Standard and Normal Evolution (SANE)

• SANE is defined as the weak-flux, MRI-turbulent accretion state where the magnetic flux remains low, allowing a quasi-steady, matter-dominated disk.
• Simulations initialize SANE flows with varied poloidal magnetic configurations, resulting in gas-pressure–dominated dynamics that contrast with magnetically arrested (MAD) disks.
• Observational and radiative studies indicate that SANE states exhibit moderate spectral features and stochastic flaring driven by turbulent disk behavior.

Standard and Normal Evolution (SANE) denotes the weak-flux, non-arrested branch of black-hole accretion in which the magnetic flux threading the horizon remains modest, the dense inner flow stays matter dominated, and accretion proceeds as a turbulent, quasi-steady disk rather than as a magnetically choked inner flow. In current GRMHD and GRRMHD usage, SANE is defined in opposition to the magnetically arrested disk (MAD) state: SANE disks are MRI-driven and magnetized, but they do not accumulate enough coherent large-scale magnetic flux to make magnetic pressure and tension the leading regulators of the inflow (Wong et al., 8 Jul 2026, Aktar et al., 2024).

1. Definition and state variables

The modern definition of SANE is operational rather than purely descriptive. In non-radiative GRMHD, the primary discriminator is the dimensionless horizon magnetic flux,

$$\phi_{\rm BH} \equiv \frac{\Phi_{\rm BH}}{\sqrt{|\dot M|}}, \qquad \Phi_{\rm BH}=\frac{1}{2}\int_0^{2\pi}\int_0^\pi |B^r|\sqrt{-g}\,d\theta\,d\phi,$$

with SANE identified by low $\phi_{\rm BH}$ and MAD by saturation at large $\phi_{\rm BH}$. In one three-dimensional comparison, a “standard quantitative hallmark” of MAD is $\phi_{\rm BH}\sim 15$, while SANE remains in the low-flux regime; in that same framework, SANE is a turbulent, quasi-steady, matter-dominated disk (Wong et al., 8 Jul 2026). Magnetization is usually expressed as

$\sigma \equiv \frac{b^2}{\rho},$

or, in some radiative work,

$\sigma_{\rm M}=\frac{B^2}{\rho},$

and SANE corresponds to low $\sigma$ in the dense flow and near the horizon.

Different simulation programs use different normalizations and thresholds. In one three-state sequence, the classification is explicitly SANE: $\phi_{\rm BH}<20$, INT: $20 \lesssim \phi_{\rm BH} \lesssim 50$, MAD: $\phi_{\rm BH}\gtrsim 50$ (Raha et al., 17 May 2026). In a dynamo-and-jet study, standard SANE disks typically have $\phi_{\rm BH}$0 and a corresponding MAD parameter well below the MAD threshold $\phi_{\rm BH}$1 (Santhiya et al., 1 Dec 2025). In a radiative RMHD study of spinning AGN accretion, SANE is instead defined by initial plasma-$\phi_{\rm BH}$2 choices $\phi_{\rm BH}$3 and $\phi_{\rm BH}$4, with the normalized magnetic flux staying below the MAD threshold $\phi_{\rm BH}$5 (Aktar et al., 2024).

Study	Primary diagnostic	SANE condition
(Wong et al., 8 Jul 2026)	$\phi_{\rm BH}$6	low horizon flux; below MAD saturation
(Raha et al., 17 May 2026)	$\phi_{\rm BH}$7	$\phi_{\rm BH}$8
(Santhiya et al., 1 Dec 2025)	$\phi_{\rm BH}$9 and MAD parameter	$\phi_{\rm BH}$0; below MAD threshold
(Aktar et al., 2024)	$\phi_{\rm BH}$1 and $\phi_{\rm BH}$2	$\phi_{\rm BH}$3 and $\phi_{\rm BH}$4

A recurrent misconception is that SANE is equivalent to “non-magnetic.” The simulations do not support that usage. SANE disks can retain ordered horizon-threading flux, sustain MRI turbulence, and launch jets or outflows; the defining point is that the flux is insufficient to arrest the accretion flow (Santhiya et al., 1 Dec 2025, Curd et al., 2022).

2. Numerical realization and initial conditions

Canonical SANE simulations usually start from a magnetized equilibrium torus, but the magnetic topology and its coherence vary by study. A conventional SANE initialization uses a single large-scale poloidal loop generated by a density-tied vector potential such as

$\phi_{\rm BH}$5

so that the subsequent horizon flux is largely set by inward advection of the imposed large-scale field (Santhiya et al., 1 Dec 2025). A related weak-flux prescription in another BHAC study is

$\phi_{\rm BH}$6

contrasted there with a MAD initialization explicitly designed to concentrate coherent large-scale flux near the hole (Pathak et al., 10 Jun 2026).

A notable radiative AGN result is that SANE need not require a separate torus geometry. In the spinning-AGN Rad-RMHD comparison, the same equilibrium torus and the same field prescription,

$\phi_{\rm BH}$7

are used for both SANE and MAD; only the initial field strength is changed through the plasma beta parameter $\phi_{\rm BH}$8, with larger $\phi_{\rm BH}$9 corresponding to weaker initial magnetization. In that setup, $\phi_{\rm BH}\sim 15$0 and $\phi_{\rm BH}\sim 15$1 remain SANE, whereas $\phi_{\rm BH}\sim 15$2 and $\phi_{\rm BH}\sim 15$3 evolve into MAD (Aktar et al., 2024).

The literature also contains multi-loop SANE realizations. For Sgr A* flare modeling, a SANE disk with several poloidal loops of alternating polarity is initialized through

$\phi_{\rm BH}\sim 15$4

with the alternating-loop topology deliberately creating polarity reversals, current sheets, and reconnection sites (Dimitropoulos et al., 2024). By contrast, “sub-SANE” models with multiple same-polarity small-scale loops are used to erase magnetic memory rapidly and expose MRI-driven dynamo action; these begin in an even weaker-flux regime than standard SANE (Santhiya et al., 1 Dec 2025).

SANE-like behavior can also be generated without an initially favorable poloidal seed field. In an axisymmetric mean-field dynamo study, the initial field is purely toroidal, $\phi_{\rm BH}\sim 15$5, with maximum initial magnetization $\phi_{\rm BH}\sim 15$6. Intermediate dynamo strengths reproduce the principal SANE diagnostics of thick-disk accretion, including low normalized flux and SANE-like accretion and luminosity proxies (Tomei et al., 2021).

3. Dynamical structure and force balance

The characteristic SANE morphology is smoother than MAD and less strongly reorganized by magnetic support. In three-dimensional non-radiative comparisons, SANE is described as a thick, matter-dominated disk with comparatively smooth midplane morphology, turbulent spiral structure rather than large evacuated cavities, large plasma $\phi_{\rm BH}\sim 15$7, low magnetization, near-Keplerian rotation, and broad inward mass-flux channels that can peak away from the equatorial plane near the disk/funnel interface (Wong et al., 8 Jul 2026). Angular-momentum transport is more disk-body confined, with substantial matter and fluctuating contributions, rather than being dominated by magnetized surface layers and funnel-wall stresses.

A central dynamical result is that SANE is primarily hydrodynamically supported. The radial force balance is written as

$\phi_{\rm BH}\sim 15$8

with gas-pressure, magnetic-pressure, and magnetic-tension contributions treated separately. In SANE, the gas-pressure gradient is the dominant source of radial support, while magnetic pressure and magnetic tension are present only as smaller corrections. In MAD, by contrast, magnetic pressure and tension enter the radial force budget at comparable order to the gas-pressure term (Wong et al., 8 Jul 2026). This distinction is one of the clearest dynamical separators between the two regimes.

Radiative RMHD calculations around spinning AGN recover the same qualitative picture. There, SANE remains the weak-field, non-arrested branch: $\phi_{\rm BH}\sim 15$9 stays low, especially near the horizon and funnel, the torus evolves more slowly, the hot rarefied atmosphere outside the torus is not fully swept away, and vertical motions remain weak, with $\sigma \equiv \frac{b^2}{\rho},$0. In the corresponding MAD runs, $\sigma \equiv \frac{b^2}{\rho},$1, radiation energy density is higher, and the funnel outflow becomes strongly relativistic (Aktar et al., 2024).

Quantified state properties from a three-state GRMHD sequence further specify the regime: SANE has $\sigma \equiv \frac{b^2}{\rho},$2, plasma-$\sigma \equiv \frac{b^2}{\rho},$3, $\sigma \equiv \frac{b^2}{\rho},$4, $\sigma \equiv \frac{b^2}{\rho},$5, $\sigma \equiv \frac{b^2}{\rho},$6, and jet efficiency $\sigma \equiv \frac{b^2}{\rho},$7. Its variability is driven mainly by stochastic MRI turbulence rather than by flux-eruption cycles (Raha et al., 17 May 2026).

4. Radiative output, spectra, and timing

The radiative phenomenology of SANE is not described uniformly across the literature. In a dense-torus, two-temperature Rad-RMHD model of spinning AGN accretion, the total luminosity is dominated by bremsstrahlung rather than synchrotron, with

$\sigma \equiv \frac{b^2}{\rho},$8

and bremsstrahlung and radiative luminosities reaching values around $\sigma \equiv \frac{b^2}{\rho},$9 at late times. In that setup, SANE and MAD show no dramatic separation in total luminosity because the dense torus makes the bremsstrahlung output similar across magnetic states. The same study finds the same fundamental QPO peak for both SANE and MAD,

$\sigma_{\rm M}=\frac{B^2}{\rho},$0

corresponding to a period of roughly 8 days, and the broadband spectrum has the same two-hump structure in both states, with synchrotron near $\sigma_{\rm M}=\frac{B^2}{\rho},$1 and bremsstrahlung near $\sigma_{\rm M}=\frac{B^2}{\rho},$2 (Aktar et al., 2024).

A height-integrated hot-flow treatment reaches a similar conclusion at the level of spectral degeneracy: MAD spectra are generally very similar to SANE spectra, even though MAD is systematically brighter at fixed accretion rate and can have X-ray luminosities larger by a factor of about $\sigma_{\rm M}=\frac{B^2}{\rho},$3. In that framework, the maximum luminosity reachable by the hot MAD branch is comparable to, but slightly lower than, SANE because the critical accretion rate is lower in MAD (Xie et al., 2019).

Other calculations instead report much stronger spectral separation. A BHAC-based spectral post-processing study finds that MAD magnetic field strength is about an order of magnitude larger than SANE, that MAD bolometric luminosity is about three orders of magnitude higher than SANE for both spins considered, and that the emission peaks shift markedly: in SANE the synchrotron peak is around $\sigma_{\rm M}=\frac{B^2}{\rho},$4 and the SSC peak around $\sigma_{\rm M}=\frac{B^2}{\rho},$5, whereas MAD peaks are stronger and harder. In that study the synchrotron-to-SSC luminosity ratio is drastically different, with SANE giving $\sigma_{\rm M}=\frac{B^2}{\rho},$6 at $\sigma_{\rm M}=\frac{B^2}{\rho},$7 and $\sigma_{\rm M}=\frac{B^2}{\rho},$8 at $\sigma_{\rm M}=\frac{B^2}{\rho},$9 (Pathak et al., 10 Jun 2026).

A plausible implication is that spectral distinguishability is model dependent rather than universal. The outcome depends on whether the radiative budget is dominated by density-sensitive bremsstrahlung, as in dense radiative tori, or by synchrotron and Comptonization, which respond more strongly to magnetic topology and near-horizon compression (Aktar et al., 2024, Pathak et al., 10 Jun 2026).

5. Observational interpretations

The observational status of SANE is source dependent. For M87, a direct RM comparison strongly disfavors SANE. Using 3D GRMHD models plus extrapolation to jet scales of roughly $\sigma$0 to $\sigma$1, the predicted rotation measures from MAD agree with the observed negative RM values along the jet, whereas the SANE model overestimates the RM by over two orders of magnitude and is therefore ruled out in that analysis (Yuan et al., 2022).

For Sgr A*, SANE has been adopted for the opposite reason: the absence of a clearly established steady jet makes a non-jet-dominated SANE baseline attractive. A 2D BHAC multi-loop SANE model, lacking a stable jet structure, identifies current sheets and plasmoid chains at magnetic polarity reversals and produces 2.2 $\sigma$2m light curves with several flares above 1.5 mJy, one particularly strong flare near 7 mJy, flare durations in the 40–60 minute range, and bright-state spectral indices $\sigma$3 and $\sigma$4. In that interpretation, the dominant NIR flare emission arises from current-sheet plasmoid chains and the turbulent disk/funnel boundary rather than from a persistent jet base (Dimitropoulos et al., 2024).

SANE is also relevant in super-Eddington transients. In KORAL-based GRRMHD models of TDE disks around $\sigma$5 SMBHs, both analyzed cases are super-Eddington SANE flows, with $\sigma$6 and $\sigma$7 for $\sigma$8, and $\sigma$9 and $\phi_{\rm BH}<20$0 for $\phi_{\rm BH}<20$1. Synthetic ngEHT observations indicate that jets launched by a rapidly spinning SANE super-Eddington disk can reach the ngEHT detection threshold out to 100 Mpc in favorable cases, whereas limiting cases such as $\phi_{\rm BH}<20$2 or $\phi_{\rm BH}<20$3 are detectable only to about 10 Mpc; the maximum reconstructed apparent speed reported is about $\phi_{\rm BH}<20$4 (Curd et al., 2022).

Timing-based source classification has also been attempted. One GRMHD variability study maps the least hard and more thermal-disk-dominated GRS 1915+105 classes to SANE, while a nonlinear time-series analysis identifies a SANE-like cluster with stronger diskbb contribution and lower mean Higuchi fractal dimension than the MAD-like cluster (Raha et al., 17 May 2026, Aggarwal et al., 17 Apr 2026).

6. Variants, intermediate states, and limits of classification

Recent work has complicated any simple binary opposition between SANE and MAD. A three-state sequence introduces an intermediate INT regime, with SANE at $\phi_{\rm BH}<20$5, INT at $\phi_{\rm BH}<20$6, and MAD at $\phi_{\rm BH}<20$7, emphasizing a continuous magnetic-flux sequence rather than a purely dichotomous taxonomy (Raha et al., 17 May 2026). A separate “Chimera” flow reaches MAD-level horizon flux and powerful electromagnetic jets without reproducing the standard MAD’s bursty horizon-flux variability, radial-force structure, or eruptive inner morphology. That result leads to the explicit claim that MAD-like behavior is not captured by any single diagnostic but by a dynamical coupling among horizon flux, jet power, magnetic support, Maxwell transport, surface-layer flow, disk morphology, and eruption activity (Wong et al., 8 Jul 2026).

Within the weak-flux end itself, standard SANE is not the only variant. “Sub-SANE” simulations start from multiple same-polarity small-scale loops, erase magnetic memory rapidly through reconnection, and develop regular dynamo cycles with periods of about ten orbits. Those runs can launch early jets, but the jets shut down when the horizon-field coherence parameter

$\phi_{\rm BH}<20$8

falls below $\phi_{\rm BH}<20$9, whereas the SANE reference run retains $20 \lesssim \phi_{\rm BH} \lesssim 50$0 and maintains its jet (Santhiya et al., 1 Dec 2025).

Advanced diagnostics increasingly differentiate SANE and MAD statistically rather than by a single threshold. Nonlinear time-series analysis finds that SANE generally has lower Higuchi fractal dimension, higher Hurst index, and steeper power-spectral slopes than MAD across most spins, consistent with more persistent and less eruptive variability (Aggarwal et al., 17 Apr 2026). A density-fluctuation study using Taylor’s frozen-in hypothesis likewise reports broken power-law spatial spectra in SANE, with a steeper low-frequency slope than MAD and a high-frequency slope tending toward $20 \lesssim \phi_{\rm BH} \lesssim 50$1; in that framework, SANE is specifically the regime where the bulk velocity exceeds the Alfvén speed and therefore sets the temporal-to-spatial mapping (Hallur et al., 10 Oct 2025).

The composite picture is therefore narrow in one sense and broad in another. SANE remains the standard name for the weak-flux, non-arrested, MRI-turbulent branch of black-hole accretion, but recent simulations show that neither jet production, nor spectral hardness, nor any single horizon-flux number by itself exhausts the physical content of the state (Wong et al., 8 Jul 2026, Santhiya et al., 1 Dec 2025).