnetically arrested, a state independent of initial magnetic flux content. This allows for a robust determination of jet efficiency that stands free from the uncertainties of initial simulation setup.

Theoretical and Practical Implications

The findings necessitate a revision of models predicting retrograde dominance in jet ejection power. This calls into question assumptions regarding the effects at the innermost stable circular orbit (ISCO) and the dynamics within plunging regions in flux-trapping models. It implies that future research should incorporate the effects of the magnetic field's interaction with plunging inflows and its susceptibility to magnetic interchange.

Practically, these results provide a framework for interpreting observations of active galactic nuclei (AGN) and black hole binaries (BHBs). The efficiencies calculated serve as functional upper limits when using observed jet powers to place constraints on the spin of astrophysical black holes.

Future Directions

The research hints at wide-ranging future inquiries, including exploring thinner ($h/r \lesssim 0.1$) accretion discs and examining radiative effects not covered in the current simulations. Bridging the gap between observational data and theoretical models of jet formation and evolution could greatly enhance our understanding of black hole accretion processes.

In conclusion, this paper represents a crucial step in refining our comprehension of jet ejection mechanisms and efficiency differentials between prograde and retrograde black holes, presenting essential data that could realign current theoretical models in this domain.