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Accreting Primordial Black Holes: Dark Matter Constituents

This paper utilizes general relativistic magnetohydrodynamic simulations to demonstrate that primordial black holes accreting positronium plasma via the magnetorotational instability during the early Universe's Positronium Era could have grown to masses of $10^{16}$ – $10^{17}$ g, thereby constituting a significant portion of dark matter and explaining the observed gamma-ray background.

Original authors: Brandon Curd, Richard Anantua, Nathaniel Lujan, T. Kenneth Fowler

Published 2026-03-24

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CC BY 4.0

Original authors: Brandon Curd, Richard Anantua, Nathaniel Lujan, T. Kenneth Fowler

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 the universe as a giant, chaotic kitchen right after the Big Bang. For the first few seconds, it's a super-hot soup of energy, but then, between 0.01 seconds and 14 seconds after the explosion, something special happens. The temperature drops just enough for electrons and their antimatter twins (positrons) to pair up and dance together. The authors call this the "Positronium Era."

For decades, scientists have been hunting for "Dark Matter"—the invisible glue that holds galaxies together. The usual suspects are new, undiscovered particles. But this paper suggests a different idea: What if Dark Matter isn't a particle at all, but a swarm of tiny, ancient black holes?

Here is the story of how they think these black holes were made, explained simply.

1. The Problem: Too Much Soup, Not Enough Glue

In that early "Positronium Era," there was a massive amount of this electron-positron soup. If nothing stopped it, these particles would eventually annihilate each other and vanish, leaving the universe with very little mass. But we know the universe has a lot of mass (Dark Matter).

The paper asks: How did some of this soup get "trapped" before it could vanish?

2. The Solution: The "Magnetic Whirlpool" (MRI)

Usually, if you drop a pebble in a pond, the water just flows around it. But in space, if you have a spinning black hole and a magnetic field, things get crazy.

The authors use a concept called Magnetorotational Instability (MRI).

The Analogy: Imagine a figure skater spinning on ice. If they pull their arms in, they spin faster. Now, imagine the ice is made of magnetic field lines. If the skater (the black hole) is spinning, and the magnetic field lines get tangled, they act like a whirlpool.
The Effect: This whirlpool doesn't just spin; it grabs the surrounding soup (the positronium) and drags it inward, much faster than gravity alone could. It's like a cosmic vacuum cleaner powered by a magnetic tornado.

3. The Simulation: A Digital Time Machine

The team didn't just guess; they built a super-computer simulation (using a code called KORAL) to watch this happen.

They simulated a tiny black hole seed in that early universe soup.
They turned on the magnetic "whirlpool" (MRI).
The Result: The simulation showed that the whirlpool could grab a huge amount of the surrounding soup from far away and dump it onto the tiny black hole.

Think of it like a tiny ant (the black hole seed) sitting in a hurricane. Normally, the ant would just get blown away. But with MRI, the hurricane creates a funnel that sucks the ant into a giant boulder.

4. The Outcome: A Swarm of "Asteroid-Sized" Black Holes

Because this process happened so efficiently during those 14 seconds:

Tiny black hole seeds grew into black holes weighing about 10^16 to 10^17 grams.
To put that in perspective: That's about the mass of a large asteroid or a small mountain. They are too small to see with telescopes, but they have enough gravity to act as Dark Matter.
The paper suggests that 30% or more of all the Dark Matter in the universe today could be these ancient, asteroid-sized black holes.

5. Why This Matters

The "Particle" Hunt: Scientists have been spending billions looking for new "Dark Matter particles" in underground labs, but haven't found any yet. This paper says, "Maybe we don't need new particles. Maybe the answer is right there in the black holes we already know about."
The Gamma Ray Clue: These tiny black holes aren't just sitting there; they are slowly evaporating and shooting out gamma rays (high-energy light). The paper notes that the amount of gamma rays we see in the background of the universe matches what these black holes would produce. It's like finding a pile of ash that perfectly matches the size of a campfire that was supposed to be there.

The Big Picture

The authors are saying: "Let's stop guessing about invisible particles and look at the physics we already understand."

If you imagine the early universe as a giant blender:

The Ingredients: Positronium soup.
The Blender: The magnetic whirlpool (MRI).
The Result: A smoothie of tiny black holes that make up the invisible skeleton of our universe.

This theory offers a concrete, testable explanation for Dark Matter that relies on fluid dynamics and magnetism rather than mysterious new physics. If their math is right, the "Dark Matter" holding our galaxy together might just be a ghostly cloud of ancient, asteroid-sized black holes.

1. Problem Statement

The nature of dark matter remains one of the most significant unsolved problems in cosmology. While the standard model assumes dark matter consists of undiscovered particles in a "dark sector," direct detection efforts have so far been unsuccessful. Primordial Black Holes (PBHs) remain a leading alternative hypothesis. However, a critical gap exists in understanding the accretion mechanism that could allow PBH seeds formed in the early universe to grow to the specific mass range ( $10^{16}–10^{17}$ g) required to constitute a significant fraction of dark matter today without evaporating via Hawking radiation.

Specifically, the authors address the conditions during the "Positronium Era" (0.01 s to 14 s after the Big Bang), a period dominated by electron-positron plasma. The challenge is to determine if accretion during this era, driven by specific instabilities, could efficiently convert a fraction of this massive plasma into black holes that survive to the present day.

2. Methodology

The authors employ a multi-faceted approach combining analytical derivations, scaling laws, and numerical simulations:

Analytical Derivation (Section II):
- They derive the dark matter abundance ratio ( $M_{DM}/M_0$ ) using fluid momentum conservation and the scaling of magnetic helicity, without initially assuming a specific transport mechanism.
- They establish a scaling law for the accretion radius $R_0 \propto (MG)^{1/3}t^{2/3}$ , derived from the conservation of magnetic helicity in gravitational flows.
- They compare standard Bondi accretion (spherical, non-rotating) against Magneto-Rotational Instability (MRI) driven accretion.
General Relativistic Magnetohydrodynamic (GRMHD) Simulations (Section III):
- The authors utilize the KORAL code, a state-of-the-art GRMHD solver, to simulate accretion flows.
- Simulation Setup:
  - Domain: 2D axisymmetric simulations (verified against 3D tests) covering radii from $R_{min} = 100 R_g$ to $R_{max} = 10^6 R_g$ .
  - Physics: Radiation-dominated plasma ( $\gamma = 4/3$ ), Schwarzschild black hole metric, and initial Keplerian rotation.
  - Conditions: The simulations model the Positronium Era environment (high temperature, relativistic speeds) using a hydrogen gas analog with adjusted temperature to match the positronium sound speed.
  - Magnetic Fields: Initialized with a poloidal field ( $B_r, B_z$ ) and a plasma-to-magnetic pressure ratio $\beta \approx 10^3$ .
- Collisionality Check: The authors verify that the MHD approximation is valid for the primordial plasma by calculating collision timescales, noting that while the plasma is relativistic, turbulent transport and magnetic coupling dominate over collisionless effects in the relevant regimes.

3. Key Contributions

Identification of the Positronium Era as the Critical Window: The paper identifies the time interval $0.01\text{s} < t < 14\text{s}$ as the unique epoch where the mass density of positronium plasma was sufficient to fuel PBH growth, whereas earlier times were too hot and later times had insufficient mass due to annihilation.
MRI as the Primary Growth Mechanism: The authors demonstrate that MRI, rather than Bondi accretion, is the dominant mechanism for growing PBH seeds in the early universe. MRI allows for accretion at radii far exceeding the Schwarzschild radius ( $R_0 \gg R_g$ ), compensating for slower local velocities with a vastly larger capture cross-section.
Scaling Law Validation: They provide numerical evidence supporting the theoretical scaling law $R_0 \propto t^{2/3}$ , linking the growth of the accretion radius directly to the expansion of the universe and magnetic helicity conservation.
Mass Range Constraints: The study defines a specific "mass window" for PBHs ( $10^{15}\text{g} < M < 10^{18}\text{g}$ ) that are viable candidates for dark matter, constrained by Hawking evaporation (lower limit) and the transition from viscous flow to MRI (upper limit).

4. Key Results

Dark Matter Abundance:
- Using the derived scaling law with a parameter $F=100$ (extrapolated from simulation data), the model predicts that accreted positronium mass can account for 30% to 100% of the total dark matter abundance.
- The ratio of accreted dark matter mass to baryonic mass is calculated as $(M_{DM}/M_0) \approx 2$ for $F=100$ , implying that a small fraction of the positronium mass is sufficient to explain the observed dark matter density.
Simulation Findings:
- MRI Growth: Simulations show that MRI drives turbulence and angular momentum transport, creating an accretion jet that propagates outward.
- Accretion Velocity: The accretion velocity $v_R$ follows the MRI scaling $v \propto A v_K (R_g/R)^{1/2}$ (where $0.001 < A < 0.01$ ), distinct from the $v \propto R^{-2}$ scaling of Bondi accretion.
- Magnetic Field Evolution: The magnetic field grows and oscillates in correlation with the accretion flow, confirming the dynamo action required to sustain MRI.
- Angular Momentum: MRI effectively ejects angular momentum, allowing matter to spiral inward despite the centrifugal barrier, eventually leading to the formation of black holes.
Gamma-Ray Background Consistency: The resulting population of $10^{16}–10^{17}$ g black holes would emit Hawking radiation consistent with the observed diffuse gamma-ray background, providing an observational signature for this model.

5. Significance

Alternative to New Physics: This work offers a compelling alternative to the search for new dark sector particles. It suggests that dark matter could be entirely or partially explained by well-understood astrophysical processes (GRMHD and MRI) acting in the early universe, rather than requiring undiscovered fundamental particles.
Resolution of the Mass Gap: The paper resolves the "mass gap" problem for PBHs by showing how MRI can grow seeds to the specific $10^{16}–10^{17}$ g range, which is otherwise difficult to achieve via standard Bondi accretion in the early universe.
Observational Implications: The model predicts that if dark matter is indeed composed of these PBHs, the observed gamma-ray background is a direct signature of their Hawking radiation. This provides a testable hypothesis that does not rely on particle collider experiments.
Future Directions: The authors conclude that while current simulations support the theory, longer-duration GRMHD simulations are needed to precisely pin down the parameter $F$ and determine the exact fraction of dark matter contributed by this mechanism versus potential dark sector particles.

In summary, the paper presents a robust theoretical and numerical framework suggesting that MRI-driven accretion of primordial positronium plasma is a highly efficient mechanism for generating the population of primordial black holes that could constitute a significant portion of the universe's dark matter.