The puzzle of composition of cosmic rays with energies (2-12.5) EeV according to muon detectors data of the Yakutsk EAS array

This paper presents a study of cosmic ray composition in the 2–12.5 EeV energy range using muon correlation data from the Yakutsk EAS array (1974–2018), confirming the existence of four distinct groups of primary particles with different origins.

The Gist

Imagine the universe is constantly raining down on us, but instead of water, it's a storm of invisible, super-fast particles called Cosmic Rays. These aren't just raindrops; they are the most energetic particles in existence, traveling faster than anything else we know.

For decades, scientists have been trying to figure out what these "raindrops" are made of. Are they tiny hydrogen atoms (protons)? Heavy iron nuclei? Or something even stranger?

This paper from the Yakutsk EAS Array in Russia is like a team of detectives using a very specific, clever trick to solve this mystery. Here is the story of their investigation, explained simply.

The Detective's Tool: The "Muon Fingerprint"

When a cosmic ray hits the Earth's atmosphere, it doesn't just hit the ground; it explodes into a massive shower of billions of secondary particles, like a firework bursting in the sky. This is called an Extensive Air Shower (EAS).

Inside this shower, there are two main types of "debris":

1. Electrons: Light, fast, and easy to spot.
2. Muons: Heavy, stubborn particles that can punch through the ground.

The scientists at Yakutsk have built a giant net of detectors underground to catch these muons. They realized that the number of muons caught tells you what the original cosmic ray was made of.

The Analogy: Imagine throwing two different types of balls into a pile of sand.

• If you throw a light ping-pong ball (a proton), it creates a small, shallow splash.
• If you throw a heavy bowling ball (an iron nucleus), it creates a huge, deep crater with lots of sand flying everywhere.

In this cosmic game, the "sand flying everywhere" is the muons.

• Heavy particles (Iron) = Lots of muons (Big splash).
• Light particles (Protons) = Fewer muons (Small splash).

The Big Surprise: The "Four Groups"

The scientists looked at nearly 2,000 of these cosmic showers with energies between 2 and 12.5 EeV (that's a number so big it's hard to write down, but think of it as "super-duper high energy").

They expected to see a smooth mix of light and heavy particles. Instead, they found four distinct groups, like finding four different types of animals in a forest when you only expected to see deer and bears.

1. The "Proton" Group (The Lightweights): About 45% of the showers looked exactly like they were started by protons. This is the "normal" crowd.
2. The "Iron" Group (The Heavyweights): About 10% were clearly heavy iron nuclei.
3. The "X" Group (The Muon Overachievers): About 12% of the showers had way too many muons. It was like throwing a ping-pong ball and getting a bowling-ball-sized splash. The scientists don't know what these are yet. They might be a new type of particle or a weird interaction we haven't seen before.
4. The "D" Group (The Muon Underachievers): This was the biggest surprise. About 33% of the showers had very few muons. It was like throwing a bowling ball and getting almost no splash at all.

The "Gamma Ray" Theory

The scientists have a strong hunch about the "D" group (the ones with too few muons). They suspect these might be Gamma Rays (pure energy, like light, but super powerful).

The Analogy: If a proton is a rock and an iron nucleus is a brick, a gamma ray is a laser beam.

• When a rock or brick hits the sand, it kicks up a lot of debris (muons).
• When a laser beam hits the sand, it doesn't kick up much debris at all; it just passes through or creates a very different kind of reaction.

The data suggests that about one-third of these ultra-high-energy cosmic rays might actually be pure energy (gamma rays) rather than matter. This is a huge deal because we don't fully understand how the universe accelerates pure energy to such crazy speeds.

Why This Matters

For a long time, scientists tried to solve this puzzle by taking an "average" of all the showers. It's like trying to figure out the average weight of a group of people by weighing them all together. You might get a number that doesn't match anyone in the group (e.g., if you mix a baby and an elephant, the average is a toddler, but there are no toddlers there!).

This paper shows that averaging is misleading. Because there are these four distinct groups (especially the weird "X" and "D" groups), the "average" composition looks like it's mostly protons, but that's a lie. The reality is a complex mix of different origins.

The Conclusion

The Yakutsk team has opened a new door. They proved that the universe is sending us a much more diverse "menu" of particles than we thought.

• We have the standard Protons.
• We have the heavy Iron.
• We have mysterious Overachievers (too many muons).
• We have mysterious Underachievers (possibly pure gamma rays).

Understanding this mix is the key to unlocking the secrets of the most violent explosions in the universe, like black holes and supernovas, which act as the cosmic accelerators launching these particles at us. The Yakutsk array is essentially the first to clearly see these four distinct "flavors" of cosmic rain.

Technical Summary

Here is a detailed technical summary of the paper "The Puzzle of Composition of Cosmic Rays with Energies (2 - 12.5) EEV According to Muon Detectors Data of the Yakutsk EAS Array."

1. Problem Statement

The composition of Ultra-High-Energy Cosmic Rays (UHECRs) with energies $E \ge 10^{15}$ eV remains a significant unsolved problem in astroparticle physics. While Extensive Air Showers (EAS) are used to study these particles, results from various global experiments (e.g., Pierre Auger, Telescope Array, KASCADE) are often contradictory, showing conflicting trends in mass composition (proton vs. heavy nuclei) as energy increases.

A major challenge is that standard analyses often rely on average characteristics of EAS (such as mean muon density or lateral distribution functions). The authors argue that these averages can be misleading because the sample of cosmic rays may contain distinct sub-populations with different origins that are obscured when averaged together. Specifically, there is a need to understand if the primary flux consists of a single mass group or a mixture of distinct groups (e.g., protons, iron, gamma rays, or exotic particles).

2. Methodology

The study utilizes data from the Yakutsk EAS Array in Russia, collected between 1974 and 2018. The analysis focuses on 1,887 individual EAS events with energies between 2 and 12.5 EeV ($2 \times 10^{18}$to$1.25 \times 10^{19}$eV) and zenith angles$\theta \le 60^\circ$.

Key Technical Components:

• Muon Correlation Method: The core of the analysis is a method proposed in a previous work [31] that compares experimental muon densities with simulated values for individual events.
  • Experimental Data: Muon density ($\rho_\mu^{exp}$) is measured by underground Muon Detectors (MD) at a distance of $r = 600$ m from the shower axis.
  • Simulation: The expected muon density ($\rho_\mu^{calc}$) is calculated using the QGSjet-II-04 hadronic interaction model within the CORSIKA software package, assuming a primary proton with energy $E^* = 10^{19}$ eV.
  • Correction: The simulation is adjusted for the specific energy ($E$) and zenith angle ($\theta$) of the experimental event using the lateral distribution function (LDF) of the surface detector (SD) electron component to normalize the muon density.
• Correlation Parameter ($\xi$): The study defines a ratio parameter:
  $$\xi = \frac{\rho_\mu^{exp}(E, \theta, r)}{\rho_\mu^{calc}(E^*, \theta, r)}$$
  This parameter quantifies the deviation of the observed muon content from the proton expectation.
• Statistical Analysis: The distribution of $\xi$ values across the entire sample is analyzed to identify distinct peaks, which correspond to different primary particle types.

3. Key Contributions

• Event-by-Event Analysis: Unlike previous studies that averaged data over energy bins, this paper analyzes the composition of individual events, revealing a multi-modal distribution that averages would hide.
• Identification of Four Distinct Groups: The analysis confirms the existence of four separate groups of primary particles, rather than a continuous transition from light to heavy elements.
• Hypothesis on Gamma Rays: The paper provides strong evidence suggesting that a significant fraction of UHECRs (the "D" component) may be primary ultra-high-energy gamma rays, based on their anomalously low muon content.
• Discovery of "X" Events: The identification of a group with anomalously high muon content ("X" events), the origin of which remains unknown, challenges current interaction models.

4. Results

The distribution of the correlation parameter $\xi$ reveals four distinct peaks, corresponding to four components of the cosmic ray flux:

Component	Peak Location ($\langle \xi \rangle$)	Interpretation	Fraction of Total Flux
p	$1.00 \pm 0.06$| **Primary Protons** (Matches QGSjet-II-04 simulation) | **45$\pm$ 2%**
Fe	$1.41 \pm 0.09$| **Iron Nuclei** (Shifted by$\approx 0.3$log units, consistent with$A=56$) | **10$\pm$ 3%**
X	$2.26 \pm 0.15$| **Muon-Excessive Events** (Anomalously high muon content) | **12$\pm$ 3%**
D	$0.20 \pm 0.09$| **Muon-Deficient Events** (Anomalously low muon content) | **33$\pm$ 2%**

Detailed Findings:

• The "D" Component (Muon-Deficient): This group constitutes the second-largest fraction (33%). The low muon content is consistent with the signature of primary gamma rays. The authors note that if these were gamma rays, the energy reconstruction based on electron density would underestimate the true energy by a factor of 1.2 to 3.7 depending on the zenith angle.
• The "X" Component (Muon-Excessive): This group (12%) shows a muon density more than double that of protons. Its origin is currently unexplained; it could represent exotic particles or a specific interaction mechanism not captured by current models.
• Temporal Variations: The study observed that the relative proportions of these components fluctuate over time. Notably, between 1999 and 2002, the fractions of "Fe" and "X" increased synchronously while "p" and "D" decreased, suggesting potential transient astrophysical sources or "grand explosive processes."
• Flaw of Averages: If one calculates the average $\xi$ for the entire sample, the result is $\approx 0.81$. This would lead to the erroneous conclusion that the flux is dominated by protons. The paper demonstrates that this average is a mathematical artifact caused by the mixing of the four distinct populations.

5. Significance

• Paradigm Shift in Composition Analysis: The results suggest that the UHECR composition is not a simple mixture of standard nuclei (protons to iron) but includes significant populations of non-standard particles (likely gamma rays and potentially exotic "X" particles).
• Implications for Interaction Models: The existence of the "X" component (high muons) and "D" component (low muons) challenges the validity of current hadronic interaction models (like QGSjet-II-04) when applied to the full spectrum of UHECRs.
• Astrophysical Sources: The temporal correlation between the "Fe" and "X" components implies that these particles may share a common, transient source mechanism, distinct from the steady sources of protons and gamma rays.
• Future Directions: The authors plan to extend this muon correlation method to lower energies where the Yakutsk array has higher statistics, to better constrain the nature of the "D" and "X" components.

In conclusion, the paper argues that the "puzzle" of cosmic ray composition can only be solved by moving away from average characteristics and analyzing the distribution of individual event properties, revealing a complex, multi-component flux that includes a substantial fraction of potential gamma rays and unknown high-muon particles.