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Inherent self-consistency of the electron fraction between neutrino-dominated accretion flows and their progenitors

This study demonstrates that the electron fraction distributions in neutrino-dominated accretion flows (NDAFs) naturally align with the distinct nucleosynthetic signatures of their respective progenitors—collapsars and compact object mergers—thereby providing robust self-consistent support for NDAFs as the central engines of gamma-ray bursts.

Original authors: Rui-Qi Cui, Tong Liu

Published 2026-03-30

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CC0 1.0

Original authors: Rui-Qi Cui, Tong Liu

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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

The Big Picture: The Cosmic Engine Room

Imagine the universe is full of cosmic fireworks called Gamma-Ray Bursts (GRBs). These are the brightest explosions in existence, outshining entire galaxies for a few seconds. For decades, scientists have been trying to figure out exactly what kind of "engine" powers these explosions.

The leading theory is that these engines are Black Holes surrounded by a swirling, super-hot disk of matter (like a cosmic whirlpool). This disk is so hot that it glows with neutrinos (ghostly particles that rarely interact with anything). This setup is called a Neutrino-Dominated Accretion Flow (NDAF).

The big question this paper asks is: "Does the fuel in this engine match the type of explosion we see?"

To answer this, the authors looked at a specific ingredient in the fuel: the Electron Fraction ( $Y_e$ ).

The Ingredient: The "Proton-Neutron Balance"

Think of the matter in the disk as a soup made of two main ingredients: Protons (positively charged) and Neutrons (neutral).

High Electron Fraction ( $Y_e \approx 0.5$ ): The soup has an equal mix of protons and neutrons. It's "balanced."
Low Electron Fraction ( $Y_e < 0.4$ ): The soup is heavy on neutrons. It's "neutron-rich."

Why does this matter? Because the type of explosion (and what it leaves behind) depends entirely on this balance.

Balanced Soup $\rightarrow$ Creates a specific type of supernova (from a dying massive star).
Neutron-Rich Soup $\rightarrow$ Creates a "kilonova" (from two dead stars crashing together).

The Experiment: Cooking the Cosmic Soup

The authors built a super-computer model of these black hole engines. They cooked up different scenarios by changing three "knobs":

How fast matter is falling in (The Accretion Rate).
How fast the black hole is spinning (The Spin).
How much matter is being blown away (The Outflow).

They wanted to see how these knobs changed the "Proton-Neutron balance" in the soup.

The Results: Two Distinct Recipes

The paper found that the engine naturally sorts itself into two distinct recipes based on how fast it's eating:

1. The "Slow Cooker" (Low Accretion Rate)

The Scenario: Imagine a massive star collapsing at the end of its life. It dumps a huge amount of material onto the black hole, but the flow is relatively steady and "slow" (in cosmic terms).
The Physics: The outer edges of the disk are like a slow-moving river. The heat doesn't escape fast enough to change the chemistry. The protons and neutrons stay in a balanced state.
The Result: The electron fraction stays high ( $\approx 0.5$ ).
The Match: This perfectly matches the Long Gamma-Ray Bursts we see, which come from collapsing massive stars. The engine's fuel matches the star's origin.

2. The "High-Pressure Fryer" (High Accretion Rate)

The Scenario: Imagine two dead stars (neutron stars) smashing into each other. They dump a massive amount of material onto the black hole all at once, very quickly.
The Physics: The disk is so dense and hot that it becomes a "neutron factory." The intense pressure forces protons to grab electrons and turn into neutrons. The disk becomes "neutron-rich."
The Result: The electron fraction drops low ( $\approx 0.3$ or less).
The Match: This perfectly matches the Short Gamma-Ray Bursts we see, which come from merging compact objects. Again, the engine's fuel matches the origin.

The "Self-Consistency" Discovery

The most exciting part of this paper is the concept of Self-Consistency.

Think of it like a lock and key.

The Key: The type of star that died (Massive Star vs. Merging Stars).
The Lock: The chemical makeup of the black hole's engine.

The authors found that the universe is perfectly designed. If you have a massive star dying, the engine automatically adjusts to have a balanced fuel mix. If you have two stars merging, the engine automatically adjusts to have a neutron-rich fuel mix.

They didn't have to force the engine to match the star; the physics of the accretion disk naturally creates the right "flavor" of matter for the specific type of explosion.

Why This Matters

Before this, scientists knew the engines existed, but they weren't 100% sure if the physics inside the disk made sense with the stars that created them.

This paper says: "Yes, it works."

The "Slow Cooker" engines explain the Long Bursts and the supernovae we see.
The "High-Pressure Fryer" engines explain the Short Bursts and the kilonovae (which create heavy elements like gold and platinum).

The Bottom Line

The universe is a master chef. Whether a black hole is born from a dying giant star or a collision of dead stars, the resulting engine naturally cooks up the exact type of "fuel" needed to power the specific explosion we observe. The math checks out, the physics holds up, and the story of these cosmic explosions is now even more consistent than before.

1. Problem Statement

Gamma-ray bursts (GRBs) are classified into long-duration (LGRBs) and short-duration (SGRBs) events, generally associated with massive star core collapse (collapsars) and compact object mergers (neutron star-neutron star or neutron star-black hole), respectively. While Neutrino-Dominated Accretion Flows (NDAFs) surrounding stellar-mass black holes are a leading model for GRB central engines, a critical gap remains in establishing a robust, self-consistent link between the physical properties of these accretion disks and their specific progenitor systems.

Specifically, the electron fraction ( $Y_e \equiv n_p / (n_p + n_n)$ ) is a crucial parameter. It determines the nucleosynthetic outcomes of disk outflows (e.g., whether they produce $^{56}$ Ni for supernovae or heavy r-process elements for kilonovae). Previous studies have characterized $Y_e$ distributions, but a dedicated correspondence linking the $Y_e$ at the outer boundaries of NDAFs to the expected $Y_e$ of specific progenitors (collapsars vs. mergers) has been largely missing. This paper aims to verify if NDAF models naturally reproduce the $Y_e$ signatures expected from their respective progenitors across varying accretion rates, black hole (BH) spins, and outflow strengths.

2. Methodology

The authors developed a comprehensive 1D radial global relativistic model of NDAFs around Kerr black holes.

Hydrodynamics & Relativity: The model incorporates the Kerr metric with dimensionless spin parameter $a_*$ . It solves conservation equations for mass, angular momentum, and energy, including relativistic correction factors ( $A, B, C, D$ ) derived from Riffert & Herold (1995).
Thermodynamics: The energy balance equation equates viscous heating ( $Q_{vis}$ $Q_{v i s}$ ) with total cooling ( $Q_-$ $Q_{-}$ ). Cooling mechanisms include:
- Photodissociation of $\alpha$ -particles ( $Q_{photo}$ ).
- Advection ( $Q_{adv}$ ).
- Neutrino losses ( $Q_\nu$ ), calculated via Urca processes, $e^-e^+$ annihilation, nucleon-nucleon bremsstrahlung, and plasmon decay.
- Radiative cooling ( $Q_{rad}$ ), noted as negligible in high-density regimes.
Equation of State (EOS): Includes gas pressure (nucleons/ $\alpha$ -particles), photon radiation, electron/positron pressure (calculated via exact Fermi-Dirac integration to account for degeneracy), and neutrino pressure.
Electron Fraction ( $Y_e$ ): The model calculates $Y_e$ based on $\beta$ -equilibrium conditions. In neutrino-trapped regions, reversible weak interactions maintain equilibrium. In transparent regions, the model uses a weighting factor approach (Liu et al. 2007) to relate $Y_e$ to the free-nucleon mass fraction ( $X_{nuc}$ ) and the electron chemical potential ( $\mu_e$ ).
Outflows: A parametric disk outflow is implemented where the accretion rate varies with radius as a power law: $\dot{m} = \dot{m}_{outer}(R/R_{outer})^p$ , with $p=0.5$ or $0.8$.
Parameters:
- BH Mass: Fixed at $3 M_\odot$ .
- Viscosity: Fixed at $\alpha = 0.1$ .
- Variables: Accretion rates ( $\dot{m} = 0.1, 1, 5$ ), BH spins ( $a_* = 0.1, 0.5, 0.9$ ), and outflow strengths ( $p$ ).

3. Key Contributions

Progenitor-Disk Self-Consistency: The paper establishes a direct, self-consistent link between the outer boundary electron fraction of NDAFs and the nature of the progenitor system.
Differentiation Mechanism: It demonstrates that the accretion rate is the primary driver determining the $Y_e$ profile, effectively distinguishing between collapsar (LGRB) and merger (SGRB) scenarios without requiring fine-tuned initial conditions.
Outflow Robustness: The study confirms that the inclusion of disk outflows does not disrupt the fundamental $Y_e$ trends dictated by the accretion rate, reinforcing the validity of NDAFs as central engines.

4. Key Results

A. Low Accretion Rates (Collapsar/LGRB Scenario)

Conditions: $\dot{m} \sim 0.1$ (typical of massive star collapse).
Physics: The outer disk is advection-cooled. Neutrino cooling is relatively weak in these regions.
Electron Fraction: The electron fraction at the outer boundary remains high, $Y_e \sim 0.5$ .
Implication: This indicates a proton-neutron symmetric composition, consistent with the presupernova structure of massive stars (collapsars). The outflows from these disks are proton-rich, favoring the synthesis of $^{56}$ Ni and powering Type Ib/c supernovae.

B. High Accretion Rates (Merger/SGRB Scenario)

Conditions: $\dot{m} \sim 1 - 5$ (typical of compact object mergers).
Physics: The inner disk becomes highly efficient at neutrino cooling, leading to mild electron degeneracy. The Urca processes favor electron capture ( $e^- + p \to n + \nu_e$ ), producing excess neutrons.
Electron Fraction: Even at the outer boundary of the disk, $Y_e$ drops significantly to $Y_e \lesssim 0.38$ (and can be as low as $\sim 0.05 - 0.2$ in the inner regions).
Implication: This neutron-rich composition is consistent with materials ejected from compact object mergers. These outflows drive heavy r-process nucleosynthesis, producing lanthanide-rich "red" kilonovae.

C. Impact of Spin and Outflows

BH Spin ( $a_*$ ): Variations in spin ($0.1$ to $0.9$) have only a minor impact on the global $Y_e$ trends. The accretion rate remains the dominant factor.
Outflows: The presence of outflows (parameterized by $p$ ) reduces the overall density and temperature but does not alter the fundamental cooling regime (advection vs. neutrino) or the resulting $Y_e$ trends. The self-consistency between the disk boundary and progenitor holds regardless of outflow strength.

5. Significance

This work provides strong theoretical support for the NDAF model as the central engine for GRBs by resolving a key consistency check:

Validation of Engine Models: It proves that NDAFs naturally evolve to match the electron fraction properties expected from their specific progenitors. Low-accretion disks mimic collapsars ( $Y_e \sim 0.5$ ), while high-accretion disks mimic mergers ( $Y_e \lesssim 0.38$ ).
Nucleosynthesis Predictions: The results offer testable predictions for electromagnetic counterparts. LGRBs should be associated with high- $Y_e$ outflows (supernovae), while SGRBs should be associated with low- $Y_e$ outflows (kilonovae with distinct red/blue components).
Unified Framework: The study unifies the understanding of GRB central engines, suggesting that the observed diversity in GRB properties and their counterparts arises naturally from the accretion rate evolution of a single physical model (NDAF) rather than requiring fundamentally different engine mechanisms.

In conclusion, the inherent self-consistency of the electron fraction between NDAFs and their progenitors strongly validates the NDAF framework as the central engine for both short and long gamma-ray bursts.