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A grid of fast-rotating, chemically-homogeneous, supernova and/or long-GRB progenitors

This paper presents a grid of 113 chemically-homogeneous, rapidly rotating single-star models computed with MESA at low metallicity, designed to serve as improved progenitors for understanding the mechanisms behind stripped-envelope supernovae, collapsars, and long gamma-ray bursts.

Original authors: M. Renzo, O. Gottlieb, H. S. Chan, J. A. Goldberg, A. Grichener, K. Sen, N. Shah, E. Farag, Matteo Cantiello

Published 2026-06-23

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CC BY 4.0

Original authors: M. Renzo, O. Gottlieb, H. S. Chan, J. A. Goldberg, A. Grichener, K. Sen, N. Shah, E. Farag, Matteo Cantiello

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 as a giant, spinning top made of gas and nuclear fire. For decades, scientists have been trying to figure out exactly how these spinning tops eventually crash, explode, or turn into black holes. The problem is that the "blueprints" (the computer models) scientists use to predict these crashes often have missing details or are too simple to be accurate.

This paper presents a new, highly detailed set of blueprints for 113 of these spinning stars, specifically designed to help scientists understand the most violent explosions in the universe: supernovae and gamma-ray bursts.

Here is a breakdown of what the researchers did and why it matters, using everyday analogies:

1. The Problem: The "Blurry Map"

Imagine trying to navigate a ship through a storm using a map that only shows the coastline but misses the hidden reefs and currents. That is what scientists have been doing with star explosions.

The Missing Detail: Most previous models of dying stars used a "small menu" of nuclear ingredients (about 20 types of atoms) to simulate the star's core.
The Reality: The core of a dying star is a complex kitchen where hundreds of different atomic ingredients are mixing and reacting. The paper argues that using a small menu is like trying to bake a soufflé with only flour and water; you miss the crucial chemistry that determines if it rises or collapses.
The Rotation Issue: Many of the most dramatic explosions happen in stars that are spinning incredibly fast. Previous models often ignored this spin or added it in a "fake" way that didn't match how the star actually evolved.

2. The Solution: A "High-Definition" Grid

The authors created a new library (a "grid") of 113 star models. Think of this as a massive, high-definition video game level where every single variable is accounted for.

The Ingredients: Instead of a small menu, they used a 128-isotope network. This is like having a full, professional chef's pantry with every spice and ingredient needed to perfectly simulate the star's internal cooking process.
The Spin: They started the simulations with stars spinning at 50% to 99% of their maximum possible speed (the "critical" speed where they would fly apart).
The Result: Because these stars spin so fast, they mix themselves up completely. Instead of having a distinct core and a separate outer shell (like an onion), the whole star becomes a uniform, homogeneous mixture. This is called Chemically Homogeneous Evolution (CHE).

3. The Journey: From Birth to the Edge of Collapse

The paper tracks these stars from their birth until the very last second before they collapse.

The "Hook": As the stars burn their fuel, they don't expand into giant red giants like normal stars. Because they are spinning so fast and mixing so well, they stay small, hot, and compact. It's like a dancer spinning so fast they stay in one spot rather than sprawling out.
The Crunch: The researchers pushed the simulations all the way to the point where the star's core starts to fall inward at speeds of over 300 kilometers per second. This is the "point of no return" just before the star either explodes or implodes.
The Spin Preservation: Crucially, these models show that the core retains a massive amount of spin right up until the crash. This is vital because if a spinning core collapses, that spin can create a whirlpool (an accretion disk) around the new black hole or neutron star, which is the engine that powers the explosion.

4. Why This Matters: The "Engine" of the Explosion

The paper explains that the structure of the star before it explodes decides how it explodes.

The Pressure Cooker: The core is supported by electron pressure. The new models show that the "small menu" (old models) gets the electron pressure wrong. This is like miscalculating the pressure in a steam engine; you might think it will explode gently, but in reality, the pressure is so different that the outcome is completely wrong.
The Magnetic Dynamo: The spinning motion generates magnetic fields (like a giant dynamo). The paper shows that these fields are structured and strong enough to potentially launch jets of energy, creating the long gamma-ray bursts we see in the sky.

5. The Caveats: It's Not Perfect

The authors are honest about the limitations.

Rare Birds: Stars spinning this fast are rare in our local universe. The researchers admit these models might represent a "best-case scenario" or a specific type of star that only exists in the early universe or through rare binary interactions (like two stars merging).
The "Envelope" Issue: The models had to artificially stop the outer layers of the star from behaving strangely because the computer code struggled with the extreme speeds. They focused on the core, where the explosion happens, and smoothed out the edges.

Summary

In short, this paper provides a new, ultra-detailed set of instructions for how fast-spinning massive stars die. By including a much larger list of atomic ingredients and simulating the spin realistically, they have created a better starting point for scientists to run super-computer simulations of stellar explosions.

Think of it as upgrading from a sketch on a napkin to a 3D architectural blueprint. While the paper doesn't tell us exactly which star will explode next, it gives physicists the correct tools to understand why some stars explode with jets of light (gamma-ray bursts) while others just collapse silently into black holes.

Technical Summary: A Grid of Fast-Rotating, Chemically-Homogeneous Supernova and Long-GRB Progenitors

Problem Statement
The mechanism governing the collapse and potential explosion of massive stars remains a central challenge in astrophysics. While numerical simulations of neutrino-driven core collapse have advanced, they are heavily dependent on the initial structure of the stellar progenitor. A critical bottleneck exists in the availability of progenitor grids that satisfy two specific conditions:

Late Evolutionary Stage: Models must be evolved well into the sub-sonic collapse phase (typically until the iron-core infall velocity $v_{\text{infall}} \lesssim -300$ km s $^{-1}$ ), a stage where thermodynamic quantities often exceed the bounds of standard equations of state in stellar evolution codes.
Detailed Microphysics: Models must employ sufficiently large nuclear reaction networks (specifically $\sim$ 100 isotopes) to accurately capture weak interactions (electron captures) that deleptonize the core during and after silicon burning.

Existing grids often rely on small networks ( $\sim$ 20 isotopes) that approximate weak interactions via compound reactions, sacrificing the accuracy of the core's electron fraction ( $Y_e$ ) profile and density structure. Furthermore, there is a severe lack of publicly available, self-consistent grids for fast-rotating progenitors, which are essential for understanding jetted explosions, collapsars, magnetar-powered transients, and long gamma-ray bursts (LGRBs). Most existing rotating models either use small networks or impose ad-hoc angular momentum profiles inconsistent with the progenitor's evolution.

Methodology
The authors present a grid of 113 single-star models computed using the open-source stellar evolution code MESA (version r24.03.1).

Parameter Space: The grid covers initial Zero-Age Main Sequence (ZAMS) masses ( $M_{\text{ZAMS}}$ ) from 30 to 90 $M_{\odot}$ and initial rigid rotation rates ( $\omega_{\text{ZAMS}}$ ) from 0.5 to 0.99 of the critical rotation rate ( $\omega_{\text{crit}}$ ). The metallicity is fixed at $Z = 0.001$ .
Physics Inputs:
- Nuclear Network: A fully coupled 128-isotope network (mesa 128.net) is used to track weak reactions and deleptonization accurately.
- Equation of State & Opacities: The Skye equation of state, electron screening, thermal neutrino losses, OPAL radiative opacities, and Cassisi electron conduction opacities.
- Mixing & Transport: Rotational mixing is treated in the diffusion approximation (Heger et al. 2000), including angular momentum transport via convection and a "classical" Tayler-Spruit dynamo in radiative regions. Core overshooting is modeled as a step-function.
- Mass Loss: Wind mass loss rates follow Vink et al. (2000) or Nugis & Lamers (2000) depending on surface helium abundance, with metallicity and rotational enhancements.
Numerical Strategy:
- The models are constructed to undergo rotationally-induced chemically homogeneous evolution (CHE).
- To reach the collapse phase (Condition i), models are evolved until $v_{\text{infall}} \leq -300$ km s $^{-1}$ .
- An artificial damping scheme is applied to suppress spurious numerical velocities in the outer layers during late-stage burning.
- The code operates in "operator split" mode for central temperatures $\log_{10}(T) \geq 9.2$ .

Key Contributions and Results

Grid Success and Composition: From an initial set of 781 models, 113 models successfully reached the onset of core collapse without exhibiting unphysical luminosity or effective temperature excursions. The success rate is approximately 14%, with higher failure rates at higher masses and rotation rates, attributed primarily to numerical stiffness rather than physical hypotheses.
Stellar Evolution: The models exhibit CHE, preventing the formation of extended hydrogen envelopes. Stars evolve blueward on the Hertzsprung-Russel diagram, remaining compact ( $R_{\text{max}} \lesssim 31 R_{\odot}$ ) and hot ( $T_{\text{eff}} \gtrsim 10^{4.5}$ K). They retain helium at the surface but lack hydrogen.
Core Structure at Collapse:
- Entropy and Density: The inner specific entropy profiles show nearly flat "steps" indicative of efficient convection. The density profiles are strongly influenced by the electron fraction ( $Y_e$ ) due to electron degeneracy pressure.
- Impact of Nuclear Network: Comparisons between the 128-isotope models and identical models using a 22-isotope network reveal that the small network introduces systematic errors in the $Y_e$ and density profiles of the inner core. These errors are comparable to or larger than the variations caused by changing mass or rotation, significantly biasing explosion dynamics.
- Angular Momentum: The models retain large amounts of specific angular momentum ( $j$ ) at collapse. The profiles suggest that accretion disks are likely to form on the proto-compact object (either before or during the proto-neutron star phase).
- Magnetic Fields: The Tayler-Spruit dynamo generates azimuthal and radial magnetic fields, with local field strengths reaching $10^{12}$ G in the core.
- Compactness: The compactness parameter $\xi_{1.75}$ generally decreases with increasing rotation, though the trend is non-linear. Most models fall in the regime favoring black hole formation, though high angular momentum may prevent direct collapse.

Significance and Claims
The paper claims that this grid provides a homogeneous set of models with updated input physics and improved algorithmic accuracy, specifically addressing the lack of self-consistent, fast-rotating progenitors for explosion simulations.

Utility: These models serve as initial conditions for multi-dimensional, multi-physics simulations of stellar explosions where rotation and magnetic fields are dominant. They are intended to study stripped-envelope supernovae (potentially jetted or broad-lined), collapsars, magnetar-powered transients, and long GRBs.
Limitations: The authors acknowledge that the specific evolutionary path (single-star, extremely fast initial rotation) is likely rare in the local Universe and may approximate binary interaction scenarios (e.g., mergers, tidal spin-up) rather than single-star evolution. They also note caveats regarding the specific nuclear reaction rates used (e.g., $^{12}\text{C}(\alpha, \gamma)^{16}\text{O}$ ), the Tayler-Spruit dynamo prescription, and the artificial damping of envelope velocities.
Availability: The grid and associated processing scripts are publicly available, aiming to facilitate systematic numerical experiments on rotating massive star explosions.