High-energy neutrino constraints on primordial black holes as dark matter

This paper presents the first constraints on sub-asteroid mass primordial black holes as dark matter using high-energy neutrino data from IceCube and ANTARES, establishing independent limits that future detectors like IceCube-Gen2 and KM3NeT could significantly improve.

The Gist

Imagine the universe is filled with invisible "ghosts" that make up most of its mass. We call this invisible stuff Dark Matter. For decades, scientists have been trying to figure out what these ghosts are made of. One very popular theory suggests they might be Primordial Black Holes (PBHs).

Think of PBHs not as the massive, galaxy-swallowing black holes you see in movies, but as tiny, ancient fossils from the Big Bang. Some are as heavy as a mountain, while others are as light as a small asteroid.

This paper is a new detective story. The authors, Mainak Mukhopadhyay and Joaquim Iguaz Juan, ask a simple question: Can we catch these tiny black holes by listening to the "screams" they make as they die?

The Story of the Dying Black Hole

According to a famous physicist named Stephen Hawking, black holes aren't truly black. They slowly leak energy and particles, a process called Hawking Radiation.

• The Analogy: Imagine a block of dry ice sitting on a table. It doesn't just sit there; it slowly sublimates, turning into gas and disappearing. The smaller the piece of dry ice, the faster it vanishes and the hotter it gets right before it's gone.
• The Physics: Tiny PBHs are like the small pieces of dry ice. Because they are so small, they are incredibly hot and evaporate very quickly. As they evaporate, they spit out a shower of particles, including neutrinos.

Neutrinos are "ghost particles." They have almost no mass and can pass through entire planets without hitting anything. They are incredibly hard to catch, but they are the perfect messengers for this job because they travel in straight lines from the black hole to our detectors.

The Detective Work: Listening with Giant Ears

The authors used data from two massive underwater and under-ice telescopes: IceCube (in Antarctica) and ANTARES (in the Mediterranean Sea).

• The Analogy: Imagine trying to hear a specific bird chirp in a noisy forest. You need a super-sensitive microphone. These telescopes are like giant, deep-sea microphones waiting for a specific "chirp" (a high-energy neutrino) that only a dying black hole would make.

The team looked for two types of signals:

1. The Background Hum (Diffuse Flux): If there are millions of these tiny black holes everywhere in the universe, they should be evaporating constantly, creating a faint, constant "hum" of neutrinos coming from all directions.

   • The Result: The telescopes didn't hear a hum louder than the background noise of the universe. This means there aren't as many tiny black holes as some theories hoped. The authors drew a line in the sand: "If these black holes exist, they can't make up 100% of the dark matter if they are smaller than a certain size."

2. The Flash in the Sky (Transit Events): What if a single tiny black hole flew right past our solar system? It would create a sudden, bright flash of neutrinos, like a firework going off right in front of your face.

   • The Result: The telescopes didn't see any fireworks. This puts a limit on how close a black hole could be to us without us noticing.

The "Asteroid Mass Gap" Mystery

There is a specific size range for these black holes (between the mass of a small asteroid and a large mountain) that scientists call the "Asteroid Mass Gap." It's a sweet spot where PBHs could theoretically be the entirety of dark matter.

• The Analogy: Think of a puzzle where we have pieces for "too heavy" and "too light," but the middle pieces are missing. This paper tries to fill in the middle.

The authors found that high-energy neutrinos are a powerful new tool to check this gap. While their current limits are slightly weaker than limits from gamma-ray telescopes (which look for light), they are independent. It's like checking your bank balance with two different banks; if both say you don't have enough money, you can be sure.

The Future: Bigger Ears

The paper is very optimistic about the future. New, even bigger telescopes are being built (like IceCube-Gen2 and KM3NeT).

• The Analogy: If the current telescopes are like a pair of binoculars, the new ones will be like a giant space telescope.
• The Prediction: With these new tools, scientists might be able to rule out the existence of these tiny black holes entirely, even up to masses of a few billion tons. If they don't find them, we'll know that dark matter must be something else entirely.

Why Does This Matter?

There was a recent event where a detector (KM3NeT) saw a neutrino with an energy so high it was almost unbelievable (220 PeV). Some people wondered, "Could this be a tiny black hole exploding nearby?"

This paper says: "We looked really hard at the data. While it's possible a black hole did it, the odds are low because we haven't seen enough of these explosions to support that theory."

The Bottom Line

This paper is a new chapter in the hunt for dark matter. By using high-energy neutrinos as a new kind of "ear," the authors have tightened the noose around the theory that tiny, asteroid-sized black holes are the answer to the universe's biggest mystery. They haven't caught the ghost yet, but they've proven that the ghost can't be hiding in the specific room they were looking at.

In short: We are listening for the death screams of tiny black holes. So far, the silence is telling us that if these black holes exist, they are much rarer than we thought.

Technical Summary

1. Problem Statement

Primordial Black Holes (PBHs) remain a compelling candidate for Dark Matter (DM), particularly in the "asteroid mass gap" ($10^{17} \text{ g} \lesssim M_{\text{PBH}} \lesssim 10^{22} \text{ g}$). While PBHs in this range are too massive to have evaporated completely by the present day, those at the lower end of the spectrum ($M_{\text{PBH}} \lesssim 10^{18} \text{ g}$) are hot enough to undergo Hawking evaporation, emitting particles including neutrinos.

Existing constraints on these low-mass PBHs rely heavily on gamma-ray observations (e.g., from INTEGRAL/SPI) and antimatter searches. However, the high-energy neutrino regime ($E_\nu \gtrsim \text{GeV}$) has been largely unexplored as a probe for PBH abundance ($f_{\text{PBH}}$), despite the existence of powerful neutrino telescopes like IceCube and ANTARES. Furthermore, recent observations of ultra-high-energy neutrinos (e.g., the 220 PeV event by KM3NeT) have sparked interest in whether such events could originate from transient PBH fly-bys.

The authors aim to:

1. Derive the first constraints on sub-asteroid mass PBHs using high-energy neutrino data from current detectors.
2. Forecast the sensitivity of next-generation detectors (IceCube-Gen2, KM3NeT).
3. Investigate the potential for detecting transient PBH fly-by events (singular transits) versus the diffuse flux from the PBH population.

2. Methodology

A. Theoretical Framework

• Mass Function: The authors assume an Extended Mass Function rather than a monochromatic one, specifically the Generalized Critical Collapse (GCC) model. This is characterized by a peak mass ($\bar{M}_{\text{PBH}}$) and power-law slopes for the low-mass ($\alpha$) and high-mass ($\beta$) tails. They adopt $\alpha=1$ and $\beta=2.78$.
• Evolution: They account for the time evolution of the mass function due to Hawking evaporation. PBHs with initial masses $M_{\text{init}} \lesssim 5 \times 10^{14} \text{ g}$ have already evaporated; the current population is the remnant of the initial distribution.
• Emission: They calculate the neutrino spectrum from Hawking radiation, including both primary neutrinos (direct emission) and secondary neutrinos (from the decay of other emitted particles like pions and muons). They use the BlackHawk code to compute greybody factors and spectra for Schwarzschild PBHs.

B. Diffuse Flux Constraints

The authors calculate the total diffuse neutrino flux ($\phi_\nu$) composed of two components:

1. Galactic Flux: Calculated by integrating the PBH density over the line of sight using an NFW halo profile. They specifically model the Galactic Ridge and Galactic Plane.
2. Extragalactic Flux: Calculated by integrating over redshift ($z$) and cosmic time, accounting for the expansion of the universe and the evolving PBH mass function.

Constraint Derivation:
They compare the predicted PBH-induced flux against observational upper limits from:

• ANTARES: Diffuse flux from the Galactic Ridge ($1-100$ TeV).
• IceCube: Diffuse flux from the Galactic Plane and the all-sky astrophysical neutrino flux (broken power-law fit).
• Criterion: The limit on $f_{\text{PBH}}$ is set conservatively by requiring that the PBH flux does not exceed the observational limit at any energy:
  $$f_{\text{PBH}}^{\text{lim}}(\bar{M}_{\text{PBH}}) = \min_{E_\nu} \left[ \frac{\phi_{\nu}^{\text{obs, lim}}(E_\nu)}{\phi_{\nu}(E_\nu, \bar{M}_{\text{PBH}})} \right]$$

C. Transient (Fly-by) Constraints

The authors investigate the detection of a single PBH passing near Earth.

• Geometry: A PBH moves at a characteristic DM velocity ($v \approx 200$ km/s) at a closest approach distance $d_{\text{hor}}$ (impact parameter).
• Significance: They calculate the number of signal events ($N_\nu$) over a 12.5-year observation window.
• Detection Threshold: They assume a background-free scenario (justified by focusing on the Northern Sky for IceCube to shield against atmospheric muons) and require a $5\sigma$ significance ($S = N_\nu / \sqrt{N_\nu}$).
• Rate Calculation: They compute the expected transit rate based on the local DM density and the derived horizon distance $d_{\text{hor}}$.

3. Key Results

A. Diffuse Flux Constraints

• Current Limits: Using existing data from IceCube and ANTARES, the authors exclude the possibility that PBHs constitute 100% of Dark Matter ($f_{\text{PBH}}=1$) for peak masses $\bar{M}_{\text{PBH}} \lesssim 3 \times 10^{17} \text{ g}$. The best constraints reach up to $\bar{M}_{\text{PBH}} \sim 10^{18} \text{ g}$.
• Future Projections:
  • IceCube-Gen2 and KM3NeT are projected to improve sensitivity significantly.
  • Future detectors could exclude $f_{\text{PBH}}=1$ for peak masses up to $\bar{M}_{\text{PBH}} \sim 2 \times 10^{18} \text{ g}$.
• Comparison: These limits are slightly weaker than the tightest gamma-ray constraints but provide a completely independent and complementary probe. The constraints are robust against variations in the mass function slope $\beta$ but weaken by a factor of $\sim 10$ if $\alpha$ is doubled.

B. Transient Fly-by Constraints

• Detection Probability: The analysis shows that detecting a single PBH fly-by is highly unlikely with current or near-future detectors.
• Horizon Distance: For a $5\sigma$ detection, the maximum horizon distance $d_{\text{hor}}$ is extremely small (sub-parsec scale) for PBHs with masses $M_{\text{PBH}} \gtrsim 10^{12} \text{ g}$.
• Transit Rate: The expected rate of detectable transits is very low (significantly less than 1 event per decade) for the mass ranges considered. The constraints derived from the absence of such events are much weaker than the diffuse flux constraints.
• KM3NeT Event: The authors note that while the 220 PeV KM3NeT event could theoretically be a PBH, the non-observation of accompanying gamma rays challenges the standard Schwarzschild PBH hypothesis, though non-standard scenarios remain possible.

C. Sensitivity to Spin

• The authors briefly analyze Kerr (spinning) PBHs ($a^* = 0.999$). They find that high spin enhances the evaporation rate, improving the constraints by a factor of $\sim 7$ compared to Schwarzschild PBHs. This suggests the main results are conservative.

4. Significance and Conclusions

• Independent Messenger: This work establishes high-energy neutrinos as a viable, independent messenger for constraining the PBH Dark Matter parameter space, complementing gamma-ray and antimatter searches.
• Asteroid Mass Gap: The study successfully probes the lower end of the asteroid mass gap ($10^{17} - 10^{18} \text{ g}$), a region where PBHs could potentially make up all of the DM.
• Future Reach: The results highlight the transformative potential of next-generation detectors (IceCube-Gen2, KM3NeT), which could potentially rule out PBHs as the sole DM component for masses up to a few $\times 10^{18} \text{ g}$.
• Transient vs. Diffuse: The study concludes that while the diffuse background provides strong constraints, the transient detection of individual fly-bys is unlikely to be the primary discovery channel for PBHs in this mass range due to the low event rates and small horizon distances.
• Timeliness: The work is particularly relevant given the recent KM3NeT ultra-high-energy event and the ongoing accumulation of high-energy neutrino data, offering a framework to interpret future data in the context of PBH Dark Matter.

In summary, this paper provides the first rigorous high-energy neutrino constraints on extended PBH mass functions, demonstrating that current data already excludes PBHs as the entirety of DM for masses below $\sim 10^{18} \text{ g}$, with future detectors poised to push this limit further.