🔭 astrophysics

Constraining primordial black holes and primordial curvature power spectrum with extragalactic muon neutrino

This paper investigates extragalactic muon neutrino fluxes from WIMP annihilation within ultracompact minihalos formed around primordial black holes to derive new constraints on the fraction of dark matter composed of primordial black holes and the primordial curvature power spectrum using IceCube data.

Original authors: Yupeng Yang

Published 2026-07-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Yupeng Yang

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, invisible ocean made of "dark matter," a mysterious stuff that holds galaxies together but refuses to show its face. For a long time, scientists thought this ocean was made of one thing: tiny, ghostly particles called WIMPs (Weakly Interacting Massive Particles). But despite hunting for them with giant detectors, no one has ever caught a WIMP in the act.

Then, a new idea surfaced: maybe the ocean isn't just made of ghosts. Maybe it's a mix of ghosts and "primordial black holes" (PBHs)—tiny, ancient black holes born from the chaotic first seconds of the Big Bang, long before stars even existed.

This paper by Yupeng Yang asks a simple, playful question: If these two types of dark matter are hanging out together, what kind of noise would they make?

The Cosmic Snowball Effect

Here is the setup. When a primordial black hole forms, it acts like a cosmic vacuum cleaner. It starts sucking in the surrounding WIMPs. Because the black hole is so dense, it pulls these particles in so tightly that they form a super-dense "snowball" around it, called an Ultracompact Minihalo (UCMH).

Think of a normal dark matter halo as a fluffy cloud of cotton candy. Now, imagine a UCMH as a rock-hard, compressed ball of that same cotton candy. The particles inside are packed so tightly that they are practically bumping into each other.

When WIMPs bump into each other, they annihilate—poof! They disappear and release energy. Because the particles in a UCMH are so crowded, this "poof" happens way more often than in a normal cloud. This explosion of energy should send out a signal.

The Detective Work: Listening for Neutrinos

Previous detectives looked for this signal in the form of gamma rays (high-energy light). But this paper decides to listen for something else: muon neutrinos. These are ghostly particles that can pass through almost anything, including the entire Earth.

The author imagines the IceCube experiment, a giant telescope buried deep in the ice at the South Pole. IceCube is like a massive, transparent jellyfish waiting to catch a neutrino. When a neutrino hits the ice, it creates a muon (a heavy cousin of the electron) that zips through the ice, leaving a trail of blue light (Cherenkov radiation) that IceCube can see.

The paper looks at two ways IceCube catches these muons:

Contained Events: The muon is born inside the detector.
Upward Events: The muon is born outside the detector, on the other side of the Earth, and travels upward through the planet to hit the detector.

The Big Find: The "No-Go" Zone

The author runs the numbers to see how many neutrinos we should see if the universe is full of these WIMP-black hole snowballs. Then, they compare that to the "background noise"—the natural neutrinos that rain down on Earth from the atmosphere (like cosmic static).

The Result: The paper finds that if there were too many of these black holes, the neutrino signal would be so loud that it would drown out the atmospheric noise. Since IceCube hasn't heard a roar (yet), the author can draw a line in the sand.

They calculate the maximum amount of dark matter that can be made of primordial black holes without breaking the rules of the universe.

For a WIMP mass of 10³ GeV and a black hole mass of 10³ M⊙ (solar masses), the fraction of dark matter that can be black holes (fPBH) must be less than 10⁻⁴ for contained events.
For upward events, the limit is even stricter: fPBH must be less than 4 × 10⁻⁵.

In plain English: If primordial black holes made up more than about 0.01% (or 0.004%) of all dark matter, we would have seen a massive spike in neutrinos by now. We didn't. So, they can't be that common.

What This Tells Us

This study establishes strict upper limits on the fraction of dark matter that can be primordial black holes. It suggests that while black holes might exist, they are likely just a tiny sprinkle in the dark matter soup, not the whole meal, at least within the mass ranges tested (specifically around 10³ M⊙).

Crucially, the paper relies on the "mixed" scenario (WIMPs + Black Holes) to make these discoveries. It doesn't refute the idea that they coexist; rather, it uses the unique, loud signature created by their interaction to set new, tighter rules on how many black holes can exist.

The Ripple Effect: Ripples in Spacetime

Here is the cool part. The formation of these black holes depends on how "bumpy" the universe was when it was a baby. Scientists call this the primordial curvature power spectrum (PR). It's like measuring the size of the waves in the ocean of the early universe.

By saying "there can't be too many black holes," the paper effectively says "the waves in the early universe couldn't have been too big."

Based on their strongest limit, the authors suggest that at a specific scale (k ∼ 3 × 10¹² Mpc⁻¹), the power of these waves (PR) must be less than 10⁻¹.⁶⁵.

This is a new, tighter rule for the early universe. It's like saying, "We know the ocean waves couldn't have been taller than 5 feet, because if they were, the boats (black holes) would have capsized the whole fleet."

How Sure Are They?

The authors are careful. They didn't find the black holes; they didn't find the WIMPs. Instead, they used simulations and theoretical calculations to say, "If these things existed in large numbers, we would have seen X. Since we didn't see X, they probably aren't that big."

They are confident in their math and the data from IceCube, but they are presenting upper limits (a "ceiling" on how big these things can be), not a discovery. They are essentially telling us what the universe isn't, which is just as important as knowing what it is.

So, the next time you look up at the stars, remember: the universe is likely a quiet place where dark matter is mostly made of ghosts, with only a tiny, tiny sprinkling of ancient black holes hiding in the dark, keeping their noise down so we don't hear them.

Problem Statement
The fundamental nature of dark matter remains unknown, with Weakly Interacting Massive Particles (WIMPs) and Primordial Black Holes (PBHs) being leading candidates. While PBHs formed from early-universe density perturbations cannot account for all dark matter across all mass ranges, a mixed scenario involving both WIMPs and PBHs is theoretically viable. In this scenario, WIMPs accrete onto PBHs to form Ultracompact Minihalos (UCMHs). These structures possess significantly higher WIMP number densities than classical dark matter halos (e.g., NFW profiles), leading to enhanced WIMP annihilation rates. Previous investigations into this mixed scenario have primarily focused on constraining the PBH fraction ( $f_{PBH}$ ) using gamma-ray fluxes. However, the potential for these annihilation events to produce detectable extragalactic muon neutrino fluxes, and the subsequent constraints this places on the primordial curvature power spectrum ( $P_R$ ), requires further exploration.

Methodology
The authors investigate the extragalactic muon neutrino flux resulting from WIMP annihilation within UCMHs formed around PBHs. The study proceeds through the following steps:

UCMH Modeling: The density profile of WIMPs within UCMHs is modeled based on the accretion of WIMPs onto PBHs. The profile transitions from $r^{-3/4}$ to $r^{-3/2}$ and finally to $r^{-9/4}$ depending on the radius and the relative importance of WIMP kinetic energy versus gravitational potential energy. The central density is capped by the maximum density allowed by WIMP annihilation ( $\rho_{max}$ ).
Neutrino Flux Calculation: The differential neutrino flux is calculated by integrating the WIMP annihilation rate over the UCMH density profiles and redshift. The study considers three specific annihilation channels: $\mu^+\mu^-$ , $\tau^+\tau^-$ , and $\nu_\mu\bar{\nu}_\mu$ .
Event Classification: The resulting muon flux at Earth is categorized into two detection classes for the IceCube experiment:
- Contained events: Muons generated within the detector volume.
- Upward events: Muons generated outside the detector by neutrinos traversing the Earth.
  The analysis incorporates the effective volume ( $V_{eff}$ ) and effective area ( $A_{eff}$ ) of IceCube, along with the atmospheric neutrino background as the dominant noise source.
Constraint Derivation: Upper limits on the PBH fraction ( $f_{PBH}$ ) are derived by requiring that the predicted neutrino flux does not exceed the atmospheric background at a $2\sigma$ statistical significance for a one-year exposure.
Power Spectrum Translation: The derived bounds on $f_{PBH}$ are translated into upper limits on the primordial curvature power spectrum ( $P_R$ ) using the Press-Schechter formalism, relating the PBH abundance to the amplitude of initial density perturbations.

Key Contributions and Results

Expanded Annihilation Channels: Unlike previous studies that focused primarily on the $\mu^+\mu^-$ channel, this work analyzes the $\tau^+\tau^-$ and $\nu_\mu\bar{\nu}_\mu$ channels, finding that the $\nu_\mu\bar{\nu}_\mu$ channel provides the most stringent constraints.
Neutrino Constraints on $f_{PBH}$ : For a WIMP mass of $m_\chi = 10^3$ $m_{χ} = 1 0^{3}$ GeV and a PBH mass of $M_{PBH} = 10^3 M_\odot$ $M_{P B H} = 1 0^{3} M_{⊙}$ , the study derives upper limits on the dark matter fraction in PBHs:
- $f_{PBH} \sim 10^{-4}$ for contained events.
- $f_{PBH} \sim 4 \times 10^{-5}$ for upward events.
  The constraints are strongest for upward events due to the longer propagation distance of high-energy muons.
Mass Dependence: The constraints on $f_{PBH}$ exhibit a characteristic dependence on PBH mass. For PBH masses above a critical scale (dependent on $m_\chi$ ), the limits remain nearly constant. Below this scale, where WIMP kinetic energy becomes non-negligible, the constraints weaken as PBH mass decreases.
Primordial Curvature Power Spectrum ( $P_R$ ): Based on the strongest constraints (upward events, $\nu_\mu\bar{\nu}_\mu$ channel, $m_\chi = 10^3$ GeV), the authors derive an upper limit on the primordial curvature power spectrum of $P_R \sim 10^{-1.65}$ at the scale $k \sim 3 \times 10^{12} \text{ Mpc}^{-1}$ .
Comparison with Other Probes: The paper notes that while the isotropic gamma-ray background (IGRB) provides constraints on $f_{PBH}$ that are roughly four orders of magnitude stronger than the neutrino limits, the corresponding constraints on $P_R$ derived from IGRB are only about a factor of 1.2 stronger than those derived from neutrino fluxes in this specific mass range.

Significance
The paper claims to provide valuable complementary constraints on the abundance of PBHs in the mass range $M_{PBH} > 10^{-15} M_\odot$ , a regime where other observational methods may have gaps or different sensitivities. By utilizing extragalactic muon neutrino fluxes, the study extends the analysis of mixed dark matter scenarios to additional annihilation channels and a broader PBH mass range. Furthermore, the derived limits on the primordial curvature power spectrum are reported to be stronger than previous limits derived from PBH-only analyses over the scale range $10^7 \lesssim k \lesssim 10^{13} \text{ Mpc}^{-1}$ . The work demonstrates that neutrino observations offer a distinct and competitive probe for testing early-universe physics and the nature of dark matter.