Published December 26, 2025 | Version Published
Journal Article Open

Universal radial scaling of large-scale black hole accretion for magnetically arrested and rocking accretion disks

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon Canadian Institute for Theoretical Astrophysics
  • 3. ROR icon Northwestern University
  • 4. NSF-Simons AI Institute for the Sky
  • 5. ROR icon University of Toronto
  • 6. ROR icon Perimeter Institute
  • 7. ROR icon University of Maryland, College Park
  • 8. ROR icon Georgia Tech Research Institute

Abstract

Accretion onto supermassive black holes (BHs) can launch relativistic outflows and jets that inject energy and momentum into their surroundings. Understanding how such feedback shapes large-scale accretion is key to bridging observations from galactic scales (e.g., the Bondi radius, π‘ŸB) down to event horizon scales (π‘Ÿg), spanning five to six orders of magnitude. To address this challenge directly, we treat the spatial scale separation as a free parameter, varying it across two to four orders of magnitude. We perform a suite of the longest contiguous 3D general relativistic magnetohydrodynamic simulations to date (𝑑≤4×10βΆπ‘Ÿg/𝑐), modeling Bondi-like accretion of rotating, nonrelativistic gas with weak vertical magnetic fields onto a rapidly spinning BH, achieving inflow equilibrium out to π‘Ÿβ‰³10³β’π‘Ÿg. We find that, regardless of scale separation or ambient gas rotation, all simulations reach a magnetically arrested disk (MAD) state in which the BH becomes magnetically saturated. In this state, the mass inflow rate follows a universal radial scaling relative to the Bondi rate: ˙𝑀in⁑(π‘Ÿ)/˙𝑀B ∼(π‘Ÿ/π‘ŸB)𝑠 with 𝑠 =0.66 ±0.03. The MAD state self-regulates through jets, outflows, and magnetic flux eruptions that can ultimately disrupt coherent angular momentum inflow, giving rise to a rocking accretion disk (RAD) state. This RAD state features chaotically oriented inflows, weak intermittent jets, and a steeper inflow slope of 𝑠 =0.87 ±0.05, along with significantly weaker outflows. For rapidly spinning BHs, the MAD and RAD BH accretion rates become comparable at typical scale separations, π‘ŸB/π‘Ÿg ≳10⁡. The weaker outflows in the RAD state allow large-scale inflows to resume, eventually restoring the MAD state and enabling a repeating MAD-RAD cycle. We find that the MAD-RAD timescales can last from a few to hundreds of Bondi timescales, 𝑑B ∼0.2  Myr ×(π‘ŸB/10β΅β’π‘Ÿg^(3/2) ×(𝑀BH/10βΉπ‘€βŠ™), where 𝑀BH is the BH mass, potentially setting the duty cycle of jetted active galactic nucleus outbursts, like M87*.

Copyright and License

© 2025 American Physical Society.

Acknowledgement

We thank Martijn Oei, Ioannis Liodakis, Anthony Readhead, and Eliot Quataert for helpful discussions. A. T. was supported by NSF Grants No. AST-2009884, No. AST-2107839, No. AST-1815304, No. AST-1911080, No. AST-2206471, No. AST-2407475, and No. OAC-2031997, and by NASA Grants No. 80NSSC22K0031, No. 80NSSC22K0799, No. 80NSSC18K0565, and No. 80NSSC21K1746. Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award No. TM1-22005X issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under Contract No. NAS8-03060. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC and visualization resources that have contributed to the research results reported within this paper via the LRAC allocation AST20011 [75]. This research used resources from the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract No. DE-AC05-00OR22725. An award of computer time was provided by the ASCR Leadership Computing Challenge (ALCC), Innovative and Novel Computational Impact on Theory and Experiment (INCITE), and the OLCF Director’s Discretionary Allocation programs under award PHY129. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 using NERSC award ALCC-ERCAP0022634. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231 using NERSC ERCAP Award No. m2401 for 2022–2025. E. R. M. acknowledges support through the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725, and the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, and NERSC Award No. NP-ERCAP0028480. B. R. acknowledges support by the Natural Sciences & Engineering Research Council of Canada (NSERC), the Canadian Space Agency (23JWGO2A01), and by a grant from the Simons Foundation (Grant No. MP-SCMPS-00001470). B. R. acknowledges a guest researcher position at the Flatiron Institute, supported by the Simons Foundation.

Data Availability

The data that support the findings of this article are not publicly available. The data are available from the authors upon reasonable request.

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Additional details

Related works

Is new version of
Discussion Paper: arXiv:2505.23888 (arXiv)

Funding

National Science Foundation
AST-2009884
National Science Foundation
AST-2107839
National Science Foundation
AST-1815304
National Science Foundation
AST-1911080
National Science Foundation
AST-2206471
National Science Foundation
AST-2407475
National Science Foundation
OAC-2031997
National Aeronautics and Space Administration
80NSSC22K0031
National Aeronautics and Space Administration
80NSSC22K0799
National Aeronautics and Space Administration
80NSSC18K0565
National Aeronautics and Space Administration
80NSSC21K1746
National Aeronautics and Space Administration
TM1-22005X
National Aeronautics and Space Administration
NAS8-03060
Smithsonian Astrophysical Observatory
United States Department of Energy
DE-AC05-00OR22725
United States Department of Energy
DE-AC02-05CH11231
United States Department of Energy
DE-AC02-05CH11231
National Energy Research Scientific Computing Center
ALCC-ERCAP0022634
National Energy Research Scientific Computing Center
m2401
National Energy Research Scientific Computing Center
NP-ERCAP0028480
Lawrence Berkeley National Laboratory
DE-AC02-05CH11231
Oak Ridge National Laboratory
Natural Sciences and Engineering Research Council
Canadian Space Agency
23JWGO2A01
Simons Foundation
MP-SCMPS-00001470

Dates

Submitted
2025-07-10
Accepted
2025-12-02

Caltech Custom Metadata

Caltech groups
Astronomy Department, TAPIR, Walter Burke Institute for Theoretical Physics, Division of Physics, Mathematics and Astronomy (PMA)
Publication Status
Published