Active galactic nuclei with similar accretion powers differ in jet power by four or more orders of magnitude. In the Blandford–Znajek picture both the black hole spin and the magnetic flux threading the horizon set the jet power, and two competing paradigms attribute the dominant role to one or the other: the spin paradigm and the magnetic-flux paradigm, under which only sources that have accreted enough poloidal flux to form a magnetically arrested disk (MAD) reach high jet-production efficiency. Powerful (radio-loud) sources are observationally consistent with MAD-saturated flux, and the single radio-intermediate quasar studied so far, III Zw 2, shows jet magnetic flux at least a factor of five below the MAD saturation level despite a near-maximal spin. The open problem is to determine, at the population level, whether the horizon-threading magnetic flux rather than spin controls jet production efficiency: measure jet magnetic flux (as a proxy for horizon flux) in a sample of radio-quiet and radio-intermediate AGN spanning a range of efficiencies, and combine with spin estimates to discriminate the flux and spin paradigms decisively.

Background

Active galactic nuclei (AGN) are accreting supermassive black holes, some of which launch relativistic plasma jets. A long-standing puzzle is that sources with similar accretion disk luminosities span at least four orders of magnitude in jet power. This spread is conventionally traced with the radio-loudness parameter R=L5/LBR = L_5/L_B, the ratio of the monochromatic radio luminosity at 5 GHz to the optical luminosity at 4400 Å; sources with R≲10R \lesssim 10 are called radio-quiet, sources with roughly R≳100R \gtrsim 100 are called radio-loud, and sources with intermediate values of RR are called radio-intermediate (the exact boundaries vary somewhat by author). Since mass and accretion rate alone cannot reproduce the spread, at least one further parameter is needed. In the Blandford–Znajek (BZ) mechanism, a rotating black hole threaded by ordered magnetic field extracts rotational energy and can power a jet, so the two additional control parameters are the dimensionless black hole spin aa and the magnetic flux ΦBH\Phi_{\mathrm{BH}} threading the horizon. General relativistic magnetohydrodynamic (GRMHD) simulations show that when the accumulated poloidal flux reaches ΦBH∼50(M˙rg2c)1/2\Phi_{\mathrm{BH}} \sim 50(\dot{M} r_g^2 c)^{1/2} (with M˙\dot{M} the accretion rate, rgr_g the gravitational radius, and cc the speed of light), magnetic pressure arrests the accretion flow — a magnetically arrested disk (MAD) — and jet power approaching or exceeding the accretion power becomes possible (Tchekhovskoy et al. 2011). The magnetic-flux paradigm (Sikora & Begelman 2013) holds that only high-spin sources that have also accreted enough flux to reach the MAD state become radio-loud, so radio loudness reflects the source's accretion history rather than its spin; the competing spin paradigm attributes the spread mainly to the spin distribution. Two observational facts frame the test. First, for radio-loud AGN the jet magnetic flux inferred from very long baseline interferometry (VLBI) agrees with the MAD saturation prediction, ∼52±5\sim 52 \pm 5 in the above normalization (Zamaninasab et al. 2014), and horizon-scale polarimetry of M87* by the Event Horizon Telescope favors strongly magnetized, MAD-like horizon fields (EHT Collaboration 2021). Second, radio-quiet AGN with apparently high spins exist (Reynolds 2021), which is difficult for a spin-only explanation — though X-ray reflection spin measurements are model-dependent. The magnetic flux threading the horizon cannot be measured directly except for M87* and Sgr A*, so for other AGN the best available proxy is the jet magnetic flux Φjet\Phi_{\mathrm{jet}} inferred from multi-frequency VLBI: either the core-shift method, which converts the frequency-dependent displacement of the synchrotron self-absorbed VLBI core into an equipartition magnetic field strength along the jet, or the spectral turnover of the self-absorbed synchrotron core (SSA method), which does not require assuming equipartition between magnetic and particle energy densities. Assuming flux freezing (field lines advected with the flow), Φjet\Phi_{\mathrm{jet}} is then equated with ΦBH\Phi_{\mathrm{BH}}. Applying this program to the radio-intermediate quasar III Zw 2, Chamani et al. (2021) obtained upper limits placing its jet magnetic flux at least a factor of five below the MAD level under equipartition, about 70 below without equipartition, and about 15 below from the SSA turnover, while XMM-Newton/NuSTAR reflection spectroscopy gives a near-maximal spin a>0.98a > 0.98 (Chamani et al. 2020) — a single-source data point compatible with the flux paradigm.

Problem Statement

The underlying question is: why do accreting black holes with similar accretion powers produce jet powers spanning at least four orders of magnitude — what conditions are required to make a powerful jet? In the Blandford–Znajek framework this reduces to deciding whether the magnetic flux threading the black hole horizon or the black hole spin is the dominant parameter setting the jet production efficiency (radio loudness) of active galactic nuclei. The problem is to settle this discrimination observationally, which requires, as jointly necessary components of one objective: (1) measuring — or placing tight upper limits on — the jet magnetic flux Φjet\Phi_{\mathrm{jet}} of a population of radio-quiet and radio-intermediate AGN spanning a range of jet production efficiencies, using multi-frequency VLBI core-shift measurements and synchrotron self-absorption turnover spectra, and establishing whether these sources in general have Φjet\Phi_{\mathrm{jet}} (and hence the horizon-threading flux ΦBH\Phi_{\mathrm{BH}}) well below the MAD saturation level ΦBH∼50(M˙rg2c)1/2\Phi_{\mathrm{BH}} \sim 50(\dot{M} r_g^2 c)^{1/2}, or whether III Zw 2 (the single measured case, a factor ≳5\gtrsim 5 below saturation with spin a>0.98a > 0.98) is atypical; and (2) combining the flux constraints with black hole spin estimates (e.g., from X-ray reflection spectroscopy) for the same sources to test whether high spin coexists with sub-MAD flux across the low-radio-loudness population. A decisive answer establishes whether magnetic flux, spin, or their combination controls jet production efficiency — or refutes the dichotomy itself.

References

  1. Savolainen, T. & Chamani, W. (2025). MAD accretion and AGN jets – an observational perspective. Proceedings of the 16th European VLBI Network Symposium (Bonn: Max-Planck-Institut für Radioastronomie, 2024). arXiv:2502.06602, DOI: 10.48550/arXiv.2502.06602. https://arxiv.org/abs/2502.06602
  2. Chamani, W., Savolainen, T., Hada, K. & Xu, M. H. (2021). Testing the magnetic flux paradigm for AGN radio loudness with a radio-intermediate quasar. Astronomy & Astrophysics 652, A14. DOI: 10.1051/0004-6361/202140676, arXiv:2106.01089. https://doi.org/10.1051/0004-6361/202140676
  3. Chamani, W., Koljonen, K. & Savolainen, T. (2020). Joint XMM-Newton and NuSTAR observations of the reflection spectrum of III Zw 2. Astronomy & Astrophysics 635, A172. DOI: 10.1051/0004-6361/201936992, arXiv:2002.04454. https://doi.org/10.1051/0004-6361/201936992
  4. Sikora, M. & Begelman, M. C. (2013). Magnetic flux paradigm for radio loudness of active galactic nuclei. The Astrophysical Journal Letters 764, L24. DOI: 10.1088/2041-8205/764/2/L24. https://doi.org/10.1088/2041-8205/764/2/L24
  5. Tchekhovskoy, A., Narayan, R. & McKinney, J. C. (2011). Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole. Monthly Notices of the Royal Astronomical Society 418, L79. DOI: 10.1111/j.1745-3933.2011.01147.x. https://doi.org/10.1111/j.1745-3933.2011.01147.x
  6. Zamaninasab, M., Clausen-Brown, E., Savolainen, T. & Tchekhovskoy, A. (2014). Dynamically important magnetic fields near accreting supermassive black holes. Nature 510, 126. DOI: 10.1038/nature13399. https://doi.org/10.1038/nature13399
  7. Reynolds, C. S. (2021). Observational Constraints on Black Hole Spin. Annual Review of Astronomy and Astrophysics 59, 117. DOI: 10.1146/annurev-astro-112420-035022. https://doi.org/10.1146/annurev-astro-112420-035022
  8. Blandford, R. D. & Znajek, R. L. (1977). Electromagnetic extraction of energy from Kerr black holes. Monthly Notices of the Royal Astronomical Society 179, 433. DOI: 10.1093/mnras/179.3.433. https://doi.org/10.1093/mnras/179.3.433
  9. Event Horizon Telescope Collaboration (Akiyama, K., et al.) (2021). First M87 Event Horizon Telescope Results. VIII. Magnetic Field Structure near The Event Horizon. The Astrophysical Journal Letters 910, L13. DOI: 10.3847/2041-8213/abe4de, arXiv:2105.01173. https://doi.org/10.3847/2041-8213/abe4de
  10. Wang, A., An, T., Kellermann, K. I., Feng, H., Bempong-Manful, E. K., Timmerman, R. & Guo, S. (2025). A Relativistic Jet in the Radio-quiet Active Galactic Nucleus Mrk 110. The Astrophysical Journal Letters 987, L26. DOI: 10.3847/2041-8213/ade14a, arXiv:2506.03970. https://doi.org/10.3847/2041-8213/ade14a
  11. Wang, A., An, T., Guo, S., Mohan, P., Chamani, W., Baan, W. A., Hovatta, T., Falcke, H., Galvin, T. J., Hurley-Walker, N., Jaiswal, S., Lahteenmaki, A., Lao, B., Lv, W., Tornikoski, M. & Zhang, Y. (2023). Interactions between the Jet and Disk Wind in Nearby Radio-intermediate Quasar III Zw 2. The Astrophysical Journal 944, 187. DOI: 10.3847/1538-4357/acaf02, arXiv:2212.13735. https://doi.org/10.3847/1538-4357/acaf02
  12. Kharb, P., Blackman, E. G., Clausen-Brown, E., Das, M., Schwartz, D. A., Siemiginowska, A., Subramanian, S. & Vaddi, S. (2024). Relativistic Jet Motion in the Radio-quiet LINER Galaxy KISSR 872. The Astrophysical Journal 962, 180. DOI: 10.3847/1538-4357/ad168e, arXiv:2312.11402. https://doi.org/10.3847/1538-4357/ad168e
  13. Shablovinskaia, E., Ricci, C., Paladino, R., Laor, A., Chang, C.-S., Belfiori, D., Kawamuro, T., Lopez-Rodriguez, E., Rosario, D. J., Aalto, S., Koss, M., Mushotzky, R. & Privon, G. C. (2025). ALMA 3 mm polarimetry of radio-quiet active galactic nuclei. Astronomy & Astrophysics 703, A82. DOI: 10.1051/0004-6361/202555796, arXiv:2506.05973. https://doi.org/10.1051/0004-6361/202555796
  14. Xiong, D., Fan, J., Yuan, F., Wang, J.-X., Gu, M., Xue, Y., Mao, J., Chen, L., Xue, R., Fan, X.-L., Chen, Y., Ding, N., Guo, F., Li, J.-W., Yan, D., Zheng, Y. G. & Bai, J. (2026). Jet Power, Bulk Lorentz Factor, Black Hole Spin, and Magnetic Field of Accretion Disk in Jetted Active Galaxies: A Large Gamma-Ray Emission Sample. arXiv:2608.15498. https://arxiv.org/abs/2608.15498
  15. An, T. (2026). Time-domain Radio-loudness of Active Galactic Nuclei: Intermittency, Memory, and Jet Escape. The Astrophysical Journal Letters 1004, L5. DOI: 10.3847/2041-8213/ae6cde, arXiv:2603.21119. https://doi.org/10.3847/2041-8213/ae6cde
  16. Lowell, B., Jacquemin-Ide, J., Liska, M. & Tchekhovskoy, A. (2025). Evidence for low universal equilibrium black hole spin in luminous magnetically arrested disks. Physical Review D 112, 123023. DOI: 10.1103/q956-3wr5, arXiv:2502.17559. https://doi.org/10.1103/q956-3wr5
  17. Wong, G. N. & Stone, J. M. (2026). The SANE, the MAD, and the Chimera. arXiv:2607.07784. https://arxiv.org/abs/2607.07784
  18. Laha, S., Meyer, E. T., Sadaula, D. R., Ghosh, R., Sengupta, D., Masterson, M., Shuvo, O. I., Guainazzi, M., Ricci, C., Begelman, M. C., Philippov, A., Mbarek, R., Hankla, A. M., Kara, E., Panessa, F., Behar, E., Zhang, H., Pacucci, F., Pal, M., Ricci, F., Villani, I., Bisogni, S., La Franca, F., Bianchi, S., Bruni, G., Oates, S., Hahn, C., Nicholl, M., Cenko, S. B., Chattopadhyay, S., Becerra González, J., Acosta-Pulido, J. A., Rakshit, S., Svoboda, J., Gallo, L., Ingram, A. & Kakkad, D. (2025). Multiwavelength Observations of a Jet Launch in Real Time from the Post-changing-look Active Galaxy 1ES 1927+654. The Astrophysical Journal 981, 125. DOI: 10.3847/1538-4357/adaea0, arXiv:2501.02340. https://doi.org/10.3847/1538-4357/adaea0
  19. Zhang, X. A., Ricarte, A., Pesce, D. W., Johnson, M. D., Nagar, N., Narayan, R., Ramakrishnan, V., Doeleman, S. & Palumbo, D. C. M. (2025). Accessing a New Population of Supermassive Black Holes with Extensions to the Event Horizon Telescope. The Astrophysical Journal 985, 41. DOI: 10.3847/1538-4357/adbd45, arXiv:2406.17754. https://doi.org/10.3847/1538-4357/adbd45
  20. Paraschos, G. F., Kim, J.-Y., Wielgus, M., Röder, J., Krichbaum, T. P., Ros, E., et al. (2024). Ordered magnetic fields around the 3C 84 central black hole. Astronomy & Astrophysics 682, L3. DOI: 10.1051/0004-6361/202348308, arXiv:2402.00927. https://doi.org/10.1051/0004-6361/202348308
  21. Ricarte, A., Natarajan, P., Narayan, R. & Palumbo, D. C. M. (2025). Multimessenger Probes of Supermassive Black Hole Spin Evolution. The Astrophysical Journal 980, 136. DOI: 10.3847/1538-4357/ad9ea9, arXiv:2410.07477. https://doi.org/10.3847/1538-4357/ad9ea9