Measuring contributions from single and multiple atmospheric secondary cosmic rays in the {\it Princess Sirindhorn Neutron Monitor} using cross-counter neutron time delay distributions

This paper presents measurements from the Princess Sirindhorn Neutron Monitor using new electronics to analyze cross-counter time delay distributions, revealing that approximately 4.5% of detected counts arise from multiple secondary particles within the same cosmic-ray shower rather than single particles, a finding that validates Monte Carlo simulations and refines the understanding of neutron monitor spectral variations.

The Gist

Imagine the Earth is constantly being pelted by invisible rain made of high-speed particles from deep space. These are called cosmic rays. When they hit our atmosphere, they don't just stop; they crash into air molecules and create a massive, chaotic splash of new particles, like a stone thrown into a pond creating ripples. This splash is called a "shower."

Some of these particles are neutrons. To catch them, scientists use giant detectors called Neutron Monitors. Think of the Princess Sirindhorn Neutron Monitor (PSNM) in Thailand as a long row of 18 giant, high-tech "ears" (counters) sitting on a mountain. Their job is to listen for the "pings" of these cosmic neutrons.

The Big Mystery: Who is Knocking on Whose Door?

For a long time, these monitors could just count how many pings they heard. But recently, the team upgraded the electronics to record exactly when each ping happened, down to a tiny fraction of a second.

This allowed them to ask a new question: If one counter hears a ping, does a neighbor counter hear a ping right after it?

If two counters hear a ping at almost the same time, it usually means they were both hit by particles from the same cosmic splash. The scientists call this a "follower." If a counter hears a ping that has no partner nearby, it's a "leader."

The Detective Work: Measuring the Distance

The researchers looked at the time gaps between pings in different counters. They noticed something interesting based on how far apart the counters were:

1. Close Neighbors (The "Family" Effect): When two counters are right next to each other, they often hear pings together. The scientists realized this is usually because a single particle from the cosmic shower hit a lead ring nearby, creating a small cluster of "children" particles (tertiary neutrons) that scattered and hit both counters almost instantly. It's like one person clapping their hands, and the sound waves hitting two people standing right next to each other.
2. Distant Neighbors (The "Crowd" Effect): Here is the surprise. Even when the counters were far apart (up to 7.5 meters), they still heard pings that were linked in time.
   • The Old Theory: Scientists thought a single particle couldn't travel that far to hit two distant counters.
   • The New Discovery: The team used computer simulations (a virtual lab) to prove that a single particle simply can't explain these distant links. Instead, these distant pings come from multiple different particles from the same giant cosmic shower.
   • The Analogy: Imagine a massive fireworks display. If you stand close to the explosion, you might see sparks hit two nearby trees at the same time (single particle effect). But if you stand far away, you might see a spark hit one tree and a different spark hit another tree a split second later. They are both from the same firework, but they are separate sparks. The monitor is detecting these separate sparks from the same "firework" (cosmic ray shower).

The Numbers: How Often Does This Happen?

The team calculated that about 4.5% of all the pings the monitor hears are actually "followers" from a different particle in the same cosmic shower.

• Why does this matter? It helps scientists understand the "multiplicity" of the shower—basically, how many particles are in the splash.
• The "Leader Fraction": They found that for distant counters, the "leader fraction" (the chance that a ping is not followed by a partner) is incredibly high (about 99.7%). This means 99.7% of the time, a distant counter is hearing a lonely ping. But that tiny 0.3% of the time when it is followed by a distant partner is the key evidence that multiple particles from the same shower are arriving together.

The Weather Factor

The scientists also had to account for the weather. They found that changes in air pressure and water vapor in the atmosphere act like a "volume knob" for the detector, making it hear more or fewer pings. By mathematically turning that knob back to a standard setting, they could see the true cosmic signals without the weather noise.

The Bottom Line

This paper doesn't just count cosmic rays; it maps out how they behave when they hit the ground. It proves that:

1. Close pings are usually from one particle scattering.
2. Far-away pings are usually from different particles in the same cosmic shower arriving together.

This new way of looking at the data helps scientists build better computer models of how cosmic rays crash into our atmosphere, improving our understanding of the space weather that surrounds our planet. It's like upgrading from just counting the number of raindrops to understanding exactly how the raindrops are falling in relation to each other.

Technical Summary

Technical Summary: Measuring Contributions from Single and Multiple Atmospheric Secondary Cosmic Rays in the Princess Sirindhorn Neutron Monitor

Problem Statement
Neutron monitors (NMs) are the premier ground-based instruments for tracking Galactic cosmic ray (GCR) flux variations. However, traditional NM analysis relies on count rates, which integrate over a broad energy spectrum, making spectral measurements at a single station challenging. While previous work utilized "leader fractions" (the inverse of neutron multiplicity) within a single counter to infer spectral variations, this metric conflates contributions from single atmospheric secondary particles and multiple secondaries from the same primary cosmic ray shower. Furthermore, the spatial distribution and temporal association of neutrons across multiple counters in a single NM station had not been systematically analyzed to distinguish between these two physical origins. Understanding the distinction is critical for validating Monte Carlo (MC) simulations of atmospheric showers and NM yield functions, particularly for precise spectral tracking and extending observation ranges to higher energies.

Methodology
The study utilizes the Princess Sirindhorn Neutron Monitor (PSNM), an 18NM64 station located at Doi Inthanon, Thailand (2560 m altitude, ~17 GV rigidity cutoff). The station comprises 18 BP-28 proportional counters arranged in a single row with 50 cm spacing.

1. Data Acquisition: Following a 2015 electronics upgrade, the PSNM records absolute timing for neutron events with GPS synchronization (accuracy ±3 µs). The system generates cross-counter time-delay histograms for all pairs of counters, categorized by separation distance ($\Delta = |i - j|$) and counter position (middle 'm' or end 'e'). Data from April 2018 to December 2024 were analyzed.
2. Cross-Counter Leader Fraction ($L_{ij}$): The authors define the cross-counter leader fraction as the fraction of counts in counter $i$ that are not temporally associated with a subsequent count in counter $j$. This is derived by fitting the long-time tail of the time-delay distribution (dominated by chance coincidences) with an exponential function and extrapolating to $t=0$ to determine the total count versus the "associated" excess.
3. Atmospheric Corrections: The analysis corrects for atmospheric pressure ($p_a$) and precipitable water vapor (PWV). The study demonstrates that correcting for $p_a$ effectively removes the dependence on PWV due to their strong seasonal anticorrelation at the site.
4. Monte Carlo Simulations: Using the FLUKA 4 package, the authors simulated the interaction of single mono-energetic secondary neutrons (10 MeV to 1 GeV) and nucleons (1–500 GeV) with the PSNM geometry to estimate the cross-counter multiplicity expected from single secondary particles alone.

Key Results

• Distance-Dependent Multiplicity: The cross-counter leader fraction $L_\Delta$ increases with counter separation, saturating at $L \approx 0.997$ for separations $\Delta \ge 12$ (distance $\ge 6$ m). This implies that even at large distances, approximately 0.3% of counts in one counter are temporally associated with a later count in a distant counter.
• Single vs. Multiple Secondaries:
  • Small Separations ($\Delta \le 4$): The associated counts are dominated by tertiary neutrons produced by a single atmospheric secondary particle interacting with the lead producer. The measured multiplicity agrees well with FLUKA simulations of single secondary interactions, which can be modeled as a sum of Gaussian and exponential functions of distance.
  • Large Separations ($\Delta \ge 12$): Single secondary particles cannot account for the observed association at these distances (simulations show <0.1% contribution). The observed association is attributed to multiple secondary particles from the same primary cosmic ray shower.
• Quantitative Contribution: By analyzing the far-counter leader fraction and correcting for "double counting" (where one secondary triggers multiple counters), the authors estimate that approximately 4.5% of all PSNM counts are associated with a later count from a different secondary particle within the same shower.
• Temporal Characteristics: The "follower" time-delay distributions (associated counts) decay more slowly for far-counter pairs than for same-counter pairs. This suggests that the multiple secondary particles contributing to far-counter associations include low-energy neutrons with significant arrival time delays relative to the primary shower front.
• Solar Modulation: Unlike single-counter leader fractions at low-rigidity stations (e.g., Antarctica), the far-counter leader fraction at PSNM shows no statistically significant variation over the 2018–2024 solar cycle. The expected variation is estimated to be $\sim 10^{-5}$, which is below the current measurement sensitivity.

Significance and Claims
The paper claims to provide a novel technique for a single NM station to statistically distinguish between neutron counts arising from single atmospheric secondaries and those from multiple secondaries in the same shower.

• Validation of Simulations: The measurements of neutron multiplicity across counters provide a new benchmark for validating atmospheric shower simulations and NM yield functions, specifically regarding the contribution of multiple secondaries which were previously unaccounted for in single-counter leader fraction models.
• Refinement of Spectral Tracking: The findings suggest that approximately 4.5% of counts in the PSNM (and likely other similar NMs) are "followers" from different secondaries. This fraction must be accounted for when using leader fractions to track cosmic ray spectral variations, as current simulations often assume only single secondary contributions.
• Cost-Effective Upgrade: The study demonstrates that upgrading NM electronics to include absolute timing and cross-counter analysis significantly enhances scientific capability without requiring additional hardware costs, offering a pathway for similar upgrades at NM stations worldwide.

The authors maintain a modest tone regarding the detection of solar cycle variations in the far-counter leader fraction, noting that while the effect is theoretically present, it is currently too small to measure at the PSNM's high rigidity cutoff. Future work is proposed to explore these variations at polar stations with lower cutoff rigidities.