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Hydrodynamical simulation of wind production from hot accretion flows in tidal disruption events

This hydrodynamical study reveals that in tidal disruption events, more massive black holes launch faster, mildly-relativistic equatorial winds from hot accretion flows, whereas lower viscosity leads to bound convective outflows, offering potential explanations for delayed radio brightening and intermediate-mass black hole detection.

Original authors: Mingjun Liu, De-Fu Bu, Xiao-Hong Yang, Jiaqi Li, Huaqing Cheng, Qinyu Wu, Wenjie Zhang, B. F. Liu

Published 2026-05-12

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CC BY 4.0

Original authors: Mingjun Liu, De-Fu Bu, Xiao-Hong Yang, Jiaqi Li, Huaqing Cheng, Qinyu Wu, Wenjie Zhang, B. F. Liu

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 cosmic drama where a star wanders too close to a supermassive black hole and gets ripped apart. This event is called a Tidal Disruption Event (TDE). Think of the star as a giant ball of dough and the black hole as a hungry giant. When the dough gets too close, the giant's gravity stretches it into a long noodle and then shreds it.

Usually, scientists focus on the messy, chaotic moment when the black hole is eating the star at a frantic pace. But this paper asks a different question: What happens after the feast slows down?

Once the black hole has eaten the easy-to-reach bits, it settles into a "sub-Eddington" phase. This is like the black hole going on a diet, eating slowly and steadily. The paper investigates the "wind" or gas that blows away from this slow-feeding black hole.

Here is what the researchers found, explained through simple analogies:

1. The Size of the Black Hole Matters

The team simulated black holes of different sizes (some with a million times the mass of our Sun, others with ten million).

The Analogy: Imagine two whirlpools. One is small and shallow; the other is massive and deep.
The Finding: The bigger the black hole, the deeper its "gravity well" (the whirlpool). Because the gravity is so strong, it holds onto more of the shredded star. However, the little bit of gas that does manage to escape has to run much faster to get away. So, massive black holes launch faster, more energetic winds, but they actually swallow a larger percentage of the star's debris.

2. The "Stickiness" of the Gas (Viscosity)

The most important discovery in the paper is about how "sticky" or turbulent the gas is as it swirls around the black hole. In physics, this is called the viscosity parameter (represented by the Greek letter alpha, $\alpha$ ).

The Analogy: Think of the gas swirling around the black hole like traffic on a highway.
- High Viscosity ( $\alpha = 0.1$ ): This is like a highway where cars are constantly changing lanes and pushing each other forward efficiently. This "traffic jam" pushes the gas outward so hard that it breaks free from the black hole's gravity entirely. These are true winds that fly off into space at about 10% the speed of light.
- Low Viscosity ( $\alpha = 0.01$ ): This is like a highway where cars are stuck in a slow, swirling circle. They move up and down (convection) but don't actually escape. The gas just bounces around in a loop, held back by gravity. These are bound outflows, not true winds.

3. The Temperature Doesn't Matter Much

The researchers tested if the temperature of the shredded star (whether it was injected as hot gas or cooler gas) changed the outcome.

The Finding: It didn't matter.
The Analogy: Imagine dropping a hot potato and a cold potato into a giant blender. The heat of the potato is negligible compared to the sheer power of the blender. Similarly, the energy released by the black hole's gravity completely overwhelms the initial temperature of the star's debris.

4. Why This Matters for Real Observations

The paper connects these simulations to things astronomers actually see in the sky:

The "Late Radio Glow": Sometimes, after a TDE, astronomers see a radio signal that gets brighter years later (around 1,000 days). The paper suggests this is caused by the "High Viscosity" winds (the fast, escaping ones) hitting the gas around the galaxy, creating a shockwave that glows in radio waves.
Finding Hidden Black Holes: The paper suggests that if we look at small galaxies or star clusters with radio and X-ray telescopes, we might find "Intermediate-Mass Black Holes" (black holes that are in the middle size range). These black holes might be slowly eating stars and creating these long-lasting, low-level winds that we can detect.

Summary

In short, this paper uses computer simulations to show that when a black hole eats a star slowly, it doesn't just sit there. It blows wind.

If the gas is "sticky" enough (high viscosity), it blows fast, powerful winds that can be seen from Earth.
If the gas is "slippery" (low viscosity), the gas just swirls in circles and stays trapped.
The size of the black hole changes how fast the wind blows, but the temperature of the star doesn't change the outcome.

This helps astronomers understand why some black holes seem to have strong winds and others don't, and gives them a new tool to hunt for hidden black holes in the universe.

Technical Summary: Hydrodynamical Simulation of Wind Production from Hot Accretion Flows in Tidal Disruption Events

Problem Statement
While winds from super-Eddington accretion phases in Tidal Disruption Events (TDEs) are well-studied, the properties of winds from the subsequent, long-lasting sub-Eddington phase remain underexplored. In this late stage, the accretion flow transitions from a standard thin disk to a hot accretion flow (e.g., Advection-Dominated Accretion Flow, ADAF). Although winds from hot accretion flows in Active Galactic Nuclei (AGN) and X-ray binaries (XRBs) have been extensively modeled, TDEs present a distinct physical scenario: stellar debris is injected directly into the immediate vicinity of the black hole, forming a transient, compact flow rather than a steady supply from large radii. This paper investigates the formation and properties of winds in this specific sub-Eddington TDE regime, focusing on how black hole mass, viscosity ( $\alpha$ ), and stellar debris temperature influence outflow dynamics.

Methodology
The authors performed two-dimensional axisymmetric hydrodynamic simulations using the ZEUS-MP code in spherical coordinates. The simulations modeled the evolution of hot accretion flows following the disruption of a solar-type star ( $M_* = M_\odot, R_* = R_\odot$ ) by supermassive black holes (SMBHs) of $10^6 M_\odot$ and $10^7 M_\odot$ .

Initial Conditions: The study focused on the late-time phase (decades to centuries post-disruption) where the accretion rate has declined to $\sim 0.01 \dot{M}_{\text{Edd}}$ . Stellar debris was injected at the circularization radius ( $R_c = 2R_t$ ) with a fallback rate following the standard $t^{-5/3}$ decay.
Parameter Space: Eight models were run varying three key parameters:
1. Black Hole Mass ( $M_{\text{BH}}$ ): $10^6 M_\odot$ and $10^7 M_\odot$ .
2. Viscosity Parameter ( $\alpha$ ): $0.01$ and $0.1$.
3. Debris Injection Temperature ( $T_{\text{inj}}$ ): $1 \times 10^4$ K (adiabatic evolution) and $2 \times 10^7$ K (isothermal/hydrostatic equilibrium).
Analysis: The authors defined inflow, outflow, and net accretion rates, distinguishing between "true" unbound winds (Bernoulli parameter $B_e > 0$ ) and bound convective outflows ( $B_e < 0$ ). They analyzed time-averaged radial and angular profiles of velocity, mass flux, momentum flux, and kinetic energy.

Key Results

Quasi-Steady State: The accretion flows rapidly evolve to a quasi-steady state within a few viscous timescales, validating the use of quasi-steady approximations for modeling sub-Eddington TDEs.
Influence of Black Hole Mass: More massive black holes ( $10^7 M_\odot$ ) result in a higher fraction of accreted mass and launch faster winds. This is because debris is injected at a smaller radius scaled by the Schwarzschild radius ( $R_c/R_S$ ), making the gas more tightly bound; escaping gas must therefore achieve higher velocities to overcome the deeper potential well.
Influence of Viscosity ( $\alpha$ ):
- $\alpha = 0.1$ : Efficient angular momentum transfer launches unbound, mildly-relativistic winds ( $\sim 0.1c$ ). These winds are predominantly launched from the equatorial plane outside the injection region. The kinetic energy of these winds is approximately $\sim 10^{-4} L_{\text{Edd}}$ .
- $\alpha = 0.01$ : Inefficient angular momentum transfer leads to convectively bound outflows. The gas exhibits vortex structures and negative Bernoulli parameters, meaning it does not escape to infinity but rather circulates within the flow. This contrasts with typical AGN/XRB hot flows at similar $\alpha$ , which often exhibit unbound winds (ADIOS scenario). The authors attribute this difference to the unique TDE initial conditions: cold debris injected deep into the potential well with low initial Bernoulli parameters.
Influence of Temperature: The initial temperature of the stellar debris ( $10^4$ K vs. $10^7$ K) has a negligible effect on the accretion flow structure, as the gravitational energy released during accretion dominates the initial internal energy of the gas.
Wind Geometry: For $\alpha = 0.1$ , unbound winds are launched over a wide angular range (exceeding $40^\circ$ from the pole for $10^6 M_\odot$ ), carrying more mass, momentum, and energy at edge-on (equatorial) angles compared to polar angles.

Significance and Applications
The paper claims that these findings offer a mechanism to explain specific observational features of TDEs and provide a new method for constraining physical parameters:

Delayed Radio Brightening: The kinetic energy of the unbound winds ( $\sim 10^{-4} L_{\text{Edd}}$ ) for $\alpha \approx 0.1$ is sufficient to power the delayed radio brightening observed in TDEs like ASASSN-14ae, AT2018fyk, and AT2019teq at $\sim 10^3$ days post-disruption. This suggests that the viscosity parameter in these specific TDEs likely lies in the range $0.01 < \alpha < 0.1$ .
Intermediate-Mass Black Hole (IMBH) Detection: The simulations suggest that TDEs involving IMBHs ( $10^4 - 10^5 M_\odot$ ) produce extremely low accreted fractions and readily form winds. The authors propose that radio and X-ray surveys of globular clusters and dwarf galaxies could detect these persistent, low-level activities, offering a promising avenue for discovering IMBHs.
Viscosity Constraints: The distinct difference in outflow structure between TDEs and AGN/XRBs at low $\alpha$ (bound vs. unbound) provides a new diagnostic tool to constrain the viscosity parameter in TDEs through late-stage wind observations.

The authors conclude that while the magnetic field origin of viscosity remains an open question, the hydrodynamic behavior of TDE winds offers a distinct signature of the accretion physics in these transient events, differing fundamentally from steady-state AGN accretion due to the initial injection conditions of the stellar debris.

1. The Size of the Black Hole Matters

2. The "Stickiness" of the Gas (Viscosity)

3. The Temperature Doesn't Matter Much

4. Why This Matters for Real Observations

Summary

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