Magnetically Arrested Accretion Flow

• Magnetically arrested accretion flow is defined by the saturation of large-scale poloidal magnetic flux near black holes, fundamentally altering disk dynamics and jet launching.
• It enables efficient energy extraction via the Blandford–Znajek mechanism, resulting in super-efficient jet production particularly in high-spin systems.
• MAD influences angular momentum transport, disk variability, and multiwavelength observational features in systems like AGNs and X-ray binaries.

A magnetically arrested accretion flow (MAD) is a physical regime of black hole accretion in which the inward transport of large-scale magnetic flux and the accumulation of dynamically significant magnetic field at the event horizon fundamentally alters the structure and evolution of the accretion flow. The MAD state is defined by the saturation of net poloidal magnetic flux near the black hole, which exerts magnetic pressure and tension forces sufficient to impede or regulate further inflow. This process leads to the formation of powerful relativistic jets, modifies angular momentum transport, and can produce observational signatures distinct from standard accretion disk models, especially in low-luminosity active galactic nuclei (AGNs), X-ray binaries, and in the direct vicinity of supermassive black holes.

1. Fundamental Physics of the MAD State

The MAD regime emerges when the accumulated net magnetic flux near the black hole becomes dynamically dominant. This occurs when the magnetic pressure local to the horizon is comparable to or exceeds the ram pressure of infalling matter. The key quantity characterizing this regime is the dimensionless magnetic flux at the black hole:

$$\phi_{\rm BH} \equiv \frac{\Phi_{\rm BH}}{\sqrt{\dot{M} r_g^2 c}},$$

where $\Phi_{\rm BH}$ is the poloidal magnetic flux threading the black hole and $\dot{M}$ is the mass accretion rate. In global GRMHD simulations, MAD states consistently reach $\phi_{\rm BH}$ values between $\sim 40$ and $60$ (Tchekhovskoy et al., 2011), and their qualitative properties are robust across a range of spins and boundary field strengths (Narayan et al., 2021, Zhang et al., 2023).

When accreting material drags in magnetic flux from large radii, if the rate of inward advection exceeds diffusive losses, the flux near the event horizon accumulates until it impedes further inflow—at which point the system reaches magnetic flux saturation. Excess magnetic flux is then expelled outward intermittently via magnetic flux eruptions (interchange and reconnection events), restoring the quasi-steady flux balance in the inner accretion flow.

2. Jet Production and Energy Extraction

The MAD state is ideal for the efficient extraction of energy from the black hole via the Blandford–Znajek (BZ) mechanism, which operates as follows:

$$P_{\rm BZ} = \frac{\kappa}{4\pi c}\ \Omega_{\rm H}^2\, \Phi_{\rm BH}^2\, f(\Omega_{\rm H}),$$

where $\kappa$ is a field geometry constant, $\Omega_{\rm H}$ is the horizon’s angular frequency, and $f(\Omega_{\rm H})$ encodes high-spin corrections (Tchekhovskoy et al., 2011, Narayan et al., 2021). For rapidly spinning black holes ($a \gtrsim 0.9$), the jet efficiency $\eta$ (i.e., the fraction of accretion energy ejected in jets) attains or exceeds 100%, unambiguously demonstrating that rotational energy is tapped from the black hole (Tchekhovskoy et al., 2011). This result correlates directly with observations of jet power in FR I galaxies and AGNs that cannot be explained by rest-mass accretion alone (He et al., 22 Mar 2024).

Relativistic jets in the MAD regime are Poynting-flux dominated and exhibit parabolic or collimated profiles at radii $\lesssim100\,r_g$; their width, collimation, and power depend on both the spin and the saturation value of $\phi_{\rm BH}$ (Narayan et al., 2021, Zhang et al., 2023).

3. Disk Structure, Variability, and Angular Momentum Transport

MAD disks are characterized by:

• Efficient Angular Momentum Removal: Outwards transport is dominated by vertical Maxwell (magnetic) stresses—particularly during flux eruption events (Chatterjee et al., 2022). The dimensionless angular momentum flux carried by the jet exceeds that delivered by accretion for high-spin MADs, explaining both black hole spindown and efficient jet launching (Zhang et al., 2023).
• Saturated Magnetic Flux: The disk’s inner regions—typically dozens of gravitational radii—reach a plasma $\beta \equiv P_{\rm gas}/P_{\rm mag} \lesssim 1$, and the flow is highly sub-Keplerian with $\Omega \simeq 0.4–0.6\,\Omega_K$ (Begelman et al., 2021, Li et al., 27 Nov 2024).
• Flux Eruptions and Variability: Saturated flux episodes are recurrently interrupted by magnetic flux eruptions that drive powerful disk winds and nonaxisymmetric variability (Chatterjee et al., 2022). Following an eruption, the disk can temporarily revert to a SANE-like (Standard And Normal Evolution) state before returning to a MAD configuration.
• Role of MRI and Instabilities: While early models ascribed MAD properties to suppression of the magneto-rotational instability (MRI), detailed turbulence analyses and new stability criteria show that the MRI remains active but modified; the MRI dynamo generates the dominant toroidal field, and interaction with convective/interchange instabilities drives radial transport and vertical flux eruption (Begelman et al., 2021).

4. Observational Signatures and Multiwavelength Phenomenology

MADs exhibit several observationally accessible features:

• Super-Eddington Jet Efficiencies: Jet kinetic powers and radiative outputs can exceed accretion energy input, especially for high-spin systems, as observed in luminous FR I jets and extreme AGNs (Tchekhovskoy et al., 2011, He et al., 22 Mar 2024).
• Spectral Distinction: In hot (two-temperature) MAD accretion flows, the emergent spectrum (synchrotron, bremsstrahlung, and inverse Compton) is generically similar to that of SANE disks, but MADs are systematically brighter at a fixed accretion rate due to enhanced surface density and optical depth (Xie et al., 2019). However, distinguishing MADs from SANEs via spectral shape alone is difficult; additional diagnostics such as multiwavelength light curve timing (as in XRBs (You et al., 2023)), polarization, and spectral index shifts during NIR flares (as in Sgr A* (Grigorian et al., 17 Apr 2024)) are more discriminating.
• Polarimetric Signatures: Resolved linear and circular polarization at mm/sub-mm wavelengths (as observed in M87* and Sgr A*) are sensitive indicators of magnetic field geometry and electron temperature. MAD states produce robust signatures, including persistent handedness in circular polarization and Faraday depolarization (Moscibrodzka et al., 2021).
• Flaring and Variability: MADs naturally explain episodic NIR and X-ray flares as magnetic flux eruptions or reconnection events that generate magnetically dominated “bubbles,” leading to coincident NIR flares and delayed sub-mm size increases, as observed in Sgr A* (Grigorian et al., 17 Apr 2024).
• EUV Deficit: Magnetically arrested inner regions are associated with suppression of local radiative dissipation, yielding an EUV deficit in RLQ spectra (Punsly, 2014).

5. Parameter Dependence and Requirements for the MAD State

MAD formation is regulated by both environmental and accreted flow parameters:

• External Magnetic Field Strength: The accretion flow can only form a MAD if the large-scale magnetic flux advected from outer radii is sufficiently strong. For ADAFs with a boundary plasma $\beta_{\rm out}\gtrsim100$, inward advection cannot establish a MAD; for $\beta_{\rm out}\lesssim100$, an inner MAD region develops (Li et al., 27 Nov 2024).
• Plasma Angular Momentum Content: The maintenance and stability of a MAD and its jets also depend critically on the angular momentum of the accreted plasma (Chan et al., 21 Apr 2025). Extremely low angular momentum flows tend to produce transient MAD phases that are rapidly destroyed by turbulent magnetic bubble expulsion unless sufficient centrifugal support is present to mediate flux accumulation.
• Binary Effects and Circumbinary MADs: In circumbinary environments (BMADs), strong magnetic fields in the cavity can magnetically arrest accretion in a similar manner, leading to periodic flux eruptions, transient flares, and possible enhancement of binary inspiral rates via magnetic angular momentum extraction (Most et al., 1 Aug 2024, Wang et al., 23 Aug 2025).
• Spin Dependence: MAD properties and the associated jet power are steep functions of black hole spin. Prograde high-spin systems reach higher $\phi_{\rm BH}$ and power more energetic jets, while retrograde and nonrotating cases exhibit reduced flux, narrower or weaker jets, and altered turbulent properties (Narayan et al., 2021, Zhang et al., 2023, Xie et al., 2019).

6. Kinetic Phenomena and Particle Acceleration

Recent GRPIC simulations of collisionless MADs demonstrate that flux eruption events, current sheet reconnection, and formation of spark gaps inside the magnetosphere are loci of maximal particle acceleration (Vos et al., 24 Oct 2024). Kelvin–Helmholtz-like instabilities at the jet–disk interface facilitate mixing and further energization. Pair production rates and nonthermal leptonic populations peak in the aftermath of flux eruptions, providing a plasma physics basis for flaring observed in low-luminosity AGNs.

7. Implications, Open Directions, and Connections to Observations

MADs provide a natural explanation for several otherwise puzzling phenomena:

• Jet–accretion connection: High jet powers at low accretion rates, especially in FR I radio galaxies and LLAGNs.
• Multi-timescale variability: Delays between hard X-rays, radio, and optical bands in XRBs as signatures of magnetic field transport and MAD triggering (You et al., 2023).
• Broadband polarization: Polarimetric imaging at event-horizon scales as a diagnostic of magnetic flux distribution and accretion state (Moscibrodzka et al., 2021).
• Circumbinary and multi-accretor systems: Accumulation and eruption cycles in binary environments; implications for black hole mergers and electromagnetic counterparts (Most et al., 1 Aug 2024, Wang et al., 23 Aug 2025).
• Collisionless/kinetic physics: Relationship between magnetospheric pair creation, reconnection, and high-energy emission near black holes (Vos et al., 24 Oct 2024).

Future high-resolution multiwavelength and polarimetric observations, combined with kinetic-scale simulations and improved modeling of magnetic field advection and reconnection, will continue to sharpen the distinction between standard and magnetically arrested accretion flows, enabling robust identification of the MAD regime in both stellar-mass and supermassive black hole systems.