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Three-dimensional GRMHD simulations of jet formation and propagation in self-gravitating collapsing stars

This study presents the first three-dimensional GRMHD simulations of collapsars with self-gravity and demonstrates that self-gravity significantly alters jet properties by causing a temporary suppression, generating narrower opening angles, and potentially leading to failed outbursts, thereby offering a new explanation for specific features of the prompt emission of gamma-ray bursts.

Original authors: Piotr Płonka, Agnieszka Janiuk

Published 2026-05-06

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CC BY 4.0

Original authors: Piotr Płonka, Agnieszka Janiuk

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 massive star, far larger than our Sun, reaching the end of its life. Instead of fading away quietly, it collapses inward under its own weight, crushing itself to form a black hole. Often, this violent event does not just create a black hole; it fires two powerful beams of energy in opposite directions, like a cosmic fire hose. These are the "jets" that produce gamma-ray bursts (GRBs), the brightest explosions in the universe.

For decades, scientists have tried to simulate these events on computers to understand how the jets form. However, most simulations made a simplifying assumption: they treated the outer layers of the collapsing star as merely "falling matter" that does not truly attract each other. They ignored the star's own gravity.

This work by Piotr Płonka and Agnieszka Janiuk poses a simple but crucial question: What happens if we let the star's own gravity do its work? They conducted new, incredibly complex 3D simulations in which the gravity of the collapsing star was fully active, comparing the results with the old, simplified models.

Here is what they found, explained through everyday analogies:

1. The "Heavy Blanket" Effect (Self-Gravity)

Imagine the collapsing star as a heavy, wet blanket falling onto a trampoline (the black hole). In the old simulations, scientists acted as if the blanket were made of loose feathers that did not stick together. In this new study, they treated the blanket as a heavy, cohesive cloth.

Because the "blanket" is heavy and attracts itself, it piles up much faster and harder against the trampoline. This additional weight generates enormous pressure.

2. The "Choked Fire Hose" (Jet Quenching)

In the old models (without self-gravity), the fire hose (the jet) turned on and sprayed steadily. But in the new models (with self-gravity), the story was different.

The heavy blanket piled up so quickly that it temporarily choked the fire hose. The jet started, then suddenly paused or "fell asleep" for a while before waking up again. The authors call this a "quiescent interval."

The Analogy: Imagine trying to inflate a balloon while someone sits on it. You blow, the balloon inflates a little, but then the person's weight prevents the air from escaping. You must press harder or wait until the weight shifts before the air can escape again.
The Result: This "choking" explains why some gamma-ray bursts show gaps or pauses in their light. The jet is not broken; it is merely temporarily choked by the heavy, self-attracting star.

3. The "Narrower Beam"

When the jet does manage to break through in the models with self-gravity, it is much narrower and more focused.

The Analogy: Without self-gravity, the jet is like a garden hose spraying water in a wide, messy arc. With self-gravity, the additional pressure from the surrounding star squeezes the jet together, transforming it into a laser-like beam.
The Result: The jets in these new simulations are narrower, which aligns better with what astronomers actually observe in the sky than the wide jets of the old models.

4. The "Failed Start"

In some cases, gravity was simply too strong. In a specific scenario (Model-2-SG), the star collapsed, but the jet failed to get out at all. The "fire hose" was completely blocked by the weight of the star.

The Analogy: It is like trying to start a car engine, but the brakes are locked so tightly that the wheels cannot turn. The engine runs, but the car does not move.
The Result: This suggests that some stars may collapse into black holes and produce no visible explosion—a "failed" gamma-ray burst.

5. The "Energy Thief"

The simulations also examined how much energy the black hole released to power the jet.

The Analogy: The black hole is like a spinning top. To power the jet, it must slow down its rotation (and thereby release energy).
The Result: In the models without self-gravity, the black hole slowed down significantly and released much energy to the jet. In the models with self-gravity, the jet was choked and less efficient, so the black hole continued spinning faster for longer. The heavy star essentially stole the black hole's opportunity to release its energy efficiently.

Summary

The work concludes that ignoring the star's own gravity provides an incomplete picture. When it is included:

Jets can be temporarily choked, creating pauses in the explosion's light.
Jets become narrower and more focused.
Gravity is sometimes so strong that the jet fails to start at all.
The black hole slows down differently than previously assumed.

By adding this "heavy blanket" of self-gravity to their simulations, the authors created a more realistic model that better explains the chaotic, variable, and sometimes failed explosions we see in the universe.

Technical Summary: Three-Dimensional GRMHD Simulations of Jet Launching and Propagation in Self-Gravitating Collapsing Stars

Problem Statement and Motivation
Long Gamma-Ray Bursts (GRBs) are widely associated with the collapse of rapidly rotating massive stars (Collapsars) into stellar black holes. Although the Collapsar model represents the standard explanation for long GRBs, many numerical simulations simplify the physics by assuming a fixed black hole mass and spin or neglecting the self-gravity of the progenitor star's envelope. In reality, the mass of the stellar envelope often exceeds the initial black hole mass by a large factor, suggesting that self-gravity could significantly alter the accretion flow, jet launching, and propagation. Previous two-dimensional studies by the authors showed that self-gravity enhances accretion variability and can disrupt jet launching; however, a three-dimensional analysis including jet propagation was lacking. This study aims to directly compare Collapsar models with and without self-gravity under identical initial conditions to quantify the influence of self-gravity on jet properties such as opening angle, power, terminal Lorentz factor, and variability.

Methodology
The authors performed a series of time-dependent, three-dimensional General Relativistic Magnetohydrodynamics (GRMHD) simulations using the code HARM-SELFG, an updated version of HARM. The simulations evolve the system in a dynamic spacetime, where components of the Kerr metric are dynamically updated to reflect changes in the black hole mass ( $M$ ) and angular momentum ( $J$ ).

Implementation of Self-Gravity: Instead of solving the full Einstein equations, which would be computationally prohibitive, the authors implemented self-gravity via perturbative terms added to the Kerr metric. This approach, motivated by the Teukolsky equation and the CCK formalism, treats the self-gravity of the stellar envelope as a perturbation that modifies the metric mass coefficient $M(t,r)$ and the spin parameter $a(t,r)$ . These modifications are calculated by integrating components of the energy-momentum tensor ( $T^t_t$ and $T^r_\phi$ ) over the volume between the event horizon and a given radius.
Initial Conditions: The models assume a quasi-spherical accretion flow onto a seed black hole ( $M_0 = 3 M_\odot$ , spin $a_0 = 0.8$ ) surrounded by a stellar core ( $M_\star = 25 M_\odot$ ). The gas follows a polytropic equation of state ( $\gamma = 4/3$ ). Angular momentum is scaled relative to the innermost stable circular orbit (ISCO). Magnetic fields are initialized with a plasma parameter $\beta_0$ (ratio of gas to magnetic pressure) of either 1 or 10 at $2 r_g$ , corresponding to field strengths of $\sim 10^8$ G to $\sim 10^{15}$ G.
Simulation Parameters: Four models were executed: two with self-gravity (Model-1-SG, Model-2-SG) and two without (Model-1-NSG, Model-2-NSG), differing primarily in initial magnetization ( $\beta_0 = 1$ vs. $\beta_0 = 10$ ). The simulations ran for $5 \times 10^4$ gravitational time units ( $t_g$ ).

Main Contributions and Results
This work presents the first three-dimensional GRMHD simulations of jet launching in self-gravitating Collapsars. Key findings include:

Jet Suppression and Quiescent Intervals: In models with self-gravity, the authors observe a "quiescent interval" during which jet ejection is temporarily suppressed or completely halted. In Model-1-SG, the jet launches but is subsequently suppressed due to mass accumulation and rapid accretion, leading to an inactive central engine. In Model-2-SG (weaker magnetization), self-gravity completely prevents jet launching, resulting in a "failed GRB." This suppression is not observed in the non-self-gravitating counterparts under the same conditions.
Jet Energetics and Variability: Self-gravity significantly reduces the total energy emitted by the jet. The ratio of emitted energy between self-gravitating and non-self-gravitating models is approximately 0.17–0.21. The terminal Lorentz factor ( $\Gamma_\infty$ ) is generally lower and more variable in self-gravitating models, characterized by sharp initial peaks followed by declines. In contrast, non-self-gravitating models maintain more stable, powerful jets.
Jet Opening Angle: Self-gravity leads to narrower jet opening angles. In Model-1-SG, the angle decreases from $\approx 10^\circ$ to $\approx 4^\circ$ as the jet approaches the quiescent phase. This is attributed to the additional pressure exerted by the self-gravitating fluid on the jet funnel. Non-self-gravitating models exhibit broader, more strongly expanding jets (up to $\approx 22^\circ$ ).
Black Hole Evolution: Self-gravitating models exhibit significantly higher mass accretion rates (temporarily exceeding $10^3 M_\odot \text{s}^{-1}$ ) compared to non-self-gravitating models. Consequently, the black hole mass grows rapidly, reaching $\approx 28 M_\odot$ in SG models versus $\approx 5\text{--}16 M_\odot$ in NSG models. The black hole spin evolution also differs; non-self-gravitating models extract more rotational energy via the Blandford-Znajek process, leading to lower final spins, whereas self-gravitating models maintain higher spins due to the disruption of efficient energy extraction.
Stability of the MAD State: The Magnetically Arrested Disk (MAD) state, crucial for efficient jet launching, is difficult to maintain in self-gravitating models. The rapid mass inflow driven by self-gravity prevents sufficient magnetic flux accumulation to choke the accretion flow, resulting in a lower dimensionless magnetic flux ( $\phi_{MAD}$ ) and reduced jet efficiency ( $\eta$ ). In non-self-gravitating models, the MAD state remains stable over longer periods.

Significance and Claims
The authors claim that their calculations demonstrate that self-gravity is a critical factor that significantly alters jet propagation and properties. Specifically, they argue that:

Self-gravity can explain certain features of GRB prompt emission, particularly quiescent intervals and variability, through the mechanism of temporary jet suppression due to mass accumulation.
Including self-gravity restricts the range of initial conditions (magnetic field strength, rotation, spin) capable of producing successful relativistic jets and potentially leads to failed GRBs in scenarios where non-self-gravitating models would succeed.
The timescales, variability, and opening angles of jets fundamentally depend on whether self-gravity is included, suggesting that previous models neglecting this effect may have overestimated jet stability and efficiency.

The study concludes that while self-gravity does not necessarily delay the timing of initial jet launching (if the jet is feasible), it drastically alters the subsequent evolution and frequently leads to intermittent or failed jet activity, offering a complementary explanation for the complex light curve structures observed in long GRBs.