🔭 astrophysics

Primordial black holes as dark matter candidates: Multi-frequency constraints from cosmic radiation backgrounds

This study evaluates primordial black holes as dark matter candidates by modeling their accretion-driven emissions across cosmic X-ray, Lyman-Werner, and radio backgrounds, concluding that while they can constitute a significant portion of the unresolved soft X-ray background, observational constraints limit their contribution to dark matter to less than 1% for masses between 1 and 100 solar masses.

Original authors: C. Casanueva-Villarreal, N. Padilla, P. B. Tissera, B. Liu, V. Bromm

Published 2026-06-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: C. Casanueva-Villarreal, N. Padilla, P. B. Tissera, B. Liu, V. Bromm

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 is a giant, dark ocean. For decades, scientists have been trying to figure out what makes up the "water" in this ocean. We know about the islands (stars and galaxies), but there's a massive amount of invisible stuff holding everything together, called Dark Matter.

For a long time, a popular theory suggested that this invisible ocean might be filled with Primordial Black Holes (PBHs). These aren't the black holes formed by dying stars; they are ancient, tiny (or sometimes huge) black holes that formed in the very first split-second after the Big Bang.

This paper is like a cosmic detective story. The authors asked: "If the ocean were actually filled with these ancient black holes, what would they leave behind?"

The Clues: Cosmic Backgrounds

Just as a campfire leaves behind smoke, heat, and embers, black holes that are "eating" gas leave behind radiation. The authors looked at three specific types of "cosmic smoke" that fill the universe:

The X-Ray Fog (CXB): A faint, high-energy glow that permeates space.
The UV "Sunburn" (LWB): Ultraviolet light that acts like a cosmic sunburn, breaking apart the gas clouds needed to make new stars.
The Radio Static (CRB): A low-frequency hum that we can pick up with radio telescopes.

The paper argues that if the universe were full of these primordial black holes, they would be "eating" gas and spitting out so much of this radiation that the sky would look very different than it does now.

The Investigation: How They Did It

The team built a complex computer model to simulate the universe. They imagined different scenarios:

Different Sizes: They tested black holes ranging from the mass of our Sun (1 solar mass) to 100 times heavier.
Different Diets: They modeled how these black holes eat gas. Sometimes they eat slowly and quietly (like a thin disk of food), and sometimes they eat chaotically and hotly (like a messy, swirling flow).
Different Locations: They checked if the black holes were floating alone in the empty space between galaxies or huddled inside the dense clusters of galaxies.

The Verdict: The "Too Much Noise" Problem

Here is the main finding, explained simply:

If the universe were made entirely of these black holes, the "noise" they would create would be deafening.

The X-Ray Limit: If you filled the universe with 1-solar-mass black holes, they would produce so much X-ray fog that it would be 99% brighter than what we actually see. Since we don't see that much light, we know there can't be that many black holes.
The Star-Formation Limit: If there were too many black holes, their ultraviolet "sunburn" would be so strong that it would destroy the gas clouds needed to make the very first stars. The universe would be dark and empty. Since we do see ancient stars, the black hole population must be much smaller.

The Result: The authors calculated the maximum amount of Dark Matter that could be made of these black holes without breaking the universe's "noise limits."

For 1-solar-mass black holes, they can make up at most 0.7% of Dark Matter.
For heavier ones (10 to 100 solar masses), they can make up less than 0.1% of Dark Matter.

In short: Primordial black holes cannot be the entire solution to the Dark Matter mystery. They can only be a tiny sprinkle on top of the cake, not the whole cake.

The "Radio" Mystery

There is one interesting twist. Astronomers have detected a strange, extra-bright radio signal (the EDGES signal) that we can't explain. The authors checked if these black holes could be the cause.

The Bad News: Even if the universe were 100% made of these black holes, they still wouldn't produce enough radio static to explain this mystery.
The Conclusion: Something else entirely must be causing that radio signal.

The "Recipe" Matters

The paper also highlights that the answer depends heavily on how you cook the model.

Imagine baking a cake. If you use a specific recipe (a specific model of how black holes eat gas), you get a very strict limit on how many black holes are allowed.
If you change the recipe slightly (e.g., assume the black holes eat in a different way), the limit relaxes a bit. For the smallest black holes, changing the "recipe" allowed the limit to go from 0.7% up to 3%.
However, even with the most lenient recipes, the limit remains very low. They can't be the main ingredient.

Summary

Think of the universe as a quiet library. If Primordial Black Holes were the main occupants, they would be shouting so loudly (emitting too much X-ray and UV light) that the library would be chaotic. The authors measured the actual volume of the library and concluded: There are only a few people whispering in the corners (a tiny fraction of black holes), but the vast majority of the "invisible people" (Dark Matter) must be something else entirely.

Technical Summary: Primordial Black Holes as Dark Matter Candidates: Multi-frequency Constraints from Cosmic Radiation Backgrounds

Problem Statement
The nature of dark matter (DM) remains one of the most significant open questions in cosmology. Primordial black holes (PBHs), formed from density fluctuations in the early Universe, are a compelling candidate that could constitute a fraction or all of the DM. However, their viability is constrained by their potential to accrete gas and emit radiation across the electromagnetic spectrum. This study addresses the tension between the observed anomalies in cosmic radiation backgrounds—specifically the unresolved Cosmic X-ray Background (CXB), the Lyman-Werner Background (LWB), and the Cosmic Radio Background (CRB)—and the theoretical limits imposed by PBH accretion. The primary objective is to constrain the maximum fraction of DM ( $f_{\text{PBH}}$ ) that can be composed of PBHs across a mass range of $1$ to $100 \, M_\odot$ by comparing model predictions against observational and theoretical thresholds.

Methodology
The authors employ a comprehensive analytical framework to model PBH accretion and subsequent radiation emission, building upon previous work (Casanueva-Villarreal et al. 2024, CV2024).

Cosmological Distribution: The study assumes a monochromatic PBH mass distribution within a $\Lambda$ CDM cosmology. PBHs are distributed according to the DM density, residing both in virialized halos (modeled with Navarro-Frenk-White profiles) and in the intergalactic medium (IGM). The Halo Mass Function (HMF) is modified to account for PBH-induced isocurvature perturbations and mode mixing, following the formalism of Zhang et al. (2024a).
Accretion Physics: The Bondi-Hoyle-Lyttleton model is used to determine accretion rates. Crucially, the study distinguishes between multiple accretion regimes based on the dimensionless accretion rate ( $\dot{m}$ $\overset{m}{˙}$ ):
- Thin Disks: For high accretion rates ( $\dot{m} \geq 0.07\alpha$ ).
- Luminous Hot Accretion Flows (LHAF): $0.1\alpha^2 < \dot{m} < 0.07\alpha$ .
- Standard ADAF: $10^{-3}\alpha^2 < \dot{m} < 0.1\alpha^2$ .
- Electron ADAF (eADAF): $\dot{m} < 10^{-3}\alpha^2$ .
  The emission spectra for these regimes are calculated using analytical prescriptions (Takhistov et al. 2022), including synchrotron, inverse-Compton, and bremsstrahlung processes.
Environmental Variations: To test robustness, the authors explore three distinct gas density profiles within halos: a simple isothermal profile, the Makino et al. (1998) profile, and a rescaled profile from Liu et al. (2022). Additionally, variations in relative velocities (virial vs. sound speed) and PBH spatial distributions (NFW vs. isothermal) are examined.
Background Calculation: The comoving emissivity is integrated over redshift and the HMF to derive the background intensity for the soft ($0.5-2$ keV) and hard ($2-10$ keV) X-ray bands, the Lyman-Werner band ($11.2-13.6$ eV), and the radio continuum. These are compared against:
- CXB: Observational limits on the non-source component (nsCXB) from Cappelluti et al. (2017).
- LWB: Theoretical limits where the dissociation rate of molecular hydrogen ( $H_2$ ) exceeds its formation rate ( $J_{\text{LW}} \sim 1$ ), which would suppress early star formation.
- CRB: Observational limits from ARCADE 2 and constraints related to the EDGES 21-cm signal.

Key Contributions and Results

Refined Constraints on $f_{\text{PBH}}$ : The study derives stringent upper limits on the fraction of DM composed of PBHs for masses between $1$ and $100 \, M_\odot$ . Under the baseline model (using Makino+1998 and simple isothermal profiles), the constraints are:
- $1 \, M_\odot$ : $f_{\text{PBH}} \leq 7 \times 10^{-3}$
- $10 \, M_\odot$ : $f_{\text{PBH}} \leq 6 \times 10^{-4}$
- $33 \, M_\odot$ : $f_{\text{PBH}} \leq 6 \times 10^{-4}$
- $100 \, M_\odot$ : $f_{\text{PBH}} \leq 7 \times 10^{-4}$
  These limits are primarily driven by the soft X-ray background constraints, with the LWB providing complementary, consistent bounds.
Contribution to Cosmic Backgrounds: At these maximum allowed fractions, PBHs could account for a significant portion of the observed excess in the soft X-ray background (up to 99% for $1 \, M_\odot$ , 93% for $10 \, M_\odot$ , 80% for $33 \, M_\odot$ , and 91% for $100 \, M_\odot$ ) and approximately 33–39% of the hard X-ray excess. However, their contribution to the CRB is negligible (less than 1% of the observed excess at $z=0$ ).
Impact of Accretion Sub-regimes: The inclusion of distinct accretion sub-regimes (LHAF, eADAF) is critical. Excluding these sub-regimes (considering only standard ADAF and thin disks) relaxes the constraints for low-mass PBHs ( $1 \, M_\odot$ ) by up to an order of magnitude (e.g., $f_{\text{PBH}}$ could reach $3 \times 10^{-2}$ ), highlighting the sensitivity of limits to the detailed physics of accretion flows.
Model Robustness: Variations in gas density profiles, velocity prescriptions, and the HMF modification generally result in moderate changes (factors of $\sim 2$ ) to the constraints, except for the exclusion of accretion sub-regimes. The study finds that the IGM contribution to the total background is subdominant compared to halo contributions, except in specific high-redshift or high-fraction scenarios.
EDGES and CRB Excess: The paper explicitly addresses the EDGES 21-cm signal and the ARCADE 2 radio excess. The authors find that explaining these anomalies would require PBH fractions ( $f_{\text{PBH}} \sim 1$ ) that are strictly ruled out by the CXB and LWB constraints. Even if the EDGES signal is astrophysical, PBHs alone cannot account for the required radio background enhancement without violating X-ray limits.

Significance and Claims
The paper claims to provide a more nuanced and physically grounded assessment of PBHs as dark matter candidates by integrating detailed accretion physics with multi-frequency observational constraints.

Exclusion of Total DM: The authors conclude that PBHs in the mass range of $1-100 \, M_\odot$ cannot constitute the entirety of the dark matter. The derived constraints are more restrictive than many existing bounds in the intermediate mass range ( $1-10 \, M_\odot$ ), particularly when the full suite of accretion sub-regimes is considered.
Complementarity of Backgrounds: The study demonstrates the complementarity of the CXB and LWB. While the CXB provides direct observational limits, the LWB offers theoretical constraints on the thermal and chemical history of the early Universe, specifically regarding the suppression of molecular cooling and Population III star formation.
Model Dependence: A key finding is the significant dependence of constraints on the modeling of accretion physics. The exclusion of specific accretion regimes (like LHAF) can artificially relax constraints, suggesting that robust limits require a comprehensive treatment of accretion flow physics.
Consistency with Other Probes: The derived constraints align with and, in some cases, tighten limits from microlensing (OGLE, EROS-2/MACHO), gravitational waves (LIGO/Virgo), and CMB spectral distortions, reinforcing the multi-messenger approach to constraining PBH abundance.

In summary, while PBHs in this mass range cannot be the sole component of dark matter, the study emphasizes that even small fractions could play a pivotal role in shaping early cosmic structures, provided their abundance remains within the tightly constrained limits derived from cosmic radiation backgrounds.