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A universal critical accretion rate for black hole jet formation

This paper demonstrates that tidal disruption events reveal a universal, scale-invariant critical accretion rate of approximately 0.02 $L_{\rm Edd}$ for jet formation, proving that supermassive black holes share the same accretion-outflow coupling mechanisms as stellar-mass black holes.

Original authors: Adelle J. Goodwin, Andrew Mummery

Published 2026-02-17

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CC BY 4.0

Original authors: Adelle J. Goodwin, Andrew Mummery

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a black hole as a cosmic vacuum cleaner. Usually, it just sucks up dust and gas from space. But sometimes, it gets so full that it starts spitting out massive, high-speed jets of energy, like a firehose blasting out of a garden hose.

For decades, astronomers have been puzzled by a big question: Does the size of the vacuum cleaner matter?

Small Black Holes (about the size of a star) are like fast-food restaurants. They eat and spit out jets quickly. We can watch them change their "mood" (accretion state) in real-time. We know exactly when they decide to turn on their jets: it happens when they are eating at a very specific, critical speed.
Supermassive Black Holes (millions of times heavier, sitting in the centers of galaxies) are like slow-cooking stews. They evolve so slowly that a single human lifetime is just a blink of an eye to them. We've never been able to catch one in the act of turning on a jet, so we didn't know if they followed the same rules as the small ones.

The Breakthrough: The "Cosmic Car Crash"

This paper solves the mystery by looking at a special event called a Tidal Disruption Event (TDE).

Think of a TDE as a cosmic car crash. A star wanders too close to a supermassive black hole and gets ripped apart by gravity. This creates a massive, swirling disk of star-stuff falling into the black hole. Because this is a sudden "crash" rather than a slow meal, the black hole's behavior speeds up dramatically. Instead of taking thousands of years to change, it changes in just a few years. It's like fast-forwarding a movie of a slow-cooking stew to see it boil in real-time.

The Two "Switches"

The authors studied 10 of these "crash" events and found something amazing. The black holes didn't just turn on jets randomly. They turned them on at two specific "speed limits" for how fast they were eating:

The "Feast" Switch (Super-Eddington): When the black hole is eating incredibly fast (faster than it theoretically should be able to), it launches a prompt jet almost immediately. This is like a chef getting overwhelmed by a huge order and throwing food out the back door right away.
The "Diet" Switch (Critical Low Rate): As the black hole finishes its meal and slows down, it hits a very specific, low eating speed (about 2% of its maximum capacity). At this exact moment, it flips a second switch and launches a delayed jet. This is like a chef finally calming down, organizing the kitchen, and then firing up a specific, steady espresso machine.

The Big Discovery: Scale Invariance

The most exciting part? The "Diet Switch" happens at the exact same speed for both tiny black holes and giant supermassive ones.

It's like discovering that a Mini Cooper and a massive semi-truck both have a fuel efficiency switch that clicks at exactly 30 miles per hour. No matter how big the engine is, the physics of how they "drive" (launch jets) is identical. The universe has a universal rulebook for black holes.

Why This Matters

Before this, we had two different theories for small and big black holes. Now, we know they are all part of the same family.

Explaining the "Late Bloomers": Some black holes don't shoot jets until years after the star crash. This paper explains why: they were just waiting for their eating speed to drop to that specific "2%" threshold before flipping the switch.
Universal Physics: It proves that the laws of physics governing these extreme objects don't change based on size. A black hole is a black hole, whether it's the size of a mountain or a galaxy.

In a Nutshell

The authors used the "fast-forward" button provided by stellar crashes to watch giant black holes in action. They discovered that these giants follow the exact same "jet-launching rules" as their tiny cousins. Whether the black hole is small or huge, it has two specific "eating speeds" that trigger it to blast energy into space. The universe, it turns out, is surprisingly consistent.

1. Problem Statement

The coupling between black hole accretion flows and the outflows (jets/winds) they launch is a fundamental problem in high-energy astrophysics.

Scale Invariance Hypothesis: It has long been hypothesized that the physics governing accretion-outflow coupling is scale-invariant, meaning the mechanisms in stellar-mass black holes (X-ray Binaries, XRBs) should apply to supermassive black holes (SMBHs) in Active Galactic Nuclei (AGN).
The Observational Gap: In XRBs ( $M_\bullet \sim 10 M_\odot$ ), accretion states and jet launching are well-constrained because these systems evolve on timescales of days to months. In contrast, typical AGN ( $M_\bullet \sim 10^6 - 10^9 M_\odot$ ) evolve over viscous timescales of $10^5$ to $10^6$ years. This makes it impossible to observe a single AGN transition through different accretion states or to pinpoint the exact accretion rate at which jets are launched.
The TDE Opportunity: Tidal Disruption Events (TDEs), where a star is disrupted by an SMBH, create transient accretion disks that evolve on human-observable timescales (years). However, the physical origin of radio outflows in TDEs (prompt vs. delayed) and the specific accretion rates triggering them have remained debated.

2. Methodology

The authors utilized a population of 20 TDEs with multi-wavelength data (optical, UV, X-ray, and radio) to constrain the accretion rate at the precise moment of outflow launch.

A. Sample Selection and Data Processing

Initial Sample: 20 TDEs with well-sampled optical, UV, X-ray, and radio data.
Filtering: Sources were removed if late-time optical/UV data was insufficient to constrain the disk or if early-time X-ray data was missing (preventing early disk constraint).
Final "Gold" Sample: 10 TDEs yielding 11 distinct radio flares (5 prompt, 6 delayed) where both the outflow launch time and the disk accretion rate could be robustly constrained.

B. Radio Modeling (Outflow Launch Time)

Spectral Fitting: Radio spectra were modeled using a synchrotron self-absorption model to determine the peak frequency and flux density.
Equipartition Analysis: Using the equipartition method, the authors derived the minimum radius of the emitting region ( $R_{eq}$ ) as a function of time.
Launch Time Inference: By fitting the expansion of $R_{eq}(t)$ assuming a constant velocity, they extrapolated backward to determine the exact launch time ( $t_{launch}$ ) of the outflow. This method was shown to be robust against variations in geometry (spherical vs. conical) and microphysics assumptions.

C. Disk Modeling (Accretion Rate)

Relativistic Disk Theory: The authors used the FitTeD code, which solves time-dependent relativistic disk equations, to model the multi-band light curves (Optical/UV/X-ray).
Parameter Extraction: This modeling constrained the black hole mass ( $M_\bullet$ ), spin ( $a_\bullet$ ), disk mass, and viscous timescale.
Accretion Rate Calculation: From the disk parameters, the authors calculated the Eddington-normalized mass accretion rate ( $\dot{m} = \dot{M}/\dot{M}_{Edd}$ ) at the specific time $t_{launch}$ inferred from the radio data.

D. Population Synthesis

To test the detection rates and timing, the authors performed a Monte Carlo population synthesis ( $N=10^6$ simulations) using the observed TDE black hole mass function and stellar initial mass function.
They simulated the evolution of accretion rates to determine the fraction of TDEs that reach super-Eddington rates ( $\dot{m} \sim 1$ ) and the time it takes to decay to the critical low rate ( $\dot{m} \sim 0.02$ ).

3. Key Contributions and Results

A. Bimodal Distribution of Accretion Rates
The study reveals a distinct bi-modal distribution of accretion rates at the time of outflow launch:

Prompt Flares: Launched when the accretion rate is super-Eddington, with a posterior average of $\dot{m}_{launch, high} \approx 2.2$ (consistent with $\dot{m} \gtrsim 1$ ).
Delayed Flares: Launched when the accretion rate drops to a critical low threshold, with a posterior average of $\dot{m}_{launch, low} \approx 0.03$ (consistent with $\dot{m} \approx 0.02$ ).

B. Confirmation of Scale Invariance
The critical low accretion rate for jet formation in SMBHs ( $\dot{m} \approx 0.02$ ) is identical to the critical rate observed for state transitions in stellar-mass XRBs. This confirms that the accretion-outflow coupling mechanism is scale-invariant across black hole masses spanning $\sim 7$ orders of magnitude.

C. Physical Mechanisms for TDE Outflows
The results resolve the debate on TDE radio emission mechanisms:

Prompt Outflows: Driven by super-Eddington accretion winds. These rise slowly (power-law index $1-2.5$) consistent with ballistic expansion sweeping up circumnuclear material.
Delayed Outflows: Driven by the formation of a compact, persistent jet as the disk transitions into the "low-hard" state. These rise steeply (power-law index $>4$ ), requiring sustained energy injection consistent with a jet.

D. Corroborating Observational Evidence

X-ray Correlation: TDEs with delayed radio flares show hard X-ray emission (indicative of a corona) appearing coincident with the radio flare, matching the XRB state transition signature.
Population Statistics: The population synthesis predicts that $\sim 42\%$ of TDEs undergo a super-Eddington phase (matching the observed $\sim 30-50\%$ prompt flare rate) and $\sim 42\%$ transition through $\dot{m}=0.02$ within the first 7 years (matching the observed $\sim 40\%$ delayed flare rate).
Null Hypothesis Test: A statistical test assuming random launch times (uncoupled from accretion state) yields a unimodal distribution centered at $\dot{m} \sim 0.15$ , which is statistically distinct from the observed bimodal distribution, confirming the physical coupling.

4. Significance

Unification of Black Hole Physics: This work provides the first rigorous observational evidence that the critical thresholds for jet launching are universal, applying equally to stellar-mass and supermassive black holes.
Solving the TDE Puzzle: It provides a unified physical framework explaining the timing, detection rates, and distinct radio properties (rise indices, energetics) of both prompt and delayed outflows in TDEs.
Future Probes: The study establishes TDEs as unique laboratories for studying SMBH accretion physics on human timescales. As future surveys (e.g., LSST) discover $10^4-10^5$ TDEs, this framework will allow for detailed mapping of jet-launching conditions in SMBHs, potentially revealing new physics in the disk-jet coupling regime.

In summary, Goodwin and Mummery demonstrate that the "rules of the game" for black hole jet formation are the same regardless of the black hole's mass, with the critical trigger being a specific accretion rate threshold ( $\dot{m} \approx 0.02$ ) that has now been observationally confirmed in the supermassive regime.

1. Problem Statement

2. Methodology

3. Key Contributions and Results

4. Significance

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