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Outflow from unmagnetized shocked radiative transonic accretion disk around a black hole

Using multidimensional hydrodynamics simulations with radiative cooling, this study demonstrates that an unmagnetized, shocked, geometrically thick accretion disk around a non-rotating supermassive black hole can launch sustained, collimated bipolar outflows reaching thousands of gravitational radii with terminal velocities up to 0.14c, driven solely by hydrodynamic shocks rather than magnetic fields.

Original authors: Arghya Chaudhuri, Apurba Ghosh, Sudip K Garain

Published 2026-03-03

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CC BY 4.0

Original authors: Arghya Chaudhuri, Apurba Ghosh, Sudip K Garain

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 not as a cosmic vacuum cleaner that sucks everything in, but as a massive, spinning whirlpool in the middle of a vast ocean. Usually, we think of black holes as the ultimate trap: once something gets close, it's doomed to fall in forever. But this paper asks a fascinating question: Can some of that falling matter actually fight back and shoot out as a powerful jet, even without any magnetic "ropes" to pull it?

The authors, Arghya Chaudhuri and his team, used a super-computer to simulate this scenario. They wanted to see if a black hole could launch a steady, focused beam of matter (a jet) using only the laws of physics related to spinning and heat, without needing magnetic fields.

Here is the story of their discovery, broken down into simple concepts:

1. The Setup: A Spinning Slide

Imagine you are sliding down a very steep, slippery slide (gravity) toward a giant hole in the ground (the black hole).

The Problem: If you slide straight down, you fall right in.
The Twist: But what if you are spinning as you slide? As you get closer to the center, your spin makes you want to fly outward, like a child on a merry-go-round who feels like they are being thrown off.
The Result: In the simulation, the spinning matter hits a "wall" of its own making. It can't fall in fast enough because its spin is pushing back. This creates a shockwave—a sudden, violent pile-up of matter, much like a traffic jam on a highway where cars suddenly stop and crash into each other.

2. The "Traffic Jam" That Gets Hot

When all this matter piles up at the shockwave (which the scientists call a CENBOL), two things happen:

Compression: The matter gets squished incredibly tight, like a sponge being squeezed.
Heating: Because it's being squished and spinning so fast, it gets incredibly hot. Think of it like rubbing your hands together quickly; they get hot. Here, the "hands" are trillions of tons of gas, so they get millions of degrees hot.

3. The Launch: The Pressure Cooker

Now, imagine this hot, squished pile of gas is sitting in a pressure cooker.

The gravity of the black hole is pulling it down.
But the heat (pressure) and the spin (centrifugal force) are pushing it up and out.
Since the matter is being squeezed from the sides by the incoming flow, the only place it can go is up and down, like steam escaping a kettle.

The simulation showed that this "steam" doesn't just puff out randomly. It forms two powerful, focused beams (jets) shooting out in opposite directions, one up and one down, reaching thousands of times the size of the black hole itself.

4. How Fast Does It Go?

The team tested different amounts of "spin" (angular momentum) for the falling matter:

Low Spin: The matter barely slows down, the shock is weak, and the jet is weak.
Medium Spin: The shock is strong, the gas gets very hot, and the jet shoots out fast.
Too Much Spin: The system gets chaotic. The "traffic jam" becomes turbulent and wobbly, which actually weakens the jet slightly.

The Winner: The sweet spot was a specific amount of spin where the jet reached a top speed of 14% the speed of light. That's about 42,000 kilometers per second!

5. The Light Show

As this super-hot gas flies out, it glows. The scientists calculated what kind of light this would produce.

Because the gas is so hot, it emits high-energy X-rays and gamma rays.
They found that the light is "hard" (very energetic), which matches what astronomers actually see coming from real black holes in the universe.
Interestingly, they found that even without magnetic fields, the heat and spin alone were enough to create these spectacular light shows.

The Big Picture

For a long time, scientists thought you needed magnetic fields to launch these powerful jets from black holes. This paper suggests that you might not.

It's like a fountain. You don't need a pump (magnetic field) if you have enough water pressure (heat) and a spinning mechanism (angular momentum) to push the water up. The black hole acts as the base, the spinning matter creates a shockwave that acts as a pressure cooker, and the resulting heat launches a jet that can travel across the galaxy.

In short: The paper proves that a spinning, hot, shockwave-filled disk of gas around a black hole is powerful enough to launch its own cosmic fireworks, all without needing a magnetic safety net.

1. Problem Statement and Motivation

The formation of bipolar outflows (jets/winds) from black hole accretion systems is a fundamental problem in high-energy astrophysics. While magnetic fields (via Blandford-Znajek or Blandford-Payne mechanisms) are widely accepted as primary drivers for jet launching, the authors investigate whether hydrodynamic forces alone (specifically centrifugal and thermal pressure gradients) can sustain collimated outflows in the absence of magnetic fields.

The study focuses on:

Whether a shocked, sub-Keplerian accretion flow around a non-rotating (Schwarzschild) black hole can launch sustained, collimated outflows reaching thousands of gravitational radii.
The terminal velocities achievable by such outflows.
The relationship between the specific angular momentum of the infalling matter, the strength of the shock, and the resulting outflow properties.
The spectral characteristics (self-Comptonized bremsstrahlung) of these hydrodynamic disk-jet systems.

2. Methodology

The authors employed multidimensional hydrodynamic simulations with radiative cooling to model the accretion flow.

Physical Model:
- Geometry: 2D axisymmetric cylindrical coordinates ( $R, Z$ ).
- Equations: Inviscid hydrodynamics equations (mass, momentum, energy conservation) with a source term for thermal bremsstrahlung cooling.
- Equation of State: Polytropic ( $P = K\rho^\gamma$ ) with adiabatic index $\gamma = 4/3$ .
- Gravity: Pseudo-Newtonian potential (Paczyński-Wiita) to approximate the Schwarzschild black hole metric.
- Radiation: Thermal bremsstrahlung cooling is included in the energy equation. Radiative transfer (self-Comptonization) is calculated via a post-processing Monte Carlo method.
Simulation Setup:
- Domain: Vertically elongated cylinder $[0, 250] \times [-2651, 2651]$ in units of gravitational radii ( $r_g$ ).
- Black Hole Mass: $M_{bh} = 6.5 \times 10^9 M_\odot$ .
- Accretion Rate: $\dot{m} = 0.01 \dot{m}_{Edd}$ .
- Boundary Conditions: Absorbing inner boundary ( $r < 1.8 r_g$ ), inflow at outer radial boundary ( $R=250$ ) with specific angular momentum ( $l$ ) and energy ( $\epsilon$ ), and outflow at vertical boundaries.
- Numerical Scheme: Finite-volume method (second-order accurate) using van-Leer slope limiter, HLL Riemann solver, and Strong-Stability Preserving Runge-Kutta time integration.
Parameter Space: Five simulations (A1–A5) were run with increasing specific angular momentum ( $l = 1.50$ to $1.80$) while keeping specific energy constant ( $\epsilon = 0.001$ ).

3. Key Contributions

Hydrodynamic Jet Launching: Demonstrates that strong centrifugal barriers in unmagnetized, shocked accretion flows can naturally launch sustained, collimated bipolar outflows without requiring magnetic fields.
Shock Dynamics: Detailed characterization of the Centrifugal Pressure-Supported Boundary Layer (CENBOL) and its transition from stationary to turbulent states as angular momentum increases.
Spectral Synthesis: Computed self-Comptonized bremsstrahlung spectra for the disk-jet system, linking hydrodynamic variability to spectral states.
Terminal Velocity Limits: Established the maximum terminal velocity achievable by purely hydrodynamic outflows in this regime ( $\sim 0.14c$ ).

4. Key Results

A. Flow Dynamics and Shock Formation

Shock Formation: As sub-Keplerian matter falls inward, the centrifugal force creates a barrier. For sufficiently high angular momentum, this leads to a standing shock (or oscillating shock) where the flow transitions from supersonic to subsonic.
CENBOL Structure: The post-shock region forms a hot, dense, geometrically thick torus (CENBOL).
- Low $l$ (A1, A2): The shock is weak or absent; the CENBOL is nearly stationary.
- Intermediate $l$ (A3, A4): A well-defined shock forms. The CENBOL exhibits quasi-periodic radial oscillations.
- High $l$ (A5): The centrifugal barrier is so strong that the flow becomes unsteady, exhibiting turbulent vortices and significant temporal variability in the shock position.

B. Outflow Characteristics

Launch Mechanism: Outflows are launched vertically from the post-shock region (CENBOL) due to the combined action of the thermal pressure gradient (created by shock heating) and centrifugal force.
Collimation: The ram pressure of the infalling disk confines the outflow, preventing radial expansion and forcing it into a collimated, bipolar structure along the $Z$ -axis.
Terminal Velocity:
- Outflows accelerate initially and reach a terminal velocity.
- Maximum Velocity: Achieved in run A4 ( $l=1.75$ ) at $0.14c$ .
- Velocity Trend: Velocity increases with $l$ up to A4, then drops for A5 ( $l=1.80$ ) because excessive turbulence and shock dilution reduce the effective compression and pressure gradient.
Mass Outflow Rate: The mass outflow rate increases with angular momentum, reaching a maximum of $\sim 0.04\%$ of the injection rate for the highest $l$ case (A5), confined within a $\sim 5^\circ$ opening angle.

C. Radiative Properties

Luminosity: Bolometric bremsstrahlung luminosity increases with angular momentum due to the larger volume and higher density of the CENBOL.
Variability: Luminosity variability correlates with the dynamical state of the CENBOL (stationary vs. oscillating vs. turbulent).
Spectrum:
- The spectra are dominated by thermal bremsstrahlung with an exponential cutoff.
- Self-Comptonization: Due to low optical depth ( $\tau \approx 0.15$ ), Comptonization is weak (only $\sim 0.25\%$ of seed photons scatter).
- Hard State: The spectra peak at high energies ( $\sim 5000$ keV), corresponding to a "hard" spectral state, consistent with observations of outflow-enhanced states in X-ray binaries and AGNs.
- Pair Production: The radiation density is too low ( $\ell \ll 1$ ) to trigger significant electron-positron pair production, even at MeV energies.

5. Significance and Conclusion

This study provides robust evidence that magnetic fields are not strictly necessary to launch collimated, high-velocity outflows from black hole accretion disks. The authors demonstrate that:

Centrifugal barriers in sub-Keplerian flows can generate the necessary shock compression and thermal pressure to drive matter away from the black hole.
The terminal velocity of such hydrodynamic jets can reach relativistic speeds ( $0.14c$ ), comparable to observed jet velocities in some systems.
The spectral state (hard X-ray) and variability of the system are intrinsically linked to the hydrodynamic stability of the post-shock region.

These findings offer an alternative or complementary mechanism to magnetohydrodynamic (MHD) models, suggesting that purely hydrodynamic processes can explain the existence of jets in systems where magnetic fields might be weak or absent, or where the jet launching is dominated by thermal/centrifugal effects. The results also reinforce the connection between the "hard" spectral state and the presence of outflows in accreting black hole systems.